TC221

EINDRAPPORT
TC221-01-08
TC221
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TC221 Nieuwe boortechnieken kleine infra
COB – Nederlands kenniscentrum voor ondergronds
­bouwen en ondergronds ruimtegebruik
Nieuwe boortechnieken
kleine infra
Modelling the soil pipeline interaction during the
pull back operation of horizontal directional drilling
EINDRAPPORT
TC221-08-01
TC221
Nieuwe boortechnieken
kleine infra
Modelling the soil pipeline interaction during the
pull back operation of horizontal directional drilling
Auteur
ir. J.P. Pruiksma
dr. H.M.G. Kruse
Fotografie omslag
Deltares
Lay-out
Sirene Ontwerpers
Druk
Repro Europoint
Auteursrechten
Alle rechten voorbehouden. Niets uit deze uitgave mag worden verveelvoudigd, opgeslagen in een geautomatiseerd gegevensbestand of openbaar gemaakt, in enige vorm of op enige wijze, hetzij elektronisch, mechanisch,
door fotokopieën, opnamen of op enig andere manier, zonder voorafgaande schriftelijke toestemming van de COB.
Het is toegestaan overeenkomstig artikel 15a Auteurswet 1912 gegevens uit deze uit gave te citeren in artikelen,
scripties en boeken, mits de bron op duidelijke wijze wordt vermeld, alsmede de aanduiding van de maker, indien
deze in de bron voorkomt. ‘Nieuwe boortechnieken kleine infra, 2009, Stichting COB, Gouda.‘
Aansprakelijkheid
COB en degenen die aan deze publicatie hebben meegewerkt, hebben een zo groot mogelijke zorgvuldigheid
betracht bij het samenstellen van deze uitgave. Nochtans moet de mogelijkheid niet worden uitgesloten dat er
toch fouten en onvolledigheden in deze uitgave voorkomen. Ieder gebruik van deze uitgave en gegevens daaruit is
geheel voor eigen risico van de gebruiker en COB sluit, mede ten behoeve van al degenen die aan deze uitgave hebben meegewerkt, iedere aansprakelijkheid uit voor schade die mocht voortvloeien uit het gebruik van deze uitgave
en de daarin opgenomen gegevens, tenzij de schade mocht voortvloeien uit opzet of grove schuld zijdens COB en/
of degenen die aan deze uitgave hebben meegewerkt.
ISBNnummer
978-90-77374-24-5
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Table of contents
1 Introduction
5
2 Description of phenomena during pull back
7
2.1
2.2
2.3
2.4
3 The pipeline pull back model
3.1
3.2
3.3
3.4
3.5
3.6
3.6.1
3.6.2
3.7
3.8
Bore path geometry
The pipeline and drill pipe
Forces on the pipeline and drill pipe (Soil-pipeline, weight etc..)
3D modelling
Friction on the rollers
Simulation steps and geometric linearity/non-linearity
Geometrically nonlinear simulations
Geometrically linear simulations
List of input parameters
Running the simulations
4 Simulation results
4.1
4.2
4.3
4.4
4.5
4.5.1
4.5.2
4.5.3
4.6
4.7
Drilling rig and rollers
The drill pipes
The pipeline
The drilling fluid
Comparison with analytical solution
Comparison of results with and without gap and using nonlinear and linear geometric behaviour
Simulations with a circular section and added straight section without gap
Simulations with a circular section and added straight section with 0.1 m gap
Pullback simulation of half circle borehole
Half circle geometry with friction only
Half circle geometry with friction and cohesion
Half circle geometry with friction, cohesion and gravity
Pullback simulation with drilling pipe in 100 steps, no cohesion or gravity effects
Simulation with measured XY data
5 Soil spring stiffness FEM simulations
5.1
5.2
Dutch common practice
FEM simulations of pipeline penetration into a borehole in plane strain
6 Conclusions
6.1
Recommendations
8
8
9
10
11
11
12
13
15
16
16
16
18
19
20
21
21
25
28
30
32
32
34
38
40
42
45
45
46
53
53
7 References
55
3
Nieuwe boortechnieken kleine infra
Appendices
Appendix 1 Source code of the model
Appendix 2 Derivation of analytical solution
Appendix 3 Simulation results
Appendix 4 Members of the committee
4
57
95
105
153
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
1 Introduction
The pull back operation is the most important stage of horizontal directional drilling
(HDD). The cost of jammed pipelines, damaged pipelines and the costs for additional
measures during and after the pull back operation can be considerable. Recently in the
Netherlands several problems occurred during the pull back operation at some locations
where relatively large diameter pipelines where installed.
The objective of the Delft Cluster Horizontal Directional Drilling (HDD) project, is to find a
detailed method for modelling the pulling of pipelines through a borehole created using
HDD’s. The main objective is to get a better understanding of the behaviour of the pipeline in the borehole. Penetration of the borehole wall during the pullback operation and
friction in between the pipe and the borehole are important parameters.
The current Dutch method for calculating the pull back force on the product pipe was
developed more then 10 years ago. For global design purposes and global engineering
practice it is a quick and relative simple method which gives a reasonable estimate of
the maximum pull back force. But large differences with field measurements have also
been observed, hence a more detailed analysis of the processes occurring in the soil-pipe
interaction during the pullback operation is required. Such analysis has been made from
which a new model for the pull back operation is developed.
In this report first the various processes occurring during pull back are described in
Chapter 2. In Chapter 3 the model is presented, what elements are included in the model,
what processes they describe. Chapter 4 presents pull back simulation results for a
variety of cases, from simple to extensive. Simple cases are used to compare the model to
analytical solutions, and to compare geometrically linear to nonlinear behaviour.
More detailed cases include more and more phenomena and processes. The complexity
is increased gradually to better understand the influence of various parameters. Chapter
5 presents conclusions that can be drawn from the simulations. In Chapter 6 a study is
presented that investigates the soil-pipe interaction behaviour for various combinations
of pipe dimensions and soil types. From this study a better understanding is obtained
for the behaviour of soil springs in pipe-soil interaction contact as used in the model.
Chapter 7 gives some general conclusions about the model and the project, including
suggestions for future research.
5
Nieuwe boortechnieken kleine infra
6
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
2 Description of phenomena during
pull back
In the installation of pipelines using the Horizontal Directional Drilling (HDD) method a
borepath is created under a certain object, say a river or road, this is called a pilot drilling.
This pilot tries to follow a previously designed borepath as closely as possible. After the
pilot boring is performed, the borehole is reamed to a larger diameter using reamer tools.
The result is a borehole through which the pipeline will be pulled back. During the three
stages of the HDD the borehole is filled with drilling fluid.
For the pullback model that is to be developed in this project, it is assumed that a
pre-reamed borehole is established. This borehole can in principle have an arbitrary
shape in axial direction that possibly deviates from the design path (usually made up of
three straight sections and two circular arcs). In radial direction the borehole is assumed
to be a circle.
During the pull back operation of the pipeline through the borehole, the interaction
between pipeline, drill pipe, reamer, soil and drilling fluid plays an important role. There
are rollers supporting the pipe-line on one side and the drilling rig on the other side that
contribute to the interplay of forces. In the figure below these components and interactions are depicted graphically. In this Chapter these phenomena during the pull back
operation are discussed in more detail. The creation of a model is mainly finding suitable
formulations for these phenomena.
7
Nieuwe boortechnieken kleine infra
2.1
Drilling rig and rollers
The rollers support the pipeline and are usually set up in a curved shaped bend to guide
the pipeline into the borehole. This curved shaped bend is generally followed by the pipeline, but the pipeline doesn’t have to make contact to the rollers everywhere as a result of
the forces in the pipeline (weight and moments, bending stiffness). Where the pipeline
is in contact with the rollers there is a contribution to the friction force. This friction
depends locally on the normal force that the pipeline exerts on the rollers. The friction on
the rollers contributes to the required pulling force.
The weight of the pipeline can also provide a part of the pulling force when the roller track
is aligned downward in the direction of the borepath, but work against the pulling when
the roller track is in upward direction. For a track which starts and ends on a horizontal
surface both of these forces cancel out. For a roller track lying above the surface at a
certain height and at the end bends downward into the borehole a small net gravity force
is present reducing the pulling force a little.
The drilling rig pulls the drill pipe upward at a fixed angle and provides the pulling force.
Because the pipe is consisting of a string of connected drill pipes with a maximum length
of 9 m, the drill pipe segments are removed as they come out of the hole during pulling. During the removal of a segment of the drill pipe, the pulling force is momentarily
reduced.
2.2
The drill pipes
Since the maximum length of the drill pipes is 9 m generally, the drill pipe is made up
of multiple segments. Initially the drill pipe lies through the borehole from beginning to
end. At the beginning it is connected to a reamer which is connected to the pipeline using
a swivel. The drill pipe rotates during the pull back operation.
Because a pulling force is needed to pull the pipeline through the hole, this force is acting
along the entire string of drill pipes. The pulling force changes direction along the drill
pipe and this leads to radial displacements (perpendicular to the axis of the borepath)
which magnitude depends on the bending stiffness of the rod and it’s interaction with
the soil, since at some places the drill pipe might touch or penetrate the borehole wall.
The soil then exerts a force on the drill pipe. The stiffness of the soil-drill pipe contact is
determined by soil type, pipe diameter and presence of drilling fluid and whether the drill
pipe is rotating.
Contact with the soil or penetration into the soil results in an increase of the friction
force, which is in turn increasing the overall pulling force.
The net weight of the drill pipe surrounded by the drilling fluid contributes to the deformation and penetration into the soil, however it is considered negligible compared to the
normal force the drill pipe exerts on the borehole wall due to the pulling force in the rod.
The drill pipe is surrounded by drilling fluid and undergoes a friction force in the drilling
fluid, which is small compared to the friction between pipeline and the drilling fluid.
8
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
2.3
The pipeline
The pipeline is pulled through the borehole connected to a swivel and a reamer which in
turn connect the pipe to the drill pipe. The reamer has a larger diameter than the pipeline.
For the part of the pipeline outside the bore hole there is a friction over the rollers.
Inside the bore hole the pipeline is surrounded by drilling fluid. Depending on the weight
difference between drilling fluid and pipeline (partly water filled) there is a net upward
or downward force. The pipeline is pulled through the drilling fluid which results in a
frictional force. This force is considered to depend on the flow of the drilling fluid past
the pipeline, which is dependent on the pull back velocity. Also, the “age” expressed in
strength of the drilling fluid can have an effect because of stiffening of the drilling fluid
over time causing an increased friction force.
In addition to the upward/downward force due to weight differences, the pulling force
in the pipeline combined with the bending moment leads to a distribution of normal
forces which the pipeline exerts on the borehole wall. Depending on the magnitude of
the forces/moments and the soil properties (stiff, soft, plastic/ non plastic) the pipeline
penetrates to soil to a greater or lesser extent. Plastic behaviour of the soil surrounding the borehole wall can furthermore affect the shape of the bore hole. The pipeline
soil contact causes an extra friction force depending on the normal force exerted on the
borehole wall. In the above figure it is also shown that the drilling fluid penetrates into
the borehole wall to a certain extent. This makes the properties of the soil at the bore hole
wall different from the usual properties of the soil.
The soil is usually build up of multiple layers and the interaction of the pipeline with the
soil differs per location.
During pull back, the head of the pipeline may directly penetrate the soil as opposed to
elsewhere along the pipeline where there is only penetration of the pipeline in the direction normal to the axis of the bore path. At the head of the pipeline penetration in the
direction of the axis of the pipeline can occur. Such phenomena is expected to be more
pronounced in the bends in the bore path where due to the moments in the pipeline the
axis of the bore path and pipeline don’t coincide. The pipeline is inclined to bend to it’s
straight original form in the bends of the borepath. This bending leads to higher forces on
the borehole wall and extra penetration into the bore hole wall.
9
Nieuwe boortechnieken kleine infra
2.4
The drilling fluid
The drilling fluid is pumped through the drill pipe and comes out through the nozzles
in the reamer. The flow direction of the drilling fluid is determined by the “path of least
resistance”. Initially the drilling fluid will flow past the pipeline but when the pipeline is
being further pulled in the flow changes direction to the side of the pulling rig, see Figure
2.1 and Figure 2.2. This changing of flow direction is related to the specific behaviour of
the drilling fluid, which is often described as a Bingham fluid. The fluid undergoes also
motions because the pipeline is pulled through it. The fluid flow along the pipeline (due
to pulling or pumping) causes a friction force on the pipeline.
productbuis
swivel
Figure 2.1. Sketch of the situation where the drilling fluid flows along the pipeline.
productbuis
swivel
Figure 2.2. Sketch of the situation past the turning Point where the drilling fluid flows toward the
pulling rig.
The flow of the drilling fluid causes a pressure at the head of the pipeline also contributing to the pulling force.
As described above, the drilling fluid also penetrates the soil of the bore hole wall, changing the usual properties of the soil and the friction between soil and pipeline.
10
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
3 The pipeline pull back model
In the previous Chapter, an overview has been given of the phenomena that take place
during the pull back operation. A model has been created that describes the pull back
using the finite element code ABAQUS. Matlab is used to make input and control the
calculations. This Chapter gives an overview of the model. The complete Matlab code is
presented in Appendix 1, together with an overview of all the functions and a flow chart
of how Matlab controls the FEM code ABAQUS. When owning both programs one can
reproduce any simulation presented in this report by using the code in Appendix 1.
3.1
Bore path geometry
The first thing that needs to be done is to establish a geometry for the bore path.
­Currently the model is two-dimensional and the geometry can be defined by either reading a two-column (ASCII) data file with x,y pairs of the bore path or by defining a design
geometry consisting of straight lines and a circular arc as depicted below.
R
L1
L2
L3
Figure 3.1. Design geometry that can be input by the user, when not using an XY data file.
If not choosing an XY data file, the user can input values for L1, L2, L3 and R to model one
half of a bore path. The user can furthermore select the symmetry option to mirror this
geometry to make a complete design path. For studies on the behaviour of the pipeline
in the upward bend, as described in this report, the geometry shown in Figure 3.1 can be
used.
The XY data file needs to be increasing in X, but needs not to be equally spaced. Spline
interpolation used in the program allows the user to enter non equally spaced data.
The program currently is 2D only. In section 3.4, a possible extension to 3D modelling is
discussed, and the main problem to be solved in the soil-pipeline interaction is pointed
out.
11
Nieuwe boortechnieken kleine infra
3.2
The pipeline and drill pipe
The most basic ingredients of the model are the pipeline and drill pipe. Both are
modeled using beam elements. Given a certain length of the pipeline and puling rod both
are divided into beam elements with a bending stiffness and pulling stiffness that differs
for the pipeline and drill pipe.
pipe line:
EI pipe , EA pipe
Pulling rod:
EIrod , EArod
Figure 3.2. Pipeline and drill pipe modeled as beam elements, with different bending and pulling
stiffness, initially a straight line when no forces act upon it.
The beam elements are suitable for large deflectio ns (non linear geometry) which can be
turned on or off. Currently in the model, the connection between pipeline and drill pipe
is a fixed one, meaning that the rotations and translations of the end of the pipeline and
start of the rod are the same. Ideally the connection should be a free rotating one, but
tests showed that the stiff connection is sufficient for large diameter steel pipes where
the bending stiffness of the pipeline is much higher than that of the drill pipe. For PE
pipelines the stiff connection is expected to be less realistic.
In the model the pipeline and drill pipe are straight initially and they are bend into the
shape of the bore path in the first simulation step, as shown below:
Äu
1
pipe line
nel
n
nel_pipe
drilling
pipe
Figure 3.3. Pipeline and drill pipe bend into the shape of the bore path.
As mentioned above this geometry can be defined either by an XY data set or by a combination of straight sections and a circular arc.
The model assumes that the pipeline is as long as the length of the entire bore path, but
only the part of the pipeline that’s in the bore path is modeled. The part of the pipeline
that’s outside the bore hole is modeled by the application of a friction force on the pipeline at the entry point.
The user can give the total number of elements nel in which the pipeline and drill pipe
are divided as well as the number of elements nel_pipe of the pipeline. With the latter the
user can decide how much of the pipeline has been pulled in. Obviously nel_pipe ≤ nel.
The current model can not pull the pipeline in continuously. Instead the simulation starts
from a situation where the pipeline has been pulled in to a certain extent by setting
12
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
nel_pipe. From this position, on the end of the drill pipe a prescribed displacement Δu is
used to pull the rod and pipeline to be able to calculate the resulting forces and displacements. In the current model Δu needs to be smaller than an element length, to avoid
problems with the soil-pipeline interaction.
3.3
Forces on the pipeline and drill pipe (Soil-pipeline, weight etc..)
In the simulation, in the first step the beam (pipeline + drill pipe) is bend into the shape
of the borepath as shown in Figure 3.3 by prescribing displacements on the nodes of the
beam. To describe the penetration of the pipeline and the drill pipes into the borehole
wall and the forces arising from pulling, the interaction between the soil and pipeline
and between soil and drill pipe is described in the model. To visualize this interaction an
arbitrary element of the pipeline or drill pipe is taken out from Figure 3.3 and presented
in Figure 3.4. The beam elements have 2 nodes. On each side the node on the beam is
connected to another node by a kind of spring element (called Tube-support elements
in ABAQUS). These other nodes are kept fixed in position and are placed at the centre of
the bore path. The Tube support elements have an orientation, that makes a distinction
between displacements parallel to the bore path, ut and displacements normal to the
bore path, un. The orientation is derived from the position of the fixed nodes in the bore
path by the Matlab script generating the ABAQUS input file.
ut
net force,
submerged weight
nodes on beam elements
friction force fw
spring k(Un)
un
nodes on centre line
of bore path
Figure 3.4. one element of a pipeline or drill pipe and the interaction with soil and drilling fluid.
For each node on the beam which undergoes a displacement normal to the bore path, a
user defined spring stiffness k(un) describes the interaction with the soil (and bore hole),
see Figure 3.5.
13
Nieuwe boortechnieken kleine infra
p
plastic
s
spring
force F(un)
w of bore hole
wall
b= gap
g between pipe and wall
pipe line
line wall
wall
k(un)
-b
b
un
c
centre
of bore hole
un
Figure 3.5. Spring stiffness of tube support element between beam and bore hole.
In principle the spring stiffness k(un) can be defined arbitrarily using piecewise linear
segments. In the current model the gap between the pipe (or drill pipe) and the bore hole
wall can be given by the user. The stiffness inside the borehole(gap) can be specified too.
Usually this stiffness is set to zero so that no spring force is build up inside the gap, but
for numerical stability it’s necessary to have a low stiffness in the borehole(gap). A value
of about 1/500 of the soil stiffness is recommended. This can be set in the program by
the user. The penetration into the wall is done with a constant stiffness (linear spring). At
the moment there is no plastic region used for the model, but this is easily implemented
if necessary (see Chapter 6 for a discussion on expected spring functions for different soil
types and pipe diameters).
As can be seen in Figure 3.5 the spring behaviour is symmetric. Because the base node of
the spring is in the centre of the borehole, when the beam node’s normal displacement is
either + or – the gap width b, then the pipeline touches the borehole wall, see Figure 3.5.
By defining the spring function k(un) the forces normal to the borehole wall can be
calculated. The tube support springs also have a friction component parallel to the borehole wall, see Figure 3.4. The friction force is related to the normal force by:
Fw = µFn
(3.1)
The friction force is related to the normal force by a constant friction coefficient µ which
can be given by the user. Besides this dependency there is also a friction force due to the
friction of the pipeline in the drilling fluid, which is independent on the normal force. This
is implemented by adding a constant nodal force parallel to the bore path as a friction
force in addition to the force given in (3.1) which is calculated internally. This force is applied during the pulling phase of the simulation.
14
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
The friction that effectively is modeled for each node is then:
Fw = c + µFn
(3.2)
With Fw the total friction force at a node, c a cohesion giving rise to friction in the
borehole regardless of the pipeline soil reaction, µ the friction coefficient as in (3.1)
and Fn the normal force exerted on the borehole wall as in (3.1).
Note that the soil type can vary along the bore path and also in the first part the soil
interacts with the pipeline and in the second part with the drill pipe. This results in a k(un)
function, a friction coefficient µ and possibly also a cohesion c that vary with each node of
the beam along the bore path. In the current model however, the interaction between soil
and pipeline is considered constant as well as the interaction between soil and drill pipe.
Thus the user gives as input two sets of k(un), µ, and c ( pipeline and drill pipe).
All simulations in this report have been performed this way. Extension to include properties that vary along the bore path can be implemented in the program in a straightforward manner.
Besides the forces discussed above, there is a gravity force acting on the pipeline and
drill pipe, see Figure 3.4. This force always acts in the direction of the earth’s gravitational field. In the model this is the negative Y direction if the user defines a borepath in
XY coordinates. The pipeline is usually filled with water by a water filled tube inside the
pipeline. The upward force of the pipeline or drill pipe in the drilling fluid is calculated
from the drilling fluid density and the gravitational constant and the cross section of the
pipeline or drill pipe. The downward force is calculated from the density of the pipeline or
drill pipe and their cross sections as well as by specifying which percentage of the pipeline
is water filled. In case of the drill pipe it is assumed to be entirely filled with drilling fluid
having the same density as the drilling fluid in the bore hole.
Currently in the model the force due to gravity is constant over the length of the pipeline
and constant over the length of the drill pipe. A varying force would be due to a varying
percentage water filled in the pipeline, which might be applied in some practical cases.
This can be implemented in a future update of the model.
3.4
3D modelling
As mentioned, the current model is two-dimensional. Building a three-dimensional
model in the same way is possible by using spring elements in the other direction perpendicular to the bore path. Doing things this way however, models a square borehole
instead of a circular one as shown in Figure 3.6. Depicted is the motion that the pipeline
can make. It can travel the gap width in upper, lower, left and right direction before penetrating the wall of the borehole. The effect of 3D bore paths on the soil pipeline interaction can be studied using the current 2D model. Three dimensional shapes of bore paths
should be delivered as two dimensional shapes (equivalent bending radii).
15
Nieuwe boortechnieken kleine infra
gap
Figure 3.6. Picture showing a possible extension to 3D resulting in a square borehole instead of a
circular one.
3.5
Friction on the rollers
The friction on the rollers is taken into account as an extra friction force applied at the
entry of the borehole. This friction force is calculated by multiplying the weight of the
pipeline that’s outside of the borehole with a friction coefficient. The length of the pipeline outside of the borehole is determined from the difference in length of the borehole
and length of the pipeline in the borehole. It is implicitly assumed that the pipeline’s
total length equals the length of the bore path. For this length the weight is determined
using the cross section of the pipeline, the density of the pipeline material and the
acceleration of gravity. This weight is then multiplied by a friction coefficient. The NEN
code sets this friction coefficient to 0.1 if there is a roller track or to 0.3 if the pipeline
lies on the soil surface.
3.6
Simulation steps and geometric linearity/non-linearity
It is known that geometric non-linearity needs to be used for an accurate description of
large deflections of beams. This has been implemented in the code, but the user can also
choose geometrically linear behaviour. Some finite element codes don’t have the geometrically nonlinear option. It might be possible to implement the pulling model in those
codes with rather good approximation to the results of a geometrically nonlinear simulation. Therefore a geometric linear option has been implemented in the model as well. The
differences between the approaches differ fundamentally. In this section a brief overview
is given of the way the simulations are performed by the finite element program ABAQUS
and this is done separately for the geometrically linear and nonlinear variants.
3.6.1
Geometrically nonlinear simulations
The most realistic simulations are considered to be the simulations where geometric
nonlinearities are taken into account. Then large deformations can be simulated. One
pull back step of a geometric nonlinear simulation is performed in four steps:
1. The first simulation step is visualized in Figure 3.7. The simulation starts with a beam
(pipeline - drill pipe combination) that is initially horizontal and straight without internal stresses. The length of the beam is as long as the length of the bore path created
16
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
from the XY data file or from the lines and circle sections as described above. The bore
path is divided into nel elements using an algorithm which assures that the distance
between neighboring nodes is approximately the same, ΔL. Nodes are placed along the
bore path that form the base nodes for the tube support elements that describe the
soil-pipeline interaction. After this division the distance between neighboring nodes
is computed and from these distances the element lengths are created along the horizontal beam. A node that is close to the center of the model is selected as mid node
and the x-position of the corresponding mid node on the horizontal beam is set to the
same position (it can be selected to have this node at the left of the model to have for
example a cantilever beam type boundary condition). This node is kept fixed horizontally and rotationally in the first simulation step. In this first simulation step the nodes
on the beam are shifted by a vertical displacement corresponding to the difference
in y value between their corresponding points on the bore path and the y position of
the beam. Because the center is fixed horizontally and the simulation is geometrically
nonlinear, the nodes of the beam end up very near the corresponding location of the
base nodes along the bore path for the tube support elements. These soil-pipeline
interaction elements are turned off in this first simulation step.
L
first step:
upward displacement
of nodes
horizontally and rotationally
fixed node
L
initial state
(straight beam)
Figure 3.7. geometrically nonlinear simulation.
2. In the second simulation step the tube support elements nodes are turned on and
all prescribed displacements on the beam are relaxed except for the mid node which
is now kept fixed vertically, horizontally and rotationally. This means it is fixed in the
centre of the bore hole. In this step the beam tends to straighten out because of the
internal moments that were build up in the first step. Because the soil-pipeline
interaction elements are turned on an equilibrium is found whereby the beam
penetrates the soil and soil stresses are computed as well as the penetration.
3. In this step everything is kept the same except for the centre node for which the
vertical and rotational constraints are relaxed. The centre node is only fixed
horizontally at this point.
4. The horizontal boundary condition of the centre node is relaxed, so that there is no
boundary condition on this node. The right end of the model is pulled a distance of
Δu in the direction parallel to the bore path. This is the actual pulling step. At the same
time the extra friction forces or an additional thrust force are applied now on
the nodes of the beam. These are: the roller track friction at the left end of the model,
a thrust force at the left end of the model if the user selected that, and the friction
force due to cohesion in the drilling fluid.
The code always performs these four simulation steps in the geometric nonlinear case.
As output the user gets normally the third step, which is the final stage of the way the
17
Nieuwe boortechnieken kleine infra
pipeline lies in the bore hole without pulling and the fourth step, which is the penetration
and soil reaction during the pull back step. The user also can select “fixed=1”, then the
code generates output only for step 2 where the centre node (or left node) is kept fixed
horizontally, vertically and rotationally. This allows the user to study phenomena of a
clamped pipe in a bore hole, which will be used in this report for comparison with some
analytical results.
3.6.2
Geometrically linear simulations
In the geometrically linear case, the simulation is also started from a horizontal straight
beam, divided in elements of the same size. But contrary to the nonlinear simulation, the
length of the beam is shorter, it is as long as the difference in between the maximum and
the minimum x position of the bore path, see Figure 3.8. In other words, as long as the
bore path projected on the x-axis. This is because a linear geometric simulation assumes
small deflections (in axial sense, bending of the beam) and there is no update of geometry. From this it can be seen that when the deflections become large, the geometric linear
simulation becomes less and less realistic. But for steel pipelines and small deflections
the results might not differ too much from a full nonlinear simulation. The geometric
linear simulations are performed in three steps described below:
1. First, the minimum and maximum x-positions of the bore path are used to make a
horizontal beam (pipeline and drill pipe combination) simply between these positions
and equally split in nel elements. Contrary to the nonlinear case, the base nodes for
the tube support elements for soil pipe interaction are also created horizontally at the
same position as the initial beam nodes. The coordinate system that defines parallel
and perpendicular direction to the borehole is now simple. The parallel direction is
taken as (1,0,0) and perpendicular as (0,1,0). This is because in a geometrically linear
system even though the beam undergoes deflection, it is in fact still the same straight
geometry and is not updated. Once these nodes and beam elements are generated,
the nodes of the tube support elements are moved upward to their corresponding positions at the centre the bore path while keeping a centre (or left) node fixed horizontally and rotationally, see Figure 3.8. Although the end result is exactly the bore path
and the beam should have stretched there are no axial forces in the beam after this,
because of geometric linearity. Also because the pipe soil interaction elements were
already on, the result of this first step is already a beam penetrating in the bore hole
and obtaining soil reactions. Thus this first step is comparable to the second step in
the nonlinear simulation.
first step:
upward displacement
of nodes
horizontally and rotationally
fixed node
initial state
(straight beam)
Figure 3.8. geometrically linear simulation.
2. Just as in the geometric nonlinear simulation, everything is kept the same except for
the centre node for which the vertical and rotational constraints are relaxed. The
centre node is only fixed horizontally at this point.
3. The horizontal boundary condition of the centre node is relaxed, so that there is no
18
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
boundary condition at all on this node. The right end of the model is pulled a distance
of Δu horizontally. This is the actual pulling step. At the same time the extra friction
forces or push force are applied now on the nodes of the beam (as previously: roller
track friction, push force, and the friction force due to cohesion in the drilling fluid).
Note that this pulling to horizontally is different from the direction of the bore path as
used in the nonlinear simulation. The pulling needs to be horizontal because that is
the geometry that the program “thinks” the beam is still in, because there is no update
of geometry in a geometric linear simulation. For this reason the so called
Capstan forces are not generated. Those forces are that when pulling across a bend,
due to the pulling force also the force perpendicular to the bore path increases. But
since the beam is still straight, there is no bend in linear geometry and no increase
of forces perpendicular during pulling. This also means that from the soil reaction in
step 2 and including the friction of the drilling fluid, one can calculate the pulling force
exactly in this linear situation. And it’s not really necessary to do a FEM simulation.
The code always performs these three simulation steps in the geometric nonlinear case.
As output the user gets normally the second step, which is the final stage of the way the
pipeline lies in the bore hole without pulling and the third step, which is the penetration
and soil reaction during the pull back step. The user also can select “fixed=1”, then the
code generates output only for step 1 where the centre node (or left node) is kept fixed
horizontally, vertically and rotationally. This allows the user to study phenomena of a
clamped pipe in a bore hole, which will be used in this report for comparison with some
analytical results.
3.7
List of input parameters
With the description of all components of the current model completed, here a complete
list of input parameters is given as a summary of what is included in the model.
Bore path Geometry
L1, L2, L3, R, sym
Straight sections and radius and symmetry option
XY data file
If not using the above, a 2 column data file can be used
nel, nel_pipe
Number of elements along bore path, number of elements that are pipeline (the remainder is drill pipe)
Pipeline
D0_pipe, t_pipe
Pipeline diameter and wall thickness
rho_pipe, E_pipe, nu_pipe
Pipeline material. Density, Young’s modulus and
poisson’s ratio.
Drill pipe
D0_rod, t_rod
Drill pipe diameter and wall thickness
rho_rod, E_rod, nu_rod
Drill pipe material. Density, Young’s modulus and
poisson’s ratio.
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Nieuwe boortechnieken kleine infra
Pipeline soil interaction
k_ps, gap_ps, fric_ps
Pipe-soil spring stiffness, gap around pipe, friction.
Drill pipe soil interaction
k_rs, gap_rs, fric_rs
rod-soil spring stiffness, gap around rod, friction.
Other soil pipe/rod interaction
k_red_fact
Factor by which spring stiffness is reduced inside the
gap as compared to soil penetration stiffness k_gap=k_
red_fact*k_ps (or k_rs)
Gravity force upward/downward
rho_bf, rho_water
Drilling fluid and water density
Tfilled
Fraction of pipeline filled with water
g
Acceleration of gravity
Friction of pipeline and rod through drilling fluid
f2
Friction per square meter of surface (NEN=50 N/m2)
Roller track friction and push force
f1
Roller track friction coefficient, friction is f1 times gravity force of pipe outside bore path
Fpush
Push force at entry point of bore path
Simulation controls
nl
Geometrical nonlinear simulation (nl=1) or linear
(nl=0)
left
Keep left fixed (left=1) instead of middle (left=0)
during first simulation steps
3.8
Running the simulations
The pull back simulations are performed by the finite element code ABAQUS and the
input is created with Matlab scripts. The postprocessing is performed by python scripts
(part of the ABAQUS environment) and finally by Matlab scripts with which all the graphs
in this report have been created. The entire Matlab code is presented in Appendix 1,
together with an explanation of all the functions, a flow chart as well as instructions to
how to run the script. The script can be copied from the Appendix and pasted into
Matlab. When Abaqus is installed on the same PC as Matlab, all simulations presented
in this report can be reproduced.
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Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
4 Simulation results
The model discussed in the previous chapter has been implemented. The program code
can be found in Appendix 1. With this program simulations have been performed from
simple cases that can be compared with analytical solutions to complex cases with
irregular bore paths and a multitude of interactions between the pipeline and its
surroundings. The results of these simulations are presented in this chapter.
4.1
Comparison with analytical solution
The first simulations consider a pipeline fixed on one end which lies in a borepath of
circular radius R. This is equal to Figure 3.1 with L1 and L3 are zero and L2 nonzero. There
is no gap between borehole wall and pipeline. The spring stiffness describing pipeline soil
interaction is linear. This simulations are based on geometrically linear behaviour.
It is possible to find an analytical solution for this problem and find the soil penetration and soil reaction forces on the pipeline. The solution is non-trivial and is derived in
Appendix 2. In subsequent sections it will be shown that this analytical solution helps to
understand many phenomena of pipeline soil interaction in more complex situations.
The input parameters for the numerical model are shown in Appendix 3.1.1. The main
input parameters are a pipe cross section of 1.21 m and wall thickness of 2.27 cm, material is steel. The radius is chosen 1210 m, which is approximately the minimum allowed
radius for those kinds of steel pipelines (R>1000 D0). L2 is set to 310 m. The spring stiffness is set to 130 kN/m2 which can be thought of as a soft clay material (see chapter 6 for
a discussion on spring stiffness).
The results of the ABAQUS simulation and the analytical solution are presented in
Appendix 3.1.5. As can be seen the results match perfectly. The maximum borehole wall
penetration is 14 cm, small compared to the overall length of the pipeline and it can be
seen that the pipeline closely follows the circular arc in both the analytical and numerical
models, this is shown in Figure 4.1 below.
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Nieuwe boortechnieken kleine infra
Figure 4.1. Comparison of vertical displacements resulting from the analytical solution and the
numerical ABAQUS model discussed in this report.
When looking at the moment in the pipeline, Figure 4.2, the solutions also are in agreement. From elementary beam theory it is known that if a beam is bent into a perfect circle
the bending moment is:
M =
EI
R
(4.1)
Where EI is the bending stiffness of the beam and R the circle radius. EI can be calculated
as follows:
EI = E
π
( D04 − Di4 )
64
(4.2)
With E the Youngs modulus of the pipeline material, D0 the outer diameter and Di the
inner diameter of the pipeline. Using the values from Appendix 3.1.1.1 and R=1210 m.
M=2590 kNm. It can be seen that this is exactly the value at the left clamped end of the
pipeline in Figure 4.2. The right end of the pipeline is a free end and the moment there
should be zero, which is also visible in Figure 4.2. The distance over which the
moment goes to zero is related to the ratio of the soil spring stiffness to the beam bending stiffness. Over the first 200 m of the pipeline the moment is fairly constant at the
value calculated above from beam theory.
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Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Figure 4.2. Comparison of moment in the pipeline resulting from the analytical solution and the
numerical ABAQUS model discussed in this report.
The soil spring reaction (forces exerted on the pipeline by the soil) is shown in Figure 4.3.
It can be seen that the force is zero upto a distance of about 250 m. Then the force becomes negative between 250 and 300 m and positive after that. A negative force means
the pipeline is pushed downward and a positive force means the pipeline is pushed
upward. It might seem a contradiction to have a force pushing downward, but opposite
forces are in fact necessary to create the constant moment in the beam belonging to a
circular bore path as mentioned above. It can be observed by comparing Figure 4.3 to
Figure 4.2 that (starting from the right) when the force becomes almost zero that is the
point where the moment becomes constant. Coupled to the soil reaction force is the
borehole wall penetration shown in Figure 4.4. Penetration is positive when the force is
negative and vice verse. Note that since there is no gap around the pipeline (for modelling
the borehole) used in these simulations that the borehole wall penetration is equal to the
displacement normal to the bore path. In simulations with gap the displacement normal
to the bore path is larger than the penetration, this effect can then be observed in the soil
spring reaction graphs as well.
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Figure 4.3. Comparison of the soil spring reaction resulting from the analytical solution and the
numerical ABAQUS model discussed in this report.
Figure 4.4. Comparison of the wall penetration resulting from the analytical solution and the
numerical ABAQUS model discussed in this report.
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Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
It can be concluded that the implemented model and analytical solutions are closely
matching and the results can also be understood using basic facts from beam theory.
4.2 Comparison of results with and without gap and using nonlinear
and linear geometric behaviour
Starting from the numerical solution in the previous section without gap between borehole wall and pipeline an extra simulation has been performed with the model with a
gap of 0.1 m. The two simulations have been performed again with geometric nonlinear
behaviour instead of linear behaviour, resulting in four simulations that are compared in
this section. The input parameters of the four simulations are presented in Appendices
3.1.1 to 3.1.4 and the simulation results are plotted together in Appendix 3.1.6. The top
left figure doesn’t show any differences between results, which was to be expected since
the borehole is basically followed in all the simulations. The top right figure where the
moment in the pipeline is presented shows subtle differences in results (Figure 4.5). The
first thing that can be observed is that the moment is more constant in the first 200 m for
the geometrically nonlinear case compared to the linear case where the moment seems
to increase slightly compared to the theoretical value of 2590 kNm calculated from beam
theory. This is due to the fact that in geometric linearity the bending radius R is approximated and this approximation fails to a greater extent when axial deflections become
larger. Then the moment also diverges from the theoretical value more. In this case of a
large diameter steel pipeline, the behaviour between geometric linearity and nonlinearity
doesn’t differ much.
Figure 4.5. Comparison of the moment in the pipeline for the four simulations.
Another thing that can be observed from the moment graph is that in the case with gap
the moment decreases gradually while in the case without gap there is first a slight increase between 200 to 250 m and then a decrease. This is related to the soil reaction plot
25
Nieuwe boortechnieken kleine infra
shown in Figure 4.6 below. First thing that can seen is that the graphs of the geometrically nonlinear simulations extend to a further distance than the ones for the geometrically linear simulations. This is because the distance plotted is the distance along the
pipeline and, as mentioned in Chapter 3, the pipeline (beam) is longer in a geometrically
nonlinear simulation because it has to be as long as the length of the bore path, while
in a geometrically linear simulation the beam is as long as the projected bore path on
the horizontal axis. However this difference in length is small for this case where a large
diameter steel pipeline is used with its minimum allowed bending radius, in PE pipelines
where bending takes place with smaller radii and over larger angles this difference can be
considerably larger.
The second thing observed in Figure 4.6 is that for the simulations with gap the force is
zero to about 250 m and then negative and then zero over a certain distance from about
280 m to 300 m again after which becoming positive, while the simulation without gap
the force switches from negative to positive instantly without a zone of zero force. This
is due to the fact that from going from upward borehole wall penetration to downward
borehole wall penetration the pipeline does not touch the borehole wall and the force is
zero. This can be seen in Figure 4.7 where for the simulations with gap the displacement
gradually rises and around 240 m the displacement is larger than 0.1 m (the gap width),
this is also the location where negative soil reaction forces are generated due to penetration in the borehole wall. Then between 280 and 300 m the displacement is smaller than
0.1 m and larger than -0.1 m and the pipeline is also inside the gap not touching the wall.
It can be observed from Figure 4.6 that the peaks of the soil reaction forces are lower
for the model with gap compared to the situation without gap. A possible explanation
for this is that the moment that has to be created in the pipeline needs to be the same
in both the simulations with and without gap because the pipeline needs to follow the
circular arc. The moment is in fact caused by positive and negative forces being separated
by some distance. In case of the gap, the distance is larger as can be seen in Figure 4.6.
The negative force starts earlier and the positive force peaks later. If the distance is larger
the force must be lower to obtain the same moment.
26
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Figure 4.6. Comparison of the soil spring reaction for the four simulations.
Figure 4.7. Comparison of the displacement normal to the borepath for the four simulations.
In general it can be concluded that the differences between geometric linearity and nonlinearity are small for the large diameter steel pipeline used in this simulation. In case of
PE pipelines with larger (axial) deflection angles the differences can be much larger.
27
Nieuwe boortechnieken kleine infra
4.3 Simulations with a circular section and added straight section
without gap
The basic parameters of the previous sections are used in this simulation. The bore path
geometry is changed to include a straight horizontal section L1=200 m (see Figure 3.1
for the meaning of L1, L2 and L3), L2 is the same as in previous sections, 310 m and L3
is varied from 0, 10, 20, 40, 60, 80, 100 m. A situation with no gap is considered and the
pipeline was not pulled back. Geometrically nonlinear behaviour is used. The goal of the
simulation is to study the soil reaction forces and borehole penetration for a varying L3.
The complete list of input parameters for L3=100 m is shown in Appendix 3.2.1 and the
results of all simulations are shown in Appendix 3.2.2.
Looking at Figure 4.8 it can be seen that where the circular arc begins after a 200 m horizontal bore path the moment of 2590 kNm is generated again and brought back to zero
at the end of the circular arc. The decrease to zero differs for the various simulations. The
end of the pipeline is free and has by definition a moment of zero. In the last simulations
for L3=100 it can be seen that the straight section is long enough to have a moment of
zero before the end of the pipeline.
Figure 4.8. Comparison of the moment for simulations without gap and varying L3.
This length effect is reflected in the soil reaction forces and normal displacement, Figure
4.9 and Figure 4.10. For L3=0 m, the maximum normal displacement and soil reaction
force is equal to the simulation performed in section 4.2. For increasing L3 the maximum
soil reaction force becomes less and the normal displacement at the end also decreases
in amplitude. For L3=100 m the forces and displacements at the end of the circular arc
show the same magnitude and shape as those at the beginning of the circular arc. And
the force has become zero again, meaning there is no change in moment from that point
on as seen in the moment graph.
28
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
It can be concluded that the soil reaction forces are much higher when the head of the
pipeline is in the bend as compared to when the head of the pipeline has passed through
the bend. Here it can be remarked that the Dutch NEN code estimates the soil reaction
based on a pipeline lying entirely in the borehole and doesn’t describe the higher forces
as found when the head is in the bend.
Figure 4.9. Comparison of the soil reaction forces for simulations without gap and varying L3.
Figure 4.10. Comparison of the normal displacement for simulations without gap and varying L3.
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Simulations with a circular section and added straight section with
0.1 m gap
4.4
The basic parameters of the previous sections are used and the bore path geometry is
changed to include a straight horizontal section L1=200 m (see Figure 3.1 for the meaning of L1, L2 and L3), L2 is the same as in previous sections, 310 m and L3 is varied from
0, 10, 20, 40, 60, 80, 100 m. A situation with 0.1 m gap is considered and the pipeline
was not pulled back. Geometrically nonlinear behaviour is used. The goal is to study the
soil reaction forces and borehole wall penetration for a varying L3. The complete list of
input parameters for L3=100 m is shown in Appendix 3.3.1 and the results of all simulations are shown in Appendix 3.3.2.
Just like in Figure 4.8 it can be seen in Figure 4.11 that where the circular arc begins after
200 m horizontal borehole the moment of 2590 kNm is generated again and brought
back to zero at the end of the circular arc. The decrease to zero differs for the various
simulations. The end of the pipeline is free and has by definition a moment of zero. But
only in the last simulations for L3=100 it can be seen that the straight section is long
enough to have a moment of zero before the end of the pipeline.
Figure 4.11. Comparison of the moment for simulations with 0.1 m gap and varying L3.
As in the previous section without gap, for L3=0, the maximum normal displacement
and soil reaction force (Figure 4.12 and Figure 4.13) are equal to those of the simulation
performed in section 4.2 for the nonlinear case with gap. For increasing L3 the maximum
soil reaction force becomes less and the normal displacement at the end also decreases
in amplitude. For L3=100 m the forces and displacements at the end of the circular arc
show the same magnitude and shape as those at the beginning of the circular arc. And
the force has become zero again, meaning there is no change in moment from that point
on as seen in the moment graph.
30
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Comparing Figure 4.12 to Figure 4.9 for L3=100 m it can clearly be observed that the
maximum magnitude of the force is higher for the case without gap compared to the
case without gap. This is due to the fact seen earlier that when the arm (distance between
positive and negative forces) becomes longer when a gap is present, there is less force
needed to generate the same moment.
It can be concluded that the soil reaction forces are much higher when the head of the
pipeline is in the bend as compared to when the pipeline head has passed through the
bend. Here it can be remarked, as in section 4.4, that the Dutch NEN code estimates the
soil reaction based on a pipeline lying entirely in the borehole and doesn’t describe the
higher forces as found when the head is in the bend.
Figure 4.12. Comparison of the soil reaction forces for simulations with 0.1 m gap and varying L3.
31
Nieuwe boortechnieken kleine infra
Figure 4.13. Comparison of the normal displacement for simulations with 0.1 m gap and varying L3.
4.5
Pullback simulation of half circle borehole
A borehole geometry of half a circle with radius of 1210 m is chosen to study the
displacements and forces during pullback. Of course the result is a borehole that is very
unrealistic, however a lot can be observed from these simulations and they form also a
verification of the model. To obtain a better understanding of the phenomena involved,
more effects are added to the simulations. Geometric nonlinearity is used and a gap
of 0.1 m. The first simulation is done with friction only, no cohesion due to the yield
strength of the drilling fluid or gravity effects are included. In the second simulation
cohesion is added and in the third simulation gravity effects are added.
4.5.1
Half circle geometry with friction only
The input parameters of this simulation are given in Appendix 3.4.1 and the results of
the simulation are presented in Appendix 3.4.2. The basic geometry and moment plots
are shown in Figure 4.14. The pullback is performed on the right end. there the pipeline
is pulled upward over a distance of 1 m.
It can be seen that the moment is almost constant over the entire geometry at 2590
kNm, the value corresponding to a radius of 1210 m as determined in previous sections
for the large diameter steel pipeline. The ends are free initially and the moment tends to
zero there. Note that the moment doesn’t change much during pulling compared to the
static situation when the pipeline just lies in the borehole. This is because the pipeline
has to follow the same half circle when pulling. The pipeline has to remain in the bend in
the same way as without pulling.
32
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Figure 4.14. Geometry and moment graphs of the half circle geometry simulation with friction only.
As in previous sections there is only soil reaction force where the moment is generated, in
this case at the beginning and end of the borehole only.
Figure 4.15. Displacements normal and parallel to the borehole for the half circle geometry simulation with friction only.
Figure 4.15. Displacements normal and parallel to the borehole for the half circle geometry
simulation with friction only.
33
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Observing the displacements parallel to the borehole (right plot of Figure 4.15), it can
be seen that at the right end of the borehole the displacement is 1 m. This is the prescribed upward displacement of the pullback operation. One would perhaps expect a
displacement of 1 m also at the left end of the borehole for such a stiff pipeline, but the
displacement at the left end is only about 0.68 cm. The explanation for this difference
can be found when looking at the plot for the normal displacement (right plot of Figure
4.15). When there is no pull back the pipeline lies approximately on the centerline of the
borehole, this is because the centre line was the prescribed displacement and there is
no gravity loading and only displacements at the beginning and end of the borehole are
needed to generate the moment. But during pulling, the normal displacement is 0.1 m
for the most part. This is exactly the gap width and the pipeline simply is pulled upward
to the top of the borehole. This makes the needed length in the borehole about π(12101209.9)= π 0.1=0.314 m shorter. This is exactly the difference between parallel pipeline
displacement at the right and left ends.
Figure 4.16. Pulling force for the half circle geometry simulation with friction only.
The pulling force, Figure 4.16, is remarkably low. This is because no cohesion has been
used and the only contribution to the pulling force is the friction which is equal to a factor
multiplied with the normal force caused by penetration of the borehole wall. There are
two jumps in the pulling force at the beginning and end of the borehole, because of the
reaction forces which are required to generate the moment and a slight increase of the
pulling force along the pipeline due to friction against the top borehole wall.
Because the pulling force is so low, there is hardly any length change of the pipeline.
The plot of the length change in Appendix 3.4.2 shows about 7 mm length change.
On a beam of almost 4000 m length this is a strain of only 1.75 e-6.
4.5.2
Half circle geometry with friction and cohesion
The input parameters of this simulation are given in Appendix 3.5.1. The simulation is
basically the same as in the previous section except for the addition of a cohesion due
to the yield strength of the drilling fluid of 50 N/m2. the results of the simulation are
presented in Appendix 3.5.2. The moment plot is almost the same. Figure 4.17 shows
34
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
the soil reaction and normal displacement. Compared to the situation without cohesion,
it can be observed that during pulling the soil reaction force is not almost zero anymore
along the bore path. Instead a growing force is visible between beginning and end. Also,
the pipeline visibly penetrates the top of the borehole instead of just touching it as in the
previous section.
Figure 4.17. Soil reaction and normal displacement for half circle geometry simulation with friction
and cohesion.
This phenomenon is caused by the so called Capstan forces appearing. Because of the
added resistance in the drilling fluid, the needed pulling force is considerably larger,
and because the pipeline is being pulled not through a straight borehole but a curved
one, an increase in pulling force results in an increase of force normal to the borehole,
this increase of normal force in turn contributes to the pulling force until equilibrium is
reached. So the pulling force increases nonlinearly with distance compared to the situation with a straight borehole where the force would increase linearly. This is shown in Figure 4.18. Comparing this figure to the Figure 4.16 without cohesion, still the two jumps
can be observed at the beginning and end of the borehole and they have approximately
the same magnitude, but they are negligible to the contribution to the pulling force along
the borepath whereas without cohesion that contribution was much smaller.
35
Nieuwe boortechnieken kleine infra
Figure 4.18. Pulling force for half circle geometry simulation with friction and cohesion.
Figure 4.19 shows the force balance resulting in these Capstan forces. In the figure, a
pipeline is bend along a circular arc of radius R and an infinitesimal section of the pipeline over an angle dϕ is considered. The length of this pipeline section is Rdϕ . During
pulling the normal force is N and using a friction force per length c the total friction force
in this element is cRdϕ + µN . The pulling force on one end is T and on the other end
T + dT and increase due to friction.
cRd +N
N
d/2
d/2
_ _
T
T+dT
_
R
d
Figure 4.19. Forces acting on an infinitesimal pipeline element bend in a circle with radius R.
Considering horizontal equilibrium of forces leads to:
T cos
(4.3)
36
dϕ
dϕ
+ cRdϕ + µN = (T + dT ) cos
2
2
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Vertical equilibrium gives:
T sin
dϕ
dϕ
+ (T + dT ) sin
=N
2
2
(4.4)
In the limit for dϕ to zero and eliminating N from the equations results in the
differential equation:
dT
= cR + µT
dϕ
(4.5)
Under the boundary condition that the pulling force is zero at the solution of this
differential equation is:
T (ϕ ) =
cR µϕ
(e − 1)
µ
(4.6)
Figure 4.20 shows this function with the pulling force from the simulation (Figure 4.18).
The parameters for (4.6) are taken from the list of input parameters and output summary
of the simulation, Appendix 3.5.1. c=190 N/m, R=1210 m and µ =0.2. It can be seen
that the pulling force shows the same trend as the force resulting from the simulation
and the differences are small. The differences are mainly caused by the fact that the soil
spring reaction needed to create the moment also causes a friction and contribution to
the pulling force. But this contribution is small compared to the contribution to the
pulling force by the cohesion.
Figure 4.20. Pulling force compared with differential equation for the Capstan forces resulting from
cohesion.
37
Nieuwe boortechnieken kleine infra
Due to the larger pulling force the length change of the pipeline is also larger. The pipeline is extended by approximately 0.1 m over its length (Figure 4.21). This corresponds
to the parallel displacement which is about 0.1 m less on the left side of the borehole
compared to the previous simulation.
;
Figure 4.21. Length increase and horizontal displacement for half circle geometry simulation with
friction and cohesion.
4.5.3
Half circle geometry with friction, cohesion and gravity
The previous simulation is extended to include net buoyancy gravity effects. The pipeline
is for 50% filled with water. The input parameters are shown in Appendix 3.6.1 and the
simulation results in Appendix 3.6.2. The moment graph is quite similar to the previous
simulations as expected. Figure 4.22 shows that already in the initial situation before
pulling the pipeline penetrates the top of the borehole. This is due to the upward force.
The soil spring reaction is large at the lowest point and smaller further away from the
lowest point. During pulling the soil reaction is larger than in the previous simulation.
The pulling force is also much larger than in the previous simulation, see Figure 4.23 due
to the higher friction because of the higher soil reaction forces. Another thing that can be
seen in Figure 4.23 is that the pulling force is not maximum at the end of the pipeline,
but peaks before the end. This is because more toward the end the borehole becomes
almost vertical and the net upward buoyant force helps in the pulling and less force is
needed from the rig.
38
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Figure 4.22. Soil reaction forces and normal displacement for half circle geometry simulation with
friction, cohesion and gravity.
Figure 4.23. Pulling force for half circle geometry simulation with friction, cohesion and gravity.
Because of the larger pulling force the length change of the pipeline is also larger compared to the situation without gravity effects, Figure 4.24. In this case it can be seen
that in the initial state without pulling the pipeline extends because of the buoyant force
and becomes approximately 0.16 m longer. At the left end there is an upward (negative)
displacement of about 0.24 m and at the right end there is an upward (positive) displacement also of about 0.24 m. There is a total elongation of 0.48 m in the beam. This
is again due to the fact that originally the beam was in the centre of the borehole and to
39
Nieuwe boortechnieken kleine infra
touch the top of the borehole wall about 0.314 m extra length is available without
straining the pipeline as mentioned before. This means an actual elongation in the pipeline of about 0.48-0.314=0.166 m which is precisely the calculated length change in the
situation without pulling.
Figure 4.24. Length change and parallel displacement for half circle geometry simulation with
friction, cohesion and gravity.
During pulling the length change of the pipeline is in total 0.46 m, an 0.3 m increase
from the situation without pulling. At the right end it can be seen that the increase in
horizontal displacement is 1m as prescribed (from 0.24 to 1.24 m) and at the left end
the displacement is from -0.24 to 0.4 m, totaling about 0.64 cm. The difference is covered by the length change of the beam and extra penetration into the top of the borehole.
4.6 Pullback simulation with drilling pipe in 100 steps, no cohesion
or gravity effects
In the previous simulations the pipeline was present along the entire borehole. In this
section a more realistic design bore path is studied. The simulation considers pulling
back by positioning the head of the pipeline at 100 different positions in the borehole.
This was presented in Figure 3.3 where the borepath was divided into nel elements and
the head of the pipeline was from element number 1 to element number nel_pipe. The
remainder elements are drilling pipe. In this situation in total 200 elements were chosen
and 100 simulations were performed with nel_pipe varying from 2, 4, etc… to 200. The
geometry is L1=100 m, L2=150 m, L3=80 m and R=1210 m. The symmetry option was
used to create an actual bore path. The resulting total length of the bore path is 662 m.
The same pipeline parameters have been chosen as in previous simulations and a gap of
0.1 m was used. The drilling pipe was chosen to have a diameter of 0.125 m, resulting in
a lower bending stiffness and also the gap width was adapted to 0.6425 m. The complete
set of input parameters for a pipeline at 50% of the length of the borepath is given in
40
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Appendix 3.7.1. For five of the simulations all the results have been presented in the five
pages of Appendix 3.7.2, corresponding to the head of the pipeline at 1%, 30%, 50%,
80% and 100% of the borepath. The motivation for the selection of these is described
below.
For each of these 100 simulations with the head of the pipeline at a different position
further along the borehole the pulling force was output as well as the maximum penetration into the borehole wall. Figure 4.25 shows the result. Because the borehole’s total
length is 662 m, in the final simulation the head of the pipeline is located at 662 m. In
the first 100 m, the pulling force and wall penetration is almost zero and after that the
wall penetration and pulling force increase to a constant value. This is the point where
the head of the pipeline is in the first circular bend. After that the penetration and pulling
force decrease. In the section 4.4 it has been observed that the wall penetration of the
head of the pipeline in the bend is about 13 cm while the maximum wall penetration for
the pipeline when the head is 100 m through the bend is about 1 cm. These values are
close to the observed values in Figure 4.25. The increase of the wall penetration when the
head of the pipeline passes through the second circular arc and decrease when it’s past
the bend is equal to the first. The slight decrease of the pulling force after the first bend is
directly related to the decrease in wall penetration reducing the friction force. However at
the entry and exit of each bend a moment needs to be created resulting in extra normal
forces and friction, so overall the pulling force is increasing.
Figure 4.25. Pulling force and borehole wall penetration versus the pulled in distance of the pipeline
as a result of the 100 pullback simulations.
From Figure 4.25 it can be seen that the five simulations that are presented in Appendix
3.7.2, corresponding to the head of the pipeline at 1%, 30%, 50%, 80% and 100% are
corresponding to positions where the head is before the first bend, in the middle of the
first bend, in the middle of the horizontal flat section, in the middle of the second band
and all the way through the borehole. From these it can be deduced that the maximum
penetration in the bends is at the pipeline head.
41
Nieuwe boortechnieken kleine infra
The drill pipe present in the simulations shows the expected behaviour. This can be seen
in the plot where the pipeline is 50% pulled in, see Figure 4.26. The gap around the drill
pipe is 0.6425 m and it can be seen that the drill pipe touches and penetrates the upper
borehole wall in between a distance of about 450 to 550 m where we also see a penetration of about 1 mm.
Figure 4.26. Normal displacement and borehole wall penetration when the pipeline is pulled in
for 50%.
4.7 Simulation with measured XY data
To look at differences between the idealized design bore path and a more realistic bore
path, a measurement is used of a realized bore path. This measurement was in xyz data
but only the xz data were used as XY data for creation of the bore path. Only one simulation has been performed with all elements being pipeline and no drilling pipe. Pipeline
parameters, soil stiffness and gap have been unchanged from previous simulations. The
simulation is performed without cohesion and gravity to observe specifically what are
the difference resulting from geometry only. The complete list of input parameters is
presented in Appendix 3.8.1 and the simulation results are presented in Appendix 3.8.2.
Figure 4.27 shows the bore path shape and moment plot.
42
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Figure 4.27. Bore path shape and moment plot for the simulation with measured XY data.
If the bore path would be as smooth as the design path (see the 100% simulation in the
previous section), one would expect a smooth moment plot with a moment from zero to
almost constant value to zero in the horizontal section. For the final and the second bend.
Here however, the moment plot is far less smooth, even though the general trend is still
the same as for the design bore path: zero at the end, approximately zero in the horizontal section and largest amplitude in the middle of the bends. The same can be observed
from the soil reaction and borehole wall penetration plots.
It’s interesting to note that even with such irregular shaped bore path the pulling force
doesn’t differ much from the pulling force found for the design path simulation for the
100% pulled in pipeline in section 4.6.
43
Nieuwe boortechnieken kleine infra
44
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
5 Soil spring stiffness FEM simulations
The soil spring stiffness that has been used in the pullback simulations has been linear.
In the model description it has been stated that ABAQUS can in principle perform calculations with arbitrary spring characteristics made up of multiple linear segments and can
therefore include effects like softening and plasticity. The common Dutch practice is to
use a linear spring characteristic calculated by using the formula of [Schleicher 1926] for
a rectangular plate on an elastic halfspace. Here FEM simulations are performed to study
the penetration of pipelines to see what a more realistic spring stiffness function is.
5.1
Dutch common practice
The formula of [Schleicher 1926] considers a rectangular plate on an elastic halfspace.
The plate has length L and width B. From the ratio of soil stiffness to beam bending stiffness EI the characteristic length is determined and this is considered to be L. B is considered to be equal to the diameter D. With these the stiffness can be calculated using:
kv =
Esoil
m(1 −ν 2 ) A
L=
kv D
π
, λ=4
4 E pipe I
λ
(5.1)
with:
Esoil
A
ν
EpipeI
m
λ
Young’s modulus
Loaded area = L*B
Poisson’s ratio
Bending stiffness of pipe, see equation (4.2)
shape factor as shown in the below graph
coefficient arising from beam on elastic foundation theory, used to determine
the characteristic length L = π / λ .
Figure 5.1. relation between the shape factor m and the ratio of the loaded length and width.
45
Nieuwe boortechnieken kleine infra
The use of the characteristic length π / λ for L is not in Schleicher’s original article.
Schleicher derived his formula based on a plate with length L. The characteristic length
is used in Dutch practice to estimate a value for L. It is based on solutions for a beam
on an elastic foundation in which π / λ arises as half a wavelength in many solutions.
Depending on loading conditions of the pipe in a borehole the length over which the pipe
penetrates the borehole wall is not equal everywhere and also the penetration over this
length is not at all constant, contrary to the Schleicher formula which treats a loaded
plate of given dimensions.
The dimension of kv is [N/m3] whereas the dimension of the spring stiffness that’s used
in the code is [N/m2]. Schleicher’s spring stiffness needs to be multiplied by the width of
the loaded area k=kvB to have a required stiffness per length unit.
The general idea is that Schleicher’s formula overestimates the soil spring stiffness for
pipelines because the area of a pipeline that penetrates the soil is becoming larger and
the width B in the formula is only equal to the diameter when the pipeline is pushed
halfway into the soil. Also it is based on linear elasticity and plastic deformations are
neglected that are considered important. Furthermore there is the problem that the load
does not act on top of a halfspace but inside a hole in a halfspace. The soil above is not
taken into account.
Application of Schleicher’s equation for determining the soil spring stiffness for pipelines
in a borehole is therefore questionable. A better way would be to determine the force-displacement relation of a rigid pipe of radius r in a hole of radius R in an elastic halfspace or
layer. Such analytical solution is not known however. Therefore numerical analyses have
been performed to obtain insight into the spring stiffness.
5.2
FEM simulations of pipeline penetration into a borehole in plane strain
The finite element analysis is carried out for in plane strain conditions. A circular hole
was created in the subsoil and a rigid pipe inside the hole is pushed down into the soil. In
the hole there is a drilling fluid pressure preventing the hole from collapsing. The soil has
been modeled by a homogeneous linear elastic Mohr-Coulomb plastic model. For various
soil types the force displacement curves have been determined.
Two different borehole depths have been studied. A deep variant at 25 m below surface
at an effective fluid pressure of 275 kN/m2 and a shallow variant at 10 m below the
surface at an effective fluid pressure of 110 kN/m2. Simulations have been made for a
borehole with a diameter of 1.52 m and a pipeline 1.219 m, this will be called series 1
and a situation with a smaller hole of 0.6 m with a pipeline diameter of 0.406 m which
will be called series 2.
The simulations have been performed for 8 soil types in deep and shallow variants for
each series, resulting in 2 series * 8 soil types * 2 depths=32 simulations. The parameters for a deep and shallow borehole are presented below.
46
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
simulation
soil
Ywet
[kN/m3]
Cu [kPa]
C [kPa]
ϕ [˚]
E [kPa]
v [-]
K0 [-]
Yeff
[kN/m3]
1
Sand
20
-
1
30
15000
0.35
0.5
10
2
Sand
21
-
1
35
50000
0.35
0.8
11
3
Clay
13
-
1
17.5
2000
0.45
0.7
3
4
Clay
13
40
0
0
2000
0.45
0.7
3
5
Clay
17
-
10
22.5
4000
0.45
0.6
7
6
Clay
17
75
0
0
4000
0.45
0.6
7
7
Clay
17
-
10
22.5
6000
0.45
1.5
7
8
Clay
17
150
0
0
6000
0.45
1.5
7
Table 5.1. soil parameters for the deep variant at reference depth of 25 m below surface.
simulation
soil
Ywet
[kN/m3]
Cu [kPa]
C [kPa]
ϕ [˚]
E [kPa]
v [-]
K0 [-]
Yeff
[kN/m3]
1
Sand
20
-
1
30
10000
0.35
0.5
10
2
Sand
21
-
1
35
50000
0.35
0.8
11
3
Clay
13
-
1
17.5
1000
0.45
0.7
3
4
Clay
13
25
0
0
1000
0.45
0.7
3
5
Clay
17
-
10
22.5
2000
0.45
0.6
7
6
Clay
17
50
0
0
2000
0.45
0.6
7
7
Clay
17
-
10
22.5
6000
0.45
1.5
7
8
Clay
17
150
0
0
6000
0.45
1.5
7
Table 5.2. Soil parameters for the shallow variant at reference depth of 10 m below surface.
47
Nieuwe boortechnieken kleine infra
The simulation results are presented in Figure 5.2 to Figure 5.5. It can be seen that the
general trend for a specific soil type is similar regardless of the depth or diameter, there is
merely a visible difference in scale of the vertical axis.
Figure 5.2. Vertical force versus displacement for the large diameter series 1, deep variant.
Figure 5.3. Vertical force versus displacement for the small diameter series 2, deep variant.
48
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Figure 5.4. Vertical force versus displacement for the large diameter series 1, shallow variant.
Figure 5.5. Vertical force versus displacement for the small diameter series 2, shallow variant.
49
Nieuwe boortechnieken kleine infra
The derivative of the force displacement graph for the deep and large diameter variant
and soil type 8 is shown in the figure below.
Figure 5.6. Derivative (tangent stiffness) of the force-displacement curve of the deep large diameter
variant and soil type 8.
This is the tangent stiffness. It can be observed that the stiffness increases to a maximum
and then decreases to a low value for a displacement of about 0.2 m. Such increase and
decrease is visible in all simulations, only the vertical displacement differs. For sands
the real plateau is not reached for displacements of even 2 m, while for clays the plateau
is reached at displacements of 3.0 m or less. From Figure 5.2 to Figure 5.5 it can be
observed that a linear stiffness fits quite well for vertical displacements upto 0.1 m. For
this displacement the secant stiffness has been determined for each simulations and
they are presented in Table 5.3 below. The values in the table give a good picture of the
initial stiffness for the pipeline penetrating the borehole wall. Simulations using these
values are valid upto 0.1 m of penetration. It is observed that for the considered soil types
and depths the stiffness is higher than the 130 kN/m/m used in the simulations in this
report, which represents an even softer soil. The maximum penetration found in the
simulations was about 12 cm, and in these simulations curvature radii have been used
that are at the allowed minimum. It is expected that for the soil types used in the FEM
simulations the linear approximation is a good approximation.
50
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Using the stiffness values and poisson’s ratios in Table 5.1 and Table 5.2 it’s possible to
calculate It’s noted that the calculated stiffness from the FEM are higher than the values
calculated using Schleicher’s equation for the clay soil types and in most cases lower than
the values calculated with Schleicher’s equation for sand soil types, see Table 5.4.
Soil spring stiffness of first 0.1 m borehole penetration [kN/m/m’]
soil type
deep, large
deep, small
shallow, large
shallow small
diameter
diameter
diameter
diameter
1
7516
4323
3799
2115
2
21078
11433
12702
6815
3
1398
830
643
362
4
1756
1119
840
587
5
2924
2183
1417
1071
6
3508
2274
1624
1223
7
4172
3230
3861
2430
8
5267
4383
5028
3721
Table 5.3. Derived soil spring stiffness from the FEM simulations for borehole wall penetrations
upto 0.1 m.
Soil spring stiffness [kN/m/m’]
soil type
deep, large
deep, small
shallow, large
shallow small
diameter
diameter
diameter
diameter
1
5630
5810
3542
3655
2
22287
23000
22287
23000
3
628
648
284
293
4
628
648
284
293
5
1386
1431
628
648
6
1386
1431
628
648
7
1386
1431
628
648
8
1386
1431
628
648
Table 5.4. Soil spring stiffness computed using Schleicher’s formula and m=0.72. The length L was
calculated using the characteristic length pi/lambda.
51
Nieuwe boortechnieken kleine infra
Caution still needs to be taken when using the stiffness values calculated either by FEM
or by Schleicher. The main problem is that the length of penetration is not known and
it’s unknown how the spring stiffness changes when settlement is not uniform. A related
issue is that the simulations have been performed in plane strain and therefore assume
an infinite length. Performing 3D simulations might show significant differences in stiffness. Such simulations are however outside the scope of this report.
52
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
6 Conclusions
A model for the pullback of pipelines has been created and simulations have been performed to study various effects of pipelines in the borehole. From the simulations following conclusions can be made:
• The model is identical to analytical solution for the situation without pulling and the
simple geometry of a circular arc, geometric linearity and no gap between the pipeline
and borehole wall.
• Results of geometric linear and geometric nonlinear simulations don’t differ much for
cases with small (axial) deflections. This is generally the case with large diameter steel
pipes.
• For a circular arc with constant radius the moment is constant. This moment is
created at the beginning and end of the arc, giving rise to normal soil reaction forces at
the entry and exit of a circular bend.
• The soil reaction force is much higher when the head of the pipeline is inside the bend
as compared to the situation where the head of the pipeline has passed the bend.
• Taking into account a gap between pipeline and borehole wall, reduces the soil
reaction forces, because the arm between positive and negative forces becomes larger.
There is not much difference in overall behaviour compared to the situation without
gap.
• The simulations with pulling behave as expected with the change in length (axial
strain) of the pipeline corresponding to the difference in parallel displacements at the
end and beginning of the borehole and the reduction of length due to the pipeline
being pulled to the top of the borehole.
• The pulling force is relatively low for a design bore path if there is no cohesion because
of the creation of a moment only needs normal forces at the entry and exit of the
circular sections that give rise to friction.
• Simulations with cohesion show much higher pulling forces. Due to the nonlinear
effect of the Capstan forces these pulling forces are increased significantly in long
curved sections of a borehole (like in the half circle geometry).
• The maximum wall penetration and normal force during pullback for the considered
design path geometries with constant soil stiffness are described quite well with the
simple analytical model that was derived for the circular section.
Overall the model can describe a complex set of interactions between pipeline, drilling
pipe, drilling fluid and borehole. The model gives results that can be explained rationally
using basic facts from beam theory and geometrical considerations. The understanding
of the forces in the bend is new and currently unaccounted for in the Dutch NEN code.
Many variants can be calculated quickly and the model is ideal to make parameter
studies to gain insights in various effects during the pullback.
6.1
Recommendations
In this report a linear spring stiffness has been used for the simulations. This can be
extended to a piecewise linear arbitrary spring characteristic with plastic behaviour. From
2D FEM simulations for various geometries of borehole and pipeline and at two different depths it was found that for the simulations considered in this report the linearized
53
Nieuwe boortechnieken kleine infra
spring stiffness is sufficiently accurate. However it can be argued that the 2D and 3D
situations differ significantly because of the assumed infinite contact length and uniform
penetration over that length in 2D. Further study into spring stiffness for 3D geometries
is recommended.
It has been observed that when the head of the pipeline is inside a circular bend the wall
penetration and reaction forces are much higher compared to the situation where the
head of the pipeline is in the straight section. It is expected that when the borehole XY
function is not that of a circle section but would have the shape of a beam bend under a
constant distributed load, the borehole wall penetration and reaction forces would show
a more smooth behaviour overall. This has yet to be investigated.
In the current model only a single soil material is modeled with two different linear
springs for pipeline soil interaction and drilling pipe soil interaction. It is recommended
to extend the model to include multiple soil types to be able to study the behaviour
for when the pipeline passes from one soil material to another, say from sandy soil to
soft soil.
Most simulations in this report have been performed to study a certain aspect of the
pipeline soil interaction problem, be it bore path shape, cohesion, gravity etc. Simulations with more realistic parameters have to be made to compare the model to measurements. In such a study a detailed comparison with the Dutch NEN method is useful to
observe under what circumstances the model yields essentially different results.
54
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
7 References
[Schleicher 1926]
“Zur theorie der Baugrundes”
Schleicher
Der Bauingenieur, Heft 48/49, 1926
[Hetényi 1946]
Beams on Elastic Foundation
M. Hetényi
University of Michigan, 1946
[polytechnisch zakboekje]
Koninklijke PBNA, 1975
55
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56
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Appendix 1
Source code of the model
In this appendix the complete source code for the Matlab program is given as well as the
two python scripts needed for postprocessing the Abaqus simulations. Matlab is used to
control the Abaqus FEM simulations. The flow chart below shows what’s been controlled
by the Matlab script. The user inputs the main parameters as presented in section 3.7.
The script runs and from these parameters makes an Abaqus input file (with extension
*.inp). This input file is in ASCII and contains all elements needed for the simulation,
from the nodes, the mesh to material parameters and simulation steps. Then the Abaqus
FEM program is called from within the Matlab script with the generated input file. Matlab
waits until the script is finished and then calls python (included with Abaqus) with a python script file (also ASCII). This python script gets information from the ABAQUS binary
results database (*.odb) and writes it to an ASCII file which is then read by the Matlab
script for more postprocessing and plotting.
Matlabscript
Ababus input file
(ASCII) with nodes,
Generate Abaqus
mesh boundary
inputfile from user
conditions
input parameters
simulation steps,
Ababus FEM
program
materials, etc.
Call: Run Abaqus
with inputfile
Ababus output
Call: Python Script
for postprocessing
Python Script
database (binair)
abaqus results
Call: Python Script
Ababus textoutput
for postprocessing
abaqus results
The Matlab script contains various functions which are grouped into three *.m files for
overview:
main.m
do_abaqus_sim.m
plot_results.m
57
Nieuwe boortechnieken kleine infra
In the first script main.m, the user can input the problem parameters. The second script
generates the Abaqus input, runs Abaqus and does postprocessing. The third script
makes plots using the results.
The two python scripts that get data from the Abaqus binary database are for geometric
linear problems and geometric nonlinear problems and are called from within the script
do_abaqus_sim.m
python_postprLIN.py
python_postprNL.py
The scripts and python files are presented in the next pages and can be copied to Matlab
for execution. The scripts were made in Matlab version 2007b, and perhaps need modification in future Matlab versions.
Appendix 1.1 For developpers
The main routine is the Matlab script do_abaqus_sim.m. This script has various matlab
functions inside.
Here follows a brief description of what happens in the script and what functions are
called in sequential order
First an array of xy data for the borepath is needed, this is either directly read from a user
given file or generated from the geometry parameters L1,L2,L3,R,sym given by the user.
This is done in the routine
[xy]=xycircle(L1,L2,L3,R,nel,sym)
This function calls also the help function
[x,y]=along_borepath(L1,L2,R,D)
From a set of xy borepath data the actual XY data for the elements is created.
This happens in the routine
[XY]=genXY(xy_in,nel,nl)
The result is an array of XY pairs representing the actual nodes that will be used in the
simulation. Using this array together with the other input parameters the function
genAbaqus(filename,XY,D0_pipe,t_pipe,rho_pipe,E_pipe,nu_pipe,...
D0_rod,t_rod,rho_rod,E_rod,nu_rod,...
k_ps,k_rs,k_red_fact,gap_ps,gap_rs,fric_ps,fric_rs,...
gravforce_tube,gravforce_rod,bf_res_tube,bf_res_rod,...
T1,nel,nel_pipe,nl,left)
is called that generates the actual Abaqus input file specified by filename. After this, the
call to Abaqus is made and the call with the postprocessing python scripts. Then the
postprocessing is performed on the ASCII file resulting from the python script. This is
done in the function
[PostOut]=abaqus_postprocessing([‘py_’ filename ‘.txt’],nl,nel,nel_pipe,gap_ps,gap_rs)
The results are stored in the Matlab structure PostOut which now contains all relevant
simulation results of each step. The PostOut structure is further filled with also the input
parameters, for user reference and plotting. This is done in the function
[input,summary]=genInputSummary(...)
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Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Appendix 1.2 Matlab script main.m
clc;clear;
max_force=[];tube_length=[];
max_penetration_pipe=[];pos_max_pen_pipe=[];
max_penetration_rod=[];
% give filename (without extension) for the problem
filename=’Bijl3_8_leiding_realXY’;
for i=1:1
close all
% general description of simulation
description1=’geometric nonlinear simulation’;
description2=’with gap’;
%
% Input parameters for Geometry
%
uitfile=1; % read geometry from file (=1) or not (=0)
XY_inputfile=’VSHAkkrumA32Spoor.txt’; % only used if uitfile=1
L1=100.0; % only used if uitfile=0
R=1210; % only used if uitfile=0
fi=pi/2.0; % 310/R % only used if uitfile=0
L2=150;%R*sin(fi);%310; % only used if uitfile=0
L3=80.0; % only used if uitfile=0
sym=1; % half a borepath or symmetric (whole) borepath only used if
%
uitfile=0
%
% input parameters for simulation and boundary conditions
%
nel=200; % set total number of elements % nel_pipe=i*2
nel_pipe=200;%number of elements in the tube (not pullingrod)
nl=1;
%simulation is geometrically nonlinear (nl=1) or linear (nl=0)
left=0; %boundary condition at left side (left=1) or middle(left=0)
%
% pipe line parameters
%
D0_pipe=1.21;
% outer diameter [m]
t_pipe=0.0227; % wall thickness [m]
rho_pipe=7850; % density of pipe material [kg/m^3]
E_pipe=2.1E+11; % Young’s modulus of pipe material [N/m^2]
nu_pipe=0.3;
% Poisson’s ratio of pipe material [-]
%
% pulling rod parameters
%
D0_rod=0.125;
% outer diameter [m]
t_rod=D0_rod/2-1E-6; % wall thickness [m]
rho_rod=7850; % density of pulling rod material [kg/m^3]
E_rod=2.1E+11; % Young’s modulus of pulling rod material [N/m^2]
nu_rod=0.3;
% Poisson’s ratio of pulling rod material [-]
%
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Nieuwe boortechnieken kleine infra
% Soil stiffness, friction and gap for pipe line/soil interaction
%
k_ps=130E3;
% spring stiffness of pipe line/soil [N/m^2]
gap_ps=1.0E-1; % gap between pipe line and wall borehole [m]
fric_ps=0.2;
% friction coefficient pipe/soil [-]
%
% Soil stiffness, friction and gap for pulling rod/soil interaction
%
k_rs=0.1*130E3; % spring stiffness of pulling rod/soil [N/m^2]
gap_rs=6.425E-1; % gap between pulling rod and wall borehole [m]
fric_rs=0.2;
% friction coefficient pulling rod/soil [-]
k_red_fact=0.001; %factor with which stiffness is multiplied in borehole
%
% parameters for calculating the upward force of the pipeline and
% pulling rod as well as the friction force in the borefluid and rollenbaan
%
rho_bf=1150; % density of bore fluid in [kg/m^3]
rho_water=1000; % density of water in [kg/m^3]
Tfilled=0.5;
% fraction of tube filled with water [-]
g=0.0;
% acceleration of gravity [m/s^2]
f2=0; % resistance of tube/rod through bore fluid [N/m^2] NEN=50 N/m^2
f1=0.0;
% rollenbaan friction [-]
Fpush=0.0;
% pushforce at other end of borepath [N]
%
% parameters for plotting only
%
fixed=0;
%only used for plotting. fixed=1 plots results of
%fixed end
AppendixNo=’3.8’; % appendix number
projectID=’417161’; % project number
drawnby=’prk’; % person who created the appendix
checkedby=’kse’; % person who checked the appendix
GD_boun=1;
% put GeoDelft boundary around plot (1) or not (0) and
% only standard Matlab functions
%%%%%%SIMULATION AND POSTPROCESSING%%%%%%%%%
[PostOut]=do_abaqus_sim(filename,nel,nel_pipe,nl,...
uitfile,XY_inputfile,L1,L2,L3,R,sym,left,...
D0_pipe,t_pipe,rho_pipe,E_pipe,nu_pipe,gap_ps,k_ps,fric_ps,...
D0_rod ,t_rod ,rho_rod ,E_rod ,nu_rod ,gap_rs,k_rs,fric_rs,...
k_red_fact,Fpush,f1,description1,description2,...
rho_bf,rho_water,Tfilled,g,f2);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
max_force=[max_force; PostOut.summary.max_pullingforce];
max_penetration_pipe=[max_penetration_pipe;PostOut.summary.max_penetration_pipe_pull];
pos_max_pen_pipe=[pos_max_pen_pipe;PostOut.summary.position.max_penetration_pipe_pull];
max_penetration_rod=[max_penetration_rod;PostOut.summary.max_penetration_
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Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
rod_pull];
tube_length=[tube_length;PostOut.summary.length_tube ];
%%%%%%%%%PLOTTING%%%
plot_results(filename,PostOut,fixed,projectID,AppendixNo,drawnby,...
checkedby,GD_boun,i)
end
Appendix 1.3Matlab script do_abaqus_sim.m
function [PostOut]=do_abaqus_sim(filename,nel,nel_pipe,nl,...
uitfile,XY_inputfile,L1,L2,L3,R,sym,left,...
D0_pipe,t_pipe,rho_pipe,E_pipe,nu_pipe,gap_ps,k_ps,fric_ps,...
D0_rod ,t_rod ,rho_rod ,E_rod ,nu_rod ,gap_rs,k_rs,fric_rs,...
k_red_fact,Fpush,f1,description1,description2,rho_bf,...
rho_water,Tfilled,g,f2)
% start
if uitfile==0
% Define traditional geometry with straight sections
% and circle radius
[xy]=xycircle(L1,L2,L3,R,10000,sym);
else
% Read geometry from file
% XY_inputfile=’VSHAkkrumA32Spoor.txt’;
M = dlmread(XY_inputfile, ‘\t’);
x=M(:,1);y=-M(:,3);
xy=[x y];
end
% generate XY elements for simulation from general xy data
[XY]=genXY(xy,nel,nl);
% calculate the length of the pipe outside of the borehole
pdif=diff(XY);
Xdist=[0 ;cumsum(sqrt(pdif(:,1).*pdif(:,1)+pdif(:,2).*pdif(:,2)))];
len_borepath=Xdist(end);
len_pipe=Xdist(nel_pipe+1);
len_buiten=len_borepath-len_pipe;
Di_pipe=D0_pipe-2*t_pipe;
force_roll=f1*g*pi/4*(D0_pipe^2-Di_pipe^2)*rho_pipe*len_buiten;
T1=-Fpush+force_roll;
%weigh of tube under borefluid +=upward force - downward in MN/m length;
gravforce_pipe=g*0.25*pi*(D0_pipe^2*rho_bf-(D0_pipe^2-Di_pipe^2)...
*rho_pipe-Di_pipe^2*Tfilled*rho_water);
Di_rod=D0_rod-2*t_rod;
gravforce_rod=g*0.25*pi*(D0_rod^2-Di_rod^2)*(rho_bf-rho_rod);
bf_res_pipe=f2*D0_pipe*pi;% resistance of tube through bore fluid per meter
bf_res_rod=f2*D0_rod*pi; %resistance of rod through bore fluid per meter
genAbaqus([filename ‘.inp’],XY,D0_pipe,t_pipe,rho_pipe,E_pipe,nu_pipe,...
D0_rod,t_rod,rho_rod,E_rod,nu_rod,...
k_ps,k_rs,k_red_fact,gap_ps,gap_rs,fric_ps,fric_rs,...
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gravforce_pipe,gravforce_rod,bf_res_pipe,bf_res_rod,...
T1,nel,nel_pipe,nl,left);
str1=[‘dos(‘ char(39) ‘abaqus job=’ filename ‘ interactive’ char(39) ‘)’];
eval(str1)
if nl==0
string2=[‘dos(‘ char(39) ‘abaqus python python_postprLIN.py ‘,...
filename ‘.odb’ ‘ > ‘ ‘py_’ filename ‘.txt’ char(39) ‘)’];
else
string2=[‘dos(‘ char(39) ‘abaqus python python_postprNL.py ‘,...
filename ‘.odb’ ‘ > ‘ ‘py_’ filename ‘.txt’ char(39) ‘)’];
end
eval(string2)
%postprocessing
[PostOut]=abaqus_postprocessing([‘py_’ filename ‘.txt’],nl,nel,nel_pipe,...
gap_ps,gap_rs);
if (uitfile==1)
L1=-99;L2=-99;L3=-99;R=-99;sym=-99;
else
XY_inputfile=’-’;
end
[input,summary]=genInputSummary(D0_pipe,t_pipe,rho_pipe,E_pipe,nu_pipe,...
D0_rod,t_rod,rho_rod,E_rod,nu_rod,k_ps,k_rs,k_red_fact,...
gap_ps,gap_rs,fric_ps,fric_rs,gravforce_pipe,...
gravforce_rod,bf_res_pipe,bf_res_rod,Fpush,f1,nel,...
nel_pipe,nl,left,uitfile,PostOut,L1,L2,L3,R,sym,...
XY_inputfile,description1,description2,rho_bf,rho_water,...
Tfilled,g,f2,force_roll);
PostOut.input=input;
PostOut.summary=summary;
PostOut.XY_orig=XY;
return
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [XY]=genXY(xy_in,nel,nl)
% generate xy pairs of borepath. Note if nl=0 (geometrically linear) then
% the difference between x positions is constant, while for nl=1
% (geometrically nonlinear) then the length of the elements along the
% borepath should be approximately constant. The function gen XY generates
% pairs of xy data that describe the borepath from a general xy input
% vector
%
% Jitse Pruiksma 12-12-2007
%
M=1000;
xmin=min(xy_in(:,1));xmax=max(xy_in(:,1));
if nl==0
% geometrically linear
t=linspace(xmin,xmax,nel+1);
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Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
p = pchip(xy_in(:,1),xy_in(:,2),t);
XY=[t’ p’];
else
% geometrically nonlinear
% use interpolation on x axis in M times as much as number of elements
XY=zeros(nel,2);
t=linspace(xmin,xmax,M*nel+1);
p = pchip(xy_in(:,1),xy_in(:,2),t);
l=sqrt(diff(t).^2+ diff(p).^2);
L=sum(l);
li=L/nel;
%start with first point
XY(1,:)=[t(1) p(1)];
n=0;
for i=2:nel
len=0;
while len<li
n=n+1;
len=len+l(n);
end
if abs(len-li)<abs(len-l(n)-li)
% len is closer to li than len-l(n) (the previous)
XY(i,:)=[t(n+1) p(n+1)];
else
n=n-1;
XY(i,:)=[t(n+1) p(n+1)];
end
end
XY=[XY;t(end) p(end)];
end
return
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function genAbaqus(filename,XY,D0_pipe,t_pipe,rho_pipe,E_pipe,nu_pipe,...
D0_rod,t_rod,rho_rod,E_rod,nu_rod,...
k_ps,k_rs,k_red_fact,gap_ps,gap_rs,fric_ps,fric_rs,...
gravforce_tube,gravforce_rod,bf_res_tube,bf_res_rod,...
T1,nel,nel_pipe,nl,left)
% this function generates an inputfile for the finite element program
% ABAQUS for the pulling of a pipe line through a hole created with HDD
% (Horizontal Directional Drilling). The inputfile is an ASCII file and can
% be run with the program ABAQUS without any additional tools using the
% command:
% abaqus job=filename
% in a DOS window (or by using the DOS function within Matlab to create a
% call.)
%
% creation:
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% version 1.00 by Jitse Pruiksma 11th of december 2007
%
% input variables:
% name
description
%
% filename the name of the ABAQUS input file (usually with extension
%
*.inp)
% XY
a vector with 2 columns, one with X positions, one with Y
%
positions of points along the borehole. For a geometric
%
linear simulation the intervals in X are best equidistant,
%
for a geometric linear simulation the distance from one
%
(X,Y) point to the next is best approximately equidistant
%
(see also matlab function genXY.m which can generate such
%
approximate equidistant points from an arbitrary x,y
%
dataset.)
% D0_pipe outside diameter of the pipeline
% t_pipe wall thickness of the pipeline
% rho_pipe density of the pipeline material
% E_pipe Youngs modulus of the pipeline material
% nu_pipe Poisson’s ratio of the pipeline material
% D0_rod outside diameter of the pulling rod
% t_rod
wall thickness of the pulling rod
% rho_rod density of the pulling rod material
% E_rod
Youngs modulus of the pulling rod material
% nu_rod Poisson’s ratio of the pulling rod material
% k_ps
spring stiffnes of soil in force per length unit, used for
%
pipeline-soil interaction.
% k_rs
spring stiffnes of soil in force per length unit, used for
%
pulling rod-soil interaction.
% k_red_fact the factor with which the spring stiffness is reduced in the
%
borehole k_hole=k*k_red_fact
% gap_ps the gap between the pipeline and the borehole wall, gap is
%
measured from the borehole wall to the pipeline outer
%
surface when the pipeline lies in the centre of the borehole
% gap_rs the gap between the pulling rod and the borehole wall.
% fric_ps friction coefficient gives the factor between the force
%
normal to the borehole wall and the generated friction force
%
parallel to the borehole wall for the pipe-soil contact.
% fric_rs friction coefficient gives the factor between the force
%
normal to the borehole wall and the generated friction force
%
parallel to the borehole wall for the pulling rod -soil
%
contact.
% gravforce_tube net gravity force of pipeline under borefluid (partially
%
filled with water). negative is downward, positive is
%
upward (buoyancy force). the force acts on the entire
%
pipeline that’s in the borehole.
% gravforce_rod net gravity force of the pulling rod.
% bf_res_tube resistance of the pipeline in the borefluid (per unit length
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Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
%
of pipeline)
% bf_res_rod resistance of the pulling rod in the borefluid (per unit
%
length of pulling rod)
% T1
pulling force at left end of borehole. This could be used
%
for example to incorporate the rollenbaan friction or a
%
pushing force or a combination.
% nel
number of elements in which the borehole is divided (has to
%
correspond exactly to the number of points (minus 1) in the
%
XY input vector of borepath positions.
% nel_pipe number of elements that are pipeline. If this number is
%
smaller than nel then the elements numbered higher than
%
nel_pipe will automatically be pulling rod elements.
% nl
integer number to determine wether or not the simulation is
%
geometrically nonlinear (nl=1) or geometrically linear
%
(nl=0).
% left
integer number to determine wether the left end is
%
constrained during initial stages (left=1) or the
%
approximate middle (of the X positions ) of the model
%
(left=0).
%
offset=10000;
fid = fopen(filename, ‘w+’);
% write header in Abaqus input file
fprintf(fid, ‘%s\n’,’*HEADING’ );
fprintf(fid, ‘%s\n’,’Siminput generated with Matlab’ );
fprintf(fid, ‘%s\n’,’Preprint, echo=NO, model=NO, history=NO,contact=NO’ );
fprintf(fid, ‘%s\n’,’*NODE’ );
% write nodes for beam elements
% determine the approximate middle node and its x-position (only used if
% left=0
nmid=round((nel+1)/2);
xmid=XY(nmid,1);
% ymid=XY(nmid,1);
if nl==0
% beam nodes are just the x-positions in XY along the horizontal axis.
for i=1:nel+1
fprintf(fid, ‘%d%s%e%s%e\n’,i,’,’,XY(i,1),’,’,0.0 );
end
L=XY(end,1)-XY(1,1);
else
% geometrically nonlinear case
dxy=diff(XY);
ll=sqrt(dxy(:,1).^2+ dxy(:,2).^2); %lengths of elements along borepath
L=sum(ll);
if left==1
dist=cumsum(ll);
xx=[XY(1,1);XY(1,1)+dist];
length(xx)
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Nieuwe boortechnieken kleine infra
else
% start from this x position and go back and forward with nodes using the
% ll(i) to make the other x positions
right=cumsum(ll(nmid:end));
aa=flipud(ll(1:nmid-1));
left=cumsum(aa);
xx=[xmid-flipud(left);xmid;xmid+right];
end
for i=1:nel+1
fprintf(fid, ‘%d%s%e%s%e\n’,i,’,’,xx(i),’,’,0.0);
end
end
% write nodes for tube support elements, simply horizontal for
% geometrically linear case, but following the borepath for the nonlinear
% case with evenly spaced intervals along the defined path
if nl==0
for i=1:nel+1
fprintf(fid, ‘%d%s%e%s%e\n’,offset+i,’,’,XY(i,1),’,’,0.0 );
end
else
for i=1:nel+1
fprintf(fid, ‘%d%s%e%s%e\n’,offset+i,’,’,XY(i,1),’,’,XY(i,2) );
end
end
%write beam elements
fprintf(fid, ‘%s\n’,’*Element, type=B21,Elset=PIPELINE’ );
for i=1:nel_pipe
fprintf(fid, ‘%d%s%d%s%d\n’,i,’,’,i,’,’,i+1 );
end
fprintf(fid, ‘%s\n’,’*Element, type=B21,Elset=PullRod’ );
for i=nel_pipe+1:nel
fprintf(fid, ‘%d%s%d%s%d\n’,i,’,’,i,’,’,i+1 );
end
%write tube support elements
for i=1:nel+1
fprintf(fid, ‘%s%04d\n’,’*Element, type=ITSUNI, Elset=TUB’,i );
fprintf(fid, ‘%d%s%d%s%d\n’,offset+i,’,’,i,’,’,offset+i );
end
%make sets for loading and boundary conditions
fprintf(fid, ‘%s\n’,’*ELSET,ELSET=support_els,GEN’ );
fprintf(fid, ‘%d%s%d\n’,offset+1,’,’,offset+nel+1 );
fprintf(fid, ‘%s\n’,’*ELSET,ELSET=ALLBEAM,GEN’ );
fprintf(fid, ‘%d%s%d\n’,1,’,’,nel);
fprintf(fid, ‘%s\n’,’*NSET,NSET=left_end’ );
fprintf(fid, ‘%d\n’,1);
fprintf(fid, ‘%s\n’,’*NSET,NSET=mid_beam’ );
fprintf(fid, ‘%d\n’,nmid);
fprintf(fid, ‘%s\n’,’*NSET,NSET=right_end’ );
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Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
fprintf(fid, ‘%d\n’,nel+1);
fprintf(fid, ‘%s\n’,’*NSET,NSET=beam_all,GEN’ );
fprintf(fid, ‘%d%s%d\n’,1,’,’,nel+1 );
fprintf(fid, ‘%s\n’,’*NSET,NSET=tube_upper,GEN’ );
fprintf(fid, ‘%d%s%d\n’,offset+1,’,’,offset+nel+1 );
% attach properties to tube support element sets
% define spring behaviour for tube support elements.We use: “nonlinear”
% Abaqus requres an emty line after the spring command (in case of ITS
% elements) then lines with Force and relative displacement pairs follow
% note that we wish a spring stiffness per length instead of a point spring
% but Abaqus requires springs as point springs, not over element length
% so in using linear elements we have element length=L/Nels and we multiply
% k in kN/m2 with L/Nels to obtain the average point spring stiffness in
% kN/m over an element. this is usually set up by having half of it on one
% node and the other half on the other node, but when there is an element
% before and after the total is 1 on each node and only at the end points
% is it 0.5*L/Nels*k suppose we have L=310, Nels=80 and k=130 kN/m2 then
% the spring stiffness is 503.75 kN/m and 251.875 kN/m at the end nodes of
% the beam. but dimensions are MN and m hence a stiffness of
% k= 503.75 kN/m =0.50375 MN/m etc.
%
kmid_ps=k_ps*L/nel;
kend_ps=0.5*k_ps*L/nel;
kmid_rs=k_rs*L/nel;
kend_rs=0.5*k_rs*L/nel;
for i=1:nel+1
fprintf(fid, ‘%s%04d\n’,’*ITS, Elset=TUB’,i );
%write direction of tube support element, inner diameter, outer diameter,
%n perpendicular to tube axis,n parallel to tube axis
% inner and outer diameter don’t matter, we set them equal to eachother and
% put the gap in the nonlinear spring definition
% as for the directions for geometrically linear sims this is simply 1,0,0
% and 0,1,0 as the simulation is always made according to the original
% geometry
% for gemetrically nonlinear sims this is more complicated and the angle
% has to be calculated.
if nl==0
fprintf(fid, ‘%e%s%e%s%e%s%e%s%e%s%e%s%e%s%e\n’,0.5,’,’,0.5,’,’,...
1.0,’,’,0.0,’,’,0.0,’,’,0.0,’,’,1.0,’,’,0.0);
else
if (i==1)
[unorm]=make_tube_normals_fromXY(XY);
end
fprintf(fid, ‘%e%s%e%s%e%s%e%s%e%s%e%s%e%s%e\n’,0.5,’,’,0.5,’,’,...
-unorm(i,2),’,’,unorm(i,1),’,’,0.0,’,’,...
unorm(i,1),’,’,unorm(i,2),’,’,0.0);
end
fprintf(fid, ‘%s\n\n’,’*SPRING, NONLINEAR’ );
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if (i<=nel_pipe+1)
if (i==1 || i==nel_pipe+1)
fprintf(fid,’%e%s%e\n’,-kend_ps*10-k_red_fact*kend_ps*gap_ps,...
‘,’,-10-gap_ps);
fprintf(fid,’%e%s%e\n’,-k_red_fact*kend_ps*gap_ps,’,’,-gap_ps);
fprintf(fid,’%e%s%e\n’,0.0,’,’, 0.0);
fprintf(fid,’%e%s%e\n’,k_red_fact*kend_ps*gap_ps,’,’,gap_ps);
fprintf(fid,’%e%s%e\n’,kend_ps*10+k_red_fact*kend_ps*gap_ps,...
‘,’,10+gap_ps);
fprintf(fid,’%s\n’,’*FRICTION’ );
fprintf(fid,’%e\n’,fric_ps);
else
fprintf(fid,’%e%s%e\n’,-kmid_ps*10-k_red_fact*kmid_ps*gap_ps,...
‘,’,-10-gap_ps);
fprintf(fid,’%e%s%e\n’,-k_red_fact*kmid_ps*gap_ps,’,’,-gap_ps);
fprintf(fid,’%e%s%e\n’,0.0,’,’, 0.0);
fprintf(fid,’%e%s%e\n’,k_red_fact*kmid_ps*gap_ps,’,’,gap_ps);
fprintf(fid,’%e%s%e\n’,kmid_ps*10+k_red_fact*kmid_ps*gap_ps,...
‘,’,10+gap_ps);
fprintf(fid,’%s\n’,’*FRICTION’ );
fprintf(fid,’%e\n’,fric_ps);
end
elseif (i>nel_pipe+1)
if (i==1 || i==nel+1)
fprintf(fid,’%e%s%e\n’,-kend_rs*10-k_red_fact*kend_rs*gap_rs,...
‘,’,-10-gap_rs);
fprintf(fid,’%e%s%e\n’,-k_red_fact*kend_rs*gap_rs,’,’,-gap_rs);
fprintf(fid,’%e%s%e\n’,0.0,’,’, 0.0);
fprintf(fid,’%e%s%e\n’,k_red_fact*kend_rs*gap_rs,’,’,gap_rs);
fprintf(fid,’%e%s%e\n’,kend_rs*10+k_red_fact*kend_rs*gap_rs,...
‘,’,10+gap_rs);
fprintf(fid,’%s\n’,’*FRICTION’ );
fprintf(fid,’%e\n’,fric_rs);
else
fprintf(fid,’%e%s%e\n’,-kmid_rs*10-k_red_fact*kmid_rs*gap_rs,...
‘,’,-10-gap_rs);
fprintf(fid,’%e%s%e\n’,-k_red_fact*kmid_rs*gap_rs,’,’,-gap_rs);
fprintf(fid,’%e%s%e\n’,0.0,’,’, 0.0);
fprintf(fid,’%e%s%e\n’,k_red_fact*kmid_rs*gap_rs,’,’,gap_rs);
fprintf(fid,’%e%s%e\n’,kmid_rs*10+k_red_fact*kmid_rs*gap_rs,...
‘,’,10+gap_rs);
fprintf(fid,’%s\n’,’*FRICTION’ );
fprintf(fid,’%e\n’,fric_rs);
end
end
end
% attach properties to Pipeline Set
fprintf(fid, ‘%s\n’,...
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Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
‘*BEAM SECTION, SECTION=PIPE,ELSET=PIPELINE,MATERIAL=MAT1’ );
fprintf(fid, ‘%e%s%e\n’,D0_pipe/2,’,’,t_pipe);
fprintf(fid, ‘%s\n’,’*MATERIAL, NAME=MAT1’ );
fprintf(fid, ‘%s\n’,’*DENSITY’ );
fprintf(fid, ‘%e\n’,rho_pipe);
fprintf(fid, ‘%s\n’,’*ELASTIC’ );
fprintf(fid, ‘%e%s%e\n’,E_pipe,’,’,nu_pipe);
% attach properties to PullRod Set (if present)
if (nel_pipe<nel)
fprintf(fid, ‘%s\n’,...
‘*BEAM SECTION, SECTION=PIPE, ELSET=PullRod,MATERIAL=MAT2’ );
fprintf(fid, ‘%e%s%e\n’,D0_rod/2,’,’,t_rod);
fprintf(fid, ‘%s\n’,’*MATERIAL, NAME=MAT2’ );
fprintf(fid, ‘%s\n’,’*DENSITY’ );
fprintf(fid, ‘%e\n’,rho_rod);
fprintf(fid, ‘%s\n’,’*ELASTIC’ );
fprintf(fid, ‘%e%s%e\n’,E_rod,’,’,nu_rod);
end
% boundary conditions valid for both linear/nonlinear geometric sims
fprintf(fid, ‘%s\n’,’*BOUNDARY,FIXED’ );
fprintf(fid, ‘%s\n’,’beam_all, 3’ );
fprintf(fid, ‘%s\n’,’beam_all, 4’ );
fprintf(fid, ‘%s\n’,’beam_all, 5’ );
if left==1
fprintf(fid, ‘%s\n’,’left_end, 1’ );
fprintf(fid, ‘%s\n’,’left_end, 6’ );
else
fprintf(fid, ‘%s\n’,’mid_beam, 1’ );
fprintf(fid, ‘%s\n’,’mid_beam, 6’ );
end
if nl==0
% make simulation steps for geometrically linear simulation
fprintf(fid, ‘%s\n’,’*BOUNDARY,FIXED’ );
fprintf(fid, ‘%s\n’,’tube_upper, 1’ );
fprintf(fid, ‘%s\n’,’tube_upper, 3’ );
fprintf(fid, ‘%s\n’,’tube_upper, 4’ );
fprintf(fid, ‘%s\n’,’tube_upper, 5’ );
fprintf(fid, ‘%s\n’,’tube_upper, 6’ );
fprintf(fid, ‘%s\n’,’*STEP, name=beambend, nlgeom=NO, inc=10000’ );
fprintf(fid, ‘%s\n’,’load beam end’ );
fprintf(fid, ‘%s\n’,’*STATIC’ );
fprintf(fid, ‘%s\n’,’1.0E-6,1.00,1E-10,1.0’ );
% move tube support base upward in shape of borepath
fprintf(fid, ‘%s\n’,’*BOUNDARY’ );
if left==1
fprintf(fid, ‘%s%d\n’,’left_end, 2, 2, ‘,XY(1,2));
else
fprintf(fid, ‘%s%d\n’,’mid_beam, 2, 2, ‘,XY(nmid,2));
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end
fprintf(fid, ‘%s\n’,’*BOUNDARY’ );
for i=1:nel+1
fprintf(fid, ‘%d%s%d%s%d%s%e\n’,offset+i,’,’,2,’,’,2,’,’,XY(i,2));
end
fprintf(fid, ‘%s\n’,’*DLOAD’ );
fprintf(fid, ‘%s%d\n’,’PIPELINE,PY,’,gravforce_tube);
if (nel_pipe<nel)
fprintf(fid, ‘%s%d\n’,’PullRod,PY,’,gravforce_rod);
end
fprintf(fid, ‘%s\n’, ‘*RESTART,write,frequency=0’ );
fprintf(fid, ‘%s\n’, ‘*OUTPUT, field’ );
fprintf(fid, ‘%s\n’, ‘*Node Output’ );
fprintf(fid, ‘%s\n’, ‘U’ );
fprintf(fid, ‘%s\n’, ‘*Element Output, ELSET=ALLBEAM’ );
fprintf(fid, ‘%s\n’, ‘SF’ );
fprintf(fid, ‘%s\n’, ‘*Element Output, ELSET=support_els’ );
fprintf(fid, ‘%s\n’, ‘S’ );
fprintf(fid, ‘%s\n’, ‘*END STEP’ );
% second simulation step (relax boundary conditions)
fprintf(fid, ‘%s\n’,’*STEP, name=relaxboun, nlgeom=NO, inc=10000’ );
fprintf(fid, ‘%s\n’,’relaxboun’ );
fprintf(fid, ‘%s\n’,’*STATIC’ );
fprintf(fid, ‘%s\n’,’1.0E-8,1.00,1E-10,1.0’ );
fprintf(fid, ‘%s\n’,’*BOUNDARY,OP=NEW,FIXED’ );
fprintf(fid, ‘%s\n’,’tube_upper, 1,6’ );
fprintf(fid, ‘%s\n’,’beam_all, 3,5’ );
if left==1
fprintf(fid, ‘%s\n’,’left_end, 1’ );
else
fprintf(fid, ‘%s\n’,’mid_beam, 1’ );
end
fprintf(fid, ‘%s\n’,’*DLOAD’ );
fprintf(fid, ‘%s%d\n’,’PIPELINE,PY,’,gravforce_tube);
if (nel_pipe<nel)
fprintf(fid, ‘%s%d\n’,’PullRod,PY,’,gravforce_rod);
end
fprintf(fid, ‘%s\n’, ‘*RESTART,write,frequency=0’ );
fprintf(fid, ‘%s\n’, ‘*OUTPUT, field’ );
fprintf(fid, ‘%s\n’, ‘*Node Output’ );
fprintf(fid, ‘%s\n’, ‘U’ );
fprintf(fid, ‘%s\n’, ‘*Element Output, ELSET=ALLBEAM’ );
fprintf(fid, ‘%s\n’, ‘SF’ );
fprintf(fid, ‘%s\n’, ‘*Element Output, ELSET=support_els’ );
fprintf(fid, ‘%s\n’, ‘S’ );
fprintf(fid, ‘%s\n’, ‘*END STEP’ );
%third simulation step (pulling)
fprintf(fid, ‘%s\n’,’*STEP, name=pullbeam, nlgeom=NO, inc=10000’ );
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Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
fprintf(fid, ‘%s\n’,’pull the beam displacement’ );
fprintf(fid, ‘%s\n’,’*STATIC’ );
fprintf(fid, ‘%s\n’,’1.0E-8,1.00,1E-10,1.0’ );
fprintf(fid, ‘%s\n’,’*BOUNDARY,OP=NEW,FIXED’ );
fprintf(fid, ‘%s\n’,’beam_all, 3,5’ );
fprintf(fid, ‘%s\n’,’tube_upper, 1,6’ );
fprintf(fid, ‘%s\n’,’right_end, 2’ );
fprintf(fid, ‘%s\n’,’*BOUNDARY,OP=NEW, TYPE=VELOCITY’ );
fprintf(fid, ‘%s%d%s%d%s%f\n’,’right_end,’, 1,’,’,1,’,’,1.0);
fprintf(fid, ‘%s\n’,’*DLOAD’ );
fprintf(fid, ‘%s%d\n’,’PIPELINE,PY,’,gravforce_tube);
if (nel_pipe<nel)
fprintf(fid, ‘%s%d\n’,’PullRod,PY,’,gravforce_rod);
end
% resistance force of tube/rod through bore fluid
fprintf(fid, ‘%s\n’,’*CLOAD’ );
% make force array
force_on_nodes=zeros(nel+1,1);
% loop over elements to fill force array
for i=1:nel
if i>nel_pipe
force_per_element=L/nel*bf_res_rod ;
else
force_per_element=L/nel*bf_res_tube;
end
force_on_nodes(i)=force_on_nodes(i)+0.5*force_per_element;
force_on_nodes(i+1)=force_on_nodes(i+1)+0.5*force_per_element;
end
%add force T1 (rollenbaan or push force) to friction
force_on_nodes(1)=force_on_nodes(1)+T1;
% now plot in Abaqus file
for i=1:nel+1
fprintf(fid, ‘%d%s%d%s%d\n’, i,’,’,1,’,’,-force_on_nodes(i));
end
fprintf(fid, ‘%s\n’, ‘*RESTART,write,frequency=0’ );
fprintf(fid, ‘%s\n’, ‘*OUTPUT, field’ );
fprintf(fid, ‘%s\n’, ‘*Node Output’ );
fprintf(fid, ‘%s\n’, ‘U’ );
fprintf(fid, ‘%s\n’, ‘*Element Output, ELSET=ALLBEAM’ );
fprintf(fid, ‘%s\n’, ‘SF’ );
fprintf(fid, ‘%s\n’, ‘*Element Output, ELSET=support_els’ );
fprintf(fid, ‘%s\n’, ‘S’ );
fprintf(fid, ‘%s\n’, ‘*END STEP’ );
else
% make simulations steps for geometrically nonlinear simulation
fprintf(fid, ‘%s\n’,’*STEP, name=beambend, nlgeom=YES, inc=10000’ );
fprintf(fid, ‘%s\n’,’bend the beam with support elements off’ );
fprintf(fid, ‘%s\n’,’*STATIC’ );
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Nieuwe boortechnieken kleine infra
fprintf(fid, ‘%s\n’,’1.0,1.00,1E-10,1.0’ );
% move beam upward to bring beam to position of tube support elements
fprintf(fid, ‘%s\n’,’*MODEL CHANGE,REMOVE’ );
fprintf(fid, ‘%s\n’,’support_els’ );
fprintf(fid, ‘%s\n’,’*BOUNDARY’ );
if left==1
fprintf(fid, ‘%s%d\n’,’left_end, 2, 2, ‘,XY(1,2));
else
fprintf(fid, ‘%s%d\n’,’mid_beam, 2, 2, ‘,XY(nmid,2));
end
fprintf(fid, ‘%s\n’,’*BOUNDARY’ );
for i=1:nel+1
fprintf(fid, ‘%d%s%d%s%d%s%e\n’,i,’,’,2,’,’,2,’,’,XY(i,2));
end
fprintf(fid, ‘%s\n’,’*DLOAD’ );
fprintf(fid, ‘%s%d\n’,’PIPELINE,PY,’,gravforce_tube);
if (nel_pipe<nel)
fprintf(fid, ‘%s%d\n’,’PullRod,PY,’,gravforce_rod);
end
fprintf(fid, ‘%s\n’, ‘*RESTART,write,frequency=0’ );
fprintf(fid, ‘%s\n’, ‘*OUTPUT, field’ );
fprintf(fid, ‘%s\n’, ‘*Node Output’ );
fprintf(fid, ‘%s\n’, ‘U’ );
fprintf(fid, ‘%s\n’, ‘*Element Output, ELSET=ALLBEAM’ );
fprintf(fid, ‘%s\n’, ‘SF’ );
fprintf(fid, ‘%s\n’, ‘*Element Output, ELSET=support_els’ );
fprintf(fid, ‘%s\n’, ‘S’ );
fprintf(fid, ‘%s\n’, ‘*END STEP’ );
% second simulation step
fprintf(fid, ‘%s\n’,’*STEP, name=tubeson, nlgeom=YES, inc=10000’ );
fprintf(fid, ‘%s\n’,...
‘turn on tube support elements and observe displacement’ );
fprintf(fid, ‘%s\n’,’*STATIC’ );
fprintf(fid, ‘%s\n’,’1.0E-8,1.00,1E-10,1.0’ );
fprintf(fid, ‘%s\n’,’*MODEL CHANGE,ADD’ );
fprintf(fid, ‘%s\n’,’support_els’ );
fprintf(fid, ‘%s\n’,’*BOUNDARY,OP=NEW,FIXED’ );
fprintf(fid, ‘%s\n’,’beam_all, 3,5’ );
if left==1
fprintf(fid, ‘%s\n’,’left_end, 1’ );
fprintf(fid, ‘%s\n’,’left_end, 2’ );
fprintf(fid, ‘%s\n’,’left_end, 6’ );
else
fprintf(fid, ‘%s\n’,’mid_beam, 1’ );
fprintf(fid, ‘%s\n’,’mid_beam, 2’ );
fprintf(fid, ‘%s\n’,’mid_beam, 6’ );
end
fprintf(fid, ‘%s\n’,’tube_upper, 1,6’ );
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Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
fprintf(fid, ‘%s\n’,’*DLOAD’ );
fprintf(fid, ‘%s%d\n’,’PIPELINE,PY,’,gravforce_tube);
if (nel_pipe<nel)
fprintf(fid, ‘%s%d\n’,’PullRod,PY,’,gravforce_rod);
end
fprintf(fid, ‘%s\n’, ‘*RESTART,write,frequency=0’ );
fprintf(fid, ‘%s\n’, ‘*OUTPUT, field’ );
fprintf(fid, ‘%s\n’, ‘*Node Output’ );
fprintf(fid, ‘%s\n’, ‘U’ );
fprintf(fid, ‘%s\n’, ‘*Element Output, ELSET=ALLBEAM’ );
fprintf(fid, ‘%s\n’, ‘SF’ );
fprintf(fid, ‘%s\n’, ‘*Element Output, ELSET=support_els’ );
fprintf(fid, ‘%s\n’, ‘S’ );
fprintf(fid, ‘%s\n’, ‘*END STEP’ );
% third simulation step, relax vertical and rotary boundary condition
% on the left or mid-node
fprintf(fid, ‘%s\n’,’*STEP, name=relaxboun, nlgeom=YES, inc=10000’ );
fprintf(fid, ‘%s\n’,...
‘relax boundary condition of mid/left node only hor fixed’ );
fprintf(fid, ‘%s\n’,’*STATIC’ );
fprintf(fid, ‘%s\n’,’1.0E-8,1.00,1E-10,1.0’ );
fprintf(fid, ‘%s\n’,’*BOUNDARY,OP=NEW,FIXED’ );
fprintf(fid, ‘%s\n’,’beam_all, 3,5’ );
if left==1
fprintf(fid, ‘%s\n’,’left_end, 1’ );
else
fprintf(fid, ‘%s\n’,’mid_beam, 1’ );
end
fprintf(fid, ‘%s\n’,’tube_upper, 1,6’ );
fprintf(fid, ‘%s\n’,’*DLOAD’ );
if (nel_pipe<nel)
fprintf(fid, ‘%s%d\n’,’PullRod,PY,’,gravforce_rod);
end
fprintf(fid, ‘%s%d\n’,’PIPELINE,PY,’,gravforce_tube);
fprintf(fid, ‘%s\n’, ‘*RESTART,write,frequency=0’ );
fprintf(fid, ‘%s\n’, ‘*OUTPUT, field’ );
fprintf(fid, ‘%s\n’, ‘*Node Output’ );
fprintf(fid, ‘%s\n’, ‘U’ );
fprintf(fid, ‘%s\n’, ‘*Element Output, ELSET=ALLBEAM’ );
fprintf(fid, ‘%s\n’, ‘SF’ );
fprintf(fid, ‘%s\n’, ‘*Element Output, ELSET=support_els’ );
fprintf(fid, ‘%s\n’, ‘S’ );
fprintf(fid, ‘%s\n’, ‘*END STEP’ );
% fourth simulation step Pulling
fprintf(fid, ‘%s\n’,’*STEP, name=pullbeam, nlgeom=YES, inc=10000’ );
fprintf(fid, ‘%s\n’,’pull the beam displacement’ );
fprintf(fid, ‘%s\n’,’*STATIC’ );
fprintf(fid, ‘%s\n’,’1.0E-8,1.00,1E-10,1.0’ );
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Nieuwe boortechnieken kleine infra
fprintf(fid, ‘%s\n’,’*BOUNDARY,OP=NEW,FIXED’ );
fprintf(fid, ‘%s\n’,’beam_all, 3,5’ );
fprintf(fid, ‘%s\n’,’tube_upper, 1,6’ );
fprintf(fid, ‘%s\n’,’*BOUNDARY,OP=NEW, TYPE=VELOCITY’ );
fprintf(fid, ‘%s%d%s%d%s%f\n’,’right_end,’, 1,’,’,1,’,’,unorm(end,2));
fprintf(fid, ‘%s%d%s%d%s%f\n’,’right_end,’, 2,’,’,2,’,’,-unorm(end,1));
fprintf(fid, ‘%s\n’,’*DLOAD’ );
fprintf(fid, ‘%s%d\n’,’PIPELINE,PY,’,gravforce_tube);
if (nel_pipe<nel)
fprintf(fid, ‘%s%d\n’,’PullRod,PY,’,gravforce_rod);
end
% resistance force of tube/rod through bore fluid
fprintf(fid, ‘%s\n’,’*CLOAD’ );
% make force array
force_on_nodes=zeros(nel+1,1);
% loop over elements to fill force array
for i=1:nel
if i>nel_pipe
force_per_element=ll(i)*bf_res_rod;
else
force_per_element=ll(i)*bf_res_tube;
end
force_on_nodes(i)=force_on_nodes(i)+0.5*force_per_element;
force_on_nodes(i+1)=force_on_nodes(i+1)+0.5*force_per_element;
end
%add force T1 (rollenbaan or push force) to friction
force_on_nodes(1)=force_on_nodes(1)+T1;
% now plot in Abaqus file
for i=1:nel+1
fprintf(fid, ‘%d%s%d%s%d\n’,...
i,’,’,1,’,’,-force_on_nodes(i)*unorm(i,2));
fprintf(fid, ‘%d%s%d%s%d\n’,...
i,’,’,2,’,’,force_on_nodes(i)*unorm(i,1));
end
fprintf(fid, ‘%s\n’, ‘*RESTART,write,frequency=0’ );
fprintf(fid, ‘%s\n’, ‘*OUTPUT, field’ );
fprintf(fid, ‘%s\n’, ‘*Node Output’ );
fprintf(fid, ‘%s\n’, ‘U’ );
fprintf(fid, ‘%s\n’, ‘*Element Output, ELSET=ALLBEAM’ );
fprintf(fid, ‘%s\n’, ‘SF’ );
fprintf(fid, ‘%s\n’, ‘*Element Output, ELSET=support_els’ );
fprintf(fid, ‘%s\n’, ‘S’ );
fprintf(fid, ‘%s\n’, ‘*END STEP’ );
end
fclose(fid);
return
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
function [unorm]=make_tube_normals_fromXY(tubesXY)
% creates the normal vectors of the tube support elements by averaging
% normals of beam-axis over 2 elements
% 25-sept-2007 - J.P. Pruiksma - creation
%
%take normal of first element to be the normal
vec1=tubesXY(2,:)-tubesXY(1,:);
unorm(1,:)=[-vec1(2) vec1(1)]/sqrt(vec1*vec1’);
N=length(tubesXY);
for i=2:N-1
vec1=tubesXY(i,:)-tubesXY(i-1,:);
vec1n=[-vec1(2) vec1(1)]/sqrt(vec1*vec1’);
vec2=tubesXY(i+1,:)-tubesXY(i,:);
vec2n=[-vec2(2) vec2(1)]/sqrt(vec2*vec2’);
avn=0.5*(vec1n+vec2n);unorm(i,:)=avn/sqrt(avn*avn’);
end
%take normal of last element to be the normal
vec1=tubesXY(N,:)-tubesXY(N-1,:);
unorm(N,:)=[-vec1(2) vec1(1)]/sqrt(vec1*vec1’);
return;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [PostOut]=abaqus_postprocessing(filename,nl,nel,nel_pipe,...
gap_ps,gap_rs)
% postprocessing of Abaqus simulations of a file created with Python from
% an Abaqus Odb. nl=0 for Geometrical linear simulation, nl=1 for a
% Geometrical nonlinear simulation
%
% 25-sept-2007 - J.P. Pruiksma - creation (no pulling implemented)
% 24-oct-2007 - J.P. Pruiksma - modified to include pulling of beam
% 12-dec-2007 - J.P. Pruiksma - code cleaned up
% read python output file
[Out] = read_Abaqus_output(filename,nl);
% get basic information from Output database stored in Out
Nsteps=Out.Nsteps;
% number of simulation steps
Nbeam=length(Out.Nodnr)/2;
% number of nodes on beam
Nels=Out.Nel_tot-Nbeam;
% number of elements on beam
beamXY=Out.XYZ(1:Nbeam,1:2); % original nodal coordinates of beam
tubesXY_orig=Out.XYZ(Nbeam+1:end,1:2); % coordinates of support element
%
nodes (remain fixed during nl=1 sim)
%
% loop from i=1+nl to Nsteps, so from 2 to 3 in nl and pulling, from 2 to 2
% in nl and non pulling, from 1 to 1 in lin and non pulling and from 1 to 2
% in lin and pulling
for i=1+nl:Nsteps
Uy_beam=Out.Uy{i}(1:Nbeam);
Ux_beam=Out.Ux{i}(1:Nbeam);
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Nieuwe boortechnieken kleine infra
Ux_sup=Out.Ux{i}(Nbeam+1:end);
Uy_sup=Out.Uy{i}(Nbeam+1:end);
% x,y coordinates of beam nodes after step, displacement added to original
% position
xpos=beamXY(:,1)+Ux_beam;
ypos=beamXY(:,2)+Uy_beam;
XY=[xpos ypos]; % coordinates of beam nodes after step in matrix
%calculate tube support nodes position after step
%(is the same as original in nonlin sim)
xtubpos=tubesXY_orig(:,1)+Ux_sup;
ytubpos=tubesXY_orig(:,2)+Uy_sup;
tubesXY=[xtubpos ytubpos];
if nl==0
%if nl=0 distance along beam is same as original Xposition
Xdist=xpos;
else
%if nl=1 then distance along beam is calculated from the updated XY
%positions
pdif=diff(XY);
Xdist=[0 ;cumsum(sqrt(pdif(:,1).*pdif(:,1)+pdif(:,2).*pdif(:,2)))];
end
%calculate the midpoints along the beam for moment plot
Xmom=Xdist;Xmom(end)=[];Xmom=Xmom+diff(Xdist)/2;
%Moment
M=Out.SM{i};
%Soil Spring reaction, use average element length
ellen=(Xdist(end)-Xdist(1))/Nels;
S11=Out.S11{i};
S11_m=zeros(Nbeam,1);
S11_m(2:Nbeam-1)=S11(2:Nbeam-1)/ellen;
S11_m(1)=S11(1)/(0.5*ellen);
S11_m(Nbeam)=S11(Nbeam)/(0.5*ellen);
Spring=S11_m;
% calculate displacement normal to tube axis
if nl==0
DeltaW=Uy_beam-Uy_sup;
DeltaH=Ux_beam;
else
[unorm]=make_tube_normals_fromXY(tubesXY_orig);
%difference with tube support elements
xy_diff=XY-tubesXY;
% displacement normal to tube axis
DeltaW=xy_diff(:,1).*unorm(:,1)+xy_diff(:,2).*unorm(:,2);
% displacement parallel to tube axis (the pulling displacement)
DeltaH=xy_diff(:,1).*unorm(:,2)-xy_diff(:,2).*unorm(:,1);
end
PostOut.XY{i-nl}=XY;
PostOut.Xdist{i-nl}=Xdist;
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Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
PostOut.Xmom{i-nl}=Xmom;
PostOut.M{i-nl}=M;
PostOut.Spring{i-nl}=Spring;
PostOut.DeltaW{i-nl}=DeltaW;
PostOut.DeltaH{i-nl}=DeltaH;
PostOut.SF1{i-nl}=Out.SF1{i};
PostOut.S11{i-nl}=Out.S11{i};
% separate between pipe and pulling rod
idx_pipe=1:nel_pipe+1;
idx_rod=nel_pipe+2:nel+1;
UNormal_pipe=DeltaW(idx_pipe);
UNormal_rod=DeltaW(idx_rod);
% start with pipe
idxtop=find(UNormal_pipe>=gap_ps);
idxbot=find(UNormal_pipe<=-gap_ps);
topbot = union(idxtop, idxbot);
notb = setdiff(1:length(idx_pipe), topbot);
PBW=zeros(length(idx_pipe),1);
PBW(idxtop)=UNormal_pipe(idxtop)-gap_ps;
PBW(idxbot)=UNormal_pipe(idxbot)+gap_ps;
PBW(notb)=0;
% then pulling rod
idxtop=find(UNormal_rod>=gap_rs);
idxbot=find(UNormal_rod<=-gap_rs);
topbot = union(idxtop, idxbot);
notb = setdiff(1:length(idx_rod), topbot);
PBW2=zeros(length(idx_rod),1);
PBW2(idxtop)=UNormal_rod(idxtop)-gap_rs;
PBW2(idxbot)=UNormal_rod(idxbot)+gap_rs;
PBW2(notb)=0;
PostOut.WallPenetration{i-nl}=[PBW;PBW2];
end
return;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [Out] = read_Abaqus_output(filename,nl)
% reads Abaqus output processed with a python script from a text file
% currently only simulations without pulling are implemented
% 25-sept-2007 - J.P. Pruiksma - creation
%
% if nl=1 then Abaqus NLGEOM=ON and geometrical nonlinear simulation
% if nl=0 then Abaqus NLGEOM=OFF and geometrical linear simulation
% Check for existence of the Abaqus output file
if ~exist(filename,’file’)
errordlg([‘File: ‘ filename ‘ does not exist. Stop!’],...
‘read_Abaqus_output’);
return;
end
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Nieuwe boortechnieken kleine infra
range=[2, 0,2,2];
M = dlmread(filename, ‘,’,range );
Nel_tot=M(2);Nnod=M(3);Nel_beam=Nnod/2-1;
range=[4, 0,4,0];
Nsteps = dlmread(filename, ‘,’,range );
%read node labels and coordinates
range=[7,0,6+Nnod,3];
M = dlmread(filename, ‘,’,range );
Nodnr=M(:,1);XYZ=M(:,2:4);
Out.Nel_tot=Nel_tot;Out.Nsteps=Nsteps;Out.Nodnr=Nodnr;Out.XYZ=XYZ;
% for each step read the necessary data, for first step in NLGEOM case,
% skip reading the S11 S12 S13 tube support els data because the tube
% support elements are turned off
startpos=9+Nnod;
Ux = cell(Nsteps, 1);
Uy = cell(Nsteps, 1);
SF1= cell(Nsteps, 1);
SF2= cell(Nsteps, 1);
SM= cell(Nsteps, 1);
S11= cell(Nsteps, 1);
S12= cell(Nsteps, 1);
S13= cell(Nsteps, 1);
for i=1:Nsteps
range=[startpos, 0,startpos+Nnod-1,2];
M = dlmread(filename, ‘,’,range );
Ux{i}=M(:,2);Uy{i}=M(:,3);
startpos=startpos+Nnod+1;
range=[startpos, 0,startpos+Nel_beam-1,3];
M = dlmread(filename, ‘,’,range );
SF1{i}=M(:,2);SF2{i}=M(:,3);SM{i}=M(:,4);
startpos=startpos+Nel_beam+1;
if nl==0
%geometrical linear case
range=[startpos, 0,startpos+Nel_beam,3];
M = dlmread(filename, ‘,’,range );
startpos=startpos+Nel_beam+3;
S11{i}=M(:,2);S12{i}=M(:,3);S13{i}=M(:,4);
else
%geometrical nonlinear case
if i~=1
range=[startpos, 0,startpos+Nel_beam,3];
M = dlmread(filename, ‘,’,range );
startpos=startpos+Nel_beam+1;
S11{i}=M(:,2);S12{i}=M(:,3);S13{i}=M(:,4);
startpos=startpos+2;
else
startpos=startpos+1;
end
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Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
end
end
Out.Ux=Ux;Out.Uy=Uy;Out.SF1=SF1;Out.SF2=SF2;Out.SM=SM;
Out.S11=S11;Out.S12=S12;Out.S13=S13;
return;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [input,summary]=genInputSummary(...
D0_pipe,t_pipe,rho_pipe,E_pipe,nu_pipe,...
D0_rod,t_rod,rho_rod,E_rod,nu_rod,k_ps,k_rs,k_red_fact,...
gap_ps,gap_rs,fric_ps,fric_rs,gravforce_pipe,...
gravforce_rod,bf_res_pipe,bf_res_rod,Fpush,f1,nel,...
nel_pipe,nl,left,uitfile,PostOut,L1,L2,L3,R,sym,...
XY_inputfile,description1,description2,rho_bf,rho_water,...
Tfilled,g,f2,force_roll)
if (uitfile==1)
input.XYfile=XY_inputfile;
input.L1=’-’;
input.L2=’-’;
input.L3=’-’;
input.R=’-’;
input.sym=’-’;
else
input.XYfile=’-’;
input.L1=L1;
input.L2=L2;
input.L3=L3;
input.R=R;
input.sym=yes_no(sym);
end
input.description1=description1;
input.description2=description2;
input.nel=nel;
input.nel_pipe=nel_pipe;
input.nonlin=yes_no(nl);
input.leftBC=yes_no(left);
input.D0_rod=D0_rod;
input.t_rod=t_rod;
input.rho_rod=rho_rod;
input.E_rod=E_rod;
input.nu_rod=nu_rod;
input.D0_pipe=D0_pipe;
input.t_pipe=t_pipe;
input.rho_pipe=rho_pipe;
input.E_pipe=E_pipe;
input.nu_pipe=nu_pipe;
input.k_ps=k_ps;
input.k_rs=k_rs;
79
Nieuwe boortechnieken kleine infra
input.k_red_fact=k_red_fact;
input.fric_ps=fric_ps;
input.fric_rs=fric_rs;
input.gap_ps=gap_ps;
input.gap_rs=gap_rs;
input.rho_bf=rho_bf;
input.rho_water=rho_water;
input.Tfilled=Tfilled;
input.g=g;
input.f2=f2;
input.Fpush=Fpush;
input.f1=f1;
summary.upforce_tube=gravforce_pipe;
summary.upforce_rod=gravforce_rod;
summary.resforce_pipe=bf_res_pipe;
summary.resforce_rod=bf_res_rod;
summary.force_roll=force_roll;
summary.length_borepath=PostOut.Xdist{1}(end);
summary.length_tube=PostOut.Xdist{1}(nel_pipe+1);
summary.max_moment=max(PostOut.M{1});
summary.min_moment=min(PostOut.M{1});
summary.max_pullingforce=max(PostOut.SF1{3});
[C,idx]=max(abs(PostOut.Spring{2}));
summary.max_soilreaction_nopull=PostOut.Spring{2}(idx(end));
summary.position.max_soilreaction_nopull=PostOut.Xdist{1}(idx(end));
[C,idx]=max(abs(PostOut.Spring{3}));
summary.max_soilreaction_pull=PostOut.Spring{3}(idx(end));
summary.position.max_soilreaction_pull=PostOut.Xdist{1}(idx(end));
summary.soilreaction_headpipe_nopull=PostOut.Spring{2}(nel_pipe+1);
summary.soilreaction_headpipe_pull=PostOut.Spring{3}(nel_pipe+1);
[C,idx]=max(abs(PostOut.WallPenetration{2}(1:nel_pipe+1)));
summary.max_penetration_pipe_nopull=PostOut.WallPenetration{2}(idx(end));
summary.position.max_penetration_pipe_nopull=PostOut.Xdist{1}(idx(end));
[C,idx]=max(abs(PostOut.WallPenetration{3}(1:nel_pipe+1)));
summary.max_penetration_pipe_pull=PostOut.WallPenetration{3}(idx(end));
summary.position.max_penetration_pipe_pull=PostOut.Xdist{1}(idx(end));
if nel_pipe<nel
[C,idx]=max(abs(PostOut.WallPenetration{2}(nel_pipe+2:nel+1)));
summary.max_penetration_rod_nopull=PostOut.WallPenetration{2}(nel_
pipe+1+idx(end));
[C,idx]=max(abs(PostOut.WallPenetration{3}(nel_pipe+2:nel+1)));
summary.max_penetration_rod_pull=PostOut.WallPenetration{3}(nel_
pipe+1+idx(end));
else
summary.max_penetration_rod_nopull=0;
summary.max_penetration_rod_pull=0;
end
return
80
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function out=yes_no(input)
if input==1
out=’yes’;
elseif input==0
out=’no’;
else
out=’weetniet’;
end
return
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [xy]=xycircle(L1,L2,L3,R,nel,sym)
% This function creates a borepath consisting of a straight horizontal
% section of length L1, a circular arc of radius R with a projected
% horizontal length L2 and a straight section with the same slope as the
% end of the circular arc and projected horizontal length L3. the number of
% points on this borepath is nel+1. if sym=1 the path is made symmetrical
% by flipping the geometry and the number of points is 2*nel+1
%
% 12-dec-2007, Jitse Pruiksma, creation
%
fi=asin(L2/R);
L=L1+R*fi+L3/cos(fi);
D=linspace(0,L,nel+1);
xy=zeros(nel+1,2);
for i=1:nel+1
[x,y]=along_borepath(L1,L2,R,D(i));
xy(i,:)=[x y];
end
if sym==1
xy=[flipud([-xy(2:end,1) xy(2:end,2)]);xy];
end
return
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [x,y]=along_borepath(L1,L2,R,D)
% L1,L2,L3 are lengths measured along the x-axis of the flat piece,
% the curved section with radius R and the straight section after the
% curved section. For a given distance D along the path we would like to
% find x and y
fi=asin(L2/R);
if (0<=D && D<L1)
x=D;y=0;
elseif (L1<=D && D<=L1+fi*R)
fitmp=(D-L1)/R;
x=L1+R*sin(fitmp);
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Nieuwe boortechnieken kleine infra
y=R-R*cos(fitmp);
elseif (L1+fi*R<D)
D2=D-L1-fi*R;
x=L1+L2+D2*cos(fi);
y=R-R*cos(fi)+D2*sin(fi);
end
return
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Appendix 1.4 Matlab script plot_results.m
function plot_results(filename,PostOut,fixed,projectID,AppendixNo,drawnby,checkedby
,GD_boun,i)
%plotting
% description1: ‘geometric nonlinear simulation’
% description2: ‘gap 0.1 m’
str=[filename ‘_’ num2str(i,’%03d’)];
figure
n=5;m=1;
plotindeling(n,m,’A4’,’Portrait’);
tableText1 = { ‘XY data Inputfile name’, PostOut.input.XYfile;
‘L1 [m]’, num2str(PostOut.input.L1);
‘L2 [m]’, num2str(PostOut.input.L2);
‘L3 [m]’, num2str(PostOut.input.L3);
‘R [m]’, num2str(PostOut.input.R);
‘Symmetric geometry’, PostOut.input.sym;
‘Number of elements’, num2str(PostOut.input.nel);
‘Number of elements in pipe’, num2str(PostOut.input.nel_pipe);
‘Geometric Nonlinear Simulation’, PostOut.input.nonlin;
‘Left BC (yes) or Middle BC (no)’, PostOut.input.leftBC;
‘Pipe outer diameter [m]’, num2str(PostOut.input.D0_pipe,’%12.3E’);
‘Pipe wall thickness [m]’, num2str(PostOut.input.t_pipe,’%12.3E’);
‘Density pipe [kg/m^3]’, num2str(PostOut.input.rho_pipe,’%12.3E’);
‘Youngs modulus pipe [N/m^2]’, num2str(PostOut.input.E_pipe,’%12.3E’);
‘Poissons ratio pipe [-]’, num2str(PostOut.input.nu_pipe,’%12.3E’);
‘Pulling rod outer diameter [m]’, num2str(PostOut.input.D0_rod,’%12.3E’);
‘Pulling rod wall thickness [m]’, num2str(PostOut.input.t_rod,’%12.3E’);
‘Density pulling rod material [kg/m^3]’, num2str(PostOut.input.rho_
rod,’%12.3E’);
‘Youngs modulus pulling rod material [N/m^2]’, num2str(PostOut.input.E_
rod,’%12.3E’);
‘Poissons ratio pulling rod material [-]’, num2str(PostOut.input.nu_rod,’%12.3E’);
‘Spring Stiffness soil-pipe [N/m^2]’, num2str(PostOut.input.k_ps,’%12.3E’);
‘Friction factor soil-pipe [-]’, num2str(PostOut.input.fric_ps,’%12.3E’);
‘gap around pipe [m]’, num2str(PostOut.input.gap_ps,’%12.3E’);
‘Spring Stiffness soil-pulling rod [N/m^2]’, num2str(PostOut.input.k_
rs,’%12.3E’);
82
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
‘Friction factor soil-pulling rod [-]’, num2str(PostOut.input.fric_rs,’%12.3E’);
‘gap around pulling rod [m]’, num2str(PostOut.input.gap_rs,’%12.3E’);
‘Reduction factor spring stiffness in borehole [-]’, num2str(PostOut.input.k_red_
fact,’%12.3E’);
‘Density of bore fluid [kg/m^3]’, num2str(PostOut.input.rho_bf,’%12.3E’);
‘Density of water [kg/m^3]’, num2str(PostOut.input.rho_water,’%12.3E’);
‘Fraction of pipe water filled [-]’, num2str(PostOut.input.Tfilled,’%12.3E’);
‘Acceleration of gravity [m/s^2]’, num2str(PostOut.input.g,’%12.3E’);
‘Resistance of tube/rod in bore fluid [N/m^2]’, num2str(PostOut.input.
f2,’%12.3E’);
‘Friction coefficient of pipeline rollers [-]’, num2str(PostOut.input.f1,’%12.3E’);
‘Pushing force at entrance of borepath [N]’, num2str(PostOut.input.
Fpush,’%12.3E’);
};
tableText2 = {‘Upward force of pipe in borefluid [N/m]’,num2str(PostOut.summary.
upforce_tube,’%12.3E’);
‘Upward force of pulling rod in borefluid [N/m]’,num2str(PostOut.summary.
upforce_rod,’%12.3E’);
‘Friction force of pipe in borefluid [N/m]’,num2str(PostOut.summary.resforce_
pipe,’%12.3E’);
‘Friction force of pulling rod in borefluid [N/m]’,num2str(PostOut.summary.
resforce_rod,’%12.3E’);
‘Total pipeline rollers friction [N]’,num2str(PostOut.summary.force_
roll,’%12.3E’);
‘Length of borepath [m]’,num2str(PostOut.summary.length_borepath,’%12.3E’);
‘Length of pipe line in borepath [m]’,num2str(PostOut.summary.length_
tube,’%12.3E’);
‘Maximum moment [Nm]’,num2str(PostOut.summary.max_moment,’%12.3E’);
‘Minimum moment [Nm]’,num2str(PostOut.summary.min_moment,’%12.3E’);
‘Maximum pulling force [N]’,num2str(PostOut.summary.max_
pullingforce,’%12.3E’);
‘Maximum Soil reaction (without pulling) [N/m]’,num2str(PostOut.summary.
max_soilreaction_nopull,’%12.3E’);
‘Maximum Soil reaction (during pulling) [N/m]’,num2str(PostOut.summary.
max_soilreaction_pull,’%12.3E’);
‘Soil reaction head of pipe (without pulling) [N/m]’,num2str(PostOut.summary.
soilreaction_headpipe_nopull,’%12.3E’);
‘Soil reaction head of pipe (during pulling) [N/m]’,num2str(PostOut.summary.
soilreaction_headpipe_pull,’%12.3E’);
‘Maximum borehole wall penetration of pipe (without pulling)
[m]’,num2str(PostOut.summary.max_penetration_pipe_nopull,’%12.3E’);
‘Maximum borehole wall penetration of pipe (during pulling)
[m]’,num2str(PostOut.summary.max_penetration_pipe_pull,’%12.3E’);
‘Maximum borehole wall penetration of rod (without pulling)
[m]’,num2str(PostOut.summary.max_penetration_rod_nopull,’%12.3E’);
‘Maximum borehole wall penetration of rod (during pulling)
[m]’,num2str(PostOut.summary.max_penetration_rod_pull,’%12.3E’);
};
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Nieuwe boortechnieken kleine infra
% title(h1,’Simulation Input Parameters’)
columnwidth = [3 1];
firstrowbold = false;
hold on;
hax1=subplot(n,m,1:3);
table([0.1,0.0,0.9,1.0], [34,2], tableText1, columnwidth, firstrowbold);
set(hax1,’Title’,text(‘String’,’\bf Simulation Input Parameters’,’Color’,’k’));
hold off;
hax2=subplot(n,m,4:5);
if fixed==1
tab_col1=tableText2([1 2 6 7 8 9 11 13 15 17],1);
tab_col2=tableText2([1 2 6 7 8 9 11 13 15 17],2);
tab3=[tab_col1 tab_col2];
table([0.1,0.0,0.9,1.0], [10,2],tab3 , columnwidth, firstrowbold);
else
table([0.1,0.0,0.9,1.0], [18,2], tableText2, columnwidth, firstrowbold);
end
hold on;
set(hax2,’Title’,text(‘String’,’\bf Output Summary’,’Color’,’k’));
hold off;
% h2=subplot(n,m,3);
%
% set(h1,’Title’,text(‘String’,’New Title’,’Color’,’r’))
% % set(h1,’Title’,’Input Parameters’ )
% title(h2,’Output Summary’)
% axis(‘off’)
ktxt = cell(1,8);
ktxt{1} = [‘simulation: ‘ str];
ktxt{2} = ‘Input parameters and output summary’;
ktxt{3} = ‘Abaqus FEM pipeline simulation’;
ktxt{4} = iso_vandaag;
ktxt{5} = projectID;
ktxt{6} = [ AppendixNo ‘.1’];
ktxt{7} = drawnby;
ktxt{8} = checkedby;
if GD_boun
psckader([filename ‘_’ num2str(i,’%03d’) ‘_param.eps’], ktxt,’A4’,’UK’);
else
print(‘-depsc’,[filename ‘_’ num2str(i,’%03d’) ‘_param.eps’]);
end
figure
if fixed==1
n=2;m=2;
plotindeling(n,m,’A3’,’Landscape’);
subplot(n,m,1);plot(PostOut.XY{1}(:,1),PostOut.XY{1}(:,2));
axis equal
84
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
% ylim([0 55])
xlabel(‘x-position borepath [m]’)
ylabel(‘y-position borepath [m]’)
grid on
subplot(n,m,2);plot(PostOut.Xmom{1},PostOut.M{1});
xlabel(‘distance [m]’);
ylabel(‘moment [Nm]’);
grid on
subplot(n,m,3);plot(PostOut.Xdist{1},PostOut.Spring{1})
grid on
xlabel(‘distance [m]’)
ylabel(‘soil spring reaction [N/m]’)
subplot(n,m,4);plot(PostOut.Xdist{1},PostOut.DeltaW{1})
grid on
xlabel(‘distance [m]’)
ylabel(‘displacement normal to borepath [m]’)
else
n=2;m=4;
plotindeling(n,m,’A3’,’Landscape’);
subplot(n,m,1);plot(PostOut.XY{1}(:,1),PostOut.XY{1}(:,2))
axis equal
% ylim([0 55])
xlabel(‘x-position borepath [m]’)
ylabel(‘y-position borepath [m]’)
grid on
subplot(n,m,2);plot(PostOut.Xmom{2},PostOut.M{2},’b’,PostOut.
Xmom{3},PostOut.M{3},’m’);
[legend_h] =legend(‘without pulling’,’during pulling’,’Location’,’North’);
set(legend_h,’FontSize’,8)
legend(‘boxoff’)
xlabel(‘distance [m]’);
ylabel(‘moment [Nm]’);
grid on
subplot(n,m,3);plot(PostOut.Xdist{2},PostOut.Spring{2},’b’,PostOut.
Xdist{3},PostOut.Spring{3},’m’)
[legend_h] =legend(‘without pulling’,’during pulling’,’Location’,’North’);
set(legend_h,’FontSize’,8)
legend(‘boxoff’)
grid on
xlabel(‘distance [m]’)
ylabel(‘soil spring reaction [N/m]’)
subplot(n,m,4);plot(PostOut.Xdist{2},PostOut.DeltaW{2},’b’,PostOut.
Xdist{3},PostOut.DeltaW{3},’m’)
[legend_h] =legend(‘without pulling’,’during pulling’,’Location’,’South’);
set(legend_h,’FontSize’,8)
legend(‘boxoff’)
grid on
xlabel(‘distance [m]’)
85
Nieuwe boortechnieken kleine infra
ylabel(‘displacement normal to borepath [m]’)
subplot(n,m,5);plot(PostOut.Xmom{3},PostOut.SF1{3},’b’)
grid on
xlabel(‘distance [m]’)
ylabel(‘pulling force [N]’)
XY=PostOut.XY_orig;
pdif=diff(XY);
Xdist_orig=[0 ;cumsum(sqrt(pdif(:,1).*pdif(:,1)+pdif(:,2).*pdif(:,2)))];
subplot(n,m,6);plot(PostOut.Xdist{1},PostOut.Xdist{2}-Xdist_orig,’b’,PostOut.
Xdist{1},PostOut.Xdist{3}-Xdist_orig,’m’)
[legend_h] =legend(‘without pulling’,’during pulling’,’Location’,’South’);
set(legend_h,’FontSize’,8)
legend(‘boxoff’)
grid on
xlabel(‘distance [m]’)
ylabel(‘length change of beam [m]’)
subplot(n,m,7);plot(PostOut.Xdist{1},PostOut.DeltaH{2},’b’,PostOut.
Xdist{1},PostOut.DeltaH{3},’m’)
[legend_h] =legend(‘without pulling’,’during pulling’,’Location’,’South’);
set(legend_h,’FontSize’,8)
legend(‘boxoff’)
grid on
xlabel(‘distance [m]’)
ylabel(‘horizontal displacement along borepath [m]’)
subplot(n,m,8);plot(PostOut.Xdist{1},PostOut.WallPenetration{3},’m’)
[legend_h] =legend(‘during pulling’,’Location’,’South’);
set(legend_h,’FontSize’,8)
legend(‘boxoff’)
grid on
xlabel(‘distance [m]’)
ylabel(‘borewall penetration [m]’)
end
%kaderteksten
nel=PostOut.input.nel;
nel_pipe=PostOut.input.nel_pipe;
ktxt{2} = [‘Pipeline pulled in for ‘ num2str(nel_pipe/nel*100) ‘ %’];
ktxt{6} = [ AppendixNo ‘.2’];
if GD_boun
psckader([filename ‘_’ num2str(i,’%03d’) ‘_plot.eps’], ktxt,’A3’,’UK’);
else
print(‘-depsc’,[filename ‘_’ num2str(i,’%03d’) ‘_plot.eps’]);
end
eval([filename ‘_’ num2str(i,’%03d’) ‘=PostOut;’]);
% eval([‘save ‘ str str]);
eval([‘save(str,’ char(39) filename ‘_’ num2str(i,’%03d’) char(39) ‘)’]);
return
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
86
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function table(varargin)
%
% table(handle, area, layout, txt, columnwidth);
%
% Draws a table in a graphical context
%
% Input:
% handle
handle of the axes in which the table
%
is to be drawn. Optional
% area
A four element vector containing the
%
lower left and upper right coordinates
%
in relative values (0 .. 1)
% layout
A two element vector containing the
%
number of rows and columns in the table
% txt
A 2D cell array of strings to be
%
tablelised.
% columnwidth
An array with the width of the columns.
%
The number of elements should be the
%
same as the number of columns.
%
Optional.
%
% Remarks:
% 1) handle is optional. If no handle is provided, the current axes are
% used.
% 2) area may be empty. By default the entire area is used.
% 3) layout may be empty []. By default the sizes of the text array are used.
% 4) txt may be empty []. In that case only the lines of the table are drawn.
% 5) when layout is empty, txt must be present.
% 6) columnwidth is optional. Values are normalised. Either [0.2 0.1] or
% [10, 5] create the same relative widths
%
% 2006-09-20, Adel Variable columnwidth added
% 2006-05-18, Adel Updated and generic version of local functions
%
%
%
%
%
%
(c) Copyright GeoDelft, The Netherlands. This source is property of GeoDelft.
This source may be freely used. GeoDelft accepts no responsibility for
the use of this source. If this source is integrated in or distributed with
other sources, this copyright message may not be removed.
If the source is improved, changed or extended in its possibilities, please notify
us and send a copy of the new source to us at [email protected]
% Index of the first argument.
st = 1;
% Is a handle provided?
if ishandle(varargin{st})
subplot(varargin{st});
87
Nieuwe boortechnieken kleine infra
% remove the number on the axis
set(varargin{st}, ‘visible’, ‘off’, ‘xlim’, [0 1], ‘ylim’, [0 1]);
st = st + 1;
else
set(gca, ‘visible’, ‘off’, ‘xlim’, [0 1], ‘ylim’, [0 1]);
end
% Is the (next) argument empty?
if isempty(varargin{st})
xo = 0;
% Default values: the entire field
yo = 0;
xb = 1;
yb = 1;
else
frame = varargin{st};
xo = frame(1);
yo = frame(2);
xb = frame(3);
yb = frame(4);
end
st = st + 1;
% Rows and columns empty?
if isempty(varargin{st})
if isempty(varargin{st+1})
% No table can be drawn
errordlg(‘No table can be drawn’, ‘Too little arguments’);
return;
end
s = size(varargin{st+1});
row = s(1);
% Default the size of the cell array
col = s(2);
else
frame = varargin{st};
row = frame(1);
col = frame(2);
end
txt = varargin{st+1};
% The text to be printed in the table
% Optional width of the columns. default: all the same width
if nargin > st+1
colwidth = varargin{st+2};
lkw = length(colwidth);
if lkw > col
col_width = colwidth(1:col);
elseif lkw < col
88
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
col_width = ones(1, col) * colwidth(end);
col_width(1:lkw) = colwidth;
colwidth = col_width;
end
br = (xb-xo);
% Total width of the table
kw = cumsum([0 colwidth]);
% Relative position of the lines
% Maximum width of 1.0 should not be exceeded. Scale if necessary
if kw(end) > 1
colwidth = colwidth / kw(end);
kw = kw / kw(end);
end
x = xo + (br*kw);
% Absolute position of the lines
xs = min(br*colwidth) / 10;
% Shift within a column
else
stepx = (xb-xo)/col;
x = [xo:stepx:xb];
xs = stepx / 10;
if col == 1
xs = stepx / 50;
end
end
% Increment for rows and columns
stepy = (yb-yo)/row;
% Y values for the lines in the table
y = [yo:stepy:yb];
% Keep the hold status of the axes
do_hold = ishold;
% In ieder geval vastzetten
hold on
% When a table has 1 column, don’t plot the horizontal lines
if col == 1
% Draw the horizontal lines: top, heading and bottom
for yp=[y(1) y(end-1) y(end)]
plot([x(1) x(end)], [yp yp], ‘k’);
end
else
% Draw the horizontal lines
for yp=y
plot([x(1) x(end)], [yp yp], ‘k’);
end
end
89
Nieuwe boortechnieken kleine infra
% Draw the vertical lines
for xp=x
plot([xp xp], [y(1) y(end)], ‘k’);
end
% X shift in a cell
% xs = stepx / 10;
if nargin > st
% Write the texts
% Loop over the columns
for k = 1:col
xp = x(k);
% Alias
% Loop over the rows
for r = 1:row
yp = y(row+1-r);
% Alias
if ~isempty(txt{r, k})
if r == 1 && varargin{st+3} % First row in BOLD
text(xp+xs, yp+stepy/2, txt{r, k}, ‘Fontsize’, 7, ...
‘Interpreter’, ‘tex’, ‘FontWeight’, ‘bold’);
else
text(xp+xs, yp+stepy/2, txt{r, k}, ‘Fontsize’, 7,...
‘Interpreter’, ‘tex’);
end
end
end
end
end
% Restore hold status. Untill here hold is on.
if ~do_hold
% It was not hold, so: hold off
hold off
end
return;
90
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Appendix 1.5 Python script python_postprLIN.py
#
# ABAQUS PYTHON Script to extract information from an Abaqus odb file.
#
from odbAccess import *
import sys
# Check that an output database was specified.
if len(sys.argv) != 2:
print ‘Error: you must supply the name \
of an odb on the command line’
sys.exit(1)
# Get the command line argument.
odbPath = sys.argv[1]
# Open the output database and set assembly object
odb = openOdb(path=odbPath)
assembly = odb.rootAssembly
# Model name
print ‘Model data for ODB: ‘, odbPath
# Find total number of nodes and elements
numNodes = numElements = 0
for name, instance in assembly.instances.items():
n = len(instance.nodes)
numNodes = numNodes + n
n = len(instance.elements)
numElements = numElements + n
print ‘Number of instances, Elements, Nodes’
print ‘%d,%d,%d’ % (len(assembly.instances),numElements,numNodes)
# find total number of steps and stepNames
StepList=[‘string1’,’string2’,’string3’,’string4’]
i=0
for stepName in odb.steps.keys():
StepList[i]=stepName
i=i+1
Nsteps=i-1
print ‘Number of steps in output’
print ‘%d’ % (Nsteps+1)
# PRINT NODE INFORMATION
for name, instance in assembly.instances.items():
print ‘NODAL COORDINATES’
if instance.embeddedSpace == THREE_D:
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Nieuwe boortechnieken kleine infra
print ‘ X
Y
Z’
for node in instance.nodes:
print ‘%d, %.8E, %.8E, %.8E’ % (node.label,
node.coordinates[0],node.coordinates[1],node.coordinates[2])
else:
print ‘ X
Y’
for node in instance.nodes:
print ‘%d, %.8E, %.8E’ % (node.label,
node.coordinates[0],
node.coordinates[1])
# extract NODAL and ELEMENT output
i=0
while i<Nsteps+1:
lastFrame=odb.steps[StepList[i]].frames[-1]
displacement=lastFrame.fieldOutputs[‘U’]
fieldValues=displacement.values
#for each displacement value, print the nodeLabel and data members
print ‘Step= %s’ % (StepList[i])
print ‘Node, Ux, Uy’
for v in fieldValues:
print ‘%d, %.8E, %.8E’ % (v.nodeLabel,v.data[0],v.data[1])
print ‘Element, SF1, SF2, SM1’
k=0
while k <= numElements-1-numNodes/2:
SFi=lastFrame.fieldOutputs[‘SF’].values[k]
SMi=lastFrame.fieldOutputs[‘SM’].values[k]
print ‘%d, %.8E, %.8E, %.8E’% (SFi.elementLabel,SFi.data[0],SFi.data[1],SMi.
data[0])
k=k+1
stress=lastFrame.fieldOutputs[‘S’]
fieldValues=stress.values
print ‘Element, S11, S12, S13’
for v in fieldValues:
print ‘%d, %.8E, %.8E, %.8E’ % (v.elementLabel,v.data[0],v.data[3],v.data[4])
i=i+1
92
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Appendix 1.6 Python script python_postprNL.py
#
# ABAQUS PYTHON Script to extract information from an Abaqus odb file.
#
from odbAccess import *
import sys
# Check that an output database was specified.
if len(sys.argv) != 2:
print ‘Error: you must supply the name \
of an odb on the command line’
sys.exit(1)
# Get the command line argument.
odbPath = sys.argv[1]
# Open the output database and set assembly object
odb = openOdb(path=odbPath)
assembly = odb.rootAssembly
# Model name
print ‘Model data for ODB: ‘, odbPath
# Find total number of nodes and elements
numNodes = numElements = 0
for name, instance in assembly.instances.items():
n = len(instance.nodes)
numNodes = numNodes + n
n = len(instance.elements)
numElements = numElements + n
print ‘Number of instances, Elements, Nodes’
print ‘%d,%d,%d’ % (len(assembly.instances),numElements,numNodes)
# find total number of steps and stepNames
StepList=[‘string1’,’string2’,’string3’,’string4’]
i=0
for stepName in odb.steps.keys():
StepList[i]=stepName
i=i+1
Nsteps=i-1
print ‘Number of steps in output’
print ‘%d’ % (Nsteps+1)
# PRINT NODE INFORMATION
for name, instance in assembly.instances.items():
print ‘NODAL COORDINATES’
if instance.embeddedSpace == THREE_D:
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Nieuwe boortechnieken kleine infra
print ‘ X
Y
Z’
for node in instance.nodes:
print ‘%d, %.8E, %.8E, %.8E’ % (node.label,
node.coordinates[0],node.coordinates[1],node.coordinates[2])
else:
print ‘ X
Y’
for node in instance.nodes:
print ‘%d, %.8E, %.8E’ % (node.label,
node.coordinates[0],
node.coordinates[1])
# extract NODAL and ELEMENT output
i=0
while i<Nsteps+1:
lastFrame=odb.steps[StepList[i]].frames[-1]
displacement=lastFrame.fieldOutputs[‘U’]
fieldValues=displacement.values
#for each displacement value, print the nodeLabel and data members
print ‘Step= %s’ % (StepList[i])
print ‘Node, Ux, Uy’
for v in fieldValues:
print ‘%d, %.8E, %.8E’ % (v.nodeLabel,v.data[0],v.data[1])
print ‘Element, SF1, SF2, SM1’
k=0
while k <= numElements-1-numNodes/2:
SFi=lastFrame.fieldOutputs[‘SF’].values[k]
SMi=lastFrame.fieldOutputs[‘SM’].values[k]
print ‘%d, %.8E, %.8E, %.8E’% (SFi.elementLabel,SFi.data[0],SFi.data[1],SMi.
data[0])
k=k+1
if i>0:
stress=lastFrame.fieldOutputs[‘S’]
fieldValues=stress.values
print ‘Element, S11, S12, S13’
for v in fieldValues:
print ‘%d, %.8E, %.8E, %.8E’ % (v.elementLabel,v.data[0],v.data[3],v.data[4])
i=i+1
94
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Appendix 2
Derivation of analytical solution
Appendix 2.1Derivation of the analytical solution
Consider a geometrically linear Bernoulli beam with length L and bending stiffness EI
fixed at x=0. The vertical displacement is called w(x), where w is considered positive in
upward direction. This displacement is zero at the fixed end and the slope w’ is also zero
at the fixed end. The beam is subjected to a distributed load q(x) caused for example by
the weight of the beam, positive in upward direction. At the end, at x=L there is a force
F and an applied moment M. The beam is embedded on elastic springs with stiffness
k. Furthermore there is a prescribed displacement at the bottom of the springs w0(x)
which is positive in the upward direction. The class of solutions where this displacement
represents part of a circle with radius R is considered. w0(x) could represent a part of the
borepath for example. The system is graphically represented in the figure below:
F
q (x )
M
-w 0 (x )
x= 0
x=L
w=0, w'= 0
The differential equation for a standard beam on elastic foundation (with w0(x)=0) is
[Hetényi 1946]:
d 4w
EI 4 kw q
dx
If w is positive, the springs give a force downward. The prescribed displacements w0(x)
can be taken into consideration by realising that the net force on the beam is determined
by the displacement difference w(x)-w0(x). The differential equation then becomes:
d 4w
EI
+ kw = q + kw0
dx 4
(1.1)
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Nieuwe boortechnieken kleine infra
Because if w would be zero and w0 positive, there would be a net force upward.
[Hetényi 1946] solves this type of equations by first solving the homogeneous differential
equation:
EI
d 4 wH
+ kw H = 0
4
dx
(1.2)
The superscript H is added to make the distincion of the homogeneous solution. Hetényi
shows that the general solution for this homogeneous equation can be written as:
w H = e λx (C1 cos λx + C 2 sin λx) + e − λx (C 3 cos λx + C 4 sin λx)
λ=4
k
4EI
(1.3)
C1 to C4 are constants that need to be determined later. Next a particular solution wP
needs to be found which is a solution to the original differential equation (1.1). It can
be proved that addition of the homogeneous and particular solution together with the
boundary conditions for a unique solution to the problem.
w = wP + wH
(1.4)
It is assumed that q(x)=q, a constant load. As prescribed groundmovement w0(x) we
define a circular arc as is commonly used in the design of HDD’s:

x 
w0 ( x ) = R 1 − 1 − ( ) 2 
R 

(1.5)
R is the radius of the circle. At x=0 the displacement is zero and at x=R the displacement
is R and a quarter of a circle has been described. Pipelines are not pulled at angles larger
than 45 degrees and therefore x/R<1/√2. Solving the differential equation with this
function w0(x) is very complex and perhaps not possible in closed form. But because of
our imitation to values of x/R<1/√2 the function w0(x) can be written as a Taylor expansion. Written to the 8th order this becomes:

x 
1 x
1 x
5 x 8
1 x
w0 ( x) = R 1 − 1 − ( ) 2  ≈ R  ( ) 2 + ( ) 4 + ( ) 6 +
( )
R 
8 R
16 R
128 R 
2 R

(1.6)
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Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
if we plot the approximate Taylor expansion to 8th order together with the original
function upto x/R=1/√2, it can be seen that this is a good approximation:
With this Taylor expansion the equation that needs to be solved is:
1 x
1 x
5 x 8
d 4wP
1 x
+ kw P = q + kR  ( ) 2 + ( ) 4 + ( ) 6 +
( )
EI
4
8 R
16 R
128 R 
dx
2 R
(1.7)
If a solution of the form
x
x
x
x
w P ( x ) = a0 + a1 ( ) 2 + a2 ( )4 + a3 ( )6 + a4 ( )8
R
R
R
R
(1.8)
is attempted then:
d 4 w P 24a2 360a3 x 2 1680a4 x 4
= 4 +
( ) +
( )
dx 4
R
R4 R
R4
R
and
EI
d 4 wP
24a 360a3 x 2 1680a4 x 4
+ kw P = EI ( 4 2 +
( ) +
( ) )
4
dx
R
R4 R
R4
R
x 2
x 4
x 6
x
+ k (a0 + a1 ( ) + a2 ( ) + a3 ( ) + a4 ( )8 )
R
R
R
R
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Nieuwe boortechnieken kleine infra
Equalling this with the right side of equaiton 1.7 gives:
24 EIa2
+ ka0 = q
R4
360 EIa3 x 2
x
R x
( ) + ka1 ( ) 2 = k ( )2
4
2 R
R
R
R
1680 EIa4 x 4
x
R x
( ) + ka2 ( ) 4 = k ( ) 4
4
R
R
R
8 R
x
R x
ka3 ( ) 6 = k ( ) 6
16 R
R
x
5R x 8
ka4 ( )8 = k
( )
R
128 R
writing this out yields:
w P ( x) =
q 24 EI 1 525 EI
−
R( −
)+
k kR 4
8
8 kR 4
5 x 8
 1 45 EI x 2 1 525 EI x 4 1 x 6
R ( −
)( ) + ( −
)( ) + ( ) +
( ) 
4
4
8
8 kR R
16 R
128 R 
 2 2 kR R
(1.8)
It can be seen that when k reaches infinity the solution is equal to w0(x), which is as it
should. Adding (1.8) to the homogeneous solution, the overall solution becomes:
w( x) =
q
24
1 525 1
− 4 4 R( −
)+
k 4λ R
8
8 4λ4 R 4
x
1 525 1
x
1 x
5 x 8
 1 45 1
R ( −
)( ) 2 + ( −
)( ) 4 + ( )6 +
( ) 
4 4
4 4
8 8 4λ R R
16 R
128 R 
 2 2 4λ R R
+ e λx (C1 cos λx + C2 sin λx ) + e −λx (C3 cos λx + C 4 sin λx)
(1.9)
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Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
The C1 to C4 have to be determined from the boundary conditiohns. Because of the fixed
end at x=0 the displacement there is zero and the slope is zero as well. At the end x=L
we let the moment be zero and the force F. Then the four boundary conditions can be
expressed as:
w(0) = 0 ⇒ w H (0) = − w P (0)
dw
dw H
dw P
(0) = 0 ⇒
(0) = −
( 0)
dx
dx
dx
d 2 wP
d 2 wH
d 2w
(
)
=
0
⇒
(
)
=
( L)
L
L
dx 2
dx 2
dx 2
d 3w
F
d 3w H
d 3 wP
F
L
L
(
)
=
−
⇒
(
)
=
−
( L) −
3
3
3
dx
EI
dx
dx
EI
(1.10)
This way of writing will turn out to be convenient for the determination of the unknown
constants. For wP it holds that:
w P ( x) =
q 24 EI 1 525 EI
−
R( −
)+
k kR 4
8
8 kR 4
5 x 8
 1 45 EI x 2 1 525 EI x 4 1 x 6
R ( −
)( ) + ( −
)( ) + ( ) +
( ) 
4
4
8
8 kR R
16 R
128 R 
 2 2 kR R
dw P
EI x
1 525 EI x 3 3 x 5 5 x 7
( x) = (1 − 45 4 )( ) + ( −
)( ) + ( ) + ( )
dx
kR R
2
2 kR 4 R
8 R
16 R
2 P
d w
1
EI
3 1 525 EI x 2 15 x 4 35 x 6
( x) = (1 − 45 4 ) + ( −
)( ) +
( ) +
( )
2
dx
R
kR
R 2
2 kR 4 R
8R R
16 R R
d 3 wP
6 1 525 EI x
15 x
105 x
( x) = 2 ( −
)( ) + 2 ( )3 + 2 ( )5
3
4
dx
R 2
2 kR R 2 R R
8R R
4 P
6 1 525 EI
45 x
525 x
d w
( x) = 3 ( −
) + 3 ( )2 + 3 ( ) 4
4
4
2 kR
2R R
8R R
dx
R 2
(1.11)
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Nieuwe boortechnieken kleine infra
The 4th derivative is not needed, but is written down to check the solution by substituting it in equation (1.1). For wH it holds:
w H = e λx (C1 cos λx + C2 sin λx) + e − λx (C3 cos λx + C4 sin λx)
dw H
= λe λx ((C1 + C2 ) cos λx + (C2 − C1 ) sin λx) + λe −λx ((C4 − C3 ) cos λx − (C3 + C4 ) sin λx )
dx
d 2 wH
= 2λ2 e λx (C2 cos λx − C1 sin λ x) + 2λ2 e −λx (−C4 cos λx + C3 sin λx)
2
dx
d 3wH
= 2λ3e λx ((C2 − C1 ) cos λx − (C1 + C2 ) sin λx ) + 2λ3e −λx ((C3 + C4 ) cos λx + (C4 − C3 ) sin λx)
dx 3
Now, the matrix equation can be determined from which the constants can be calculated.
 a11
a
 21
 a31

a41
a12
a13
a22
a23
a42
a43
a32
a33
a14   C1   b1 
a24  C 2  b2 
=
a34  C3  b3 
   
a44  C 4  b4 
The coefficients of the right hand vector b are given by:
b1 = − w P (0), b2 = −
1 dw P
1 d 2 wP
1  d 3 wP
F
(0), b3 = − 2
(
),
( L) − 
L
b
=
−
4
2
3 
3
λ dx
2λ dx
2λ  dx
EI 
which can be calculated from (1.11). From this it can be seen that b2=0. The coefficients
of the matrix A are given by:
a11 = 1, a12 = 0, a13 = 1, a14 = 0
a21 = 1, a22 = 1, a23 = −1, a24 = 1
a31 = −e λL sin λL, a32 = e λL cos λL, a33 = e −λL sin λL, a34 = −e −λL cos λL
a41 = −e λL (cos λL + sin λL), a42 = e λL (cos λL − sin λL)
a43 = e −λL (cos λL − sin λL), a44 = e −λL (cos λL + sin λL)
It can be seen that the coefficients aij are dimensionless and the coefficients bi have the
dimension of length. This means that the constants Ci also have the dimension of length,
which is correct. This 4x4 matrix equation can be solved with a computer program and
the found constants C1 t/m C4 can be substituted in (1.9) to obtain the overall solution.
Because the system has several zero’s it can be attempted to simplify them so that no
solver is necessary.
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Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
The system ban be simplified as follows:
1
1

 a31

a41
0
1
a32
a42
 1
 2

 a31 − a33

a41 − a43
0   C1   b1 
− 1 1  C2   0 
=
a33 a34  C3  b3 
   
a43 a44  C4  b4 
1
0
1
a32
a42

1

2

a31 − a33 − 2a34

a41 − a43 − 2a44
1
2

 a31

a41
0
1
1
0
a32
a42
a33
a43
0   C1   b1 
1  C2   b1 
=
a34  C3  b3 
   
a44  C4  b4 
0   C1   b1 
0 1  C2   b1 
=
0 a34  C3  b3 − a33b1 

  
0 a44  C4  b4 − a43b1 
1
0
1
a32 − a34
a42 − a44

1 0C1  
b1
  

b1
0 1C 2  

=
0 0C 3  b3 − a33b1 − a34 b1
  

0 0C 4  b4 − a43b1 − a44 b1
This can be written as a 2x2 system with two back substitutions:
 a31 − a33 − 2a34
a − a − 2a
44
 41 43
a32 − a34   C1   b3 − a33b1 − a34b1 
=
a42 − a44  C2  b4 − a43b1 − a44b1 
C3 = b1 − C1
C4 = b1 − 2C1 − C2
write the system as:
 a'11
a '
 21
a '12   C1   b'1 
=
a'22  C2  b'2 
with:
a '11 = a31 − a33 − 2a34
a '12 = a32 − a34
a '21 = a41 − a43 − 2a44
a '22 = a42 − a44
b'1 = b3 − a33b1 − a34b1
b'2 = b4 − a43b1 − a44b1
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Nieuwe boortechnieken kleine infra
then the solution is:
C1 =
C2 =
a'22 b'1 − a'12 b'2
a '11 a'22 − a '21 a '12
a'11 b'2 − a'21 b'1
a'11 a '22 − a'21 a'12
and using backsubstitution C3 and C4 are found. This method is programmed in a Matlab
script
Appendix 2.2 Matlab script for the analytical solution
Below is the Matlab script used for calculation of the analytical solution. As input a vector x has to be given with points where the output is required, the length L of the beam,
the radius R, the bending stiffness EI, the distributed load q and force F. output is the
displacement w and w0 as well as the reaction force per length unit.
file calc_WAll.m:
function [w w0 r_force_m]=calc_WAll(x,L,R,k,EI,q,F)
lambda=(k/(4*EI))^(1/4);
[A b]=calc_A_b(lambda,R,q,k,EI,F,L);
%calc coefficients c
a(1,1)=A(3,1)-A(3,3)-2*A(3,4);
a(1,2)=A(3,2)-A(3,4);
a(2,1)=A(4,1)-A(4,3)-2*A(4,4);
a(2,2)=A(4,2)-A(4,4);
bb(1)=b(3)-b(1)*(A(3,3)+A(3,4));
bb(2)=b(4)-b(1)*(A(4,3)+A(4,4));
det_a=a(1,1)*a(2,2)-a(2,1)*a(1,2)
c(1)=(bb(1)*a(2,2)-bb(2)*a(1,2))/det_a;
c(2)=(bb(2)*a(1,1)-bb(1)*a(2,1))/det_a;
c(3)=b(1)-c(1);
c(4)=b(1)-2*c(1)-c(2);
%calculate and sum homogeneous and particular solutions
wP=WP_calc(0,R,q,EI,k,x);
wH=WH_calc(lambda,c,x);
w=wH+wP;
w0=W0_calc(R,x);
r_force_m=k*(w-w0);
end
%setup matrix coefficients
function [A b]=calc_A_b(lambda,R,q,k,EI,F,L)
g=lambda*L;
A=zeros(4,4);
A(1,1)=1;A(1,2)=0;A(1,3)=1;A(1,4)=0;
A(2,1)=1;A(2,2)=1;A(2,3)=-1;A(2,4)=1;
A(3,1)=-exp(g)*sin(g);A(3,2)=exp(g)*cos(g);
102
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
A(3,3)=exp(-g)*sin(g);A(3,4)=-exp(-g)*cos(g);
A(4,1)=-exp(g)*(cos(g)+sin(g));
A(4,2)=exp(g)*(cos(g)-sin(g));
A(4,3)=exp(-g)*(cos(g)-sin(g));
A(4,4)=exp(-g)*(cos(g)+sin(g));
%calculate b vector, use Particular solution
w0p0=WP_calc(0,R,q,EI,k,0);
w1p0=WP_calc(1,R,q,EI,k,0);
w2pL=WP_calc(2,R,q,EI,k,L);
w3pL=WP_calc(3,R,q,EI,k,L);
b=zeros(4,1);
b(1)=-w0p0;
b(2)=-w1p0/lambda;
b(3)=-w2pL/(2*lambda^2);
b(4)=-1/(2*lambda^3)*(w3pL+F/EI);
end
%calculate particular solution
function wp_out=WP_calc(graad,R,q,EI,k,x)
xx=x/R;
C=EI/(k*R^4);
if graad==0
wp_out=q/k-24*C*R*(1/8-525/8*C)+R*( (1/2-45/2*C)*xx.^2 +
(1/8-525/8*C)*xx.^4 + 1/16*xx.^6 + 5/128*xx.^8 );
elseif graad==1
wp_out=(1-45*C)*xx + (1/2-525/2*C)*xx.^3 + 3/8*xx.^5 + 5/16*xx.^7;
elseif graad==2
wp_out=1/R*( (1-45*C) + 3*(1/2-525/2*C)*xx.^2 + 15/8*xx.^4 + 35/16*xx.^6);
elseif graad==3
wp_out=1/R^2*( 3*(1-525*C)*xx + 15/2*xx.^3 + 105/8*xx.^5);
elseif graad==4
wp_out=1/R^3*( 3*(1-525*C) + 45/2*xx.^2 + 525/8*xx.^4);
end
end
% calculate homogeneus solution
function wH=WH_calc(lambda,c,x)
wH= exp(lambda*x).*( c(1)*cos(lambda*x) + c(2)*sin(lambda*x) )+ ...
exp(-lambda*x).*( c(3)*cos(lambda*x) + c(4)*sin(lambda*x) );
end
% calculate homogeneus solution
function w0=W0_calc(R,x)
xx=x/R;
w0=R*(1/2*xx.^2+1/8*xx.^4+1/16*xx.^6+5/128*xx.^8);
end
103
Nieuwe boortechnieken kleine infra
104
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Appendix 3
Simulation results
Appendix 3.1
Comparison of Abaqus results with analytical solution.
Annex. 3.1.1.1 Abaqus FEM pipeline simulation
Simulation Input Parameters
XY data Inputfile name
−
L1 [m]
0
L2 [m]
310
L3 [m]
0
R [m]
1210
Symmetric geometry
no
Number of elements
200
Number of elements in pipe
200
Geometric Nonlinear Simulation
no
Left BC (yes) or Middle BC (no)
yes
Pipe outer diameter [m]
1,21E+03
Pipe wall thickness [m]
2.270E−002
Density pipe [kg/m3]
7,85E+06
Youngs modulus pipe [N/m2]
2,10E+14
Poissons ratio pipe [−]
3.000E−001
Pulling rod outer diameter [m]
1.250E−001
Pulling rod wall thickness [m]
6.250E−002
Density pulling rod material [kg/m3]
7,85E+06
Youngs modulus pulling rod material [N/m2]
2,10E+14
Poissons ratio pulling rod material [−]
3.000E−001
Spring Stiffness soil−pipe [N/m2]
1,30E+08
Friction factor soil−pipe [−]
2.000E−001
gap around pipe [m]
1.000E−010
Spring Stiffness soil−pulling rod [N/m2]
1,30E+06
105
Nieuwe boortechnieken kleine infra
Friction factor soil−pulling rod [−]
2.000E−001
gap around pulling rod [m]
6.425E−010
Reduction factor spring stiffness in borehole [−]
5.000E−003
Density of bore fluid [kg/m3]
1,15E+06
Density of water [kg/m3]
1,00E+06
Fraction of pipe water filled [−]
5.000E−001
Acceleration of gravity [m/s2]
0.000E+000
Resistance of tube/rod in bore fluid [N/m2]
0.000E+000
Friction coefficient of pipeline rollers [−]
0.000E+000
Pushing force at entrance of borepath [N]
0.000E+000
Output Summary
Upward force of pipe in borefluid [N/m]
0.000E+000
Upward force of pulling rod in borefluid [N/m]
−0.000E+000
Length of borepath [m]
3,10E+05
Length of pipe line in borepath [m]
3,10E+05
Maximum moment [Nm]
−1.092E+004
Minimum moment [Nm]
−2.895E+006
Maximum Soil reaction (without pulling) [N/m]
1,82E+07
Soil reaction head of pipe (without pulling) [N/m]
1,82E+07
Maximum borehole wall penetration of pipe (without pulling) [m]
−1.399E−001
Maximum borehole wall penetration of rod (without pulling) [m]
0.000E+000
Annex. 3.1.2.1 Abaqus FEM pipeline simulation
Simulation Input Parameters
XY data Inputfile name
−
L1 [m]
0
L2 [m]
310
L3 [m]
0
R [m]
1210
Symmetric geometry
no
106
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Number of elements
200
Number of elements in pipe
200
Geometric Nonlinear Simulation
no
Left BC (yes) or Middle BC (no)
yes
Pipe outer diameter [m]
1,21E+03
Pipe wall thickness [m]
2.270E−002
Density pipe [kg/m3]
7,85E+06
Youngs modulus pipe [N/m2]
2,10E+14
Poissons ratio pipe [−]
3.000E−001
Pulling rod outer diameter [m]
1.250E−001
Pulling rod wall thickness [m]
6.250E−002
Density pulling rod material [kg/m3]
7,85E+06
Youngs modulus pulling rod material [N/m2]
2,10E+14
Poissons ratio pulling rod material [−]
3.000E−001
Spring Stiffness soil−pipe [N/m2]
1,30E+08
Friction factor soil−pipe [−]
2.000E−001
gap around pipe [m]
1.000E−001
Spring Stiffness soil−pulling rod [N/m2]
1,30E+06
Friction factor soil−pulling rod [−]
2.000E−001
gap around pulling rod [m]
6.425E−010
Reduction factor spring stiffness in borehole [−]
5.000E−003
Density of bore fluid [kg/m3]
1,15E+06
Density of water [kg/m3]
1,00E+06
Fraction of pipe water filled [−]
5.000E−001
Acceleration of gravity [m/s2]
0.000E+000
Resistance of tube/rod in bore fluid [N/m2]
0.000E+000
Friction coefficient of pipeline rollers [−]
0.000E+000
Pushing force at entrance of borepath [N]
0.000E+000
107
Nieuwe boortechnieken kleine infra
Output Summary
Upward force of pipe in borefluid [N/m]
0.000E+000
Upward force of pulling rod in borefluid [N/m]
−0.000E+000
Length of borepath [m]
3,10E+05
Length of pipe line in borepath [m]
3,10E+05
Maximum moment [Nm]
−1.081E+004
Minimum moment [Nm]
−2.734E+006
Maximum Soil reaction (without pulling) [N/m]
1,80E+07
Soil reaction head of pipe (without pulling) [N/m]
1,80E+07
Maximum borehole wall penetration of pipe (without pulling) [m]
−1.379E−001
Maximum borehole wall penetration of rod (without pulling) [m]
0.000E+000
Annex. 3.1.3.1 Abaqus FEM pipeline simulation
Simulation Input Parameters
XY data Inputfile name
−
L1 [m]
0
L2 [m]
310
L3 [m]
0
R [m]
1210
Symmetric geometry
no
Number of elements
200
Number of elements in pipe
200
Geometric Nonlinear Simulation
yes
Left BC (yes) or Middle BC (no)
yes
Pipe outer diameter [m]
1,21E+03
Pipe wall thickness [m]
2.270E−002
Density pipe [kg/m3]
7,85E+06
Youngs modulus pipe [N/m2]
2,10E+14
Poissons ratio pipe [−]
3.000E−001
Pulling rod outer diameter [m]
1.250E−001
Pulling rod wall thickness [m]
6.250E−002
Density pulling rod material [kg/m3]
7,85E+06
108
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Youngs modulus pulling rod material [N/m2]
2,10E+14
Poissons ratio pulling rod material [−]
3.000E−001
Spring Stiffness soil−pipe [N/m2]
1,30E+08
Friction factor soil−pipe [−]
2.000E−001
gap around pipe [m]
1.000E−010
Spring Stiffness soil−pulling rod [N/m2]
1,30E+06
Friction factor soil−pulling rod [−]
2.000E−001
gap around pulling rod [m]
6.425E−010
Reduction factor spring stiffness in borehole [−]
5.000E−003
Density of bore fluid [kg/m3]
1,15E+06
Density of water [kg/m3]
1,00E+06
Fraction of pipe water filled [−]
5.000E−001
Acceleration of gravity [m/s2]
0.000E+000
Resistance of tube/rod in bore fluid [N/m2]
0.000E+000
Friction coefficient of pipeline rollers [−]
0.000E+000
Pushing force at entrance of borepath [N]
0.000E+000
Output Summary
Upward force of pipe in borefluid [N/m]
0.000E+000
Upward force of pulling rod in borefluid [N/m]
−0.000E+000
Length of borepath [m]
3,14E+05
Length of pipe line in borepath [m]
3,14E+05
Maximum moment [Nm]
−1.022E+004
Minimum moment [Nm]
−2.700E+006
Maximum Soil reaction (without pulling) [N/m]
1,66E+07
Soil reaction head of pipe (without pulling) [N/m]
1,66E+07
Maximum borehole wall penetration of pipe (without pulling) [m]
−1.277E−001
Maximum borehole wall penetration of rod (without pulling) [m]
0.000E+000
109
Nieuwe boortechnieken kleine infra
Annex. 3.1.4.1 Abaqus FEM pipeline simulation
Simulation Input Parameters
XY data Inputfile name
−
L1 [m]
0
L2 [m]
310
L3 [m]
0
R [m]
1210
Symmetric geometry
no
Number of elements
200
Number of elements in pipe
200
Geometric Nonlinear Simulation
yes
Left BC (yes) or Middle BC (no)
yes
Pipe outer diameter [m]
1,21E+03
Pipe wall thickness [m]
2.270E−002
Density pipe [kg/m3]
7,85E+06
Youngs modulus pipe [N/m2]
2,10E+14
Poissons ratio pipe [−]
3.000E−001
Pulling rod outer diameter [m]
1.250E−001
Pulling rod wall thickness [m]
6.250E−002
Density pulling rod material [kg/m3]
7,85E+06
Youngs modulus pulling rod material [N/m2]
2,10E+14
Poissons ratio pulling rod material [−]
3.000E−001
Spring Stiffness soil−pipe [N/m2]
1,30E+08
Friction factor soil−pipe [−]
2.000E−001
gap around pipe [m]
1.000E−001
Spring Stiffness soil−pulling rod [N/m2]
1,30E+06
Friction factor soil−pulling rod [−]
2.000E−001
gap around pulling rod [m]
6.425E−010
Reduction factor spring stiffness in borehole [−]
5.000E−003
Density of bore fluid [kg/m3]
1,15E+06
Density of water [kg/m3]
1,00E+06
Fraction of pipe water filled [−]
5.000E−001
110
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Acceleration of gravity [m/s2]
0.000E+000
Resistance of tube/rod in bore fluid [N/m2]
0.000E+000
Friction coefficient of pipeline rollers [−]
0.000E+000
Pushing force at entrance of borepath [N]
0.000E+000
Output Summary
Upward force of pipe in borefluid [N/m]
0.000E+000
Upward force of pulling rod in borefluid [N/m]
−0.000E+000
Length of borepath [m]
3,14E+05
Length of pipe line in borepath [m]
3,14E+05
Maximum moment [Nm]
−1.016E+004
Minimum moment [Nm]
−2.624E+006
Maximum Soil reaction (without pulling) [N/m]
1,65E+07
Soil reaction head of pipe (without pulling) [N/m]
1,65E+07
Maximum borehole wall penetration of pipe (without pulling) [m]
−1.266E−001
Maximum borehole wall penetration of rod (without pulling) [m]
0.000E+000
111
Nieuwe boortechnieken kleine infra
geometric linear simulation, without gap
120Annex 3.1.5
Abaqus FEM & Analytical solution
Analytical solution
L1=0 m, L2=310 m, L3=0 m, R=1.21e+003
100
y-position borepath
[m] borepath [m]
y-position
EI=3.134E+009 Nm^2, k=1.300E+005 N/m^2
80
120
60
100
40
80
20
60
0
40
-20
20
-40
0
-60
-20
-80
-40
geometric linear simulation, without gap
Analytical solution
0
50
100
-60
200
150
x-position borepath [m]
250
300
-80
0
50
100
200
150
x-position borepath [m]
250
300
20000
geometric linear simulation, without gap
Analytical solution
soil spring reaction
[N/m]reaction [N/m]
soil spring
15000
20000
geometric linear simulation, without gap
Analytical solution
10000
15000
5000
10000
0
5000
5000
0 0
50
100
150
200
distance [m]
250
300
350
112
5000
0
50
100
150
200
250
300
350
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
6
0
x 10
geometric linear simulation, without gap
Analytical solution
-0.5
0
6
x 10
geometric linear simulation, without gap
Analytical solution
moment [Nm] moment [Nm]
-1
-0.5
-1.5
-1
-2
-1.5
-2.5
-2
-3
-2.5
-3
0
50
100
150
200
distance [m]
250
300
350
0
50
100
150
200
distance [m]
250
300
350
250
300
350
0.04
displacement normal
to borepath
[m]
displacement
normal
to borepath [m]
0.02
0
0.04
-0.02
0.02
-0.04
0
-0.06
-0.02
-0.08
-0.04
-0.1
-0.06
-0.12
-0.08
-0.14
-0.1
geometric linear simulation, without gap
Analytical solution
-0.16
-0.12 0
-0.14
-0.16
50
100
150
200
distance [m]
geometric linear simulation, without gap
Stieltjesweg 2, NL 2628 CK DELFT
Telephone 31 (0) 15 269 35 00
Analytical
solution
P.O.Box 69, NL 2600 AB DELFT
Telefax
31 (0) 15 261 08 21
0
50
100
150
200
250
113
Homepage:
www.geodelft.nl
300
date
2007-12-19
350
drw.
prk
ctr.
y-position borepath
[m] borepath [m]
y-position
Nieuwe boortechnieken kleine infra
geometric linear simulation, without gap
120Annex 3.1.6
Abaqus FEM & Analytical solution
geometric linear simulation, with gap
L1=0 m, L2=310 m, L3=0 m, R=1.21e+003
geometric nonlinear simulation, without gap
100
EI=3.134E+009 Nm^2, k=1.300E+005 N/m^2
geometric nonlinear simulation, with gap
Analytical solution
80
geometric
linear simulation, without gap
120
60
geometric linear simulation, with gap
geometric nonlinear simulation, without gap
100
40
geometric nonlinear simulation, with gap
Analytical solution
80
20
60
0
40
-20
20
-40
0
-60
-20
-80
-40
0
50
200
100
150
x-position borepath [m]
-60
250
300
-80
0
50
100
200
150
x-position borepath [m]
250
300
20000
geometric linear simulation, without gap
geometric linear simulation, with gap
geometric nonlinear simulation, without gap
geometric nonlinear simulation, with gap
Analytical solution
geometric linear simulation, without gap
geometric linear simulation, with gap
geometric nonlinear simulation, without gap
geometric nonlinear simulation, with gap
Analytical solution
soil spring reaction
[N/m]reaction [N/m]
soil spring
15000
20000
10000
15000
5000
10000
0
5000
-5000
0 0
50
100
150
200
distance [m]
250
300
350
114
-5000
0
50
100
150
200
250
300
350
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
6
0
-0.5
0
x 10
6
x 10
moment [Nm] moment [Nm]
-1
-0.5
-1.5
geometric linear simulation, without gap
geometric linear simulation, with gap
geometric nonlinear simulation, without gap
geometric nonlinear simulation, with gap
Analytical solution
geometric linear simulation, without gap
geometric linear simulation, with gap
geometric nonlinear simulation, without gap
geometric nonlinear simulation, with gap
Analytical solution
-1
-2
-1.5
-2.5
-2
-3
-2.5
-3
0
50
100
150
200
distance [m]
250
300
350
0
50
100
150
200
distance [m]
250
300
350
300
350
0.15
displacement normal
to borepath
[m]
displacement
normal
to borepath [m]
0.1
0.15
0.05
0.1
0
0.05
-0.05
0
-0.1
-0.05
-0.15
-0.1
-0.2
-0.15
-0.25
0
-0.2
-0.25
0
geometric linear simulation, without gap
geometric linear simulation, with gap
geometric nonlinear simulation, without gap
geometric nonlinear simulation, with gap
Analytical solution
geometric linear simulation, without gap
50
100 simulation,
150with gap 200
250
geometric
linear
distance
[m]
geometric nonlinear simulation, without gap
geometric nonlinear simulation, with gap
Stieltjesweg 2, NL 2628 CK DELFT
Telephone 31 (0) 15 269 35 00
Analytical
solution
P.O.Box 69, NL 2600 AB DELFT
Telefax
31 (0) 15 261 08 21
50
100
150
200
250
115
Homepage:
www.geodelft.nl
300
date
2007-12-19
350
drw.
prk
ctr.
Nieuwe boortechnieken kleine infra
Appendix 3.2
Results for a simulation with a circular arc and added straight section
of 0, 10, 20, 40, 60, 80 and 100 m for the situation without gap.
Annex. 3.2.1 Abaqus FEM pipeline simulation
Simulation Input Parameters
XY data Inputfile name
−
L1 [m]
200
L2 [m]
310
L3 [m]
100
R [m]
1210
Symmetric geometry
no
Number of elements
200
Number of elements in pipe
200
Geometric Nonlinear Simulation
yes
Left BC (yes) or Middle BC (no)
yes
Pipe outer diameter [m]
1,21E+03
Pipe wall thickness [m]
2.270E−002
Density pipe [kg/m3]
7,85E+06
Youngs modulus pipe [N/m2]
2,10E+14
Poissons ratio pipe [−]
3.000E−001
Pulling rod outer diameter [m]
1.250E−001
Pulling rod wall thickness [m]
6.250E−002
Density pulling rod material [kg/m3]
7,85E+06
Youngs modulus pulling rod material [N/m2]
2,10E+14
Poissons ratio pulling rod material [−]
3.000E−001
Spring Stiffness soil−pipe [N/m2]
1,30E+08
Friction factor soil−pipe [−]
2.000E−001
gap around pipe [m]
1.000E−010
Spring Stiffness soil−pulling rod [N/m2]
1,30E+06
Friction factor soil−pulling rod [−]
2.000E−001
gap around pulling rod [m]
6.425E−010
Reduction factor spring stiffness in borehole [−]
5.000E−003
116
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Density of bore fluid [kg/m3]
1,15E+06
Density of water [kg/m3]
1,00E+06
Fraction of pipe water filled [−]
5.000E−001
Acceleration of gravity [m/s2]
0.000E+000
Resistance of tube/rod in bore fluid [N/m2]
0.000E+000
Friction coefficient of pipeline rollers [−]
0.000E+000
Pushing force at entrance of borepath [N]
0.000E+000
Output Summary
Upward force of pipe in borefluid [N/m]
0.000E+000
Upward force of pulling rod in borefluid [N/m]
−0.000E+000
Length of borepath [m]
6,17E+05
Length of pipe line in borepath [m]
6,17E+05
Maximum moment [Nm]
8,56E+07
Minimum moment [Nm]
−2.675E+006
Maximum Soil reaction (without pulling) [N/m]
2,68E+06
Soil reaction head of pipe (without pulling) [N/m]
2,28E+04
Maximum borehole wall penetration of pipe (without pulling) [m]
−2.064E−002
Maximum borehole wall penetration of rod (without pulling) [m]
0.000E+000
117
Nieuwe boortechnieken kleine infra
250
no gap, 0 m leiding voorbij bocht
Annex 3.2.2
Abaqus
FEM,voorbij
Simulations
with linear k, without gap
no gap,
10 m leiding
bocht
no gap, 20
leiding voorbij
bocht
m,m
R=1200
m, EI=3.13e+009
kNm^2, k=130000 kN/m^2
200L1=200 m, L2=310
no0gap,
40 mmleiding voorbij bocht
L3 varied from
to 100
y-position borepath
[m] borepath [m]
y-position
150
250
100
200
50
150
no gap, 60 m leiding voorbij bocht
no gap, 80 m leiding voorbij bocht
nogap,
gap,0100
m leiding
voorbij
bocht
no
m leiding
voorbij
bocht
no gap, 10 m leiding voorbij bocht
no gap, 20 m leiding voorbij bocht
no gap, 40 m leiding voorbij bocht
no gap, 60 m leiding voorbij bocht
no gap, 80 m leiding voorbij bocht
no gap, 100 m leiding voorbij bocht
1000
-50
50
-100
0
-150
-50
-100 0
200
100
400
300
x-position borepath [m]
500
600
-150
0
200
100
400
300
x-position borepath [m]
500
600
20000
no gap, 0 m leiding voorbij bocht
no gap, 10 m leiding voorbij bocht
no gap, 20 m leiding voorbij bocht
no gap, 40 m leiding voorbij bocht
no gap, 60 m leiding voorbij bocht
no gap, 80 m leiding voorbij bocht
nogap,
gap,0100
m leiding
voorbij
bocht
no
m leiding
voorbij
bocht
no gap, 10 m leiding voorbij bocht
no gap, 20 m leiding voorbij bocht
no gap, 40 m leiding voorbij bocht
no gap, 60 m leiding voorbij bocht
no gap, 80 m leiding voorbij bocht
no gap, 100 m leiding voorbij bocht
soil spring reaction
[kN/m]
soil spring
reaction [kN/m]
15000
20000
10000
15000
5000
10000
0
5000
-5000
0 0
100
200
300
400
distance [m]
500
600
700
118
-5000
0
100
200
300
400
500
600
700
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
6
0.5
x 10
no gap, 0 m leiding voorbij bocht
no gap, 10 m leiding voorbij bocht
no gap, 20 m leiding voorbij bocht
no gap, 40 m leiding voorbij bocht
no gap, 60 m leiding voorbij bocht
no gap, 80 m leiding voorbij bocht
no gap, 0
100
m leiding
voorbij
bocht
m leiding
voorbij
bocht
no gap, 10 m leiding voorbij bocht
no gap, 20 m leiding voorbij bocht
no gap, 40 m leiding voorbij bocht
no gap, 60 m leiding voorbij bocht
no gap, 80 m leiding voorbij bocht
no gap, 100 m leiding voorbij bocht
0
6
moment [kNm]moment [kNm]
0.5
-0.5
x 10
0
-1
-0.5
-1.5
-1
-2
-1.5
-2.5
-2
-3
0
100
200
300
400
distance [m]
500
600
700
0
100
200
300
400
distance [m]
500
600
700
600
700
-2.5
-3
0.04
displacement normal
to borepath
[m]
displacement
normal
to borepath [m]
0.02
0
0.04
-0.02
0.02
-0.04
0
-0.06
-0.02
-0.08
-0.04
-0.1
-0.06
-0.12
-0.08
-0.14
-0.1
0
-0.12
-0.14
0
no gap, 0 m leiding voorbij bocht
no gap, 10 m leiding voorbij bocht
no gap, 20 m leiding voorbij bocht
no gap, 40 m leiding voorbij bocht
no gap, 60 m leiding voorbij bocht
no gap, 80 m leiding voorbij bocht
100
m leiding
voorbij
bocht
no gap, 0
m leiding
voorbij
bocht
no gap, 10 m leiding voorbij bocht
100
200 voorbij bocht
300
400
500
no
gap, 20 m leiding
no gap, 40 m leiding voorbij bochtdistance [m]
no gap, 60 m leiding voorbij bocht
no gap, 80 m leiding voorbij bocht
Stieltjesweg 2, NL 2628 CK DELFT
Telephone 31 (0) 15 269 35 00
no gap, 100
m leiding voorbij bocht
P.O.Box 69, NL 2600 AB DELFT
Telefax
31 (0) 15 261 08 21
100
200
300
400
500
119
Homepage:
www.geodelft.nl
600
date
2007-12-19
700
drw.
prk
ctr.
Nieuwe boortechnieken kleine infra
Appendix 3.3
Results for a simulation with a circular arc and added straight section
of 0, 10, 20, 40, 60, 80 and 100 m for the situation with 0.1 m gap.
Annex 3.3.1 Abaqus FEM pipeline simulation
Simulation Input Parameters
XY data Inputfile name
−
L1 [m]
200
L2 [m]
310
L3 [m]
100
R [m]
1210
Symmetric geometry
no
Number of elements
200
Number of elements in pipe
200
Geometric Nonlinear Simulation
yes
Left BC (yes) or Middle BC (no)
yes
Pipe outer diameter [m]
1,21E+03
Pipe wall thickness [m]
2.270E−002
Density pipe [kg/m3]
7,85E+06
Youngs modulus pipe [N/m2]
2,10E+14
Poissons ratio pipe [−]
3.000E−001
Pulling rod outer diameter [m]
1.250E−001
Pulling rod wall thickness [m]
6.250E−002
Density pulling rod material [kg/m3]
7,85E+06
Youngs modulus pulling rod material [N/m2]
2,10E+14
Poissons ratio pulling rod material [−]
3.000E−001
Spring Stiffness soil−pipe [N/m2]
1,30E+08
Friction factor soil−pipe [−]
2.000E−001
gap around pipe [m]
1.000E−001
Spring Stiffness soil−pulling rod [N/m2]
1,30E+06
Friction factor soil−pulling rod [−]
2.000E−001
gap around pulling rod [m]
6.425E−010
Reduction factor spring stiffness in borehole [−]
5.000E−003
120
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Density of bore fluid [kg/m3]
1,15E+06
Density of water [kg/m3]
1,00E+06
Fraction of pipe water filled [−]
5.000E−001
Acceleration of gravity [m/s2]
0.000E+000
Resistance of tube/rod in bore fluid [N/m2]
0.000E+000
Friction coefficient of pipeline rollers [−]
0.000E+000
Pushing force at entrance of borepath [N]
0.000E+000
Output Summary
Upward force of pipe in borefluid [N/m]
0.000E+000
Upward force of pulling rod in borefluid [N/m]
−0.000E+000
Length of borepath [m]
6,17E+05
Length of pipe line in borepath [m]
6,17E+05
Maximum moment [Nm]
3,66E+07
Minimum moment [Nm]
−2.653E+006
Maximum Soil reaction (without pulling) [N/m]
−1.295E+003
Soil reaction head of pipe (without pulling) [N/m]
3,64E+04
Maximum borehole wall penetration of pipe (without pulling) [m]
9.462E−003
Maximum borehole wall penetration of rod (without pulling) [m]
0.000E+000
121
Nieuwe boortechnieken kleine infra
250
gap, 0 m leiding voorbij bocht
Annex 3.3.2 gap,
Abaqus
Simulations
10 mFEM,
leiding
voorbij bochtwith linear k, with 0.1 m gap
gap,
20
m
leiding
voorbij
bocht
L1=200
m,
L2=310
m,
R=1200
m, EI=3.13e+009
Nm^2, k=1.30e+005 N/m^2
200
gap,
40
m
leiding
voorbij
bocht
L3 varied from 0 to 100 m
y-position borepath
[m] borepath [m]
y-position
150
250
100
200
50
150
gap, 60 m leiding voorbij bocht
gap, 80 m leiding voorbij bocht
gap,0100
m leiding
voorbij
bocht
gap,
m leiding
voorbij
bocht
gap, 10 m leiding voorbij bocht
gap, 20 m leiding voorbij bocht
gap, 40 m leiding voorbij bocht
gap, 60 m leiding voorbij bocht
gap, 80 m leiding voorbij bocht
gap, 100 m leiding voorbij bocht
1000
-50
50
-100
0
-150
-50
-100 0
200
100
400
300
x-position borepath [m]
500
600
-150
0
200
100
400
300
x-position borepath [m]
500
600
20000
gap, 0 m leiding voorbij bocht
gap, 10 m leiding voorbij bocht
gap, 20 m leiding voorbij bocht
gap, 40 m leiding voorbij bocht
gap, 60 m leiding voorbij bocht
gap, 80 m leiding voorbij bocht
gap,0100
m leiding
voorbij
bocht
gap,
m leiding
voorbij
bocht
gap, 10 m leiding voorbij bocht
gap, 20 m leiding voorbij bocht
gap, 40 m leiding voorbij bocht
gap, 60 m leiding voorbij bocht
gap, 80 m leiding voorbij bocht
gap, 100 m leiding voorbij bocht
soil spring reaction
[kN/m]
soil spring
reaction [kN/m]
15000
20000
10000
15000
5000
10000
0
5000
-5000
0 0
100
200
300
400
distance [m]
500
600
700
122
-5000
0
100
200
300
400
500
600
700
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
6
0.5
x 10
gap, 0 m leiding voorbij bocht
gap, 10 m leiding voorbij bocht
gap, 20 m leiding voorbij bocht
gap, 40 m leiding voorbij bocht
gap, 60 m leiding voorbij bocht
gap, 80 m leiding voorbij bocht
gap, 0
100
m leiding
voorbij
bocht
m leiding
voorbij
bocht
gap, 10 m leiding voorbij bocht
gap, 20 m leiding voorbij bocht
gap, 40 m leiding voorbij bocht
gap, 60 m leiding voorbij bocht
gap, 80 m leiding voorbij bocht
gap, 100 m leiding voorbij bocht
0
6
moment [kNm]moment [kNm]
0.5
-0.5
x 10
0
-1
-0.5
-1.5
-1
-2
-1.5
-2.5
-2
-3
0
100
200
300
400
distance [m]
500
600
700
0
100
200
300
400
distance [m]
500
600
700
600
700
-2.5
-3
0.15
displacement normal
to borepath
[m]
displacement
normal
to borepath [m]
0.1
0.15
0.05
0.1
0
0.05
-0.05
0
-0.1
-0.05
-0.15
-0.1
-0.2
-0.15
-0.25
0
-0.2
-0.25
0
gap, 0 m leiding voorbij bocht
gap, 10 m leiding voorbij bocht
gap, 20 m leiding voorbij bocht
gap, 40 m leiding voorbij bocht
gap, 60 m leiding voorbij bocht
gap, 80 m leiding voorbij bocht
100
m leiding
voorbij
bocht
gap, 0
m leiding
voorbij
bocht
gap, 10 m leiding voorbij bocht
10020 m leiding200
400
500
gap,
voorbij bocht 300
gap, 40 m leiding voorbij bocht distance [m]
gap, 60 m leiding voorbij bocht
gap, 80 m leiding voorbij bocht
Stieltjesweg 2, NL 2628 CK DELFT
Telephone 31 (0) 15 269 35 00
gap, 100 m
leiding voorbij bocht
P.O.Box 69, NL 2600 AB DELFT
Telefax
31 (0) 15 261 08 21
100
200
300
400
500
123
Homepage:
www.geodelft.nl
600
date
2007-12-19
700
drw.
prk
ctr.
Nieuwe boortechnieken kleine infra
Appendix 3.4
Pullback simulation in half circle geometry with friction only.
Annex. 3.4.1 Abaqus FEM pipeline simulation
Simulation Input Parameters
XY data Inputfile name
−
L1 [m]
0
L2 [m]
1210
L3 [m]
0
R [m]
1210
Symmetric geometry
yes
Number of elements
200
Number of elements in pipe
200
Geometric Nonlinear Simulation
yes
Left BC (yes) or Middle BC (no)
no
Pipe outer diameter [m]
1,21E+03
Pipe wall thickness [m]
2.270E−002
Density pipe [kg/m3]
7,85E+06
Youngs modulus pipe [N/m2]
2,10E+14
Poissons ratio pipe [−]
3.000E−001
Pulling rod outer diameter [m]
1.250E−001
Pulling rod wall thickness [m]
6.250E−002
Density pulling rod material [kg/m3]
7,85E+06
Youngs modulus pulling rod material [N/m2]
2,10E+14
Poissons ratio pulling rod material [−]
3.000E−001
Spring Stiffness soil−pipe [N/m2]
1,30E+08
Friction factor soil−pipe [−]
2.000E−001
gap around pipe [m]
1.000E−001
Spring Stiffness soil−pulling rod [N/m2]
1,30E+06
Friction factor soil−pulling rod [−]
2.000E−001
gap around pulling rod [m]
6.425E−010
Reduction factor spring stiffness in borehole [−]
1.000E−003
Density of bore fluid [kg/m3]
1,15E+06
124
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Density of water [kg/m3]
1,00E+06
Fraction of pipe water filled [−]
5.000E−001
Acceleration of gravity [m/s2]
0.000E+000
Resistance of tube/rod in bore fluid [N/m2]
0.000E+000
Friction coefficient of pipeline rollers [−]
0.000E+000
Pushing force at entrance of borepath [N]
0.000E+000
Output Summary
Upward force of pipe in borefluid [N/m]
0.000E+000
Upward force of pulling rod in borefluid [N/m]
−0.000E+000
Friction force of pipe in borefluid [N/m]
0.000E+000
Friction force of pulling rod in borefluid [N/m]
0.000E+000
Total pipeline rollers friction [N]
0.000E+000
Length of borepath [m]
3,80E+06
Length of pipe line in borepath [m]
3,80E+06
Maximum moment [Nm]
−5.485E+005
Minimum moment [Nm]
−2.608E+006
Maximum pulling force [N]
5,36E+07
Maximum Soil reaction (without pulling) [N/m]
6,16E+06
Maximum Soil reaction (during pulling) [N/m]
6,22E+06
Soil reaction head of pipe (without pulling) [N/m]
6,14E+06
Soil reaction head of pipe (during pulling) [N/m]
6,14E+06
Maximum borehole wall penetration of pipe (without pulling) [m]
−4.727E−002
Maximum borehole wall penetration of pipe (during pulling) [m]
−4.777E−002
Maximum borehole wall penetration of rod (without pulling) [m]
0.000E+000
Maximum borehole wall penetration of rod (during pulling) [m]
0.000E+000
125
Nieuwe boortechnieken kleine infra
6
x 10
-0.5
Annex 3.4.2 Abaqus FEM pipeline simulation
simulation: Bijl3_4_half_circle_001
Pipeline pulled in for 100 %
2000
6000
6
-1 x 10
-0.5
5000
7000
2000
1000
1500
500
1000
0
500
-500
soil spring reaction
[N/m]reaction [N/m]
soil spring
without pulling
during pulling
moment [Nm] moment [Nm]
-1.5
-1
-2
-1.5
-2.5
-2
0
-1000
-500 -1000
-500
0
500
x-position borepath [m]
1000
-3
-2.5 0
1000
2000
3000
distance [m]
4000
-1000
-500
0
500
x-position borepath [m]
-3
1000
0
4
2000
4000
1000
3000
0
2000
-1000
1000
-2000
0
-3000
-1000
2000
3000
distance [m]
4000
4
-3
x 10
7
5
length changelength
of beam
[m] of beam [m]
change
x 10
4.5
5.5
54
3.5
4.5
43
2.5
3.5
32
1.5
2.5
1.5
1000
2000
3000
distance [m]
4000
6
4
5
3
4
2
3
1
2
0
1
-1
without pulling
during pulling
0
1000
0
126
0
0
1.2
6
0
-3000
x 10
7
5
21
1000
-3
x 10
5.5
pulling force [N]
pulling force [N]
3000
5000
-2000
-1000
1
4000
6000
1000
2000
3000
distance [m]
4000
horizontal displacement
along borepath
[m] borepath [m]
horizontal displacement
along
y-position borepath
[m] borepath [m]
y-position
1500
7000
without pulling
during pulling
1
1.2
0.8
1
0.6
0.8
0.4
0.6
0.2
0.4
0
0.2
-0.2
0
without pulling
during pulling
2000
3000
4000
-1
0
1000
2000
3000
4000
-0.2
0
0
0
0.15
without pulling
during pulling
6000
soil spring reaction
[N/m]reaction [N/m]
soil spring
5000
7000
4000
without pulling
during pulling
4000
6000
3000
5000
2000
4000
1000
3000
0
2000
-1000
1000
-2000
0
-3000
-1000 0
1000
2000
3000
distance [m]
4000
displacement displacement
normal to borepath
normal[m]
to borepath [m]
0.1
0.15
0.05
0.1
0
0.05
-0.05
0
-0.1
-0.05
-0.15
without pulling
during pulling
-0.1
-0.2
0
1000
-0.15
2000
3000
distance [m]
-2000
4000
4000
-3000
0
1000
2000
3000
distance [m]
0.02
1
0.01
1.2
0.02
0.8
0
1
0.6
0.8
0.4
0.6
0.2
0.4
0
without pulling
during pulling
0.2
0
1000
0
2000
3000
distance [m]
4000
-0.2
1000
2000
3000
1000
4000
2000
3000
distance [m]
4000
0.01
-0.01
0
-0.02
-0.01
-0.03
-0.02
-0.04
-0.03
-0.05
DELFT
P.O.Box 69, NL 2600 AB DELFT
0
0
during pulling
0
1000
-0.04
without pulling
Stieltjesweg 2, NL 2628 CK
during pulling
4000
-0.2
4000
1.2
-0.2
4000
without pulling
during pulling
borewall penetration
[m]
borewall
penetration [m]
0
7000
horizontal displacement
along borepath
[m] borepath [m]
horizontal displacement
along
0
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
2000
3000
distance [m]
Telephone 31 (0) 15 269 35 00
Telefax
31 (0) 15 261 08 21
-0.05
0
1000
127
Homepage:
during
pulling
date
2007-12-19
3000
4000
www.geodelft.nl
2000
4000
drw.
prk
ctr.
Nieuwe boortechnieken kleine infra
Appendix 3.5
Pullback simulation in half circle geometry with friction and
cohesion effects
Annex. 3.5.1 Abaqus FEM pipeline simulation
Simulation Input Parameters
XY data Inputfile name
−
L1 [m]
0
L2 [m]
1210
L3 [m]
0
R [m]
1210
Symmetric geometry
yes
Number of elements
200
Number of elements in pipe
200
Geometric Nonlinear Simulation
yes
Left BC (yes) or Middle BC (no)
no
Pipe outer diameter [m]
1,21E+03
Pipe wall thickness [m]
2.270E−002
Density pipe [kg/m3]
7,85E+06
Youngs modulus pipe [N/m2]
2,10E+14
Poissons ratio pipe [−]
3.000E−001
Pulling rod outer diameter [m]
1.250E−001
Pulling rod wall thickness [m]
6.250E−002
Density pulling rod material [kg/m3]
7,85E+06
Youngs modulus pulling rod material [N/m2]
2,10E+14
Poissons ratio pulling rod material [−]
3.000E−001
Spring Stiffness soil−pipe [N/m2]
1,30E+08
Friction factor soil−pipe [−]
2.000E−001
gap around pipe [m]
1.000E−001
Spring Stiffness soil−pulling rod [N/m2]
1,30E+06
Friction factor soil−pulling rod [−]
2.000E−001
gap around pulling rod [m]
6.425E−010
Reduction factor spring stiffness in borehole [−]
1.000E−003
128
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Density of bore fluid [kg/m3]
1,15E+06
Density of water [kg/m3]
1,00E+06
Fraction of pipe water filled [−]
5.000E−001
Acceleration of gravity [m/s2]
0.000E+000
Resistance of tube/rod in bore fluid [N/m2]
5,00E+04
Friction coefficient of pipeline rollers [−]
0.000E+000
Pushing force at entrance of borepath [N]
0.000E+000
Output Summary
Upward force of pipe in borefluid [N/m]
0.000E+000
Upward force of pulling rod in borefluid [N/m]
−0.000E+000
Friction force of pipe in borefluid [N/m]
1,90E+05
Friction force of pulling rod in borefluid [N/m]
1,96E+04
Total pipeline rollers friction [N]
0.000E+000
Length of borepath [m]
3,80E+06
Length of pipe line in borepath [m]
3,80E+06
Maximum moment [Nm]
−5.485E+005
Minimum moment [Nm]
−2.608E+006
Maximum pulling force [N]
1,05E+09
Maximum Soil reaction (without pulling) [N/m]
6,16E+06
Maximum Soil reaction (during pulling) [N/m]
6,21E+06
Soil reaction head of pipe (without pulling) [N/m]
6,14E+06
Soil reaction head of pipe (during pulling) [N/m]
6,14E+06
Maximum borehole wall penetration of pipe (without pulling) [m]
−4.727E−002
Maximum borehole wall penetration of pipe (during pulling) [m]
−4.768E−002
Maximum borehole wall penetration of rod (without pulling) [m]
0.000E+000
Maximum borehole wall penetration of rod (during pulling) [m]
0.000E+000
129
Nieuwe boortechnieken kleine infra
6
x 10
-0.5
Annex 3.5.2 Abaqus FEM pipeline simulation
simulation: Bijl3_5_half_circle_001
Pipeline pulled in for 100 %
2000
6000
6
5000
7000
-1 x 10
-0.5
1500
moment [Nm] moment [Nm]
1500
500
1000
0
500
-500
soil spring reaction
[N/m]reaction [N/m]
soil spring
without pulling
during pulling
2000
1000
-1.5
-1
-2
-1.5
-2.5
-2
0
-1000
-500 -1000
-500
0
500
x-position borepath [m]
-3
-2.5 0
1000
1000
2000
3000
distance [m]
4000
4000
6000
3000
5000
2000
4000
1000
3000
0
2000
-1000
1000
-2000
0
-3000
-1000
-2000
-1000
-1000
-500
0
500
x-position borepath [m]
-3
1000
0
1000
2000
3000
distance [m]
4000
-3000
0
5
length changelength
of beam
[m] of beam [m]
change
10
5
x 10
12
8
10
6
8
4
6
2
4
0
2
0
1000
2000
3000
distance [m]
4000
0.12
1.2
0.1
1
0.12
0.08
0.1
0.06
0.08
0.04
0.06
0.02
0.04
0
without pulling
during pulling
0.02
-0.02
0
1000
0
130
0
0
1000
2000
3000
distance [m]
4000
horizontal displacement
borepathalong
[m] borepath [m]
horizontal along
displacement
x 10
12
pulling force [N]
pulling force [N]
y-position borepath
[m] borepath [m]
y-position
7000
without pulling
during pulling
1.2
0.8
1
0.6
0.8
0.4
0.6
0.2
0.4
0
0.2
-0.2
0
without pulling
during pulling
2000
3000
4000
-0.02
0
1000
2000
3000
4000
-0.2
0
0
0
0.15
without pulling
during pulling
6000
soil spring reaction
[N/m]reaction [N/m]
soil spring
5000
7000
4000
without pulling
during pulling
4000
6000
3000
5000
2000
4000
1000
3000
0
2000
-1000
1000
-2000
0
-3000
-1000 0
1000
2000
3000
distance [m]
4000
displacement normal
to borepath
[m]
displacement
normal
to borepath [m]
0.1
0.15
0.05
0.1
0
0.05
-0.05
0
-0.1
-0.05
-0.15
without pulling
during pulling
-0.1
-0.2
0
1000
-0.15
2000
3000
distance [m]
-2000
4000
4000
4000
-3000
0
1000
2000
3000
distance [m]
-0.2
4000
1.2
0.03
1
0.02
1.2
0.8
0.03
0.01
1
0.6
0.8
0.4
0.6
0.2
0.4
0
without pulling
during pulling
0.2
-0.2
0
1000
0
-0.2
4000
without pulling
during pulling
borewall penetration
[m]penetration [m]
borewall
0
7000
horizontal displacement
borepathalong
[m] borepath [m]
horizontal along
displacement
0
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
2000
3000
distance [m]
4000
1000
2000
3000
1000
4000
0.01
-0.01
0
-0.02
-0.01
-0.03
-0.02
-0.04
-0.03
-0.05
during pulling
0
1000
-0.04
4000
2000
3000
distance [m]
0.02
0
without pulling
Stieltjesweg 2, NL 2628 CK DELFT
during pulling
P.O.Box 69, NL 2600 AB DELFT
0
0
2000
3000
distance [m]
Telephone 31 (0) 15 269 35 00
Telefax
31 (0) 15 261 08 21
-0.05
0
1000
131
Homepage:
during
pulling
www.geodelft.nl
2000
4000
date
2007-12-19
3000
4000
drw.
prk
ctr.
Nieuwe boortechnieken kleine infra
Appendix 3.6
Pullback simulation in half circle geometry with friction, cohesion and
gravity effects.
Annex. 3.6.1 Abaqus FEM pipeline simulation
Simulation Input Parameters
XY data Inputfile name
−
L1 [m]
0
L2 [m]
1210
L3 [m]
0
R [m]
1210
Symmetric geometry
yes
Number of elements
200
Number of elements in pipe
200
Geometric Nonlinear Simulation
yes
Left BC (yes) or Middle BC (no)
no
Pipe outer diameter [m]
1,21E+03
Pipe wall thickness [m]
2.270E−002
Density pipe [kg/m3]
7,85E+06
Youngs modulus pipe [N/m2]
2,10E+14
Poissons ratio pipe [−]
3.000E−001
Pulling rod outer diameter [m]
1.250E−001
Pulling rod wall thickness [m]
6.250E−002
Density pulling rod material [kg/m3]
7,85E+06
Youngs modulus pulling rod material [N/m2]
2,10E+14
Poissons ratio pulling rod material [−]
3.000E−001
Spring Stiffness soil−pipe [N/m2]
1,30E+08
Friction factor soil−pipe [−]
2.000E−001
gap around pipe [m]
1.000E−001
Spring Stiffness soil−pulling rod [N/m2]
1,30E+06
Friction factor soil−pulling rod [−]
2.000E−001
gap around pulling rod [m]
6.425E−010
Reduction factor spring stiffness in borehole [−]
1.000E−003
132
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Density of bore fluid [kg/m3]
1,15E+06
Density of water [kg/m3]
1,00E+06
Fraction of pipe water filled [−]
5.000E−001
Acceleration of gravity [m/s2]
9,81E+03
Resistance of tube/rod in bore fluid [N/m2]
5,00E+04
Friction coefficient of pipeline rollers [−]
0.000E+000
Pushing force at entrance of borepath [N]
0.000E+000
Output Summary
Upward force of pipe in borefluid [N/m]
1,23E+06
Upward force of pulling rod in borefluid [N/m]
−8.066E+002
Friction force of pipe in borefluid [N/m]
1,90E+05
Friction force of pulling rod in borefluid [N/m]
1,96E+04
Total pipeline rollers friction [N]
0.000E+000
Length of borepath [m]
3,80E+06
Length of pipe line in borepath [m]
3,80E+06
Maximum moment [Nm]
−5.483E+005
Minimum moment [Nm]
−3.177E+006
Maximum pulling force [N]
3,02E+09
Maximum Soil reaction (without pulling) [N/m]
6,15E+06
Maximum Soil reaction (during pulling) [N/m]
6,15E+06
Soil reaction head of pipe (without pulling) [N/m]
6,13E+06
Soil reaction head of pipe (during pulling) [N/m]
6,13E+06
Maximum borehole wall penetration of pipe (without pulling) [m]
−4.724E−002
Maximum borehole wall penetration of pipe (during pulling) [m]
−4.723E−002
Maximum borehole wall penetration of rod (without pulling) [m]
0.000E+000
Maximum borehole wall penetration of rod (during pulling) [m]
0.000E+000
133
Nieuwe boortechnieken kleine infra
6
x 10
0
2000
without pulling
during pulling
-1
2000
1000
moment [Nm] moment [Nm]
y-position borepath
[m] borepath [m]
y-position
1500
6000
-0.5
6
x 10
0
1500
500
1000
0
500
-500
0
-1000
soil spring reaction
[N/m]reaction [N/m]
soil spring
Annex 3.6.2 Abaqus FEM pipeline simulation
simulation: Bijl3_6_half_circle_001
Pipeline pulled in for 100 %
8000
without pulling
during pulling
-0.5
-1.5
-1
-2
-1.5
-2.5
-2
-500 -1000
-500
0
500
x-position borepath [m]
-3
1000
-2.5
0
1000
2000
3000
distance [m]
4000
8000
4000
6000
2000
4000
0
2000
-2000
0
-4000
-2000
-6000
-4000
-1000
-1000
-500
0
500
x-position borepath [m]
-3
1000
0
1000
2000
3000
distance [m]
4000
-6000
0
6
x 10
0.6
3
1.4
1.2
0.5
6
length changelength
of beam
[m] of beam [m]
change
pulling force [N]
pulling force [N]
x 10
3.5
2.5
3
2
2.5
1.5
2
1
1.5
0.5
1
0
0
1000
0.5
2000
3000
distance [m]
4000
0.6
0.4
0.5
0.3
0.4
0.2
0.3
0.1
0.2
0
without pulling
during pulling
0.1
-0.1
0
1000
0
134
0
0
1000
2000
3000
distance [m]
4000
3000
4000
-0.1
0
1000
2000
3000
1.41
0.8
1.2
0.6
1
0.4
0.8
0.2
0.6
0.40
-0.2
0.2
-0.4
0
-0.2
without pulling
during pulling
2000
horizontal displacement
borepathalong
[m] borepath [m]
horizontal along
displacement
3.5
4000
-0.4
0
0
0
0.15
without pulling
during pulling
0.1
4000
8000
4000
without pulling
during pulling
6000
2000
4000
0
2000
-2000
0
-4000
-2000
-6000
0
-4000
1000
2000
3000
distance [m]
4000
displacement normal
to borepath
[m]
displacement
normal
to borepath [m]
soil spring reaction
[N/m]reaction [N/m]
soil spring
6000
0.15
0.05
0.1
0
0.05
-0.05
0
-0.1
-0.05
-0.15
without pulling
during pulling
-0.1
-0.2
0
-0.15
1000
2000
3000
distance [m]
4000
without pulling
during pulling
4000
4000
-6000
0
1000
-0.2
0
4000
1.4
0.04
1.2
0.03
1
1.4
0.02
0.04
0.8
1.2
0.6
1
0.4
0.8
0.2
0.6
0
0.4
-0.2
0.2
-0.4
0
0
without pulling
during pulling
1000
-0.2
4000
2000
3000
distance [m]
borewall penetration
[m]penetration [m]
borewall
0
8000
horizontal displacement
borepathalong
[m] borepath [m]
horizontal along
displacement
0
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
-0.4
0
2000
3000
distance [m]
2000
3000
2000
3000
distance [m]
4000
0.01
0.03
0
0.02
-0.01
0.01
-0.02
0
-0.03
-0.01
-0.04
-0.02
during pulling
4000
without pulling
Stieltjesweg 2, NL 2628 CK DELFT
during pulling
P.O.Box 69, NL 2600 AB DELFT
1000
1000
4000
-0.05
-0.03
0
1000
2000
3000
distance [m]
-0.04
Telephone 31 (0) 15 269 35 00
Telefax
31 (0) 15 261 08 21
-0.05
0
1000
135
Homepage:
during
pulling
www.geodelft.nl
2000
4000
date
2007-12-19
3000
4000
drw.
prk
ctr.
Nieuwe boortechnieken kleine infra
Appendix 3.7
Pullback simulation with drill pipe in 100 steps, without cohesion or
gravity effects.
Annex. 3.7.1 Abaqus FEM pipeline simulation
Simulation Input Parameters
XY data Inputfile name
−
L1 [m]
100
L2 [m]
150
L3 [m]
80
R [m]
1210
Symmetric geometry
yes
Number of elements
200
Number of elements in pipe
100
Geometric Nonlinear Simulation
yes
Left BC (yes) or Middle BC (no)
no
Pipe outer diameter [m]
1,21E+03
Pipe wall thickness [m]
2.270E−002
Density pipe [kg/m3]
7,85E+06
Youngs modulus pipe [N/m2]
2,10E+14
Poissons ratio pipe [−]
3.000E−001
Pulling rod outer diameter [m]
1.250E−001
Pulling rod wall thickness [m]
6.250E−002
Density pulling rod material [kg/m3]
7,85E+06
Youngs modulus pulling rod material [N/m2]
2,10E+14
Poissons ratio pulling rod material [−]
3.000E−001
Spring Stiffness soil−pipe [N/m2]
1,30E+08
Friction factor soil−pipe [−]
2.000E−001
gap around pipe [m]
1.000E−001
Spring Stiffness soil−pulling rod [N/m2]
1,30E+07
Friction factor soil−pulling rod [−]
2.000E−001
gap around pulling rod [m]
6.425E−001
Reduction factor spring stiffness in borehole [−]
1.000E−003
136
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Density of bore fluid [kg/m3]
1,15E+06
Density of water [kg/m3]
1,00E+06
Fraction of pipe water filled [−]
5.000E−001
Acceleration of gravity [m/s2]
0.000E+000
Resistance of tube/rod in bore fluid [N/m2]
0.000E+000
Friction coefficient of pipeline rollers [−]
0.000E+000
Pushing force at entrance of borepath [N]
0.000E+000
Output Summary
Upward force of pipe in borefluid [N/m]
0.000E+000
Upward force of pulling rod in borefluid [N/m]
−0.000E+000
Friction force of pipe in borefluid [N/m]
0.000E+000
Friction force of pulling rod in borefluid [N/m]
0.000E+000
Total pipeline rollers friction [N]
0.000E+000
Length of borepath [m]
6,62E+05
Length of pipe line in borepath [m]
3,31E+05
Maximum moment [Nm]
3,91E+08
Minimum moment [Nm]
−2.646E+006
Maximum pulling force [N]
2,69E+07
Maximum Soil reaction (without pulling) [N/m]
1,25E+06
Maximum Soil reaction (during pulling) [N/m]
1,25E+06
Soil reaction head of pipe (without pulling) [N/m]
5,18E+03
Soil reaction head of pipe (during pulling) [N/m]
5,03E+03
Maximum borehole wall penetration of pipe (without pulling) [m]
−9.515E−003
Maximum borehole wall penetration of pipe (during pulling) [m]
−9.540E−003
Maximum borehole wall penetration of rod (without pulling) [m]
0.000E+000
Maximum borehole wall penetration of rod (during pulling) [m]
1.483E−003
137
Nieuwe boortechnieken kleine infra
200
400
Annex 3.7.2 Abaqus FEM pipeline simulation
simulation: Bijl3_7_leiding_001
Pipeline pulled in for 1 %
200
400
100
300
0
200
-100
100
-200
0
-300
-100
-400
-200
-500
-300
0
0.4
200
-200
moment [Nm] moment [Nm]
y-position borepath
[m] borepath [m]
y-position
300
500
0.6
without pulling
during pulling
without pulling
during pulling
soil spring reaction
[N/m]reaction [N/m]
soil spring
500
0
-400
-200
-600
-400
-800
-600
-1000
-800
-1200
-200
0
200
x-position borepath [m]
0
200
-1000
400
600
distance [m]
0.6
0.2
0.4
0
0.2
-0.2
0
-0.4
-0.2
-0.6
-0.4
-0.8
800
0
-0.6
-400
-500
-1200
-200
0
200
x-position borepath [m]
0
200
400
600
distance [m]
-0.8
800
0
-5
35
2
-5
x 10
4
length changelength
of beam
[m] of beam [m]
change
40
30
pulling force [N]
pulling force [N]
1.2
35
25
30
20
25
15
20
10
15
5
0
200
5
600
400
distance [m]
800
0
2
-2
0
-4
-2
-6
-4
without pulling
during pulling
-8
-6
0
200
0
200
800
1
1.2
0.8
1
0.6
0.8
0.4
0.6
0.2
0.4
0
0.2
-0.2
0
0
without pulling
during pulling
138
0
600
400
distance [m]
horizontal displacement
borepathalong
[m] borepath [m]
horizontal along
displacement
4
40
10
0
x 10
400
600
800
-8
0
200
400
600
800
-0.2
0
0
0
without pulling
during pulling
0.04
0.6
0.2
0.4
0
0.2
-0.2
0
-0.4
-0.2
-0.6
-0.4
-0.8
800
without pulling
during pulling
0
200
-0.6
400
600
distance [m]
800
displacement normal
to borepath
[m]
displacement
normal
to borepath [m]
soil spring reaction
[N/m]reaction [N/m]
soil spring
0.4
0.03
0.05
0.02
0.04
0.01
0.03
0
0.02
-0.01
0.01
-0.02
0
-0.03
-0.01
-0.04
-0.02
without pulling
during pulling
-0.05
-0.03 0
200
400
600
distance [m]
-0.04
-0.8
800
0
200
400
600
distance [m]
-0.05
800
1.2
800
without pulling
during pulling
0
200
400
600
distance [m]
800
1
0.8
800
1
0.6
1
1.2
0.8
borewall penetration
[m]penetration [m]
borewall
0
0.05
0.6
horizontal displacement
borepathalong
[m] borepath [m]
horizontal along
displacement
0
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
1
0.6
0.8
0.4
0.6
0.2
0.4
0
without pulling
during pulling
0.2
-0.2
0
200
0
400
600
distance [m]
800
without pulling
Stieltjesweg 2, NL 2628 CK
during pulling
800
-0.2
DELFT
P.O.Box 69, NL 2600 AB DELFT
0
200
400
600
800
0.4
0.8
0.2
0.6
0
0.4
-0.2
0.2
-0.4
0
-0.6
-0.2
-0.8
-0.4
during pulling
-1
-0.6 0
200
600
400
distance [m]
-0.8
Telephone 31 (0) 15 269 35 00
Telefax
31 (0) 15 261 08 21
-1
0
200
139
Homepage:
during
pulling
www.geodelft.nl
400
600
800
date
2007-12-20
800
drw.
prk
ctr.
Nieuwe boortechnieken kleine infra
6
500
0
0.5
-0.5
moment [Nm] moment [Nm]
200
400
100
300
0
200
-100
100
-200
0
-300
-100
8000
6
x 10
without pulling
during pulling
soil spring reaction
[N/m]reaction [N/m]
soil spring
300
500
10000
without pulling
during pulling
Annex 3.7.3 Abaqus FEM pipeline simulation
simulation: Bijl3_7_leiding_030
Pipeline pulled in for 30 %
400
y-position borepath
[m] borepath [m]
y-position
x 10
0.5
0
-1
-0.5
-1.5
-1
-2
-1.5
-2.5
-400
-200
-2
-500
-300
-3
-200
0
200
x-position borepath [m]
0
200
-2.5
400
600
distance [m]
800
10000
6000
8000
4000
6000
2000
4000
0
2000
-2000
0
-4000
0
-2000
-400
-3
-200
0
200
x-position borepath [m]
4
x 10
4
800
-3
length changelength
of beam
[m] of beam [m]
change
x 10
7
5
3.5
2.5
3
2
2.5
1.5
2
1
1.5
0.5
0
200
0.5
600
400
distance [m]
800
6
4
5
3
4
2
3
1
2
0
1
-1
without pulling
during pulling
0
200
0
140
0
200
-4000
0
1.2
6
x 10
4
3
0
400
600
distance [m]
x 10
7
4
pulling force [N]
pulling force [N]
200
-3
3.5
1
0
0
600
400
distance [m]
800
horizontal displacement
borepathalong
[m] borepath [m]
horizontal along
displacement
-500
1
1.2
0.8
1
0.6
0.8
0.4
0.6
0.2
0.4
0
0.2
-0.2
0
0
without pulling
during pulling
400
600
800
-1
0
200
400
600
800
-0.2
0
0
0
without pulling
during pulling
0.6
800
10000
6000
without pulling
during pulling
8000
4000
6000
2000
4000
0
2000
-2000
0
-4000
0
200
-2000
400
600
distance [m]
800
0.5
0.7
displacement normal
to borepath
[m]
displacement
normal
to borepath [m]
soil spring reaction
[N/m]reaction [N/m]
soil spring
8000
0.4
0.6
0.3
0.5
0.2
0.4
0.1
0.3
0
0.2
-0.1
0.1
-0.2
0
without pulling
during pulling
-0.3
-0.1 0
200
400
600
distance [m]
-0.2
800
800
800
-4000
0
200
400
600
distance [m]
-0.3
800
1.2
0.02
1
0
1.2
0.8
0.02
-0.02
borewall penetration
[m]penetration [m]
borewall
0
0.7
10000
horizontal displacement
borepathalong
[m] borepath [m]
horizontal along
displacement
0
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
1
0.6
0.8
0.4
0.6
0.2
0.4
0
without pulling
during pulling
0.2
-0.2
0
200
0
-0.2
400
600
distance [m]
800
200
400
600
without pulling
during pulling
0
200
800
-0.02
-0.06
-0.04
-0.08
-0.06
-0.1
-0.08
-0.12
-0.1
-0.14
during pulling
0
200
-0.12
800
400
600
distance [m]
0
-0.04
without pulling
Stieltjesweg 2, NL 2628 CK DELFT
during pulling
P.O.Box 69, NL 2600 AB DELFT
0
800
600
400
distance [m]
Telephone 31 (0) 15 269 35 00
Telefax
31 (0) 15 261 08 21
-0.14
0
200
141
Homepage:
during
pulling
www.geodelft.nl
400
600
800
date
2007-12-20
800
drw.
prk
ctr.
Nieuwe boortechnieken kleine infra
6
Annex 3.7.4 Abaqus FEM pipeline simulation
simulation: Bijl3_7_leiding_050
Pipeline pulled in for 50 %
400
300
500
1500
without pulling
during pulling
0
1000
6
x 10
0.5
-0.5
moment [Nm] moment [Nm]
200
400
100
300
0
200
-100
100
-200
0
-300
-100
-400
-200
1500
without pulling
during pulling
soil spring reaction
[N/m]reaction [N/m]
soil spring
500
y-position borepath
[m] borepath [m]
y-position
x 10
0.5
0
-1
-0.5
-1.5
-1
-2
-1.5
-2.5
-2
-500
-300
-3
-200
0
200
x-position borepath [m]
0
200
-2.5
400
600
distance [m]
800
500
1000
0
500
-500
0
-1000
-500
-1500
-1000
-400
-500
-3
-200
0
200
x-position borepath [m]
4
x 10
3
0
200
400
600
distance [m]
800
-1500
-3
x 10
4
1.2
2.5
4
x 10
3
-3
length changelength
of beam
[m] of beam [m]
change
x 10
43
pulling force [N]
pulling force [N]
2
2.5
1.5
2
1
1.5
0.5
1
0.5
0
200
400
600
distance [m]
800
0
200
32
1.5
2.5
21
0.5
1.5
10
-0.5
0.5
without pulling
during pulling
0
200
0
142
0
2.5
3.5
400
600
800
-0.5
400
600
distance [m]
800
horizontal displacement
borepathalong
[m] borepath [m]
horizontal along
displacement
3.5
0
0
1
1.2
0.8
1
0.6
0.8
0.4
0.6
0.2
0.4
0
0.2
-0.2
0
without pulling
during pulling
0
200
400
600
800
-0.2
0
0
0
without pulling
during pulling
0.6
soil spring reaction
[N/m]reaction [N/m]
soil spring
1500
800
without pulling
during pulling
500
1000
0
500
-500
0
-1000
-500
-1500
-1000
0
200
400
600
distance [m]
800
displacement normal
to borepath
[m]
displacement
normal
to borepath [m]
1000
0.5
0.7
0.4
0.6
0.3
0.5
0.2
0.4
0.1
0.3
0
0.2
-0.1
0.1
-0.2
0
without pulling
during pulling
0
200
400
600
distance [m]
-0.1
800
-1500
0
200
400
600
distance [m]
-0.2
800
1.2
800
without pulling
during pulling
0
200
400
600
distance [m]
800
0.01
0.008
800
1
0.006
0.01
1.2
0.8
borewall penetration
[m]penetration [m]
borewall
0
0.7
1500
horizontal displacement
borepathalong
[m] borepath [m]
horizontal along
displacement
0
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
1
0.6
0.8
0.4
0.6
0.2
0.4
0
without pulling
during pulling
0.2
-0.2
0
200
0
400
600
distance [m]
800
0.004
0.008
0.002
0.006
0
0.004
-0.002
0.002
-0.004
0
-0.006
-0.002
-0.008
-0.004
during pulling
-0.01
-0.006 0
200
400
600
distance [m]
-0.008
800
-0.2
without pulling
Stieltjesweg 2, NL 2628 CK DELFT
during pulling
P.O.Box 69, NL 2600 AB DELFT
0
200
400
600
800
Telephone 31 (0) 15 269 35 00
Telefax
31 (0) 15 261 08 21
-0.01
0
200
143
Homepage:
during
pulling
www.geodelft.nl
400
600
800
date
2007-12-20
800
drw.
prk
ctr.
Nieuwe boortechnieken kleine infra
6
Annex 3.7.5 Abaqus FEM pipeline simulation
simulation: Bijl3_7_leiding_080
Pipeline pulled in for 80 %
400
300
500
moment [Nm] moment [Nm]
200
400
100
300
0
200
-100
100
-200
0
-300
-100
-400
-200
10000
without pulling
during pulling
0
8000
6
x 10
0.5
-0.5
without pulling
during pulling
soil spring reaction
[N/m]reaction [N/m]
soil spring
500
y-position borepath
[m] borepath [m]
y-position
x 10
0.5
0
-1
-0.5
-1.5
-1
-2
-1.5
-2.5
-2
-500
-300
-3
-200
0
200
x-position borepath [m]
0
200
-2.5
400
600
distance [m]
800
10000
6000
8000
4000
6000
2000
4000
0
2000
-2000
0
-4000
0
-2000
-400
-500
-3
-200
0
200
x-position borepath [m]
4
x 10
7
800
-4000
length changelength
of beam
[m] of beam [m]
change
x 10
43
5
3
4
2
3
1
2
200
1
600
400
distance [m]
800
200
32
1.5
2.5
21
0.5
1.5
10
-0.5
0.5
without pulling
during pulling
0
200
0
144
0
2.5
3.5
400
600
800
-0.5
600
400
distance [m]
800
horizontal displacement
borepathalong
[m] borepath [m]
horizontal along
displacement
-3
6
4
0
0
1.2
3.5
x 10
7
5
pulling force [N]
pulling force [N]
400
600
distance [m]
x 10
4
4
0
200
-3
6
0
0
1
1.2
0.8
1
0.6
0.8
0.4
0.6
0.2
0.4
0
0.2
-0.2
0
0
without pulling
during pulling
0
200
400
600
800
-0.2
0
0
0
without pulling
during pulling
0.3
800
10000
6000
without pulling
during pulling
8000
4000
6000
2000
4000
0
2000
-2000
0
-4000
0
200
-2000
400
600
distance [m]
800
displacement normal
to borepath
[m]
displacement
normal
to borepath [m]
soil spring reaction
[N/m]reaction [N/m]
soil spring
8000
0.4
0.2
0.3
0.1
0.2
0
0.1
-0.1
0
-0.2
-0.1
-0.3
-0.2
-0.4
without pulling
during pulling
0
200
-0.3
400
600
distance [m]
800
without pulling
during pulling
800
-4000
0
200
400
600
distance [m]
-0.4
800
1.2
800
800
400
600
distance [m]
800
0
0.04
1.2
0.8
1
0.6
0.8
0.4
0.6
0.2
0.4
0
without pulling
during pulling
0.2
0
200
0
-0.2
200
0.02
1
-0.2
0
0.04
borewall penetration
[m]penetration [m]
borewall
0
0.4
10000
horizontal displacement
borepathalong
[m] borepath [m]
horizontal along
displacement
0
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
400
600
distance [m]
-0.02
0.02
-0.04
0
-0.06
-0.02
-0.08
-0.04
-0.1
-0.06
-0.12
-0.08
during pulling
800
-0.14
-0.1
0
200
600
400
distance [m]
-0.12
without pulling
Stieltjesweg 2, NL 2628 CK DELFT
during pulling
P.O.Box 69, NL 2600 AB DELFT
0
200
400
600
800
Telephone 31 (0) 15 269 35 00
Telefax
31 (0) 15 261 08 21
-0.14
0
200
145
Homepage:
during
pulling
www.geodelft.nl
400
600
800
date
2007-12-20
800
drw.
prk
ctr.
Nieuwe boortechnieken kleine infra
6
500
0
1000
6
x 10
0.5
-0.5
moment [Nm] moment [Nm]
200
400
100
300
0
200
-100
100
-200
0
-300
-100
1500
without pulling
during pulling
soil spring reaction
[N/m]reaction [N/m]
soil spring
300
500
1500
without pulling
during pulling
Annex 3.7.6 Abaqus FEM pipeline simulation
simulation: Bijl3_7_leiding_100
Pipeline pulled in for 100 %
400
0
-1
-0.5
-1.5
-1
-2
-1.5
-2.5
-400
-200
-2
-500
-300
-3
-200
0
200
x-position borepath [m]
0
200
-2.5
400
600
distance [m]
800
500
1000
0
500
-500
0
-1000
-500
-1500
-1000
-400
-3
-200
0
200
x-position borepath [m]
4
x 10
6
length changelength
of beam
[m] of beam [m]
change
3
4
2
3
1
2
200
400
600
distance [m]
0
200
-1500
0
1.2
800
6
8
4
6
2
4
0
2
without pulling
during pulling
-2
0
0
200
146
0
800
8
-4
x 10
10
5
1
400
600
distance [m]
x 10
10
4
0
200
-4
5
4
x 10
6
0
0
400
600
distance [m]
800
horizontal displacement
borepathalong
[m] borepath [m]
horizontal along
displacement
-500
pulling force [N]
pulling force [N]
y-position borepath
[m] borepath [m]
y-position
x 10
0.5
1
1.2
0.8
1
0.6
0.8
0.4
0.6
0.2
0.4
0
0.2
-0.2
0
without pulling
during pulling
400
600
800
-2
0
200
400
600
800
-0.2
0
0
0
without pulling
during pulling
0.1
soil spring reaction
[N/m]reaction [N/m]
soil spring
1500
without pulling
during pulling
500
1000
0
500
-500
0
-1000
-500
-1500
0
-1000
800
200
400
600
distance [m]
800
displacement normal
to borepath
[m]
displacement
normal
to borepath [m]
1000
0.15
0.05
0.1
0
0.05
-0.05
0
-0.1
-0.05
-0.15
without pulling
during pulling
-0.1
-0.2
0
200
-0.15
400
600
distance [m]
800
without pulling
during pulling
-1500
0
800
200
400
600
distance [m]
-0.2
800
1.2
0
200
400
600
distance [m]
800
0.01
0.008
800
1
0.006
0.01
1.2
0.8
borewall penetration
[m]penetration [m]
borewall
0
0.15
1500
horizontal displacement
borepathalong
[m] borepath [m]
horizontal along
displacement
0
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
1
0.6
0.8
0.4
0.6
0.2
0.4
0
without pulling
during pulling
0.2
-0.2
0
200
0
400
600
distance [m]
800
0.004
0.008
0.002
0.006
0
0.004
-0.002
0.002
-0.004
0
-0.006
-0.002
-0.008
-0.004
during pulling
-0.01
-0.006 0
200
400
600
distance [m]
-0.008
800
-0.2
without pulling
Stieltjesweg 2, NL 2628 CK DELFT
during pulling
P.O.Box 69, NL 2600 AB DELFT
0
200
400
600
800
Telephone 31 (0) 15 269 35 00
Telefax
31 (0) 15 261 08 21
-0.01
0
200
147
Homepage:
during
pulling
www.geodelft.nl
400
600
800
date
2007-12-20
800
drw.
prk
ctr.
Nieuwe boortechnieken kleine infra
Appendix 3.8
Simulation with measured XY borepath data.
Annex. 3.8.1 Abaqus FEM pipeline simulation
Simulation Input Parameters
XY data Inputfile name
VSHAkkrumA32Spoor.txt
L1 [m]
−
L2 [m]
−
L3 [m]
−
R [m]
−
Symmetric geometry
−
Number of elements
200
Number of elements in pipe
200
Geometric Nonlinear Simulation
yes
Left BC (yes) or Middle BC (no)
no
Pipe outer diameter [m]
1,21E+03
Pipe wall thickness [m]
2.270E−002
Density pipe [kg/m3]
7,85E+06
Youngs modulus pipe [N/m2]
2,10E+14
Poissons ratio pipe [−]
3.000E−001
Pulling rod outer diameter [m]
1.250E−001
Pulling rod wall thickness [m]
6.250E−002
Density pulling rod material [kg/m3]
7,85E+06
Youngs modulus pulling rod material [N/m2]
2,10E+14
Poissons ratio pulling rod material [−]
3.000E−001
Spring Stiffness soil−pipe [N/m2]
1,30E+08
Friction factor soil−pipe [−]
2.000E−001
gap around pipe [m]
1.000E−001
Spring Stiffness soil−pulling rod [N/m2]
1,30E+07
Friction factor soil−pulling rod [−]
2.000E−001
gap around pulling rod [m]
6.425E−001
Reduction factor spring stiffness in borehole [−]
1.000E−003
Density of bore fluid [kg/m3]
1,15E+06
148
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Density of water [kg/m3]
1,00E+06
Fraction of pipe water filled [−]
5.000E−001
Acceleration of gravity [m/s2]
0.000E+000
Resistance of tube/rod in bore fluid [N/m2]
0.000E+000
Friction coefficient of pipeline rollers [−]
0.000E+000
Pushing force at entrance of borepath [N]
0.000E+000
Output Summary
Upward force of pipe in borefluid [N/m]
0.000E+000
Upward force of pulling rod in borefluid [N/m]
−0.000E+000
Friction force of pipe in borefluid [N/m]
0.000E+000
Friction force of pulling rod in borefluid [N/m]
0.000E+000
Total pipeline rollers friction [N]
0.000E+000
Length of borepath [m]
7,11E+05
Length of pipe line in borepath [m]
7,11E+05
Maximum moment [Nm]
6,75E+08
Minimum moment [Nm]
−2.762E+006
Maximum pulling force [N]
6,10E+07
Maximum Soil reaction (without pulling) [N/m]
7,51E+06
Maximum Soil reaction (during pulling) [N/m]
7,72E+06
Soil reaction head of pipe (without pulling) [N/m]
8,84E+03
Soil reaction head of pipe (during pulling) [N/m]
8,84E+03
Maximum borehole wall penetration of pipe (without pulling) [m]
−5.769E−002
Maximum borehole wall penetration of pipe (during pulling) [m]
−5.925E−002
Maximum borehole wall penetration of rod (without pulling) [m]
0.000E+000
Maximum borehole wall penetration of rod (during pulling) [m]
0.000E+000
149
Nieuwe boortechnieken kleine infra
6
Annex 3.8.2 Abaqus FEM pipeline simulation
simulation: Bijl3_8_leiding_realXY_001
Pipeline pulled in for 100 %
400
moment [Nm] moment [Nm]
300
500
200
400
100
300
0
200
-100
100
-200
0
-300
-100
-400
-200
-500
-300
8000
without pulling
during pulling
0
6000
6
x 10
0.5
-0.5
without pulling
during pulling
soil spring reaction
[N/m]reaction [N/m]
soil spring
500
y-position borepath
[m] borepath [m]
y-position
x 10
0.5
0
-1
-0.5
-1.5
-1
-2
-1.5
-2.5
-2
-3
200
400
600
x-position borepath [m]
-400
0
200
-2.5
400
600
distance [m]
800
8000
4000
6000
2000
4000
0
2000
-2000
0
-4000
-2000
-6000
0
-4000
-500
-3
200
400
600
x-position borepath [m]
0
4
5
3
4
2
3
1
2
200
1
600
400
distance [m]
800
200
128
106
84
62
40
-2
2
without pulling
during pulling
0
200
0
150
0
10
14
400
600
800
-2
600
400
distance [m]
800
horizontal displacement
borepathalong
[m] borepath [m]
horizontal along
displacement
length changelength
of beam
[m] of beam [m]
change
x 10
12
16
6
4
0
0
1.2
-4
x 10
7
5
pulling force [N]
pulling force [N]
-6000
14
4
0
800
x 10
16
6
0
400
600
distance [m]
-4
x 10
7
200
1
1.2
0.8
1
0.6
0.8
0.4
0.6
0.2
0.4
0
0.2
-0.2
0
0
without pulling
during pulling
0
200
400
600
800
-0.2
0
0
0
0.15
without pulling
during pulling
0.1
800
8000
4000
without pulling
during pulling
6000
2000
4000
0
2000
-2000
0
-4000
-2000
-6000
0
200
-4000
400
600
distance [m]
800
displacement normal
to borepath
[m]
displacement
normal
to borepath [m]
soil spring reaction
[N/m]reaction [N/m]
soil spring
6000
0.15
0.05
0.1
0
0.05
-0.05
0
-0.1
-0.05
-0.15
without pulling
during pulling
-0.1
-0.2
0
200
-0.15
400
600
distance [m]
800
without pulling
during pulling
800
-6000
0
200
400
600
distance [m]
-0.2
800
1.2
0
200
400
600
distance [m]
800
0.04
0.03
800
1
0.02
0.04
1.2
0.8
borewall penetration
[m]penetration [m]
borewall
0
8000
horizontal displacement
borepathalong
[m] borepath [m]
horizontal along
displacement
0
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
1
0.6
0.8
0.4
0.6
0.2
0.4
0
without pulling
during pulling
0.2
-0.2
0
200
0
400
600
distance [m]
800
0.01
0.03
0
0.02
-0.01
0.01
-0.02
0
-0.03
-0.01
-0.04
-0.02
-0.05
-0.03
during pulling
-0.06
-0.04 0
200
600
400
distance [m]
-0.05
800
-0.2
without pulling
Stieltjesweg 2, NL 2628 CK DELFT
during pulling
P.O.Box 69, NL 2600 AB DELFT
0
200
400
600
800
Telephone 31 (0) 15 269 35 00
Telefax
31 (0) 15 261 08 21
-0.06
0
200
151
Homepage:
during
pulling
www.geodelft.nl
400
600
800
date
2007-12-20
800
drw.
prk
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Nieuwe boortechnieken kleine infra
152
Modelling the soil pipeline interaction during the pull back operation of horizontal directional drilling
Appendix 4
Members of the committee
Naam
Organisatie
ir. H.J. Brink
ir. D.R. Mastbergen ir. H. Lentfert
ir. J. Stoelinga
ir. H.J.A.M. Hergarden Nederlandse Gasunie n.v.
Deltares (Wl Hydraulics)
Visser en Smit Hanab b.v.
Nacap b.v.
Deltares (Geodelft)
153
Nieuwe boortechnieken kleine infra
154
EINDRAPPORT
TC221-01-08
TC221
Het Nederlands kenniscentrum voor ondergronds bouwen en
­ondergronds ruimtegebruik (COB) heeft tot doel om kennis, kunde
en innovatie voor ondergronds ruimtegebruik en ondergronds
­bouwen te ontwikkelen. Dit doet COB door praktijkonderzoek en door
­samen­werking binnen een netwerk van deskundigen.
Kennis komt tot stand in een publiekprivate, maatschappelijke
context, om te komen tot ­resultaten die breed worden geaccepteerd
en die leiden tot een verantwoorde toepassing met maatschappelijk
en economisch ­rendement. COB bestaat sinds 1995 en maakt deel uit
van CURNET.
Consortium DC-COB
Door het ondertekenen van de overeenkomst ‘Consortium Ondergronds
Bouwen’ d.d. 18 december 2003 bevestigen COB en Delft Cluster de
voorgenomen plannen met betrekking tot het uitvoeren vangezamenlijk
onderzoek binnen het consortium ‘Ondergronds Bouwen’.
Bij de formulering van de onderzoeksactiviteiten binnen beide
­organisaties voor de periode 2003-2010 leek een verdere afstemming
van de activiteiten winst voor beide organisaties te kunnen betekenen.
Delft Cluster kan profiteren van de goede relaties die het COB heeft
opgebouwd met diverse marktpartijen op het gebied van ondergronds
bouwen en ondergronds ruimtegebruik. Deze marktpartijen zijn nood­
zakelijk om te komen tot een uitvoerbaar Bsik-programma voor de
­periode 2003-2010. Het COB kan van de samenwerking profiteren
omdat het een eerste aanzet betekent naar een gezonde financiële basis
voor onderzoeksactiviteiten. Daarnaast biedt de samenwerking voor
beide organisaties kansen op het gebied van kennisdeling en kennis­
verspreiding. Dat is de insteek van de twee projecten:
Beheerst Boren in Stedelijk Gebied en Innovatief Ondiep Bouwen.
Gemeenschappelijk praktijkonderzoek boortunnels (GPB)
Na het succesvolle verloop van het praktijkonderzoek bij de Tweede
Heinoordtunnel en de Botlekspoortunnel bleek het voor vijf nog
op handen zijnde Nederlandse boorprojecten efficiënter om het
nog b
­ enodigde onderzoek te verdelen. Daarom gaven de opdrachtgevers van vijf Nederlandse boortunnelprojecten en COB half
september 2000 door de ondertekening van de Overeenkomst
­Gemeen­­schappelijk Praktijkonderzoek Boortunnels (GPB) hun
­goedkeuring aan een masterplan praktijkonderzoek. Onder de paraplu
van het Centrum Ondergronds Bouwen bepaalden zij welk onderzoek
waar het beste zou kunnen plaatsvinden.
Binnen het masterplan GPB wordt onderzoek gedefinieerd ter plaatse
van Westerscheldetunnel (F100), Sophiaspoortunnel (F200), ­­
Tunnel Pannerdensch Kanaal (F500), Boortunnel Groene Hart (F510),
Noord-Zuidlijn (F530) en RandstadRail (F540). Tijdens de u
­ itvoering
van deze boortunnels met grote diameter zullen metingen en
­experimenten worden uitgevoerd, waarmee de kennis ten aanzien van
de geboorde tunnel als bouwmethode wordt vergroot. Hierbij worden
ondermeer zaken onderzocht als metingen aan dwarsverbindingen,
mogelijkheden tot hergebruik van vrijkomende grond, optreden
van zwel van diepgelegen kleilagen, volgen van het boorproces en
gerichte evaluatie van meetgegevens. Het betreft dan ook uitvoerings­
gerelateerd onderzoek met oog op het verkleinen van risico’s en
kosten bij toekomstige tunnelprojecten.
De partijen vertegenwoordigd binnen het Platformoverleg GPB
• Managementgroep Betuweroute van NS RailInfrabeheer,
• Projectbureau Noordelijk Holland - Directie HLS-Zuid - Ministerie
van Verkeer & Waterstaat,
• Projectbureau Noord-Zuidlijn - Dienst Infrastructuur Verkeer en
Vervoer van de Gemeente Amsterdam,
• Centrum Ondergronds Bouwen (COB),
• Projectbureau RandstadRail
• Bouwdienst Rijkswaterstaat - Directoraat-Generaal Rijkswaterstaat
- Ministerie van Verkeer & Waterstaat
• Delft Cluster
partner curnet
Groningenweg 10
2803 PV Gouda
Postbus 420
2800 AK Gouda
T +31 (0)182 - 540 660
F +31 (0)182 - 540 661
[email protected]
www.cob.nl
TC221 Nieuwe boortechnieken kleine infra
COB – Nederlands kenniscentrum voor ondergronds
­bouwen en ondergronds ruimtegebruik
Nieuwe boortechnieken
kleine infra
Modelling the soil pipeline interaction during the
pull back operation of horizontal directional drilling