Deep Foundation Pit’s Fluid-Solid Coupling Analysis of Seepage Under Non-Saturated Conditions

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Deep Foundation Pit’s Fluid-Solid Coupling Analysis of Seepage Under Non-Saturated Conditions
Physical and Numerical Simulation of Geotechnical Engineering
1st Issue, Sep. 2010
Fluid-Solid Coupling Analysis of Deep Foundation Pit’s
Seepage Under Non-Saturated Conditions
CHENG Wei, HE Xiang
School of Civil Engineering and Architecture, Wuhan Polytechnic University, P.R. China, 430023
[email protected]
ABSTRACT: The phenomenon which micro-artesian seepage effects on foundation Pit with rainfall
is a typically non-saturated seepage process. However, underground water seepage and rainfall
infiltration during the deep foundation pit’s excavation and support exert a significant impact upon the
stability of engineering itself. The authors have given some countermeasures after modeling and
calculating of this phenomenon and make an explanation of problems which confronted during deep
foundation pit’s excavation and support by relevant theories. Conclude the flow path and velocity
around foundation pit through calculation under non-saturated conditions. Then it combined the
predictions and practical applications, proposed correspondingly protective measures.
KEYWORDS: Fluid-solid coupling, Deep foundation pit’s seepage, Non-saturated conditions
Since the elastic modulus of soft ground is small and the
intensity of the soil itself relatively low, it will be easily
lead to foundation pit’s global instability during its
excavation and support process. Yet during the excavation
in domestic coastal areas, disposal of underground water
and waterproof or diaphragm retaining walls remains to be
improved. Particularly rainfall and its infiltration during
excavation and support of foundation pit. It will
significantly decrease the shear strength of rock and soil,
and then effect on the stability of engineering itself. And
the effect that seepage and deformation have on the bottom
of the foundation pit will cause the bottom of foundation pit
swell or piping erosion [1], and threaten to the stability of
foundation pit. Foundation pit with different geological
conditions have a great difference of permeability and
boundary conditions, thus the pore pressure of foundation
pit and effective stress with the action of its pore pressure is
different. The influencing factors of foundation pit are
variety, such as design depth of diaphragm retaining walls
and block about underground water during the excavation
and support of foundation pit is very important.
Foundation pit’s excavation is meanwhile a stress release
process. Excavate a foundation pit from a geological
balance plain will change the stress structure of around
environment. In order to avoid the advert effects to the
surrounding production and construction after long period
of foundation pit’s excavation, it’s necessary to observe and
experiment of the seepage field and stress field in time, and
seek out its change law. Because of the underground water
seepage effect, there will be deformation around foundation
pit. It is useful to control and ameliorate the poor state of
foundation pit that make a fluid-solid analysis to the
seepage and stress deformation around foundation pit.
Nowadays, the main issues of domestic deep foundation pit
focus on: (1) Dynamic process of stress release; (2) The
deformation for seepage, precipitation stability of
foundation pit. (3) Soil liquefaction for dynamic load, and
the uneven sedimentation under effect of layer seepage.
The analysis on the seepage field and stress field which
micro-artesian seepage effects on foundation Pit with
rainfall under non-saturated conditions is based on the
analytic calculation of correlation model.
2.1 The mechanism of groundwater migration’s impact
on the stability and deformation of foundation pit
Between two impermeable layers, as soon as the
foundation pit was excavated, confined water have a water
head. The groundwater starts to migrate under the pore
pressure effect. This effect made hydraulic pressure
gradually strengthen along with the increase of foundation
pit depth directly. The water head was loss as well. Since
the pore water pressure is lower than steady water pressure
in certain area out of the foundation pit, the situation in the
bottom of foundation pit is reverse. And this caused the
groundwater seepage into the inside of the foundation pit.
At the same time, there will be an opposite trend of water
pressure and flow way of underground water between two
sides of the wall. This will be made an induced cause to
unstable foundation that is excavation. Combined with the
flow characteristics of underground water, if the foundation
located in river or lack where contain abundant water, the
flow size will be ascent, and there should be some
appropriate emergency measures. Moreover, with different
terrain, the characteristic and strength of soil must be
different, and the impression that water seepage to the
foundation stable should be under the premise that doing a
serials of cogent and detail experiment previously. While
the basic principle is similar, are due to the underground
water flow for water head difference, and then cause the
dynamic excavation problems of deep foundation pit.
Because of timely supplement rainfall, the underground
water level is not determined. With different rainfall
intensity, the quantity of underground water float range will
Fluid-Solid Coupling Analysis of Deep Foundation Pit’s Seepage Under Non-Saturated Conditions
DOI: 10. 5503/J. PNSGE. 2010. 01.007
be different. And the circumstance that near river or lake
area, must be considered independently. When it rains at
certain time after the foundation pit have been excavate,
there will be a great impression on the integrated support of
the foundation. It is prone to piping if we didn’t have
reinforce interface that initial stress release or some
correspondingly drainage treatment of it, meanwhile,
consider the alter of stress during this non-saturated process,
and the change of underground water seepage and pore
pressure that results from it, there will be a certain
deformation along with it in a significant area. And in the
process of raining, there will be hint of remain rainfall and
seepage water in the foundation pit, and it is the
micro-artesian. The seepage process under foundation pit is
complicated under the micro-artesian effect.
u a is pore air pressure; and u w is pore water pressure;
(u a  u w ) is soil suction;  is a constant between 0
and 1.
b) Oberg and Sallfors proposed the shear strength
forecast equation of non-saturated soil as follows[6]:
  c '  (  u a ) tan  '  (u a  u w )( S ) tan  ' (5)
And S is the saturation in this equation.
2.2.3 Considered non-saturated condition, the calculate
equation of permeability along with pore pressure change is
as follows[7]:
K rs*  K r ( S ) K rs
Kr 
2.2 Relevant theories of non-saturated soil
2.2.1 The relationship between soil suction and its
Because of rock and soil is porous media, the total pore
pressure must be lower than zero under non-saturated
condition, and the negative value of the total pore pressure
reflect the soil suction. The saturation of soil maintains in a
range for the effect results from soil suction. Assignation
the absorption and dehydration curve previously, and the
alter law between these two.
The inside seepage of non-saturated soil obey Darcy’s
law, the solid and liquid coupling by strain and pore
The coupled mathematical equations of
saturated-unsaturated seepage of rock and soil are as follow
after referenced by multiphase seepage theory of porous
 ij' , j  (Sp ij ) j  f i  0
 ij
is valid stress;
 kk
is volume strain;
derivation of the x coordinate;
derivation of time t;
(K x
)  (K y
)Q 0
Q is water flow.
2.3.2 Transient seepage equation
(k x
)  (k y
)  ct
K x , K y are permeability in x and y directions, unit
m / s ,H is total water head, H ( x, y, t ) .
H ( x, y, t ) C  H 0 ( x, y, t )
H 0 ( x, y, t )
( )j
stands for the
( )
stands for the
is given water head boundary, with t=0,
initial water head is
H 0 ( x, y) .
2) Water flow boundary
is Darcy’s velocity; and the
calculate equation of c is as follow:
ns ds
k ' dp
And c is storage constant; n is porosity; k
modulus; s is the function of pore pressure p ;
2.3.3 Boundary conditions
1) Water head boundary
is kronecker constant;
2.3.1 Steady seepage equation
(S  S r ) 3
3/ 2
(1  S r ) 3
p  
1  
  
 
F  
2.3 2-D seepage equations[8]
S  vkF,k  cp  0
 q(h, x, y, t )
is bulk
3.1 Rainfall infiltration boundary conditions
Mein and Larson[9] using rainfall intensity q, the soil
allowable infiltration capacity f P , and the permeability
2.2.2 The strength theory and reference computer equations
of non-saturated soil are as follows:
a) In 1959, Bishop proposed the strength equation of
non-saturated soil to single stress state variables [5]:
when soil is saturated
K rs . When it meet the
condition: f P  q  K rs , all of the rainfall is infiltration
  c '  [(  u a )   (u a  u w )] tan  ' (4)
In the equation,  is shear strength; c stands for
valid cohesion;  stands for valid internal friction angle;
into soil and the capacity is decrease along with the depth
Physical and Numerical Simulation of Geotechnical Engineering
1st Issue, Sep. 2010
 a ,  r are gas
3.2 Modeling and calculating
K rs is
This example is using 2-D finite element method to do
the numerical calculation of foundation pit.
All monitor area is the seepage range, or the flow region
of the groundwater. The bottom, left, and right boundary
and diaphragm retaining walls boundaries have a constraint.
Considered the permeability of soil is changed along with
the change of saturation, we defined a set of data based on
the following two equations:
pressure and water pressure in soil, and
ar K rs
[ar  (br  (  a   r )) cr ]
(S n  S i )
Su  Si 
[at  (bt  (  a   t )) ct ]
Kr 
permeability when soil saturated.
at , bt , ct
are material coefficients,
S n is maximum saturation.
ar , br , cr
is residual
The breath of foundation pit is 3m, depth 20.32m, height
52.46m,using whole breath 200m, therefore can consider
large range, and after excavation, the diaphragm retaining
walls depth is 25m, thickness 0.1m, elastic modulus
10.8 MPa , Poisson’s ratio 0.3, cohesion c' 16 KPa ,
friction angle 30 degree. Model in mesh as follow:
Figure .1 Simplified diagram of model
After parameter setting, the calculation results are as follows:
Figue.2 Distribution of pore pressure
Vertical effective stress distribution:
Figue.3 Distribution of vertical effect
Horizontal and vertical displacement:
Fluid-Solid Coupling Analysis of Deep Foundation Pit’s Seepage Under Non-Saturated Conditions
DOI: 10. 5503/J. PNSGE. 2010. 01.007
Figue.4 Horizontal displacement
Figue.5 Vertical displacement
Displacement vector graph:
Figue.6 Velocity of flow vector graph
level and the wall depth. The finite element analysis of this
process will be discovered that the characteristic and
saturation of soil will be change gradually along with the
infiltration degree of rainfall. And it will take a gradually
difference of underground water infiltrate feature, then the
following change of porosity and permeability of soil. It
can also predict the relative change trend graph thorough
the calculating date that the stress and strain change of
foundation element and node, or the valid stress path of
node. Combine these date, we concluded that the stress and
strain of element will be change when we give different
rainfall intensity and endure time, and the result suit to the
rainfall infiltration conclusion.
4.1.2 The finite element analysis of soil stress and strain
In terms of the analysis of date that node or element
displacement internal soil, we can concluded stress path of
every node and total stain trend. We can also observe the
total strain in different saturation and pore pressure, and the
potential region of initial destruction and adverse
geological phenomena, or see the impression area integrity.
Finite element method will be accurately calculated the
date of stress and strain of every node and element, then
doing a stress and deformation analysis with these results.
With the stress path that the method had been calculated,
we can forecast the strain of soil under certain force
circumstance. And then forecast the general trend of soil
4.1 Analysis the numerical simulation of the fluid-solid
In figure 1 and 2, the displacement in the bottom and
near area of the pit is comparatively large, and hydraulic
gradient in the bottom of pit is very large, the soil around
the pit start to swell and its intensify is reduce for the
gravity and static water pressure effect.
From the vector graph, we can see the discrepancy of
velocity between inside and outside foundation pit area
clearly. As the main drainage orientation, the water pressure
and velocity of flow inside the pit is larger than outside any
more, meanwhile, inside the pit, there is a upward seepage.
The effective stress decrease gradually, and in certain
situation, it will evolve to piping.
4.1.1 Analysis of foundation rebound and surrounding
surface subsidence
Overall, since the frequently flow of underground water,
there formed a large area of displacement and deformation,
and red stands for positive displacement, blue area stands
for comprehensive deformation region in terms of
underground water flow effect. When it effect for a period
of time, the stress concentrate in downside interface of the
wall, inside of the foundation there are uplift deformation.
The calculate result reveal that the rebound float of
foundation pit relatively large, and it determined mainly by
porosity of soil and the relationship between groundwater
Physical and Numerical Simulation of Geotechnical Engineering
1st Issue, Sep. 2010
strain. The last project we must accomplish is that
reasonable projection the might phenomena during
foundation pit excavation in a certain circumstance.
rational answer about these questions.
(1) The soil strength is significantly relevant to its pore
pressure and permeability under the rainfall infiltration
non-saturated condition. It is benefit for foundation pit’s
devise of support program and construction that combine
with rainfall situation and forecast the dynamic change of
underground water.
(2) Use the practical computer equation of soil under
non-saturated condition enable us make a detail analysis of
the dynamic change path of stress and strain during rainfall
and filtration process.
However, it need further research in these issues: Stability
of the foundation pit under different rainfall intensity and
stability in different kinds of layer and soil properties which
this paper didn’t calculate.
4.2 Proposal to the deep foundation pit’s excavation and
4.2.1 Great importance should be attached to the change of
the groundwater seepage and we should avoid the rainy
season and make good support when excavate foundation
pit. Make a prediction about seepage property in a certain
period before excavation, and seek out the best support way
of this time. Similarly, make a discussion about the benefit
way to excavation in different location.
4.2.2 When the aquifer thickness is comparatively large and
the same as permeability, the conventional method is
combine using diaphragm retaining walls and grouting
curtain, but rarely used vertical back cover. And the
grouting curtain is a good way to block the groundwater
under the bottom of foundation pit.
4.2.3 The depth that diaphragm retaining walls into rock
layer should be enough, however, for economic
consideration, how to determine the best depth should be
based on technology and the permeability of environment
that foundation pit locate. In the bottom of the foundation
pit, intensity is not necessary but we must ensure that the
waterproof ability of diaphragm retaining walls is sufficient.
Meanwhile, we should consider the environment property
around foundation pit when it drainage. This work should
be based on the ample environmental investigation in all,
and then make a rational distribution.
The problem that groundwater seepage during the
excavation and support of foundation pit continuously the
key issue of foundation pit excavation. Based on the
abundant investigation of around environment, we can
predict the seepage field of groundwater and its change law
before construction through numerical calculation. It will
provide valuable reference material to determine the
excavation method in time, to choose the rational program
consider economical factors. Deep foundation pit’s
excavation in rainy season will form differently seepage
situation. Under water seepage effect, there will be
comprise displacement and sedimentation in large field,
and reduce the foundation pit’s stability. We give the
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