 # Numerical Analysis of the Seepage Field in Core-Dam

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Numerical Analysis of the Seepage Field in Core-Dam
```Numerical Analysis of the Seepage Field in Core-Dam
LI Quanshu, LIU Jianjun
School of Civil Engineering and Architecture, Southwest Petroleum University, Chengdu, China,
610500
[email protected]
Abstract: The analysis of the seepage field of dam is important to the safety and stability evaluation.
Numerical simulation method is adopted in this paper to analyse the seepage field, and through the
comparison of the seepage field under different conditions the effect of the core and other factors would
be clear. Based on the permeation fluid mechanics, the steady model and transient model are established
by using the finite element software Seep/W. Firstly the effect of the core to the seepage of dam is
discussed in the steady analysis, then the variation of the upstream water level and the permeability
coefficient are discussed in the subsequent transient analysis, which are measured by the hydraulic head,
pressure head and velocity of the infiltration. These analysis could guide the design of the dam, provide
a strong measurement to the stability and safety.
Keywords: seepage field, core-dam, Seep/W, numerical analysis, steady analysis, transient analysis
1. Introduction
Seepage may bring adverse effect to a building especially an earthy one and to it's foundation, so the
seepage computation is necessary in the designation and operation of a hydraulic structure. The task of
the seepage analysis can be concluded as the following: (1)Compute the seepage flux crossing the
building and the foundation to get the infiltration loss, then to determine whether to take extra
anti-leakage protection measures;(2)Figure out the saturation line in the earth and rock-fill dam to
analyse the stability of the dam slope;(3)Calculate the hydraulic head and pressure at each point in the
building and in it's foundation to make sure of their distribution and change to predict the possibility of
seepage deformation;(4)Reckon the uplift pressure on the subsurface to analyse the stability of the
building and then to take steps to prevent and discharge seepage;(5)Work out the leakage velocity and
hydraulic gradient within the building and it's foundation, especially at the leakage escape site, so as to
analyse the seepage stabilization and what methods should be taken to prevent and discharge the
leakage.
Core-dam is common in hydraulic engineering. The anti-seepage body with a small permeability
coefficient is located at the middle of the dam as the core, and besides the core there is the dam shell that
consists of materials with high permeability like grit to bring down the moment seepage line as soon as
possible to ensure the stable of the upstream slope. It can make full use of the different materials of the
core and the shell to let the dam work at its best but at the lowest price. The state of the seepage field
within a dam is directly affecting the dam's safety and stability especially when it comes to extremely
environment changes such as speedy change of upstream water level. Various factors could affect the
seepage field within a dam, and there are lots of methods to compute and measure them. Here using
numerical simulation method to analyse the seepage field by the software Seep/W. Seep/W is a finite
element software which is part of geo-studio 5. It can be used to model the movement and pore-water
pressure distribution within porous materials such as soil and rock. The needed information would be
presented in graphics, from which users can conveniently and visually judge the situation.
2. Computation Theory
To the two dimensional seepage that fits Darcy law in aeolotropic continuum, the seepage could be
described by this differential equation:
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∂Θ
∂  ∂H  ∂  ∂H 
 + Q =
 +  k y
 kx
∂t
∂x  ∂x  ∂y  ∂y 
(1)
Where H is the total hydraulic head, kx and ky is hydraulic conductivity respectively in horizontal
direction and vertical direction, Q is the infiltration or evaporation flux, Θ is the volumetric water
content, t is the time.
The volumetric water content is defined as the porosity multiplied by the degree of saturation:
Θ = nS
(2)
Where n is the porosity, S is the degree of saturation.
A change in Θ can be related to a change in pore-water pressure by the equation:
∂Θ = mω∂uω
(3)
Where mw is the slope of the storage curve, uw is the pore-water pressure
The total head is defined as:
H=
uω
+y
γw
(4)
Where γw is the unit weight of water, y is the elevation.
So, substituting Equation (3) and (4) into (1), leading to the following expression:
∂(H-y )
∂  ∂H  ∂  ∂H 
 + Q = mω γω
 +  k y
 kx
∂t
∂x  ∂x  ∂y  ∂y 
(5)
Since the elevation is a constant, the derivative of y with respect to time disappears, giving the
governing equation as below:
∂ (H )
∂  ∂H  ∂  ∂H 
 + Q = mω γω
 +  k y
 kx
∂t
∂x  ∂x  ∂y  ∂y 
(6)
When it is under steady state condition, the right side of the Equation(1) disappears and the equation
becomes to:
∂  ∂H  ∂  ∂H 
+Q =0
 +  ky
 kx
∂x  ∂x  ∂y  ∂y 
(7)
The boundary conditions of the Equation(4) generally consist of the following three types:
1. The head on the boundary is known, namely H=H0;
2. Both the inflow and the outflow on the boundary are known, and the boundary surface should satisfy
the following expressing:
kx
∂H
∂H
lx + k y
ly + q = 0
∂x
∂y
(8)
Where lx ,ly respectively is the normal cosine of the boundary surface, q is the inflow or the outflow of
the unit boundary surface.
3. To the impermeable boundary, there should be:
∂H
=0
∂n
(9)
Where n is the outward normal of the boundary.
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The boundary conditions of the Equation(1) contain four types, the first three of which are the same as
the above,the forth one is that the free surface of the seepage should satisfy H=y.
3. Computation Model
Consider a dam with a height of 80 meters, a cross section width of 500 meters at the bottom, based on
impermeable foundation. Both the upstream and downstream side slope of the dam are 1:3. In order to
better describe the effect of the core, there are two groups of computation. One is a core-dam, the other
without core. The materials of the dam shell and the core are independently homogeneous isotropy, and
the permeability is 8.6 10-3 m/d of the shell, and 5 10-5 of the core. On the downstream side there's a
drainage system at the toe, the slope of which is 1:3 on both sides. The transient analysis is based on a
models of upstream water level falling situations, the upstream slope boundary is set in head type at 75
meters which is 15 in the initial steady models of upstream water level rising case. The left side of the
drainage is set in flux type at 0 except the bottom node which is set at 0 in head. The others boundary
conditions are assumed as Q=0 by default.
In the transient analysis the time t should be considered, so the upstream boundary condition is assumed
as a function of the head H with respect to the time t. It consists of twelve steps starting from 0 to 1970
days. The initial time increment size is set as 2 and the expansion factor is 2,then the maximum
increment size is 365. The data are saved at every other step. Between every step the change of the head
is 5 meters. So the change of rate of head respected to time of the early steps is faster than the later steps.
The others boundary conditions are the same as in the steady analysis.
×
×
Figure 1 Computation model
4. Results
A steady analysis is to consider the situation without respect to time. From the steady analysis of the two
types of dams, the distributions of total head and pressure head are shown in the following graphics. As
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what are shown in the figures, the water table is painted as a thick blue line, which smoothly across the
dam without core but a polyline in the core-dam. The vertical lines are the total head isolines. They
beginning at 0 at intervals of 5 from downstream to upstream. Those contour lines are evenly distributed
in the left picture in Fig.2,but intensively concentrated within the core on the right side picture. In Fig.2,
the head line is 75 at left toe, through a wide isosurface it gets to 70,then gradually reduce to 0 at the
right toedrain while in Fig.6 within the scope of the core the head is sharply reduced from 70 to 10. This
illustrates that the core has beared the most head loss which is 93%.
The arrows represent the velocity vectors, and the size of the arrow is in scale with the value of the
velocity. The velocity at point(260,75) which is on the left side of the core at the same height of
upstream water level is 2.38 10-4 m/d, while point(280,75) 1.66 -4 m/d on the other side of the core.
At (460,0),the toedrain bottom point, the speed is 3.74 10-3 m/d. At the same position in the left picture
the velocity is respectively 5.58 10-2 m/d,3.29 10-2 m/d,2.93 10-1 m/d. So as it gets closer to the
toedrain, the bigger the arrows exhibit. This states that the seepage gets faster when it gets closer to the
drainage system and the core has effectively reduced the seepage speed.
×
×
×
×
×
×
Figure 2 Result: the total head distribution
The following pictures display the pressure head distribution. Fig.3 shows a series of smooth contours of
equal pressure head uniformly distributed within the dam. The isoline of equal pressure head is 0 at
water table and getting larger at intervals at 5 to the bottom till the last one that can be seen at 70. Above
the water table there are isolines at negative values, which is because of the suction that considered in
the software by default. To the contrast, the contours are zigzag in the right side. They begin at 0 from
the water table and end at 60 at intervals of 20,and become very steepy within the core, then gently
reach the drainage system. The elevation of the water table on the downstream side directly reflects the
core's impermeability, and the slopes within different sections are the important index of the evaluation
of the security. In Fig.3, in the left side picture, the slope in each section is respectively
1:20,1:0.3,1:22.5,which shows that the core undertakes the most pressure head loss, and the slope is
steepy within the core and gentle within the upstream and downstream dam shell.
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Figure 3 Result: the pressure head distribution without core
4.2 Transient Analysis
The transient analysis is actually an unsteady analysis. It can take the steady state as the initial
condition. From the transient analysis the variation of the free surface can be figured out,which is an
unsteady analysis considering several factors such as the size of the upstream shell of the core-dam,the
fall speed of the water level,the permeability and the discharge capacity of the shell. The calculation
starts at t=0,the next step is begin at t=2,then t rise as twice as the former at each step. The maximum
increment size is set to 365. There are twelve steps,and the head boundary reduce 5 meters at every step.
The speed at each step is shown in the following table.
Step
1
2
Velocity
(m/d)
2.500
1.250
Table1: the descendent or increase velocity at each step
3
4
5
6
7
8
9
0.625
0.313
0.156
0.078
0.039
0.020
0.010
10
11
12
0.005
0.002
0.001
From the distribution of the water table the head reduction rate can be reflected. In Fig.4, at the
beginning steps, as the velocity changes from 2.5 to 0.313,the head decreases speedy, so the phreatic
lines are closely gathered together. When the reduction rate lowered from 0.156 to 0.005,the region
between the seepage line gets wider, and with the rate lowered further more from 0.005 to 0.001,the
water table concentrated together again, as convergenced to one saturation line. To make a better
comparison two lines are sketched at the site where located the core in the core dam. The water table at
step0 reaches the left line at the height of 69.5,subsequent steps reach the line at intervals of
0.5,2.3,5.5,9.5,9.8,5.4,respectively,and the step12 line approaches the line at the height of 37.5. Between
the two sketched lines, the contours are gentle. To the contrast, in Fig.5, the seepage lines are nearly as
the same as those in Fig.4 on the left of the core, but within the core, the lines concentrated together and
the slope decreased sharply. The step0 line achieves the right edge at 74.4,then the height reached is
reduced at intervals of 0.1,0.4,1.4,8.3,7.4,4.4,ends at 51.2. When across the core, the isolines are slide
sharply down and nearly similarly reach the right edge of the core at the height of 8 with errors no more
than 0.1.This is because the permeability coefficient of the core is small while the shell's is large. The
small coefficient which reduced the leakage may cause excess hydrostatic pressure that would effect the
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stability of the core.
Figure 4 Result: the water table distribution from step 1 to step 12
Fig.5 shows the situation in which the upstream water level is rising but falling. The initial head is set at
15,and it gradually rise at 75 at intervals of 10. As shown in the following picture, the phreatic lines on
the upstream side are concave down, then rapid glide down within the core, and when extend into the
downstream side it becomes approximate horizontal. From top to bottom, the seepage lines reach the
core at a start of 42.2,then reduce at intervals of 21.0,7.2,0.4..From step6 to step 0 the lines overlap
together when approaching the core. If the hydraulic conductivity gets larger, the shell will be more
sensitive to the change of the water level, and the water table would seem kin to horizontal line on the
upstream side, as what is shown in Fig.12 where the step12 line get to the core at 74.95,step10
65.4,step8 54.2,step6 25.5.The gap between step8 and step6 is relatively large due to the decreasing rate
of speed. From step4 to step0 the distance is so tiny that it seems they arrive the core at the same point at
13.4.
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Fig.5 Result: the water table distribution when upstream water level is rising
5. Conclusion
The numerical simulation is adopted and realized by the finite element software Seep/W in this paper.
Based on the seepage fluid theory, different two-dimensional seepage fields due to various conditions
are established. From the analyses above we can conclude that the core is important to the dam. The
core's size, the permeability and the velocity of water level fluctuation are important factors that effect
the safety and stability of the dam. So when design a core-dam, there are many considerations:
1) The seepage field in downstream slope changes little while in upstream side changes a lot. If the
infiltration coefficient of the dam shell is small, the water held in it cannot be discharged timely. The
core bears the most head loss due to it's little permeability, which may lead to excess hydrostatic
pressure exerted on the core and adversely effect the stability of the dam.
2) The speed of rising and falling of the upstream water level directly impacts the safety and stability
of the upstream shell then further influence the whole dam, so there must be sufficient feasible effective
methods to deal with the extreme situations.
3) If the dam is based on soft permeable foundation which may cause sedimentation and leakage, the
seepage analysis should include the leakage distribution within the basement. Different base is of
specified characteristics, which should be considered cautiously when design a dam.
：
Author in brief or Acknowledgment
This work was financial supported by National Natural Science Foundation of China (Grant No.
50874082), Hubei Excellent Young and Middle aged Innovation Group Project, major project (Grant No.
T200603 and No.Z20091801) from Hubei Education Department and major project (09ZA139) from
Education Department of Sichuan Province.
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