Seepage Analysis of Walter F. George Dam, USA: A case Study

Abstract

Earth dams' failure may occur due to different reasons such as structural instability conditions, hydraulic conditions, seepage through the dam body and/or rapid drawdown. In this work, Finite Element modeling is employed for simulating seepage and stress analysis of earth dam problems. Thus, phreatic seepage surface, pore water pressure distribution and total hydraulic head variation of an earth dam are analyzed. The model is verified, and then it is employed to analyze seepage of a failed dam, Walter F. George Dam (USA), for different cases of operation. Benchmark safety regulation criteria (BDS) and (USBR) are obeyed. The results confirm the design of Walter F. George dam is unsafe and seepage failure was expected. A suggestion for the dam design to prevent the seepage failure is presented and checked. As a conclusion, accurate simulation of either existing dams or failed dams is vital.

Full text

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Seepage Analysis of Walter F. George Dam, USA: A case Study
M. S. Kirra, B. A. Zeidan, M. Shahien, M. Elshemy
Faculty of Engineering, Tanta University, Egypt
drbakenaz@yahoo.com
ABSTRACT
Earth dams’ failure may occur due to different reasons such as structural instability conditions, hydraulic
conditions, seepage through the dam body and/or rapid drawdown. In this work, Finite Element modeling is
employed for simulating seepage and stress analysis of earth dam problems. Thus, phreatic seepage surface,
pore water pressure distribution and total hydraulic head variation of an earth dam are analyzed. The model is
verified, and then it is employed to analyze seepage of a failed dam, Walter F. George Dam (USA), for
different cases of operation. Benchmark safety regulation criteria (BDS) and (USBR) are obeyed. The results
confirm the design of Walter F. George dam is unsafe and seepage failure was expected. A suggestion for the
dam design to prevent the seepage failure is presented and checked. As a conclusion, accurate simulation of
either existing dams or failed dams is vital.
Keywords: Earth dams, Seepage failure, Finite element modeling, Walter F. George dam.
1. Introduction
Dams are built for functions such as water supply, irrigation, flood control and hydroelectric power
generation. Most of large dams in the world were built during the middle decades of the twentieth century.
There are two types of modern dams, namely: embankment dam and concrete dam. Embankment dams can
be classified into two main categories earth-fill dams and rock-fill dams, Embankment dams represent about
85% of all dams built M. Elshemy (2002).There are several factors to be considered in selecting an earth dam
type such as: topography; foundation conditions; environmental impacts, construction facilities and socio-
economic studies. A feasible dam should be; built from locally available materials; stable under all operating
and loading conditions; watertight enough to control seepage; has appropriate outlet works to crest dam
overtopping. ( Ismail and K. Gey,2012) and Zeidan (1993).
This paper is a part of major study with scope of; a) review of geometrical, seepage and stability
requirements in major codes and regulations, b) analyze two existing dams are analyzed with the selected
dams have enough published data regarding the geometry, geology, soil and material property of the
different shells of the dam, hydraulic design requirements such as maximum and minimum water levels in
the reservoir in the upstream as well as the levels in the downstream, c) analyze several existing published
dam case histories that experienced failure either due to seepage or stability so that the safety requirements
and regulations can be checked, and d) analyze those cases in c) with different proposed scenarios that would
modify the status of the analyzed dam from failing the requirements to passing those requirements. In the
process, the use of both finite element seepage analysis and stability analysis can be assessed.
To prevent the seepage failure through foundations there are the different methods to control seepage of
water through foundations are explained below. MST (2005)
Grouting and grout curtain; Cut off by using trenches, sheet piling and Cast in situ concrete diaphragm;
upstream blanket and Pressure relief wells. Cast in situ concrete diaphragm method was considered in this
work.
The GeoStudio software GEO – Slope(2004) is a Finite element technique which is mostly used in various
civil engineering application and their problem analysis by considering different consideration.

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In this paper, the Walter Dam, USA is analyzed and studied as case history of an operating dam.
GeoStudio software GEO- Slope(2004 ) is utilized in the analyses. Finite Element modeling is employed for
simulating seepage analysis of the dam. The results of the analyses are used to assess the adequacy of safety
regulation criteria set by both the British Dam Society BDS(1994) at the Institution of Civil Engineers in
United Kingdom, United States department of Army Corps of Engineers USACE(2004) and United State
Department of interior Bureau of Reclamation USBR (2014).
2. Seepage Flow through Earth Dams
Seepage flow of water through porous media depends on the soil media, type of flow, properties of
liquid and hydraulic gradient. Seepage failures more than 35% of all earth dam failures and Structural
failures about 25% of the dam failures M. Elshemy (2002). For example of seepage failures are; Fontenelle
Dam (USA, 1964) and Walter F. George Dam (USA, 1970) (Rice, 2007).Thus seepage analysis in earth dams is
an essential requirements for the design and analysis of dams.
Seepage analysis is addressed via many authors since Darcy(1856) as referenced in Harr(1962), who gave
the basic law of flow through porous media. Darcy’s law was based on series of experiments conducted in a
vertical pipe filled with sand. Seepage flow of water through porous media depends on the soil media, type
of flow, properties of liquid and hydraulic gradient. Different methods have been developed to solve seepage
problems, these methods can be classified as analytical, experimental and numerical methods. Ground water
flows in the direction of decreasing potential energy caused by differences in pressure and elevation. A
common measure of this potential energy is the total head, H which is simply the sum of pressure head and
elevation head. The volume rate of flow per unit area is directly proportional to the rate of change of head as
given by the differential form of Darcy's Law. For 3-D transient state conditions, the following general
governing equation is considered as Zeidan(1993):

 
  
 
  
 
  
 ………………………………..(1)
where, Kx, Ky and Kz are the coefficients of permeability in x, y and z directions, respectively, Sy is specific
yield and= p/γw + z = total fluid head, P = pressure, γw = unit weight of water and z = elevation head and

 is the time first derivative. Equation (1) is known as Laplace’s equation which is a partial second order
differential equation governs groundwater flow through aquifers. In the present study, it is assumed that, the
soil media is isotropic and physically stable; the pressure is atmospheric everywhere on the water table
(phreatic surface); and the flow of ground water through the flow domain is steady and Darcian. Zeidan(1993)
2.1 Initial and Boundary Conditions
Figure (1) shows a schematic representation for the problem statement and boundary conditions for a
typical earth dam with toe filter. These boundary conditions are summarized as:
Γ4 Γ4
Fig. (1): Problem statement and boundary conditions
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elev
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H1
Γ1
Γ3
Γ2
Ω
Reservoir
Exit point
Foundation

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2.1.1 Entrance Surface (Γ1)
The upstream boundary surface (Γ1) is the entrance surface at which the percolation of reservoir
water through the media starts. This surface is considered as an equipotential line which is known as
Dirchlet Condition Elshemy (2002) for a prescribed head as:
H1 (t)…………………………………………………………..…………… (2)
2.1.2 Phreatic Surface (Γ2)
The boundary surface (Γ2) is the phreatic surface of the flow through the dam. This boundary is
considered as a stream line. The phreatic surface, although it is considered as a boundary condition, its
location and its profile are unknown a priori. For the unknown phreatic surface the boundary condition is:
 (x, y, z, t) = y ……………….…………………………………………………...…...….... (3)

   = 0 ..…………………..………………………………………………............. (4)
where n is the normal directions to the boundary (Γ2).
2.1.3 Exit Surface (Seepage surface) (Γ3)
The boundary surface (Γ3) is the exit surface or seepage surface. This boundary is considered as an
isobar at which the pressure along it is atmospheric, hence, the boundary condition along such a surface is:
(x,y,z, t) =y …………………………………………………….................................... (5)
The geometry of the seepage surface is known, except its upper limit the exit point, which is laying on the
unknown phreatic surface. The location of this point is a part of the required solution.
2.1.4 Dam Foundation Boundary (Γ4)
The boundary surface (Γ4) is the dam foundation boundary, which is also known as Neumann Condition M.
Elshemy (2002).In the present study, this boundary is assumed to be impervious i.e. this surface prevents the
flow of water across it such that:

 = 0…………………………………………………………………………………….…. (6)
where n is the normal directions to the boundary (Γ4).
3. Finite Element Modeling
Zienkiewiez and Chung (1967) published the first finite element simulation to solve the Laplace equation
for steady ground water seepage. Taylor and Chow (1976), recorded that the Finite Element Method was used
to assess the potential seepage flows and uplift pressure in the foundation rock for Bannett Dam in Canada.
Kratochvil(2004), used thermal method at ANSYS computer code to simulate numerically the case of no
stationary free surface in earth dams.
The basic concept of the finite element method is to divide the problem region into sub domains (Finite
Elements) connected at their common nodal points and that the unknown function of the field variable is
defined approximately within each element. The approximate solution of each element expressed by
continuous function is as follows (Zeidan, 1993):
 


 
……………………………………...………………………… (7)

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where, 
 nodal value of (H) for ith node in element (e), noe = total number of elements and
shape
function of element 7(e).
There are different approaches to formulate the approximate solution of the problem. In the present
study, the standard weighted residual method with Galerkin’s (1967)criterion is used to approximate the
solution of the unknown variable (H). Thus, equation (1) can be written in a matrix form as:
 ………………………………………….…………………………… (8)
in which is the unknown nodal potential head vector, is the nodal external flux vector and  is the
conductivity matrix given by:
 
 

 + 
 
 ……………………………….………….. (9)
where,  = the domain of element (e) and= interpolation or shape function.Derivations of the above
functions are given in detail by Zeidan(1993).
The solution of seepage problem with phreatic surface requires successive adjustments for the location of the
phreatic surface and the finite element mesh size till the desired degree of convergence for the nodal head H
is achieved. In all iterative methods, the solution is started by using initial guess for the unknown phreatic
surface and the solution is obtained by repeating the solution of the system of equations successively
through recurrence relations such as:
 =  ……………………………………………………………………….. (10)
For all nodes on the phreatic surface to update the old values until the solution converges closely enough to a
prescribed tolerance of error.
4. Geostudio Software
Geostudio is often used for seepage and slope stability analyses for earth dams. Karjani(2012) used
GeoStudio computer software to analyze Maroon dam, estimated flow net and slope stability factor at overall
stability for different operating conditions. Zomorodian and Abodollahzadeh (2010),used GeoStudio software to
investigate the effect of horizontal drains on upstream slope of earth fill dams during rapid drawdown.
Tatewar and Pawade(2012),used GeoStudio software to investigate the slope stability of the 21m high Bhimdi
earth dam, by changing different parameters such as berm width and position of filter drains. Hasani et al.,
(2013), studied the seepage analysis in Ilam earth dam for four mesh sizes in order to assess the effect of
meshing on results accuracy.
In this work, GeoStudio software, a Finite element technique for simulating seepage and stresses of earth
dam problems, was developed to check the stability of earth fill dams.
5. Model Verification
Both Geostudio computer code GEO – Slope(2004) and ANSYS software ANSYS (2005), are employed
in the present study to simulate seepage analysis of through earth dams, Figures (2) and (3). The model is
verified by using GeoStudio and ANSYS soft wares with reference (Fadaei Kermani and Barani1 2012) for
embankment dam for seepage analysis. Figures (4- 7) show the phreatic seepage surface and total hydraulic
head variation of a typical earth dam. Comparison of obtained results show a good agreement and harmony
between ANSYS and Geostudio results.

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Figure (2) Finite element meshes by GeoStudio software
Figure (3) Finite element meshes by ANSYS software
Figure (4) Water head variation through dam body and its phreatic surface by GeoStudio
Figure (5) Water head variation through dam body by ANSYS software
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Figure (6) Flow pattern through dam body by Geostudio the velocity is (1.4e-5 m/sec)
Figure (7) Flow Pattern Through Dam Body by ANSYS the Velocity is (0.4 e-5 m/sec)
6. Hydraulic Safety Criteria of earth dams
Hydraulic design and safety evaluation of embankment dams should satisfy the recommended criterion
of the experienced agencies in the design of embankment dams. Among the numerous dam safety regulation,
USACE (2004), BDS (1994) and USBR (2014) criterion are considered as the benchmark for their broad
area of validation in the present study.
Based on the experience of failures, the following main design criteria may be laid down for the safety of an
earth dam.
1. To prevent hydraulic failures the dam must be so designed that erosion of the embankment is
prevented. This implies that the following conditions are satisfied.
(a) Spillway capacity is sufficient to pass the peak flow; (b) Overtopping by wave action at maximum water
level is prevented; (c) The original height of structure is sufficient to maintain the minimum safe freeboard
after settlement has occurred; (d) Erosion of the embankment due to wave action and surface run-off does
not occur; (e) The crest should be wide enough to withstand wave action and earthquake shock.
2. To prevent the seepage failures, the flow of water through the body of the dam and its foundation must
not be sufficiently large in quantity to defeat the purpose of the structure nor at a pressure sufficiently high
to cause piping. This implies that: (a) Quantity of seepage water through the dam section and foundation
should be limited; (b) The seepage line should be well within the downstream face of the dam to prevent
sloughing; (c) Seepage water through the dam or foundation should not remove any particle or in other
words cause piping. The driving force depends upon the pressure gradient while the resisting force depends
upon the strength characteristics of the boundary material and (d) There should not be any leakage of water
from the upstream to downstream face. Such leakage may occur through conduits, at joints between earth
and concrete sections or through holes made by aquatic animals.
1.4011e-005
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3. Normal freeboard is defined as the difference in elevation between the crest of the dam and normal
reservoir water surface. According to the fetch of reservoir the freeboard may be provided as given in Table
(4). It is also recommended that freeboard shown in Table (1) be increased by 50 percent if a smooth
pavement is provided as protection on the upstream slope. MST (2005)
Table 1. Recommended Values of Freeboards MST (2005)
Fetch in km
Normal freeboard in meter
Minimum freeboard in meter
Less than 1.5
1.25
1.00
1.50
1.50
1.25
4.0
1.80
1.50
8.0
2.50
1.80
15.0
3.00
2.20
4. The factor of safety against boiling or heave in seepage analysis of dams, exit gradients refer to
hydraulic gradients at a free face or into more pervious materials. The critical gradient (Ic) is most commonly
expressed as the ratio of the buoyant unit weight of the soil (γb) to the unit weight of water (γw):
Ic = γb/ γw ……………………………………………………………………..(11)
An alternate form of this equation, assuming the foundation soil is saturated, utilizes the specific gravity (G)
and the void ratio (e) of the soil:
Ic = (G-1)/(1+e) ………………………………………………………………(12)
The factor of safety (FS) with respect to exit gradients (against boiling or heave) is generally defined as the
ratio of the critical gradient (Ic) to the predicted or measured exit gradient (Ie):
FS = Ic / Ie ………………………………………………………………..…..(13)
5. The factor of safety against uplift at the downstream toe of an embankment, dangerously high
pressures may exist in the previous layer. If the seepage pressures in the previous layer are higher than the
overburden pressure of the confining layer, uplift of the confining layer may occur. In simplest terms, the
factor of safety against uplift can be calculated in total stresses (or forces) as the total downward pressure
exerted by the weight of the confining layer divided by the upward water pressure at the base of the layer.
This factor of safety by the total stress method is defined as:
FS = (γt ) (t) / (γw) hp……………………………………………..……………..…..(14)
where: γt = the total unit weight of the confining layer soil, t = the vertical thickness of the confining layer,
γw = the unit weight of water , hp = the pressure head at the base of the confining layer.
Table 2. Recommended Factors of Safety Against Heave USBR (2014)
Type of Facility
Recommended Safety Factor
New dam
4.0
Existing dam
3.0
Table 3. Recommended Factors of Safety Against Uplift USBR (2014)
Type of Facility
Recommended Safety Factor
New dams
2.0
Existing dams
1.5

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7. Walter F. George Dam:
Walter F. George dam is managed by the U.S. Army Corps of Engineers (USACE 1972), Mobile
District and is located on the Chattahoochee River on the border between Georgia and Alabama
approximately 84 miles southeast of Mobile, Alabama, Figure (8), (USACE 1982). The dam consists of a
central concrete section with long earth embankments extending to the edges of the flood plain on both
sides. Figure (9) shows the dam cross-section. The hydraulic conductivity parameters of the dam materials
used in the seepage analysis are listed in Table (4). These parameters are obtained based on the typical
hydraulic conductivity parameters, k.
Figure (8) Map of Walter F. George Dam (Rice, 2007)
Figure (9) Cross section of Walter F. George Dam refer to Table (4)
Table 4. Material properties of Walter F. George Dam (Taylor & Francis 2007).
Layer
(1) Impervious
Clay
(2) Upstream
Blanket
(3) Downstream
Filter
(4)
Alluvium
(5) Earthly
Lime Stone
(6) Shell
Lime Stone
(7) Sandy
Lime Stone
Hydraulic
Conductivity K
1* m/s
1* m/s
1*
1* m/s
1*
1* m/s
1* m/s
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1
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7
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6

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7.1 Safety Criteria of Walter F. George Dam
The Geometric properties of Walter dam were checked using BDS (1994). Table (5) gives the results of
the comparison. It can be noticed that the geometric design of the Walter dam is acceptable based on the
recommendations of the British Dam Society BDS.
Table 5. Comparison between original section of Walter dam and (BDS) safety limits
7.2 Seepage Analysis of Walter F. George Dam
The Finite Element Mesh of the model can be seen in Figure (10). While Figures (11) and (12) present
the water head variation and seepage velocity through the dam body, respectively. As can be seen in the
presented figures, the phreatic line has not been lowered down through the dam body and thus the pore water
pressure in the internal surface of downstream are not under control.
The total head variation through the dam body also shows that the seepage through the dam is not satisfy the
recommendations of the (BDS 1994). The seepage water indicated by the flow lines in fig. (11) are near to
the downstream toe of the dam. Table (6) gives the hydraulic safety criteria. It can be noticed that the
hydraulic safety criteria based on United State Department of interior Bureau of Reclamation not acceptable
(USBR, 2014).
For these reasons seepage or piping failure occurred through the dam body, although the dam content the
horizontal upstream blanket. Piping failure through the dam body is shown by Figure (13).
Figure (10) Finite element mesh of Walter dam
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Parameter
Walter F. George Dam
(BDS) Safety Limits
Safety of dam
status
Crest width
9.14 m
Not less than 2.0 m
Acceptable
Upstream slope
3:1
2.5:1
Acceptable
Downstream slope
2.5:1
2:1
Acceptable
Free board
3.0 m
Min. free board = 2.20 m at Fitch = 15 km.
Acceptable
Bed width of core
138.2 m

 (17.67/3)
Acceptable
Core slope
1:2.5
1:12
Acceptable

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Figure (11) Water head variation and flow line through the dam body
Table 6. The hydraulic safety criteria of Walter dam based on (USBR, 2014).
Factor of Safety
Walter F. George Dam
(USBR, 2014) Safety
Limits
Safety of dam status
Against Heave
Ie= (18/130)=0.138
FS = (1/0.138) = 7.25
4.0
Acceptable
Against Uplift
FS = 1.9
2.0
Not acceptable
Figure (12) Seepage velocity through the dam body
Figure (13) The piping failure through the dam body before (left) and after (right) seepage barrier construction. (Rice,
2007).
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1.0379e-006
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8. Scenario To Secure Walter F. George Dam
As failure of this dam was due to seepage or piping, a parametric study was essential to control the
seepage through the dam body using the following scenario. Figure (12) presents a modification which uses
a concrete diaphragm wall with penetration depth 8m through the foundation layers and its width is 0.6 m.
Figures (13), (14) and (15) present the water head variation, pore water pressure and seepage velocity after
modification through the dam body, respectively.
As can be seen in the presented figures, the phreatic line has been lowered down effectively by the concrete
diaphragm wall and thus the pore water pressure in the internal surface of downstream are estimated to be
under control. Moreover, the seepage water determined by the flow lines are conveyed to the downstream
toe of the dam and the drainage have aided to minimize the development of pore water pressure in the
downstream.
Table (6) shows that the seepage velocity through the dam body before seepage barrier construction is
(1.0379* m/s) its value not enough to control the seepage. While after using concrete diaphragm wall
the seepage velocity through the dam body reduced to (1.0276*m/s), that enough to prevent the
seepage failure based on the modes of failure.
Figure (14) cross section of the dam with the modification
Figure (15) Water head variation and flow line through the dam body
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Figure (16) Pore Water Pressure through dam body
Figure (17) Seepage velocity through Walter F. George Dam
Table 6. Seepage velocity analysis of Walter F. George dam
Walter F. George dam seepage velocity
Cases of Walter Dam
Velocity(m/s)
Safety of dam status
Original Walter Walter F.
George failed dam
1.0379*
Seepage (piping) failure
Modified Walter Dam After
present scenario
6.0276*
Acceptable
9. Conclusion
Finite Element Modeling was employed in this study to verify the stability of Walter F. George dam
(USA), earth dam as a case study. The dam safety criteria is checked based on the BDS’ recommendations.
Obtained results confirm that although the geometric design of the dam is acceptable according to seepage
criteria (USBR 2014 and USACE 2004), the seepage through the dam does not satisfy safety regulations.
Moreover, the dam failure occurred due to seepage or piping failure is assured by code recommendations. A
scenario for preventing failure of Walter F. George dam using a concrete diaphragm wall is presented. As a
result, the seepage velocity and gradients through the dam body is reduced significantly enough to prevent
seepage failure and to secure dam safety.
0
5
10
15
20
25
30
35
40
45
dist
010 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340
elev
0
10
20
30
40
50
60
70
6.0276e-010
dist
010 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340
elev
0
10
20
30
40
50
60
70

International Conference on Advances in Structural and Geotechnical
Engineering, 6-9 April 2015, Hurghada, Egypt
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