Earth Dam Design Problem
Objectives
Embankment dams come in two types the rockfilled dam and the earthfilled dam made of compacted earth (also called an earthen dam or terrain dam). In this analysis we deal with Queensland dam. Analysis has been done using the Geo studio software and the results discussed.
Configuration
Properties of the earth dam
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Dam Dimensions 

Hunfilled water 
Hservice 
Hfoundation 
Hfilter 
HCE 
Ltop 
S1 
S2 
(m) 
(m) 
(m) 
(m) 
(m) 
(m) 
(m) 
(m) 
1.9 
22.8 
16 
1.2 
0 
6.3 
3.5 
2.5 
Material Properties 

Material 
Undrained 
Effective 
Effective 
Saturated 
Saturated 
coefficient of 
Saturated 
kPa 
kPa 
Degree 
kN/m3 
m3/m3 
m2/kN 
m/S 

Core 
68.5 
7.6 
30 
21 
0.41 
20.5 *105 
1*1011 
Embankment 
68.5 
17 
26 
20.5 
0.33 
1.6 *105 
3*107 
Foundation 
42.6 
20 
34 
19.8 
0.29 
1.1 *105 
7.9*1012 
Filter 
— 
0 
35 
21.1 
0.31 
0 
2.54*104 
The client has requested from your design to provide your recommendations on the following points:
1) Model the earth dam in SEEP/W (GeoStudio software) and assign relevant material properties and boundary conditions. Analyze the earth dam for steadystate seepage conditions when the upstream water is at the service level. Using SEEP/W results, calculate the total seepage loss through the dam and foundation per year in m3.
This is the resultant of our geometry
 Draw the dam geometry using the given dimensions
 Define materials by clicking on
 Define
 Hydraulic Functions
 Volume water content as shown
 Select saturated/unsaturated since there may be unsaturated regions
 Do this for all the parts i.e the core, embankment, foundation, and filter keying in the values given for each.
 Define the Hydraulic conductivity in this case Silk K as shown
Picture showing the hydraulic conditions
 Allocate material properties to the different regions by clicking on draw the allocating the properties with the small box which appears on the cursor
The resultant diagram is as shown
2) Using the results of steadystate seepage analysis (SEEP/W), determine the total head and porewater pressure at Points “A” and “B” under steadystate seepage conditions with upstream water at the service level. Use following relationships to define the locations of points “A” and “B”.
=3+ =5 x =2 + `=8(1+ )
where, M: mean of the final two digits of all group figures
Ex: figure 01: d ××××56, figure 02: d ××××04, and figure 03: d ××××00, M = 20
Points A and B are shown by 14 and 15 initials
The results for point A are as shown below
(we use the results below to determine the Total head and Pore water pressure of the two points)
Total head is 27.185454
Pore water pressure is 70.467748
For point B
Total head is 26.119675
Pore water pressure is 128.66465
3) Obtain two different flow nets from the above steadystate seepage analysis using SEEP/W (service water level). Using Darcy’s equation for 2D seepage and Bernoulli’s equation, calculate the total seepage loss through the dam and foundation per year in m3 and the total head and porewater pressure at Points “A” and “B” for each flow net.
Use only the permeability of embankment soil to estimate the total seepage loss through the dam and foundation. Compare the calculated total seepage loss, total head at A & B, and Porewater pressure at A & B with the values obtained from SEEP/W ((1) and
(2)).and provide three possible reasons for any deviation
Head at B
heB= 2m
hpB= 13m
therefore total head at B
Task
= 13+2= 15m
Head at A
17+ 2
=19m
Loss in total head between points A and B
= htA htB
1915= 4
The gradient of total head
I= change in h÷L
4÷ 22 = 0.18
Using Darcy’s law, the rate of seepage flow:
Since i= 0.18
Q= KiA
= 10^{6}×i×A
= 10^{6}×0.18×0.2
=3.6×10^{8}m^{3}/sec
Pore pressure :
Ρw= 1000kg/m^{3}
G= 9.81 m/sec^{2}
Pore pressure= 1000 ×9.81×water pressure
Pore pressure= 1000 ×9.81×65.413
=641,701.53
4) The council expects to minimise the seepage through the dam by selecting the best material properties for the core of the dam. Using at least four different saturated permeability values for the core of the dam, select optimal saturated permeability for the core of the dam considering the steadystate seepage loss under serviceability conditions (service water level). Typical values of the permeability of core materials are between 1 109 m/S and 1 1014 m/S.
Using the DruckerPrager assuming that the DruckerPrager yield surface touches on the interior of the MohrCoulomb yield surface
Material 
Undrained 
Effective 
Effective 
Saturated 
Saturated 
coefficient of 
Saturated 
kPa 
kPa 
Degree 
kN/m3 
m3/m3 
m2/kN 
m/S 

Core 
68.5 
7.6 
30 
21 
0.41 
20.5 *105 
1*1011 
Embankment 
68.5 
17 
26 
20.5 
0.33 
1.6 *105 
3*107 
Foundation 
42.6 
20 
34 
19.8 
0.29 
1.1 *105 
7.9*1012 
Filter 
— 
0 
35 
21.1 
0.31 
0 
2.54*104 
The optimal saturated permeability is 7.9*1012
5) Using SEEP/W, reanalysis the dam for steadystate seepage when the reservoir water is at the overtopping level. Calculate the total seepage loss per year in m3, total head and porewater pressure at A & B. Compare these values when the reservoir water is at the service level and give the reasons for differences.
At A
At B
To calculate quantity of water escaping as seepage, following formula can be used;
Seepage water (in m^{3}/Day) = Seepage losses (in m/Day) X Surface area of the pond (in m^{2})
In this case we calculate as follows:
Surface area of the pond = let’s take 40,000 m^{2} (Width in meter X Length in meter)
Seepage losses = 9 mm (Soil type: silt,)
Seepage water (in m^{3}/Day) = 360m^{3 }per day
Per year we multiply by 365 days
360×365
=131,400 m^{3}
Head and Pore pressure is calculated as shown below
Using Darcy’s law, the rate of seepage flow:
Since i= 0.18
Q= KiA
= 10^{6}×i×A
= 10^{6}×0.18×0.8
=1.44×10^{7}m^{3}/sec
Pore pressure :
Ρw= 1000kg/m^{3}
G= 9.81 m/sec^{2}
Pore pressure= 1000 ×9.81×water pressure
Pore pressure= 1000 ×9.81×128.66
=1,262,154.60
6) Model the earth dam in SLOPE/W and assign the relevant material properties and boundary conditions. Analyse both the upstream and downstream slopes of the dam for stability after the construction by using MorgensternPrice, Bishop’s simplified, Janbu’s simplified, Spencer, and Fellenious (Ordinary) methods. Briefly describes the reasons for different factor of safety (FOS) values obtained from different method of analysis for a given slope. Further, provide three recommendations to increase the stability of the dam during/after construction.
Dam Details
Geometry after material allocation
The resultant geometry is as shown
Slice 1 – MorgensternPrice Method
Factor of Safety 0.133
Phi Angle 0 °
C (Strength) 17 kPa
Pore Water Pressure 0 kPa
Pore Water Force 0 kN
Pore Air Pressure 0 kPa
Pore Air Force 0 kN
Phi B Angle 0 °
Slice Width 0.55004 m
MidHeight 1.1345 m
Base Length 0.77788 m
Base Angle 45 °
Anisotropic Strength Mod. 1
Applied Lambda 0.1
Weight (incl. Vert. Seismic) 12.792 kN
Base Normal Force 78.951 kN
Base Normal Stress 101.5 kPa
Base Shear Res. Force 13.224 kN
Base Shear Res. Stress 17 kPa
Base Shear Mob. Force 99.527 kN
Base Shear Mob. Stress 127.95 kPa
Left Side Normal Force — kN
Left Side Shear Force — kN
Right Side Normal Force 126.79 kN
Right Side Shear Force 1.5203 kN
Horizontal Seismic Force 0 kN
Point Load 0 kN
Reinforcement Load Used 0 kN
Reinf. Shear Load Used 0 kN
Surcharge Load 0 kN
Polygon Closure 1.4175 kN
Top Left Coordinate 9.6238238, 33.574449 m
Top Right Coordinate 10.173865, 35.293327 m
Bottom Left Coordinate 9.6238238, 33.574449 m
Bottom Right Coordinate 10.173865, 33.024409 m
7) Using SEEP/W & SLOPE/W, calculate the stability (FOS) of the downstream slope of the dam under steadystate conditions at both service and overtopping water levels by using MorgensternPrice, Bishop’s simplified, Janbu’s simplified, Spencer, and Fellenious (Ordinary) methods. Provide three recommendations to increase the stability of the downstream slope of an earth dam during steadystate seepage condition.
Result showed that average flow rate of leakage under the different mesh size for ilam dam equal 0.836 liters per second for the entire length of the dam.
Slice 28 – MorgensternPrice Method
Factor of Safety 0.133
Phi Angle 0 °
C (Strength) 17 kPa
Pore Water Pressure 0 kPa
Pore Water Force 0 kN
Pore Air Pressure 0 kPa
Pore Air Force 0 kN
Phi B Angle 0 °
Slice Width 0.47777 m
MidHeight 3.0984 m
Base Length 0.48884 m
Base Angle 12.219 °
Anisotropic Strength Mod. 1
Applied Lambda 0.1
Weight (incl. Vert. Seismic) 30.346 kN
Base Normal Force 20.614 kN
Base Normal Stress 42.169 kPa
Base Shear Res. Force 8.3103 kN
Base Shear Res. Stress 17 kPa
Base Shear Mob. Force 62.545 kN
Base Shear Mob. Stress 127.95 kPa
Left Side Normal Force 179.3 kN
Left Side Shear Force 5.5245 kN
Right Side Normal Force 122.06 kN
Results and Analysis
Right Side Shear Force 2.5302 kN
Horizontal Seismic Force 0 kN
Point Load 0 kN
Reinforcement Load Used 0 kN
Reinf. Shear Load Used 0 kN
Surcharge Load 0 kN
Polygon Closure 0.44226 kN
Top Left Coordinate 22.566704, 28.314712 m
Top Right Coordinate 23.04447, 26.987585 m
Bottom Left Coordinate 22.566704, 24.604509 m
Bottom Right Coordinate 23.04447, 24.501045 m
Results showing summary of safety factor for stability SEEP/W & SLOPE/W analysis:
Figure displayed are according to simulation results:
Method of analysis 
Upstream slope after construction 
Downstream slope after construction 
Upstream slope in steady stage leakage 
Downstream slope in steady state leakage 
Sudden drop in reservoir water level 
Jambu simplified method 
1.9282 
1.8170 
1.7119 
1.8891 
1.9101 
Bishop simplified method 
2.0191 
2.2812 
1.8101 
2.0101 
2.1910 
Morgenstern price method 
2.2282 
2.4722 
1.9191 
1.9191 
2.2292 
Fellenious (Ordinary) method 
1.8190 
2.1282 
1.7171 
1.7181 
1.9191 
FOS= 20.6
8) To satisfy the peak water demand of a dry season, water in the reservoir is proposed to release to the water treatment plant in very short time (sudden drawdown). Calculating the stability of upstream slope during drawdown using SEEP/W and SLOPE/W, estimate the safest rapid drawdown level of the reservoir using at least four drawdown levels to ensure the stability of the dam during this operation using MorgensternPrice method. Assume that 30 days are required to dissipate the excess porewater pressure from the dam after the rapiddrawdown operation.
Slice 30 – MorgensternPrice Method
Factor of Safety 0.133
Phi Angle 0 °
C (Strength) 17 kPa
Pore Water Pressure 0 kPa
Pore Water Force 0 kN
Pore Air Pressure 0 kPa
Pore Air Force 0 kN
Phi B Angle 0 °
Slice Width 0.47777 m
MidHeight 0.62487 m
Base Length 0.48399 m
Base Angle 9.2007 °
Anisotropic Strength Mod. 1
Applied Lambda 0.1
Weight (incl. Vert. Seismic) 6.1201 kN
Base Normal Force 3.1412 kN
Base Normal Stress 6.4902 kPa
Base Shear Res. Force 8.2279 kN
Base Shear Res. Stress 17 kPa
Base Shear Mob. Force 61.925 kN
Base Shear Mob. Stress 127.95 kPa
Left Side Normal Force 62.098 kN
Left Side Shear Force 0.64716 kN
Right Side Normal Force — kN
Right Side Shear Force — kN
Horizontal Seismic Force 0 kN
Point Load 0 kN
Reinforcement Load Used 0 kN
Reinf. Shear Load Used 0 kN
Surcharge Load 0 kN
Polygon Closure 0.98186 kN
Top Left Coordinate 23.522235, 25.660457 m
Top Right Coordinate 24.000001, 24.33333 m
Bottom Left Coordinate 23.522235, 24.410717 m
Bottom Right Coordinate 24.000001, 24.33333 m
The rapid drawdown condition arises when submerged slopes experience a rapid
reduction of the external water level. In a coupled analysis, the magnitude of pore pressure changes depends on the stressstrain behavior of the soil skeleton. In the analysis presented here several elastic soil moduli are considered ( E= 10,000 MPa, 1000 MPa and 100 MPa).
Using the formula
Z_{0}= 2c/y
Y=30
Z_{0= safest rapid drawdown }
Z_{0}= 2× 10,000/20
= 1,000
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