Earth Dam Design Problem

Understand key features of an earth dam and its design

Learn how to use SEEP/W to analyse seepage in an earth dam

Lean how to use SLOPE/W to calculate the stability of earth dam slopes under different conditions

Verification of results obtained from numerical software

Give experience on team work in designing geotechnical engineering structures

Compose a report following the CRA provided

In the tropical and subtropical climates, dry season agriculture cannot be commenced using only the streamflow. Evaporation and high temperature increase the uncertainty of continuous water supply for the commercial crops. Considering primarily for irrigation, local council in the Queensland state is proposed to construct a 200 m long earth dam for increasing the security of domestic water supply and flood amelioration. Figure 1 illustrates the proposed site for the earth dam.

Figure 1 Proposed site for the new earth dam

Accounting the generic representatives of existing earth dams in Queensland, the dam configuration shown in Figure 2 was selected for this proposed dam. According to the guidelines, this dam is required to achieve very low hazard potential in stability as it is proposed in highly populated area. Your design group was selected in this purpose to check the stability of the dam at four design conditions: 1) during the construction period, 2) at service level, 3) at overtopping level, and 4) during rapid drawdown events. The dimensions and material properties of the dam are illustrated in Table 1. The client has requested from your design to provide your recommendations on the following points:

• Model the earth dam in SEEP/W (GeoStudio software) and assign relevant material properties and boundary conditions. Analyse the earth dam for steady-state 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.

• Using the results of steady-state seepage analysis (SEEP/W), determine the total head and pore-water pressure at Points “A” and “B” under steady-state seepage conditions with upstream water at the service level. Use following relationships to define the locations of points “A” and “B”.

 

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

• Obtain two different flow nets from the above steady-state seepage analysis using SEEP/W (service water level). Using Darcy’s equation for 2-D seepage and Bernoulli’s equation, calculate the total seepage loss through the dam and foundation per year in m³ and the total head and pore-water 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 Pore-water pressure at A & B with the values obtained from SEEP/W ((1) and

(2)).and provide three possible reasons for any deviation

• 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 steady-state seepage loss under serviceability conditions (service water level). Typical values of the permeability of core materials are between 1 10^-9m/S and 1 10^-14 m/S.
• Using SEEP/W, re-analysis the dam for steady-state seepage when the reservoir water is at the overtopping level. Calculate the total seepage loss per year in m³, total head and pore-water pressure at A & B. Compare these values when the reservoir water is at the service level and give the reasons for differences.

• 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 Morgenstern-Price, 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.

• Using SEEP/W & SLOPE/W, calculate the stability (FOS) of the downstream slope of the dam under steady-state conditions at both service and overtopping water levels by using Morgenstern-Price, 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 steady-state seepage condition.

• 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 Morgenstern-Price method. Assume that 30 days are required to dissipate the excess pore-water pressure from the dam after the rapid-drawdown operation.

Embankment dams come in two types the rock-filled dam and  the earth-filled 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 

Dam Dimensions
Hunfilled water	Hservice	Hfoundation	Hfilter	HC-E	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 type Core	Undrained cohesion, Cu	Effective cohesion, C’	Effective friction angle, ?’	Saturated unit weight, γsat	Saturated volumetric water content, φw	coefficient of volume compressibility, mv	Saturated permeability, ksat
kPa	kPa	Degree	kN/m3	m3/m3	m2/kN	m/S
Core	68.5	7.6	30	21	0.41	20.5 *10-5	1*10-11
Embankment	68.5	17	26	20.5	0.33	1.6 *10-5	3*10-7
Foundation	42.6	20	34	19.8	0.29	1.1 *10-5	7.9*10-12
Filter	--	0	35	21.1	0.31	0	2.54*10-4

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 steady-state 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

1. Draw the dam geometry using the given dimensions
2. 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.  

3. Define the Hydraulic conductivity in this case Silk K as shown

Picture showing the hydraulic conditions

4. 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 steady-state seepage analysis (SEEP/W), determine the total head and pore-water pressure at Points “A” and “B” under steady-state 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 steady-state seepage analysis using SEEP/W (service water level). Using Darcy’s equation for 2-D seepage and Bernoulli’s equation, calculate the total seepage loss through the dam and foundation per year in m3 and the total head and pore-water 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 Pore-water 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

19-15= 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^-8m³/sec

Pore pressure :

Ρw= 1000kg/m³

G= 9.81 m/sec²

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 steady-state seepage loss under serviceability conditions (service water level). Typical values of the permeability of core materials are between 1 10-9 m/S and 1 10-14 m/S.

Using the Drucker-Prager assuming that the Drucker-Prager yield surface touches on the interior of the Mohr-Coulomb yield surface

Material type Core	Undrained cohesion, Cu	Effective cohesion, C’	Effective friction angle, ?’	Saturated unit weight, γsat	Saturated volumetric water content, φw	coefficient of volume compressibility, mv	Saturated permeability, ksat
kPa	kPa	Degree	kN/m3	m3/m3	m2/kN	m/S
Core	68.5	7.6	30	21	0.41	20.5 *10-5	1*10-11
Embankment	68.5	17	26	20.5	0.33	1.6 *10-5	3*10-7
Foundation	42.6	20	34	19.8	0.29	1.1 *10-5	7.9*10-12
Filter	--	0	35	21.1	0.31	0	2.54*10-4

 

The optimal saturated permeability is 7.9*10-12

5) Using SEEP/W, re-analysis the dam for steady-state seepage when the reservoir water is at the overtopping level. Calculate the total seepage loss per year in m3, total head and pore-water 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 m³/Day) = Seepage losses (in m/Day) X Surface area of the pond (in m²)

In this case we calculate as follows:

Surface area of the pond = let’s take 40,000 m² (Width in meter X Length in meter)

Seepage losses = 9 mm (Soil type: silt,)

Seepage water (in m³/Day) = 360m³ per day

Per year we multiply by 365 days

360×365

=131,400 m³

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^-7m³/sec

Pore pressure :

Ρw= 1000kg/m³

G= 9.81 m/sec²

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 Morgenstern-Price, 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 - Morgenstern-Price  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

Mid-Height 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 steady-state conditions at both service and overtopping water levels by using Morgenstern-Price, 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 steady-state 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 - Morgenstern-Price  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

Mid-Height 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 Morgenstern-Price method. Assume that 30 days are required to dissipate the excess pore-water pressure from the dam after the rapid-drawdown operation.

Slice  30 - Morgenstern-Price  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

Mid-Height 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 stress-strain behavior of the soil skeleton. In the analysis presented here several elastic soil moduli are consid-ered ( E= 10,000 MPa, 1000 MPa and 100 MPa).

Using the formula

Z₀= 2c/y

Y=30

Z_{0= safest rapid drawdown}

Z₀= 2× 10,000/20

= 1,000

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