5.0 Stability Analysis of Dam Embankment

69

5.0 Stability Analysis of Dam Embankment

Stability analysis of dam embankment is carried out base on the recommendations made for

the stability analysis for the embankment dams by United States Society on Dams (2007) as

given in this report sub chapter 2.2.4.

The embankment stability is assessed on the basis of the factor of safety against sliding

failure by means of,

Circular slip analysis by Computer software- Geo studio 2004 version 6.02

Wedge analysis and

Infinite slope analysis of external slope

Wedge analysis and Infinite slope analysis of external slope were carried out manually.

5.1 Geo Studio 2004(Version 6.02)

Numerous slope stability programs are available. Virtually all have facilities for both

circular and non-circular analyses by various limit equilibrium methods, and can handle

applied external forces and distributed loads, multiple soil layers, specification of

groundwater conditions by water table, pore pressures or Ru values, seismic loading

coefficients and tension cracks. In most cases the circular slip surfaces may be defined as a

grid of circle centers, a tangent to a common surface or as passing through a common point.

Non-circular slip surfaces are individually defined by the user. The various programs are

distinguished mainly by the limit equilibrium methods that they employ and the user

interface. With the more modern programs the geometry can also be input graphically in a

CAD style interface.

In the Stability analysis of this study Slope/W of Geo studio 2004(Version 6.02) is used.

5.1.1 Loading conditions on the Dam

The stability of the upstream and downstream slopes of the dam embankment is analyzed

for the most critical or severe loading conditions that may occur during the life of the dam

using the shear parameters which were estimated in previous chapter for different grade of

weathering of rocks.

The following loading conditions as mentioned in the sub chapter 2.2.4 are used to analyze

the stability with slope/W.

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5.1.1(a)Steady State Seepage

When the long-term phreatic surface within the embankment has been established, the

following events are considered for analyzing.

Steady state Seepage at normal pool level or Normal High Water Level( NHWL)

460m-masl

Steady state seepage at flood surcharge or embankment crest level 463.5m-masl

Steady state seepage at Partial pool Level or Minimum Operating Level(MOL) 424 m-

masl

5.1.1(b) Rapid (or Sudden) Drawdown

When the reservoir is drawn down faster than the pore pressures can dissipate within the

embankment after the establishment of steady-state seepage conditions, the following

events are considered for this loading condition.

From Normal pool (460m-masl) to Minimum Operating Level (424m-masl)

From Normal pool (460m- masl) to Elevation 385m-masl

5.1.2 Determination of Shear Strengths

Shear Strength parameters estimated from empirical equation by Barton and Kjǽrnsh

(1981) as in the sub chapter 4.5.1.6 are effective stress parameters. However, the effective

stress analysis can be carried out for all loading conditions as per the recommendation

made by USBR as explained in the sub chapter 2.2.4.2. Hence, all analysis was carried out

as effective stress analysis with the computer software slope/w 2004.

5.1.3 Material Properties

The following figure 5.1 shows different zones of the dam and table 5.1 shows the material

properties used for slope/w analysis for the different weathering grades considered. It had

been assumed that the cohesion of all material (c´) is equal to zero at the design stage. This

assumption is conserved the analysis but it may need some value for clay core zone for

cohesion. However this analysis is also considered with same assumption due to there is no

any reliable values found to use for cohesion of the clay core zone in report of design

calculations (Sir Alexander Gibb& Partners, 1987).

71

X

8

87

6

5

9

1

2

44

101112

9

12

6

7

5

31110 2

Table 5.1: Material Properties

Zone No

as per fig

5.1

γwet rockfill(kN/m3) γsat rockfill(kN/m3) ´(degrees) c´(kN/m2)

SW MW HW SW MW HW SW MW HW Design

1(Clay)* 19.62 - - 20.60 - - 30 - - 0 0

2(filter)* 19.62 - - 21.58 - - 37 - - 0 0

3(filter)* 21.58 - - 21.58 - - 39 - - 0 0

4(filter)* 22.45 - - 21.58 - - 42 - - 0 0

5(rockfill) 20.69 19.13 18.42 23.80 22.21 21.63 40 36 34 39 0

6(rockfill) 20.69 19.13 18.42 23.80 22.21 21.63 43 39 37 43 0

7(rockfill) 20.69 19.13 18.42 23.80 22.21 21.63 46 42 40 48 0

8(rockfill) 20.69 19.13 18.42 23.80 22.21 21.63 51 47 44 55 0

9(rockfill) 20.69 19.13 18.42 23.80 22.21 21.63 37 33 31 34 0

10(rockfill)* - - 22.56 - - 24.53 - - - 53 0

11(rockfill)* - - 22.56 - - 24.53 - - - 49 0

12(rockfill)* - - 22.56 - - 24.53 - - - 47 0

*These values are taken from Report of design calculations (Sir Alexander Gibb and

Partners, 1987).

Figure 5.1: Typical Cross Section of the Dam with Different Zones

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5.1.4 Minimum Factor of Safety

Minimum values factor of safety published by various agencies are given in the annex 2

and recommendation of USBR and Wilson and Marsal (“Current trends in design and

construction of embankment dams”-ASCE) are given in the table 5.2.

Table 5.2: Minimum Factor of Safety for Slope Stability

Design Condition

Minimum FOS

Wilson &

Marsal*

USBR**

Steady stage at 460m-masl

(Normal pool) 1.5 1.5

Steady stage at 463.5m-masl

(Maximum pool level) 1.2 1.5

Steady stage at 424 m-masl(partial pool ) 1.5 1.5

Rapid draw down from 460m to 424m 1.2 1.3

Rapid draw down from 460m to 385m 1.2 1.2

Steady stage seepage at NHWL plus earth quake 1.0 1.2

Steady stage at 424 m-masl(partial pool ) plus earth quake 1.0 1.2

USBR**- United States Bureau of Reclamation (1987)

Wilson & Marsal*- Sir Alexander Gibb& Partners (1987).

Results of the slope/W analysis are depicted from figures 5.2 to 5.7.

Minimum Values of Factor of Safety obtained from the Slope/W 2004 analysis for

loading conditions and different stability analysis procedures on the Dam

Figure 5.2: Steady Stage Seepage at NHWL (460.0m masl)-Downstream Face

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Design SW MW HWMin

imu

m F

OS

fo

r M

om

ent

Grade of Weathering

Ordinary

Bishop

Morgenatern-Price

Wilson & Marshal

Recommendation for Minimum

FOS required

USBR Recommendation for

Minimum FOS required

73

Figure 5.3: Steady Stage Seepage at NHWL (463.5m masl)-Downstream Face

Figure 5.4: Steady Stage Seepage at Partial Pool (424 m masl)-Downstream Face

Figure 5.5: Steady Stage Seepage at Partial Pool (424 m masl)-Upstream Face

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Design SW MW HW

Min

imu

m F

OS

fo

r M

om

ent

Grade of Weathering

Ordinary

Bishop

Morgenatern-Price

Wilson & Marshal

Recommendation for




1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Design SW MW HW

Min

imu

m F

OS

fo

r M

om

ent

Grade of Weathering

Ordinary

Bishop

Morgenatern-Price

Wilson & Marshal

Recommendation for




1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Design SW MW HWMin

imu

m F

OS

fo

r M

om

ent

Grade of Weathering

Ordinary

Bishop

Morgenatern-Price

Wilson & Marshal

Recommendation for


USBR Recommendation

for Minimum FOS

required

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Figure 5.6: Rapid draw down from NHWL to 424 m masl-Upstream Face

Figure 5.7: Rapid draw down from NHWL to 385m masl-Upstream Face

5.2 Infinite Slope method

Stability of downstream slope (Sir Alexander Gibb& Partners, 1987)

Factor of safety against surface sliding is given by

For static stability,

𝐹 =𝑡𝑎𝑛

𝑡𝑎𝑛 -----------------------------------(5.1)

For earth quake,

𝐹 =𝑡𝑎𝑛(1−𝑡𝑎𝑛)

𝑡𝑎𝑛(+) ------------------------------------(5.2)

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Design SW MW HW

Min

imu

m F

OS

fo

r M

om

ent

Grade of Weathering

Ordinary

Bishop

Morgenatern-Price

Wilson & Marshal

Recommendation for




1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

Design SW MW HW

Min

imu

m F

OS

fo

r M

om

ent

Grade of Weathering

Ordinary

Bishop

Morgenatern-Price

Wilson & Marshal

Recommendation for




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Where = Friction angle of rockfill at surface

= Embankment slope

= Earth quake coefficient (0.1g)

Stability of Upstream slope

Factor of safety is same as equation 5.1 and 5.2, but factor of R is applied to .

Where R=𝑆𝑎𝑡𝑢𝑟𝑎𝑡𝑒𝑑𝑑𝑒𝑛𝑠𝑖𝑡𝑦

𝑆𝑢𝑏𝑚𝑒𝑟𝑔𝑒𝑑𝑑𝑒𝑛𝑠𝑖𝑡𝑦, 𝛾𝑠𝑢𝑏𝑚𝑒𝑟𝑔𝑒𝑑 = 𝛾𝑠𝑎𝑡 − 𝛾𝑤

Angle of friction for different weathering grades at surface and Saturated Unit Weights

From Zone 6 data of table 2.5 and Zone 8 of table 5.1

Table 5.2: Shear strength parameters for infinite slope analysis

Parameter Design stage used SW MW HW

´at surface of

rockfill(degrees) 55 51 47 44

γsat (kN/m3) 21.7 23.80 22.21 21.63

γsubmerged (kN/m3) 11.89 13.99 12.40 11.82

R 1.83 1.70 1.79 1.83

0.183 0.170 0.179 0.183

SW; Slightly Weathered, MW; Moderately Weathered, HW; Highly Weathered rocks

Angle of slopes of the dam rockfill ()

Slope of the down Stream slope ds=tan−1 (1.8

1)

Slope of the down Stream slope us=tan−1 (2.1

1)

From the equations 5.1 and 5.2, following results are obtained for the values of factor of

safety for each grade of weathering of the rocks and the design parameters.

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Table 5.3: Factors of Safety from infinite slope analyzing method

Parameter Design stage SW MW HW

´at surface of rockfill(degrees) 55 51 47 44

Downstream face Static 2.57 2.22 1.93 1.74

Earth quake 2.06 1.78 1.54 1.39

Upstream face Earth quake 1.98 1.76 1.50 1.34

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5.0 Stability Analysis of Dam Embankment