Analysis of stability of earthen dams in kachchh region, Gujarat, India

Available online at www.sciencedirect.com

Engineering Geology 94 (2007) 123 – 136 www.elsevier.com/locate/enggeo

Analysis of stability of earthen dams in kachchh region, Gujarat, India G.L. Sivakumar Babu ⁎, Amit Srivastava 1 , V. Sahana 1 Department of Civil Engineering, Indian Institute of Science, Bangalore — 560 012, India Received 31 July 2006; received in revised form 25 April 2007; accepted 2 May 2007 Available online 29 June 2007

Abstract The Kachchh region of Gujarat, India bore the brunt of a disastrous earthquake of magnitude Mw = 7.6 that occurred on January 26, 2001. The major cause of failure of various structures including earthen dams was noted to be the presence of liquefiable alluvium in the foundation soil. Results of back-analysis of failures of Chang, Tappar, Kaswati and Rudramata earth dams using pseudo-static limit equilibrium approach presented in this paper confirm that the presence of liquefiable layer contributed to lesser factors of safety leading to a base type of failure that was also observed in the field. Following the earthquake, earth dams have been rehabilitated by the concerned authority and it is imperative that the reconstructed sections of earth dams be reanalyzed. It is also increasingly realized that risk assessment of dams in view of the large-scale investment made and probabilistic analysis is necessary. In this study, it is demonstrated that the probabilistic approach when used in conjunction with deterministic approach helps in providing a rational solution for quantification of safety of the dam and in the estimation of risk associated with the dam construction. © 2007 Elsevier B.V. All rights reserved. Keywords: Earth dam failures; Earthquakes; Stability; Risk; Reliability; Liquefaction

1. Introduction The Kachchh region of Gujarat, India experienced a disastrous earthquake of magnitude 7.6 (Mw 7.6) on January 26, 2001. The earthquake caused large-scale damages to the man made structures like earth dams, buildings, bridges, ports etc. in the vicinity of the epicenter as well as nearby areas. The failure of most of these structures is attributed to liquefaction of the saturated liquefiable soil beneath the foundation. Fig. 1 ⁎ Corresponding author. Tel.: +91 80 22933124; fax: +91 80 23600404. E-mail addresses: [email protected] (G.L. Sivakumar Babu), [email protected] (A. Srivastava). 1 Tel.: +91 80 22932815; fax: +91 80 23600404. 0013-7952/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.enggeo.2007.05.007

shows the location of folds and faults in the Kachchh region of Gujarat and distribution of liquefaction affected area. Fig. 2 shows the Epicentral area (near Bachau at latitude 23.3°N and Longitude 70.34°E, with a focal depth of about 23.6 km) and locations of seven dams that experienced varying amount of damage during the earthquake. The liquefaction of foundation soil was relatively localized in the earthquake affected area and since the earthquake struck in the middle of a prolonged dry season, the liquefaction of the foundation soil beneath majority of earthen dams was limited (Singh et al., 2005). Due to insufficient geotechnical data, although it was difficult to assess the liquefaction susceptibility of the foundation soil under the preearthquake conditions, it is well understood that the top 2.0 to 3.0 m layer of foundation soil was susceptible to

124

G.L. Sivakumar Babu et al. / Engineering Geology 94 (2007) 123–136

Fig. 1. Location of folds and faults in the Kuchchh region of Gujarat and distribution of liquefaction affected area.

liquefaction but it did not liquefy due to lack of saturation of these layers, specially on the downstream side and the effect was limited to reduction in strength of the foundation soil. After the earthquake, various remedial measures were implemented by the concerned authority (Narmada, Water Resources and Water Supply Department, Government of Gujarat, India) to reconstruct and rehabilitate the earthen dams in the affected region.

1.1. Objective of the present study The objective of the present work is to report on the results of back analysis as well as to present the analysis of rehabilitated four dam sections i.e. Chang, Tappar, Kaswati and Rudramata. Deterministic and probabilistic analyses are performed to assess the safety of dams for static and pseudo-static loading conditions.

Fig. 2. Epicentral area showing location of seven large dams.

G.L. Sivakumar Babu et al. / Engineering Geology 94 (2007) 123–136

125

The observations of the failure of four dam sections at the sites revealed a base type failure, which indicates reduction of shear strength of foundation soil due to the presence of a liquefiable layer. The liquefiable layer, which lost its strength during earthquake shaking, is the possible reason of failure or damage of various earthen dams in the earthquake affected region. This feature was also observed in the analysis, when the failed dam sections were back analyzed by taking into consideration the presence of liquefiable layer beneath the foundation. 2. Observed damages and remedial measures

Chang dam was constructed in the year 1959 with a design reservoir capacity of 6.9 million m3. This earthen dam had a total length of 370 m and a maximum height of 15.5 m. The dam, located at the heart of the epicentral region, is the single most severe case of large scale damage of an earthen dam due to presence of liquefiable layer beneath the foundation. Fig. 3 shows the cross sectional details of old Chang dam section. The central hearting or core zone consisted of impervious fill and central masonry core wall. The upstream and downstream shell specified as semi-impervious earth fill consisted of locally available silty sands, sandy silts and sandy clays materials. During earthquake, potentially liquefiable fine to medium sands and silty sands up to 3.0 m depth beneath the upstream and down stream side of the embankment were considered to be the major cause of the failure of the dam. A large scale translational slide on the upstream side, maximum crest loss of up to 6.5 m, development of large cracks and fissures were the observed damages of the dam. After the earthquake, following remedial measures (BIS:1893–2002) were taken by the concerned authority to make the dam safe against liquefaction failure as well as for the future earthquakes. 1. The existing soil was excavated to a depth up to which the standard penetration test (SPT) values did not meet the prescribed level (N60 ≥ 14) and it was replaced with compacted soil to achieve the specified SPT values. 2. Treated wooden piles of 15 cm diameter in a 1.5 m square grid were driven through full depth of the foundation from 3.5 m up to the rock in the cut portion in a width of dam seat plus 10 m on either side to densify the foundation material below 3.5 m. 3. On the upstream side near toe in 12.5 m wide, 1.0 m deep loose soil is removed and replaced with heavy

Fig. 3. Cross-sectional details of the old Chang dam section.

2.1. Chang dam

126

G.L. Sivakumar Babu et al. / Engineering Geology 94 (2007) 123–136

1. The longitudinal cracks along the crest of earth dam were excavated to a depth up to which cracks were noticeable. The excavated trench was filled back with clay material and well compacted in thin layers. 2. The prominent cracks on the upstream slope were filled back to the original slope line with clayey soil compacted by hand held pneumatic tamper. After the filling, bentonite clay grouting was done at a low pressure to seal the gaps. 3. Cracks on lower and upper berms were harrowed and then compacted by sheep foot roller. They were raised by well compacted 0.50 m thick layer of low permeability soil and provided with a 1.0 m thick stone pitching. 2.3. Kaswati dam

Fig. 4. A. Tappar dam displayed longitudinal cracks at its upstream toe during the Bhuj earthquake. B. Lateral spreading zone at the downstream toe of Kaswati dam.

compacted material. Above this compacted layer loading berm of 11.0 m and rock key are provided. 4. The width of the dam section is increased and flatter slopes provided.

The dam was constructed in the year 1976 across the river Kaswati, with the design reservoir capacity of 8.86 million m3. It was a zoned earth dam with a crest length of 1454 m and a maximum height of 15.74 m. The dam experienced severe damages. At the time of earthquake, water level in the reservoir was 7.7 m below the full reservoir level (FRL). Longitudinal cracks developed along the crest of the dam. Cracking was most severe along a section of approximately 180 m in length where upstream toe stability failure occurred (Fig. 4B). For remedial measures, standard penetration tests (SPT) were carried out at the suggested locations for identifying the liquefaction potential of the ground. As per the provisions of the code (BIS:1893–2002), the depth up to which the SPT values did not meet the requirements, existing soil was excavated and replaced by compacted soil to achieve the specified SPT values. Further, flattening of the dam slopes was carried out and to spread the additional loading on a wider base to improve seismic stability.

2.2. Tappar dam 2.4. Rudramata dam Originally constructed in 1976, the dam is situated across river Sang, with original reservoir capacity of 48.81 million m3. It comprises 4575 m long earth dam with maximum height of 17.75 m. The dam is founded directly upon the alluvium of depth more than 30 m that fills the Sang river basin. At the time of earthquake, the reservoir level was 3.13 m below the crest of the dam. During earthquake, large scale lateral spreading and translational movement of several sections of the dam as well as longitudinal cracks along the crest of the dam were observed (Fig. 4A). The following remedial measures were implemented to rehabilitate the old dam.

The dam is located across river Khari, 16 km from Bhuj in Kachchh district. It was completed in year 1959 with a gross storage capacity of 61.53 million m3. It comprises 1217.19 m long earth dam with a maximum height of 27.57 m. During earthquake, throughout the length of the dam, longitudinal cracks were developed on over the top. The dam was badly shaken and there was large lateral displacement that left pronounced scarps and bulges at the toe of the upstream slope of earthen dam. As a remedial measure, the area in which the SPT values were below the specified limit, berm loading was used as required by the provisions of BIS:1893–2002.

G.L. Sivakumar Babu et al. / Engineering Geology 94 (2007) 123–136

127

Table 1 Summary of performance of some dams during the Bhuj earthquake Dam

Crest length (m) Height (m)

Chang 370 Tapar 4575 Kaswati 1454 Rudramata 1217.19

15.50 17.75 15.74 27.57

amax! R⁎ (km) Observed damage and distress 0.47g 18 0.43g 40 0.26g 115 0.31g 88

Failure of upstream and down stream slope, development of longitudinal cracks, slumping Shallow failure in upstream slope, cracking Shallow failure in upstream slope, cracking Upstream slope failure, moderate cracking, leakage

R⁎ is the approximate epicentral distance. Estimates of amax are based on published literature (Singh et al., 2005).

!

Table 1 summarizes the observed performance of the four dam sections during the earthquake. The following sections provide details with regard to method of stability analysis of earthen dams along with the method used for the assessment of liquefaction potential of the soil. The results of the back analyses of the four dam sections were performed with the geotechnical information available with the consideration of presence of liquefiable layer beneath the foundation of the dams as discussed in subsequent sections. Before taking up the remedial measures, geotechnical investigations were carried out and liquefaction potential of the foundation soil was re-investigated. In view of large scale investments and consequences of failure both conventional and probabilistic analysis have been conducted for the dam sections. The analysis of rehabilitated four dam sections was carried out using deterministic approach (pseudo-static limit equilibrium approach) using the commercially available software SLIDE (2005), which has options for probabilistic analysis as well. Both approaches are used in the present analysis to demonstrate the usefulness of combined analysis in the assessment of safety of the structure in a rational way. 3. Procedures for the analysis 3.1. Liquefaction analysis of the ground (SPT based procedure) Liquefaction is defined as the transformation of a granular material from a solid to a liquefied state as a consequence of increased pore water pressure and reduced effective stress (Marcuson, 1978). Following the earthquakes of Alaska and Niigata, Japan, Seed and Idriss (1971) developed a simplified procedure for evaluating the liquefaction resistance of the ground. Later it was modified and improved by Seed (1979), Seed and Idriss (1982) and Seed et al. (1985). In 1996, the procedures available for the evaluation of liquefaction resistance of level and gently sloping ground were reviewed by Prof. T. L. Youd and I. M. Idriss with 20 experts and recommendations were made based on SPT

(standard penetration test), CPT (cone penetration test), BPT (Becker penetration test for gravelly soil) and shear wave velocity measurements (Youd et al., 2001). In the present study, as recommended by Youd et al. (2001), procedure based on SPT results was used to find the liquefaction resistance of the soil. The following sections describe the procedure in a brief manner. The estimation of liquefaction resistance of the soil requires the determination of CSR (cyclic stress ratio) and CRR (cyclic resistance ratio) values as obtained by the following equations.
CSR ¼

sav V rvo

CRR7:5 ¼ For




¼ 0:65

amax g




 rvo rd V rvo

ð1Þ

ðN Þ 1 50 1 þ 1 60 þ  34  ðN1 Þ60 135 ½10ðN1 Þ60 þ 452 200

ðN1 Þ60 b30 ðN1 Þ60 z30 non−liquefiable soil ð2Þ

In the above Eqs. (1) and (2), amax is the peak horizontal acceleration at the ground surface generated by earthquake of magnitude Mw = 7.5, g = acceleration due to gravity, σvo and σvo′ are total and effective vertical overburden stress, respectively. rd is stress reduction coefficient that accounts for the flexibility of soil profile and can be calculated with the help of following equation:  rd ¼

 1:000  0:4113z0:5 þ 0:04052z þ 0:001753z1:5 ; 1:000  0:4177z0:5 þ 0:05729z  0:006205z1:5 þ 0:00121z2

ð3Þ (N1)60 is the SPT blow count normalized to an overburden pressure of approximately 100 kPa and a hammer energy ratio of 60% obtained as below:   V 0:5 ðN1 Þ60 ¼ N  Pa =rvo ER

ð4Þ

128

G.L. Sivakumar Babu et al. / Engineering Geology 94 (2007) 123–136

where N is the raw SPT blow count, Pa is the atmospheric pressure (≈100 kPa) and ER is the energy ratio normally taken as 0.92 in a typical Indian SPT setup conditions). The value of (N1)60 is considered for the clean sand conditions. Due to presence of fines (particle size smaller than 75 μm), there is an apparent increase in the CRR value and for that an equivalent clean sand SPT value [(N1)60cs] should be evaluated with the relation given below: ðN1 Þ60cs ¼ a þ bðN1 Þ60

ð5Þ

where α and β are the coefficients determined as α = 0.0, for FC ≤ 5%; α = exp[1.76 − (190 / FC 2 )], for 5% b FC ≤ 35%; α = 5.0, for FC N 35% and β = 1.0, for FC ≤ 5%; β = [0.99 + (FC 1 . 5 / 1000)], for 5% b FC ≤ 35%; β = 1.2, for FC N 35%. Knowing the values of CSR and CRR, the factor of safety against liquefaction is determined with the help of following equation: FS ¼

CRR7:5 MSF:Kr :Ka CSR

ð6Þ

where MSF is the earthquake magnitude scaling factor; Kσ, Kα are the correction factors applied for large overburden pressure (N 100 kPa) and static shear stress condition for sloping ground, respectively. The values of these correction factors are obtained using the procedure explained by Youd et al., 2001. For the estimation of liquefaction resistance of the soil, two ground motion parameters — earthquake magnitude (Mw) and peak horizontal acceleration (amax) are required (Youd et al., 2001). These parameters depend on location and nature of fault, local site conditions and distance from the seismic energy source. In this study the attenuation relationship developed by Campbell and Bozorgnia (1994) for the calculation of peak horizontal acceleration (amax) is used. The attenuation relationship was developed using worldwide accelerograms and takes into account local site conditions, type of faulting and distance of seismic source (Kramer, 2003). For the case of normal faulting, soft rock site condition, earthquake magnitude of 8.0 (Mw) and distance of seismic source 5.0 km , the value of peak horizontal acceleration (amax) is obtained as 0.5 g. With this information, the liquefaction resistance of the soil is evaluated. It was a little difficult to establish whether the local soils at the four dam sites had sufficient factors of safety before the occurrence of earthquake or not. But after the earthquake various remedial measures were taken by the concerned authority and extensive geotechnical studies

were carried out at the four dam sites and field and laboratory tests were conducted to obtain the reliable site specific geotechnical data. Based on the available information and using the procedure explained above, the liquefaction resistance of the soil was evaluated and it was found safe against liquefaction. 3.2. In situ soil properties It is well understood that during earthquake loading, pore pressure is developed and there is not enough time available for the dissipation of pore water pressure. Due to this reason, an undrained loading condition exists during earthquake loading in most of the soils irrespective of the grain size distribution characteristics. Since the pseudo-static limit equilibrium analysis is performed to obtain the seismic stability of earthen dams, it is necessary that the soil shear strength and stiffness properties should be reduced. In order to obtain the undrained shear strength (cu) of the foundation soil (for cohesionless material) under static conditions, the following equation proposed by Olson and Stark (2003) was used. V cu =rvo ¼ 0:205 þ 0:0075  ðN1 Þ60

ð7Þ

For determination of shear strength properties of the embankment material, soil samples were collected at different locations within the body of the dam and laboratory tri-axial tests were performed to obtain an average estimate of shear strength parameters of the embankment dam materials. Initially the soil sample was confined under anisotropic loading condition representing in situ stress condition and then deviatoric stress were applied under undrained condition to obtain the shear strength parameters of the soil. A review of literature (Seed, 1979; Hynes-Griffin and Franklin, 1984) reveals that a conservative estimate of factor of safety is made when the pseudo-static limit equilibrium analysis is performed with 20% reduction in soil shear strength parameters which are obtained under static conditions. In the present study, the shear strength parameters of the embankment dam materials obtained using tri-axial test results were reduced by 20% to obtain the pseudo-static limit equilibrium factor of safety and to assess the safety of the earthen dams. Typical values of input soil properties used in the analysis of the earthen dam sections are summarized in Tables 2a–2d. 3.3. Pseudo-static analysis In the pseudo-static approach, the effect of an earthquake loading is represented by constant horizontal

G.L. Sivakumar Babu et al. / Engineering Geology 94 (2007) 123–136 Table 2a Input soil properties for Chang dam Zone Old section

Core Shell Foundation (liquefiable layer) New section Core Shell Foundation

Table 2e Values of coefficient of variation of the input soil parameters

Bulk destiny c (kPa) ϕ (degrees) (kN/m3) 16.60 18.50 15.23

0.0 0.0 0.0

30 25 23

16.90 16.70 19.50

10.0 0.0 0.0

24 30 34

Table 2b Input soil properties for Tappar dam Zone Old section

Core Shell Foundation (liquefiable layer) New section Core Shell Foundation

Bulk destiny c (kPa) ϕ (degrees) (kN/m3) 17.30 16.80 14.20

0.0 0.0 0.0

32 29 22

17.62 16.30 16.60

3.9 5.0 0.0

20 24 30

Table 2c Input soil properties for Kasawathi dam Zone Old section

Core Shell Foundation (liquefiable layer) New section Core Shell Foundation

Bulk destiny c (kPa) ϕ (degrees) (kN/m3) 17.50 17.35 16.50

0.0 0.0 0.0

32 29 22

16.80 17.80 19.50

10.0 0.0 0.0

30 34 34

Table 2d Input soil properties for Rudramatha dam Zone Old section

Core Shell Foundation (liquefiable layer) New section Core Shell Foundation

129

Bulk destiny c (kPa) ϕ (degrees) (kN/m3) 16.56 17.70 15.50

0.0 0.0 0.0

32 29 25

14.90 17.80 16.70

10.0 0.0 2.5

26 27 30

and/or vertical acceleration, which produces inertial forces Fh and Fv acting at the centroid of the failure mass. The magnitudes of the pseudo-static forces in two directions are obtained by multiplying mass of the failure surface with the acceleration components in the respective directions. In the analysis, the pseudo-static

Soil property

Coefficient of variation (%)

Unit weight (γ) Angle of internal friction (ϕ) Shear strength (c)

7 13 20

coefficients kh and kv are defined as the ratio of the earthquake acceleration in the respective directions with the gravitational acceleration. The selection of appropriate value of seismic coefficient decides the magnitude of the inertial force acting on the failure mass. Considering the fact that the actual slopes are not rigid and the maximum earthquake acceleration (amax) acts for the short period, the pseudo-static coefficients used in the analysis correspond to the acceleration value well below the amax value. Hynes-Griffin and Franklin (1984) applied the Newmark sliding block analysis to over 350 accelerograms and studied the correlation between pseudo-static factor of safety and calculated deformation based on sliding block analysis. It was concluded that when the pseudo-static factor of safety is more than unity and horizontal earthquake coefficient, kh = 0.5 amax / g, there will not be significant deformations (Kramer, 2003). For the selection of appropriate value of horizontal seismic coefficient, Bureau of Indian Standard (BIS:1893–2002) divided India into four different zones (I to IV) and horizontal (αh) and vertical (αv) seismic coefficients values are recommended for different zones. As per BIS specifications, Gujarat region falls in Zone-IV and the recommended value of αh is βIαo = 0.15 [β is the factor for soil foundation system (=1.0 for dams), I is the importance factor (=3.0) and αo is the basic seismic coefficient (=0.05)]. It could be noted that the vertical pseudo-static force typically has less influence on the factor of safety since it reduces (or increases, depending on its direction) both the driving and resisting force and as a result, the effects of vertical accelerations are neglected in pseudo-static analysis (Kramer, 2003). Although several researchers in the past highlighted the limitations and drawbacks of the pseudo-static approach (Seed et al., 1969; Gazetas, 1987), the positive point in favor of pseudo-static approach lies in the fact that the method can quantify the degree of safety associated with a structure under static as well as pseudo-static loading conditions. Since the objective of the present work is to examine the stability and the associated reliability both from deterministic and probabilistic approach considerations for the old sections and reconstructed sections, respectively; use of pseudo-static approach is deemed satisfactory.

130

G.L. Sivakumar Babu et al. / Engineering Geology 94 (2007) 123–136

3.4. Deterministic vs. probabilistic approach In the deterministic approaches, uncertainties in the input soil parameters are lumped in the factor of safety. The factor of safety approach has the advantage of being easily interpreted in terms of physical or engineering meaning. However, in the recent years, the need for risk assessment in dam engineering is highlighted (Bowles et al., 1996) and it is also realized that the factor of safety alone is not a sufficient measure for risk assessment. It is difficult to evaluate how much safer a structure becomes as the factor of safety increases (Whitman, 2000; Duncan, 2000). Normally, the selection of appropriate value of allowable value of factor of safety is based on experience and engineering judgment. Conceptually, geotechnical structures with a factor of safety more than 1.0 should be stable but in practice the acceptable value of factor of safety is taken significantly greater than unity due to uncertainties related to material variability, measurement and model transformation uncertainty (Phoon and Kulhawy, 1999). In the case of dams, the methods of slope stability analysis are well established and hence model transformation uncertainty is negligible. Measurement error arises if design properties are arrived at using in situ testing and then using appropriate equations to translate the in situ measured quantities to design variables. In the probabilistic approach these uncertainties in the design parameters are considered in a mathematical framework. The main advantage of the probabilistic approach is a direct linkage between uncertainty in the design parameters and probability of failure/reliability. Considering the importance of dam from safety as well as economy point of view, it should be built with a negligibly small probability of failure. For example, USACE (1997) suggested targeted probability of failure in the range of 10− 4 to 10− 6 corresponding to reliability index values in the range of 3 to 5

Fig. 6. Variation of δf and number of simulation cycles (N).

for design purposes for earthen dams and other geotechnical structures. In the reliability based design approaches, the possible sources of uncertainties in the input variables are identified using statistical analysis of the test data and incorporated in the reliability based models to assess the safety of the structure in terms of reliability index values. The methods of evaluation of reliability index and calculation procedures for statistical parameters such as mean, coefficient of variation and the role of different types of probability distribution functions are presented in Baecher and Christian (2003). In the present work, material variability of input soil parameters is considered to be the major source of uncertainty due to controlled laboratory testing of soil samples to get the numerical values of the required input soil parameters for stability assessment and absence of model transformation uncertainty as indicated earlier. Literature indicates that material parameters follow normal or lognormal distributions for input random variables (USACE, 1997). In order to define the probabilistic assessment of the performance of the structure in terms of reliability index (β), the value of reliability index (β) is calculated from the equations given below. b¼

bLN Fig. 5. Bore log, SPT values (raw and corrected) and variation of factor of safety at the Chang dam site after taking the remedial measures for liquefaction mitigation measures taken by the concerned authority.

lFS  1 rFS

½For normally distributed FS

  lFS ln pffiffiffiffiffiffiffiffiffiffiffi ð1þV 2 Þ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi lnð1 þ V 2 Þ

ð8Þ

½ For Log normally distributed FS

ð9Þ where μFS and σFS is the mean and standard deviation of factor of safety obtained from N number of Monte Carlo

G.L. Sivakumar Babu et al. / Engineering Geology 94 (2007) 123–136

simulations. V is the coefficient of variation defined as σFS / μFS. The input random soil properties are taken as cohesion (c), friction angle (ϕ) and bulk density (γ) and numerical values of these input soil parameters are obtained from the implementing authorities of the reconstruction projects. For the probabilistic analysis, reported values of input soil parameters are taken as mean values for different dam sections as indicated in Tables 2a–2d. Typical values of coefficient of variation of these input soil parameters used for probabilistic

131

analysis are given in Table 2e in accordance with the values reported in Duncan (2000). 4. Results and discussion 4.1. Analysis of the liquefaction resistance of the ground After the remedial measures were taken, liquefaction resistance of the in situ soil at the four dam locations was obtained using SPT based procedure explained in the

Fig. 7. A. Pseudo-static analysis of the old Chang dam section with consideration of liquefiable layer beneath the foundation. B. Pseudo-static analysis of the old Chang dam section without consideration of liquefiable layer beneath the foundation.

132

G.L. Sivakumar Babu et al. / Engineering Geology 94 (2007) 123–136

previous section. Fig. 5 also shows a typical variation of factor of safety of the in situ soil against liquefaction at the Chang dam site. It can be noted that the foundation soil is safe against liquefaction as the shear stresses induced due to earthquake are lesser than the liquefaction resistance and the factors of safety against liquefaction are higher than unity. Similar results were obtained for the other dam sites. 4.2. Number of simulation cycles for Monte Carlo analysis The number of simulation cycles influences the accuracy in the estimation of reliability index values. Since the increase in number of simulations also increases the computational efforts, a compromise between accuracy and computational time should be achieved. It can be obtained by estimating the coefficient of variation of the estimated mean of the factor of safety (δf) for a particular value of number of simulation cycles (N) and the simulation is carried out several times for incrementally large number of cycles till there in no significant change in the value of δf. From Fig. 6, it can be observed that between 30 000 and 40 000 simulations, the value of δf attains almost a constant value and therefore it can be stated that a further increase in the number of simulation cycles does not affect the accuracy of the results significantly. Hence, in the present study, 40 000 simulations have been used. 4.3. Results of deterministic and probabilistic analyses of the four dam sections For the analysis of the dam sections, commercially available software SLIDE (2005) was used. It has options for the deterministic and probabilistic, static as well as pseudo-static analysis of the plain strain models of geotechnical structures such as slopes and embankments. Typical results of the analysis of the old Chang dam section are shown in Fig. 7. It is evident from the figures that the factor of safety and reliability index values are quite low. It also illustrates the occurrence of base type failure due to presence of liquefiable layer in the foundation soil (Fig. 7A). Similar results were also obtained for other dam sections where there was an existence of liquefiable layer in the foundation soil. The analysis was also performed without considering the existence of liquefiable layer beneath the foundation soil and it was observed that the slip surface was confined to the slope of the structure indicating slope failure possibilities (Fig. 7B). The estimated values of factor of safety in these cases were more than unity, which

Table 3a Results of the analysis of the old Chang dam section FOS (det.)

FOS (mean)

pf (%)

Reliability index (β) Normal distribution

Log-normal distribution

With consideration of liquefiable layer in the foundation soil U/S side 0.96 0.97 65.11 − 0.27 − 0.32 D/S side 0.80 0.81 98.28 − 2.46 − 2.26 Without consideration of liquefiable layer in the foundation soil U/S side 1.05 1.05 31.17 0.55 0.51 D/S side 1.06 1.07 20.90 0.82 0.81

Table 3b Results of the analysis of the old Tappar dam section FOS (det.)

FOS (mean)

pf (%)

Reliability index (β) Normal distribution

Log-normal distribution

With consideration of liquefiable layer in the foundation soil U/S side 0.78 0.78 94.99 − 1.83 − 1.70 D/S side 0.88 0.88 83.27 − 0.95 − 0.97 Without consideration of liquefiable layer in the foundation soil U/S side 1.01 1.01 21.17 0.38 0.31 D/S side 1.02 1.02 18.90 0.76 0.71

Table 3c Results of the analysis of the old Kasawathi dam section FOS (det.)

FOS (mean)

pf (%)

Reliability index (β) Normal distribution

Log-normal distribution

With consideration of liquefiable layer in the foundation soil U/S side 0.58 0.58 100 − 9.26 − 7.04 D/S side 0.61 0.61 100 − 8.55 − 6.66 Without consideration of liquefiable layer in the foundation soil U/S side 1.06 1.06 38.23 0.42 0.36 D/S side 1.05 1.05 32.19 0.38 0.29

Table 3d Results of the analysis of the old Rudramatha section FOS (det.)

FOS (mean)

pf (%)

Reliability index (β) Normal distribution

Log-normal distribution

With consideration of liquefiable layer in the foundation soil U/S side 0.73 0.69 100 −7.70 −6.41 D/S side 0.87 0.83 100 −3.76 −6.41 Without consideration of liquefiable layer in the foundation soil U/S side 0.93 0.92 94.51 −0.25 −0.21 D/S side 1.08 1.02 31.20 0.40 0.38

G.L. Sivakumar Babu et al. / Engineering Geology 94 (2007) 123–136

Fig. 8. Cross sectional details of the reconstructed Chang Dam section.

133

134

G.L. Sivakumar Babu et al. / Engineering Geology 94 (2007) 123–136

indicates that the dam could have been marginally safe during earthquake. The results of the analysis of all the four old dam sections are summarized in Tables 3a–3d. Since all four dams suffered different levels of damages during the earthquake, as explained earlier, various remedial measures were taken to improve liquefaction resistance of the foundation soil and to rehabilitate the damaged dam sections. Considering the case of Chang Dam, base material was compacted and piles were driven at a spacing of 1.5 m. This aspect is considered in the analysis using pile-interface resistance of 50 kN and an investigation to assess the safety of the rehabilitated dam sections was made using deterministic and probabilistic approaches. The analysis was performed for reservoir full condition as well as sudden drawdown condition (considering water level at the ground surface)

under static and pseudo-static loading conditions. Fig. 8 shows typical cross-sectional details of the rehabilitated Chang dam section and Fig. 9 shows typical results of the pseudo-static analysis of the Chang dam section under reservoir full condition. It may be noted that the deterministic and mean factor of safety indicated in figures are defined separately. The former is related to the deterministic approach (limit equilibrium approach), while the latter is the average of all the values of factor of safety obtained from the number of Monte Carlo simulations. The results of deterministic and probabilistic analyses of the all the rehabilitated dam sections are summarized in Tables 4a–4h. The results presented in the tables clearly indicate that the older sections have marginal factor of safety as well as low reliability index values and reconstructed sections have higher factors

Fig. 9. A. Pseudo-static analysis of the reconstructed/rehabilitated Chang dam section at reservoir full condition (U/S side). B. Pseudo-static analysis of the reconstructed/rehabilitated Chang dam section at reservoir full condition (D/S side).

G.L. Sivakumar Babu et al. / Engineering Geology 94 (2007) 123–136 Table 4a Results of the analysis of the new Chang dam section (reservoir full condition) FOS (det.)

Table 4e Results of the analysis of the new Kasawathi dam section (reservoir full condition)

FOS (mean)

pf (%)

Reliability index (β) Normal distribution

Log-normal distribution

1.92 2.07

0.00 0.00

4.14 3.42

5.60 4.76

Static analysis U/S side 1.95 D/S side 1.47

Pseudo-static analysis U/S side 1.89 1.92 D/S side 1.83 1.86

0.00 0.00

2.98 2.86

4.01 3.77

Static analysis U/S side 1.91 D/S side 2.04

Table 4b Results of the analysis of the new Chang dam section (sudden drawdown condition) FOS (det.)

Static analysis U/S side 2.02 D/S side 2.35

FOS (det.)

FOS (mean)

pf (%)

Reliability index (β) Normal distribution

Log-normal distribution

1.97 1.47

0.00 0.00

4.19 3.41

5.73 4.07

Pseudo-static analysis U/S side 1.41 1.42 D/S side 1.29 1.30

0.00 0.00

3.21 3.08

4.17 3.82

Table 4f Results of the analysis of the new Kasawathi dam section (sudden drawdown condition)

FOS (mean)

pf (%)

Reliability index (β) Normal distribution

Log-normal distribution

2.06 2.40

0.00 0.00

3.07 3.65

4.26 5.43

Static analysis U/S side 1.70 D/S side 1.87

0.00 0.004

3.18 2.41

4.13 3.13

Pseudo-static analysis U/S side 1.77 1.77 D/S side 1.79 1.81

Table 4c Results of the analysis of the new Tappar dam section (reservoir full condition)

FOS (det.)

FOS (mean)

P.F. (%)

Reliability index (β) Normal distribution

Log-normal distribution

1.71 1.88

0.00 0.00

3.46 4.20

4.43 5.63

Pseudo-static analysis U/S side 1.58 1.59 D/S side 1.70 1.71

0.00 0.00

3.36 3.46

4.24 4.43

Table 4g Results of the analysis of the new Rudramatha section (reservoir full condition)

FOS (mean)

pf (%)

Reliability index (β) Normal distribution

Log-normal distribution

5.07 1.78

0.00 0.00

5.17 3.00

10.44 3.89

Static analysis U/S side 2.90 D/S side 1.77

Pseudo-static analysis U/S side 5.67 5.69 D/S side 1.61 1.62

0.00 0.00

6.31 2.47

12.29 3.14

FOS (det.)

Static analysis U/S side 4.95 D/S side 1.77

Table 4d Results of the analysis of the new Tappar dam section (sudden drawdown condition) FOS (det.)

FOS (det.)

FOS (mean)

P.F. (%)

Reliability index (β) Normal distribution

Log-normal distribution

2.94 1.77

0.00 0.00

4.65 4.10

7.58 5.35

Pseudo-static analysis U/S side 1.74 1.75 D/S side 1.32 1.33

0.00 0.00

3.25 3.08

4.16 3.74

Table 4h Results of the analysis of the new Rudramatha section (sudden drawdown condition)

FOS (mean)

pf (%)

Reliability index (β) Normal distribution

Log-normal distribution

1.82 1.78

0.00 0.00

4.05 3.93

5.34 5.14

Static analysis U/S side 1.62 D/S side 1.77

Pseudo-static analysis U/S side 1.49 1.50 D/S side 1.71 1.73

0.00 0.00

3.40 3.52

4.10 4.53

Static analysis U/S side 1.82 D/S side 1.78

135

FOS (det.)

FOS (mean)

P.F. (%)

Reliability index (β) Normal distribution

Log-normal distribution

1.62 1.77

0.00 0.00

4.34 3.08

5.44 4.00

Pseudo-static analysis U/S side 1.84 1.87 D/S side 1.39 1.40

0.00 0.00

3.35 3.18

4.46 4.03

136

G.L. Sivakumar Babu et al. / Engineering Geology 94 (2007) 123–136

of safety as well as reliability index values that are considered appropriate in the context of values recommended by USACE (1997). 5. Conclusions The results of the analysis of the four old dam sections revealed that the presence of a liquefiable layer beneath the foundation was the major cause of the failure of the dam during the 26th January 2001 Bhuj earthquake resulting in the base type of failure that occurred. This feature is also captured in the analysis, where it is shown that consideration of liquefiable layer in the foundation soil reveals base type failure of the slopes of the embankment dams, while it shows slope failure when the liquefiable layer was not taken into consideration. The results of analysis of the rehabilitated dam sections using deterministic and probabilistic approaches show that the values obtained for factor of safety (FS) and reliability index (β) are in the acceptable range. Reliability analysis can be used in conjunction with the deterministic approach to ensure an appropriate level of safety for the existing degree of uncertainty and consequences of failure. Acknowledgements The authors thank the reviewers for their constructive comments which have been useful in revising the paper. The work reported in this paper is a part of that being carried out in a research project, Back Analysis of Failures of Dams due to Earthquakes, sponsored by “Department of Science and Technology, Government of India New Delhi” and their financial assistance is gratefully acknowledged. The authors thank the “Narmada, Water Resources and Water Supply Department, Gujarat, India” for their help in the studies. References Baecher, G.B., Christian, J.T., 2003. Reliability and Statistics in Geotechnical Engineering. John Wiley and Sons, New York. BIS:1893–2002. Part 1: 2002 Bureau of Indian Standards, Criteria for Earthquake Resistant Design of Structures, General Provisions and Buildings. Bowles, D.S., Anderson, L.R., Glover, T.F., 1996. Risk assessment approach to dam safety criteria, uncertainty in geologic environment, from theory to practice. Proceedings of ASCE, STP, vol. 58, pp. 451–473. Campbell, K.W., Bozorgnia, Y., 1994. Near-source attenuation of peak horizontal acceleration from worldwide accelerograms recorded from 1957 to 1993. Proceedings, Fifth U.S. National Conference on Earthquake Engineering, vol. 1. Earthquake Engineering Research Institute, Berkeley, California, pp. 283–292.

Duncan, J.M., 2000. Factors of safety and reliability in geotechnical engineering. Journal of Geotechnical and Geoenvironmental Engineering, ASCE 126 (4), 307–316. Gazetas, G., 1987. Seismic response of earth dams: some recent developments. Soil Dynamics and Earthquake Engineering 6 (1), 2–46. Hynes-Griffin, M.E., Franklin, A.G., 1984. Rationalizing the Seismic Coefficient Method, Miscellaneous Paper GL-84-13. Department of the Army, US Army Corps of Engineers, Washington, DC. Kramer, S.L., 2003. Geotechnical Earthquake Engineering. Pearson Education. Marcuson III, W.F., 1978. Definition of terms related to liquefaction. Journal of Geotechnical Engineering Division, ASCE 104 (9), 1197–1200. Olson, S.M., Stark, T.D., 2003. Yield strength ratio and liquefaction analysis of slopes and embankments. Journal of Geotechnical and Geoenvironmental Engineering, ASCE 129 (8), 727–737. hoon, K.K., Kulhawy, F.H., 1999. Characterization of geotechnical variability. Canadian Geotechnical Journal 36, 612–624. Seed, H.B., 1979. Soil liquefaction and cyclic mobility evaluation for level ground during earthquake. Journal of Geotechnical Engineering, ASCE 105 (2), 201–255. Seed, H.B., Idriss, I.M., 1971. Simplified procedure for evaluating soil liquefaction potential. Journal of Geotechnical Engineering, ASCE 97 (9), 1249–1273. Seed, H.B., Idriss, I.M., 1982. Ground Motions and Soil Liquefaction During Earthquakes. Earthquake Engineering Research Institute, Oakland, Calif. Seed, H.B., Lee, K.L., Idriss, I.M., 1969. Analysis of Sheffield Dam failure. Journal of Soil Mechanics and Foundations Division, ASCE 95 (SM6), 1453–1490. Seed, H.B., Tokimatsu, K., Harder, L.F., Chung, R.M., 1985. The influence of the SPT procedures in soil liquefaction resistance evaluation. Journal of Geotechnical Engineering, ASCE 111 (12), 1425–1445. Singh, R., Roy, D., Jain, S.K., 2005. Analysis of earth dams affected by 2001 Bhuj earthquake. Engineering Geology 80, 282–291. SLIDE, 2005. Slope Stability Software, Version 5. Rocscience Inc., Canada. USACE, 1997. Risk-based Analysis in Geotechnical Engineering for Support of Planning Studies, Engineering and Design. US Army Corps of Engineers, Department of Army, Washington D.C., p. 20314−100. Whitman, R.V., 2000. Organizing and evaluating uncertainty in geotechnical engineering. Journal of Geotechnical and Geoenvironmental Engineering, ASCE 126 (7), 583–593. Youd, T.L., Idriss, I.M., Andrus, Ronald D., Arango, Ignacio, Castro, Gonzalo, Christian, John T., Dobry, Richardo, Liam Finn, W.D., Harder Jr., Leslie F., Hynes, Mary Ellen, Ishihara, Kenji, Koester, Joseph P., Liao, Sam S.C., Marcuson III, William F., Martin, Geoffrey R., Mitchell, James K., Moriwaki, Yoshiharu, Power, Maurice S., Robertson, Peter K., Seed, Raymond B., Stokoe II, Kenneth H., 2001. Liquefaction resistance of soils: summary report from the 1996 NCEER and 1998 NCEER/NSF workshops on evaluation of liquefaction resistance of soils. Journal of Geotechnical and Geoenvironmental Engineering, ASCE 127 (10), 817–833.