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Probabilistic of a 300 m High Dam

1 2 Qun Chen and Li-Ying Chang

1Professor, State Key Laboratory of Hydraulics and Mountain River Engineering, College of Hydraulic and Hydropower Engineering, Sichuan University, P.O. Box 610065, Chengdu, Sichuan, China; PH (086) 85403351; email: [email protected] 2Doctoral student, State Key Laboratory of Hydraulics and Mountain River Engineering, College of Hydraulic and Hydropower Engineering, Sichuan University, P.O. Box 610065, Chengdu, Sichuan, China; PH (086) 85403351; email: [email protected]

ABSTRACT

Based on the statistical properties of material parameters of 314 m high Shuangjiangkou - core rockfill dam, the probabilistic slope stability analyses for the critical slip surface of the dam slope are performed using the Monte-Carlo method. The uncertainty of the and the spatial variation of the and the fluctuation of the phreatic line in the dam are considered in analysis. The factor of safety and the reliability index of the dam slope under different construction and reservoir impounding stages are investigated. The results show that the reliability index of the dam slope with a larger factor of safety is not always bigger than that with a smaller factor of safety. Therefore, for the evaluation of the stability of the embankment dam slopes, the assessment of dam safety will be more scientific and reasonable if the uncertainty of property parameters of the soils can be considered.

INTRODUCTION

Currently, the factor of safety of sliding resistance determined by the limit equilibrium method based on the determinate property parameters of soils is used to evaluate the stability of the dam slopes in China. However, the property parameters of practical soils are random variables with certain changeable range, so the probabilistic slope stability analysis should be used for safety evaluation of dam slopes. The risk and probabilistic methods have been used for the analysis of slope stability for many years (Alonso 1976; Bergadon and Anderson 1985; Li and Lumb 1987; Christian et al. 1994; Gui et al. 2000; El-Ramly et al. 2003). In recent years, some researchers started to use probabilistic methods to analyze dam slope stability. The reliability and probability theories were developed for assessing the reliability index and the corresponding probability of failure of multi-layered embankment dams and slopes (Liang et al 1999). The reliability of high earth-rock filled dams on complex foundations was studied using the Monte-Carlo method (Zhou et al. 1998).

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Impact of the statistical characteristic variables of shear strength parameters on the reliability index (Luan et al. 2004) and probability of instability (Chen et al. 2008) of the dam slope were investigated. The soils and rockfills vary in space, the spatia1 variability of the soils should be considered in the probabilistic analysis. However, the spatial correlation of the dam material was not considered in these probabilistic studies. Based on the statistical properties of material parameters of 314 m high Shuangjiangkou gravel-clay core rockfill dam, the probabilistic slope stability analyses for the critical slip surface of the dam slope have been performed using the Monte-Carlo method. The uncertainty of the shear strength and the spatial variation of the , the fluctuation of the phreatic line in the dam have been considered in analysis. The factor of safety and the reliability index of the dam slope under different construction and reservoir impounding stages have been investigated. Furthermore, the influence of the autocorrelation distance of the dam soils on the reliability index was investigated.

ANALYSIS METHOD

In this paper, the seepage in the dam during reservoir impounding has been calculated using the saturate-unsaturated seepage theory. The seepage analysis software SEEP/W (Geo-Slope International Ltd. 2007a) has been used to study the steady-state seepage in the dam. The critical slip surface is determined based on the mean values of the input parameters using a limit equilibrium method. Probabilistic analysis is performed on the critical slip surface, considering the variability of the input parameters using the Monte-Carlo method. The software SLOPE/W (Geo-Slope International Ltd. 2007b) is used to assess the dam slope stability including probabilitic analysis. Morgenstern-Price’s analysis method (Morgenstern and Price 1965) is used for slope stability analysis. A random number generation function to do the random sampling is used in the Monte-Carlo method. Each random number N has the same distribution as the input parameter. Then the parameter P needed for every deterministic analysis can be calculated by the following formula:

μ += NP σ (1)

where, μ is the mean value and σ is the standard deviation of the parameter. The effective , c′, and effective internal angle, φ′, are considered as random variables in the probabilitic analysis and can be calculated using Equation (1). The trial number used in the Monte-Carlo method is 500000 in this study. The reliability index is a parameter to indicate the reliability of the slope stability. If the mean and the standard deviation of the factors of safety are μF and σF, respectively, the reliability index β can be expressed as:

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μ − 0.1 β = F (2) σ F

The spatial variability along the slip surface was considered by sampling the properties at a specified distance, that is, autocorrelation distance, along the slip surface (Geo-Slope International Ltd. 2007b).

ANALYSIS CASES AND PARAMETERS

The 314 m high Shuangjiangkou gravel-clay core rockfill dam, located on the Dadu River in the southwest of China, will be the highest embankment dam in the world. The main zones in the embankment, shown in Figure 1, are the gravelly clay core, the double layer filter, the transition, the rockfill shell and the kentledge. The core is founded on hard granite through a concrete base slab with a grouting gallery. There is a 96 m deep grout curtain below the concrete base slab in the . The rockfill shell is founded on three overburden layers above the granite. The overburden layers consist of boulder cobble gravel on the top (overburden 3), sandy cobble gravel (overburden 2) in the middle and cobble gravel with boulder (overburden 1) at the bottom. The rockfill section has an upstream slope of 2.0H:1.0V with a berm at elevation 2330.00 m and a downstream slope of 1.9H:1.0V. The elevations of the crest and the base of the dam are 2510.00 m and 2196.00 m, respectively. The crest is 8 m wide. The top width and bottom width of the core are 4 m and 128 m, respectively.

Figure 1. Maximum profile of the Shuangjiangkou dam

The probabilistic slope stability analyses for the maximum profile (Figure 1) of the dam were conducted in three conditions including completion of construction of the dam, reservoir impounding to dead water level and to normal water level. On each condition, firstly, the variation of the shear strength was considered, then, the spatial variation of the soils and the fluctuation of the phreatic line were added separately. These analysis cases are listed in Table 1. The fluctuation of the phreatic line was only considered for upstream slope of the dam because the phreatic line behind the core is very low and it has no impact on the stability of downstream slope. In cases 7 and 8, the variation of shear strength and fluctuation of the phreatic line are considered. Besides the cases in Table 1, the influence of the autocorrelation distance of the dam soils on the reliability index was investigated. 中国科技论文在线 http://www.paper.edu.cn

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The strength and hydraulic properties of the material of the dam and the were obtained based on test results. The shear strength parameters including the internal friction angle and the cohesion were considered as random variables. It was assumed that they all follow the normal distribution. Their standard deviations were obtained based on the investigation of the shear strength uncertainty for the materials of Shuangjiangkou dam and other similar dams (Wu 2008). The saturated coefficients of permeability, strength parameters and their standard deviations of the soils are listed in Table 2. The permeability functions estimated from soil-water characteristic and grain size distribution curves (Fredlund et al. 1994 and Fredlund et al. 1997) of the dam soils used in analyses are shown in Figure 2.

Table 1. Analysis cases in different conditions Case slope Analysis conditions 1 Upstream End of construction, variation of shear strength 2 Downstream 3 Upstream End of construction, variation of shear strength and spatial 4 Downstream variation (autocorrelation distance=10 m) 5 Upstream Normal water lever, variation of shear strength 6 Upstream Dead water lever, variation of shear strength 7 Upstream Normal water lever Fluctuant height=2m 8 Upstream Dead water lever Fluctuant height=5m

Table 2. Material parameters used in analyses Unit Friction angle Saturated Cohesion c: kPa weight φ: ° Material conductivity γ: Standard Standard k : m/d Mean Mean kN/m3 sat deviation deviation Overburden 1 20.6 25.9 17 3.0 39 2.20 Overburden 2 20.3 17.3 10 3.0 37 2.20 Overburden 3 20.5 43.2 16 3.0 37 2.20 Cofferdam 20.7 86.4 0 35 2.20 Core 21.1 0.00605 35 5.0 31 2.20 Filter 1 20.0 4.32 0 41.7 2.17 Filter 2 20.2 6.91 0 43.7 2.59 Transition 20.9 25.9 0 45.3 2.31 Upstream rockfill 21.5 86.4 0 40.8 2.26 Downstream main rockfill 21.1 86.4 0 47.7 2.95 Downstream second 20.9 40.0 0 45.7 2.95 rockfill

RESULTS AND DISCUSSION

The probabilistic slope stability analysis results of the cases in Table 1 are listed in Table 3. The results are only related to the property of the upstream or downstream rockfill because the critical slip surface is very shallow and only through

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the rockfill. The mean and the standard deviation of the factor of safety of the upstream slope (case 1) are less than those of the downstream slope of the dam (case 2) in the case of considering the variation of the shear strength of the dam soils due to the bigger mean and standard deviation of the internal friction angle of the downstream rockfill. In other words, the mean and the standard deviation of the factor of safety increase with the increase in the mean and the standard deviation of the shear strength of the dam soils, respectively.

1.E+02

1.E-01

Core Filter 1 1.E-04 Filter 2 Transition Main rockfill Second rockfill 1.E-07 Permeability (m/d) function Permeability 0.1 1 10 100 1000 Matric suction (kPa) Figure 2. The permeability functions of the dam soils

Table 3. Probabilistic slope stability analysis results of the cases in Table 1 Factor of safety Case Reliability index Mean Standard deviation 1 1.770 0.143 5.395 2 2.112 0.222 5.012 3 1.770 0.031 24.504 4 2.112 0.045 24.764 5 3.742 0.211 12.970 6 1.790 0.144 5.484 7 3.739 0.244 11.225 8 1.779 0.152 5.144

Comparing case 2 with case 1, it is found that the reliability index of the upstream slope is bigger than that of the downstream slope because the standard deviation of the upstream rockfill is less than that of the downstream rockfill, which causes the standard deviation of the factor of safety of the downstream slope is bigger and its reliability index is less. This illustrates that the reliability index of the dam slope with a larger factor of safety is not always bigger than that with a smaller factor of safety. Because the reliability index increases with the increase in the mean of the 中国科技论文在线 http://www.paper.edu.cn GeoRisk 2011 © ASCE 2011 457

factor of safety but decreases with the increase in the standard deviation of it, the reliability index can be less or bigger if both the mean and the standard deviation of the factor of safety is bigger. For example, the reliability index in case 2 is less than it in case 1, nevertheless it in case 4 is a little bigger than it in case 3. When the spatial variation of the dam soils is considered (cases 3 and 4), the means of the factors of safety remains unchanged but the standard deviations of the factors of safety decrease (comparing case 3 with case 1 or case 4 with case 2) both for the upstream slope (cases 1 and 3) and the downstream slope (cases 2 and 4). This results in the increase of the reliability index of the dam slopes. If the fluctuation of the phreatic line in the dam is included (cases 7 and 8), the means of the factors of safety decrease a little and the standard deviations of the factors of safety increase (comparing case 7 with case 5 or case 8 with case 6) both for the normal water level (cases 5 and 7) and dead water level (cases 6 and 8) conditions. Therefore, the reliability indexes of the dam slopes decrease. Figure 3 shows the mean of the factor of safety and the reliability index change with the autocorrelation distance in dam soils. Both for the upstream slope (Figure 3(a)) and the downstream slope (Figure 3(b)), the means of the factors of safety almost unchange for the different autocorrelation distances. However, the reliability index decreases nonlinearly with the increase in the autocorrelation distance. When the autocorrelation distance is small, the reliability index decreases evidently; when it is bigger than a critical value, it will have no effect on the reliability index. Based on the investigation of the size of the critical slip surface, it is found that the critical value of the autocorrelation distance is nearly equal to the chordal length of the critical slip surface of the slope. Furthermore, the unchanged reliability index for the autocorrelation distance bigger than the critical value is equal to the reliability index in the case of no consideration of the autocorrelation distance. For different autocorrelation distances, the reliability indexes of the upstream slope and the downstream slope are close agreement though the mean of the factor of safety of the upstream slope is lower than that of the downstream slope. It is because that the bigger standard deviation of the shear strength of the downstream rockfill results in the bigger standard deviation of the factor of safety though the mean of the shear strength of the downstream slope is bigger.

CONCLUSIONS

The probabilistic slope stability analyses were performed for the 314 high Shuangjiangkou gravel-clay core rockfill dam. The uncertainty of the shear strength and the spatial variation of the soils and the fluctuation of the phreatic line are considered in analysis. The results show that the mean and the standard deviation of the factor of safety increase with the increase in the mean and the standard deviation of the shear strength of the dam soils, respectively. The reliability index of the dam slope with a larger factor of safety is not always bigger than that with a smaller factor of safety. A bigger standard deviation of the shear strength of the dam soil results in a bigger standard deviation of the factor of safety and a less reliability index. So, the uncertainty of the shear strength of the soils should be considered in evaluation of the

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stability of the embankment dam slopes. The mean of the factor of safety decreases a little and the reliability index of the dam slope also decreases on the conditions of considering the fluctuation of the phreatic line in the dam. The mean of the factor of safety remains unchanged but the reliability index of the dam slope increases if the spatial variation of the dam soils is considered.

25 2.2 Reliability index 2.1 β 20 Mean of factor of safety 2 15 1.9 10

Reliability index 1.8 Mean ofsafetyMean of factor 5 1.7 0 100 200 300 400

Autocorrelation distance (m) (a) Upstream slope 25 2.2

2.1 β 20 Reliability index 2 15 Mean of factor of safety 1.9 10

Reliability index 1.8 Mean Mean of factor of safety 5 1.7 0 100 200 300 400

Autocorrelation distance (m) (b) Downstream slope Figure 3. The mean of the factor of safety and the reliability index change with the autocorrelation distance

The mean of the factor of safety is almost changeless for the different autocorrelation distances. However, the reliability index decreases nonlinearly with the increase in the autocorrelation distance. It will decrease to a constant value when the autocorrelation distance bigger than chordal length of the slip surface.

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