A reliability-based approach to evaluating the stability of high rockfill dams using a nonlinear shear strength criterion

In recent years, many high rockfill dams have been constructed in China for the purpose of hydropower generation. One of the critical aspects of rockfill dam design is the analysis of slope stability. Triaxial compression tests show that the failure envelopes of rockfills are curved and that nonlinear shear strength criteria yield better predictions of the shear strengths of rockfills than the Mohr–Coulomb criterion. Because the determination of shear strength parameters involves uncertainties, a reliability-based methodology was developed for use in evaluating the failure probability of rockfill dam slopes by integrating Bishop’s simplified method, Duncan’s nonlinear strength criterion and the first-order second-moment reliability method presented in this paper. A computer program, SCU-SLIDE, was developed and its outputs validated by comparison with Monte Carlo simulation results. The approach developed was used to study the stability of the Shuang Jiang Kou rockfill embankment dam, which when completed will be the tallest dam in the world. The results of the stability analysis are discussed and conclusions are presented in this paper.     

Modeling uncertainty in stability analysis for design of embankment dams on difficult foundations

A probabilistic 3-D slope stability analysis model (PTDSSAM) is developed to evaluate the stability of embankment dams and their foundations under conditions of staged construction taking into consideration uncertainty, spatial variabilities and correlations of shear strength parameters, as well as the uncertainties in pore water pressure. The model has the following capabilities: (1) conducting undrained shear strength analysis (USA) and effective stress analysis (ESA) slope stability analysis of staged construction, (2) incorporation of field monitored data of pore water pressure, and (3) incorporation of increase of undrained shear strength with depth, effective stress, and pore water pressure dissipation. The PTDSSAM model is incorporated in a computer program that can analyze slopes located in multilayered deposits, considering the total slope width.

The main outputs of the program are the geometric parameters of the most critical sliding surface (i.e., center of rotation/radius of rotation and critical width of failure), mean 2-D safety factor, mean 3-D safety factor, squared coefficient of variation of resisting moment, and the probability of slope failure. The program is applied to a case study, Karameh dam in Jordan. Monitored data of induced pore water pressure in the dam embankment and soft foundation were gathered during dam construction.

The stability of Karameh dam embankment and foundation was evaluated during staged construction using deterministic and probabilistic analysis. Foundation stability was evaluated based on the monitored data of pore water pressure.

The study showed that the mean values of the corrective factors which account for the discrepancies between the in situ and laboratory-measured values of soil properties and for the modeling errors have significant influence on the 2-D safety factor, 3-D safety factor, slope probability of failure, and on the expected failure width.

The degree of spatial correlation associated with shear strength parameters within a soil deposit also influences the probability of slope failure and the expected failure width. This correlation is quantified by scale of fluctuation. It is found that a larger scale of fluctuation gives an increase in the probability of slope failure and a reduction in the critical failure width.     

Evaluation of the Instability Risk of the Dam Slopes Simulated with Monte Carlo method (Case Study: Alborz Dam)

Embankment dams are one of the most important geotechnical structures that their failures can lead to disastrous damages. One of the main causes of dam failure is its slope instability. Slope Stability analysis has traditionally been performed using the deterministic approaches. These approaches show the safety of slope only with factor of safety that this factor cannot take into account the uncertainty in soil parameters. Hence, to investigate the impact of uncertainties in soil parameters on slope stability, probabilistic analysis by Monte Carlo Simulation (MCS) method was used in this research. MCS method is a computational algorithm that uses random sampling to compute the results. This method studies the probability of slope failure using the distribution function of soil parameters. Stability analysis of upstream and downstream slopes of Alborz dam in all different design modes was done in both static and quasi-static condition. Probability of failure and reliability index were investigated for critical failure surfaces. Based on the reliability index obtained in different conditions, it can be said that the downstream and upstream slope of the Alborz dam is stable. The results show that although the factor of safety for upstream slope in the state of earthquake loading was enough, but the results derived from probabilistic analysis indicate that the factor of safety is not adequate. Also the upstream slope of the Alborz dam is unstable under high and uncontrolled explosions conditions in steady seepage from different levels under quasi-static terms.

     

地震工况下坝坡的抗滑安全系数取值标准研究

地震工况下的坝坡抗滑稳定性核算一直是大坝安全性评价的重要环节,采用科学合理的计算方法是评价坝坡安全性的基本保证。本文从概率极限分析的角度探讨了坝坡稳定性可靠度分析的概率意义,提出了将地震发生当做概率事件的坝坡可靠度计算方法。为验证将地震超越概率纳入坝坡稳定分析中的合理性,本文通过两个典型算例和小浪底坝坡典型剖面的抗滑稳定性分析研究了坝坡在地震工况下的单一安全系数与可靠指标的变化规律。研究结果表明在坝坡稳定分析中引入超越概率计算所得结果与工程实际相符,与以往的将地震发生当做确定性事件计算方法相比,该方法显著提高了坝坡的可靠指标值;比较可靠指标与单一安全系数的取值标准显示出在坝坡稳定分析中合理地引入地震概率分析方法能够保证坝坡在地震和正常工况下有相近的可靠指标值     

Structural stability of gravity dams: a progressive assessment considering uncertainties in shear strength parameters

Structural sliding stability of gravity dams is generally quantified using deterministic factor of safety, FS_det. Large FS_det (e.g. 3 in normal condition), are used in existing guidelines to guard against material and load uncertainties. Some guidelines allow an arbitrary reduction in FS_det (e.g. 2) when the knowledge in strength parameters increases from material test data. Yet, those reduced FS_det are not based on a rational consideration of uncertainties. Propagation of uncertainties could be done using probabilistic analyses, such as Monte-Carlo simulations (MC) which are complex and challenging for practical use. There is thus a need to develop simplified reliability based safety assessment procedures that could rationalise the adjustment of FS_det. This paper presents a progressive analysis methodology using four safety evaluation formats of increasing complexity: (i) deterministic, (ii) semi-probabilistic (partial coefficient), (iii) reliability based Adjustable Factor of Safety (AFS), and (iv) probabilistic. Comprehensive comparisons are made for the sliding safety evaluation of a 80 m gravity dam. Results are presented in terms of sliding factors of safety, allowable water levels, and demand/capacity ratios. It is shown that the AFS formulation, using direct integration, is simple and practical to use in complement to existing dam safety guidelines before undertaking MC simulations.     

路堤边坡稳定可靠度计算中的模型不确定性分析

基于均质路堤边坡Monte Carlo法的稳定可靠度计算,分析了临界滑面搜索策略和稳定分析方法两类模型不确定性对边坡可靠度的影响特性,讨论了边坡失效概率随土工参数变异性的变化规律。研究表明,选用不同的临界滑面搜索策略所得可靠度结果差异不大,参数滑面法（overall slope）的失效概率略大于均值滑面法（global minimum）,但差别对边坡稳定性分析没有实质性影响;土性参数变异水平是影响边坡可靠度的最重要因素,边坡在相同设计参数安全系数下的可靠度指标随参数变异性增大而急剧降低;不同稳定性分析方法对应的安全系数概率密度函数曲线形态基本一致,但失效概率差异明显,因此目标可靠度指标取值应与稳定性分析方法相适应。提出的考虑土工参数变异水平的安全系数取值修正原则,对改进确定性设计的边坡稳定分析技术有积极意义。     

Fuzzy algorithm for estimating average breach widths of embankment dams

Dam breach width significantly influences peak breach outflow, inundation levels, and flood arrival time, but uncertainties inherent in the prediction of its value for embankment dams make its accurate estimation a challenging task in dam risk assessments. The key focus of this paper is to provide a fuzzy logic (FL) model for estimating the average breach width of embankment dams as an alternative to regression equations (RE). The FL approach is capable of handling nonlinear behavior, imprecision in discrete measurements, and parameter uncertainty. Historical data from 69 embankment dam failures are used in the development and testing of the FL model. Application of the FL model is also presented for estimating average breach widths of two case studies that have adequately documented data. The accuracy of the FL rule-based model is investigated using uncertainty analysis: the mean prediction error between the FL estimates and the observed average breach widths is very small (=0.03) and comparable to that achieved using the best available RE. Moreover, the FL uncertainty band is found to be approximately ±0.51 order of magnitude smaller than the ±0.56 order of magnitude achieved with the best available RE. The simulation results indicate the potential of the FL model to be used as a predictive tool for estimating the average breach width of embankment dams.     

Logistic regression model for predicting the failure probability of a landslide dam

Landslides may obstruct river flow and result in landslide dams; they occur in many regions of the world. The formation and disappearance of natural lakes involve a complex earth–surface process. According to the lessons learned from many historical cases, landslide dams usually break down rapidly soon after the formation of the lake. Regarding hazard mitigation, prompt evaluation of the stability of the landslide dam is crucial. Based on a Japanese dataset, this study utilized the logistic regression method and the jack-knife technique to identify the important geomorphic variables, including peak flow (or catchment area), dam height, width and length in sequence, affecting the stability of landslide dams. The resulting high overall prediction power demonstrates the robustness of the proposed logistic regression models. Accordingly, the failure probability of a landslide dam can also be evaluated based on this approach. Ten landslide dams (formed after the 1999 Chi-Chi Earthquake, the 2008 Wenchuan Earthquake and 2009 Typhoon Morakot) with complete dam geometry records were adopted as examples of evaluating the failure probability. The stable Tsao-Ling landslide dam, which was induced by the Chi-Chi earthquake, has a failure probability of 27.68% using a model incorporating the catchment area and dam geometry. On the contrary, the Tangjiashan landslide dam, which was artificially breached soon after its formation during the Wenchuan earthquake, has a failure probability as high as 99.54%. Typhoon Morakot induced the Siaolin landslide dam, which was breached within one hour after its formation and has a failure probability of 71.09%. Notably, the failure probability of the earthquake induced cases is reduced if the catchment area in the prediction model is replaced by the peak flow of the dammed stream for these cases. In contrast, the predicted failure probability of the heavy rainfall-induced case increases if the high flow rate of the dammed stream is incorporated into the prediction model. Consequently, it is suggested that the prediction model using the peak flow as causative factor should be used to evaluate the stability of a landslide dam if the peak flow is available. Together with an estimation of the impact of an outburst flood from a landslide-dammed lake, the failure probability of the landslide dam predicted by the proposed logistic regression model could be useful for evaluating the related risk.     

Optimization of reinforcement strategies for dangerous dams considering time-average system failure probability and benefit�Ccost ratio using a life quality index

Lifetime-oriented multi-objective optimization for structural reinforcement based on series-system reliability and benefit?Ccost analysis has already been proposed. It is still needed, however, to incorporate the life quality index (LQI) in the lifetime reinforcement optimization process of complex massive infrastructure engineering with correlated series?Cparallel failure modes (e.g., dams). An improved technique combining overall system failure probability with benefit?Ccost analysis based on the LQI is developed. An approach to obtain time-average system failure probability with correlated series?Cparallel failure modes is proposed to measure the structural performance. Then, the concept for benefit?Ccost ratio based on LQI including failure consequence and life quality objective is introduced. As an application of the methodology, the optimal reinforcement strategy for an existing earth dam is shown. Three types of reinforcement strategies, that is, preventive reinforcement, essential reinforcement and that lies between them, are selected. The results show that the preventive reinforcement strategy is the most beneficial for a dam, whose failure loss involving human life is tremendous. The advantage of the proposed approach is its ability to harmonize overall structural safety with reinforcement cost and can be extended to optimization of reinforcement strategies for other massive infrastructure engineering projects.     

Estimation of the Variability of Tailings Dams Properties in Order to Perform Probabilistic Assessment

Dams are often used for storing mine tailings. These structures present failure mechanisms that can lead to major risks for surrounding populations. In view to managing these risks, it is necessary to take a probabilistic approach in predicting their behaviour. The application of such approaches is limited by the difficulty of obtaining experimental data to estimate the variability of the parameters and conditioned by the relevance of the probability models chosen to represent this variability. This article proposes (1) a probabilistic modelling of the index properties of the mine tailings constituting these dams based on statistical analyses and (2) a method using dynamic penetration tests to estimate on site the mine tailings friction angle and its variability. This method, applied to chilean tailings dams proposes a single model for all tailings dams in order to associate a probability law to the effective friction angle (ϕ′). The procedure is illustrated on the probabilistic study of slope stability carried out at the global scale of a dam and also at the local scale of each of its constituent layers.     

Reliability assessment of granular filters in embankment dams

Empirical criteria have been used successfully to design filters of most embankment large dam projects throughout the world. However, these empirical rules are only applicable to a particular range of soils tested in laboratory and do not take into account the variability of the base material and filter particle sizes. In addition, it is widely accepted that the safety of fill dams is mainly dependent on the reliability of their filter performance. The work herein presented consists in a new general method for assessing the probability of fulfilling any empirical filter design criteria accounting for base and filter heterogeneity by means of first‐order reliability methods (FORM), so that reliability indexes and probabilities of fulfilling any particular criteria are obtained. This method will allow engineers to estimate the safety of existing filters in terms of probability of fulfilling their design criteria and might also be used as a decision tool on sampling needs and material size tolerances during construction. In addition, sensitivity analysis makes possible to analyse how reliabilities are influenced by different sources of input data. Finally, in case of a portfolio risk assessment, this method will allow engineers to compare the safety of several existing dams in order to prioritize safety investments and it is expected to be a very useful tool to evaluate probabilities of failure due to internal erosion. Copyright © 2006 John Wiley & Sons, Ltd.     

Efficient system reliability analysis of rock slopes based on Subset simulation

How to efficiently assess the system reliability of rock slopes is still challenging. This is because when the probability of failure is low, a large number of deterministic slope stability analyses are required. Based on Subset simulation, this paper proposes an efficient approach for the system reliability analysis of rock slopes. The correlations among multiple potential failure modes are properly accounted for with the aid of the “max” and “min” functions. A benchmark rock slope and a real engineered rock slope with multiple correlated failure modes are used to demonstrate the effectiveness of the proposed approach.     

Dam-break risk analysis of the Attabad landslide dam in Pakistan and emergency countermeasures

The Attabad landslide dam caused significant property losses and many human casualties in Pakistan, and also greatly affected the operation of the China-Pakistan Karakoram Highway (KKH). This paper discusses the risk of dam breach and hazards to the KKH project construction site following a dam breach. The paper examines the following three topics. (1) The geomorphologic dimensionless blockage index (DBI) and the analogy method were used to analyze the stability of the Attabad landslide dam. The long-term behaviors of landslide dams downstream of the Attabad landslide dam indicate that the risk of a dam breach exists, but the probability of a total dam failure is low. (2) The peak discharge of a potential breach of the Attabad landslide dam was calculated for scenarios in which 1/4, 1/3, 1/2, and total failure of the dam was breached. The potential breach discharge decreases with the downstream distance. (3) The potential impacts of the landslide dam breach on the KKH project construction site were analyzed. Based on the composition of the landslide dam, the probability of a 1/3 dam breach is high. To ensure the safety of downstream areas, disaster preparedness plans that correspond to the 1/2 dam breach scenario should be developed. Based on experience in addressing the landslide dam that was caused by the Wenchuan Earthquake, artificial controlled drainage measures are suggested and provide a technical reference for addressing the Attabad landslide dam and achieving recovery and normal operation of KKH.     

Interpretation of shear strength uncertainty and reliability analyses of slopes

The variance of the friction angle or friction coefficient (tan ?) is often considered in geotechnical reliability analyses, which implies that the variance of the shear strength as defined by a Mohr-Coulomb envelope increases as the normal stress on the shearing surface increases. However, shear strength data sometimes has approximately constant variance, and most simple regression techniques assume constant variance. Four effective stress shear strength data sets are evaluated using both the constant variance (homoscedastic) and constant coefficient of variation (heteroscedastic) interpretations. The impact of the variance interpretation on slope stability is evaluated using infinite slope, homogeneous dam, and zoned dam examples. For relatively shallow infinite slope surfaces, the reliability index for the heteroscedastic interpretation of shear strength variance was about twice the reliability index obtained using the homoscedastic approach. In the dam examples, the difference in the reliability indices resulting from the heteroscedastic and homoscedastic interpretations was about one, indicating a tenfold increase in the probability of failure. The typical assumption of constant coefficient of variation of shear strength may result in unconservative estimates of the reliability of shallow failure surfaces and overly conservative results for deeper failure surfaces.     

天然土石坝稳定性初步研究

滑坡堵塞江河形成的天然土石坝是自然作用的产物，不同于人工土石坝，天然土石坝形成后有些存在几十年，几百年，有些形成后不久就溃决，这与坝体本身的性质和河水入流量有关，依据野外实测资料，证了土石坝的稳定性的主要是同土石坝的物质组成，几何形状和堰塞湖入流量等因素决定的，这一研究为天然土石坝的稳定性预测奠定了基础。     

Reliability analysis of soil liquefaction based on standard penetration test

A review of probabilistic and deterministic liquefaction evaluation procedures reveals that there is a need for a comprehensive approach that accounts for different sources of uncertainty in liquefaction evaluations. For the same set of input parameters, different models provide different factors of safety and/or probabilities of liquefaction. To account for the different uncertainties, including both the model and measurement uncertainties, reliability analysis is necessary. This paper presents a review and comparative study of such reliability approaches that can be used to obtain the probability of liquefaction and the corresponding factor of safety. Using a simplified deterministic Seed method, this reliability analysis has been performed. The probability of liquefaction along with the corresponding factor of safety have been determined based on a first order second moment (FOSM) method, an advanced FOSM (Hasofer–Lind) reliability method, a point estimation method (PEM) and a Monte Carlo simulation (MCS) method. A combined method that uses both FOSM and PEM is presented and found to be simple and reliable for liquefaction analysis. Based on the FOSM reliability approach, the minimum safety factor value to be adopted for soil liquefaction analysis (depending on the variability of soil resistance, shear stress parameters and acceptable risk) has been studied and a new design safety factor based on a reliability approach is proposed.     

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

The Kachchh region of Gujarat, India bore the brunt of a disastrous earthquake of magnitude M_w = 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.     

Geologic problems related to dam sites in Jordan and their solutions

The geologic structures associated with several selected dam sites in Jordan and the tectonic effects on dam foundations and reservoir margins are reviewed. Rock defects, especially discontinuities represented by faults and closely spaced, open joints are investigated. Related problems, such as loss of water from the reservoir by seepage and leakage within the dam foundation are evaluated. The regional seismicity is analyzed and a design earthquake is established for each dam site.

Two major embankment dams are investigated, together with two large proposed dams and several small dams.

This paper discusses in some detail the regional setting and site-specific geology, and the occurrence, size and inclination of faults and joints at each dam site. Moreover, the effects of the faults on the operational performance of each dam are described and specific techniques are used or proposed for remediation are outlined.

The study shows that the combination of faults and joint features cause leakage problems at the operational dams in Jordan. Although, preventive measures such as grouting have been implemented, further leakage and/or seepage problems are anticipated and a monitoring system is needed to control and foresee such problems.

Jordan is an earthquake-prone region. Consequently, it is recommended that the design of embankment dams in the vicinity of the Dead Sea-Jordan Valley Rift should include such considerations as dynamic loading and associated hazards, including embankment acceleration zoning, foundation liquefaction risk and rockhead rupture. The magnitude of the design earthquake at each dam site can be estimated following the guidelines of ICOLD (1989), which are based on probabilistic seismic hazard analysis.     

Evaluation of the overflow failure scenario and hydrograph of an embankment dam with a concrete upstream slope protection

The standard procedure in Quebec, Canada, for evaluating the failure of an embankment dam, per the Loi sur la sécurité des barrages, specifies a 30-min-long failure scenario with a breach width equal to four times the maximal height of the dam. We demonstrate a new method for evaluating the flood overtopping failure scenario for embankment dams with concrete upstream slope protection, using Toulnustouc dam for example computations. Our new methodology computes safety factors for a range of potential failure mechanisms taking into account geotechnical, hydraulic, and structural factors. We compile the results of our investigations of the various dam failure mechanisms and compare the corresponding dam failure hydrographs to the current hydrograph specified in the standard analysis procedures. Our investigations tend to invalidate the current standard procedures for evaluating the failure of rock-fill dams with concrete upstream faces, by indicating that the current standard procedures underestimate the peak failure discharge and overestimate the time to the peak discharge.     

A simple approach to evaluating leakage through thin impervious element of high embankment dams

Internal erosion is the most common reason which induces failure of embankment dams besides overtopping. Relatively large leakage is frequently concentrated at defects of impervious element, and this will lead to eventual failure. The amount of leakage depends not only on integrity of impervious element, but also on dam height, shape of valley, shape of impervious element and water level in reservoir. The integrity of impervious element, which represents the relative level of seepage safety, is not easy to be determined quantitatively. A simple method for generalization of steady seepage state of embankment dams with thin impervious element is proposed in this paper. The apparent overall value of permeability coefficient for impervious element can be obtained by this method with reasonable accuracy and efficiency. A defect parameter of impervious element is defined as an index to characterize seepage safety of embankment dams. It equals the ratio of the apparent overall value of permeability coefficient to the measured value in laboratory for intact materials. Subsequently, seepage safety of three dams is evaluated and the evolution of defect level of impervious element of dams is investigated. It is proved that the newly proposed method in this paper is feasible in the evaluation of relative seepage safety level of embankment dams with thin impervious element.