MCS-based probabilistic design of embedded sheet pile walls

A probabilistic approach to the design of embedded sheet pile walls is developed in this paper. The approach is based on Monte Carlo simulation (MCS), and it is used to investigate the performance of the partial factors and different design approaches in Eurocode 7 in achieving the target degrees of reliability. The approach is illustrated through an embedded sheet pile wall design example that has been used in literature for the evaluation of Eurocode 7. The approach deals rationally with the correlated load and resistance, and it bypasses a difficult but frequently asked question in Eurocode 7 (i.e. should the passive earth pressure be considered as a load (i.e. action) or a resistance?). The probabilistic design approach (DA) is also used to explore the effects of the soil unit weight variability and uncertainties in over-digging depth and wall friction. The effects of uncertainties in over-digging depth and wall friction are found to be significant. It is also found that, although the soil unit weight variability is generally minor, its effect on the design of embedded sheet pile walls is significant and should be properly accounted for in the design. The MCS-based probabilistic DA proposed in this study provides a straightforward way for proper consideration of such variability with relative ease.     

Reviewing probabilistic soils modelling

The probabilistic approach to soils and foundation engineering requires a suitable set of models. Consistency and comparability require that these models are to a certain extent standardized but capable of incorporating the most important aspects. The concept of ergodicity is introduced as an important tool of probabilistic modelling. For layered soils some standard random field models are proposed. Their properties are discussed. Especially for soils and foundation engineering a Bayesian approach to handle different types of knowledge is mandatory — even in simplified form. An attempt is made to quantify prior information about different soil types and a simple update formula is presented. A methodology to treat classification errors is proposed. An illustrating example is presnted.     

Reliability Analysis of Earth Slopes Considering Spatial Variability

The paper presents a computational procedure for reliability analysis of earth slopes considering spatial variability of soils under the framework of the Limit Equilibrium Method. In the reliability analysis of earth slopes, the effect of spatial variability of soil properties is generally included indirectly by assuming that the probabilistic critical slip surface is the same as that determined without considering spatial variability. In contrast to this indirect approach, in the direct approach, the effect of spatial variability is included in the process of determination of the probabilistic critical surface itself. While the indirect approach requires much less computational effort, the direct approach is definitely more rigorous. In this context this paper attempts to investigate, with the help of numerical examples, how far away are the results obtained from the indirect approach from that obtained from the direct approach. In both the approaches, it is required to use a model of discretization of random fields into finite random variables. A few such models are available in the literature for one-dimensional (1D) as well as two-dimensional (2D) spatial variability. The developed computational scheme is based on the First Order Reliability Method (FORM) coupled with the Spencer Method of Slices valid for limit equilibrium analysis of general slip surfaces. The study includes bringing out the computational advantages and disadvantages of the three commonly used discretization models. The sensitivity of the reliability index to the magnitudes of the scales of fluctuation has also been studied.     

边坡可靠度分析的一种新的优化求解方法

介绍了Low & Tang提出的一种新的可靠度优化求解方法,并将之用于边坡可靠度分析中：该方法适用于任何概率分布的相关变量,不必计算当量正态均值和方差、相关变量独立变换,直接在变量的原始空间内搜索边坡的最小可靠指标和概率临界滑面,可采用任何合适的约束优化方法进行求解,方法清晰简洁。边坡可靠度分析常用的滑面有2个：最小安全系数（变量均值处）对应的确定性临界滑面和最小可靠指标对应的概率临界滑面,但这2个滑面在有些情况下差别较大,Hassan & Wolff提出了一种简化方法可以方便地获得概率临界滑面,但由于方法简单,受到质疑。通过一系列算例分析,优化求解方法得到的概率临界滑面和Hassan & Wolff的简化方法滑面非常接近,显示了简化方法的有效性,值得在工程实践中推广。     

Numerical modelling of the improvements to primary and creep settlements offered by granular columns

Analytical vibro-replacement design approaches typically quantify the settlement reduction using a dimensionless settlement improvement factor, defined as the ratio of the settlements without and with treatment. Most approaches do not explicitly consider the improvement to creep settlement. This is unfortunate because the ‘stone column’ technique is being increasingly used to reduce settlement and improve bearing capacity in soft normally consolidated and lightly overconsolidated cohesive soils (in which creep settlement tends to account for a significant proportion of the total settlement). Analytical design approaches typically consider primary settlement only. In this study, two-dimensional axisymmetric analyses have been carried out using PLAXIS 2D to establish the variation of improvement factor with time using different soil models, one of which incorporates creep behaviour. Two different approaches have been used to establish the influence of creep on predicted settlement improvement factors. The first approach is based on a direct comparison of two different soil models (one of which incorporates creep) whereas the second approach is based solely on the model incorporating creep. The settlement improvement factors have been evaluated for different area-replacement ratios, modular ratios and column lengths. The primary settlement improvement factors are in good agreement with some of the more popular analytical design methods while the creep settlement improvement factors are either equivalent or lower (depending on the approach used). The primary settlement improvement factors show a dependence on the modular ratio whereas it appears that the corresponding creep settlement improvement factors are relatively independent of it.     

Probabilistic analysis of collapsing soil by indicator kriging

Collapsing soils, which undergo a large decrease in bulk volume virtually instantaneously upon saturation and/or load application, are found in arid and semi-arid regions of the world. In the western and midwestern U.S., problems resulting from collapsing soils are being recognized due to rapid industrial and urban developments. A probabilistic analysis of the distribution of such soils would be a rational approach for quantifying risk involved for a project in an area where such soils are found. Indicator kriging was applied to seven sets of collapse and collapse-related soil parameters to obtain the probability that a certain parameter is more or less than a predefined critical value for low, medium, and high collapse susceptibility. Results are presented in the form of probability contour plots with known variance of estimation of the probability. The ability to predict the probability of occurrence of collapse and collapse-related soil parameters for different critical values with a known degree of certainty is invaluable to planners, developers, and geotechnical engineers.     

The Role of Data Processing and Uncertainty Management in Seismic Hazard Evaluations: Insights from Estimates in the Garfagnana–Lunigiana Area (Northern Italy)

Significantly different estimates of seismic hazard may result for the same site as aneffect of different methodological choices underlying the adopted procedures. In orderto explore this aspect, two approaches devoted to probabilistic seismic hazard assessment are considered for the evaluation of hazard in a seismic area in Northern Italy. In particular, results of a standard procedure are compared with those obtained by an innovative approach. Fundamental features of this last methodology are the extensive use of intensity data relative to seismic effects observed at the site of interest during past earthquakes and the basic role attributed to the parameterisation of uncertainty which affects the considered pieces ofinformation. The analysis indicates that the new approach supplies results significantlydifferent from those obtained from standard methodology and that these differences strongly depend on strategies adopted for data processing and for the management of uncertainties which affect input parameters.     

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.

     

A genetic algorithm approach for assessing soil liquefaction potential based on reliability method

Deterministic approaches are unable to account for the variations in soil’s strength properties, earthquake loads, as well as source of errors in evaluations of liquefaction potential in sandy soils which make them questionable against other reliability concepts. Furthermore, deterministic approaches are incapable of precisely relating the probability of liquefaction and the factor of safety (FS). Therefore, the use of probabilistic approaches and especially, reliability analysis is considered since a complementary solution is needed to reach better engineering decisions. In this study, Advanced First-Order Second-Moment (AFOSM) technique associated with genetic algorithm (GA) and its corresponding sophisticated optimization techniques have been used to calculate the reliability index and the probability of liquefaction. The use of GA provides a reliable mechanism suitable for computer programming and fast convergence. A new relation is developed here, by which the liquefaction potential can be directly calculated based on the estimated probability of liquefaction (P _L ), cyclic stress ratio (CSR) and normalized standard penetration test (SPT) blow counts while containing a mean error of less than 10% from the observational data. The validity of the proposed concept is examined through comparison of the results obtained by the new relation and those predicted by other investigators. A further advantage of the proposed relation is that it relates P _L and FS and hence it provides possibility of decision making based on the liquefaction risk and the use of deterministic approaches. This could be beneficial to geotechnical engineers who use the common methods of FS for evaluation of liquefaction. As an application, the city of Babolsar which is located on the southern coasts of Caspian Sea is investigated for liquefaction potential. The investigation is based primarily on in situ tests in which the results of SPT are analysed.     

Modeling 3-D desiccation soil crack networks using a mesh fragmentation technique

The problem of desiccation cracks in soils has received increasing attention in the last few years, in both experimental investigations and modeling. Experimental research has been mainly focused on the behavior of slurries subjected to drying in plates of different shapes, sizes and thickness. The main objectives of these studies were to learn about the process of crack formation under controlled environmental conditions, and also to understand better the impact of different factors (e.g. soil type, boundary conditions, soil thickness) on the morphology of the crack network. As for the numerical modeling, different approaches have been proposed to describe the behavior of drying cracks in soils. One aspect that it is still difficult to simulate properly is the 3-D crack pattern typically observed in desiccated soils. In this work we present a numerical technique to model the behavior of drying soils. The proposed approach inserts high aspect ratio elements in-between standard elements of a finite element mesh. This mesh fragmentation technique can be easily adapted to standard finite element programs. We used this technique to analyze multiple case studies related to soil desiccation cracks developed under laboratory and field conditions. We focused our attention in some key factors that control the 3-D morphology of the drying cracks network in soils. We show that the proposed technique is able to simulate very satisfactorily the main patterns typically observed in cracked soils.     

Probabilistic winter storm risk assessment for residential buildings in Germany

Losses resulting from winter storms contribute a significant part to the overall losses among all natural hazards in most mid-latitude European countries. A realistic assessment of storm risk is therefore essential for prevention and coping measures. The paper presents a framework for probabilistic storm risk assessment for residential buildings which is exemplarily performed for Germany. Two different approaches are described, and results are presented. The hazard-based approach brings together hazard, vulnerability and building assets to calculate risk curves for each community. The storm-based approach uses loss information from past storm events to calculate statistical return periods of severe storms. As a result, a return period of 83 years to the most severe storm series in 1990 is calculated. Average annual losses of €170 million to residential buildings are calculated for all over Germany. The study demonstrates how the approaches complement each other and how validation is performed.     

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.     

An approximate dynamic programming approachto decision making in the presence of uncertainty for surfactant-polymer flooding

The least squares Monte Carlo method is a decision evaluation method that can capture the effect of uncertainty and the value of flexibility of a process. The method is a stochastic approximate dynamic programming approach to decision making. It is based on a forward simulation coupled with a recursive algorithm which produces the near-optimal policy. It relies on the Monte Carlo simulation to produce convergent results. This incurs a significant computational requirement when using this method to evaluate decisions for reservoir engineering problems because this requires running many reservoir simulations. The objective of this study was to enhance the performance of the least squares Monte Carlo method by improving the sampling method used to generate the technical uncertainties used in obtaining the production profiles. The probabilistic collocation method has been proven to be a robust and efficient uncertainty quantification method. By using the sampling methods of the probabilistic collocation method to approximate the sampling of the technical uncertainties, it is possible to significantly reduce the computational requirement of running the decision evaluation method. Thus, we introduce the least squares probabilistic collocation method. The decision evaluation considered a number of technical and economic uncertainties. Three reservoir case studies were used: a simple homogeneous model, the PUNQ-S3 model, and a modified portion of the SPE10 model. The results show that using the sampling techniques of the probabilistic collocation method produced relatively accurate responses compared with the original method. Different possible enhancements were discussed in order to practically adapt the least squares probabilistic collocation method to more realistic and complex reservoir models. Furthermore, it is desired to perform the method to evaluate high-dimensional decision scenarios for different chemical enhanced oil recovery processes using real reservoir data.     

Long embankment failure accounting for longitudinal spatial variation – A probabilistic study

For long earth embankments or levees, it is of interest to investigate the slope failure mode in the longitudinal direction. However, this is less commonly discussed in comparison to the plane-strain failure mode. In this paper, the longitudinal failure mode of a long embankment consisting of homogeneous soils is examined. A probabilistic approach using the first-order reliability method (FORM) is adopted to consider the uncertainty of soil properties. In particular, the spatial variability of the undrained shear strength of the soil is modelled in the probabilistic analysis. Parametric studies are subsequently conducted to examine the influence of this soil characteristic on the failure mode of the long embankment.     

Probabilistic geotechnical analyses for offshore facilities

Society requires increasingly that the hazard and risk associated with engineered constructions be quantified. The current paper presents geotechnical hazard assessment in the context of a risk framework. Concepts of uncertainties, reliability, safety and risk are briefly reviewed. The use of the approach is exemplified for offshore facilities, including piled foundations, jack-up structures, gravity foundations and underwater slopes. The applications demonstrate that probabilistic analyses complement the conventional deterministic safety factor and deformation-based analyses, and contribute to achieving a safe and optimum design. The probabilistic approach adds value to the results with a modest additional effort. The conclusions emphasize the usefulness of a risk assessment, the importance of engineering judgement in the assessment and the need for involving multi-disciplinary competences to achieve reliable estimates of hazard and risk. The profession can only gain by implementing probabilistic-based thinking and risk-based approaches more systematically than before.     

利用模糊数学方法建立汶川地震滑坡灾害评判标准

利用汶川地震主震在龙门山震区的强震资料,建立了利用地震动参数估计斜坡位移的Newmark累积位移模型。借助于模糊数学中的隶属函数方法,实现了对模型估计累积位移的隶属度定量计算,进而用以判定滑坡危险性分级。为使计算结果定量化,进一步利用模糊转换方法,将定性的滑坡危险性判定结果转换为定量的概率表达,使滑坡判定结果可以继续应用于其他环节的计算分析。以汶川地震在龙门山震区的滑坡分布为例,对模型的计算结果及其定量转换结果与实际情况进行了分析,表明模型结果与实际情况非常吻合。分析认为,以概率方式可以使滑坡灾害的空间分布描述更为准确,文中的方法使之得以实现。     

Effect of degree of saturation on mechanical behaviour of unsaturated soils and its elastoplastic simulation

The two stress-state variable approach has been widely used in interpreting unsaturated soil behaviour. However this approach cannot take into account the effect of degree of saturation or water contents on the stress–strain behaviour and strength of unsaturated soils. The triaxial test results presented in this paper show that even if the same path of net stress and suction is followed, the stress–strain relation and strength are different due to different degrees of saturation. When other conditions are the same, the higher the degree of saturation for the soil sample is, the higher the stress ratio corresponding to a given axial strain will be. This effect can be modeled by using an elasto-plastic constitutive model coupling hydraulic and mechanical behaviour of unsaturated soils. Comparisons between the predicted and measured results are presented, which demonstrate that the model can quantitatively simulate the influence of the degree of saturation on stress–strain behaviour and strength of unsaturated soils.