Influence of model type,bias and input parameter variability on reliability analysis for simple limit states in soil–structure interaction problems

ABSTRACT

A general closed-form solution for the true probability of failure of a simple limit state function with one load term and one resistance term is derived. The formulation considers contributions due to model type, uncertainty in method bias values, bias dependencies, uncertainty in estimates of nominal values for correlated and uncorrelated load and resistance terms, and average margin of safety expressed as the operational factor of safety. Example calculations are presented using different load and resistance models for the pullout internal stability limit state of steel strip reinforced soil walls together with matching bias data reported in the literature.     

Probabilistic stability analyses of slopes using the ANN-based response surface

Slope stability analysis is a geotechnical engineering problem characterized by many sources of uncertainty. Some of these sources are connected to the uncertainties of soil properties involved in the analysis. In this paper, a numerical procedure for integrating a commercial finite difference method into a probabilistic analysis of slope stability is presented. Given that the limit state function cannot be expressed in an explicit form, an artificial neural network (ANN)-based response surface is adopted to approximate the limit state function, thereby reducing the number of stability analysis calculations. A trained ANN model is used to calculate the probability of failure through the first- and second-order reliability methods and a Monte Carlo simulation technique. Probabilistic stability assessments for a hypothetical two-layer slope as well as for the Cannon Dam in Missouri, USA are performed to verify the application potential of the proposed method.     

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.

     

基于FELA的随机场方法在考虑降雨入渗的边坡开挖稳定性分析中的应用

黑山共和国南北高速公路项目部分路段处于复理石地区,降雨集中、空间变异性显著且分层分布的岩土体给道路边坡施工带来了挑战。条分法、常规有限元法等确定性分析方法不能考虑岩土材料的不确定性,给出的具有唯一性、确定性的结果不能反映边坡稳定的不确定性。以该工程某边坡为例,采用有限元极限分析方法（FELA）,考虑岩土材料强度的空间变异性,利用上下限解法得出安全系数的分布区间。由勘察资料得到材料均值、标准差和空间相关长度并重建描述抗剪强度指标的二维随机场,同时考虑开挖岩层的节理分布,分析边坡在分级开挖过程中,各施工步骤的稳定性和破坏模式。与有限元分析结果相比,随机场条件下,部分情况开挖阶段安全系数低于限值,并出现局部破坏和整体破坏两种形式。结合不饱和土理论,模拟暴雨情况下雨水的入渗深度并在饱和区采用降低后的强度参数重新计算。通过蒙特卡洛模拟,得到各工况下安全系数、滑动体体积、挡墙弯矩和锚杆内力的概率密度分布函数。挡墙结构约束土体的变形,使得破坏模式趋向于整体破坏,安全系数分布区间变小。锚杆能带动更多土体进入工作状态,同样约束安全系数分布区间。旱季施工与雨季施工边坡破坏区域不同,同等支护条件下,雨季边坡安全系数分布区间更大,且均值明显降低。      

降雨条件下考虑饱和渗透系数变异性的边坡可靠度分析

土体饱和渗透系数表现为天然的变异性,为此基于Green-Ampt模型建立了考虑饱和渗透系数变异性的降雨入渗物理模型,并藉此模型确定了坡体湿润锋深度和含水率分布。然后结合无限长非饱和土边坡稳定模型得到解析形式的反映边坡稳定性的极限状态函数。采用Monte Carlo法对饱和渗透系数进行随机抽样并最终建立降雨条件下考虑饱和渗透系数变异性的边坡概率分析框架。针对一假想边坡,探讨了饱和渗透系数的变异系数、降雨持时和降雨强度对边坡破坏概率以及破坏发生时间概率分布的影响,结果表明：在降雨初期,边坡的破坏概率随饱和渗透系数变异性的增强而逐渐增加,但随着降雨的持续,破坏概率开始随变异性的增强而显著降低;滑坡最可能发生时间的大小并不受饱和渗透系数变异性的影响,而是直接取决于降雨强度;滑坡最可能发生时间所对应的概率却随变异性的增强而逐渐减小。     

The role of uncertainty in bedrock depth and hydraulic properties on the stability of a variably-saturated slope

We investigate the uncertainty in bedrock depth and soil hydraulic parameters on the stability of a variably-saturated slope in Rio de Janeiro, Brazil. We couple Monte Carlo simulation of a three-dimensional flow model with numerical limit analysis to calculate confidence intervals of the safety factor using a 22-day rainfall record. We evaluate the marginal and joint impact of bedrock depth and soil hydraulic uncertainty. The mean safety factor and its 95% confidence interval evolve rapidly in response to the storm events. Explicit recognition of uncertainty in the hydraulic properties and depth to bedrock increases significantly the probability of failure.     

Quantitative risk assessment of landslides with direct simulation of pre-failure to post-failure behaviors

Most previous studies on the quantitative risk assessment (QRA) of landslides focused on the probability of slope failure at the pre-failure stage and adopted empirical models for consequence analysis. The conventional approaches simplify the relationship between the pre-failure state and the post-failure behavior and cannot reasonably account for the effects of uncertainty on the entire landslide process. In this paper, an efficient QRA method that involves the direct simulation of the entire landslide process is proposed. A QRA formula that considers the probability of only those landslides that can impact the element at risk is used. The coupled Eulerian–Lagrangian method is used to simulate the entire landslide process and to identify slopes that can impact the element at risk and determine the failure consequences. The subset simulation method is adopted to efficiently estimate the probability of landslide impact, and parameter uncertainty is considered. Two case histories of landslides are investigated. First, the 2011 Baqiao loess landslide in Xi’an, China, is investigated, and the results of the proposed method are compared with those of the conventional approaches. Second, the proposed method is applied to assess the risk of the 2015 Ganjingzi landslide in the Three Gorges Reservoir. The effects of the risk mitigation works are also discussed.

     

A stabilized Smoothed Particle Hydrodynamics,Taylor–Galerkin algorithm for soil dynamics problems

Modelling of failure under dynamic conditions in geomaterials with finite elements presents a series of complex problems, among which we can mention those of (i) volumetric locking, which results on higher failure loads, (ii) influence of mesh alignment, resulting to unrealistic failure surfaces, (iii) diffusion of the shear band over some element widths, (iv) nonoptimal propagation properties (numerical diffusion and dispersion), (v) fulfilling Babuska–Brezzi conditions when using the same order of interpolation for displacement and pressures in coupled problems and (vi) large deformation analysis. This paper is based on previous work done by the authors, who developed a mixed approximation based on (i) casting the dynamic problem in the form of a system of first order PDEs and (ii) using stresses and velocities as nodal variables. The equations were discretized following a Taylor–Galerkin algorithm, first in time using a Taylor expansion and then in space using Galerkin method. The model was limited to small deformations. The purpose of this paper is to show how Taylor–Galerkin method can be extended to meshless formulations, such as the SPH method. The algorithm consists of (i) discretizing in time using a Taylor series expansion complemented with integration of source terms using a Runge–Kutta scheme and then (ii) discretizing in space using the SPH method. It is shown how the proposed method keeps the advantages of the Taylor–Galerkin method in Finite Elements (good propagation properties and capturing of shear bands) and avoids the tensile instability. A set of test problems ranging from elastic propagation of a wave in a bar to failure of a slope on a cohesive softening material are used to assess the performance of the method. Copyright © 2011 John Wiley & Sons, Ltd.     

岩质边坡平面滑动的模糊可靠度分析

综合考虑了边坡平边滑动的随机性和模糊性。根据工程实际确定结构功能函数的概率密度函数及表征边坡稳定性的隶属函数,提出了边坡失稳的模糊概率和边坡稳定性模糊可靠度的计算方法,并计算了模糊可靠度的置信区间,具有一定的实际意义。     

边坡渐进破坏的模糊随机可靠性研究

研究边坡的渐进破坏过程对边坡稳定性的影响,认为边坡破坏是由局部向整体扩展的渐进过程,它具有随机性和模糊性双重特性.渐进破坏模糊随机法能很好地反映边坡体内局部破坏的产生、扩展及对边坡整体可靠性的影响.基于岩土体的空间变异性,考虑了随机变量和极限状态函数的模糊性,以模糊随机变量为基本变量建立了边坡渐进破坏的模糊极限状态方程...     

Groundwater head uncertainty analysis in unsteady-state water flow models using the interval and perturbation methods

In the numerical simulation of groundwater flow, uncertainties often affect the precision of the simulation results. Stochastic and statistical approaches such as the Monte Carlo method, the Neumann expansion method and the Taylor series expansion, are commonly employed to estimate uncertainty in the final output. Based on the first-order interval perturbation method, a combination of the interval and perturbation methods is proposed as a viable alternative and compared to the well-known equal interval continuous sampling method (EICSM). The approach was realized using the GFModel (an unsaturated-saturated groundwater flow simulation model) program. This study exemplifies scenarios of three distinct interval parameters, namely, the hydraulic conductivities of six equal parts of the aquifer, their boundary head conditions, and several hydrogeological parameters (e.g. specific storativity and extraction rate of wells). The results show that the relative errors of deviation of the groundwater head extremums (RDGE) in the late stage of simulation are controlled within approximately ±5% when the changing rate of the hydrogeological parameter is no more than 0.2. From the viewpoint of the groundwater head extremums, the relative errors can be controlled within ±1.5%. The relative errors of the groundwater head variation are within approximately ±5% when the changing rate is no more than 0.2. The proposed method of this study is applicable to unsteady-state confined water flow systems.

     

有限数据条件下边坡可靠度分析的Bootstrap方法

基于Bootstrap抽样技术提出了有限数据条件下边坡可靠度分析方法。简要介绍了传统的边坡可靠度分析方法。采用Bootstrap方法模拟了抗剪强度参数概率分布函数的统计不确定性。以无限边坡为例研究了抗剪强度分布参数和分布类型不确定性对边坡可靠度的影响规律。结果表明：基于有限数据估计的样本均值、样本标准差和AIC值具有较大的变异性,这种变异性进一步导致了抗剪强度参数概率分布函数存在明显的统计不确定性。在考虑抗剪强度参数概率分布函数的统计不确定性时,边坡可靠度指标应为具有一定置信度水平的置信区间,而不是传统可靠度分析中的固定值。边坡可靠度指标的置信区间变化范围随安全系数的增加而增大,同时考虑分布参数和分布类型不确定性计算的可靠度指标具有更大的变异性和更宽的置信区间变化范围。Bootstrap方法为有限数据条件下抗剪强度参数概率分布函数统计不确定性的模拟以及边坡可靠度的评估提供了一条有效的途径。     

Series Expansion-Based Genetic Inversion of Wireline Logging Data

An evolutionary approach is applied to solve the nonlinear well logging inverse problem. In the framework of the proposed interval inversion method, nuclear, sonic, and laterolog resistivity data measured at an arbitrary depth interval are jointly inverted, where the depth variation of porosity, water saturation, and shale volume is expanded into series using Legendre polynomials as basis functions. In the interval inversion procedure, the series expansion coefficients are estimated by using an adaptive float-encoded genetic algorithm. Since the solution of the inverse problem using traditional linear optimization tools highly depends on the selection of the initial model, a heuristic search is necessary to reduce the initial model dependence of the interval inversion procedure. The genetic inversion strategy used in interval inversion seeks the global extreme of the objective function and provides an estimate of the vertical distribution of petrophysical parameters, even starting the inversion procedure from extremely high distances from the optimum. For a faster computational process, after a couple of thousand generations, the genetic algorithm is replaced by some linear optimization steps. The added advantage of using the Marquardt algorithm is the possibility to characterize the accuracy of the series expansion coefficients and derived petrophysical properties. A Hungarian oil field example demonstrates the feasibility and stability of the improved interval inversion method. As a significance, the genetic inversion method does not require prior knowledge or strong restrictions on the values of petrophysical properties and gives highly reliable estimation results practically independent of the initial model and core information.

     

基于聚类分析的边坡稳定性研究

在边坡稳定性分析中,滑面搜索方法对于得到边坡的稳定性系数至关重要。现今两种常用的边坡稳定性分析方法,极限平衡法以及强度折减法,可以得到极限应力状态下边坡的潜在滑面。而为了评价边坡在当前应力场下的稳定性,提出一种基于聚类分析概念的滑面搜索方法。这种方法综合考虑了边坡各点的位移以及点安全系数,采用K均值聚类法将具有相近性质的点进行分类,把边坡体分为潜在危险区以及稳定区。潜在危险区的边界即为边坡在当前应力状态下的潜在滑面,并运用矢量和方法计算得到其稳定性系数。采用上述方法对3个算例进行验算,并与极限平衡法以及强度折减法进行对比。结果表明：（1）基于聚类分析的边坡稳定性评价方法具有较好的合理性和可靠性;（2）当边坡处于临界状态附近,通过聚类分析得到的潜在滑面与其他两种方法得到的滑面基本一致;当边坡处于较稳定状态时,当前应力状态下的潜在滑面要比强度折减法得到的滑动带范围要更深更广,但求出的稳定性系数也较高;当存在软弱夹层时,矢量和计算出的滑面更为陡峻,稳定性系数比其他两种方法的结果要小。     

有限元强度折减系数法在北门沟坡滑坡稳定性评价中的应用

利用有限元强度折减系数法求得的滑坡安全稳定性系数进行北门沟滑坡稳定性评价。通过强度折减,当滑坡达到不稳定状态时,有限元计算不再收敛,此时的折减系数就是滑坡的安全稳定性系数。经计算,可以得到滑坡体破坏形式和破坏扩张趋势,有助于对滑体破坏机制的理解。计算表明,有限元强度折减法与传统刚体极限平衡法计算的稳定性系数很接近,这为滑坡稳定性评价提供了另一条途径。     

条形荷载下不排水土坡破坏模式判定及极限承载力估算

为了确定边坡放置地基的极限承载力,采用弹-理想塑性有限元,分析了不排水土坡(u=0)的坡肩上放置条形基础的地基极限承载力。结果表明,不排水土坡地基极限承载力仍可沿用Terzaghi水平地基极限承载力计算公式qu=cuNc。不考虑重度条件下,土坡地基的破坏模式类似于水平地基破坏模式,承载力系数Nc与极限分析法计算的结果一致;考虑重度条件下,可用土坡实际状态的Taylor数与其极限状态的Taylor数的差值N作为判别指标,当该值较小时将发生边坡破坏模式,较大时发生地基破坏模式,找出了两种破坏模式的N分界点,确定了Nc与N的关系,建立起坡肩作用条形荷载下不排水土坡极限承载力计算公式。     

含弱面块状结构岩质边坡稳定概率计算

首先采用不平衡推力模式分析块状结构岩体边坡稳定性系数的计算格式,推导了具体计算程序,并指出了该格式在可靠度计算中建立极限状态方程的困难;其次研究了解决该问题的近似方法,提出利用不平衡推力分析模式作为计算试验手段,通过计算试验提供样本数据,确定以岩体力学参数为自变量的修匀函数作为稳定性系数的近似解析式;然后以该函数为基础建立极限状态方程,利用验算点方法求解可靠度;最后分别利用该方法和传统的均差方法计算某工程问题。对比发现近似方法在精度上可满足要求,且计算工作量减少,表明了该方法的有效性。     

锚杆多种失效模式与双滑块边坡锚固系统可靠性分析

考虑锚杆拉杆拉断、拉杆从注浆体中拔出、锚固段注浆体从岩体中拔出、外锚头破坏以及垫墩底岩体的压坏等失效模式,利用系统可靠性原理和极限平衡分析方法,建立了双滑块边坡多锚杆锚固系统可靠性分析模型。基于蒙特卡罗随机抽样原理提出了该类边坡锚固系统破坏概率的直接求解方法。最后结合算例,分别基于中值安全系数和破坏概率指标分析了各计算参数对计算结果的影响,并讨论了锚杆锚固角和被动滑块可能滑裂面倾角对锚固系统稳定性的影响。     

Efficient conditional modeling for geotechnical uncertainty evaluation

A first‐order Taylor series method including direct derivative coding (DDC) is presented as a computationally efficient method for producing the probability distribution associated with calculated geotechnical performance. The probability distribution is employed in reliability analyses to calculate the probability of failure, valuable information that is not typically associated with deterministic analyses. The probability distribution also is used to identify important input parameters and to direct sampling efforts. Another approach to generate the probability distribution is the Monte Carlo (MC) method, however, Taylor series results generally are calculated in less time than the MC approach. One key to the implementation of the Taylor series approach is efficient approximation of the sensitivities required by the Taylor series calculation. DDC provides the technique to produce an efficient Taylor series algorithm. Directly coding the sensitivity analysis into the engineering model is accomplished by automatic and hand programming of derivatives. ADIFOR 2.0 was employed to automatically add derivatives to an existing engineering analysis model. For this paper a meshing program and 3D FEM for soil deformation is used to demonstrate the DDC approach. Although DDC requires a large up‐front programming effort, it is not site or data specific. Therefore, once the derivative programming has been performed, the numerical model can be applied to a wide variety of problems without additional user intervention. Copyright © 2001 John Wiley & Sons, Ltd.     

Physically-based landslide susceptibility analysis using Monte Carlo simulation in a tropical mountain basin

ABSTRACT

Physically-based distributed models are implemented for landslide susceptibility and hazard assessment around the world. Probabilistic methodologies are considered appropriate to study and quantify the uncertainties derived from the input parameters of these models. In this paper, three sets of Monte Carlo simulations, each one with 10,000 iterations, were applied for a slope stability analysis in a small basin of Envigado (Colombia), using the TRIGRS model, to characterise the uncertainty in the landslide assessment. Different parameters to determine the minimum number of realizations required to ensure a small variation in the failure probability were proposed and analyzed. The quality of the landslide susceptibility assessment was studied. Unexpected and probably erroneous results that may be common in the maps generated using this and other similar methodologies were identified and explained. Additionally, the distribution of the factor of safety was calculated for different grid cells of the basin, showing that the probability density function with the best adjustment to the frequency histogram of the factor of safety can vary between grid cells. The assumption of a normal distribution for the factor of safety would be inappropriate and would lead to miscalculations in this case study.