Reliability assessment of excavation systems considering both stability and serviceability performance

Excavation projects related to urban redevelopment and infrastructure improvement are often governed by serviceability-based design, rather than failure prevention criteria. Deformation tolerance specifications are often prescribed based on minimizing potential damage to adjacent structures. A risk-based approach to serviceability performance that systematically incorporates design parameter uncertainty will allow engineers to address soil uncertainty in performance-based design. This paper demonstrates the use of various kinds of reliability methods, such as response surface method (RSM), first-order reliability method (FORM), second-order reliability method (SORM), adaptive importance sampling (AIS), Monte Carlo simulation (MCS) and system reliability, to assess the risk of stability and/or serviceability failure of an entire excavation support system throughout the entire construction process. By considering multiple failure modes (including serviceability criteria) of an excavation, the component and system reliability indices for each excavation step are assessed during the entire excavation process. Sensitivity analyses are conducted for the system reliability calculations, which demonstrate that the adjacent structure damage potential limit state function is the dominant factor for determining excavation system reliability. An example is presented to show how the serviceability performance for braced excavation problems can be assessed based on the system reliability index.     

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.     

Reliability assessment of serviceability performance of braced retaining walls using a neural network approach

In urban environments, one major concern with deep excavations in soft clay is the potentially large ground deformations in and around the excavation. Excessive movements can damage adjacent buildings and utilities. There are many uncertainties associated with the calculation of the ultimate or serviceability performance of a braced excavation system. These include the variabilities of the loadings, geotechnical soil properties, and engineering and geometrical properties of the wall. A risk‐based approach to serviceability performance failure is necessary to incorporate systematically the uncertainties associated with the various design parameters. This paper demonstrates the use of an integrated neural network–reliability method to assess the risk of serviceability failure through the calculation of the reliability index. By first performing a series of parametric studies using the finite element method and then approximating the non‐linear limit state surface (the boundary separating the safe and ‘failure’ domains) through a neural network model, the reliability index can be determined with the aid of a spreadsheet. Two illustrative examples are presented to show how the serviceability performance for braced excavation problems can be assessed using the reliability index. Copyright © 2005 John Wiley & Sons, Ltd.     

Calibration and assessment of reliability-based serviceability limit state procedures for foundation engineering

This paper uses an existing reliability-based serviceability limit state (RBSLS) procedure to illustrate some of the critical elements in the calibration of RBSLS models and to serve as guide for future calibration work. The impact of copula model selection and therefore correlation structure of bearing pressure-displacement model parameters on reliability is assessed. Then, a framework for evaluating bearing pressure-displacement normalisation techniques is presented as a revision to the existing RBSLS procedure proposed. The reliability of the revised RBSLS procedure is then evaluated by comparing its accuracy to newly conducted, full-scale loading tests of spread footings on aggregate pier-reinforced ground. It is shown that the new RBSLS procedure produces a more accurate estimate of the actual reliability and validates the proposed framework.     

Practical second‐order reliability analysis applied to foundation engineering

A practical and efficient approach of implementing second‐order reliability method (SORM) is presented and illustrated for cases related to foundation engineering involving explicit and implicit limit state functions. The proposed SORM procedure is based on an approximating paraboloid fitted to the limit state surface in the neighborhood of the design point and can be easily carried out in a spreadsheet. Complex mathematical operations are relegated to relatively simple user‐created functions. The failure probability is calculated automatically based on the reliability index and principal curvatures of the limit state surface using established closed‐form SORM formulas. Four common foundation engineering examples are analyzed using the proposed method and discussed: immediate settlement of a flexible rectangular foundation, bearing capacity of a shallow footing, axial capacity of a vertical single pile, and deflection of a pile under lateral load. Comparisons with Monte Carlo simulations are made. In the case of the laterally loaded pile, the friction angle of the soil is represented as a one‐dimensional random field, and pile deflections are computed based on finite element analysis on a stand‐alone computer package. The implicit limit state function is approximated via the response surface method using two quadratic models. Copyright © 2011 John Wiley & Sons, Ltd.     

浅论岩土工程极限状态设计基本思想

论述了岩土工程极限状态设计的基本思想,包括极限状态的概念、土工参数设计值的确定过程和方法、构造物的重要度和场地地基复杂程度的划分、岩土工程类别、作用载荷组合、分项安全系数和极限状态设计等;给出了土工参数的实测值、导出值、标准值和设计值的确定原则或方法;指出在极限状态设计中,可通过增大设计作用效应或降低设计抗力的方法来进行岩土工程的可靠性设计.     

Moving least squares method for reliability assessment of rock tunnel excavation considering ground-support interaction

A practical approach is proposed in this paper for the reliability assessment of rock tunnel excavations using the moving least squares method (MLSM) and the uniform design. The failure probability is computed by the first-order and the second-order reliability method (FORM/SORM), which is based on the generated MLSM response surface (MLSM-RS) via an iterative algorithm. The proposed approach is first implemented in the analysis of a circular tunnel that consists of three limit state functions to illustrate the efficiency and accuracy of the approach. Then, the method is applied to a non-circular tunnel to demonstrate the feasibility and validity of the method for practical problems, in which numerical procedures are commonly employed to solve the implicit limit state functions.     

考虑参数和模型不确定性的基桩正常使用极限状态可靠度分析

考虑承载力计算模型和荷载不确定性,利用可靠度分析方法和概率统计理论,推导出承载能力极限状态（ULS）和正常使用极限状态（SLS）下可靠度指标的计算公式,给出了两种极限状态下可靠度指标间的线性关系式,研究了桩顶容许沉降 随机性对正常使用极限状态可靠度分析结果的影响。研究结果表明,土体类别和桩型对正常使用极限状态模型因子影响很小;正常使用极限状态下基桩可靠度指标随承载力计算模型和荷载不确定性的增大而减小,但减小幅度逐渐降低,且可靠度指标总变化量不大,工程应用中可忽略承载力计算模型和荷载不确定性在可靠度分析中的影响; 随机性对正常使用极限状态可靠性分析结果的影响很大,随 的增加,正常使用极限状态模型因子和可靠度指标逐渐增大,而模型因子变异性逐渐减小,但桩本身性质并没有任何改变,只是所允许的沉降条件不同。研究结果可为规范修订和工程应用提供参考。     

Analytical solutions for the earth pressure of narrow cohesive backfill with retaining walls rotating about the top

Currently, knowledge of the failure mechanisms of narrow backfills with retaining walls rotating about the top (RT mode) is still lacking which leads to inaccurate estimations of the earth pressure. Numerical simulations using finite element limit analysis find that under the effects of backfill geometries, interface strengths, and soil properties, the upper soil layer supported by soil arching retains its integrity and the lower soil layer is sheared by multiple curved sliding surfaces in the limit state. Based on the failure mechanisms of narrow backfills, a calculation model is established which considers the soil arching effect, curved sliding surface, and cohesive soils. Analytical solutions for the earth pressure of narrow cohesive backfills with retaining walls rotating about the top are derived by using the limit equilibrium horizontal slice method. Compared with previous studies, the present method predicts the earth pressure distribution with higher accuracy. Several extensive parametric studies have also been conducted. Thus, decreasing the aspect ratio of backfills, increasing the inclined angle of natural slopes, interface strengths, and soil cohesion are beneficial for maintaining backfill integrity and reducing earth pressure against retaining walls.

     

Efficient reliability method for implicit limit state surface with correlated non‐Gaussian variables

In contrast to the traditional approach that computes the reliability index in the uncorrelated standard normal space (u‐space), the reliability analysis that is simply realized in the original space (x‐space, non‐Gaussian type) would be more efficient for practical use, for example, with the Low and Tang's constrained optimization approach. On the other hand, a variant of Hasofer, Lind, Rackwits and Fiessler algorithm for first‐order reliability method is derived in this paper. Also, the new algorithm is simply formulated in x‐space and requires neither transformation of the random variables nor optimization tools. The algorithm is particularly useful for reliability analysis involving correlated non‐Gaussian random variables subjected to implicit limit state function. The algorithm is first verified using a simple example with closed‐form solution. With the aid of numerical differentiation analysis in x‐space, it is then illustrated for a strut with complex support and for an earth slope with multiple failure modes, both cases involving implicit limit state surfaces. Copyright © 2015 John Wiley & Sons, Ltd.     

山西乡宁—吉县地区黄土高边坡可靠度研究

在山西乡宁—吉县地区实测了7个具有代表性的自然极限状态黄土高边坡断面,建立边坡地层结构模型;选取研究区合理的黄土物理力学参数,并分地层年代对10个典型工点的黄土强度参数内聚力和内摩擦角的变异性进行分析;选取6组典型的强度参数变异系数组合,基于Monte-Carlo法进行可靠度模拟,评价该区边坡稳定性;采用自然类比法进行边坡设计。结果表明：边坡失效概率随坡高的变化趋势一致,均是中等坡高（49.8m）的边坡失效概率较大,低坡和高坡的失效概率较低;当变异系数较小时,边坡失效概率对坡高和坡度的变化敏感,而当变异系数较大时,边坡失效概率对坡高和坡度的变化不敏感;当坡型一定、强度参数变异系数较小时,边坡的稳定系数基本不变,而当参数变异系数超过某一界限时,稳定系数随变异系数的增大而增大,二者存在非线性相关关系;研究区黄土边坡处于基本稳定状态,但其失效概率最大达69.3%,平均21.1%,介于20%～30%的比例为33.3%,大于30%的比例为14.3%,可靠度指标介于-0.5～8.5,其中小于2.7的比例为88.1%;对于坡高约为50m的黄土高边坡,若取30%作为可接受失效概率,边坡坡度需降至45°以下,如果期望可接受失效概率在10%以内,则坡度不宜超过34°。     

A rational method for development of limit state for liquefaction evaluation based on shear wave velocity measurements

This papers presents a new approach for developing a limit state for liquefaction evaluation based on field performance data. As an example to illustrate the new approach, a database that consists of, among many other features, in situ shear wave velocity measurements and field observations of liquefaction/non‐liquefaction in historic earthquakes is analysed. This database is first used to train a neural network to classify liquefaction/non‐liquefaction based on soil resistance parameters and load parameters. The successfully trained and tested neural network is then used to establish a limit state, a multiple dimension boundary that separates ‘zone’ of liquefaction from ‘zone’ of non‐liquefaction. The limit state yields cyclic resistance ratio for a given set of soil resistance parameters. Examination of all cases in the database show that the developed limit state has a high degree of accuracy in predicting the occurrence of liquefaction/non‐liquefaction. The developed neural network model can accurately predict the cyclic resistance ratio of soils. Copyright © 2000 John Wiley & Sons, Ltd.     

基于二楔块法的加筋土挡墙屈服加速度及破坏模式极限分析

加筋土挡墙具有优越的抗震性能,并在土建工程中被广泛应用,因此,加筋土挡墙抗震设计方法的研究尤为重要。为了能够分析加筋体内部筋材布置方式、筋材抗拉强度等对屈服加速度的影响,假定破坏模式为双楔块模式,根据极限分析理论推导了加筋土挡墙屈服加速度系数表达式。与规范计算值相比,计算结果更接近模型测试值与数值模拟结果,同时计算方法可以反映模型的真实破坏模式。参数分析表明：屈服加速度随着筋材抗拉强度的增大而增大,特别是筋材长度较长时;随着筋材竖向间距的增大,屈服加速度逐渐减小;面板的宽度对屈服加速度几乎不产生影响;与面板宽度相比,筋材抗拉强度与竖向间距对加筋土挡墙破裂面形状的影响更大。     

An approximation to the reliability of series geotechnical systems using a linearization approach

A method based on the linearization of the limit state functions (LSFs) is applied to evaluate the reliability of series geotechnical systems. The approach only needs information provided by first order reliability method (FORM) results: the vector of reliability indices, β, of the LSFs composing the system; and their correlation matrix, R. Two common geotechnical problems—the stability of a slope in layered soil and a circular tunnel in rock—are employed to demonstrate the simplicity, accuracy and efficiency of the suggested procedure, and advantages of the linearization approach with respect to alternative computational tools are discussed. It is also found that, if necessary, the second order reliability method (SORM)—that approximates the true LSF better than FORM—can be employed to compute better estimations of the system’s reliability.     

基坑挡土墙上土压力荷载的可靠度分析

根据朗金土压力公式,以常规设计为基础,建立了分步开挖、无粘性土时主动土压力荷载增加的极限状态方程:采用可靠度分析的AFOSM法,分析了分步开挖时土压力计算中应注意的问题。并分析研究了土性参数对土压力计算可靠性的影响,最后得出了四点结论。     

Multiple response surfaces for slope reliability analysis

This paper develops a multiple response surfaces approach to approximate the limit state function for slope failure by second‐order polynomial functions, to incorporate the variation of the most probable slip surfaces, and to evaluate the slope failure probability p_f. The proposed methodology was illustrated through a cohesive soil slope example. It is shown that the p_f values estimated from multiple response surfaces agree well with those p_f values that have been obtained by searching a large number of potential slip surfaces in each Monte Carlo simulation (MCS) sample. The variation of number of the most probable slip surfaces is studied at different scale of fluctuation (λ) values. It is found that when full correlation assumed for each of random fields (i.e., spatial variability is ignored), the number of the most probable slip surfaces is equal to the number of random fields (in this study, it is 3). When the spatial variability grows significantly, the number of the most probable slip surfaces or number of multiple response surfaces firstly increases evidently to a higher value and then varies slightly. In addition, the contribution of a specific most probable slip surface varies dramatically at different spatial variability level, and therefore, the variation of the most probable slip surfaces should be accounted for in the reliability analysis. The multiple response surfaces approach developed in this paper provides a limit equilibrium method and MCS‐based means to incorporate such a variation of the most probable slip surfaces in slope reliability analysis. Copyright © 2014 John Wiley & Sons, Ltd.     

Load-displacement uncertainty of vertically loaded shallow footings on sands and effects on probabilistic settlement estimation

This article focuses on the statistical characterisation and stochastic modelling of the load-displacement behaviour of shallow footings on cohesionless soils and on the probabilistic estimation of settlement for serviceability limit state design (LSD). The study relies on a field database of 30 full-scale footings subjected to vertical loading with cone penetration testing data available for each site. The performance of three load-displacement models in replicating field data is assessed comparatively through statistical analysis. Load-displacement uncertainty is subsequently modelled probabilistically to perform Monte Carlo Simulation (MCS)-based estimation of footing settlement using the best-performing power law model. The dependence among load-displacement model parameters is investigated and replicated using copula theory. Samples are generated to account for parametric uncertainties in model inputs. The simulation output samples of settlement are examined statistically in order to assess the relevance of parametric and load-displacement uncertainties in settlement estimation, as well as the importance of accounting for correlation between power law model parameters. A simple analytical model for the estimation of settlement at any target reliability level is obtained on the basis of the outputs of MCS. The model can be practically implemented in geotechnical LSD at serviceability limit states.     

Determination of partial factors for the verification of the bearing capacity of shallow foundations under open channels

The limit state design method has been introduced into the design criteria for geotechnical structures. The current paper attempts to apply the reliability-based design method, at Level II, to the bearing capacity of the foundations of open channels from the viewpoint of the limit state design. To examine the applicability of the proposed procedure for practical structures, the reliability index is computed for evaluating the stability of the foundations of existing open channels designed by the conventional method. The conventional design procedure makes excessively safe side design. We applied the FORM to the existing open channels designed by the conventional design procedure, and consequently, large values of reliability index, 3 and 5 were obtained for clayey and sandy soils, respectively. Finally, the partial factors for the soil parameters have been determined, corresponding to the target reliability indices β _t =1, 3 and 4.     

Critical Slope and Plasticity

ＩＮＴＲＯＤＵＣＴＩＯＮＤｅｓｐｉｔｅｔｈｅｄｅｖｅｌｏｐｍｅｎｔｏｆｅｌａｓｔｉｃ－ｐｌａｓｔｉｃ－ｖｉｓｃｏｕｓｎｕｍｅｒｉ－ｃａｌｍｅｔｈｏｄｆｏｒｔｈｅａｎａｌｙｓｉｓｏｆｓｌｏｐｅｓ,ｔｒａｄｉｔｉｏｎａｌｔｅｃｈｎｉｑｕｅｓｂａｓｅｄｏｎ...     

Internal Stability Analysis of Reinforced Earth Retaining Walls

The stabilization of slopes by the technique of reinforced earth (Terre Armée) is a very economical and reliable technique. We propose in this paper to check the overall internal stability of the reinforced earth retaining walls by three mechanical models, using the analytical method of the limit equilibrium (failure). The main objective of this paper is to compare these failure mechanical models with the failure models obtained by numerical analysis (code FLAC 2D), in order to validate the most realistic and more unfavourable failure models. Parametric and comparative studies carried out have allowed us to bring a very useful knowledge concerning the study of the internal stability of the reinforced earth retaining walls. It also proposed a theoretical mechanical model of calculation proved by numerical simulation.