不同先验分布下的后验分布确定土力学参数

岩土工程中各土层参数的取值是根据现场及室内试验数据,采用经典统计学方法进行确定的,但这往往忽略了先验信息的作用.与经典统计学方法不同的是,Bayes法能从考虑先验分布的角度结合样本分布去推导后验分布,为岩土参数的取值提供一种新的分析方法.岩土工程勘察可视为对总体地层的随机抽样,当抽样完成时,样本分布密度函数是确定的,故Bayes法中的后验分布取决于先验分布,因此推导出两套不同的先验分布:利用先验信息确定先验分布及共轭先验分布.通过对先验及后验分布中超参数的计算,当样本总体符合N(μ,σ²)正态分布时,对所要研究的未知参数μ和σ展开分析,综合对比不同先验分布下后验分布的区间长度,给出岩土参数Bayes推断中最佳后验分布所要选择的先验分布.结果表明:共轭情况下的后验分布总是比无信息情况下的后验区间短,概率密度函数分布更集中,取值更方便.在正态总体情形下,根据未知参数μ和σ的联合后验分布求极值方法,确定样本总体中最大概率均值μ_max和方差σ_max作为工程设计采用值,为岩土参数取值方法提供了一条新的路径,有较好的工程意义.     

基于粒子群优化Kriging模型的边坡可靠度分析

采用传统极限平衡法进行边坡可靠度分析时,不可避免会遇到一个问题,即边坡功能函数形式的高度非线性以及隐含性.对于隐式功能函数,传统的求解方法是通过对功能函数进行多次迭代,从而得到安全系数值.但是由于功能函数的形式较为复杂,导致迭代计算的过程变得尤为繁琐且效率低下.鉴于传统边坡可靠度分析中存在的安全系数计算繁琐耗时的问题,...     

Optimal engineering design via Benders’ decomposition

The optimal engineering design problem consists in minimizing the expected total cost of an infrastructure or equipment, including construction and expected repair costs, the latter depending on the failure probabilities of each failure mode. The solution becomes complex because the evaluation of failure probabilities using First-Order Reliability Methods (FORM) involves one optimization problem per failure mode. This paper formulates the optimal engineering design problem as a bi-level problem, i.e., an optimization problem constrained by a collection of other interrelated optimization problems. The structure of this bi-level problem is advantageously exploited using Benders’ decomposition to develop and report an efficient algorithm to solve it. An advantage of the proposed approach is that the design optimization and the reliability calculations are decoupled, resulting in a structurally simple algorithm that exhibits high computational efficiency. Bi-level problems are non-convex by nature and Benders algorithm is intended for convex optimization. However, possible non-convexities can be detected and tackled using simple heuristics. Its practical interest is illustrated through a realistic but simple case study, a breakwater design example with two failure modes: overtopping and armor instability.     

On the full and block-decoupling of nonlinear functions

We review a method that decouples multivariate functions into linear combinations of a set of univariate (or simpler multivariate) functions of transformed variables. In this way the given nonlinear multiple-input-multiple-output function is decoupled into a structure having simpler parallel internal branches that are linked by linear transformations to the original inputs and outputs. The procedure collects first-order information by evaluating the Jacobian matrix of the given function in a set of points. These matrices are stacked into a three-way tensor, whose decomposition reveals the decoupled representation. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

余模范畴中的余倾斜预包络和余倾斜挠类

众所周知, Assem-Smal定理在倾斜理论中有重要的作用.本文的目的是建立一个在余模范畴中的Assem-Smal定理的版本,并通过利用预包络理论来刻画余模范畴中的余倾斜挠类.     

Groundwater regime in a slope stabilized by drain trenches

Drains are widely used in civil engineering as control works against slope instability in saturated clayey soils. The action of drains reduces pore pressures in the subsoil and consequently increases effective stresses and soil shear strength. Although drains are widely used in geotechnical design, their effect on slope stability is not fully understood and modeled. It is well known that the water table is subjected to broad variations due to atmospheric conditions and that the critical situation for slopes occurs during the wet season, when pore pressure in the subsoil attains its maximum. The real role of drains consists of avoiding this peak of pore pressure that could cause land sliding. Despite the behavior described, analyses proposed in the literature solve cases of drains working in slopes under steady hydraulic conditions at the boundaries. In this work we present a transient analysis of the phenomenon by considering the work of drain trenches in a transient regime due to variations in hydraulic conditions at the ground surface, as a consequence of rainfall. Under this hypothesis, the effect of drains is calculated to be greater than would be predicted by available design methods.     

System reliability analysis of slope stability using generalized Subset Simulation

Slope failure mechanisms (e.g., why and where slope failure occurs) are usually unknown prior to slope stability analysis. Several possible failure scenarios (e.g., slope sliding along different slip surfaces) can be assumed, leading to a number of scenario failure events of slope stability. How to account rationally for various scenario failure events in slope stability reliability analysis and how to identify key failure events that have significant contributions to slope failure are critical questions in slope engineering. In this study, these questions are resolved by developing an efficient computer-based simulation method for slope system reliability analysis. The proposed approach decomposes a slope system failure event into a series of scenario failure events representing possible failure scenarios and calculates their occurrence probabilities by a single run of an advanced Monte Carlo simulation (MCS) method, called generalized Subset Simulation (GSS). Using GSS results, representative failure events (RFEs) that are considered relatively independent are identified from scenario failure events using probabilistic network evaluation technique. Their relative contributions are assessed quantitatively, based on which key failure events are determined. The proposed approach is illustrated using a soil slope example and a rock slope example. It is shown that the proposed approach provides proper estimates of occurrence probabilities of slope system failure event and scenario failure events by a single GSS run, which avoids repeatedly performing simulations for each failure event. Compared with direct MCS, the proposed approach significantly improves computational efficiency, particularly for failure events with small failure probabilities. Key failure events of slope stability are determined among scenario failure events in a cost-effective manner. Such information is valuable in making slope design decisions and remedial measures.     

Augmented line sampling for approximation of failure probability function in reliability-based analysis

An efficient approach, called augmented line sampling, is proposed to locally evaluate the failure probability function (FPF) in structural reliability-based design by using only one reliability analysis run of line sampling. The novelty of this approach is that it re-uses the information of a single line sampling analysis to construct the FPF estimation, repeated evaluations of the failure probabilities can be avoided. It is shown that, when design parameters are the distribution parameters of basic random variables, the desired information about FPF can be extracted through a single implementation of line sampling. Line sampling is a highly efficient and widely used reliability analysis method. The proposed method extends the traditional line sampling for the failure probability estimation to the evaluation of the FPF which is a challenge task. The required computational effort is neither relatively sensitive to the number of uncertain parameters, nor grows with the number of design parameters. Numerical examples are given to show the advantages of the approach.     

极限应变法在圆形隧洞稳定分析中的应用

材料的屈服和破坏是不同的,屈服准则已有大量研究,但缺少严格的破坏准则.理想弹塑性模型用应力表述难以区别屈服与破坏,为此该文提出极限应变破坏判据,可用于判断材料的局部和整体破坏.给出了不同材料极限应变的确定方法,并作为破坏判据用于岩土类材料的稳定分析,称为极限应变法.将极限应变法应用于圆形隧洞,研究隧洞的破坏过程、围岩破坏深度及其安全系数,并与滑移线理论和实际模型试验的结果进行对比.研究表明:极限应变法能够判断圆形隧洞的破坏过程与极限状态,求得准确的安全系数,与滑移线场法和模型试验的结果一致,验证了极限应变法在隧洞中应用的可行性.极限应变判据具有明确的力学意义,能反映材料破坏的全过程,为岩土类材料极限分析提供了一种新的方法.     

Stepwise covariance matrix decomposition for efficient simulation of multivariate large-scale three-dimensional random fields

The spatial variability of geomaterials affects the failure mechanism and reliability of geotechnical structures significantly, and can be modeled rigorously as a three-dimensional (3-D) random field. However, the simulation of multivariate, large-scale and high-resolution 3-D random fields is a challenging task due to extraordinary demands in computational resources. This paper proposes a stepwise covariance matrix decomposition method (CMD) with the aid of separable correlation functions, in which the 3-D random field is generated sequentially along each single dimension with small one-dimensional correlation matrices. The method not only inherits the simplicity of the widely-used general CMD, but also significantly reduces the computational time and required memory space. It only takes a few seconds to construct large-scale and high-resolution 3-D random fields, with the requirement on memory space reduced by more than ten orders of magnitude. The maximum random field resolution is significantly improved from approximately 21 × 21 × 41 using the general CMD to over 501 × 501 × 1001 using the stepwise CMD, which suffices in most engineering applications. The stepwise CMD facilitates 3-D spatial variability modeling in probabilistic site characterization and routine geotechnical reliability analysis.     

Quantitative risk assessment of slope failure in 2-D spatially variable soils by limit equilibrium method

Quantitative risk assessment of slope failure is an important prerequisite for formulating rational strategies for landslide risk mitigation and developing a landslide risk-based warning system. Efficient risk assessment of slope failure in two-dimensional (2-D) spatially variable soils is a challenging problem. This paper proposes an efficient approach for quantitative risk assessment of slope failure considering the 2-D spatial variation of soil properties in the limit equilibrium analysis framework. To facilitate the risk assessment of slope failure, an empirical method is developed for the identification of slope key failure modes. With the proposed approach, the key failure modes of the spatially variable slope can be well identified and their contributions to the risk of slope failure can be effectively quantified. Finally, a two-layered soil slope is studied to illustrate the proposed approach. It is found that the prominent advantages of the proposed approach include being computationally efficient and accounting for the effect of the correlations among the failure modes.     

Global optimization of bounded factorable functions with discontinuities

A deterministic global optimization method is developed for a class of discontinuous functions. McCormick’s method to obtain relaxations of nonconvex functions is extended to discontinuous factorable functions by representing a discontinuity with a step function. The properties of the relaxations are analyzed in detail; in particular, convergence of the relaxations to the function is established given some assumptions on the bounds derived from interval arithmetic. The obtained convex relaxations are used in a branch-and-bound scheme to formulate lower bounding problems. Furthermore, convergence of the branch-and-bound algorithm for discontinuous functions is analyzed and assumptions are derived to guarantee convergence. A key advantage of the proposed method over reformulating the discontinuous problem as a MINLP or MPEC is avoiding the increase in problem size that slows global optimization. Several numerical examples for the global optimization of functions with discontinuities are presented, including ones taken from process design and equipment sizing as well as discrete-time hybrid systems.     

Optimum stacking sequence of composite laminates for maximum strength

A method is presented for maximum strength optimum design of symmetric composite laminates subjected to in-plane and transverse loadings. The finite element method based on shear deformation theory is used for the analysis of composite laminates. Ply orientation angles are chosen as design variables. The quadratic failure criterion which is meant to predict fracture, is used as an object function for optimum stacking sequence design of a laminated plate. The Broydon-Fletcher-Goldfarb-Shanno optimization technique is employed to solve the optimization problem effectively. Numerical results are given for various loading conditions, boundary conditions, and aspect ratios. The results show that the quadratic failure criterion such as Tsai-Hill theory is effective for the optimum structural design of composite laminates.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 3, pp. 393–404, May–June, 1995.     

Comparison of coupled and decoupled modal approaches in seismic analysis of concrete gravity dams in time domain

Different methods are available for dynamic analysis of concrete dams. Among these, modal approach is highly popular due to the efficiency of the method. This becomes more significant if the response is to be calculated for several earthquake ground motion records as required in most practical cases. In this study, two different modal approaches have been considered for dynamic analysis of concrete gravity dam–reservoir systems. These are coupled modal method and decoupled modal technique. The former approach utilizes the coupled modes of the system. It is well known that calculation of these modes involves some complications due to its corresponding unsymmetrical eigenproblem. However, the response at each step can be obtained very efficiently in this method. The latter technique, relies on the decoupled modes of the system, which are easily obtained by standard eigenvalue solvers. The equation of motion is also solved with reasonable efficiency in this approach. In the latter part of this paper, analysis of a typical dam–reservoir system is performed by both methods mentioned above. These analyses are compared from accuracy and efficiency point of view.     

Stress-dependent Failure Surface of Granular Materials

Numerical computations of geotechnical problems will become increasingly important because of the growing complexity of geotechnical applications. Therefore, a well-founded prediction of stability statements requires appropriate models, which are able to realistically depict the stress-strain behaviour of non-cohesive-frictional granular materials. On several stress paths, drained triaxial compression experiments on compact dense sand specimen exhibited that the size of the failure surface is not independent from the hydrostatic pressure. The failure surface and, thus, the maximal shear stresses at a specific confining pressure σ₃^exp can be increased by a compression preload at a level higher than σ₃^exp. This means that granular materials own several failure surfaces in dependence of the hydrostatic pressure. Consequently, the failure criteria based on the assumption of a compression stress-path-independent single-failure surface cannot recover the newly detected plastic yielding behaviour of granular materials. An improved approach for modelling the plastic hardening and softening behaviour coupled with the new yield properties at the limit state will be presented. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

岩土工程位移时间序列的组合预测研究

将组合预测方法用于岩土工程位移时间序列预测.结合实际观测数据,分别建立位移时间序列预测的GM(1,1)模型、Verhulst模型和趋势曲线模型.采用极小误差法确定各单一模型的权重,建立组合预测模型.应用表明,组合预测的精度高,为岩土工程位移预测提供了一种实用、可靠的方法.     

Nonsingular decoupled terminal sliding-mode control for a class of fourth-order nonlinear systems

This paper presents a nonsingular decoupled terminal sliding mode control (NDTSMC) method for a class of fourth-order nonlinear systems. First, the nonlinear fourth-order system is decoupled into two second-order subsystems which are referred to as the primary and secondary subsystems. The sliding surface of each subsystem was designed by utilizing time-varying coefficients which are computed by linear functions derived from the input–output mapping of the one-dimensional fuzzy rule base. Then, the control target of the secondary subsystem was embedded to the primary subsystem by the help of an intermediate signal. Thereafter, a nonsingular terminal sliding mode control (NTSMC) method was utilized to make both subsystems converge to their equilibrium points in finite time. The simulation results on the inverted pendulum system are given to show the effectiveness of the proposed method. It is seen that the proposed method exhibits a considerable improvement in terms of a faster dynamic response and lower IAE and ITAE values as compared with the existing decoupled control methods.