An artificial bee colony algorithm for locating the critical slip surface in slope stability analysis

Determination of the critical slip surface with the minimum factor of safety of a slope is a difficult constrained global optimization problem. In this article, an artificial bee colony algorithm with a multi-slice adjustment method is proposed for locating the critical slip surfaces of soil slopes, and the Spencer method is employed to calculate the factor of safety. Six benchmark examples are presented to illustrate the reliability and efficiency of the proposed technique, and it is also compared with some well-known or recent algorithms for the problem. The results show that the new algorithm is promising in terms of accuracy and efficiency.     

基于响应面法和Morgenstern-Price法土坡可靠度计算方法

基于响应面法,建立了一种高效的边坡可靠度指标和失效概率近似计算方法。该法在构造响应面函数时,抽样点计算采用Morgenstern-Price法取代传统费时的有限单元法,大大降低了计算工作量。利用Monte-Carlo随机抽样原理,提出了一种能同时确定边坡最危险非圆弧滑动面和最小可靠度指标的随机搜索新算法。该文给出的两个算例验证了方法的实用性和可靠性,其计算结果同时表明:当分别以最小可靠度指标和最小中值安全系数为目标函数时,搜索到的边坡最危险滑动面相差较大。最后,探讨了土性指标(c,φ)的分布概型及相关性对边坡可靠度计算结果的影响。     

Geotechnical system reliability of slopes

In slope stability analysis it is customary to search for the critical slip surface considering the conventional factor of safety as an index of stability. With the development of reliability analysis approaches within a probabilistic framework, alternative definitions of the critical slip surface can be adopted. Thus one may define a critical slip surface as one with the lowest reliability index or one with the highest probability of failure. However, it is important to consider the slope stability problem in terms of a system of many potential slip surfaces. For such a system, the calculation of system reliability is appropriate and desirable. In this paper, system reliability bounds are calculated within a probabilistic framework. The ‘system reliability’ or the ‘system probability of failure’ must be estimated for comparison with the corresponding reliability or probability of failure with respect to a ‘critical’ slip surface. The general slope stability problem involving non-zero internal friction angle involves a non-linear performance function. Moreover, the expression for factor of safety is usually inexplicit except for the ordinary method of slices which is not accurate except when ‘ø = 0’. This paper addresses the system reliability for inexplicit and non-linear performance functions as well as for linear and explicit ones. Any version of the method of slices may be used although the proposed approach is presented on the basis of the Bishop simplified method. It is shown that the upper bound system failure probability is higher than the failure probability associated with a critical slip surface. The difference increases as the coefficient of variation of the shear strength parameters increases.     

纯粘土边坡稳定性的解析计算

采用解析方法,建立了纯粘土边坡(0=j)圆弧滑裂时安全系数的解析表达式;利用函数取极值的条件,提出了通过求解一代数方程组来确定边坡的临界滑裂面和最小安全系数的方法;并计算了某些边坡的临界滑裂面和最小安全系数。     

An improved harmony search minimization algorithm using different slip surface generation methods for slope stability analysis

An improved harmony search algorithm is proposed which is found to be more efficient than the original harmony search algorithm for slope stability analysis. The effectiveness of the proposed algorithm is examined by considering several published cases. The improved harmony search method is applied to slope stability problems with five types of procedure for generating trial slip surfaces. It is demonstrated that the improved harmony search algorithm is efficient and effective for the minimization of factors of safety for various difficult problems, and the method of generating the trial failure surfaces can be important in the minimization process.     

深基坑复合土钉支护稳定性分析方法及其应用

探讨计算复合土钉支护边坡稳定性安全系数的一种方法,为设计提供较为科学合理的分析手段。基于土坡稳定性分析的Bishop法,建立了稳定性安全系数的计算公式。采用几何控制参数法对最危险滑移面进行搜索。通过分别移动基底、地表水平面和位于基坑高度一半处的水平面上的三个几何控制点,寻找到边坡最危险滑移面并计算出对应的稳定性安全系数。计算表明:(1)用几何控制参数法搜索的最危险滑移面有且仅有一个;(2)改进后的搜索方法趋于完善、合理和准确;(3)对于软弱土层,当边坡侧壁垂直时,滑移面通过坡趾的假设不合理;(4)用该方法计算的工程实例安全系数与实际情况吻合较好,具有较高的工程应用价值。     

基坑土钉支护稳定分析方法及其应用

探讨一种土钉支护边坡稳定分析方法，为设计提供较为科学合理的分析手段。基于土坡稳定分析常用的瑞典条分法，考虑土钉的极限拉力作用，建立稳定安全系数公式，可用于基坑土钉支护设计。提出用几何控制多数确定最危险滑动面的计算机算法，通过计算表明：安全系数是几何控制参数的单峰函数。用黄金分割法分步对几何控制多数进行优化，提高了计算速度。通过与国外方法比较和工程实例验算，确定安全系数的取值范围，一般工程安全系数应为１．２－１．５。具有较后的工程应用价值。     

Analysis of Loess Slope Stability Considering Cracking and Shear Failures

The cracks caused by tension are commonly observed on the upper border of loess slope. Most researchers assume that shear failure is the main reason for slope instability. The existing cracks and their development are not fully considered. The finite element method is applied widely in the numerical simulations of slope stability, but it converges and time problems must be considered when a crack occurs. The extended finite element method provides a new way to solve discontinuous media problems. In this paper, a composite model of cracking and shear failure is introduced. The extended finite element method was used to simulate the cracking in loess slope. The model used here had a unified enrichment function and the enriched freedom had a clear physical meaning. Numerical analyses were performed and the simulation results showed that the stress field redistributes. The crack propagated almost vertically at the beginning. The slope stability safety factor was less than that obtained without considering tension failure. Furthermore, the critical sliding surface was determined. This model can be used for analyzing the stability of loess slope and provides a reference for slope safety analyses.     

考虑土质边坡多失效模式的区域概率风险分析方法

针对现有边坡风险分析仅考虑单一失效模式及风险分析结果难以被工程师理解等问题,提出了考虑边坡多失效模式的区域概率风险分析方法。首先给出了区域概率的概念,建立了以区域概率定量表征边坡稳定性的方法,推导了基于区域概率的边坡系统风险评价公式,探讨了该公式的适用性。在此基础上采用直接蒙特卡罗模拟计算边坡区域失效概率。最后以一不排水黏性土坡为例阐明了所提方法的有效性。结果表明:区域概率风险分析方法为表征边坡的关键失效区提供了一种简单、直接的可视化工具,为工程师制定合理的边坡加固设计方案提供了参考依据。基于区域概率风险分析方法的边坡系统风险评价公式不仅能够有效地回避边坡风险评价中多滑面间安全系数及滑块体积之间相关性计算问题,而且能够准确地量化边坡多破坏模式的系统风险。传统的风险评价方法可能显著低估边坡系统风险,使得边坡设计方案偏危险。边坡失效概率最大的滑面不一定是边坡失效风险最大的滑面,在边坡加固设计中,失效风险较大的滑面也应该予以关注。     

Guided particle swarm optimization method to solve general nonlinear optimization problems

The development of hybrid algorithms is becoming an important topic in the global optimization research area. This article proposes a new technique in hybridizing the particle swarm optimization (PSO) algorithm and the Nelder–Mead (NM) simplex search algorithm to solve general nonlinear unconstrained optimization problems. Unlike traditional hybrid methods, the proposed method hybridizes the NM algorithm inside the PSO to improve the velocities and positions of the particles iteratively. The new hybridization considers the PSO algorithm and NM algorithm as one heuristic, not in a sequential or hierarchical manner. The NM algorithm is applied to improve the initial random solution of the PSO algorithm and iteratively in every step to improve the overall performance of the method. The performance of the proposed method was tested over 20 optimization test functions with varying dimensions. Comprehensive comparisons with other methods in the literature indicate that the proposed solution method is promising and competitive.     

计算土坡安全系数的辐向条分模型

本文根据土条间的几何关系提出了土坡稳定分析的辐向条分法，并利用高斯积分法计算出安全系数，再通过计算机搜索及改进的JC法求出土坡最小安全系数。该法避免了传统意义上的条分过程，消除了由于条间力简化假设所引起的计算误差，从而提供了一种高效、准确的土坡稳定性计算方法。     

A hybrid evolutionary algorithm for distribution feeder reconfiguration

Distribution feeder reconfiguration (DFR) is formulated as a multi-objective optimization problem which minimizes real power losses, deviation of the node voltages and the number of switching operations and also balances the loads on the feeders. In the proposed method, the distance (λ ₂ norm) between the vector-valued objective function and the worst-case vector-valued objective function in the feasible set is maximized. In the algorithm, the status of tie and sectionalizing switches are considered as the control variables. The proposed DFR problem is a non-differentiable optimization problem. Therefore, a new hybrid evolutionary algorithm based on combination of fuzzy adaptive particle swarm optimization (FAPSO) and ant colony optimization (ACO), called HFAPSO, is proposed to solve it. The performance of HFAPSO is evaluated and compared with other methods such as genetic algorithm (GA), ACO, the original PSO, Hybrid PSO and ACO (HPSO) considering different distribution test systems.     

基于模型修正的空间变异边坡可靠度分析方法

空间变异边坡可靠度计算需要进行多次重复性边坡稳定性分析,常用的边坡稳定性分析极限平衡方法（LEM）计算效率较高而有限元方法（FEM）可捕捉真实的边坡失效机制,边坡可靠度评价中如能充分利用这两者的优势将具有重要的工程价值。该文在发展考虑参数空间变异性边坡可靠度分析的一阶可靠度方法（FORM）基础上,提出基于模型修正的空间变异边坡可靠度分析方法,引入一修正系数将基于LEM的简化极限状态面逐渐修正为基于FEM的准确极限状态面,最后基于修正系数和LEM安全系数计算公式采用线抽样法计算边坡失效概率。通过一个考虑参数空间变异性的摩擦/粘性土坡算例验证提出方法的有效性,并探讨土体参数空间变异性和黏聚力与内摩擦角之间互相关性对边坡可靠度的影响。结果表明:提出方法的边坡可靠度计算精度与基于FEM子集模拟方法一致,但是计算效率远远大于后者,尤其对于低概率水平边坡可靠度问题,从而为解决考虑土体参数空间变异性的低概率水平边坡可靠度问题提供一条新的途径。     

The failure processes analysis of rock slope using numerical modelling techniques

The slope failure process includes crack initiation, propagation and coalescence during the formation of a slip surface (small deformation stage) and block movement, rotation and fragmentation during the sliding process (large deformation stage). Neither the finite element method (FEM) nor the discontinuous deformation analysis method (DDA) can solve such problems satisfactorily due to the complex mechanical behaviour of slope failure. To study the entire process of slope failure, we develop here a model that combines the FEM and DDA approaches. The main concept of this approach is to first apply FEM to model crack growth behaviour and then automatically switch to the DDA module to model the post-failure process when the slip surface forms. The efficiency and simplicity of this approach lies in keeping the FEM and DDA algorithms separate and solving each equation individually. The heterogeneous nature of the slope material at the mesoscopic level is considered by assuming that the mechanical properties of individual elements follow a Weibull statistical distribution. The slope models are progressively destabilized by the critical gravity approach, and both the failure onset and the slope collapse process are analysed. Our modelling reveals that shear cracks first initiate at the toe of slope and subsequently promote the propagation of tensile fractures due to the stress accumulation at the shear crack tips. Throughout the entire failure process, failure in tension occurs at a higher rate than shear failure and plays a dominant role in the formation of the slip surface. The effects of slope angle and pre-formed cracks on the post-failure process are studied using the proposed method. This study demonstrates that the modelling approach outlined herein is able to tackle the fundamental problems of rock slope failure and offers a better understanding of the slope failure mechanisms at both the macroscopic and microscopic levels.     

渗流作用下边坡最危险圆弧滑面的优化解

分析地下水渗流对岩土边坡稳定性的影响,推导了透水边坡在地下水渗流条件下边坡稳定系数的解析表达式,采用非线性规划中的变尺度方法,求出最危险圆弧滑动面的位置。在高孔隙水压力条件下,采用简单条分法(W.Fellenius)和变尺度法首先确定最危险圆弧滑面的位置,然后,再利用严格解的Spencer方法或Morgenstern-Price方法,求最危险滑面的稳定系数。计算了某工程路堑边坡稳定系数和渗流对边坡稳定性的影响系数。     

基于粒子群算法的空间直线度误差评定

提出了一种满足最小区域法的空间直线度误差评价的新方法--粒子群算法。根据最小区域条件,建立了空间直线的数学模型以及优化目标函数。阐述了粒子群优化算法的原理和实现方法,然后根据粒子群算法优化求解。实例表明该方法对于空间直线度误差评定等非线性优化问题能得到最优解,可用于三坐标测量机等测量系统的空间直线度误差测量的数据处理。     

基于坡面卸荷的土质边坡应力状态及稳定性分析

边坡稳定性分析中极限平衡法难以考虑土体应力状态,坡体滑面应力计算又长期停留在数值方法上。为解决这一问题,提出坡面卸荷应力等效思路,将坡面按半无限边界考虑后利用弹性理论求解坡体应力,并根据滑面应力进行稳定性安全系数计算,最后结合多个算例将潜在滑动面位置、滑面应力分布、安全系数与已有理论进行比较。研究结果表明:坡面卸荷应力等效思路概念清晰,符合边坡受力特征,且通过该思路求得的滑面应力与有限元分计算结果基本一致,搜索得到的潜在滑动面位置,以及对应的稳定性安全系数与有限元强度折减法、极限平衡法计算结果十分接近。此外,该计算方法还能有效与支护结构预应力结合,体现预应力的加固作用。     

基于卡箍优化布局的飞机液压管路减振分析

飞机液压管路振动过大是一个亟待解决的问题,考虑了主动消振方式较为复杂,难以在飞机液压系统实现,提出了基于系统特征阻抗,通过优化卡箍布局的被动消振方式。首先建立系统管道及各元件数学模型,利用传递矩阵法（Transfer Matrix Method, TMM）得到其频域特征阻抗变化规律。以激振源固有频率点的特征阻抗加权和为目标函数,利用粒子群优化算法（Particle Swarm Optimization, PSO）在一定范围内调整卡箍位置,使在激振源频率点的特征阻抗加权和降到最低。通过优化卡箍位置,系统特征阻抗加权和较优化前衰减28.13%,验证了其有效性,为飞机液压管路的优化布局提供了一定的理论依据。     

A limit equilibrium method for analyzing progressive failure in slopes

Abstract

A limit equilibrium method is proposed for analyzing progressive failure in the stability of brittle soil slopes. In the proposed method, the failure surface is firstly assumed and the whole failure mass is divided into many vertical slices. By satisfying force and moment equilibrium for each slice as well as for the total mass, the overall factor of safety for the assumed slip surface can be calculated. This factor of safety is then used to check the state of stress along the bottom of each slice. If the state of stress exceeds the soil strength, then local failure occurs and the residual strength is assigned. The whole procedure will be repeated unless the propagation of local failure zone stops. Finally, a more reasonable definition for factor of safety is determined. This analysis is illustrated for well documented case records, and the results are quite consistent with the field observations.     

An approach for the reliability based design optimization of laminated composites

This article aims at optimizing laminated composite plates taking into account uncertainties in the structural dimensions. As laminated composites require a global optimization tool, the Particle Swarm Optimization (PSO) method is employed. A new Reliability Based Design Optimization (RBDO) methodology based on safety factors is presented and coupled with PSO. Such safety factors are derived from the Karush–Kuhn–Tucker optimality conditions of the reliability index approach and eliminate the need for reliability analysis in RBDO. The plate weight minimization is the objective function of the optimization process. The results show that the coupling of the evolutionary algorithm with the safety-factor method proposed in this article successfully performs the RBDO of laminated composite structures.