【作者】 刘辉；

【导师】 郑俊杰；

【作者基本信息】 华中科技大学 ， 岩土工程， 2022， 博士

【摘要】 土体参数的空间变异性是影响边坡稳定的重要不确定性因素之一,为了描述该不确定性,往往采用随机场模型将土体参数离散为大量的随机变量。面对随机变量维度过高的边坡系统可靠度分析问题,既有研究大都采用计算成本较高的蒙特卡洛模拟方法进行分析,而计算简便、高效的传统可靠度分析方法的应用有限。另一方面,土体参数的空间变异性对边坡失效模式也有影响,识别代表性失效模式的效率决定了边坡系统可靠度分析的效率。目前考虑土体参数空间变异性的边坡失效模式分布规律尚不明确,缺乏高效的代表性失效模式识别方法。为此,本文围绕土体参数空间变异性下的边坡代表性失效模式识别、系统可靠度分析及风险评估等问题,以极限平衡分析为手段,采用二次可靠度方法研究边坡系统可靠度分析和代表性滑动面(Representative Slip Surface,RSS)高效识别方法。主要研究内容和成果如下。(1)采用K-L级数分解法离散土体参数随机场,并结合遗传算法搜索最危险滑动面,分别基于圆弧滑动面假设和非圆弧滑动面假设拓展了边坡系统可靠度分析的随机极限平衡方法。通过对4个典型边坡算例进行分析,讨论了两种滑动面假设对边坡系统可靠度的影响,并得到了边坡最危险滑动面的位置分布影响规律。(2)通过在滑动面上对土体参数随机场进行局部平均并引入局部平均等效参数,推导了不同失效模式极限状态方程之间的相关系数计算公式,并建立了多失效模式串联的边坡二次可靠度分析方法。研究表明若忽略局部平均等效参数的分布拟合带来的误差,对不排水边坡,在整条滑动面上局部平均后的等效参数即可表征其整体的空间变异性;而对排水边坡,则需要先将滑动面划分为若干段,再分段进行局部平均以保证随机场在滑动面上的离散精度。(3)建立了基于最优化模型的RSS识别方法,并基于得到的RSS组合对边坡的系统失效概率和失效风险进行了评估。在“RSS组合为对系统失效概率贡献最大的潜在滑动面组合”这一观点下,综合考虑潜在滑动面的可靠度指标及其它们之间的相关系数对系统失效概率的共同作用,将边坡的RSS识别问题转化为最优化问题,并将各RSS对系统失效概率的贡献程度作为其失效后果的权重,评估了边坡的失效风险。研究表明该方法能有效进行边坡系统可靠度分析与风险评估,随着识别得到的RSS数量增加,根据RSS评估得到的系统失效概率增大,且其按双曲线收敛模式逐渐收敛到边坡的系统失效概率真实值,该收敛速度随着随机场相关距离增大而增大。(4)提出了基于改进Hassan&Wolff模型的边坡RSS高效搜索方法,并通过将各RSS按其对系统失效概率的贡献重新排序得到了系统失效概率随RSS数量的变化曲线,进一步将曲线按双曲线收敛模式拟合,评估了边坡的系统失效概率和失效风险。应用该方法,以某填方路堤边坡为例进行可靠度设计优化。研究表明,改进Hassan&Wolff模型采用经验方法考虑边坡失效模式影响因素的参数平均效应和随机场波动效应,通过少量蒙特卡洛模拟进行确定性分析以识别RSS,其效率显著提升,能满足工程应用需求。更多还原

【Abstract】 The spatial variability of soil parameters is of great significant to the stability of a slope.To characterize the spatial variability,the random filed is commonly used and discretized into a large number of random variables,which leads a “curse of dimensionality” to the system reliability analysis of slopes.Most of the existing researches analyze the system reliability of spatially variable soil slopes using the Monte Carlo simulation,and the traditional reliability analysis methods seem limited due to the “curse of dimensionality”,though they are efficient and simple in computation.Besides,the failure mode of the slope is commonly influenced by the spatial variability of soil parameters.At present,the distribution law of the failure mode considering the spatial variability of soil parameters is not clear,and there is a lack of efficient representative slip surface identification method.The researches in this dissertation focus on the topics of the system reliability analysis,the identification of the important failure modes and the risk assessment of slopes with spatially varied soils.The limit equilibrium method and the second-order reliability method are used to study the reliability analysis of slopes and the efficient identification of representative slip surface(RSS).The main research contents and results are listed below.(1)The random limit equilibrium method(RLEM)for system reliability analysis and risk assessment of slope is proposed based on the circular slip surface assumption and the non-circular slip surface assumption.In this method,the K-L expansion method is adopted to simulate the random field of soil properties,and the Genetic algorithm is used to search the critical slip surface.The influence of different slip surface assumptions on the system reliability is discussed with 4 typical slope cases,and it is also found that the location of the critical slip surface is influenced by both the average effect of soil parameters and the fluctuation effect of the random fields.(2)Aiming at applying the second-order reliability method(SORM)to the reliability analysis of the individual failure mode,the random field is local averaged along the slip surface and the local averaging variables are used to reduce the number of random variables.The equations to calculate the correlation coefficient of different failure modes are derived based on the local averaging variables,and the reliability analysis for slope system with multiple failure modes is conducted based on the reliability analysis and the correlation analysis.The results show that for the undrained slope,the local averaging along the whole slip surface can characterize the spatial variability of soil parameters along the slip surface if the error caused by distribution fitting of the local averaging variables is ignored.However,for the drained slope,the slip surface should be divided into several segments to ensure the accuracy of the random field simulation by local average method.(3)A multimodal optimization method for RSS identification and risk assessment is proposed.In this method,by considering the influence of the synergy between the reliabilities and the correlation coefficients between different slip surfaces on the system failure probability,the task of RSS identification is transformed as a multimodal optimization problem,and the potential slip surfaces that make great contributions to the system failure probability are determined as RSSs.The contributions of each RSS to the system failure probability are taken as the weights of the corresponding failure consequences,and the failure risk is evaluated by summarizing all the weighted failure consequences.The results show that the proposed method is valid to evaluate the system reliability and risk of the slope.When the number of RSSs increases,the evaluated failure probability converges to the overall failure probability of the slope,and the converge speed increases with the correlation length of the random field.(4)An efficient method for RSS identification based on the modified Hassan & Wolff model is proposed.By reordering the RSSs according to their contributions to the failure probability of the slope system,the convergence curve of the evaluated failure probability with the number of RSSs is obtained,and the system reliability analysis and risk assessment are conducted by the RSSs and the convergence curve.The method is used to conduct the reliability-based design optimization of an embankment slope.The results show that the modified Hassan & Wolff model is efficient to identify the RSS by considering the average effect of the soil parameters and the fluctuation effect of the random fields on the location of critical slip surface,and it can meet the efficiency requirement for engineering application.更多还原