考虑参数空间变异性的边坡可靠度分析非侵入式 随机有限元法

提出了考虑土体参数空间变异性的边坡可靠度分析的非侵入式随机有限元法。采用Karhunen-Loeve级数展开方法表征土体抗剪强度参数空间变异性,其中通过wavelet-Galerkin技术求解Fredholm积分方程得到相关函数的特征解。基于有限元滑面应力法计算边坡安全系数,采用随机多项式展开将隐式函数表达的安全系数替换为显式函数表达的安全系数,并编写了计算程序NISFEM。研究了所提方法在考虑土体参数空间变异性的边坡稳定可靠度分析中的应用。结果表明：提出的非侵入式随机有限元法极大地提高了考虑土体参数空间变异性的边坡可靠度分析的计算效率,为解决复杂边坡稳定可靠度问题提供了一条有效的途径。考虑抗剪强度参数空间变异性的边坡可靠度分析存在临界变异系数,其随边坡安全系数的增加而增大。当抗剪强度参数的变异系数小于临界变异系数时,忽略土体参数空间变异性将会高估边坡失效概率。当边坡安全系数小于1时,边坡失效概率并不总是随着抗剪强度变异系数的增加而增大。此外,土体黏聚力和内摩擦角随机场间相关性对边坡失效概率具有十分明显的影响。     

考虑地层变异性和土体参数变异性的边坡可靠度分析

现有边坡可靠度分析大多数只考虑土体参数的固有变异性,而忽略了地层变异性的影响。为此,提出了同时考虑地层变异性和土体参数固有变异性的边坡可靠度分析方法,利用耦合马尔可夫链模拟地层分布,采用基于乔列斯基分解的中点法离散土体参数随机场,采用有限元强度折减法计算边坡安全系数,通过蒙特卡洛法模拟进行边坡可靠度分析。利用澳大利亚珀斯市钻孔资料,以边坡可靠度问题为例阐明了同时考虑地层变异性和土体参数固有变异性的重要性,研究了钻孔布置方案对边坡可靠度的影响规律,结果表明:提出的方法能够有效地反映地层变异性和土体参数固有变异性对边坡可靠度的影响。当钻孔数目较少时,模拟的边坡土体类型分布与真实边坡土体类型分布相差较大,此时忽略地层变异性将导致边坡可靠度不精确的估计结果。钻孔布置方案对边坡失效概率和安全系数有明显的影响,钻孔应尽可能多的布置在边坡关键影响区域。边坡失效概率和安全系数统计量与钻孔数目并不呈单调关系,但是随着钻孔数目的增加,边坡失效概率和安全系数统计量逐渐收敛至"精确解"。     

考虑地质成因的土坡可靠度分析

 不同地质成因的边坡在土体参数统计变异性相同的情况下,由于空间变异性不同,其稳定状态并不一定相同,传统的边坡稳定性确定性分析和基于随机变量模型的边坡可靠度分析方法无法考虑坡体的特定地质成因。由地质成因估计土体参数的波动范围,从而通过土体参数波动范围这一指标把地质成因纳入边坡稳定性分析框架,提出考虑地质成因的边坡可靠度分析方法,介绍具体的分析流程,采用一维随机场模拟和验算点法完成边坡可靠度分析。算例计算结果显示岩土参数空间变异性对边坡稳定性的影响很大,由地质成因估计土体参数的波动范围,为在边坡可靠度分析中合理考虑土体参数空间变异性提供一条现实的解决途径,值得在工程应用中推广。     

各向异性随机场下的边坡模糊随机可靠度分析

土性参数具有很大的空间变异性,且在水平方向和垂直方向上差异显著。基于随机变量模型的传统边坡模糊随机可靠度分析方法并未对此进行考虑。提出一种能合理考虑土性参数空间变异性的边坡模糊随机可靠度分析方法。首先,视黏聚力和内摩擦角的均值为正态模糊数,对其取不同的λ截集水平并在各截集水平上进行参数组合。其次,利用各向异性随机场模拟土性参数的空间变异性,将有限元法和Monte–Carlo模拟相结合,计算各参数组合对应的可靠度指标。再通过数学方法得到边坡在各截集水平上的可靠度指标。最后,运用加权平均法计算边坡的模糊随机可靠度指标。算例分析表明:与水平方向的空间变异性相比,垂直方向的空间变异性对边坡模糊随机可靠度的影响更为显著;不考虑土性参数的空间变异性在一般情况下会低估边坡的模糊随机可靠度指标,但在抗剪强度参数变异性较大时,反而可能会高估边坡的模糊随机可靠度指标;此外,黏聚力与内摩擦角之间的相关性对边坡失效概率的影响趋势基本不受土性参数空间变异性的干扰。     

结构面力学参数空间变异性表征及边坡可靠性分析

复杂的岩体结构使得岩体参数空间变异性表征与土体参数具有显著的差别。目前针对高度碎裂化/强风化和单结构面占优岩体的参数空间变异性表征及边坡可靠性研究较多,然而关于楔形体和反倾岩体的参数空间变异性表征及边坡可靠性研究非常有限。提出针对楔形体和反倾岩体的边坡结构面力学参数空间变异性表征及可靠性分析方法,并系统统计不同类型岩体力学参数的相关距离和波动范围的取值范围,编写参数空间变异性表征及边坡概率稳定性分析与FLAC3D软件的接口程序,基于反向传播(BP)神经网络构建边坡安全系数与结构面参数随机场向量之间的映射函数关系式,进而采用非侵入式随机有限差分法调查结构面力学参数空间变异性对边坡失效概率的影响规律。结果表明：不同岩体力学参数的相关距离和波动范围的取值范围存在一定的差别,指数型自相关函数是应用最为广泛的理论自相关函数。通过方向模拟和直接蒙特卡洛模拟方法验证提出方法的有效性,表明提出方法具有较高的计算精度和效率,可为楔形体或反倾岩体结构面力学参数空间变异性表征及边坡可靠性分析提供一种有效的途径。此外,忽略结构面参数的空间变异性会高估边坡失效概率,进而导致保守的边坡加固设计方案。     

基坑单支撑支护结构抗倾覆可靠度分析

采用结构可靠度方法分析基坑单支撑支护结构抗倾覆稳定性，充分考虑了参数的变异性。可靠度计算采用JC法和优化算法，分析表明两种方法计算结果相当接近，而优化算法更为简捷，便于应用。算例分析表明：当参数变异性较大时，采用安全系数评价抗倾覆稳定性不一定安全，采用可靠度指标评价则更合理；土体强度指标和支护桩嵌固深度的变异性对抗倾覆可靠度指标影响显著，支撑位置、土体重度和地面荷载的变异性影响很小，设计时可视为确定性变量：黏聚力、内摩擦角和嵌固深度的变异性对可靠度指标的影响依次增大，当嵌固深度变异性很大时可忽略黏聚力、内摩擦角的影响，而当内摩擦角变异性很大时，可忽略黏聚力的影响。     

土质边坡可靠性分析的分层非平稳随机场模型

在边坡稳定可靠度分析中使用较为广泛的土性参数平稳随机场模型,通常假设土性参数具有定值涨落尺度或相关长度。对于土壤类别差异较大、分层显著的边坡,尤其是存在局部软弱层的边坡,该模型无法有效模拟不同土层尤其是软弱层的影响。为此,针对由不同类别土壤构成的具有显著分层特性的土性边坡,建立了沿深度方向具有多涨落尺度的土性参数非平稳随机场模型。采用连续回归分析各层土性参数的均值变化函数与方差结构,利用指数相关函数构建非平稳随机场的协方差矩阵,建立了具有多涨落尺度的土性参数非平稳随机场模型,应用塑性极限分析方法,对一个实际工程边坡进行了稳定可靠性分析,研究了黏聚力、内摩擦角等强度参数的非平稳性对临界滑移面形状、位置以及边坡稳定可靠度的影响。分析结果表明,所建具有分层非平稳随机场模型,适于土性参数沿土体埋深呈明显分层特征的土质边坡,能有效反映局部软弱层对边坡稳定可靠性的影响,而平稳随机场模型或均值连续变化的非平稳随机场模型则适于由同一类型土壤构成的边坡。     

花岗岩残积土边坡稳定性可靠度分析

运用工程上广泛采用的简化Bishop法建立极限状态方程，考虑容重、粘聚力和内摩擦角为随机变量，利用简洁实用的优化方法求解边坡的可靠度指标，并利用Excel中的规划求解工具进行求解，避免了正交变换和极限状态方程求偏导数的问题。针对福建省花岗岩砂质粘性土边坡进行可靠度分析，比较土性参数不相关与相关情况下的研究结果，说明边坡可靠度不仅与土体参数均值有关，而且与其变异系数和相关性有关，且变量的相关性对可靠度有较大影响。因此，边坡用传统安全系数法分析是稳定时，也存在失稳的可能。     

土体参数对边坡稳定性的影响分析

文中依托江西某高速公路项目实际边坡工程，根据现场原位测试、室内土工试验等方法获取的土体参数，构建边坡稳定性FLAC3D模型，结合强度折减法，计算分析不同土体参数的边坡安全系数。研究结果表明，边坡稳定性正交极差分析得到影响因素的敏感性大小排序为：内摩擦角>黏聚力>重度；黏聚力和内摩擦角对边坡破坏模式影响不大，但对边坡安全系数影响较大；线性平面可以较好地拟合黏聚力、内摩擦角和安全系数三者的相互关系，拟合优度R2高达99.84%。     

考虑地层变异性和土体参数空间变异性的边坡可靠度全概率设计方法

目前边坡稳定设计研究中大多数考虑了土体参数的空间变异性,但忽略了地层变异性的影响。为此,提出了一种同时考虑这两类变异性的边坡可靠度全概率设计方法。在全概率设计框架内,将广义耦合马尔可夫链模型与随机场模型相耦合用于同时表征地层变异性和土体参数空间变异性,给出了所提方法的计算流程。利用澳大利亚珀斯市钻孔资料,以某边坡为例进行可靠度设计,为说明在边坡可靠度设计中同时考虑地层变异性和土体参数空间变异性的重要性,分析了仅考虑土体参数空间变异的情况,进一步分析了同时考虑两类变异性的情况,并对二者进行了比较。结果表明:所提出的边坡可靠度设计方法能够有效地考虑边坡中存在的地层变异性和土体参数空间变异性。当仅考虑土体参数空间变异性时,边坡可靠度设计结果很大程度上取决于所采用地层的分布情况,特别是地层分布中抗剪强度较强土体类型占比高于真实情况时,将导致得到的最优设计方案偏于危险。反之,若地层分布中抗剪强度较弱的土体类型占比高于真实情况,得到的最优设计方案偏于保守。因此,为准确地得到最优设计方案,在边坡可靠度设计中应同时考虑地层变异性和土体参数空间变异性的影响。     

基于随机场的岩石边坡三维稳定性分析

基于随机场理论,考虑了岩石材料属性的空间变异性对岩石边坡稳定性的影响,将边坡主滑面上的摩擦系数和粘聚力视为高斯随机变量,确定了主滑面上的摩擦系数和粘聚力的均值、方差和协方差,获得了两个随机量之间的相关系数和互相关长度。在此基础上,对岩石边坡进行了三维稳定性分析,确定了岩石边坡的稳定系数和失效概率。数值计算结果表明,摩擦系数和粘聚力的空间变异性对边坡稳定性有重要影响。     

Uncertainties of thermal boundaries and soil properties on permafrost table of frozen ground in Qinghai-Tibet Plateau

In the permafrost regions of the Qinghai-Tibet Plateau(QTP),the permafrost table has a significant effect on the stability of geotechnical engineering.The thermal boundaries and soil properties are the key factors affecting the permafrost table.Complex geological environments and human activities can lead to the uncertainties of thermal boundaries and soil properties.In this paper,an array of field experiments and Monte Carlo(MC) simulations of thermal boundaries and soil properties are carried out.The coefficient of variation(COV),scale of fluctuation(SOF),and autocorrelation distance(ACD) of uncertainties of thermal boundaries and soil properties are investigated.A stochastic analysis method of the probabilistic permafrost table is then proposed,and the statistical properties of permafrost table on the QTP are computed by self-compiled program.The proposed stochastic analysis method is verified with the calculated and measured temperature observations.According to the relationship between ACD and SOF for the five theoretical autocorrelation functions(ACFs),the effects of ACF,COV,and ACD of soil properties and the COV of thermal boundaries on the permafrost tables are analyzed.The results show that the effects of different ACFs of soil properties on the standard deviation(SD) of permafrost table depth are not obvious.The SD of permafrost table depth increases with time,and the larger the COVs of thermal boundaries and soil properties,the deeper the SD of permafrost table;the longer the ACD of soil properties,the shallower the SD of permafrost table.This study can provide a reference for the stability analysis of geotechnical engineering on the QTP considering the uncertainties of thermal boundaries and soil properties.     

Reliability approach to slope stability analysis with spatially correlated soilproperties

A reliability approach to a slope stability analysis, considering spatially correlated soil properties, is used to systematically evaluate the various sources of uncertainty that arise in these types of problems. Measurement errors and bias that often occur during soil investigations are now incorporated into the probabilistic model of soil properties in addition to the spatial variability and the effects of spatial averaging. The results of the analysis show that the unconditional approach, which considers spatial variability, but does not account for measurement-related uncertainties, can yield unconservative results because of an unrealistically large variance reduction. In contrast, the results obtained from the unconditional approach, which does consider spatial variability and measurement-related uncertainties, as well as those from the conditional approach, lead to significantly lower probabilities of failure that are much less sensitive to the scales of fluctuation.     

Modeling of non-stationary random field of undrained shear strength of soil for slope reliability analysis

The spatial variability of soil properties is often assumed to be modeled as stationary or weakly stationary random fields in slope reliability analyses. However, abundant site-specific data have revealed that the mean and standard deviation of soil properties, such as the undrained shear strength of soil, change with depth. Thus, the non-stationary characteristics of soil properties need to be properly accounted for. The aim of this paper is to propose a non-stationary random field (RF) model for the characterization of the spatial variability and the depth-dependent nature of the undrained shear strength of soil. With the proposed model, the uncertainties of the trend and fluctuating components can be modeled individually. As an example, a clay slope under undrained conditions is investigated to illustrate the proposed model. A subset simulation is carried out to evaluate the slope reliability incorporating the non-stationary characteristics of soil properties. The advantages of the proposed model, relative to the existing non-stationary RF models and the commonly-used stationary RF model in the literature, are demonstrated through a series of sensitivity studies.     

Reliability-based analysis of embankment on soft Bangkok clay

Six slope failures occurred at random locations along a 10 km embankment adjacent to an irrigation canal. The slope failures occurred when the embankment was raised to 2.05 m above MSL from an average elevation of 1.7 m above MSL coinciding with the lowering of the canal water level at the end of the dry season. Slope stability analysis was carried out using both conventional and reliability-based procedures. The spatial variability of undrained strength, the actual variation in embankment geometry, and the varying water level in the canal were considered in the analysis. Both idealized and empirical autocorrelation functions (ACF) of the undrained shear strengths were used in the analyses. An analysis using a factor of safety based on the deterministic soil profile defined by the mean undrained strength resulted in a prediction favoring a reverse failure pattern along the embankment. Using the probability of failure which incorporates spatial variation of undrained strength and uncertainties associated with stability prediction yielded a result conforming to the actual failure pattern along the embankment. The use of empirical autocorrelation function (ACF) seems to confirm and explain better the occurrence of the failure zones than utilizing the idealized ACF.     

Effect of spatial variability on stability and failure mechanisms of 3D slope using random limit equilibrium method

It is well known that soils are prone to spatial non-uniformity, which affects evaluations of slope stability and failure mechanisms. This paper presents a probabilistic slope stability evaluation, considering the 3D spatial variation in the soil properties, by the random limit equilibrium method (RLEM). Specifically, 3D random fields of cohesion c, friction angle ?, and soil unit weight γ are generated using a fast Fourier transform. The RLEM is applied to evaluate the effects of the 3D spatial variability of the soil properties on slope stability and failure mechanisms. A Monte Carlo simulation is used to interpret the slope reliability and variation in slope failure dimension. Based on the critical slip surface passing different portions of a slope (slope base, inclined face, and crest), four main failure mechanisms (two base failures and two face failures), and one additional failure mechanism (toe failure), are identified for spatially variable slopes, and the corresponding distributions of the stability number (N_s) and sliding volume (V) are investigated in detail. The results show that the large variation in the soil properties induces changes in the failure mechanisms, and a threshold of c-? values is found for a shift from base failure to toe failure. Lastly, associated sensitivity studies are performed to explore the effects of the uncertainties of the input parameters on the uncertainty of the output. The results estimated by partial Spearman correlation coefficients show that cohesion has the greatest influence on the stability number, and that a positive influence of the unit weight, contributing to slope stability, is found for a base failure mechanism.     

土工离心模型的空间变异性研究

土工离心模型的试验结果主要由模型箱内空间平均的土性指标影响。基于随机场的原理,研究了土工离心模型中土性指标的空间变异性。根据实测土密度和孔隙率数据,采用相关函数法计算相关距离,并讨论了模型与原型的空间变异性的相似关系。结果表明,离心模型中土性指标的点变异系数相比原位测试值偏小,相关距离则远小于原位土的相关距离。即使点变异系数和相关距离一致,不同比尺的模型对应原型的空间均值变异系数也不相等。给出了空间均值变异系数云图,可用来调整离心模型以满足原型空间均值变异系数的要求。