二维空间随机场的浅基础极限承载力可靠度分析

目前浅基础极限承载力可靠度分析普遍采用简化方法,虽然进行了多次计算,但每次计算时都是采用定值参数,不能考虑土体空间的变异性.本文利用随机场理论对一刚性浅基础进行可靠度分析,采用二维随机场与Monte-carlo方法结合,将土体的粘聚力作为一个空间二维随机场,对比随机场和定值分析的结果,分析了土体粘聚力空间变异性对浅基础极限承载力及其可靠度的影响.     

土性参数不确定性描述方法的探讨

通过分析土体自然历史形成条件,从土性参数变异性表现特征着手,对其进行归类分析,初步回答了土性指标变异性的含义;对比分析了土层剖面的两种建模方法,据此提出了基于随机场理论的变异性统计方法,并通过实际工程勘探数据的统计分析,诠释了该方法的优越性所在。结果表明:土性指标变异性并非土体分层后层与层之间土性指标的差异,而是层内土性点与点之间的空间变异;相对于传统随机变量的建模方法,这种空间变异性用随机场理论建模更加科学合理;随机场理论用空间趋势函数和随机波动分量分别表征土性指标的确定性部分和随机扰动部分,通过去趋势化处理,可把握土性参数不确定性的核心;实例分析显示,本文提出的方法可更加精确地了解土性参数的不确定性,为可靠性理念在实际工程中的应用提供有利的途径。     

考虑空间变异性的盾构隧道地层力学响应敏感性分析

针对土体变形参数(弹性模量E、泊松比μ)、强度参数(黏聚力c、内摩擦角φ)对盾构隧道施工地层力学响应的敏感性问题,以土体参数的空间变异性为切入点,结合随机场理论、有限差分法和MonteCarlo策略,采用考虑参数空间变异性的敏感性综合评价分析方法,开展地层力学响应的参数敏感性随机分析。研究结果表明:地层力学响应对内摩擦角的空间变异性最为敏感,其次是弹性模量,然后是黏聚力,最不敏感的是泊松比;不同变异水平条件下,各参数变异性的敏感程度存在差异,参数变异水平越高,其敏感性越强;3种参数变异水平下,泊松比均为不敏感因素,随机分析中可不考虑其空间变异性对地层力学响应的影响,黏聚力在变异性较小时也为不敏感因素。     

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。     

参数空间变异性对基坑周围土体变形影响分析

通过理论分析与数值模拟相结合的方法,主要对因土体参数的空间变异性及随机性对基坑周围土体的变形影响进行了分析,研究表明基坑周围土体的变形主要受到粘聚力单因素变化、粘聚力和内摩擦角双因素共同变化时的空间变异性与随机性影响,而内摩擦角单因素变化对其的影响较小;由于参数的空间变异性与随机性所影响的区域不同,基坑周围土体的变形也不相同,由此也可以反映出土体固有的结构性;因土体参数空间变异性与随机性,基坑周围土体上部多受影响,建议在工程施工过程中相对不考虑其变化特性的设计,应该增强上部的支护强度,以确保工程安全以及减少周围土体的地表沉降,研究成果对工程施工设计有一定的指导意义.     

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。     

考虑土体空间变异性的边坡最危险滑动面随机分析方法

现有边坡可靠度研究均未考虑土体空间变异性对边坡最危险滑面的影响。为此，提出了考虑土体空间变异性的边坡最危险滑动面随机分析方法。首先，采用谱表现法建立了表征土体空间变异性的随机场模型。在此基础上，提出了基于SIGMA/W和SLOPE/W的自动定位搜索最危险滑动面方法。其次，采用非侵入式随机分析方法研究了抗剪强度参数空间变异性对边坡最危险滑动面空间分布的影响。最后，采用算例验证了所提方法的有效性。结果表明：提出的边坡最危险滑动面随机分析方法能够有效地确定边坡最危险滑动面空间分布特征。土体抗剪强度参数的空间变异性对边坡最危险滑动面的空间分布特征有重要的影响，它直接决定了边坡最危险滑动面的位置和滑体规模。土体抗剪强度参数波动范围越大，最危险滑动面的空间分布范围越大。随着土体抗剪强度参数水平向和竖直向波动范围比值的增大，边坡上部发生局部滑动的可能性增大。抗剪强度参数的变异系数越大，最危险滑动面的空间分布范围越大，边坡发生小规模局部滑动的可能性越大。     

传统挡土墙设计的可靠性分析

长期以来，挡土墙的设计一直依据朗肯或库仑土压力理论。为得到闭合解，这些传统土压力理论均似定均质土体，实际上，土体性质是空间变化的，这样设计中就隐含两个问题：(1)取样获得的土体性质能否完全反映墙后所有填土的性质；(2)土体性质的空间差异是否会导致主动土压力与传统方法预测的结果有很大差别。本文把非线性有限元和随机场模拟结合起来，研究了这两个问题，并对目前设计方法的安全性进行了评价。本文对一个二维、墙壁光滑的挡土墙进行了实例研究，墙后是排水的无粘性填土，该挡墙用朗肯土压力理论进行滑移计算。设计所用的摩擦角和土体重度在模拟的随机场中某一位置取样获得，并被当作有效土体参数用于朗肯模型中。当修正后作用在挡土墙上的朗肯土压力小于实际土体参数的随机有限元计算结果时，挡土墙破坏。本文借助蒙特卡罗模拟方法，将传统设计方法的破坏概率用一个包含安全系数和土体空间变异性的函数评估。     

基于随机场理论的地基稳定性模糊可靠度分析

根据Vanmarcke提出的随机场理论描述土性参数的空间变异性,建立了考虑土性参数空间变异性的地基失稳模糊概率公式,并通过实例分析了两种情况下地基的模糊失效概率值,得出用随机场理论空间均值方差计算的模糊失效概率值比不考虑土性参数的空间变异性计算模糊失效概率值偏低的结论.     

参数空间变异性对基坑周围土体变形影响分析

通过理论分析与数值模拟相结合的方法，主要对因土体参数的空间变异性及随机性对基坑周围土体的变形影响进行了分析，研究表明基坑周围土体的变形主要受到粘聚力单因素变化、粘聚力和内摩擦角双因素共同变化时的空间变异性与随机性影响，而内摩擦角单因素变化对其的影响较小；由于参数的空间变异性与随机性所影响的区域不同，基坑周围土体的变形也不相同，由此也可以反映出土体固有的结构性；因土体参数空间变异性与随机性，基坑周围土体上部多受影响，建议在工程施工过程中相对不考虑其变化特性的设计，应该增强上部的支护强度，以确保工程安全以及减少周围土体的地表沉降，研究成果对工程施工设计有一定的指导意义。     

Soil spatial variability impact on the behavior of a reinforced earth wall

This article presents the soil spatial variability effect on the performance of a reinforced earth wall. The serviceability limit state is considered in the analysis. Both cases of isotropic and anisotropic non-normal random fields are implemented for the soil properties. The Karhunen-Loève expansion method is used for the discretization of the random field. Numerical finite difference models are considered as deterministic models. The Monte Carlo simulation technique is used to obtain the deformation response variability of the reinforced soil retaining wall. The influences of the spatial variability response of the geotechnical system in terms of horizontal facing displacement is presented and discussed. The results obtained show that the spatial variability has an important influence on the facing horizontal displacement as well as on the failure probability.     

基于随机场理论的江苏海相黏土空间变异性评价研究

土体空间变异性分析是进行岩土工程可靠度设计的理论基础。采用随机场理论,提出了典型江苏海相黏土的随机场特征及参数,对基于孔压静力触探(CPTU)测试数据的空间变异性进行了系统分析。由于竖直方向上CPTU锥尖阻力数据的样本容量较高,通过对锥尖阻力进行一次多项式去趋势来获得平稳的波动分量,并利用常用的5种自相关模型拟合波动分量的自相关系数。采用修正的Bartlett统计公式来检验波动分量的平稳性,选取最优的竖直波动范围。竖直变异系数由波动分量和去趋势函数来确定。鉴于水平方向上的CPTU锥尖阻力数据的样本容量较小,采用平均零跨距法估计水平波动范围,水平变异系数由总体变异系数来表示。结果表明,竖直向和水平向上江苏海相黏土较报道值显示出更强的空间变异性。     

Expanded reliability-based design of piles in spatially variable soil using efficient Monte Carlo simulations

Inherent spatial variability is considered as a major source of uncertainties in soil properties, and it affects significantly the performance of geotechnical structures. However, research that considers, directly and explicitly, the inherent spatial variability in reliability-based design (RBD) of geotechnical structures is limited. This paper develops a RBD approach that integrates a Monte Carlo Simulation (MCS)-based RBD approach, namely the expanded RBD approach, with random field theory to model, both directly and explicitly, the inherent spatial variability of soil properties in RBD of drilled shafts. The proposed approach is implemented in a commonly-available spreadsheet environment to effectively remove the hurdle of reliability computational algorithms and to provide a user-friendly graphical user interface to practicing engineers. To improve the efficiency and resolution of MCS at small probability levels, the expanded RBD approach is enhanced with an advanced MCS method called “Subset Simulation”. Equations are derived for the integration of the expanded RBD approach and Subset Simulation. The proposed approach is illustrated through a drilled shaft design example, and is applied to explore the effects of inherent spatial variability (including the scale of fluctuation and correlation structure) and to evaluate systematically the equivalent variance technique that is commonly used to indirectly model inherent spatial variability in current RBD approaches. It is found that inherent spatial variability significantly affects the RBD of drilled shafts, and its effects are considered in RBD using the proposed approach in a direct and explicit manner. In addition, the results show that the indirect modeling of inherent spatial variability using the equivalent variance technique with the simplified form of variance reduction function in RBD might lead to relatively conservative designs in design practice.     

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。     

Probabilistic analysis of consolidation that considers spatial variability using the stochastic response surface method

To obtain more accurate and reasonable results in the analyses of soil consolidation, the spatial variability of the soil properties should be considered. In this study, we analyzed the consolidation by vertical drains for soil improvement considering the spatial variability of the coefficients of consolidation. The coefficients for the variation in the vertical and horizontal coefficients of consolidation in Yeonjongdo, South Korea were evaluated, and the probability density function (PDF) was assumed by the Anderson–Darling goodness-of-fit test. Standard Gaussian random fields were generated based on a Karhunen–Loeve expansion, and then transformed using Hermite polynomials in the random field with the log-Gaussian PDF of the coefficient of consolidation. The average degree of consolidation was subsequently calculated using the finite difference method coupled with log-Gaussian random fields. In addition, the stochastic response surface method (SRSM) was applied for the efficient probabilistic uncertainty propagation. A sensitivity analysis was performed for the input parameters of the random field, and the spatial variability was considered using random variables from the Karhunen–Loeve expansion as the input data for the SRSM. The results indicated that when considering the spatial variability of soil properties, the probability of failure for the target degree of consolidation was smaller when the correlation distance was taken into account than when it was not. Additionally, the probability of failure decreased when the correlation distance decreased. Compared with the Monte Carlo simulation (MCS) results, the SRSM analysis can achieve results of similar accuracy to those obtained using the MCS analysis with a sample size of 100,000 (numerical runs), and a third-order SRSM expansion with only 333 numerical runs is sufficient for obtaining the probability with errors less than 0.01.     

An efficient stochastic dynamic analysis of soil media using radial basis function artificial neural network

Since a lot of engineering problems are along with uncertain parameters, stochastic methods are of great importance for incorporating random nature of a system property or random nature of a system input. In this study, the stochastic dynamic analysis of soil mass is performed by finite element method in the frequency domain. Two methods are used for stochastic analysis of soil media which are spectral decomposition and Monte Carlo methods. Shear modulus of soil is considered as a random field and the seismic excitation is also imposed as a random process. In this research, artificial neural network is proposed and added to Monte Carlo method for sake of reducing computational effort of the random analysis. Then, the effects of the proposed artificial neural network are illustrated on decreasing computational time of Monte Carlo simulations in comparison with standard Monte Carlo and spectral decomposition methods. Numerical verifications are provided to indicate capabilities, accuracy and efficiency of the proposed strategy compared to the other techniques.     

基于高斯过程回归的响应面法及边坡可靠度分析

提出了一种新型高斯过程响应面法(GPRSM),通过高斯过程回归算法构建随机变量与功能函数响应值之间的关系。该方法相较多项式响应面法对于功能函数为高维和高度非线性的可靠度问题,具有更高的精度和计算效率。此方法可以通过新增加训练点以动态更新响应面函数。与此同时,为了模拟岩土参数的空间变异性,通过KL展开构建随机场,并与极限平衡法结合进行边坡稳定性分析。使用提出的GPRSM构建替代模型并用于蒙特卡洛模拟求解边坡失稳概率,在保障计算精度的同时减少了对边坡稳定性分析程序的调用。最后将所提出的方法分别应用于功能函数为显式和隐式两个案例,并与其他论文中的方法对比,证明了该方法的有效性和适用性。     

多层地基土坡的随机有限元模型不同参数比较分析

对James Bay堤坝进行了基于随机有限元方法的蒙特卡罗模拟。该法可以给出边坡可靠度（或破坏概率）而不是更加传统的安全系数作为边坡安全评估的度量准则。不同土层的不同的土性参数由随机场产生并且投影到有限元网格的高斯积分点上。研究了非均质各向同性和各向异性的不同的一维和二维随机场模型参数对结果的影响。通过对其结果的比较分析,展示了5种随机场相关结构对边坡可靠度的影响,并强调了选择一个适合模型及其参数的重要性。根据统计分析结果,提出了基于可靠度的土强度特征设计参数,结果显示只有10%～40%（取决于不同的随机有限元模型）的土坡可以达到所期望的确定性分析中的平均结构反应。这是由于随机有限元方法可以更加严格地考虑空间相关性,使得边坡破坏可以更加自然地沿着最小阻力（即最弱材料强度）的路径发展。结果证明水平方向的相关距离在该堤坝的分析中起主导作用,并且指出随机有限元模型中若采用简单公式（不考虑破坏面几何形状）得出的等效各向同性的相关距离,可能导致错误的可靠度评估。     

Deep learning-based evaluation of factor of safety with confidence interval for tunnel deformation in spatially variable soil

The random finite difference method (RFDM) is a popular approach to quantitatively evaluate the influence of inherent spatial variability of soil on the deformation of embedded tunnels. However, the high computational cost is an ongoing challenge for its application in complex scenarios. To address this limitation, a deep learning-based method for efficient prediction of tunnel deformation in spatially variable soil is proposed. The proposed method uses one-dimensional convolutional neural network (CNN) to identify the pattern between random field input and factor of safety of tunnel deformation output. The mean squared error and correlation coefficient of the CNN model applied to the newly untrained dataset was less than 0.02 and larger than 0.96, respectively. It means that the trained CNN model can replace RFDM analysis for Monte Carlo simulations with a small but sufficient number of random field samples (about 40 samples for each case in this study). It is well known that the machine learning or deep learning model has a common limitation that the confidence of predicted result is unknown and only a deterministic outcome is given. This calls for an approach to gauge the model's confidence interval. It is achieved by applying dropout to all layers of the original model to retrain the model and using the dropout technique when performing inference. The excellent agreement between the CNN model prediction and the RFDM calculated results demonstrated that the proposed deep learning-based method has potential for tunnel performance analysis in spatially variable soils.