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。     

基于极限平衡法和有限元法的边坡协同式可靠度分析

极限平衡法和有限元法是两种常用的边坡稳定分析方法。基于极限平衡法的边坡可靠度分析计算效率较高,但需要假定失效模式,从而导致计算结果不准;与之相反,基于有限元法的边坡可靠度分析更为严格,但计算效率较低。为此,提出了一种新的基于随机模拟的边坡可靠度分析方法——边坡协同式可靠度分析方法。该方法包括初步可靠度分析和精细可靠度分析两步,可以同时利用极限平衡法和有限元法的优势,实现既高效又准确的边坡可靠度分析。通过一个考虑空间变异性的两层土坡算例验证了该方法的有效性,结果表明:协同式可靠度分析方法与基于有限元法的蒙特卡洛模拟或子集模拟相比,不仅具有一致的可靠度分析结果,而且显著提高了小概率水平下的计算效率,促进了基于有限元法的边坡可靠度分析在实际工程中的应用。该方法可以将基于极限平衡法的边坡可靠度分析成果合理纳入到基于有限元法的边坡可靠度分析中,从而获得大量的失效样本,以制定合理的边坡防治措施。该方法非常适用于高维可靠度问题,如考虑空间变异性的边坡可靠度问题。     

边坡可靠度分析的高斯过程方法

针对传统边坡可靠度分析方法的局限性,将高斯过程机器学习与重要抽样方法相结合,提出了边坡可靠度分析的高斯过程方法。利用极限平衡分析构造少量的学习样本,采用基于统计学习原理的高斯过程模型重构边坡隐式功能函数,实现边坡功能函数及其偏导数的显式表达,并构造合理的迭代方式,在计算过程中不断提升高斯过程模型对失效概率贡献较大区域的重构精度,进而应用重要抽样法计算边坡的失效概率与可靠指标。研究结果表明,该方法是可行的,具有较高的计算精度和效率。     

利用差分法计算基于Spencer分析模式的边坡稳定可靠度

首先研究边坡稳定Spencer分析模式的过程和特点,归纳出安全系数的计算流程,发现Spencer模式下边坡稳定可靠度计算的难题在于安全系数是隐函数,导致偏导数无法计算,由此引进差分方法近似求解偏导数问题。其次依据复合函数求导方法,推导采用验算点方法求解Spencer模式下边坡稳定可靠度过程中各项偏导数的计算公式和可靠度指标的线性逼近循环迭代方法。基于上述研究,给出完整的验算点求解Spencer模式边坡稳定可靠度方法的7个分析步骤,以及每一步骤中的具体计算方法。最后采用该方法分析一个工程问题,并与蒙特卡洛模拟结果进行比较。结果表明,两者的计算结果十分接近;该方法精度可满足工程要求,同时工作量大大少于蒙特卡洛模拟方法,具有较好的工程应用价值。     

基于广义子集模拟样本加权法的边坡多失效模式可靠度分析

边坡通常包含多个潜在的破坏模式,边坡多失效模式系统可靠度计算的蒙特卡洛模拟方法在求解小失效概率问题时计算效率较低。为此,提出基于广义子集模拟样本加权法的边坡多失效模式可靠度分析方法,推导了多失效模式对应于不同失效阈值时的失效概率计算公式。采用概率故障树模型构建边坡多失效模式系统可靠度分析模型,通过耦合系统模式的广义子集模拟驱动变量划分整体样本空间,基于广义子集模拟执行过程中的样本子空间概率权来估计相应空间中样本权系数,通过样本权系数计算失效模式在不同失效阈值下的失效概率。以岩质边坡楔形体稳定问题为例阐明所提方法的有效性。结果表明:提出的广义子集模拟样本加权方法极大地提高了边坡系统可靠度及其分量失效模式可靠度的计算效率。该方法不仅能够通过一次模拟实现多模式可靠度的求解,避免针对不同失效模式进行重复模拟的问题,而且能够显著地提高估计低概率水平失效模式可靠度的计算效率。此外,提出的广义子集模拟样本加权方法不仅能够高效地估计临界失效阈值对应的失效概率,也能够同时计算多模式在任一失效阈值时的失效概率。     

基于高斯过程回归的工程结构失效概率快速估计方法

高斯过程机器学习是基于严格的统计学习理论而新发展的方法,该方法在求解小样本、高维数的非线性问题上具有一定的适应性.针对采用直接蒙特卡洛方法进行功能函数计算代价较高的结构可靠度分析时计算效率过低的瓶颈问题,提出了一种基于高斯过程回归模型的直接蒙特卡洛模拟方法.该方法利用有限元等数值方法构造少量的学习样本,通过学习后的高斯过程回归模型重构隐式功能函数,直接建立随机变量与功能函数值的映射关系,进而结合直接蒙特卡洛方法推求结构的失效概率与可靠指标.算例研究表明,该方法简单易行,与传统蒙特卡洛模拟法相比较,计算效率明显较高,且易于与各种工程结构分析程序或商业计算软件相结合.     

广州科学城岩质边坡稳定性可靠度分析

边坡稳定性问题是边坡工程最关键的问题,如何研究其稳定性也是岩土工程的重点研究课题。把Monte Carlo法引入边坡稳定性分析和评价中,借助传统的极限平衡理论,建立边坡稳定性分析的极限状态函数。运算过程中采用伪随机数的方法生成服从正态分布的抗剪强度参数随机变量,进而求出边坡安全系数、安全系数的可靠度指标和失效概率。与传统的极限平衡方法相比,可靠性分析可以直观地反映边坡稳定的可靠程度及其失效概率,能为边坡工程支护设计提供更为可靠的参数,同时也能为生产提供指导作用。因此,可靠度分析方法是边坡稳定性评价的有效方法,具有广泛的应用前景。     

成都膨胀岩土边坡稳定性分析方法研究

根据膨胀岩土的工程特性,通过对单面开挖和填土边坡受膨胀力的状态进行了分区,分析了受力模式,采用极限平衡法中的Fellenius法(瑞典圆弧法)和Bishop法(简化Bishop法)分别计算边坡稳定系数,并确定是否需要采取工程措施。     

矿山边坡破坏模式与稳定性评价

矿山边坡的稳定性研究一直是岩土工程领域广泛关注的热点问题之一。结合广西田阳一处矿山工程边坡的实例,在分析其破坏模式的基础上,采用刚体极限平衡法、数值模拟方法和赤平投影方法综合评价了该边坡的稳定性,三种方法互为补充,为边坡防治提供了可靠的稳定性计算成果。提出的研究方法可为西南地区类似工程提供一定的借鉴和参考。     

边坡可靠性评价的向量投影响应面研究及应用

岩土体的力学参数存在一定的随机性,当进行边坡稳定可靠性评价时,当功能函数不能用显式表达时,响应面法成为计算可靠度指标的重要方法。将向量投影响应面法与有限元强度折减法相结合,研究隐式功能函数边坡工程稳定可靠度计算方法。首先利用强度折减法结果拟合稳定系数计算方程从而代替隐式方程,并建立极限状态方程,然后进行向量投影以确定展开点和抽样点,进行近似方程的拟合、验算点和可靠度指标的计算,直到计算达到收敛。通过与不同计算方法进行对比,表明区别于通常以插值点为中心展开生成样本点的向量投影取样法的准确性和合理性,该方法可使可靠性分析次数显著减少,改善了对非线性程度较高的极限功能函数求解可靠指标的收敛性。同时,将该方法应用于杭兰高速公路大水田边坡的稳定可靠性分析当中。     

基于二维随机场在圆弧曲线上局部平均化的边坡可靠度分析

土质参数随机场在边坡滑移面上局部平均后的"空间特性"值是控制边坡可靠性的主导因素。以边坡滑移面为圆弧为前提,基于随机场理论进行了公式推导,通过二维随机场在圆弧曲线上的一维局部平均得出了局部平均方差的计算式。以推导出的局部平均方差计算式为基础提出了适用于均质原状边坡的简便可靠度分析方法。方法首先通过少量确定性有限元分析经拟合得出极限状态曲线,然后经过一维局部平均方差计算边坡强度参数的"空间特性"统计指标,最后通过积分计算强度参数分布函数在极限状态曲线危险侧的面积得出边坡失稳概率。经与蒙特-卡罗随机有限元法进行对比表明,提出的基于二维随机场一维局部平均的边坡可靠度分析方法计算结果可靠,可为边坡可靠性分析提供一种新思路。     

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.     

A stability analysis of landslides based on random fields,part II: base circle slope

In this paper, the stability of base circle slopes is analyzed based on the theory of random fields. The closed-form solution of the safety factor and the failure probability of base circle slopes are obtained using the integration method. The effects of the spatial variation of the mechanical parameters of soils on the stability of base circle slopes are investigated. The mean values of the safety factor and the failure probability of base circle slopes are determined. The effects of spatial correlation length on the failure probability of base circle slopes are studied. The results show that for homogeneous slopes, the accuracy of the vertical integration model is greater than that of the horizontal integration model. For layered slopes, the effectiveness of the horizontal integration method is validated by a Monte Carlo simulation. Therefore, the horizontal integration model is more suitable for the layered slopes than the vertical integration model.

     

Stochastic finite element method for slope stability analysis

This paper describes a stochastic finite element method using the first-order approximation at a failure point of a set of random variables. The method is extended to equivalent normal represtation of non-normal distributions and offers two advantages: (1) It gives a consistent measure of failure probability for the limit-states defined in terms of different but equivalent performance function formulations, (2). It can be applied to reliability analysis for non-normal variants. Results using this method are compared favorably with that of Monte Carlo simulation in a simple example. Furthermore, this method will be applied to earth slope stability analysis to give probability levels for local and global failures on a potential failure surface.     

Efficient slope reliability analysis using adaptive classification-based sampling method

Slope reliability analysis can effectively account for uncertainties involved in a slope system. However, commonly used slope reliability analysis methods often require huge computational cost, especially in large-scale problems, which hinders its wide application to engineering practice. This paper proposes an efficient slope reliability analysis method based on the active learning support vector machine (SVM) and Monte Carlo simulation (MCS). The proposed method makes use of an active learning function and cross-validation techniques to select the most suitable training samples to update the SVM model. The selected training samples are associated with a small distance to the limit state surface of the slope stability model and a large local uncertainty, which are more informative to gradually tune the SVM model to approximate the actual slope performance function. As a result, the proposed method can estimate the slope reliability with a small number of evaluations of the slope performance function, thus improving the efficiency significantly. Four slope examples are employed to demonstrate the effectiveness of the proposed method. The presented approach is also compared with some other commonly used surrogate models in slope reliability analysis. It is shown that the proposed method performs better in terms of computational efficiency to obtain similar estimation accuracy of the failure probability for the investigated examples.

     

岩土破裂过程分析RFPA离心加载法

将离心加载算法引入到岩石破裂过程分析RFPA系统中,形成了RFPA离心加载法(RFPA-Centrifuge)。RFPA-Centrifuge的应力分析采用有限元基本算法,满足静力平衡、应变相容及岩土体的非线性应力–应变关系;秉承了RFPA系统的破坏分析功能,并且同样考虑材料细观非均匀的影响,对边坡等难点问题进行分析时,不需对滑动面或破坏区域做任何预先假定。通过对垂直土坡离心物理试验、倾斜的土坡、含两组平行节理岩质边坡和不同截面形状隧道的数值试验,证明该法可以直观、逼真地获得岩土结构的破坏区域或滑移破坏面,同时求得安全储备系数,分析结果与物理的试验和有限元强度折减法均比较一致。RFPA-Centrifuge不仅回避了强度折减法中有关力学参数复杂的折减规则,还克服了强度折减法难以用物理试验进行相互验证的不足,因而是一种极具前景的岩土工程稳定性分析方法。     

地震边坡破坏机制及其破裂面的分析探讨

 地震作用下边坡破坏机制是边坡动力稳定性分析的前提,目前主要采用拟静力与动力有限元时程分析的方法进行分析,认为地震边坡破坏机制为剪切破坏,并以极限平衡法计算得到的剪切滑移面作为地震动力作用下的破裂面,而不考虑地震荷载作用下的拉破坏,从而使地震边坡稳定性分析失真。汶川地震边坡调研发现,滑坡上部多数发生拉破坏,甚至有些岩土体被抛出,这是一个很好的启示,为此,采用FLAC动力强度折减法,结合具有拉和剪切破坏分析功能的FLAC3D软件对地震边坡破坏机制进行数值分析。计算表明,地震边坡的破坏由边坡潜在破裂区上部拉破坏与下部剪切破坏共同组成,而不是剪切滑移破坏,通过多种途径给出地震边坡破裂面位置的确定方法,为边坡动力稳定性分析提供更加准确的基础。     

Reliability-Based Seismic Deformation Analysis of Reinforced Soil Slopes

The paper describes a precise technique to compute the limit state exceedance probability of typical earth slopes and geosynthetic-reinforced soil (GRS) slopes using a low-discrepancy sequence Monte Carlo (LDSMC) method and an importance sampling with low-discrepancy sequence Monte Carlo (ISLDSMC) method. The LDSMC and ISLDSMC methods can efficiently compute the accurate limit state exceedance probabilities of typical earth slopes and GRS slopes with a limited number of simulations. This study presents a practically useful nomogram of seismic deformation and limit state exceedance probability with variable slope heights, backfill soil properties, and geometries. A simple estimation of the limit state exceedance probability of the GRS slopes is given based on the results of the conventional deterministic analysis. The results of these analyses show that the LDSMC and ISLDSMC methods are practically useful, efficient, and accurate for the limit state exceedance probability calculation.