考虑孔隙水压力的土坡稳定性的有限元上限分析

基于塑性极限分析的上限定理,考虑孔隙水压力的影响,以结点速度为未知量,根据塑性流动约束条件、速度间断约束条件、速度边界约束条件以及由外功功率与内功功率相等条件得到的目标函数,建立了求解孔隙水压力条件下土坡稳定性的有限元塑性极限分析线性规划数学模型;可求得边坡安全系数的上限值及相应的机动容许位移场;最后对2个经典算例进行了分析,验证了提出方法和程序是正确可行的。     

边坡稳定极限分析的单元集成法

提出的单元集成法为采用塑性力学上限定理分析边坡的稳定性提供了一种通用性较强的手段。它采用类似于有限元网格划分的方式离散边坡计算区域,并设定一个机动许可的滑动机构（包括滑裂面位置和速度场,它与网格划分方式无关）,在此滑动机构下可以很方便地计算每个单元贡献的外力功率和内能耗散率。把所有单元的能量相加就是滑坡体的总能量。然后,根据上限定理求得安全系数,并通过非线性数学规划方法找到最小值。对于直线滑裂面或对数螺旋滑裂面的单滑块机制,几个典型算例说明了该方法的有效性。     

基于土质边坡塑性极限分析条分法的可靠度计算方法研究

从土塑性极限分析上限定理出发,以土质边坡塑性极限分析条分法为基础,在引入可靠性分析方法(JC法)后,建立了土质边坡塑性极限分析条分法可靠度极限状态方程,并推导得到了塑性极限分析条分法可靠度计算公式。这种方法实现了定值计算向不确定性计算的转变,同时可靠度指标的计算结果具有概率的意义。     

岩石边坡稳定的块体单元极限分析上限法

将块体单元法与极限分析上限法相结合,提出了岩石边坡稳定的块体单元极限分析上限法。借助于块体单元法离散计算区域,通过块体系统速度场在结构面上满足Mohr-Coulomb屈服条件、关联流动法则、速度边界条件以及块体系统虚功原理,构成求解边坡强度储备安全系数上限解的非线性规划模型,模型的求解采用复合形法。最后研究了一个岩质楔形体边坡算例和小湾水电站进水口边坡实例,通过将块体单元法上限分析计算结果与刚体极限平衡法相比较,验证了该方法的正确性。     

三维塑性极限分析下限法原理及应用

介绍了三维塑性极限分析下限法的基本原理。将计算区域离散为有限个三维空间单元,利用极限分析中的下限定理,借助有限元思想建立数学规划模型,并引入非线性规划的数值方法寻求问题的下限解。以均匀土质边坡的极限荷载作为算例,比较了所得数值解与经典塑性力学理论解,论证了该方法的正确性。     

基于刚体平动运动单元的上限有限元研究

刚性块体极限分析上限法常应用于岩土工程稳定性研究,然而应用时需假定刚性块体破坏模式并递推繁琐的几何关系。为此,提出一种适应性更广的基于非线性规划模型的刚体平动运动单元上限有限元法,并解决了其优化模型初始值的确定问题。通过引入有限单元思想,将计算区域离散成刚体单元,同时以单元速度和节点坐标作为决策变量,由上限定理建立非线性规划模型获得上限解。利用编制的上限有限元程序进行边坡和浅埋隧道稳定性算例验证,表明运动单元上限有限元法能调整速度间断线至较优方位,所得破坏模式特征鲜明,上限解精度高,可广泛应用于边坡、隧道等稳定性分析研究。     

基于上限分析的边坡稳定可靠性评估

从塑性极限分析出发,基于上限分析构建边坡极限状态可靠度计算模型;针对状态函数高度非线性导致常规可靠度方法求解时存在困难的问题,将响应面模型作为极限状态函数与可靠度计算间"桥梁",利用二次正交原理优化取样点,建立考虑参数相关性的二次响应面替代函数。利用JC法直接求得边坡可靠指标的一个上限解,讨论了单个及多个参数变异性对边坡可靠度的影响。     

非均质土坡的有限元塑性极限分析

在评价现有边坡稳定分析方法的基础上,提出了边坡稳定的有限元塑性极限分析方法。借助有限单元思想和线性规划,建立了边坡稳定的数学规划模型,由此可以求出安全系数的上下限解,从而,界定了边坡的安全范围,同时,可以给出下限状态下的应力场和上限状态下的速度场。以一个经典非均质土坡的边坡稳定作为算例,比较了多种方法的分析结果,论证了本方法的正确性。     

低概率水平岩质边坡系统可靠度分析

针对目前含多个相关失效模式的低概率水平岩质边坡系统可靠度分析的难题,提出了基于子集模拟的岩质边坡系统可靠度分析方法,推导了典型边坡系统失效概率计算表达式。为表征不同失效模式间的相关性,提出采用max和min函数构建边坡系统功能函数。并通过含多个相关失效模式的双滑块岩质边坡及锦屏一级左岸坝肩边坡系统可靠度分析验证了提出方法的有效性。结果表明:提出方法计算效率明显高于蒙特卡洛模拟方法,计算精度优于一阶等效近似方法、N维等效方法和Ditlevsen上下限方法,可为解决低概率水平复杂岩质边坡系统可靠度问题提供一个重要的工具。此外,通过max和min函数构建的边坡系统功能函数不仅可以准确地表征边坡不同失效模式间的相关性,而且可为边坡系统可靠度分析提供便利。     

基于混合离散的砌石挡土墙边坡极限承载力下限分析

将极限分析下限法理论、混合数值离散思想和线性规划结合起来研究砌石挡土墙边坡的极限承载力。采用三角形有限单元离散土体来模拟土体的连续介质力学特性,构建土体静力许可应力场的约束条件,采用块体单元离散砌石体来模拟砌石体的非连续介质力学特性,构建砌石挡土墙的静力许可应力场的约束条件;同时建立有限元单元和块体单元交界面的约束条件;然后以超载系数为目标函数建立求解砌石挡土墙极限承载力的下限法线性规划模型,并使用内点算法进行最优化求解,获得边坡的极限荷载（或安全系数）和对应的应力场。通过3个算例的分析验证了所提方法的正确性。所提方法是将混合数值离散思想引入极限分析领域的一次尝试。     

Upper bound limit analysis using finite elements and linear programming

This paper describes a technique for computing rigorous upper bounds on limit loads under conditions of plane strain. The method assumes a perfectly plastic soil model, which is either purely cohesive or cohesive-frictional, and employs finite elements in conjunction with the upper bound theorem of classical plasticity theory. The computational procedure uses three-noded triangular elements with the unknown velocities as the nodal variables. An additional set of unknowns, the plastic multiplier rates, is associated with each element. Kinematically admissible velocity discontinuities are permitted along specified planes within the grid. The finite element formulation of the upper bound theorem leads to a classical linear programming problem where the objective function, which is to be minimized, corresponds to the dissipated power and is expressed in terms of the velocities and plastic multiplier rates. The unknowns are subject to a set of linear constraints arising from the imposition of the flow rulé and velocity boundary conditions. It is shown that the upper bound optimization problem may be solved efficiently by applying an active set algorithm to the dual linear programming problem. Since the computed velocity field satisfies all the conditions of the upper bound theorem, the corresponding limit load is a strict upper bound on the true limit load. Other advantages include the ability to deal with complicated loading, complex geometry and a variety of boundary conditions. Several examples are given to illustrate the effectiveness of the procedure.     

基于FELA的随机场方法在考虑降雨入渗的边坡开挖稳定性分析中的应用

黑山共和国南北高速公路项目部分路段处于复理石地区,降雨集中、空间变异性显著且分层分布的岩土体给道路边坡施工带来了挑战。条分法、常规有限元法等确定性分析方法不能考虑岩土材料的不确定性,给出的具有唯一性、确定性的结果不能反映边坡稳定的不确定性。以该工程某边坡为例,采用有限元极限分析方法（FELA）,考虑岩土材料强度的空间变异性,利用上下限解法得出安全系数的分布区间。由勘察资料得到材料均值、标准差和空间相关长度并重建描述抗剪强度指标的二维随机场,同时考虑开挖岩层的节理分布,分析边坡在分级开挖过程中,各施工步骤的稳定性和破坏模式。与有限元分析结果相比,随机场条件下,部分情况开挖阶段安全系数低于限值,并出现局部破坏和整体破坏两种形式。结合不饱和土理论,模拟暴雨情况下雨水的入渗深度并在饱和区采用降低后的强度参数重新计算。通过蒙特卡洛模拟,得到各工况下安全系数、滑动体体积、挡墙弯矩和锚杆内力的概率密度分布函数。挡墙结构约束土体的变形,使得破坏模式趋向于整体破坏,安全系数分布区间变小。锚杆能带动更多土体进入工作状态,同样约束安全系数分布区间。旱季施工与雨季施工边坡破坏区域不同,同等支护条件下,雨季边坡安全系数分布区间更大,且均值明显降低。      

考虑孔隙水压力的土坡稳定性的有限元下限分析

以极限分析下限法理论为基础,应用有限单元思想离散结构物,建立了同时满足平衡条件、应力边界条件、屈服条件和应力间断条件的静力许可应力场,其中孔隙水压力被当作一种类似于重力的外力荷载。引入线性数学规划手段后,得到了考虑孔隙水压力的边坡稳定的下限法数学规划模型,由此可以求出安全系数的下限解及其对应的应力场。最后,以2个经典的土坡为算例,与多种方法的分析结果比较,论证了该方法的正确性。     

边坡可靠度分析的非侵入式随机有限元法

提出基于非侵入式随机有限元法的边坡可靠度分析方法,并编写计算程序NISFEM。采用有限元滑面应力法计算边坡安全系数,将Hermite随机多项式展开与SIGMA/W和SLOPE/W模块有机结合实现边坡可靠度非侵入式随机分析。根据随机多项式展开系数,给出边坡安全系数前4阶统计矩（均值、标准差、偏度和峰度）和Sobol指标解析表达式,并采用Sobol指标进行边坡可靠度参数敏感性分析。最后,以均质土坡可靠度问题为例,证明该方法在边坡可靠度分析中的有效性。结果表明,边坡可靠度分析的非侵入式随机有限元法能够有效地考虑边坡变形对边坡可靠度的影响,计算效率远远高于蒙特卡罗模拟方法（MCS）,是解决复杂边坡可靠度问题一种有效地分析手段;黏聚力和内摩擦角变异性对边坡安全系数前四阶统计矩具有明显的影响,重度变异性对安全系数前4阶统计矩几乎没有影响;抗剪强度参数间负相关性对边坡安全系数均值几乎没有影响,但对安全系数标准差、偏度和峰度均有明显的影响。此外,随着抗剪强度参数间负相关性的增加,边坡安全系数由近似正态分布逐渐变为明显的非正态分布。     

Reliability analysis of serviceability performance for an underground cavern using a non-intrusive stochastic method

This paper proposes a non-intrusive stochastic analysis procedure for reliability analysis of the serviceability performance of an underground cavern with an implicit limit state function. This procedure is formulated on the basis of the stochastic response surface method (SRSM) and the deterministic finite element method. First, the SRSM is briefly introduced and implemented through a MATLAB code. Then, the software SIGMA/W is used to perform a deterministic finite element analysis. Next, a link between the MATLAB code and SIGMA/W is developed to automatically pass exchange data between the two platforms. Finally, two examples are presented to illustrate the capacity and validity of the proposed procedure. In the first example, a closed-form limit state function is adopted to validate the SRSM by comparing it with the results obtained from a direct Monte Carlo simulation. In the second example, the serviceability performance of an underground cavern is analyzed to illustrate the capacity of the proposed procedure to handle a reliability problem with an implicit limit state function. The proposed procedure does not require the user to modify the existing deterministic finite element code. The deterministic finite element analysis and the probabilistic analysis are decoupled. This is a major practical advantage because realistic probabilistic analyses are made possible. The SRSM can produce sufficiently accurate reliability results. Furthermore, the method is much more efficient than the direct Monte Carlo simulation. Sensitivity analyses show the effect of the variability of input random variables and the correlation between them on: (1) the probability density functions, (2) the first four order statistical moments, and (3) the probability of failure, which is investigated and discussed.     

Efficient system reliability analysis of soil slopes using multivariate adaptive regression splines-based Monte Carlo simulation

System effects should be considered in the probabilistic analysis of a layered soil slope due to the potential existence of multiple failure modes. This paper presents a system reliability analysis approach for layered soil slopes based on multivariate adaptive regression splines (MARS) and Monte Carlo simulation (MCS). The proposed approach is achieved in a two-phase process. First, MARS is constructed based on a group of training samples that are generated by Latin hypercube sampling (LHS). MARS is validated by a specific number of testing samples which are randomly generated per the underlying distributions. Second, the established MARS is integrated with MCS to estimate the system failure probability of slopes. Two types of multi-layered soil slopes (cohesive slope and c–φ slope) are examined to assess the capability and validity of the proposed approach. Each type of slope includes two examples with different statistics and system failure probability levels. The proposed approach can provide an accurate estimation of the system failure probability of a soil slope. In addition, the proposed approach is more accurate than the quadratic response surface method (QRSM) and the second-order stochastic response surface method (SRSM) for slopes with highly nonlinear limit state functions (LSFs). The results show that the proposed MARS-based MCS is a favorable and useful tool for the system reliability analysis of soil slopes.