浅埋隧道掌子面稳定性二维自适应上限有限元分析

为研究浅埋隧道掌子面稳定性及获取精细化的破坏模式,提出了一种上限有限元非结构化网格自适应加密策略。以单元耗散能权重指标作为网格自适应加密评判准则,该策略同时兼顾了单元尺度与塑性应变。应用高阶的6节点三角形单元并建立上限有限元线性规划模型,以多次反复计算和网格加密的方式实现了二维自适应上限有限元分析并编制了计算程序。利用条形基础地基极限承载力课题,从上限解精度和网格加密形态方面验证了该程序的有效性。针对浅埋隧道掌子面稳定性问题,展开多参数条件下的自适应上限有限元计算,分析了网格加密过程中单元总数与上限解精度的关系,列出不同隧道埋深和内摩擦角对应的隧道掌子面稳定性临界值的上限解,揭示出掌子面稳定性变化规律及精细化的破坏模式。     

Coupled computations for an elastic‐perfectly plastic soil using adaptive mesh refinement

An adaptive mesh refinement algorithm has been developed for non‐linear computations in geomechanics, based on a smoothed stress–strain finite element formulation. This uses estimates of error in the incremental shear strain invariant to guide the regeneration of unstructured meshes at regular intervals during loading. Following each mesh‐update, no re‐analysis of previous increments with the new mesh is necessary. Algorithm performance has been investigated by analysing a passive earth pressure problem using a linear elastic‐perfectly plastic Mohr–Coulomb soil model. Perfectly drained behaviour has been considered, as have partially drained situations using hydromechanical coupling, while undrained behaviour has been approximated using time steps close to zero. In all cases, mesh adaptivity has been successful in capturing regions of high strain gradient. The results have been compared with analytical solutions. Accurate computations of limit load and shear band orientation have been obtained for a wide range of material dilation angles. Copyright © 2000 John Wiley & Sons, Ltd.     

基于混合常应力−光滑应变单元的极限分析方法

极限分析是岩土工程稳定性评价的重要方法之一。传统的有限元极限分析方法,采用低阶三角形单元时需要引入速度间断面并采用特殊网格布局,或者采用高阶三角形单元等措施来克服体积锁定问题和提高数值精度。在光滑有限元法（smoothed finite element method,简称SFEM）的基础上,提出了一种基于新型混合常应力−光滑应变单元的极限分析方法（mixed constant stress-smoothed strain element limit analysis,简称MCSE-LA方法）。在服从关联流动法则和Mohr-Coulomb屈服准则的基础上,MCSE-LA方法最终将数值极限分析转化为以应力和极限荷载乘子为基本未知量的二阶锥规划（second order cone programming,简称SOCP）问题。MCSE-LA方法具有形式简单、优化变量相对较少和无需显式的写出塑性内能耗散函数的优点,并且根据凸锥优化的对偶理论,可以从对偶问题中获得速度场和塑性乘子等信息。此外,还采用基于最大塑性剪应变率的网格自适应加密算法,该算法在塑性区细化网格,显著提高了新数值极限分析方法的计算效率和精度。最后通过边坡稳定分析的结果对比,验证了MCSE-LA方法的计算精度和效率均高于传统的有限元极限分析方法。     

A space-time adaptive method for reservoir flows: formulation and one-dimensional application

This paper presents a space-time adaptive framework for solving porous media flow problems, with specific application to reservoir simulation. A fully unstructured mesh discretization of space and time is used instead of a conventional time-marching approach. A space-time discontinuous Galerkin finite element method is employed to achieve a high-order discretization on the anisotropic, unstructured meshes. Anisotropic mesh adaptation is performed to reduce the error of a specified output of interest, by using a posteriori error estimates from the dual-weighted residual method to drive a metric-based mesh optimization algorithm. The space-time adaptive method is tested on a one-dimensional two-phase flow problem, and is found to be more efficient in terms of computational cost (degrees-of-freedom and total runtime) required to achieve a specified output error level, when compared to a conventional first-order time-marching finite volume method and the space-time discontinuous Galerkin method on structured meshes.     

Coupled hydromechanical‐fracture simulations of nonplanar three‐dimensional hydraulic fracture propagation

This paper presents an algorithm and a fully coupled hydromechanical‐fracture formulation for the simulation of three‐dimensional nonplanar hydraulic fracture propagation. The propagation algorithm automatically estimates the magnitude of time steps such that a regularized form of Irwin's criterion is satisfied along the predicted 3‐D fracture front at every fracture propagation step. A generalized finite element method is used for the discretization of elasticity equations governing the deformation of the rock, and a finite element method is adopted for the solution of the fluid flow equation on the basis of Poiseuille's cubic law. Adaptive mesh refinement is used for discretization error control, leading to significantly fewer degrees of freedom than available nonadaptive methods. An efficient computational scheme to handle nonlinear time‐dependent problems with adaptive mesh refinement is presented. Explicit fracture surface representations are used to avoid mapping of 3‐D solutions between generalized finite element method meshes. Examples demonstrating the accuracy, robustness, and computational efficiency of the proposed formulation, regularized Irwin's criterion, and propagation algorithm are presented.     

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.     

极限分析有限元法讲座—— Ⅰ岩土工程极限分析有限元法

经典岩土工程极限分析方法一般采用解析方法，有些还要对滑动面作假设，且不适用于非均质材料，尤其是强度不均的岩石工程，从而使极限分析法的应用受到限制。随着计算技术的发展，极限分析有限元法应运而生，它能通过强度降低或者荷载增加直接算得岩土工程的安全系数和滑动面，十分贴近工程设计。为此，探讨了极限分析有限元法及其在边坡、地基、隧道稳定性计算中的应用，算例表明了此法的可行性，拓宽了该方法的应用范围。随着计算机技术与计算力学的发展，岩土工程极限分析有限元法正在成为一门新的学问，而且有着良好的发展前景。     

渗流问题的三维h型自适应有限元法研究

研究了三维渗流的自适应有限元法,建立了集成网格自动剖分、渗流有限元分析、网格调整、后处理等四大模块的四面体单元h型自适应系统。给出的算例证实了系统的有效性和优越性。     

不排水双层粘性土地基极限承载力的数值分析

采用弹塑性有限元分析了条形基础作用下不排水条件的双层粘性土地基极限承载力性状。采用修正的地基承载力系数表征,并将不同的几何与土层参数条件下的数值解与上下限解和经典的经验解进行比较。表明弹塑性位移有限元法可以很好地求解地基的极限承载力问题,其求解得到的修正地基承载力系数与基于下限原理的有限元解很接近,而上限解高估了地基的极限荷载值,传统的经验解在某些条件下却偏小。     

大圆筒结构倾覆稳定分析的有限元法

大直径圆筒结构的倾覆稳定性是设计中考虑的一个重要问题。采用弹塑性有限元法,求解大圆筒结构在指定波浪条件下的荷载-位移关系曲线;通过荷载-位移关系的上限,确定结构的极限承载力;定义极限承载力与设计荷载的比值为结构的倾覆稳定安全系数,从而判断结构的倾覆稳定安全裕度。该方法避免了现行极限平衡分析方法确定土压力和转动中心的困难,可以考虑土与结构的相互作用和复杂的边界条件。通过对某工程实例的分析,初步验证了该方法的可行性。     

边坡稳定分析的自适应性局部网格加密解法

常规的有限元强度折减法在确定边坡塑性区时,不能直观地反映出塑性区的形状和滑裂面位置,计算结果精度低。在塑性区范围内进行网格局部加密,不仅使安全系数的计算精度大幅度提高,而且可求出滑裂面的形状和位置。针对求解塑性区搜索滑裂面这一具体问题,提出塑性应变界限值网格加密准则,采用自适应性网格局部加密技术求解边坡的滑裂面和稳定安全系数。数值计算结果表明,所提出的加密准则能正确地确定滑裂面的形状和位置,计算所得稳定安全系数和理论稳定安全系数仅相差0.2 %。     

Three dimensional FEM of moving coordinates for the analysis of transient vibrations due to moving loads

This paper is concerned with the transient vibration analysis of railway-ground system under fast moving loads. A 3D finite element method in a convected coordinate system moving with the load is formulated, together with viscous-elastic transmitting boundary conditions in order to limit the finite element mesh. A method is proposed to introduce Rayleigh type material damping in the finite element formulation in the moving coordinate system, while measures have also been taken to improve the numerical stability of the solution procedure. The performance of the transmitting boundary and the entire solution procedure are assessed via comparison with the ordinary finite element solution of some relatively simple problems and through a comparison with field measurements. The reasonable agreement found from these comparisons demonstrates the validity of the proposed method.     

软基上沉入式大圆筒结构的水平承载力分析

大圆筒结构是一种适宜于软土地基上的新型港口水工建筑物,但目前对于软基上大圆筒结构的水平极限承载力尚缺乏合理的计算模式和分析方法.结合长江口深水航道治理二期工程,针对大圆筒结构设计方案提出了一种简便而实用的上限极限分析方法,采用有限元数值分析解验证了所提出计算方法的合理性,进而,据此进行了一系列变动参数比较计算,以此对大量的计算结果进行了系统的分析,所得到的数值计算结果与分析结论为工程设计提供参考依据.     

Residual a Posteriori Error Estimates for the Mixed Finite Element Method

In this paper, residual-based a posteriori error bounds are derived for the mixed finite element method applied to a model second order elliptic problem. A global upper bound for the error in the scalar variable is established, as well as a local lower bound. In addition, due to the fact that the scalar and vector variables are approximated to equal order accuracy, the dual problem may be modified to give an upper bound for the vector variable. Some comments on estimating more general error quantities are also made. The estimate effectively guides adaptive refinement for a smooth problem with a boundary layer, as well as detects the need to refine near a singularity.     

Stability of a circular tunnel in cohesive-frictional soil subjected to surcharge loading

The stability of circular tunnels in cohesive-frictional soils subjected to surcharge loading has been investigated theoretically and numerically assuming plane strain conditions. Despite the importance of this problem, previous research on the subject is very limited. At present, no generally accepted design or analysis method is available to evaluate the stability of tunnels/openings in cohesive-frictional soils. In this study, continuous loading is applied to the ground surface, and both smooth and rough interface conditions are modelled. For a series of tunnel diameter-to-depth ratios and material properties, rigorous lower- and upper-bound solutions for the ultimate surcharge loading are obtained by applying finite element limit analysis techniques. For practical use, the results are presented in the form of dimensionless stability charts with the actual tunnel stability numbers being closely bracketed from above and below. As an additional check on the solutions, upper-bound rigid-block mechanisms have been developed and the predicted collapse loads from these are compared with those from finite element limit analysis. Finally, an expression that approximates the ultimate surcharge load has been devised which is convenient for use by practising engineers.     

饱和砂土动静力特性的网格自适应数值模拟

在有限元数值计算平台上,建立了一套基于后验误差评估和Delaunay三角剖分的网格自适应方案,针对饱和砂土静力受压和地震液化的特性进行模拟。验证了超收敛单元片回归（SPR）误差评估中原用于四边形单元的双线性回归函数在用于三角形单元网格时的适用性和可靠性;在饱和砂土动、静力算例中,网格自适应计算获得的变形、应变、超孔压比等的变化规律与常规有限元结果趋势一致。随着网格的再生成,参考点的位移和全域的平均相对误差逼近精确值。对于初始网格,讨论了合理的自适应程度并应用于地震液化的自适应数值模拟中,也对Delaunay三角剖分实施了一些改进。最终证明该自适应方案在提高计算效率的同时,亦可以保证计算所需的精准度。     

复杂区域自适应三角形网格全自动生成方法

为了使用自适应有限单元法求解岩土工程问题，本文在行被法的基础上，提出了一种适用于多介质复杂区域的三角形网格全自动生成方法。文中给出三个工程算例．     

A plane strain yield design approach to stability analysis of a column‐reinforced soil foundation under inclined loading

The ultimate bearing capacity problem of column‐reinforced foundations under inclined loading is investigated within the framework of static and kinematic approaches of yield design theory. The configuration of a native soft clayey soil reinforced by either a group of purely cohesive columns (lime‐column technique) or a group of purely frictional columns (stone‐column technique) is analyzed under plane strain conditions. First, lower bound estimates are derived for the ultimate bearing capacity by considering statically admissible piecewise linear stress distributions that comply with the local strength conditions of the constitutive materials. The problem is then handled by means of the yield design kinematic approach of limit analysis through the implementation of several failure mechanisms, allowing the formulation of upper bound estimates for the ultimate bearing capacity. A series of finite element limit load solutions obtained from numerical elastoplastic simulations suggests that the predictions derived from the kinematic approach appear to be more accurate than the estimates obtained from the static approach. Comparison with available results obtained in the context of yield design homogenization demonstrates the accuracy of the proposed direct analysis, which may therefore be viewed as complementary approach to homogenization‐based approaches when a small number of columns is involved. Copyright © 2016 John Wiley & Sons, Ltd.     

非稳定温度场的三维p型有限元方法研究

非稳定温度场的边界往往是温度梯度较大的区域,需要划分较密的网格。但在三维温度应力的计算中太密的网格往往使得计算成本很高。将p型阶谱有限元方法引入温度场的计算,则可以开拓一条解决这类问题的有效途径。研究了p型有限元中的温度边界条件和初值,编制了有关程序,对同一个算例,采用不同网格密度的常规有限元法和p型有限元法进行了温度场计算分析和对比。研究结果表明,用p型有限元进行非稳定温度场计算,在网格稀疏的条件下能够达到较高的精度。     

Confidence bounds on risk assessments for underground nuclear waste repositories

The estimation of risk confidence bounds is an important element of a comprehensive probabilistic risk assessment for a radioactive waste repository. Normal distribution bounds may be used in the asymptotic limit of a very large number of Monte Carlo simulations, but sharp skewness of the risk distribution may severely retard the convergence process. The Tchebycheff bounds are parameter-free and may be applied regardless of distribution, save for the finiteness of variance. These bounds may be generally applicable, but they are invariably very broad. Better parameter-free bounds for mean risk are presented here, based on an inequality originally derived by Guttman.