共查询到20条相似文献，搜索用时 31 毫秒
1.
In geomechanics, limit analysis provides a useful method for assessing the capacity of structures such as footings and retaining walls, and the stability of slopes and excavations. This paper presents a finite element implementation of the kinematic (or upper bound) theorem that is novel in two main respects. First, it is shown that conventional linear strain elements (6‐node triangle, 10‐node tetrahedron) are suitable for obtaining strict upper bounds even in the case of cohesive‐frictional materials, provided that the element sides are straight (or the faces planar) such that the strain field varies as a simplex. This is important because until now, the only way to obtain rigorous upper bounds has been to use constant strain elements combined with a discontinuous displacement field. It is well known (and confirmed here) that the accuracy of the latter approach is highly dependent on the alignment of the discontinuities, such that it can perform poorly if an unstructured mesh is employed. Second, the optimization of the displacement field is formulated as a standard second‐order cone programming (SOCP) problem. Using a state‐of‐the‐art SOCP code developed by researchers in mathematical programming, very large example problems are solved with outstanding speed. The examples concern plane strain and the Mohr–Coulomb criterion, but the same approach can be used in 3D with the Drucker–Prager criterion, and can readily be extended to other yield criteria having a similar conic quadratic form. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
2.
紧支径向基函数能使支配方程中的刚度矩阵具有稀疏性,很适合应用于无网格方法中,其缺点是在插值计算时精度不高.点插值方法的插值函数具有Delta函数性质,可以很方便的施加本质边界条件,但在计算插值函数时矩阵易出现奇异.为了提高计算精度并避免点插值法的局限性,首先对紧支径向基函数进行完备性修正,然后用完备性修正的紧支径向基函数代替多项式来形成插值函数,建立了紧支径向基函数点插值方法.由于该方法中的形函数满足Delta函数性质,因此本质边界条件可以像传统的有限元方法一样很容易施加.然后将该方法用于二维弹性静力问题的求解,导出了其相应的离散方程.最后将该方法应用于一个悬臂梁的分析中,初步验证了该方法的有效性与合理性. 相似文献
3.
This paper deals with the problem of T‐bar penetration. New kinematically admissible velocity fields are derived from elastic solutions of incompressible material using Airy stress function. These velocity fields are used to obtain upper bounds to collapse loads. Two particular solutions are presented, one for a rough contact surface between the T‐bar and soil and the other for a smooth contact surface. The merit of the solutions is that within the boundaries of the velocity field, the soil is required to shear compatibly and continuously. Therefore, these solutions can easily be combined with the strain path method to estimate rate and softening effects. Analysis including consideration of strain rate effect showed that the new mechanisms predict, under certain conditions, lower values than previously published upper bound solutions. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
4.
Omid Ghaffaripour Golnaz A. Esgandani Arman Khoshghalb Babak Shahbodaghkhan 《国际地质力学数值与分析法杂志》2019,43(11):1919-1955
This paper presents the first application of an advanced meshfree method, ie, the edge-based smoothed point interpolation method (ESPIM), in simulation of the coupled hydro-mechanical behaviour of unsaturated porous media. In the proposed technique, the problem domain is spatially discretised using a triangular background mesh, and the polynomial point interpolation method combined with a simple node selection scheme is adopted for creating nodal shape functions. Smoothing domains are formed on top of the background mesh, and a constant smoothed strain, created by applying the smoothing operation over the smoothing domains, is assigned to each smoothing domain. The deformation and flow models are developed based on the equilibrium equation of the mixture, and linear momentum and mass balance equations of the fluid phases, respectively. The effective stress approach is followed to account for the coupling between the flow and deformation models. Further coupling among the phases is captured through a hysteretic soil water retention model that evolves with changes in void ratio. An advanced elastoplastic constitutive model within the context of the bounding surface plasticity theory is employed for predicting the nonlinear behaviour of soil skeleton. Time discretisation is performed by adopting a three-point discretisation method with growing time steps to avoid temporal instabilities. A modified Newton-Raphson framework is designed for dealing with nonlinearities of the discretised system of equations. The performance of the numerical model is examined through a number of numerical examples. The state-of-the-art computational scheme developed is useful for simulation of geotechnical engineering problems involving unsaturated soils. 相似文献
5.
Hydraulic fracturing is the method of choice to enhance reservoir permeability and well efficiency for extraction of shale gas. Multi‐stranded non‐planar hydraulic fractures are often observed in stimulation sites. Non‐planar fractures propagating from wellbores inclined from the direction of maximum horizontal stress have also been reported. The pressure required to propagate non‐planar fractures is in general higher than in the case of planar fractures. Current computational methods for the simulation of hydraulic fractures generally assume single, symmetric, and planar crack geometries. In order to better understand hydraulic fracturing in complex‐layered naturally fractured reservoirs, fully 3D models need to be developed. In this paper, we present simulations of 3D non‐planar fracture propagation using an adaptive generalized FEM. This method greatly facilitates the discretization of complex 3D fractures, as finite element faces are not required to fit the crack surfaces. A solution strategy for fully automatic propagation of arbitrary 3D cracks is presented. The fracture surface on which pressure is applied is also automatically updated at each step. An efficient technique to numerically integrate boundary conditions on crack surfaces is also proposed and implemented. Strongly graded localized refinement and analytical asymptotic expansions are used as enrichment functions in the neighborhood of fracture fronts to increase the computational accuracy and efficiency of the method. Stress intensity factors with pressure on crack faces are extracted using the contour integral method. Various non‐planar crack geometries are investigated to demonstrate the robustness and flexibility of the proposed simulation methodology. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
6.
This paper presents a new numerical tool to model the two-dimensional contaminant transport through saturated porous media
using a meshfree method, called radial point interpolation method (RPIM) with polynomial reproduction. In RPIM, an approximate
solution is constructed entirely in terms of a set of nodes and no characterisation of the interrelationship of the nodes
is needed. The advection–dispersion equation with sorption is considered to illustrate the applicability of the RPIM. The
Galerkin weak form of the governing equation is formulated using 2D meshfree shape functions constructed using thin plate
spline radial basis functions. MATLAB code is developed to obtain the numerical solution. Three numerical examples are presented
and the results are compared with those obtained from the finite element method and analytical solutions. In order to test
the practical applicability and performance of the RPIM, two case studies of contaminant transport through landfill liners
are presented. A good agreement is obtained between the results of the RPIM and the field investigation data. 相似文献
7.
Three‐dimensional time‐harmonic fundamental solutions for a fluid‐saturated poroelastic half‐space with partially permeable free surface 
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下载免费PDF全文 By virtue of a pair of scalar potentials for the displacement of the solid skeleton and the pore fluid pressure field of a saturated poroelastic medium, an alternative solution method to the Helmholtz decomposition is developed for the wave propagation problems in the framework of Biot's theory. As an application, a comprehensive solution for three‐dimensional response of an isotropic poroelastic half‐space with a partially permeable hydraulic free surface under an arbitrarily distributed time‐harmonic internal force field and fluid sources is developed. The Green's functions for the poroelastic fields, corresponding to point, ring, and disk loads, are reduced to semi‐infinite complex‐valued integrals that can be evaluated numerically by an appropriate quadrature scheme. Analytical and numerical comparisons are made with existing elastic and poroelastic solutions to illustrate the quality and features of the solution. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
8.
针对地表超载作用下隧道稳定性和破坏模式问题,基于刚体平动运动单元上限有限元理论编程并计算分析,获得了浅埋隧道失稳临界超载系数上限解和刚性运动块体体系破坏模式。通过与现有的刚性块体极限分析上限法以及极限分析上、下限有限元法计算结果的对比分析,验证了上限解的可靠性。研究结果表明,（1）临界超载系数 黏聚力c之比 随土体内摩擦角 和隧道埋深C与直径D之比( )的增大而相应增大,随土体重度与黏聚力参数 的增大而减小;（2） 和 对隧道破坏模式的影响较明显; 增大,则隧道破坏范围增加;内摩擦角 增大,刚性运动块体破坏模式相互错动更加显著,相比而言, 对破坏模式的影响并不显著;（3）刚体平动运动单元上限有限元上限解精度高,所得刚性运动块体破坏模式具有滑移线形态,能精细地反映隧道失稳破坏特征。 相似文献
9.
将大规模渗流有限元计算与随机响应面法相结合,对双江口心墙堆石坝进行渗透稳定可靠性分析。在基于随机响应面法的可靠度分析框架内,堆石坝稳定渗流有限元计算过程和可靠度分析过程分开独立进行,通过对心墙渗透坡降较大区域的节点建立统一的渗透稳定功能函数,采用渗流有限元分析方法和随机响应面法,计算出该区域每个节点处的渗透破坏失效概率,并将最大失效概率作为心墙的失效概率。最后,分析了心墙渗透系数、覆盖层渗透系数、上游水位与心墙具有最大失效概率节点处渗透坡降的相关关系,以及心墙渗透系数和上游水位的变异性对心墙渗透破坏失效概率的影响。计算结果表明,随机响应面法3阶Hermite展开就能够保证良好的计算精度,且计算耗时较小;双江口堆石坝心墙具有最大失效概率节点处的渗透坡降与上游水位密切相关,而与心墙本身的渗透系数呈弱负相关关系,与覆盖层渗透系数的相关性不显著;随着上游水位变异性的增大,心墙失效概率急剧增大,而这种效应对于心墙渗透系数并不明显。研究成果为随机响应面法在实际工程中的应用奠定了一定的基础。 相似文献
10.
Multi‐slicing strategy for the three‐dimensional discontinuity layout optimization (3D DLO) 下载免费PDF全文
下载免费PDF全文 Yiming Zhang 《国际地质力学数值与分析法杂志》2017,41(4):488-507
Discontinuity layout optimization (DLO) is a recently presented topology optimization method for determining the critical layout of discontinuities and the associated upper bound limit load for plane two‐dimensional and three‐dimensional (3D) problems. The modelling process (pre‐processing) for DLO includes defining the discontinuities inside a specified domain and building the target function and the global constraint matrix for the optimization solver, which has great influence on the the efficiency of the computation processes and the reliability of the final results. This paper focuses on efficient and reliable pre‐processing of the discontinuities within the 3D DLO and presents a multi‐slicing strategy, which naturally avoids the overlapping and crossing of different discontinuities. Furthermore, the formulation of the 3D discontinuity considering a shape of an arbitrary convex polygon is introduced, permitting the efficient assembly of the global constraint matrix. The proposed method eliminates unnecessary discontinuities in 3D DLO, making it possible to apply 3D DLO for solving large‐scale engineering problems such as those involving landslides. Numerical examples including a footing test, a 3D landslide and a punch indentation are considered, illustrating the effectiveness of the presented method. © 2016 The Authors. International Journal for Numerical and Analytical Methods in Geomechanics published by John Wiley & Sons Ltd. 相似文献
11.
Displacement ring load Green's functions for saturated porous transversely isotropic tri‐material full‐space 下载免费PDF全文
下载免费PDF全文 Based on the Biot's poroelastic theory and using scalar potential functions both the ring load and point load displacement Green's functions for a transversely isotropic saturated porous full‐space composed of an upper half‐space, a finite thickness middle layer and a lower half‐space is analytically presented for the first time. It is assumed that each region consists of a different transversely isotropic material. The equations of poroelastodymanics in terms of the solid displacements and the pore fluid pressure are uncoupled with the help of two scalar potential functions, so that the governing equations for the potential functions are either a second order wave equation or a repeated wave‐heat transfer equation of sixth order. With the aid of Fourier expansion with respect to circumferential direction and Hankel integral transforms with respect to the radial direction in cylindrical coordinate system, the response is determined in the form of line integrals in the real space, followed by theorem of inverse Hankel integral transforms. The solutions degenerate to a single phase elastic material, and the results are compared with previous studies, where an excellent agreement may be observed with the results provided in the literature. Some examples of displacement Green's functions are finally given to illustrate the solution. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
12.
Jinbo Chen Robert B. Gilbert Yoo Sang Choo Peter W. Marshall James D. Murff 《国际地质力学数值与分析法杂志》2016,40(9):1321-1338
The objective of this paper is to present a simplified method to determine the pile foundation system capacity based on the lower bound theorem of plasticity. The motivations for determining the lower bound capacity are the following: (1) to evaluate the accuracy of solutions based on the upper bound method; (2) to provide a conservative and efficient solution to the system capacity; and (3) to provide information about load distribution among individual piles at the verge of failure for the pile system. The failure mechanisms for a single pile and for the pile system are assumed to be two‐dimensional. For a typical long offshore pile, the upper and lower bound analyses produce identical lateral capacities. A simplified failure surface for loads at the single pile head is proposed and verified through analysis of 16 case study piles. With this proposed failure surface for a single pile, the lower bound failure load of the pile foundation system is obtained using the elastic compensation method enhanced with the linear matching method. Comparing with the existing upper bound and finite element solutions, the proposed lower bound method is capable of accurately and efficiently predicting the ultimate capacity of a pile foundation system. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
13.
The diffusion equation governs thermal conduction and groundwater flow phenomena. In this paper, we study the two‐dimensional radial propagation of a sinusoidal perturbation radiating from a cylindrical source within an infinite slab of homogeneous material. The solution of this problem has several applications. For instance, it can be used to determine the hydraulic diffusivity of the subsurface based on measurements of the hydraulic head around a vertical well during its development. For thermal problems, it can be used to determine the thermal diffusivity based on measurements of the temperature distribution around a cylindrical heat source generating a sinusoidal power per unit length. In this paper, we present a comprehensive analytical solution of this problem and we compare these solutions with numerical solutions. Two approximate analytical solutions, which can be relevant in practice, are also presented. Finally, we give an upper bound for the survival time of the transient part of the solution and we provide an estimate of the radius of influence of the sinusoidal solicitation. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
14.
In this paper we develop analytical solutions for scratch hardness–strength relations for cohesive‐frictional materials of the Mohr–Coulomb and Drucker–Prager type. Based on the lower bound yield design approach, closed‐form solutions are derived for frictionless scratch devices, and validated against computational upper bound and elastoplastic finite element solutions. The influence of friction at the blade–material interface is also investigated, for which a simple computational optimization is proposed. Illustrated for scratch tests on cement paste, we show that the proposed solutions provide a convenient way to determine estimates of cohesion and friction parameters from scratch data, and may serve as a benchmark to identify the relevance of strength models for scratch test analysis. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
15.
A procedure for solving quasi‐static large‐strain problems by the material point method is presented. Owing to the Lagrangian–Eulerian features of the method, problems associated with excessive mesh distortions that develop in the Lagrangian formulations of the finite element method are avoided. Three‐dimensional problems are solved utilizing 15‐noded prismatic and 10‐noded tetrahedral elements with quadratic interpolation functions as well as an implicit integration scheme. An algorithm for exploiting the numerical integration procedure on the computational mesh is proposed. Several numerical examples are shown. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
16.
This paper introduces sequential limit analysis (SLA) as a method for modelling large plastic deformations of purely cohesive materials such as undrained clay. The method involves solving a series of consecutive small‐deformation plastic collapse problems using finite element limit analysis, thus ensuring high levels of accuracy, efficiency, and robustness. The techniques needed to develop an SLA implementation for two‐dimensional (plane strain) problems are described in detail, including model geometry updating routines, treatment of rigid bodies, interfaces and boundaries, and periodic remeshing and interpolation of field variables. A simple total stress‐based constitutive model is used to account for strain softening and strain rate effects. Extensive verifications and validations are performed using analytical solutions and physical model test results, comparing both collapse loads and failure mechanisms, to demonstrate the effectiveness of the SLA approach. Additional solution quality checks on the bracketing discrepancy between lower‐bound and upper‐bound limit analysis solutions, and on the incompressibility of the rigid‐plastic material, are also presented. 相似文献
17.
David Nettle Galen P. Halverson Grant M. Cox Alan S. Collins Mark Schmitz James Gehling Peter R. Johnson Khalid Kadi 《地学学报》2014,26(2):120-129
The Ediacaran Jibalah Group comprises volcano‐sedimentary successions that filled small fault‐bound basins along the NW–SE‐trending Najd fault system in the eastern Arabian‐Nubian Shield. Like several other Jibalah basins, the Antaq basin contains exquisitely preserved sedimentary structures and felsic tuffs, and hence is an excellent candidate for calibrating late Ediacaran Earth history. Shallow‐marine strata from the upper Jibalah Group (Muraykhah Formation) contain a diversity of load structures and intimately related textured organic (microbial) surfaces, along with a fragment of a structure closely resembling an Ediacaran frond fossil and a possible specimen of Aspidella. Interspersed carbonate beds through the Muraykhah Formation record a positive δ13C shift from ?6 to 0‰. U‐Pb zircon geochronology indicates a maximum depositional age of ~570 Ma for the upper Jibalah Group, consistent with previous age estimates. Although this age overlaps with that of the upper Huqf Supergroup in nearby Oman, these sequences were deposited in contrasting tectonic settings on opposite sides of the final suture of the East African Orogen. 相似文献
18.
An analytical solution is proposed for transient flow and deformation coupling of a fluid‐saturated poroelastic medium within a finite two‐dimensional (2‐D) rectangular domain. In this study, the porous medium is assumed to be isotropic, homogeneous, and compressible. In addition, the point sink can be located at an arbitrary position in the porous medium. The fluid–solid interaction in porous media is governed by the general Biot's consolidation theory. The method of integral transforms is applied in the analytical formulation of closed‐form solutions. The proposed analytical solution is then verified against both exact and numerical results. The analytical solution is first simplified and validated by comparison with an existing exact solution for the uncoupled problem. Then, a case study for pumping from a confined aquifer is performed. The consistency between the numerical solution and the analytical solution confirms the accuracy and reliability of the analytical solution presented in this paper. The proposed analytical solution can help us to obtain in‐depth insights into time‐dependent mechanical behavior due to fluid withdrawal within finite 2‐D porous media. Moreover, it can also be of great significance to calibrate numerical solutions in plane strain poroelasticity and to formulate relevant industry norms and standards. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
19.
When tunneling is carried out beneath the groundwater table, hydraulic boundary is altered, resulting in seepage entering into the tunnel. The development of flow into the tunnel induces seepage stresses in the ground and the lining is subjected to additional loads. This can often cause fine particles to move, which clog the filter resulting in the long‐term hydraulic deterioration of the drainage system. However, the effect of seepage force is generally not considered in the analysis of tunnel. While several elastic solutions have been proposed by assuming seepage in an elastic medium, stress solutions have not been considered for the seepage force in a porous elasto‐plastic medium. This paper documents a study that investigates the stress behavior, caused by seepage, of a tunnel in an elasto‐plastic ground and its effects on the tunnel and ground. New elasto‐plastic solutions that adopt the Mohr–Coulomb failure criterion are proposed for a circular tunnel under radial flow conditions. A simple solution based on the hydraulic gradient obtained from a numerical parametric study is also proposed for practical use. It should be noted that the simple equation is useful for acquiring additional insight into a problem on a tunnel under drainage, because only a minimal computational effort is needed and considerable economic benefits can be gained by using it in the preliminary stage of tunnel design. The proposed equations were partly validated by numerical analysis, and their applicability is illustrated and discussed using an example problem. Comments on the tunnel analysis are also provided. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
20.
An alternative approach for quasi‐static large deformation analysis of saturated porous media using meshfree method 下载免费PDF全文
下载免费PDF全文 An alternative coupled large deformation formulation combined with a meshfree approach is proposed for flow–deformation analysis of saturated porous media. The formulation proposed is based on the Updated Lagrangian (UL) approach, except that the spatial derivatives are defined with respect to the configuration of the medium at the last time step rather than the configuration at the last iteration. In this way, the Cauchy stresses are calculated directly, rendering the second Piola–Kirchhoff stress tensor not necessary for the numerical solution of the equilibrium equations. Moreover, in contrast with the UL approach, the nodal shape function derivatives are calculated once in each time step and stored for use in subsequent iterations, which reduces the computational cost of the algorithm. Stress objectivity is satisfied using the Jaumann stress rate, and the spatial discretisation of the governing equations is achieved using the standard Galerkin method. The equations of equilibrium are satisfied directly, and the nonlinear parts of the system matrix are derived independent of the stresses of the medium resulting in a stable numerical algorithm. Temporal discretisation is effected based on a three‐point approximation technique that avoids spurious ripple effects and has second‐order accuracy. The radial point interpolation method is used to construct the shape functions. The application of the formulation and the significance of large deformation effects on the numerical results are demonstrated through several numerical examples. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献