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1.
The finite element method (FEM) and the boundary element method (BEM) are two well established numerical methods used for the analysis of underground openings. The advantages of both the methods are utilized by adopting FEBEM in which finite elements are coupled with boundary elements. A coupling procedure is presented in this paper. In using FEBEM, the effect of the location of interface boundary between finite element and boundary element regions, effect of Poisson's ratio and effect of stress ratio are discussed. It is shown that Poisson's ratio and stress ratio have significant effect on the accuracy of the results. Different discretization schemes are discussed to study their effect on accuracy and computation time. The use of different material properties in the FE region is presented. A comparative study is made with FEM for all the cases. It is shown that use of FEBEM is more advantageous than FEM.  相似文献   

2.
The bonded discrete element model (DEM) is a numerical tool that is becoming widely used when studying fracturing, fragmentation, and failure of solids in various disciplines. However, its abilities to solve elastic problems are usually overlooked. In this work, the main features of the 2D bonded DEM which influence Poisson's ratio and Young's modulus, and accuracy when solving elastic boundary value problems, are investigated. Outputs of numerical simulations using the 2D bonded DEM, the finite element method, a hyper elasticity analysis, and the distinct lattice spring model (DLSM) are compared in the investigation. It is shown that a shear interaction (local) factor and a geometric (global) factor are two essential elements for the 2D bonded DEM to reproduce a full range of Poisson's ratios. It is also found that the 2D bonded DEM might be unable to reproduce the correct displacements for elastic boundary value problems when the represented Poisson's ratio is close to 0.5 or the long-range interaction is considered. In addition, an analytical relationship between the shear stiffness ratio and the Poisson's ratio, derived from a hyper elasticity analysis and applicable to discontinuum-based models, provides good agreement with outputs from the 2D bonded DEM and DLSM. Finally, it is shown that the selection of elastic parameters used the 2D bonded DEM has a significant effect on fracturing and fragment patterns of solids.  相似文献   

3.
Analytical solutions are presented for fluid‐saturated linear poroelastic beams under pure bending. The stress‐free boundary condition at the lateral surfaces is satisfied in the St Venant's sense and the Beltrami–Michell compatibility conditions are resolved rigorously, rendering the flexure of the beams analytically tractable. Two sets of formulations are derived based on the coupled and uncoupled diffusion equations respectively. The analytical solutions are compared with three‐dimensional finite element simulations. Both sets of analytical formulations are capable of capturing exactly both the initial (undrained) and the steady‐state (fully drained) deflection of the beams. However, the analytical solutions are found to be deficient during the transient phase. The cause for the deficiency of the transient analytical solutions is discussed. The accuracy of the analytical solutions improves as Poisson's ratio and the compressibility of the constituents of the porous beam increase, where the St Venant's edge effect at the lateral surfaces is mitigated. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

4.
The displacement formulation of the finite element method is well suited to the analysis of elasto-plasticity problems involving compressible material behaviour, but it is well known that numerical difficulties occur when the material is incompressible or nearly incompressible. The effect of these additional constraints depends on both element formulation and mesh topology. A two-dimensional plane strain finite element formulation suitable for the solution of problems involving large strains and displacements (but small rotations) based on the isoparametric approach is described. The kinematics of deformation are defined in terms of the Eulerian strain rates that are invariably used in small strain analysis; the formulation therefore retains some of the character of small strain theory but includes additional geometrically non-linear terms. The results of a series of plane strain finite element analyses of two cylindrical expansion problems are presented. These results confirm the previously observed trend that as Poisson's ratio approaches 0·5 then the quality of the calculated stress deteriorates. The study also indicates that the solution quality depends increasingly on mesh topology as perfect incompressibility is reached.  相似文献   

5.
The paper presents an approach for characterizing pavement materials using the modified linear elastic behaviour. The secant modulus of elasticity is expressed in terms of the stress invariants and an expression for the secant Poisson's ratio is derived using path independence of the total work along a closed loading cycle. Triaxial test results of granular base–subbase materials which exhibit strong non-linear behaviour and dilatancy are analysed and presented. The constitutive law is included in a finite element program and results of pavement analyses are discussed. It is found that the secant Poisson's ratio of granular base materials reaches values between 0·6 and 0·7, indicating a volume increase under high stress ratios. The pavement response predicted using the above material characterization is compatible with non-destructive test results.  相似文献   

6.
An analytical solution is presented for the stress and strain fields in a Mohr–Coulomb material in plane strain around a circular hole when it is compressed by an axisymmetric far-field pressure. It is shown that several solutions arise involving one to three plastic zones depending on the values of Poisson's ratio and the friction angle. The solution chosen for presentation was obtained and used to validate the functioning of the Mohr–Coulomb yield condition that was added to the NONSAP finite element code. Stress and strain field comparisons are made.  相似文献   

7.
刘会波  陈俊涛  肖明 《岩土力学》2008,29(Z1):297-302
基于Visual C#2008.NET开发环境,利用AutoCAD ActiveX技术,对AutoCAD2008进行二次开发,开发出快速建立初始地应力场反演计算三维有限元模型的面向对象程序,通过该程序可以根据需要自动读取一定范围内的网格节点地面高程,能够为有限元模型变地面线处理直接利用,避免了常规人工读取CAD地面高程的繁琐性和误差较大的问题,极大地提高了工作效率和准确性,快速便捷。可以快速自动建立用于初始地应力反演计算的有限元网格模型,该模型能够较好地反映地形貌地的起伏状况,为有限元计算提供了良好的基础条件。  相似文献   

8.
It has been known that classical continuum mechanics laws fail to describe strain localization in granular materials due to the mathematical ill‐posedness and mesh dependency. Therefore, a non‐local theory with internal length scales is needed to overcome such problems. The micropolar and high‐order gradient theories can be considered as good examples to characterize the strain localization in granular materials. The fact that internal length scales are needed requires micromechanical models or laws; however, the classical constitutive models can be enhanced through the stress invariants to incorporate the Micropolar effects. In this paper, Lade's single hardening model is enhanced to account for the couple stress and Cosserat rotation and the internal length scales are incorporated accordingly. The enhanced Lade's model and its material properties are discussed in detail; then the finite element formulations in the Updated Lagrangian Frame (UL) are used. The finite element formulations were implemented into a user element subroutine for ABAQUS (UEL) and the solution method is discussed in the companion paper. The model was found to predict the strain localization in granular materials with low dependency on the finite element mesh size. The shear band was found to reflect on a certain angle when it hit a rigid boundary. Applications for the model on plane strain specimens tested in the laboratory are discussed in the companion paper. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

9.
Combining a geological model with a geomechanical model, it generally turns out that the geomechanical model is built from units that are at least a 100 times larger in volume than the units of the geological model. To counter this mismatch in scales, the geological data model's heterogeneous fine-scale Young's moduli and Poisson's ratios have to be “upscaled” to one “equivalent homogeneous” coarse-scale rigidity. This coarse-scale rigidity relates the volume-averaged displacement, strain, stress, and energy to each other, in such a way that the equilibrium equation, Hooke's law, and the energy equation preserve their fine-scale form on the coarse scale. Under the simplifying assumption of spatial periodicity of the heterogeneous fine-scale rigidity, homogenization theory can be applied. However, even then the spatial variability is generally so complex that exact solutions cannot be found. Therefore, numerical approximation methods have to be applied. Here the node-based finite element method for the displacement as primary variable has been used. Three numerical examples showing the upper bound character of this finite element method are presented.  相似文献   

10.
A highly efficient technique is presented for the finite element analysis of stresses around underground openings surrounded by an infinite extent of linearly elastic rock mass. The effect of unbounded rock is incorporated in the analysis by using elastic supports around the finite element model. Expressions for stiffnesses of the elastic supports are derived and these are found to depend on the location of elastic supports, the shear modulus and Poisson's ratio of the rock, and the ratio of horizontal to vertical initial stresses. With the use of the proposed technique, the extent of the finite domain to be considered in the analysis is highly reduced. This results in a great computational advantage. The other principal merit of the proposed technique is that a standard finite element code for stress analysis may be used without making any modification. Results of some numerical tests are reported to demonstrate the effectiveness and efficiency of the proposed method. The technique has the potential of being applied to more complex problems of unbounded domains in geomechanics.  相似文献   

11.
One of the important factors that lead to errors in settlement predicitions is the degree of precision in obtaining the soil parameters. Most mathematical methods for reliability modelling offered to date in the area of geomechanics are based on the classical probabilistic approach, in which soil properties are treated as random variables. In this paper, a model based on the theory of fuzzy sets is presented to take account of the uncertainty in the soil behaviour. This proposed method considers the elastic modulus and Poisson's ratio as two fuzzy numbers in the elastic matrix. An example is given to show the possibility distributions of the displacements and the stresses at some locations in the soil medium. By means of a fuzzy inference scheme, the total possibility distributions or total membership functions of the finite element results may be obtained by considering the estimated error resulting from the mesh discretization.  相似文献   

12.
As a hybrid method, the nodal‐based discontinuous deformation analysis (NDDA) greatly improves the stress accuracy within each DDA block by coupling a well‐defined finite element mesh inside the DDA block; at the same time, the NDDA inherits the unique block kinematics of the standard DDA method. Each finite element mesh line inside the DDA block is treated as a potential crack, which enables the transformation of the block material from continuum to discontinuum through the tensile and shear fracturing mechanism. This paper introduces a double minimization procedure into the NDDA method to further improve the accuracy of the stresses evaluated at the finite element mesh lines and thus to obtain a more realistic fracture model. Three numerical examples are employed to demonstrate the improved stress accuracy by the implemented double minimization procedure and the accuracy and capability of the enhanced NDDA method in capturing brittle fracturing process. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

13.
In this paper a finite element formulation for a linear viscoelastic ageing material is developed. It is shown that these equations can be solved in the from of an eigenvalue expansion thus reducing the problem to the solution of a set of Volterra Integral equations. An alternative method of solution based on expansion in terms of an operator related to Poisson's ratio is also developed and this solution method is found to significantly reduce the computational effort necessary in the solution of aproblem.  相似文献   

14.
Perhaps the most widely used non-linear elastic soil behaviour law uses the hyperbolic functions to define tangent modulus and Poisson's ratio versus strain.1,2 This paper presents the results of analytical studies with the hyperbolic elastic finite element technique for the prediction of static earth pressures against a 10-story basement wall. Carefully performed laboratory tests of the backfill material and measurements of earth pressures during backfilling provided the basis fora, refinement of the current hyperbolic elastic method. The refined analysis resulted in closer agreement of calculated earth pressures with measured values.  相似文献   

15.
This paper investigates two aspect of the direct simple shear (DSS) using three-dimensional finite element analysis. Firstly, the different total stress paths followed by DDS devices that impose constant cross-sectional area using a stiff external boundary, and those that use a constant total stress lateral boundary condition are explored. This is done by conducting finite element analysis of a single cubic element. It is shown that this element may be subjected to perfect simple shear using four different boundary condition types. Each boundary condition type results in the same effective stress path, but different total stress paths and excess pore pressures. The boundary condition types are related to DSS devices in use. The second aspect investigated is the fact that no DSS device can impose true simple shear conditions, as they are unable to generate the required complementary shear stress on the vertical boundaries. Full three-dimensional finite element analysis of a UWA/Berkeley type simple shear device, which has a constant total stress lateral boundary, is then presented. The results are compared to the ideal solution and effects of stress non-homogeneity on the friction angle and undrained shear strength, deduced from a standard interpretation, are established.  相似文献   

16.
This paper presents a rigorous analysis for the static interaction of a cylindrical thin‐walled pile with an inhomogeneous isotropic elastic half‐space under vertical, horizontal, and torsional forces individually applied at the top of pile. The inhomogeneity is specified with the exponential variation of shear modulus along depth of the embedding medium, and the Poisson's ratio is assumed to be constant. By means of a set of Green's functions for pile and soil medium and satisfying the compatibility conditions between the 2 interacting media, the formulation is reduced to coupled Fredholm integral equations. Using the adaptive‐gradient elements, capable of capturing the singular stress transfer at both ends of the pile, a numerical procedure is developed and utilized for evaluating the relevant integral equations and studying the inhomogeneity effect on the soil‐pile interaction responses. The analysis results have been validated for different soil‐pile modulus ratios under axial load and for a Poisson's ratio of 0.3 under lateral load. The procedure does not consider the nonlinear behavior of the soil medium or plastic yielding in the pile section, and the impact of the unreliable results for the case of high Poisson's ratio is not examined.  相似文献   

17.
The present paper investigates bifurcation analysis based on the second‐order work criterion, in the framework of rate‐independent constitutive models and rate‐independent boundary‐value problems. The approach applies mainly to nonassociated materials such as soils, rocks, and concretes. The bifurcation analysis usually performed at the material point level is extended to quasi‐static boundary‐value problems, by considering the stiffness matrix arising from finite element discretization. Lyapunov's definition of stability (Annales de la faculté des sciences de Toulouse 1907; 9 :203–274), as well as definitions of bifurcation criteria (Rice's localization criterion (Theoretical and Applied Mechanics. Fourteenth IUTAM Congress, Amsterdam, 1976; 207–220) and the plasticity limit criterion are revived in order to clarify the application field of the second‐order work criterion and to contrast these criteria. The first part of this paper analyses the second‐order work criterion at the material point level. The bifurcation domain is presented in the 3D stress space as well as 3D cones of unstable loading directions for an incrementally nonlinear constitutive model. The relevance of this criterion, when the nonlinear constitutive model is expressed in the classical form (dσ = Mdε) or in the dual form (dε = Ndσ), is discussed. In the second part, the analysis is extended to the boundary‐value problems in quasi‐static conditions. Nonlinear finite element computations are performed and the global tangent stiffness matrix is analyzed. For several examples, the eigenvector associated with the first vanishing eigenvalue of the symmetrical part of the stiffness matrix gives an accurate estimation of the failure mode in the homogeneous and nonhomogeneous boundary‐value problem. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

18.
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.  相似文献   

19.
A new approach is proposed for identifying elastic constants for orthotropic material bodies by using the boundary element method. The material parameters which must be determined are two Young's moduli, a shear modulus and two Poisson's ratios. The method is applied to geotechnical engineering problems.  相似文献   

20.
Owing to imperfect boundary conditions in laboratory soil tests and the possibility of water diffusion inside the soil specimen in undrained tests, the assumption of uniform stress/strain over the sample is not valid. This study presents a qualitative assessment of the effects of non‐uniformities in stresses and strains, as well as effects of water diffusion within the soil sample on the global results of undrained cyclic simple shear tests. The possible implications of those phenomena on the results of liquefaction strength assessment are also discussed. A state‐of‐the‐art finite element code for transient analysis of multi‐phase systems is used to compare results of the so‐called ‘element tests’ (numerical constitutive experiments assuming uniform stress/strain/pore pressure distribution throughout the sample) with results of actual simulations of undrained cyclic simple shear tests using a finite element mesh and realistic boundary conditions. The finite element simulations are performed under various conditions, covering the entire range of practical situations: (1) perfectly drained soil specimen with constant volume, (2) perfectly undrained specimen, and (3) undrained test with possibility of water diffusion within the sample. The results presented here are restricted to strain‐driven tests performed for a loose uniform fine sand with relative density Dr=40%. Effects of system compliance in undrained laboratory simple shear tests are not investigated here. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

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