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1.
An infinite dilatant elastic–plastic soil mass contains a single cylindrical or spherical cavity within which a slowly increasing pressure is applied. The removal of the cavity pressure takes place after a partly plastic state of the soil has been reached. Closed form solutions for the stress and displacement fields in the soil during any stage of the unloading process are derived. The non-associated Mohr–Coulomb yield criterion is used to account for dilation of the soil during shearing. Large strains are taken into account by adopting an appropriate strain definition within the plastically deforming region. 相似文献
2.
In this paper, a closed-form solution is presented for the stress and displacement distributions throughout a hollow cylinder subjected to uniform pressures acting on its internal and external boundary surfaces under plane strain conditions. The material is assumed to be elastoplastic, obeying a Mohr–Coulomb failure criterion, and exhibiting dilatant plastic deformation according to a non-associated flow rule. The newly developed analytical solution is verified through comparison with the solutions obtained from an infinite boundary problem (for which a closed-form solution exists), and numerical analyses using the program FLAC. The solution is also compared with the results of a borehole collapse test on a thick-walled hollow cylinder of synthetic shale. The analytical solution can be used to calculate the stress and displacement distributions around boreholes and other cylindrical cavities under both infinite and finite boundary conditions under both drained and undrained conditions. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
3.
The expansion of cylindrical and spherical cavities in sands is modelled using similarity solutions. The conventional Mohr–Coulomb failure criterion and the state parameter sand behaviour model, which enables hardening–softening, are used in the analysis. The sand state is defined in terms of a new critical state line, designed to account for the three different modes of compressive deformation observed in sands across a wide range of stresses including particle rearrangement, particle crushing and pseudoelastic deformation. Solutions are generated for cavities expanded from zero and finite radii and are compared to those solutions where a conventional critical state line has been used. It is shown that for initial states typical of real quartz sand deposits, pseudoelastic deformation does not occur around an expanding cavity. Particle crushing does occur at these states and causes a reduction in the stress surrounding the cavity. This has major implications when using cavity expansion theory to interpret the cone penetration test and pressuremeter test. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
4.
The problem of the symmetric quasi‐static large‐strain expansion of a cavity in an infinite granular body is studied. The body is assumed to be dry or fully drained so that the presence of the pore water can be disregarded. Both spherical and cylindrical cavities are considered. Numerical solutions to the boundary value problem are obtained with the use of the hypoplastic constitutive relation calibrated for a series of granular soils. As the radius of the cavity increases, the stresses and the density on the cavity surface asymptotically approach limit values corresponding to a so‐called critical state. For a given soil, the limit values depend on the initial stresses and the initial density. A comparison is made between the solutions for different initial states and different soils. Applications to geotechnical problems such as cone penetration test and pressuremeter test are discussed. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
5.
An analytical solution of cavity expansion in two different concentric regions of soil is developed and investigated in this paper. The cavity is embedded within a soil with finite radial dimension and surrounded by a second soil, which extends to infinity. Large‐strain quasi‐static expansion of both spherical and cylindrical cavities in elastic‐plastic soils is considered. A non‐associated Mohr–Coulomb yield criterion is used for both soils. Closed‐form solutions are derived, which provide the stress and strain fields during the expansion of the cavity from an initial to a final radius. The analytical solution is validated against finite element simulations, and the effect of varying geometric and material parameters is studied. The influence of the two different soils during cavity expansion is discussed by using pressure–expansion curves and by studying the development of plastic regions within the soils. The analytical method may be applied to various geotechnical problems, which involve aspects of soil layering, such as cone penetration test interpretation, ground‐freezing around shafts, tunnelling, and mining. © 2014 The Authors. International Journal for Numerical and Analytical Methods in Geomechanics published by John Wiley & Sons Ltd. 相似文献
6.
Finite strain elastoplastic solutions for the undrained ground response curve in tunnelling 
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下载免费PDF全文 The instantaneous response of saturated low permeability grounds to tunnel excavation is important for deformations and stability close to the tunnel face. It is characterized by zero volume change in combination with the development of excess pore pressures. In tunnelling through poor quality ground under great depth of cover and high in situ pore pressure, heavily squeezing conditions (characterized by very large convergences) may occur soon after excavation. This paper presents exact finite strain analytical solutions for the undrained ground response around cylindrical and spherical openings that are unloaded from uniform and isotropic initial stress states, on the basis of the Modified Cam Clay (MCC) model and the Mohr–Coulomb (MC) model. The solution for a Drucker–Prager material is also given as it requires only a very small modification to the MC solution. The so‐called ground response curve, that is, the relationship between the support pressure and the cavity wall displacement, is derived in closed form for the MC model. The solution for the MCC problem is semi‐analytical in that it uses the trapezium rule for the computation of a definite integral. The influence of the significant parameters of the problem on the predicted deformation behaviour is shown by means of dimensionless charts. Finally, the practical usefulness of the solutions presented is illustrated by applying them to the breccia zones of the planned Gibraltar Strait tunnel – an extreme case of weak, low permeability ground under high pore pressure. The solutions can serve as a trustworthy benchmark for numerical procedures that incorporate material and geometric nonlinearities. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
7.
A large strain analysis of undrained expansion of a spherical/cylindrical cavity in a soil modelled as non‐linear elastic modified Cam clay material is presented. The stress–strain response of the soil is assumed to obey non‐linear elasticity until yielding. A power‐law characteristic or a hyperbolic stress–strain curve is used to describe the gradual reduction of soil stiffness with shear strain. It is assumed that, after yielding, the elasto‐plastic behaviour of the soil can be described by the modified Cam clay model. Based on a closed‐form stress–strain response in undrained condition, a numerical solution is obtained with the aid of simple numerical integration technique. The results show that the stresses and the pore pressure in the soil around an expanded cavity are significantly affected by the non‐linear elasticity, especially if the soil is overconsolidated. The difference between large strain and small strain solutions in the elastic zone is not significant. The stresses and the pore pressure at the cavity wall can be expressed as an approximate closed‐form solution. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
8.
In this article we present closed‐form solutions for the undrained variations in stress, pore pressure, deformation and displacement inside hollow cylinders and hollow spheres subjected to uniform mechanical pressure instantaneously applied to their external and internal boundary surfaces. The material is assumed to be a saturated porous medium obeying a Mohr–Coulomb model failure criterion, exhibiting dilatant plastic deformation according to a non‐associated flow rule which accounts for isotropically strain hardening or softening. The instantaneous response of a porous medium submitted to an instantaneous loading is undrained, i.e. without any fluid mass exchange. The short‐term equilibrium problem to be solved is now formally identical to a problem of elastoplasticity where the constitutive equations involve the undrained elastic moduli and particular equivalent plastic parameters. The response of the model is presented (i) for extension and compression undrained triaxial tests, and (ii) for unloading problems of hollow cylinders and spheres through the use of appropriately developed closed‐form solutions. Numerical results are presented for a plastic clay stone with strain hardening and an argilite with strain softening. The effects of plastic dilation, of the strain softening law and also of geometry of the cavity on the behaviour of the porous medium have been underlined. Analytical solutions provide valuable benchmarks enabling various numerical methods in undrained conditions with a finite boundary to be verified. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
9.
A cavity expansion–based solution is proposed in this paper for the interpretation of CPTu data under a partially drained condition. Variations of the normalized cone tip resistance, cone factor, and undrained-drained resistance ratio are examined with different initial specific volume and overconsolidation ratio, based on the exact solutions of both undrained and drained cavity expansion in CASM, which is a unified state parameter model for clay and sand. A drainage index is proposed to represent the partially drained condition, and the critical state after expansion and stress paths of cavity expansion are therefore predicted by estimating a virtual plastic region and assuming a drainage-index–based mapping technique. The stress paths and distributions of stresses and specific volume are investigated for different values of drainage index, which are also related to the penetration velocity with comparisons of experimental data and numerical results. The subsequent consolidation after penetration is thus predicted with the assumption of constant deviatoric stress during dissipation of the excess pore pressure. Both spherical and cylindrical consolidations are compared for dissipation around the cone tip and the probe shaft, respectively. The effects of overconsolidation ratio on the stress paths and the distributions of excess pore pressure and specific volume are then thoroughly investigated. The proposed solution and the findings would contribute to the interpretation of CPTu tests under a random drained condition, as well as the analysis of pile installation and the subsequent consolidation. 相似文献
10.
将土骨架视为具有分数阶导数本构关系的黏弹性体,基于Biot两相饱和介质模型,建立具有球形空腔饱和分数导数黏弹性土体稳态振动的控制方程。通过引入势函数,得到球对称情形下具有球形空腔饱和分数导数黏弹性土体的位移、应力和孔隙流体压力等解析表达式。考察分数导数模型参数和饱和土参数等对土体振动特性的影响,结果表明,流体压缩性对饱和土体的动力特性有显著影响,而土骨架压缩性和流-固耦合系数的影响相对较小;分数导数阶数对土体动力特性的影响与材料参数比的取值有关。同时,边界不排水条件下饱和土体的动力响应大于排水条件下饱和土体的动力响应。 相似文献
11.
M. A. Hicks 《国际地质力学数值与分析法杂志》2000,24(5):453-476
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. 相似文献
12.
Cavity expansion in finite or infinite media has important practical implications in many engineering areas. In this study, we investigate the elastic unloading and reverse yielding behaviours of cylindrical and spherical cavities in a bounded cohesive–frictional medium. Of particular interest is the critical state when reverse yielding in the hollow cylinder/sphere is imminent in relation to the cavity pressure, the cavity dimensions, as well as the material properties. The critical pressure and optimal thickness that lead to strengthening of the hollow cylinder/sphere by so-called “overstrain” have been determined analytically. Both quantities are found to be explicit functions of the frictional angle of the material. The study considers the Mohr–Coulomb criterion and the bounded medium, which include both Tresca and purely frictional materials as special cases and, at the same time, can be readily extended to the case of an infinite medium. Finally, the results are applied to the interpretation of pressuremeter tests in soils, weak rocks and cemented sands. 相似文献
13.
Boundary value problems for hardening/softening soils, such as Cam-Clay, usually require the extensive use of finite element methods. Here analytical and semi-analytical solutions for the undrained expansion of cylindrical and spherical cavities in critical state soils are presented. The strain is finite, the initial cavity radius is arbitrary and the procedure applicable to any isotropically hardening materials. In all cases only simple quadratures are involved, and in the case of the original Cam-Clay a complete analytical solution can be found. In addition to providing models of the behaviour of displacement piles and pressuremeters these results also provide valuable benchmark solutions for verifying various numerical methods. 相似文献
14.
This paper studies the excavation of a spherical cavity subjected to hydrostatic initial stresses in the infinite homogeneous and isotropic rock mass with strain‐softening Mohr–Coulomb (M‐C) and Hoek–Brown (H‐B) behaviors. Numerical solutions of the spherical cavity are obtained and the application to determining stress–strain curve of strain‐softening M‐C and H‐B rock mass is studied. A closed‐form solution for the elastic–brittle–plastic medium is introduced first, and then a numerical procedure that simplifies the strain‐softening process into a series of brittle–plastic ones is presented. The approach is validated against the facts that the strain‐softening process evolves into a brittle–plastic one when the softening slope is very steep, whereas it evolves into an elasto‐plastic one when the softening slope approaches zero. Numerical solutions for the prediction of displacements and stresses around the spherical cavity in the strain‐softening M‐C and H‐B rock mass are presented. On the basis of the analysis of the spherical cavity in strain‐softening rock mass, the stress–strain relationship at an infinitesimal cube around the cavity is obtained and discussed with different evolution laws for the strength parameters considered. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
15.
A rigorous semi‐analytical solution for undrained cylindrical cavity expansion in critical state soils 下载免费PDF全文
下载免费PDF全文 Apostolos Vrakas 《国际地质力学数值与分析法杂志》2016,40(15):2137-2160
This paper presents a generalized, rigorous and simple large strain solution for the undrained expansion of a vertical cylindrical cavity in critical state soils using a rate‐based plasticity formulation: the initial stress field is taken as anisotropic, that is with horizontal stresses that differ from the vertical stress, and the soil is assumed to satisfy any two‐invariant constitutive model from the critical state (Cam‐clay) family; no simplifying assumption is made during the mathematical derivation; calculating the effective stresses around the cavity requires the solution of a nonlinear equation by means of the Newton–Raphson method in combination with quadrature. Cavity expansion curves and stress distributions in the soil are then presented for different critical state models (including the modified Cam‐clay model). The solution derived can be useful for estimating the instantaneous response of saturated low‐permeability soils around piles and self‐boring pressuremeters and can serve as trustworthy benchmark for numerical analysis codes. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
16.
A simple incremental model describing the pre-failure behaviour of granular soils is presented. The model describes both the dry/fully drained and undrained response. It takes into account an initial anisotropy of soil and an initial state defined as either contractive or dilative. A physically sound definition of loading/unloading is assumed, which differs from elasto-plastic approaches. The model is based on extensive empirical data and gives predictions conformable with experimental results. It also describes pre-failure instabilities of granular soils, both dry/fully drained and undrained. The Hill’s criterion was used to examine stability. It was shown that this condition can be formulated either in terms of the effective stresses or by the total stresses. In the extreme cases of either dry/fully drained or undrained conditions, these alternative formulations are equivalent. This is not so in the case of partial drainage of pore water and associated volumetric deformations as well as pore pressure changes. The model describes the pre-failure instabilities well, and additionally allows for analytical derivation of the instability line. It was shown that the second order work, appearing in the Hill’s condition, is equivalent to the entropy source. 相似文献
17.
The disturbance of a clay mass, due to either the installation of a driven pile or the expansion of a pressuremeter membrane, is often modelled as a cylindrical cavity expansion. In addition, it is usual (and convenient) to assume that the expansion occurs under conditions of plane strain. For this problem a method of analysis is presented which considers the soil to be a saturated two-phase material with a pore fluid which flows according to Darcy's Law. Non-linearity in material behaviour is permitted as long as the effective stress–strain law can be written in an incremental or rate form. The use of a consolidation analysis allows the changes in effective stress and pore pressure to be determined at any stage during both the cavity expansion and the subsequent period of reconsolidation. Expansions may occur at any prescribed rate, including the very fast (undrained) and the very slow (fully drained) case. The technique is illustrated by considering the expansion of a cavity in two different types of elastoplastic soil. It is shown how these solutions may be used to model the disturbance of the soil due to pile driving. 相似文献
18.
Large strain similarity solution for a spherical or circular opening excavated in elastic‐perfectly plastic media 下载免费PDF全文
下载免费PDF全文 K.H. Park 《国际地质力学数值与分析法杂志》2015,39(7):724-737
This paper deals with the unloading problem of a spherical or circular opening excavated in elastic‐perfectly plastic media with a nonassociated Mohr–Coulomb yield criterion. A large strain similarity solution, using incremental velocity approach, is presented by replacing partial differential equations from stress equilibrium, constitutive law, consistency condition, and displacement equation with first‐order ordinary differential equations. The classical Runge–Kutta method is used to solve the first‐order ordinary differential equations. Comparisons among small and large strain solutions are made using some data sets of soil and rock. The results show that the displacements by large strain similarity solution are smaller than those by exact small strain solution and somewhat larger than those by large strain solution using total strain approach. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
19.
The ground response to tunnel excavation is usually described in terms of the characteristic line of the ground (also called ‘ground response curve’, GRC), which relates the support pressure to the displacement of the tunnel wall. Under heavily squeezing conditions, very large convergences may take place, sometimes exceeding 10–20% of the excavated tunnel radius, whereas most of the existing formulations for the GRC are based on the infinitesimal deformation theory. This paper presents an exact closed‐form analytical solution for the ground response around cylindrical and spherical openings unloaded from isotropic and uniform stress states, incorporating finite deformations and linearly elastic‐perfectly plastic rock behaviour obeying the Mohr–Coulomb failure criterion with a non‐associated flow rule. Additionally, the influence of out‐of‐plane stress in the case of cylindrical cavities under plane‐strain conditions is examined. The solution is presented in the form of dimensionless design charts covering the practically relevant parameter range. Finally, an application example is included with reference to a section of the Gotthard Base tunnel crossing heavily squeezing ground. The expressions derived can be used for preliminary convergence assessments and as valuable benchmarks for finite strain numerical analyses. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
20.
Shear‐lag analysis is used to obtain closed‐form solutions for the problem of a stiff inclusion embedded in a poroelastic soil matrix. The following assumptions are made: the soil matrix and the inclusion are elastic; plane strain conditions apply; and shear stresses at the soil‐inclusion interface follow Coulomb's friction law. Two solutions are obtained, the first one for drained conditions where no excess pore pressures are generated, and the second one for undrained conditions where excess pore pressures are produced and the soil does not change volume during pullout. The solutions are verified by comparing analytical predictions with numerical results obtained using a finite element method. Predictions from the analytical solutions are also compared with results from experiments conducted in a large‐scale pullout box. Both comparisons show good agreement. The analytical solution shows that the pullout capacity in drained and undrained conditions is overall independent of the relative stiffness of the soil and the inclusion. The most important factor controlling the pullout capacity is the coefficient of friction between the soil and the inclusion. Both drained and undrained pullout capacities increase with the coefficient of friction; although the drained capacity shows a proportional increase, it is not so for the undrained capacity. The ratio of undrained to drained pullout capacity is about 0.9 for friction coefficients smaller than 0.2, but can be as small as 0.6 for a coefficient of friction of 1.0. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献