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1.
In view of rapid developments in iterative solvers, it is timely to re‐examine the merits of using mixed formulation for incompressible problems. This paper presents extensive numerical studies to compare the accuracy of undrained solutions resulting from the standard displacement formulation with a penalty term and the two‐field mixed formulation. The standard displacement and two‐field mixed formulations are solved using both direct and iterative approaches to assess if it is cost‐effective to achieve more accurate solutions. Numerical studies of a simple footing problem show that the mixed formulation is able to solve the incompressible problem ‘exactly’, does not create pressure and stress instabilities, and obviate the need for an ad hoc penalty number. In addition, for large‐scale problems where it is not possible to perform direct solutions entirely within available random access memory, it turns out that the larger system of equations from mixed formulation also can be solved much more efficiently than the smaller system of equations arising from standard formulation by using the symmetric quasi‐minimal residual (SQMR) method with the generalized Jacobi (GJ) preconditioner. Iterative solution by SQMR with GJ preconditioning also is more elegant, faster, and more accurate than the popular Uzawa method. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
2.
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
3.
This paper identifies imbalanced columns (or rows) as a significant source of ill‐conditioning in the preconditioned coefficient matrix using the standard Jacobi preconditioner, for finite element solution of Biot's consolidation equations. A simple and heuristic preconditioner is proposed to reduce this source of ill‐conditioning. The proposed preconditioner modifies the standard Jacobi preconditioner by scaling the excess pore pressure degree‐of‐freedoms in the standard Jacobi preconditioner with appropriate factors. The performance of such preconditioner is examined using the symmetric quasi‐minimal residual method. To alleviate storage requirements, element‐by‐element iterative strategies are implemented. Numerical experiment results show that the proposed preconditioner reduces both the number of iteration and CPU execution time significantly as compared with the standard Jacobi preconditioner. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
4.
Finite element cavity expansion analysis investigating the effect of penetration rate on piezocone tests in clay is presented. A coupled analysis was performed, in which the rate of cavity expansion was linked to the penetration rate of the cone and the cone angle, using the assumption that the deformation was wholly radial, and took place only between the cone tip and the cone shoulder. The soil was modelled using modified cam clay with two sets of parameters and varying values of overconsolidation ratio (OCR). The influence of penetration rate on the stress and pore pressure distributions was examined. For slower penetration rates, the excess pore pressure at the cone shoulder is lower since consolidation is permitted coincident with penetration. The radial profiles of post‐penetration voids ratio demonstrate that partially drained penetration is permitted by volume change in the near field, in addition to radial movement in the far field. The radial distribution of excess pore pressure after slow penetration differs from the undrained case, with a relatively low radial gradient existing at the cone face. As a result, the dissipation curves after slow penetration lag behind those following fast penetration. The cone velocity is made dimensionless by normalizing with the coefficient of consolidation and the cone diameter. ‘Backbone’ curves of normalized velocity against normalized tip resistance and excess pore pressure capturing the transition from undrained to drained penetration are derived. The normalized pore pressure backbone curve is unique, whilst the normalized tip resistance shows a small dependency on OCR. These backbone penetration curves are compared with centrifuge model piezocone tests conducted at varying rates, and subsequent dissipation tests. The numerical and experimental results suggest that the value of consolidation coefficient operative during the dissipation phase is 2–4 times higher than the virgin compression value due to changes in the operative soil stiffness, as demonstrated from the stress paths of individual soil elements. The use of multi‐rate penetration tests to deduce values of consolidation coefficient is discussed, in light of these differences. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
5.
A general solution scheme is developed for one-dimensional and non-isothermal consolidation problems for fluid-saturated, porous, thermoelastic media. Two fundamental parameters which describe the coupling effects between thermal, hydraulic and mechanical behaviour are: ratio of thermal and hydraulic diffusivity and ratio of thermomechanical deformabilities in drained and undrained conditions. The solution scheme has been applied to the nuclear waste disposal problem. A solution for a thermoporoelastic rock mass containing a decaying heat source is presented. Numerical results show that coupling effects are most pronounced for low permeability and high porosity media such as deep compressible clays. This corresponds to a low value of the ratio of hydraulic and thermal diffusivities and a high value of the ratio of deformabilities in drained and undrained conditions. Comparison with numerical simulations taking into account the non-linear and non-reversible behaviour of the rock mass is presented. It shows that the thermoelastic model is quite correct for temperature and displacement fields, and gives maxima of the pore pressure and stress elevations. 相似文献
6.
Tests on specimens of reconstituted illitic clay have examined the influence of temperature on the mechanical behaviour of clay soils. The program involved consolidation to effective confining pressures up to 1.5 MPa, heating to 100°C, and tests on normally consolidated and overconsolidated specimens with OCR = 2. The tests included isotropic consolidation, undrained triaxial compression with pore water pressure measurement, drained tests along controlled stress paths to investigate yielding behaviour, and undrained tests which involved heating and measurement of the resulting induced pore water pressures. The large strain strength envelope is independent of temperature. However, peak undrained strengths increase with temperature because smaller pore water pressures are generated during shearing. An important contribution from the study is a series of results for the yielding of illitic clay at three different temperatures. For the first time, there is clear evidence of yield loci decreasing in size with increasing temperature. An associated flow rule can be assumed without serious error. The results contribute to the confirmation of a thermal elastic-plastic soil model developed by the authors from cam clay following the addition of a small number of extra assumptions. Depending on the initial stress state, heating under undrained conditions may produce shear failure. 相似文献
7.
为了研究上海软黏土的蠕变力学特性,开展了排水和不排水条件下上海软黏土的三轴蠕变力学试验,分析了不同围压水平、加卸荷水平对饱和软黏土蠕变特性的影响,得到了不同试验条件下上海软黏土蠕变的力学特性。试验结果表明:围压水平及加卸荷水平对软黏土蠕变变形有一定影响;土体蠕变变形特性与排水条件密切相关,排水条件下,固结效应削弱了土体蠕变现象;同等条件加载过程中不排水条件下土体变形量大,卸载后不排水条件下土体回弹较明显;不排水蠕变试验加载过程中,孔隙水压力随时间发展的变化规律与土体蠕变变形规律相似;排水蠕变试验加载过程中,固结变形和蠕变变形同时存在,排水量曲线在卸载后没有出现明显下降。 相似文献
8.
通过等压固结静、动三轴试验,研究了渤海湾粉质黏土在循环荷载作用下的动力性质和循环荷载后不排水静力性质。试验结果表明,循环应力幅值比越大,平均轴向应变和轴向应变幅值越大;循环应力幅值比达到0.4时,平均轴向应变和轴向应变幅值随着循环周数增加迅速增大;循环应力幅值比相同,固结应力越大,轴向应变幅值越大,而平均轴向应变越小。在较大的循环应力幅值比下,平均孔压比值和孔压幅值比值随着循环周数的增大会达到稳定;循环应力幅值比越大平均孔压比值和孔压幅值比值均越大;相同循环应力幅值,固结应力越大平均孔压比值越小,而固结应力对孔压幅值比值影响较小。循环荷载的作用会导致循环荷载后不排水剪在q-p’平面上有效应力路径和孔压发展表现出超固结土的性质。 相似文献
9.
长期循环荷载作用下排水条件对饱和软黏土动力特性影响 总被引：1，自引：0，他引：1
由于软黏土渗透系数很小,目前针对饱和软黏土的循环荷载试验绝大多数都是在不排水条件下进行的。但对交通荷载而言,软黏土承受经年累月的长期循环荷载作用,实际的排水条件应该是部分排水的。基于此,通过对温州原状饱和软黏土进行不同循环应力比下的不排水和部分排水大周数（50 000次）循环三轴试验,分析了长期循环荷载作用下排水条件对饱和软黏土动力特性的影响。研究结果表明与不排水条件相比,部分排水条件下软黏土试样的动力特性表现出很大的不同。随着循环次数的增加,部分排水条件下的孔压随先增加后降低,存在一个峰值;经过较大的循环次数后,回弹应变逐渐减小,应力-应变滞回圈逐渐缩短,面积也明显减小。为了准确预测交通荷载作用下的长期沉降,采用部分排水条件进行试验是十分必要的。 相似文献
10.
在三轴条件下,对饱和土（砂土和黏土）进行排水与不排水条件下的冲击试验及冲击后再固结试验,对比研究了不同渗透性土在不同排水条件下的冲击动力响应和冲击后再固结性状。结果表明：饱和黏土不排水冲击时的孔隙水压力随冲击击数增加而升高并逐渐稳定,排水冲击时的孔隙水压力则是先达到峰值然后有所下降;砂土不排水冲击时的冲击能量对孔隙水压力影响最明显;饱和砂土不排水冲击时的轴向应变与冲击击数呈近似线性关系,饱和黏土冲击及饱和砂土排水冲击则呈近二次曲线关系;饱和砂土不排水冲击后再固结阶段的孔隙水压力立即消散为0,同时体变迅速增大到一定值;饱和黏土在冲击后再固结阶段的孔隙水压力在一定时间内逐渐消散完毕,同时体变逐渐增大;饱和黏土排水冲击时,冲击阶段产生的体变占冲击引起总体变的39%～49%,冲击后再固结阶段产生的体变占51%～61%;砂土和黏土的总体变均表现为排水冲击明显大于不排水冲击,改善冲击时的排水条件有利于提高加固效果。 相似文献
11.
12.
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
13.
Experimental study of poromechanical behavior of saturated claystone under triaxial compression 总被引：1，自引：1，他引：0
This paper presents experimental results of drained and undrained triaxial compression tests of saturated Meuse–Haute/Marne claystone. The emphasis is to study the evolution of pore pressure with growth of microcracks and the effect of pore pressure on mechanical behavior. Basic mechanical responses are first investigated through drained triaxial compression tests, showing nonlinear stress strain relations, volumetric dilatancy and pressure sensitivity. In undrained triaxial compression tests, the pore pressure exhibits a transition from increase to decrease due to the transition from volumetric compressibility to dilatancy caused by the growth of microcracks. The failure surfaces, determined by total stress and Terzaghi’s effective stress under undrained condition, are compared with the one under drained condition. 相似文献
14.
Derek Elsworth 《国际地质力学数值与分析法杂志》2013,37(14):2135-2153
Rate effects are examined in the steady pore pressure distribution induced as a result of penetration of standard and ball penetrometers. The incompressible flow field, which develops around the penetrometer is used to define the approximate soil velocity field local to the penetrometer tip. This prescribes the Lagrangian framework for the migration of the fluid saturated porous medium, defining the advection of induced pore pressures relative to the pressure‐monitoring locations present on the probe face. In two separate approaches, different source functions are used to define the undrained pore fluid pressures developed either (i) on the face of the penetrometer or (ii) in the material comprising the failure zone surrounding the penetrometer tip. In the first, the sources applied at the tip face balance the volume of fluid mobilized by the piston displacement of the advancing penetrometer. Alternately, a fluid source distribution is evaluated from plasticity solutions and distributed throughout the tip process zone: for a standard penetrometer, the solution is for the expansion of a spherical cavity, and for the ball penetrometer, the solution is an elastic distribution of stresses conditioned by the limit load embedded within an infinite medium. For the standard penetrometer, the transition from drained to undrained behavior occurs over about two orders of magnitude in penetration rate for pore pressures recorded at the tip (U1) and about two‐and‐a‐half orders of magnitude for the shoulder (U2). This response is strongly influenced by the rigidity of the soil and slightly influenced by the model linking induced total stresses to pore pressures. For the ball penetrometer, the transition from drained to undrained behavior also transits two‐and‐a‐half orders of magnitude in penetration rate, although it is offset to higher dimensionless penetration rates than for standard penetration. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
15.
Constantine A. Stamatopoulos 《Landslides》2009,6(3):191-207
The paper first proposes and validates a constitutive model simulating the change of resistance along a slip surface of clay
for both the undrained and drained cases. The proposed model is based on (a) the critical state theory and (b) the assumption
that the critical state changes once failure is reached, in terms of the further shear displacement. Under undrained conditions,
the proposed model simulates the excess pore pressure generation and, subsequently, the continuous change of resistance along
the slip surface from its initial value to the peak strength and then, at large displacement, the residual value. The latter
can be measured in constant-volume ring shear tests. Then, the developed constitutive model is implemented in the multi-block
sliding system model for the prediction of the triggering and deformation of slides. The improved model is applied at the
well-documented Fourth Avenue landslide of the 1964 Alaska earthquake. 相似文献
16.
Unbounded plane stress and plane strain domains subjected to static loading undergo infinite displacements, even when the zero displacement boundary condition at infinity is enforced. However, the stress and strain fields are well behaved, and are of practical interest. This causes significant difficulty when analysis is attempted using displacement‐based numerical methods, such as the finite‐element method. To circumvent this difficulty problems of this nature are often changed subtly before analysis to limit the displacements to finite values. Such a process is unsatisfactory, as it distorts the solution in some way, and may lead to a stiffness matrix that is nearly singular. In this paper, the semi‐analytical scaled boundary finite‐element method is extended to permit the analysis of such problems without requiring any modification of the problem itself. This is possible because the governing differential equations are solved analytically in the radial direction. The displacement solutions so obtained include an infinite component, but relative motion between any two points in the unbounded domain can be computed accurately. No small arbitrary constants are introduced, no arbitrary truncation of the domain is performed, and no ill‐conditioned matrices are inverted. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
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18.
In this paper a finite volume (FV) numerical method is implemented to solve a Biot consolidation model with discontinuous coefficients. Our studies show that the FV scheme leads to a locally mass conservative approach which removes pressure oscillations especially along the interface between materials with different properties and yields higher accuracy for the flow and mechanics parameters. Then this numerical discretization is utilized to investigate different sequential strategies with various degrees of coupling including: iteratively, explicitly and loosely coupled methods. A comprehensive study is performed on the stability, accuracy and rate of convergence of all of these sequential methods. In the iterative and explicit solutions four splits of drained, undrained, fixed-stress and fixed-strain are studied. In loosely coupled methods three techniques of the local error method, the pore pressure method, and constant step size are considered and results are compared with other types of coupling methods. It is shown that the fixed-stress method is the best operator split in comparison with other sequential methods because of its unconditional stability, accuracy and the rate of convergence. Among loosely coupled schemes, the pore pressure and local error methods which are, respectively, based on variation of pressure and displacement, show consistency with the physics of the problem. In these methods with low number of total mechanical iterations, errors within acceptance range can be achieved. As in the pore pressure method mechanics time step increases more uniformly, this method would be less costly in comparison with the local error method. These results are likely to be useful in decision making regarding choice of solution schemes. Moreover, the stability of the FV method in multilayered media is verified using a numerical example. 相似文献
19.
蒋小权 《地质灾害与环境保护》2016,(1):65-69
循环荷载作用下,饱和软粘土将发生应变软化现象。通过对杭州饱和软黏土进行应力控制的循环三轴试验,研究循环次数、循环应力比、固结比、频率、超固结比对土体应变软化的影响。试验结果表明,循环次数的增加,循环应力比的提高,都将加快土体软化;循环荷载作用下,软黏土存在临界循环应力比,当循环应力比较小或较大时,软化指数与lgN近似为线性关系,而当循环应力比在临界循环应力比左右时,两者表现为明显的曲线关系。 相似文献
20.
This paper compares the compression and uplift capacity of a strip foundation from numerical coupled analyses using the Modified Cam Clay (MCC) soil model. The focus is on the failure mechanism and pore pressure development in the soil. Triaxial compression and tension tests were first modelled to develop a rigorous understanding of the pore pressure responses; then, the compression and uplift of a strip foundation were modelled. The results show that the balance of excess pore pressures due to the changes in mean total stress and deviatoric stress during the compression and uplift of a strip foundation are different, although the ultimate undrained capacities are identical. Furthermore, the resistance and excess pore pressure responses during uplift differ from those in compression under the K0-consolidated condition because of the elastic unloading. Although the failure mechanisms have identical shape and size between undrained compression and uplift, the pore pressure distribution in the soil is different and affects the load–displacement behaviours under partially drained compression and uplift. 相似文献