Finite element analyses of layered visco‐elastic system under vertical circular loading

Analyses for the response of a linear visco‐elastic system subjected to axi‐symmetric vertical circular loading are presented. Hankel transforms with respect to the radial spatial coordinate are used to reduce the three‐dimensional problem to that involving only a single spatial dimension, which is then discretized using the finite element method. Three techniques are employed to handle the time factor in the visco‐elastic material: (i) direct time integration; (ii) Fourier transforms; and (iii) Laplace transforms. These methods are compared and evaluated through their numerical results. Copyright © 2007 John Wiley & Sons, Ltd.     

饱和土中弹性波在双椭圆孔洞周围的散射

利用复变函数法和多极坐标法,研究了饱和土中弹性波在双椭圆孔洞周围的散射及动应力集中的问题。首先通过引入位移势函数,将二维稳态条件下Biot波动方程解耦成势函数所满足的3个Helmholtz方程, 根据分离变量方法即可得Helmholtz方程在柱坐标下势函数的通解。利用土骨架和孔隙水的边界条件,确定波函数展开式中的未知系数,进而得到位移、应力和孔压的表达式。给出了弹性波对2个椭圆形孔洞的动应力集中系数的数值结果,并讨论了波数和孔距变化对动应力集中系数和孔压集中系数的影响。     

Boundary element analysis of Biot consolidation in layered elastic soils

Biot's linear consolidation analysis of three-dimensional fluid saturated layered soils is investigated. The time marching method, uncoupled boundary element method, and successive stiffness method are applied for the numerical modelling of this study. Settlement induced by surface loading and land subsidence due to pumping is studied. The results show that settlement induced by surface loading is mainly influenced by the properties of the soil layer, and that the settlement is larger for soil layers with smaller stiffness and greater thicknesses. The land subsidence induced by pumping is influenced by the properties of the soil layer as well as by the permeability of the pumped layer and the conditions at the top and bottom boundaries. The land subsidence is larger for soil layers with a smaller stiffness, lower permeability of the pumped layer, deeper pumping depth, larger pumping rate and an impervious top surface.     

A discrete element approach to elastic properties of layered geomaterials

Discrete element methods (DEMs) are used for layered geomaterials to investigate the dependency of traditional engineering constants on material properties and loading conditions. Shear deformations and compression tests parallel and perpendicular to layering are conducted on samples of varying kerogen volume fractions, confining pressures, porosities, and layer geometries. The goal of this article is to develop a method to better characterize oil shale (a transversely isotropic layered geomaterial) while eliminating high experimental costs. The DEM simulations conducted in this study demonstrate strong dependencies of Young's modulus, Poisson's ratio, and shear modulus on kerogen volume fraction and porosity. Furthermore, a rule of thumb for layer thickness and particle resolution is proposed for simulation design. Results agree well with robust effective medium theories, solidify the ability of DEM to model the mechanical properties of layered heterogenous materials, and encourage the use of DEM to study more complicated layered media and material failure. Copyright © 2011 John Wiley & Sons, Ltd.     

A simple boundary equation technique for elastic stress analysis of underground cavities

Summary A boundary integral equation approach is illustrated which does not require the solution of singular integrals in order to compute the coefficients of the final system of linear equations. This characteristic allows the carrying out of all the necessary integrations by means of numerical techniques, leading to a rather simple and compact solution algorithm. In addition the approach permits the evaluation of a measure of the error affecting the numerical solution. The stability and the accuracy of the procedure, which is based on the minimization of the difference between known boundary tractions and corresponding numerically derived stresses, are discussed with reference to some rock engineering problems and it is shown that the approach is particularly suitable for stress analyses related to underground openings. To get some insight into the overall performance of the procedure, the results obtained in the analysis of a tunneling problem of practical interest are compared with those deriving from a standard Finite Element calculation.     

Wave scattering and diffraction of subsurface cavities in layered half-space for incident SV-P and SH waves

A novel approach is proposed to deal with the problem of wave scattering and diffraction of subsurface cavities embedded in stratified half-space. The subsurface cavity with complex surroundings is treated as a substructure. The continuity condition at the interface between the substructure and the far field of stratified half-space is maintained by applying a free-field approach. As the boundary of the free-field ground is regular, the construction of the dynamic matrices and the evaluation of the wave input on the interface become considerably easier. Based on the previous work with some improvement, a novel approach for evaluation of Green's functions in stratified half-space is presented. The wave equation is decoupled into the one for SV-P wave components and the other one for SH wave component. The precise integration technique ensures high accuracy of the solution of wave equations. The layer merging technique and the dual form equation make it possible to obtain Green's function in closed-form solution of matrix equations. Numerical examples validate accuracy and efficiency of the proposed approach.     

用弹性板理论分析顺层岩质边坡的失稳

根据弹性板的稳定理论，利用能量法对缓倾角顺层岩质边坡的弯曲失稳机理进行了探讨，特别考虑了边坡长度的影响，推导了相应的计算公式，并通过计算实例，将文中的方法与用平面应变问题的弹性梁分析得出的结果做了对比，验证了文中方法的可行性。     

弹性矩形板下横观各向同性多层地基分析

利用弹性矩形板与多层地基表面的竖向位移协调条件与光滑接触条件,由横观各向同性多层地基应力与位移非耦合的传递矩阵解,推导出弹性矩形板下竖向应力和位移的解析解。在此基础上,编制了相应的程序,并进行了数值计算。计算结果表明：矩形板刚度对板底竖向位移及板中心下的竖向应力有着较为显著的影响;板底竖向位移及板中心下的竖向应力随着板刚度的增加而减小,相同荷载作用下横观各向同性地基与均匀各向同性地基模型的计算结果差异较大,实际工程中很有必要采用更符合土体性质的横观各向同性地基模型     

Shape detection of multiple subsurface cavities by particle filtering with elastic wave propagation

A numerical technique for detecting the number and shape of subsurface cavities is presented, applying the particle filter and the parametric level set method to elastic wave propagation under the ground. When subsurface cavities exist, the elastic wave propagating in the ground is reflected at the boundary faces of the cavities. Observing the velocity of the reflection wave at the surface of a ground that includes multiple cavities and parameterizing the shape of the cavities by the parametric level function, both the number and the shape of the cavities can be identified by the particle filter. Numerical experimentation for detecting multiple cavities is conducted with synthetic observation data. The results show that the proposed technique enables the number of cavities to be identified by the number of peaks in the posterior probabilistic distribution function and solves geometric inverse problems by estimating the shape of the cavities through the parameter identification of the level set function.     

层状地基上弹性地基梁的有限元-边界元耦合分析

将地基视为多层各向同性弹性体,对Euler-Bernoulli梁进行有限单元离散分析,对地基-梁接触面采用边界积分法求解,根据地基-梁接触面的竖向位移协调和光滑接触条件,应用有限元与边界元耦合的方法推导出各向同性成层弹性地基上的Euler-Bernoulli梁的半数值半解析解。基于文中理论,编制了相应的程序,通过与现有文献对比,验证了文中理论的正确性,对比分析了分层地基与等效均匀地基两种模型上的弹性地基梁。研究结果表明,分层地基与等效均匀地基两种模型上弹性地基梁性状差异较大,实际弹性地基梁计算中应采用分层地基模型。     

Boundary element elastic analysis of layered soils by a successive stiffness method

The elastostatic analysis of layered systems (such as a soil consisting of a set of L individually homogeneous strata) is tackled here on the basis of discretized boundary integral equations (boundary element method). By exploiting the peculiar chain-like pattern of the system, a recursive formula is obtained which generates economically a ‘stiffness matrix’ of the first n layers (from bottom) at the upper interface with the subsequent layer (n = 1…L). The ‘successive stiffness’ method proposed is shown to imply noteworthy advantages with respect to both the standard boundary element method by zones (or subregions) and another ad hoc, earlier method resting on a boundary element approach combined with the transfer matrix concept. This conclusion is corroborated by two-dimensional examples.     

Buckling of layered elastic media: A cosserat-continuum approach and its validation

In this paper the stability of layered, anisotropic, hypoelastic media under initial stress is investigated. The bifurcation problem is formulated and solved numerically by use of a semi-analytical transfer matrix method. An alternative analytical approach in dealing with inhomogeneous media is developed by representing a periodically layered medium as a homogeneous Cosserat continuum. The Cosserat-continuum approach is validated against the numerical transfer matrix solution.     

考虑成层弹性地基固结的污染物运移模型

文章在多层地基固结理论与污染物运移理论相结合的基础上,提出了污染物在成层弹性地基中运移的一维数学模型,其最大特点是考虑了土体受力变形对污染物运移的影响,然后给出了所建模型的解析解,并将计算结果与太湖疏浚污染底泥堆场的实测结果作了比较分析。结果表明堆场的地基土层对太湖疏浚底泥中的污染物具备足够的阻隔能力,在堆场的使用年限内不会对周围环境造成二次污染。实际天然防渗层中以成层土居多,故推导出的污染物在成层土中运移模型具有重要的工程价值和现实意义。     

Finite element analysis of consolidation of layered clay soils using an elastic visco-plastic model

This paper presents a general one-dimensional (1-D) finite element (FE) procedure for a highly non-linear 1-D elastic visco-plastic (1-D EVP) model proposed by Yin and Graham for consolidation analysis of layered clay soils. In formulating the 1-D FE procedure, a trapezoidal formula is used to avoid the unsymmetry of the stiffness matrix for a Newton (modified Newton) iteration scheme. Unlike many other 1-D FE approaches in which the initial in situ stresses (or stress/strain states) are considered indirectly or even not considered, the initial in situ stress/strain states are taken into account directly in this paper. The proposed FE procedure is used for analysis of 1-D consolidation of a clay with published test results in the literature. The FE modelling results are in good agreement with the measured results. The FE model and procedure is then used to analyse the consolidation of a multi-layered clay soils with a parametric study on the effects of the variations of creep parameters in Yin and Graham's 1-D EVP model. It is found that the creep parameters ψ/V and t₀ have significant influence on the compression and porewater pressure dissipation. For some boundary conditions, changes of parameters in one layer will have some effects on the consolidation behaviour of another layer due to the different consolidation rates. Finally, the importance of initial stress/strain states is illustrated and discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

A superposition scheme to obtain fundamental boundary element solutions in multi‐layered elastic media

A superposition scheme is proposed to obtain a fundamental solution for boundary elements in multi‐layered elastic media. A three‐layered elastic region is obtained by superposing two sets of bonded half‐planes and subtracting one infinite plane. Therefore, the solution for an element in a layered media can be expressed in terms of bonded half‐plane solutions and an infinite‐plane solution. The major advantages of this superposition scheme are: (1) it is unnecessary to introduce elements at the interface, (2) it can be extended to higher‐order element, and (3) it may be applicable to three dimensions easily. The accuracy and performance of the developed model is illustrated by two examples. For the problem of a pressurized two‐dimensional crack within a three‐layered system, the comparison with other numerical results shows the model is quite accurate and efficient. The model is also used for a study of a practical two‐dimensional mining problem in South Africa, i.e. stoping through a dyke with material properties different from the host rock. Copyright © 2000 John Wiley & Sons, Ltd.     

Requirements for the performance of a ground-penetrating radar system in searching for cavities

The requirements for the performance of a ground-penetrating radar (GPR) system for detecting subsurface cavities are analyzed by numerical modeling of the GPR problem. The algorithm used to solve the forward GPR problem is approximated to a real experiment with regard to the design of the GPR system, the parameters of the source and receiver, and their position relative to the medium under study and its inhomogeneity. We calculated the spatiotemporal distribution of the field of the detected signal from a pulse source located at the interface between the medium and a cavity anomaly of a given geometry. The results were used to estimate the dynamic range of the GPR system necessary for determining the anomaly. We also performed GPR surveys of low-contrast inhomogeneities (cavities in mines) using GROT 12 GPR systems and analyzed the survey results by numerical modeling. It is shown that the GPR performance required to detect and locate inhomogeneities of interest at a certain sounding depth can be estimated in the experiment design phase.     

On the use of infinite elements in the analysis of two-dimensional layered elastic systems via discretized integral equations

A boundary integral equation approach is presented for the two-dimensional plane strain analysis of horizontally layered elastic systems resting on a rough and rigid base. The validity of Somigliana identity for unbounded layers is discussed and an Infinite Boundary Element is proposed in order to take into account the lateral unboundedness of the physical problem in the discretized equations. This element is implemented in a computer code based on a successive stiffness solution procedure. A series of numerical tests concerning single- and multi-layered problems is illustrated, and the performance of the proposed solution method is compared with that of more traditional boundary element and finite element techniques.     

Frictional contact of laminated elastic half‐spaces allowing interface cavities. Part 2: Numerical results

The paper presents some numerical results of the problem on contact of stratified elastic half‐spaces possessing unevenness of their surface layers. The approach of the Jacobi polynomials is used to reduce the singular integral equation of the problem to a system of linear algebraic equations. On the basis of the system's solution the dependence of gaps' geometric characteristics on external load and friction is investigated for two types of initial boundary disturbances, namely a local symmetric recess and a periodic set of recesses at a flat boundary. Numerical results are presented in figures for a few elastic and geometric parameters of joint components. The analysis shows that elastic properties and geometric structure of a laminated half‐space have a significant influence on the shape of interface gaps and their location. Copyright © 2001 John Wiley & Sons, Ltd.     

Frictional contact of laminated elastic half‐spaces allowing interface cavities. Part 1: Analytical treatment

The paper deals with the plane problem on frictional contact of stratified elastic half‐spaces provided discontinuity of their direct touch. Imperfectness of contact of the bodies is assumed to be caused by surface unevenness of their surface layers. The problem is formulated within the framework of the homogenized model with microlocal parameters. Using the method of complex potentials in combination with the method of interface gaps the problem is reduced to a singular integral equation on the function of interface gap height. Copyright © 2001 John Wiley & Sons, Ltd.     

Settlements and stresses of multi‐layered grounds and improved grounds by equivalent elastic method

The investigation of equivalent elastic method is made to predict settlements and stresses of multi‐layered grounds and improved grounds. Analytical models to represent the heterogeneous elastic properties of layers in vertical and horizontal directions for multi‐layered grounds and improved grounds are proposed in taking into account the equivalent elastic modulus and the equivalent thickness. By introducing the equivalent thickness derived from Terzaghi's formula of the vertical stress, the equivalent elastic method of using the equivalent elastic modulus and the equivalent thickness is applied to the formulations concerning immediate settlements and vertical stresses in multi‐layered grounds and improved grounds. Comparison is performed between rigorous solutions and simulations for immediate settlements and vertical stresses in multi‐layered grounds and improved grounds. It is found that the proposed method is able to describe properly the characteristics of distributions for settlements and vertical stresses in multi‐layered grounds and improved grounds. Copyright © 2007 John Wiley & Sons, Ltd.