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1.
Axisymmetric thermal consolidation of multilayered porous thermoelastic media due to a heat source 
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下载免费PDF全文 This paper presents an analytical layer element solution to axisymmetric thermal consolidation of multilayered porous thermoelastic media containing a deep buried heat source. By applying the Laplace–Hankel transform to the state variables involved in the basic governing equations of porous thermoelasticity, the analytical layer elements that describe the relationship between the transformed generalized stresses and displacements of a finite layer and a half‐space are derived. The global stiffness matrix equation is obtained by assembling the interrelated layer elements, and the real solutions in the physical domain are achieved by numerical inversion of the Laplace–Hankel transform after obtaining the solutions in the transformed domain. Finally, numerical calculations are performed to demonstrate the accuracy of this method and to investigate the influence of heat source's types, layering, and the porous thermoelastic material parameters on thermal consolidation behavior. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
2.
A numerically efficient and stable method is developed to analyze Biot's consolidation of multilayered soils subjected to non‐axisymmetric loading in arbitrary depth. By the application of a Laplace–Hankel transform and a Fourier expansion, the governing equations are solved analytically. Then, the analytical layer‐element (i.e. a symmetric stiffness matrix) describing the relationship between generalized displacements and stresses of a layer is exactly derived in the transformed domain. Considering the continuity conditions between adjacent layers, the global stiffness matrix of multilayered soils is obtained by assembling the inter‐related layer‐elements. Once the solution in the Laplace–Hankel transformed domain that satisfies the boundary conditions has been obtained, the actual solution can be derived by the inversion of the Laplace–Hankel transform. Finally, numerical examples are presented to verify the theory and to study the influence of the layered soil properties and time history on the consolidation behavior. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
3.
Transient dynamic response of multilayered saturated media subjected to impulsive loadings 下载免费PDF全文
下载免费PDF全文 This paper presents a stable and efficient method for calculating the transient solution of layered saturated media subjected to impulsive loadings by means of the analytical layer element method. Starting with the field equations based on Biot's linear theory for porous, fluid‐saturated media, and the seepage continuity equation, an analytical layer element for a single layer is established by applying Laplace‐Hankel integral transform. The global stiffness matrix in the transform domain for a layered saturated half‐space subjected to a transient circular patch loading is obtained by assembling the layer elements of each layer. The displacements in the time domain are derived by Laplace‐Hankel inverse transform of the global stiffness matrix. Numerical examples are conducted to verify the accuracy of the method and to demonstrate the influences of type of transient loading, buried depth of loading, permeability, and stratification of materials on the transient response of the multilayered saturated poroelastic media. 相似文献
4.
A novel procedure associated with the precise integration method (PIM) and the technique of dual vector is proposed to effectively calculate the magnitude and distribution of deformations in a homogeneous multilayered transversely isotropic medium. The planes of transverse isotropy are assumed to be parallel to the horizontal surface of the soil system. The linearly elastic medium is subjected to four types of vertically acting axisymmetric loads prescribed either at the external surface or in the interior of the soil medium. There are no limits for the thicknesses and number of soil layers to be considered. By virtue of the governing equations of motion and the constitutive equations of the transversely isotropic elastic body, and based on the Hankel integral transform and a dual vector formulation in a cylindrical coordinate system, the partial differential motion equations can be converted into first‐order ordinary differential matrix equations. Applying the approach of PIM, it is convenient to obtain the solutions of ordinary differential matrix equations for the continuously homogeneous multilayered transversely isotropic elastic soil in the transformed domain. The PIM is a highly accurate algorithm to solve the sets of first‐order ordinary differential equations, which can ensure to achieve any desired accuracy of the solutions. What is more, all calculations are based on the standard method with the corresponding algebraic operations. Computational efforts can be reduced to a great extent. Finally, numerical examples are provided to illustrate the accuracy and effectiveness of the proposed approach. Some more cases are analyzed to evaluate the influences of the elastic parameters of the transversely isotropic media on the load‐displacement responses. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
5.
We develop a new numerical model based on a precise integration method to investigate the coupled thermo-mechanical performance of layered transversely isotropic media around a cylindrical/tubular heat source. To obtain the relational matrices of the extended precise integration method, we first convert the governing equations of the problem into ordinary differential matrix equations through the Laplace–Hankel transform. Then, the cylindrical heat source is divided into a series of plane heat sources, and the plane temperature load term is added to the state vector between layer elements. By combining the layer elements, we build a layered transversely isotropic numerical model containing a cylindrical heat source in the transformed domain. Finally, we solve the model in the transformed domain and obtain the solution of the problem in the real domain through the Laplace–Hankel transform inversion. The accuracy of this method is verified by comparing the solutions with the results of the analytical method and the finite element method. Then, we study the influence of the anisotropy of thermal parameters, the embedded depth, the length/radius ratio, the type of heat source and the stratification of the medium on the thermo-mechanical coupled performance.
相似文献6.
多层横观各向同性地基轴对称固结的传递矩阵解 总被引：2，自引：1，他引：1
从横观各向同性地基轴对称Biot固结的基本方程出发,通过关于t的Laplace变换和关于r的Hankel变换,得到关于z的一阶常微分方程组。然后,对变换域内的基本未知量进行线性化处理,建立了变换域内的基本状态变量在z = 0处和任意深度处z的显式关系。利用传递矩阵法,结合层间连续性条件和边界条件,得到了多层横观各向同性地基的Biot固结轴对称问题的解答。该解答能避免随着层数增加而需要求解大型方程组的困难,明显地提高了计算效率。 相似文献
7.
After the application of a Laplace–Hankel transform, the governing equations of Biot’s consolidation are solved analytically by using the eigenvalue approach. Then the analytical layer-element of a single soil layer can be obtained in the transformed domain by synthesizing the generalized displacements and stresses, which are both expressed by six arbitrary constants. The elements of the analytical layer-element only contain negative exponential functions, which leads to a considerable improvement in computation efficiency and stability. The global stiffness matrix equation of multilayered soils is further obtained by assembling the interrelated layer-elements, and the actual solution is achieved by numerical inversion of the Laplace–Hankel transform after the solution in the transformed domain is obtained. Numerical examples are given to demonstrate the accuracy of this method and to study the influence of the layered soil properties and time history on the consolidation behavior. 相似文献
8.
三维横观各向同性成层地基的传递矩阵解 总被引：1，自引：0，他引：1
通过解耦变换推导出三维直角坐标系下横观各向同性地基的非耦合状态方程;利用双重Fourier变换以及Cayley-Hamilton定理得到了单层地基的传递矩阵;结合边界条件和层间连续条件进而得其传递矩阵解。编制了相应程序并进行了数值计算与分析,结果表明：数值结果与已有文献结果十分吻合,地基的横观各向同性性质与成层性质对受荷地基中竖向位移和应力的影响较为显著。 相似文献
9.
Extended precise integration method for axisymmetric thermo‐elastic problem in transversely isotropic material 下载免费PDF全文
下载免费PDF全文 This paper presents a numerical solution for the analysis of the axisymmetric thermo‐elastic problem in transversely isotropic material due to a buried heat source by means of extended precise integral method. By virtue of the Laplace–Hankel transform applied into the basic governing equations, an ordinary differential matrix equation is achieved, which describes the relationship between the generalized stresses and displacements in transformed domain. An extended precise integration method is introduced to solve the aforementioned matrix equation, and the actual solution in the physical domain is acquired by inverting the Laplace–Hankel transform. Numerical examples are carried out to demonstrate the accuracy of the proposed method and elucidate the influence of the character of transverse isotropy, the anisotropy of linear expansion coefficient, the anisotropy of thermal diffusivity, and medium's stratification on the thermo‐elastic response. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
10.
This paper presents the analytical layer‐element method to analyze the consolidation of saturated multi‐layered soils caused by a point sink by considering the anisotropy of permeability. Starting from the governing equations of the problem, the solutions of displacements and stresses for a single soil layer are obtained in the Laplace–Hankel transformed domain. Then, the analytical layer‐element method is utilized to further derive the solutions for the saturated multi‐layered soils in the transformed domain by combining with the boundary conditions of the soil system and continuity conditions between adjacent layers. The actual solutions in the physical domain can be acquired by the inversion of Laplace–Hankel transform. Numerical results are carried out to show the accuracy and stability of the proposed method and evaluate the influence of sink depth and anisotropic permeability on excess pore pressure and surface settlement. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
11.
This paper presents an exact analytical solution to fully coupled axisymmetric consolidation of a semi‐infinite, transversely isotropic saturated soil subjected to a uniform circular loading at the ground surface. The analysis is under the framework of Biot's general theory of consolidation. First, the governing equations of consolidation are transformed into a set of equivalent partial differential equations with the introduction of two auxiliary variables. These partial differential equations are then solved using Hankel–Laplace integral transforms. Once solutions in the transformed domain have been obtained, the actual solutions in the physical domain for displacements and stress components of the solid matrix, pore‐water pressure and fluid discharge can be finally obtained by direct numerical inversion. The accuracy of the numerical solutions developed is confirmed by comparison with an existing exact solution for an isotropic and saturated soil that is a special case of the more general problem addressed. Numerical analyses are also presented to investigate the influence of the degree of material anisotropy on the consolidation settlement. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
12.
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 相似文献
13.
多层地基非轴对称Biot固结的理论解 总被引：1，自引：1，他引：0
提出了一种新方法来推导多层地基非轴对称Biot固结问题的传递矩阵,相应的理论推导工作量较少。基于柱坐标系下非轴对称Biot固结的基本方程,通过引入中间变量,并对坐标 进行Fourier级数展开,对时间 和坐标 进行Laplace-Hankel变换,得到了6×6阶和2×2阶的两组常微分方程;然后,两组常微分方程进行关于 的Laplace变换和逆变换,得到了单层地基非轴对称Biot固结问题的传递矩阵;结合边界条件和连续条件,运用传递矩阵法得到多层地基非轴对称Biot固结问题在Laplace-Hankel变换域内的解,通过Laplace-Hankel逆变换得到了该问题物理域的真实解答。编制了计算程序,并进行了数值计算与分析。该方法具有计算速度较快的特点,方便工程应用。 相似文献
14.
基于Biot固结理论,运用解析层元方法求解竖向简谐荷载作用下二维层状饱和地基的动力响应问题。从直角坐标平面应变问题控制方程出发,通过Fourier-Laplace变换将偏微分方程组转化为常微分方程组,求解得到单层饱和地基的解析层元。结合层间连续条件和边界条件,组装得到多层饱和地基的总刚度矩阵方程,进而求得变换域内的解。借助Fourier-Laplace逆变换的数值积分方法,获得平面应变动力问题在物理域内的解,编制了相应的计算程序,其计算结果与已有文献结果吻合较好。通过算例分析了荷载圆频率、荷载作用深度及地基成层性对地基竖向位移的影响。计算结果表明：随荷载圆频率的增大,地基竖向位移先增加后减小;地基竖向位移在荷载作用点处呈现波峰,且受表层土性的影响较大。 相似文献
15.
An analytical solution is presented in this paper to study the time‐dependent settlement behaviour of a rigid foundation resting on a transversely isotropic saturated soil layer. The governing equations for a transversely isotropic saturated soil, within Biot's poroelasticity framework, are solved by means of Laplace and Hankel transforms. The problem is subsequently formulated in the Laplace transform domain in terms of a set of dual integral equations that are further reduced to a Fredholm integral equation of the second kind and solved numerically. The developed analytical solution is validated via comparison with the existing analytical solution for an isotropic saturated soil case, and adopted as a benchmark to examine the sensitivities of the mesh refinement and the locations of truncation boundaries in the finite element simulations using ABAQUS. Particular attention is paid to the influences of the degree of soil anisotropy, boundary drainage condition, and the soil layer thickness on the consolidation settlement and contact stress of the rigid foundation. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
16.
Influence of a point sink on a pile group in saturated multilayered soils with anisotropic permeability 下载免费PDF全文
下载免费PDF全文 The behavior of a pile group is solved using the finite element method, and the fundamental solution of saturated multilayered soils with anisotropic permeability is obtained by the analytical layer element method. Based on the supposition of no slip occurring at the pile‐soil interface, the governing equations of the interaction between the pile group and the soils due to a point sink are established in the Laplace‐Hankel transformed domain by considering the pile‐soil compatibility condition. Numerical results are presented to study the effect of point sink pumping, the properties of soils, and the geometries of piles on the behavior of the pile group. 相似文献
17.
We rederive and present the complete closed-form solutions of the displacements and stresses subjected to a point load in a transversely isotropic elastic half-space. The half-space is bounded by a horizontal surface, and the plane of transverse isotropy of the medium is parallel to the horizontal surface. The solutions are obtained by superposing the solutions of two infinite spaces, one acting a point load in its interior and the other being free loading. The Fourier and Hankel transforms in a cylindrical co-ordinate system are employed for deriving the analytical solutions. These solutions are identical with the Mindlin and Boussinesq solutions if the half-space is homogeneous, linear elastic, and isotropic. Also, the Lekhnitskii solution for a transversely isotropic half-space subjected to a vertical point load on its horizontal surface is one of these solutions. Furthermore, an illustrative example is given to show the effect of degree of rock anisotropy on the vertical surface displacement and vertical stress that are induced by a single vertical concentrated force acting on the surface. The results indicate that the displacement and stress accounted for rock anisotropy are quite different for the displacement and stress calculated from isotropic solutions. © 1998 John Wiley & Sons, Ltd. 相似文献
18.
Steady‐state analytical solutions of flow and deformation coupling due to a point sink within a finite fluid‐saturated poroelastic layer 下载免费PDF全文
下载免费PDF全文 An exact steady‐state closed‐form solution is presented for coupled flow and deformation of an axisymmetric isotropic homogeneous fluid‐saturated poroelastic layer with a finite radius due to a point sink. The hydromechanical behavior of the poroelastic layer is governed by Biot's consolidation theory. Boundary conditions on the lateral surface are specifically chosen to match the appropriate finite Hankel transforms and simplify the transforms of the governing equations. Ordinary differential equations in the transformed domain are solved, and then the analytical solutions in the physical space for the pore pressure and the displacements are finally obtained by using finite Hankel inversions. The analytical solutions at some special locations such as the top and bottom surfaces, lateral surface, and the symmetrical axis are given and analyzed. And a case study for the consolidation of a water‐saturated soft clay layer due to pumping is conducted. The analytical solution is verified against the finite element solution. Meanwhile, an analysis of coupled hydromechanical behavior is carried out herein. The presented analytical solution is an exact solution to the practical poroelastic problem within an axisymmetric finite layer. It can provide us a better understanding of the poroelastic behavior of the finite layer due to fluid extraction. Besides, it can be applied to calibrate numerical schemes of axisymmetric poroelasticity within finite domains. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
19.
在考虑横观各向同性含液饱和多孔介质固体骨架和流体可压缩性以及固体骨架的黏弹性特征下,基于横观各向同性含液饱和多孔介质u-w形式的三维动力控制方程,以固相位移u、液相相对位移w为基本未知量,综合运用Laplace变换、双重Fourier变换等方法,在直角坐标系下通过引入中间变量,将六元2阶动力控制方程组化为两组各含4个未知变量的常微分方程组,给出了直角坐标系下横观各向同性含液饱和多孔介质三维黏弹性动力反应的积分形式一般解;作为理论推导的验证,通过引入初始条件和边界条件,对横观各向同性含液饱和多孔介质半空间黏弹性瞬态反应问题进行了求解。解答的退化验证表明,所推导的理论解是正确的。 相似文献
20.
列车荷载下轨道系统-层状横观各向同性饱和地基动力响应 总被引：4，自引：0，他引：4
基于Biot波动理论,构建列车荷载-轨道系统-双层状横观各向同性饱和地基模型,将模型分为上覆路轨系统和地层系统。对上覆路轨系统和地层系统处理,并利用双重Fourier变换技术,在变换域中将横观各向同性饱和地基动力响应的求解简化为求解一个6阶控制方程的特征值问题,进而得到了列车荷载作用下双层横观各向同性饱和地基力响应的解析结果。利用离散Fourier逆变换得到数值计算结果,重点分析了上下土层的刚度和泊松比对位移和孔隙水压力和剪切应力响应的影响,结果表明,上、下土层刚度差异对地基动力响应有较大影响,土层各向异性参数中模量的影响较泊松比大。计算结果可为软土路基加固深度的确定提供理论依据。 相似文献