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1.
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
2.
The dynamic response of a rigid strip footing lying on saturated soil is greatly affected by the pore pressure induced by a rocking moment. To consider the complex behavior of the soil under the rocking load, an analytical solution for a rigid strip foundation on saturated soil under a rocking moment is developed under the framework of Biot’s coupling theory. The boundary-value problem for the governing coupling equations for saturated soil is solved using a Fourier transform to yield a pair of dual integral equations. These dual integral equations are transformed into a set of linear equations using an infinite series of orthogonal Jacobi polynomials to yield the compliance functions. In addition, a parametric study has been carried out to examine the influence of: (1) the dimensionless frequency, (2) the dynamic permeability and (3) the Poisson’s ratio on saturated soil under a rocking rigid strip footing. 相似文献
3.
对横观各向同性地基上刚性矩形板进行了求解。首先,利用表面受矩形均布荷载作用下的层状横观各向同性地基的位移解答,获得地基的柔度矩阵;然后,通过刚性矩形基础与层状横观各向同性地基的协调条件,建立刚性矩形基础与横观各向同性地基共同作用的方程,进而求得基础的地基反力。通过编制相应的程序,确定了合理的网格划分值;最后,进行算例分析,分析了地基横观各向同性性质、矩形刚性基础的长宽比以及地基分层性对地基反力的影响。分析表明：以上3种因素对地基反力有重要影响。 相似文献
4.
研究了横观各向同性饱和土地基在地表动力荷载作用下的三维瞬态响应。基于饱和多孔介质的三维Biot波动理论,利用Laplace变换,建立圆柱坐标系下横观各向同性饱和土的波动方程;解耦波动方程后,根据算子理论,并借助Fourier展开和Hankel变换技术,得到瞬态荷载作用下,饱和土介质的土骨架位移和应力、孔隙水相对位移和孔隙水压力的一般解;利用一般解,给出横观各向同性饱和地基在地表集中荷载激励下的瞬态Lamb问题的解答。数值算例结果表明,采用各向同性饱和介质的动力学模型,不能准确描述具有明显各向异性特性的饱和土地基的瞬态动力特性。 相似文献
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6.
A simplified analytical method is presented for the vertical dynamic analysis of a rigid, massive, cylindrical foundation embedded in a poroelastic soil layer. The foundation is subjected to a time‐harmonic vertical loading and is perfectly bonded to the surrounding soil in the vertical direction. The soil underlying the foundation base is represented by a single‐layered poroelastic soil based on rigid bedrock while the soil at the side of the foundation is modeled as an independent poroelastic layer composed of a series of infinitesimally thin layers. The behavior of the soil is governed by Biot's poroelastodynamic theory and its governing equations are solved by the use of Hankel integral transform. The contact surface between the foundation base and the soil is smooth and fully permeable. The dynamic interaction problem is solved following standard numerical procedures. The accuracy of the present solution is verified by comparisons with the well‐known solutions obtained from other approaches for both the elastodynamic interaction problem and poroelastodynamic interaction problem. Numerical results for the vertical dynamic impedance and response factor of the foundation are presented to demonstrate the influence of nondimensional frequency of excitation, soil layer thickness, poroelastic material parameters, depth ratio and mass ratio on the dynamic response of a rigid foundation embedded in a poroelastic soil layer. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
7.
考虑埋置基础侧面和底面地基与基础的相互作用,研究了埋置于横观各向同性饱和地基中刚性圆柱基础的扭转振动问题。假设基础侧壁与地基完全黏结,沿侧面对剪应力积分得到了侧壁地基对基础所产生的反扭矩;通过研究位于横观各向同性饱和地基上刚性圆形基础的扭转振动,求得基础底面地基作用于基础的反扭矩。结合基础底面位移和应力连续等条件,根据基础振动的动力平衡方程,求解了相应的动力响应问题。给出了基础的角位移幅值,地基的等效刚度系数和等效阻尼系数的表达式。通过算例研究了相关参数对基础扭转振动的影响。 相似文献
8.
In this paper, a coupling method between finite element and analytical layer‐elements is utilized to analyze the time‐dependent behavior of a plate of any shape and finite rigidity resting on layered saturated soils. Based on the integral transform techniques together with the aid of an order reduction method, an analytical layer‐element solution is derived from the governing equations for three‐dimensional Biot consolidation with respect to a Cartesian coordinate system and then extended to be the fundamental solution for the layered saturated soil under a point load. The Mindlin plate is modeled by eight‐noded isoparametric elements. The governing equations of the interaction between soil and plate in the Laplace‐Fourier transformed domain are deduced by referring to the coupling theory of FEM/BEM, and the final solution is obtained by applying numerical inversion. Numerical examples concerned with the time‐dependent response of a plate are performed to demonstrate the influence of soil and plate properties on the interaction process. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
9.
从常规三轴压缩试验得到横观各向同性土层的力学参数,综合9种来自于不同国家和地区的横观各向同性土层的土样参数,研究分析了横观各向同性土层参数对建筑物沉降的影响。作为典型例子,对上海一幢剪力墙结构的箱形基础与横观各向同性土进行共同作用分析,并与各向同性土层上的分析结果进行比较,结果表明：横观各向同性土层参数对沉降的影响有些不同,尤其是不排水加载条件确定的土层参数影响的结果大不相同。 相似文献
10.
上覆单相弹性层饱和地基上刚性条形基础竖向振动的混合边值问题 总被引：1，自引：0，他引：1
根据Biot动力控制方程,运用Fourier积分变换技术,并按照混合边值条件和连续条件建立了上覆单相弹性层饱和地基上刚性条形基础竖向振动的对偶积分方程,并将其退化到完全饱和地基的情形。通过引进正交多项式将对偶积分方程化为线性代数方程组,从而得到了上覆单相弹性层的饱和地基上刚性条形基础的竖向振动规律。通过算例分析得到,单相弹性层的厚度对动力柔度系数有着较大的影响,在单相弹性层厚度较小时（小于条形基础半宽的0.1）,动力柔度系数曲线与完全饱和的基本重合;完全饱和地基上刚性基础的竖向振动是上覆弹性层厚度Hn=0的特例。 相似文献
11.
运用对偶积分方程来求解层状横观各向同性地基与墙下条形基础的共同作用问题。从直角坐标平面应变问题控制方程出发,通过傅里叶（Fourier）变换和层间连续性条件,可以得到层状横观各向同性地基的传递矩阵解。基于该传递矩阵解,并利用条形基础与地基接触的混合边值条件,推导出一组关于基础挠度和地基反力的对偶积分方程。考虑墙下条形基础受到竖向集中荷载的情况,利用弹性薄板理论先求解出条形基础挠度;随后应用雅可比（Jacobi）正交多项式和级数展开的方法,将对偶积分方程转化为线性代数方程组进行求解。编制了相应的计算程序,其计算结果与有限元软件ABAQUS的结果基本吻合,从而验证了所提理论的正确性。算例分析表明,板土相对刚度与地基成层性对地基反力、地表沉降和沿z轴竖向正应力有很大的影响。 相似文献
12.
基于Biot提出的饱和土波动方程,研究了埋置于单层饱和地基中的有质量的刚性圆柱基础的竖向振动问题。运用Hankel积分变换求解饱和土基本动力方程,并考虑基础与地基接触面的混合边值条件,求得了基础底面和基础侧面的动反力,结合基础振动的动力平衡方程,得到了基础竖向振动振幅和地基等效动力刚度的表达式。数值分析结果表明：下卧基岩饱和地基的等效动力刚度和基础振动振幅都呈现出明显的波动现象,土层厚度、基础埋深比、基础质量比对埋置基础的竖向振动有很大影响。 相似文献
13.
横观各向同性饱和土体三维粘弹性动力分析 总被引：2，自引：2，他引：0
采用针对横观各向同性饱和土体u-w形式三维粘弹性动力方程,考虑土骨架的粘弹性性质且基于粘弹性理论,通过运用Fourier 展开、Laplace 和Hankel 积分变换方法和引入中间变量,将含有粘弹性参数的六元二阶偏微分运动控制方程组,化为2组各含4个未知变量的常微分方程组,从而给出了柱坐标系下粘弹性横观各向同性饱和土体在非轴对称动力荷载作用下的瞬态反应的土骨架位移分量、孔隙流体相对于土骨架的位移分量瞬态反应一般解。在此基础上,引入初始条件和边界条件,对垂直向和水平向动力荷载作用下半空间边值问题进行了求解。根据动力时域解答的一般解,利用Laplace和Hankel 数值逆变换技术,编制了相应的数值计算程序。并进行了实例验证和弹性、粘弹性解的对比分析。结果表明,在进行横观各向同性饱和土体动力分析时,考虑土骨架的粘弹性是必要的。 相似文献
14.
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
15.
基于Terzaghi一维固结理论,分析了考虑半透水边界条件的分数阶导数黏弹性饱和土层在随时间变化的任意荷载作用下一维固结问题。首先,应用Laplace变换联立求解饱和土层一维固结微分方程和分数阶Kelvin-Voigt黏弹性本构方程,推导出有效应力和沉降在Laplace变换域内的解析解,采用Crump方法进行Laplace逆变换,得到了时间域内的半解析解。然后将本文得到的半解析解分别退化为半透水边界条件下基于黏弹性假设的一维固结半解析解和双面透水边界条件下基于分数阶黏弹性假设的一维固结半解析解,结果与已有文献的半解析解相同,验证了本研究所提出解的可靠性。最后通过算例分别考察了半透水边界参数、分数阶黏弹性模型参数和荷载参数对饱和土层固结沉降的影响。研究表明,半透水边界条件参数、分数阶次与黏滞系数主要影响饱和土层固结的发展快慢,而饱和土层的最终沉降量主要受到土层压缩模量的影响;另外,饱和土层的固结规律与外荷载变化规律一致。 相似文献
16.
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17.
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
18.
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
19.
Influence of a point sink on a pile group in saturated multilayered soils with anisotropic permeability 
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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
20.
Morteza Eskandari‐Ghadi Ammar Mirzapour Azizollah Ardeshir‐Behrestaghi 《国际地质力学数值与分析法杂志》2011,35(14):1587-1603
In this paper, forced rocking vibration of a rigid circular disc placed in a transversely isotropic full‐space, where the axis of material symmetry of the full‐space is normal to the surface of the plate, is analytically investigated. Because of using the Fourier series and Hankel integral transforms, the mixed boundary‐value problem is transformed into two separate pairs of integral equations called dual integral equations. The dual integral equations involved in this paper are reduced to Fredholm integral equations of the second kind. With the aid of contour integration, the governing integral equation is numerically evaluated in the general dynamic case. The reduced static case of the dual integral equations is solved analytically and the vertical displacement, the contact pressure and the static impedance/compliance function are explicitly determined, and it is shown that the pressure in between the plate and the full‐space and the compliance function reduced for isotropic half‐space are identical to the previously published solutions. The dynamic contact pressure in between the disc and the space and also the related impedance function are numerically evaluated in general dynamic case and illustrated. It is shown that the singularity exists in the contact pressure at the edge of the disc is the same as the static case. To show the effect of material anisotropy, the numerical evaluations are given for some different transversely isotropic materials and compared. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献