轴对称多层可压缩渗透各向异性岩基固结分析

从轴对称固结基本方程出发,通过对时间t、坐标r的Laplace-Hankel变换,再对坐标z的Laplace变换,得到三元一次方程组,解此方程组,并进行Laplace逆变换,得到了单层可压缩渗透各向异性岩基轴对称固结问题的传递矩阵,然后利用传递矩阵法,结合层间连续性条件和边界条件,得到了多层可压缩渗透各向异性岩基轴对称固结问题在积分变换域内的解。最后应用Laplace-Hankel逆变换技术得到轴对称固结问题在物理域内的理论解。编制了相应的计算程序,并进行了数值计算与分析,讨论了可压缩性和渗透各向异性对岩基固结的影响,结果表明：可压缩性越大,岩基瞬时沉降越大;渗透各向异性对固结过程影响明显,但对初始和最终沉降的影响很小。     

多层横观各向同性地基轴对称固结的传递矩阵解

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。     

多层地基非轴对称Biot固结的理论解

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。     

地埋点热源作用下层状半空间的热-力耦合响应

采用解析层元法对存在地下点热源的岩土工程问题进行解答。首先从热弹性力学三维问题的基本控制方程出发,利用拉普拉斯-傅里叶积分变换推导出其在变换域内单层介质及下卧半空间的解析层元;然后结合有限单元法原理组装得到总刚度矩阵,结合边界条件,得到其在变换域内的解答,最后应用拉普拉斯-傅里叶积分逆变换技术,得到物理域内的解。编制了相应的计算程序,算例分析表明：该结果与已有文献吻合较好,该方法求解层状半空间的热-力耦合响应问题具有较好的适用性和较高的精度;层状岩土介质体系中,热扩散系数对温度及地表隆起的变化过程影响显著,但对其初始值和最终稳定值影响不明显;分层特性对岩土介质温度分布及地表位移变化过程均有显著影响。     

非稳态热传导时层状路面体系的温度响应

利用解析层元法推导温度荷载作用下非稳态热传导时层状路面体系的温度响应解答。从热弹性理论平面应变问题的控制方程出发,借助于Laplace-Fourier积分变换,推导出单层介质及下卧半平面的精确刚度矩阵即解析层元,结合有限层法原理及边界条件,组装并求解总刚度矩阵,得到其在变换域内的解答,最后通过相应的积分逆变换得到物理域内的真实解。由于该法刚度矩阵元素中不含正指数项,计算时不会出现溢出或病态矩阵的现象。编译了相应的计算程序,所得结果与有限元模拟结果吻合较好。在此基础上,对有限深度和半平面两种假定条件下的解答进行对比分析,并分析层状路面体系中位移和温度随时间的变化趋势及沿深度的分布规律。分析表明：温度场具有一定的影响深度,超过此深度,有限深度与半平面理论解答基本一致;温度荷载的影响深度与其强度有关,强度越大,其影响深度越深。     

层状地基中单桩负摩擦问题积分方程解法

利用Biot固结理论和积分方程方法研究了表面有堆载的层状地基中单桩负摩擦问题。根据层状饱和土的圆形载荷基本解得出了单桩在圆形均布载荷作用下在时间域内的第二类Fredholm积分方程组。运用Laplace变换对上述积分方程组进行简化。再结合传递和刚度矩阵传递到各个层中去,对变换域内的积分方程采用Schapery 逆变换方法得到时域内单桩的近似积分方程。求解积分方程组并进行相应的数值逆变换,就可得出层状地基中的单桩在表面圆形均布载荷作用下的位移、轴力、孔压和桩侧摩阻力随时间的变化情况。计算结果表明,桩侧剪力和孔压分层明显。     

竖向简谐荷载下二维层状饱和地基的解析层元解

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。     

横观各向同性层状饱和土动力问题的反射、透射矩阵方法

建立了轴对称情形下横观各向同性层状饱和土(TISS)动力问题的反射、透射矩阵(RTM)方法。对横观各向同性饱和土状态向量所满足的偏微分方程组进行Fourier和Hankel变换,得到状态向量所满足的常微分方程组。求解该常微分方程组,得到横观各向同性饱和土状态向量的通解。根据该通解得出了状态向量和波向量的传递矩阵,由波向量的传递矩阵得出了层状土的反射、透射矩阵表达式。利用上述反射、透射矩阵,并结合层状饱和土的边界条件和层间连续性条件,得出了垂直力作用下横观各向同性层状饱和土在变换域内的解。对变换域内的解进行Hankel逆变换,得出了频域内层状饱和土的动力响应。     

Gibson地基的一维固结解

针对单层Gibson地基模型,运用Laplace变换,求得了单层Gibson地基的一维固结问题,得到了频域内的通解。通过Laplace逆变换,即可计算单层Gibson地基在任意荷载下的一维固结特性。此外,结合工程实例,对解进行了探讨,揭示了单层Gibson地基的固结特性。     

具有不规则界面的层状地基三维动力响应的薄层法

天然地基通常含有不规则的分层界面。对此,提出了一种计算具有不规则界面的层状地基三维动力响应的薄层法,推导了简谐点源作用下不规则分层半空间三维动力问题的基本解。基于双重Fourier变换,获得弹性介质在频域-波数域内的薄层单元系统控制方程;利用模态叠加原理,推导了半无限长和有限长薄层单元的刚度矩阵,引入完美匹配层模拟波向底层半无限空间的传播,从而构建可考虑土层界面沿横向不规则分布的三维层状地基计算模型,获得了简谐点源作用下不规则分层地基三维动力问题的基本解;通过与既有方法的对比分析,验证了新方法的正确性。最后,利用该方法计算了具有倾斜分层界面的双层地基在简谐荷载作用下的动力响应,结果表明：界面倾斜导致的动力响应差异大,且随着倾斜度以及荷载频率的增加而变大。在进行天然地基的动力分析时,需考虑地基的不规则分层特性导致的振动响应差异。     

Numerical Laplace-Fourier transform inversion technique for layered-soil consolidation problems: I. Fundamental solutions and validation

A numericl method for solving consolidation problems of layered soils is developed. Starting from the governing differential equations for the coupled poro-elastic medium, the governing partial differential equations are reduced to ordinary differential equations by means of the appropriate displacement functions and Laplace-Fourier transformation. Once the fundamental solution in the transformed domain has been found, the solution in the physical domain is obtained by numerically inverting the transformations. A series of soil consolidation problems have been solved and validated against existing solutions in order to compare the feasibility and the accuracy of the present technique.     

Dynamic Green's functions for an anisotropic poroelastic half-space

The dynamic responses of an anisotropic poroelastic half-space under an internal point load and fluid source are investigated in the frequency domain in this paper. By virtue of Fourier transform and Stroh formalism, the three-dimensional (3D) general solutions of the anisotropic Biot's coupling dynamics equations are derived in the frequency domain. Considering the two surface conditions, permeable and impermeable, the analytical solutions for displacement fields and pore pressure in half-space under a point source (point load or a fluid source) are obtained. When the material properties are isotropic, the numerical results of the poroelastic half-space are in excellent agreement with the existing analytical solutions. For anisotropic half-space cases, numerical results show the strong dependence of the dynamic Green's functions on the material properties.     

Consolidation of a poroelastic half-space with anisotropic permeability and compressible constituents by axisymmetric surface loading

The fully coupled Biot quasi-static theory of linear poroelasticity is used to study the consolidation of a poroelastic half-space caused by axisymmetric surface loads. The fluid and solid constituents of the poroelastic medium are compressible and its permeability in the vertical direction is different from its permeability in the horizontal direction. An analytical solution of the governing equations is obtained by taking the displacements and the pore pressure as the basic state variables and using a combination of the Laplace and Hankel transforms. The problem of an axisymmetric normal load is discussed in detail. An explicit analytical solution is obtained for normal disc loading. Detailed numerical computations reveal that the anisotropy in permeability as well as the compressibilities of the fluid and solid constituents of the poroelastic medium have significant effects on the consolidation of the half-space. The anisotropy in permeability may accelerate the consolidation process and may lead to a dilution in the theoretical prediction of the Mandel-Cryer effect. The compressibility of the solid constituents may also accelerate the consolidation process.     

On the indentation of a poroelastic layer

The paper examines the axisymmetric contact problem related to the indentation of a fluid saturated poroelastic layer by a smooth rigid punch. The layer rests in bonded contact with a rigid impermeable base and the surface of the layer is considered to be either permeable or impermeable. The paper develops the integral equations governing the problem for the generalized case where the pore fluid exhibits compressibility. The numerical results presented in the paper illustrate the influence of the relative layer thickness, drainage conditions and the compressibility of the pore fluid on the degree of consolidation settlement of the indenting punch.     

横观各向同性土体中压力隧洞的应力和位移计算

基于Biot固结理论,考虑了土体和孔隙流体压缩性,通过对控制方程的解耦,得到在横观各向同性饱和土体中圆形隧洞边界上作用随时间变化的轴对称荷载或流体压力所引起的应力、位移和孔隙水压力场在拉普拉斯变换域中的解析表达式,运用拉普拉斯数值逆变换进行算例分析,得到在时间域中的解,讨论了单级加载和循环加载对计算结果的影响,并与瞬时加载条件下的结果进行了比较。同时也分析了土体的横观各向同性性质对应力、位移和孔隙水压力场的影响。     

Transient response of a circular cavity in a poroelastic medium

This paper considers the transient response of a pressurized long cylindrical cavity in an infinite poroelastic medium. To obtain transient solutions, Biot's equations for poroelastodynamics are specialized for this problem. A set of exact general solutions for radial displacement, stresses, pore pressure and discharge are derived in the Laplace transform space by using analytical techniques. Solutions are presented for three different types of prescribed transient radial pressures acting on the surface of a permeable as well as an impermeable cavity surface. Time domain solutions are obtained by inverting Laplace domain solutions using a reliable numerical scheme. A detailed parametric study is presented to illustrate the influence of poroelastic material parameters and hydraulic boundary conditions on the response of the medium. Comparisons are also presented with the corresponding ideal elastic solutions to portray the poroelastic effects. It is noted that the maximum radial displacement and hoop stress at the cavity surface are substantially higher than the classical static solutions and differ considerably from the transient elastic solutions. Time histories and radial variations of displacement, hoop stress, pore pressure and fluid discharge corresponding to a cavity in two representative poroelastic materials are also presented.