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。     

成层多孔粘弹性地基在轴对称荷载作用下的解

给出一种有效的解析方法求解成层多孔粘弹性地基在轴对称荷载作用下的固结问题，通过关于时间t的拉普拉斯变换和关于半径r的亨克尔变换，将控制偏微分方程转化为常微分方程，从而得到用常微分短阵方程形式表示的控制方程，基于矩阵常微分方程的解以及拉普拉斯，亨克尔逆变换，可得到该固结问题的解，该方法理论及计算简捷，通过算例比较了该方法的精度，并研究了地基的粘弹性特性对固结过程的影响。     

饱和土表面在水平集中荷载作用下的瞬态反应

分析了水平集中荷载作用在半空间饱和土表面时的瞬态问题。利用Laplace-Hankel变换对非轴对称Biot固结方程进行解耦，利用Laplace-Hankel数值逆变换得到半空间饱和土在时域内的数值解。退化到线弹性中的解与文献中的结果进行比较，验证了文中结果的正确性和数值逆变换的可靠性.可以用于研究地震工程中地震波的传播以及饱和土与结构之间相互作用等问题。     

层状可压缩岩基三维固结问题的状态空间解

采用状态空间法求解层状可压缩岩基的三维固结问题。首先从直角坐标系下考虑可压缩性的三维Biot固结问题的控制方程出发,通过Laplace-Fourier变换得到状态空间方程,解此方程并通过Cayley-Hamilton定理,得到单层可压缩岩基三维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,得到了层状可压缩岩基三维固结问题在积分变换域内的解答;最后应用Laplace-Fourier逆变换技术,得到层状可压缩岩基三维固结问题在物理域内的理论解答。编制了相应的计算程序,进行了数值计算与分析,证明了压缩性对岩基固结问题的影响     

变荷载下层状非饱和土地基全耦合固结特性研究

非饱和土是地球表层土体一种常见的存在形式。与经典的饱和土Biot固结理论相比,非饱和土固结理论还亟待发展。基于Fredlund非饱和土双应力变量固结理论,放弃传统理论固结过程中骨架总应力不变的假设,推导出变荷载作用下非饱和土全耦合轴对称固结理论的控制方程组。通过Laplace-Hankel变换处理变量t和r,所得的控制方程被处理为常微分方程组;扩展的精细积分法将被进一步运用求解方程组以得到层状非饱和土地基在变换域内的固结解答,而最终的解答将通过Laplace-Hankel逆变换技术求得。将非饱和土地基退化为饱和土地基,与现有文献结果进行对比,验证所提方法结果的可靠性;最后,提供3个数值算例,以讨论加载时间T0、孔隙水关于净应力的体积变化系数m1w以及土体分层性对非饱和土固结特性的影响。     

成层地基在轴对称荷载下的稳态振动分析

基于Biot动力固结方程,考虑了土体和水体的惯性力以及水-土耦合作用的影响,采用Hankel积分变换求解耦联合方程组,得到动荷载下饱和土Lamb问题的解答。根据下边界为不透水基岩的边界条件,获得了地基表面作用圆形轴对称周期荷载时土层应力、位移等的一般积分形式解,并利用矩阵传递法完成了对多层地基和Gibson地基的计算。通过算例研究了层厚和激振频率等对竖向位移的影响。     

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。     

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。     

三维横观各向同性成层地基的传递矩阵解

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。     

Analytical layer‐element method for non‐axisymmetric consolidation of multilayered soils

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.     

A quasistatic analysis of a plate on consolidating layered soils by analytical layer‐element/finite element method coupling

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.     

Analytical layer-element solution to axisymmetric consolidation of multilayered soils

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.     

Axisymmetric consolidation of saturated multi-layered soils with anisotropic permeability due to well pumping

Axisymmetric consolidation of multi-layered soils induced by groundwater extraction from a dewatering well is studied with consideration of the anisotropic permeability and the well length. Laplace-Hankel transforms are utilized to solve the governing equations. The analytical layer-element method is used to build relationships between displacements, stresses, excess pore pressure and seepage velocity in the transformed domain. The real solutions can be obtained by the inversion of Laplace-Hankel transforms. A series of parametric studies, especially the length of a dewatering well and the combined effect of pumping and recharging, are conducted to analyze the consolidation behaviors of layered soils.     

层状横观各向同性地基平面应变问题的扩展精细积分解

利用扩展精细积分法求解横观各向同性地基的平面应变问题。扩展精细积分法具有高精度和较高计算效率的特点,是求解微分方程的有效方法,相比于解析法可以节省大量理论推导工作量。从直角坐标下弹性力学控制方程出发,推导出Fourier变换域内地基的常微分矩阵方程;之后对地基微层元进行消元合并,进一步得到荷载作用在地基内部时层状地基的扩展精细积解。与已有文献的对比验证了方法的精确性,并分析了横观各向同性参数、层状性质和荷载作用点对计算结果的影响。结果表明：土体竖向位移随着横观各向同性参数n的增大而减小,而随着横观各向同性参数m的增大而增大;荷载作用点 的变化只对作用点以上的土体有影响,而上层土体的模量对竖向位移计算结果的影响更为显著,土体成层性对沉降的影响要比对竖向应力的影响更为显著。