横观各向同性层状饱和土固结问题的反射—透射矩阵方法

发布时间：2018-04-22 07:21

本文选题：横观各向同性层状饱和土 + Biot理论　；参考：《江苏大学》2016年硕士论文

【摘要】：由于很多天然土体呈层状且具有横观各向同性的特征,因此,对横观各向同性层状饱和土固结问题的研究有重要的工程实际意义。本文建立了静力荷载作用下横观各向同性层状饱和土的轴对称和非轴对称固结问题的反射透射矩阵(RTM)方法,该方法继承了传统传递矩阵法计算量小的优点,又克服了传递矩阵法数值不稳定的缺点。利用所建立的RTM方法,分析了土体弹性参数的各向异性,弹性模量的层间差,渗透系数的层间差及渗透系数的各向异性对饱和土固结的影响。本文的研究包含如下内容:(1)建立了垂直荷载作用下横观各向同性层状饱和土的反射透射矩阵方法。基于轴对称Biot固结问题的基本方程,引入状态向量并建立关于状态向量的偏微分方程组,利用Hankel-Laplace变换,将上述偏微分方程组化为对垂直坐标的常微分方程组;利用该常微分方程组的通解,定义相应的静态波向量及状态向量与波向量间的变换矩阵;利用波向量的传递矩阵和土层界面处的连续条件建立了横观各向同性层状饱和土的反射透射矩阵;根据上述的反射透射矩阵,求解了横观各向同性层状饱和土的轴对称固结问题。值得指出的是,由于本文的状态向量、静态波向量及其相互间的变换矩阵均定义于整体坐标系,因此,本文所建立的反射透射矩阵具有合理的力学意义。(2)建立了求解横观各向同性层状饱和土的非轴对称固结问题的反射透射矩阵方法。对非轴对称固结问题,引入了相应的状态向量,并根据横观各向同性饱和土在非轴对称条件下的控制方程,建立了状态向量的偏微分方程;利用Hankel-Laplace变换,将该偏微分方程组转化为常微分方程组;根据该常微分方程组的通解,引入了相应的静态波向量及状态向量和波向量间的变换矩阵;利用层界面处的连续性条件和波向量的传递矩阵建立了非轴对称横观各向同性层状饱和土的反射透射矩阵表达式;利用所得的反射透射矩阵,求解了层状横观各向同性层状饱和土的非轴对称固结问题。(3)利用所建立的横观各向同性层状饱和土的反射透射矩阵方法,本文对横观各向同性层状饱和土的轴对称和非轴对称固结问题进行了数值计算。通过与已有结果的对比,验证了本文所建立模型的正确性和优点;以三层土为例,对垂直载荷,井点降水和水平力作用下横观各向同性层状饱和土的位移,应力和孔压进行了计算,分析了土层参数的层间差,弹性模量比()h vE E及渗透系数的各向异性等对横观各向同性层状饱和土固结的影响。
[Abstract]:Because many natural soils are layered and transversely isotropic, it is of great practical significance to study the consolidation of transversely isotropic layered saturated soils. In this paper, a reflection and transmission matrix method (RTM) for axisymmetric and non-axisymmetric consolidation of transversely isotropic layered saturated soils under static loading is established. This method inherits the advantages of the traditional transfer matrix method. It overcomes the disadvantage of numerical instability of transfer matrix method. The effects of anisotropy of elastic parameters, interlayer difference of elastic modulus, interlayer difference of permeability coefficient and anisotropy of permeability coefficient on the consolidation of saturated soil are analyzed by using the established RTM method. The research in this paper includes the following contents: 1) the reflection and transmission matrix method of transversely isotropic layered saturated soil under vertical load is established. Based on the basic equations of axisymmetric Biot consolidation problem, the state vector is introduced and the partial differential equations about state vectors are established. By using Hankel-Laplace transformation, the above partial differential equations are transformed into ordinary differential equations with vertical coordinates. By using the general solution of the ordinary differential equation system, the corresponding static wave vector and the transformation matrix between the state vector and the wave vector are defined. The reflection and transmission matrix of transversely isotropic layered saturated soil is established by using the transfer matrix of wave vector and the continuity condition at the interface of soil layer. The axisymmetric consolidation problem of transversely isotropic layered saturated soil is solved. It is worth pointing out that since the state vector, the static wave vector and the transformation matrix between them are defined in the global coordinate system, The reflection and transmission matrix established in this paper has reasonable mechanical significance. (2) A reflection and transmission matrix method for solving the problem of non-axisymmetric consolidation of transversely isotropic layered saturated soil is established. For the non-axisymmetric consolidation problem, the corresponding state vector is introduced, and according to the governing equation of transversely isotropic saturated soil under the condition of non-axisymmetric, the partial differential equation of the state vector is established. The system of partial differential equations is transformed into ordinary differential equations, and according to the general solution of the system of ordinary differential equations, the corresponding static wave vector and transformation matrix between state vector and wave vector are introduced. The expression of reflection and transmission matrix of non-axisymmetric transversely isotropic layered saturated soil is established by using the continuity condition at the interface of the layer and the transfer matrix of the wave vector. The non-axisymmetric consolidation problem of layered transversely isotropic layered saturated soil is solved. The reflection and transmission matrix method of transversely isotropic layered saturated soil is established. In this paper, the problem of axisymmetric and non-axisymmetric consolidation of transversely isotropic layered saturated soil is numerically calculated. By comparing with the existing results, the correctness and advantages of the proposed model are verified, and the displacement of transversely isotropic layered saturated soil under vertical load, well point precipitation and horizontal force is given as an example. The stress and pore pressure were calculated, and the effects of interlayer difference of soil layer parameters, elastic modulus ratio (E) and anisotropy of permeability coefficient on consolidation of transversely isotropic layered saturated soil were analyzed.
【学位授予单位】：江苏大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TU43

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