【作者】 秦爱芳；

【导师】 孙德安；

【作者基本信息】 上海大学 ， 结构工程， 2009， 博士

【摘要】 本文对Fredlund非饱和土一维固结方程进行适当简化,得到了大面积均布瞬时加荷及大面积加荷随时间指数变化两种情况,在多种边界条件下有限厚度非饱和土层一维固结的一系列解析解及半解析解,并将以上线弹性非饱和土一维固结半解析解的求解方法拓展到粘弹性非饱和土中。论文的主要内容可以归为以下几点:（1）对大面积均布瞬时加荷情况,由Fredlund液相及气相的控制方程、Darcy定律及Fick定律,经Laplace变换及采用Cayley-Hamilton数学方法,得到了大面积均布瞬时加荷情况,有限厚度非饱和土层任意深度状态向量与顶面状态向量之间的传递关系。（2）基于Fredlund非饱和土一维固结理论,推导了大面积加荷随时间指数变化情况下非饱和土一维固结的液相及气相控制方程。由此控制方程及Darcy定律和Fick定律,经Laplace变换及采用Cayley-Hamilton数学方法,得到了大面积加荷随时间指数变化情况,有限厚度非饱和土层顶面状态向量与任意深度处状态向量间的传递关系。（3）通过引入初始条件及边界条件,得到了大面积均布瞬时加荷和加荷随时间指数变化情况,在多种边界条件下Laplace变换域内的超孔隙水压力、超孔隙气压力以及土层沉降的解。（4）采用直接Laplace逆变换方法得到了大面积均布瞬时加荷和加荷随时间指数变化情况下,顶面排水排气、底面不排水不排气边界条件下超孔隙水压力、超孔隙气压力及土层沉降的解析解表达式。应用典型算例,进行了非饱和土的固结特性分析;分析了不同气、水渗透系数比情况下土体超孔隙水压力、超孔隙气压力、土层沉降随时间的变化规律及不同深度超孔隙水压力、超孔隙气压力的消散规律。（5）采用Crump及Durbin方法编制程序实现拉普拉斯逆变换,得到了均布瞬时加荷和加荷随时间指数变化情况下,多种边界条件下的时间域内的超孔隙水压力、超孔隙气压力的半解析解。并进行了以上情况下非饱和土的固结特性分析。将半解析解与解析解进行了比较。证明了采用Crump及Durbin方法实现Laplace逆变换的有效性。（6）采用有限差分方法,编制Fredlund一维固结方程的计算程序,对大面积均布瞬时加荷和加荷随时间指数变化两种情况下,多种边界条件进行求解,得到了非饱和土一维固结的数值解。将得到的数值解与本文得到的解析解对比,证明了本文解析解的精确性及气相控制方程简化的合理性。（7）将得到的解析解及半解析解退化成适用饱和土的解,并与太沙基饱和土固结理论结果比较。退化为饱和土时本文的解析解及半解析解与太沙基饱和土固结理论解一致。（8）采用李氏比拟法,应用Merchant粘弹性模型,得到了Laplace变换域内粘弹性非饱和土地基一维固结时超孔隙水压力,超孔隙气压力以及土层沉降的解;采用Crump及Durbin方法实现Laplace逆变换,获得大面积均布瞬时加荷,在顶面排气排水,底面不排气不排水情况下粘弹性非饱和土地基一维固结时的半解析解。分析了不同气、水渗透系数比k_a/k_w,Merchant粘弹性模型的Kelvin体中弹性模量E₁和粘滞系数η等对粘弹性非饱和土地基一维固结特性的影响,揭示了粘弹性非饱和土地基的固结特性。本文基于线性假定得到的解析解及半解析解为研究复杂的非饱和土非线性问题提供了有价值的一阶近似。线性模型通常需要相对较少的数据并且可以快速获取一个复杂的非饱和土耦合系统的的机理,分析各种材料性质和边界条件的影响。因此,面对复杂的非饱和土固结问题,对于基于线性假定的解析法的研究和发展是非常有价值的。本文的研究结果对非饱和土固结机理、固结特性的研究具有重要的学术意义,并具有较大工程应用价值。更多还原

【Abstract】 In this paper, a series of analytical and semi-analytical solutions to one-dimensional consolidation in unsaturated soil with finite thickness are obtained under several kinds of boundary conditions under the large-area uniform instantaneous loading and loading changed exponentially with time. The semi-analytical solution to one-dimensional consolidation for linearly elastic unsaturated soils is extended to that for the viscoelastic unsaturated soils.Main contents can be drawn as follows:(1) For the large-area uniform instantaneous loading, based on the Fredlund’s one-dimensional consolidation theory for unsaturated soil, the transfer relations between the state vectors at top surface and any depth are gained by using the Laplace transform and Cayley-Hamilton mathematical methods to the Fredlund’s governing equations of water and air, Darcy’s law and Fick’s law.(2) For the large-area loading changing exponentially with time, the governing equations of one-dimensional consolidation are derived based on Fredlund’s one-dimensional consolidation theory for unsaturated soil. The transfer relation between the state vectors at the top surface and at arbitrary depth are gained by using the Laplace transform and Cayley-Hamilton mathematical methods to this governing equations of water and air, Darcy’s law and Fick’s law.(3) The excess pore-air pressure, the excess pore-water pressure and the settlement in the Laplace-transformed domain are obtained by using the Laplace transform with the initial conditions and certain boundary conditions, in the cases of the large-area uniform instantaneous loading and loading changing exponentially with time.(4) For the large-area uniform instantaneous loading and loading changing exponentially with time, the analytical solutions of the excess pore-air pressure, the excess pore-water pressure and the soil settlement are obtained by performing the inverse Laplace transforms under the boundary conditions of the top surface permeable to water and air, and the bottom impermeable to water and air. A typical example result is given to show the changes in the excess pore-air pressure, the excess pore-water pressure and the soil settlement rate with time under different air-water coefficient rates.(5) For the large-area uniform instantaneous loading and loading changing exponentially with time, a computer program using the method of Crump and F. Durbin is developed to obtain the semi-analytical solutions of the excess pore-air pressure, the excess pore-water pressure and the soil settlement rate under several kinds of boundary conditions. At the same time the consolidation behavior for unsaturated soils is analyzed according to the semi- analytical solution, and the results prove that the method is of high precision. (6) For the large-area uniform instantaneous loading and loading changing exponentially with time, a computer program is developed to obtain the numerical solutions to one-dimensional consolidation in unsaturated soils by the finite difference method under several kinds of boundary conditions. Comparisons between the numerical and analytical results indicate that the results of the two methods are almost the same.(7) The analytical solution is compared with the Terzaghi solution for saturated soils and it is known that the two solutions are almost the same for saturated soils. Therefore, the analytical solution to one-dimensional consolidation in unsaturated soilis correct.(8) Unsaturated soil is assumed to obey Merchant viscoelastic model. By using Lee’s matching law, the excess pore-air pressure, excess pore-water pressure and settlement in the Laplace-transformed domain are obtained for one-dimensional consolidation in unsaturated soils, under the large-area uniform instantaneous loading. A computer program using the method by Crump and Durbin is developed to obtain the semi-analytical solution of the excess pore-air pressure, excess pore-water pressure and settlement under the boundary conditions of the top surface permeable to water and air and the bottom impermeable to water and air. At the same time the consolidation behavior of the viscoelastic unsaturated soils is analyzed according to the semi-analytical solution. The changes in the excess pore-air pressure, excess pore-water pressure and settlement of the viscoelastic unsaturated soil layer with thetime under different air-water coefficients k_a / k_w and E_l ,ηin the Merchantviscoelastic model are analyzed.In this paper, some linear assumptions associated with the transport processes and constitutive equations were made, which provided useful initial approximations for unsaturated soil consolidation, and the linear models require relatively less data and it becomes possible for the models to be solved by means of analytical methods. Such analytical solutions are often used to gain a quick insight into the physics of a complex coupled system, and the influence of various material properties and boundary conditions can be investigated. Therefore, developing simplified analytical solutions is always valuable when dealing with complex problems of consolidation in unsaturated soils. The analytical solutions have a high academic value to the studies on unsaturated soils consolidation mechanism and consolidation characteristics, and also the engineering value for solving practical problems.更多还原