【作者】 鄂建；

【导师】 陈刚；

【作者基本信息】 中国地质大学 ， 地下水科学与工程， 2007， 硕士

【摘要】 完整的饱和土体固结模型包括土体应力—应变模型和孔隙水渗流模型，这涉及到连续介质力学的两个方面：多孔介质的连续介质力学和渗流流体的连续介质力学。历年来学者们专注于非线性土体应力—应变本构模型的研究，而忽视了非线性孔隙水渗流规律对固结的影响。本文以孔隙水非线性渗流理论为基础，探讨了粘性土在非线性渗流影响下的一维非线性固结特征，探求了粘性土的非线性渗流固结规律。一维渗流固结理论是土力学最基本的课题，至今它仍然是地基沉降和大范围地面沉降计算的重要工具，虽然存在很多不足，但它揭示了土体渗流固结问题的本质，通过它容易弄清土体固结的基本规律，且通过简单的修正，仍然能很好的符合实际情况。对于较为简单的一维固结问题(如荷载瞬时施加和线弹性模型等)，解析法是最精确的计算方法，但土体的应力—应变关系往往表现为非线性，因此解析解的精度往往难以满足实际需要。此外，对于固结过程中渗流的非线性(如渗透系数的变化)，解析法也很难进行准确的刻画。数值方法就成了最有效的工具，有限差分法是进行一维渗流固结问题的数值模拟最常用的方法，其优点在于物理意义简单明确，程序编制工作量较小。本文多次运用有限差分方法进行了一维渗流固结的数值分析。关于非线性渗流理论，前人的研究面较广，本文从多孔介质的孔隙结构、流固相互作用和流体的力学性质三个方面系统总结了非线性渗流的机理，认为粘性土的渗流不符合线性的Darcy定律。虽然影响非线性渗流的机理很多，但其中很多机制还不能进行准确的刻画，因此难以提出一个考虑各项机理的渗流模型，本文通过分析非线性渗流特征的共性，从结合水动力学的角度提出了包含启动压力梯度、拟启动压力梯度、临界压力梯度和幂指数等非线性渗流特征参数的非线型渗流计算模型，考虑了孔隙比和水力梯度的影响：K=K(e)·Ψ(I)其中，K(e)是关于孔隙比e的函数，Ψ(I)是关于水力梯度I的非线性渗流特征函数。作为土力学最基础的理论之一，Terzaghi模型的许多假定在很多情况下与实际不符，不能很好的反映土体渗流固结的非线性特征，因此对土体的固结沉降计算不够准确，本文从非线性渗流规律、非线弹性应力—应变模型以及总应力随时间变化(荷载随时间变化)等方面对Terzaghi模型进行了修正。关于Terzaghi模型中渗流符合Darcy定律的基本假定，本文运用非线性渗流模型对其进行了修正，编制了数值计算程序(NDFTERM)，实现了考虑非线性渗流的一维线性固结数值模拟。模拟结果表明，非线性渗流对粘性土的固结过程有较为显著的影响，表现为超静孔隙水压力存在较为明显的滞后消散现象，这可以给予一些固结现象较为合理的解释。关于非线性渗流的适用范围，本文通过数值实验发现，启动压力(或拟启动压力梯度)所拦截的超静孔压是导致固结不充分(或固结过程滞后)的主要因素，当拦截的超静孔压远小于固结过程中的最大超静孔隙水压力时，其影响就可以忽略不计。Terzaghi固结理论中关于土体线弹性的假定与粘性土的力学特征也有很大差异，因此不能很好的反映粘性土非线性固结的规律，本文在Davis和李冰河等人的研究基础上，系统的总结了一维非线性固结理论，编制了数值计算程序(ODNLC)进行一维非线性固结数值分析，结果与Davis等人的解析解能很好的吻合，证明了按超静孔压定义的固结度与按沉降变形定义的固结度之间存在着差异，并验证出渗透系数和侧限体积压缩系数随有效应力(或孔隙比)的变化以及荷载的大小是影响土体固结的主要非线性因素，指出了非线性固结对土体沉降量的影响。同时本文将非线性渗流引入到一维非线性固结模型中，提出了考虑非线性渗流的一维非线性固结模型，并编制了数值计算程序(ODNLCNDF)，首次实现了考虑非线性渗流的一维非线性固结模拟，发现了不同于Darcy流的新规律。在很多实际情况中，作用于土体的荷载是随时间变化的，Terzaghi理论对于地基土沉降的长时间的动态预测无能为力。本文在谢康和、李冰河等人的工作基础上，进行了荷载随时间变化条件下的固结分析，证明了变化荷载下土体的固结规律与Terzaghi理论有很明显的差异。对于可以刻画为线性递增的荷载，本文通过计算发现，其瞬时固结效应并不明显，这也是工程实际问题中预测计算值偏大的主要原因。对于类似于正弦波的荷载，本文发现其荷载作用周期的大小对土体的固结有明显的影响。对于有显著波动变化的荷载，土体的有效应力也是波动变化的，因此不能只研究土体压缩的过程，还应考虑到有效应力衰减时，土体的回弹—再压缩过程与压缩过程的差异，这种差异对土体的固结特征有重要影响。本文深入分析了谢康和、李冰河和耿雪玉等人提出的考虑荷载变化的一维非线性固结理论，指出其没有分开计算压缩与回弹过程的局限，并以有效应力作为判断土体压缩或回弹—再压缩过程的指标，将变化荷载的一维非线性固结理论推广到了任意变化荷载的一维非线性固结理论，实现了一维土体非线性固结的动态模拟。通过简单的修改，本理论也能实现考虑先期最大固结应力的固结计算。根据任意变化荷载的一维非线性固结理论，本文编制了数值计算程序(ODNLCTVL)进行了数值模拟研究，发现土体在荷载变化情况下的一维非线性固结表现出了不同于瞬时加载固结的规律，这包括线性加载和波动荷载的固结。此外，考虑土体在压缩与回弹一再压缩过程中压缩性变化对土体的固结沉降有很大的影响，考虑粘性土体的塑性变形是非常有必要的。为了考察对于变化荷载下非线性渗流对粘性土一维非线性固结的影响，本文再次引入非线性渗流模型，编制了数值计算程序(ODNLCNDFTVL)进行了数值模拟研究，发现非线性渗流对变化荷载下的一维非线性固结同样有较大的影响，表现为固结度总体上小于Darcy渗流。在线性加载过程中，其固结规律与Darcy流基本保持一致，但非线性渗流的滞后固结的效应较为显著，而在循环加载过程中，滞后效应则衰减较快。更多还原

【Abstract】 The model of consolidation about complete and saturated soil which includes model of stress-strain and model of pore water seepage, involves two aspects of continuum mechanics: continuum mechanics of porous media and continuum mechanics of seepage flow. Over the years scholars have focused on the research of constitutive model of soil non-linear stress-strain, and have neglected of the effect of non-linear seepage pattern of pore water to consolidation. Based on theory of non-linear seepage of pore water, the one-dimensional non-linear consolidation characteristics in the effect of non-linear seepage and the law of non-linear seepage consolidation of cohesive soil have been discussed and explored.One-dimensional seepage consolidation is the most basic issue of soil mechanics, So far it has been still the important tool of calculation about foundation settlement and the scope of land subsidence. Although there are many disadvantages, it reveals the essence of consolidation of soil seepage through which the basic law of soil consolidation is easily understood, and it is still good consistent with the actual situation by simple amendment. For issues of more simple one-dimensional consolidation (such as instantaneous load-on and linear or elastic model), analytic method is the most accurate method of calculation. Because the relationship of stress-strain is often manifested as nonlinear, Then the accuracy of analytical solutions is often difficult to meet the actual needs. Furthermore, the analytic method is also very difficult to make accurate characterization for the nonlinearity of seepage in the process of consolidation (such as changes of the permeability coefficient). Numerical method has become the most effective tool and finite difference method has become the most common method to numerical simulation of one-dimensional consolidation of seepage, because it has simple and clear physical meaning and smaller workload of programmers, the finite difference method has been often used for numerical analysis of the one-dimensional consolidation.Predecessors have had a wide range study on theory of non-linear seepage. The mechanism of non-linear seepage has been summarized from pore structure of the porous medium, interaction between flow and solid and properties of flow, and seepage of cohesive soil has also been recognized not to be consistent with the linear Darcy’s law. Although there are many mechanisms effecting non-linear seepage, some mechanisms are not accurate for characterization. So it is difficult to establish a model of seepage considering all mechanisms. Through analysis of common characters of non-linear seepage, the calculation model of non-linear seepage containing the parameters of non-linear seepage, such as starting pressure gradient, to be starting pressure gradient, critical pressure gradient and power index, has been raised from the point of hydrodynamic of bound water. It considers effects of porosity ratio and hydraulic gradient:K=K(e)·ψ(I)In which K(e) is the function of porosity ratio e,ψ(I) is characteristics function of non-linear seepage.Terzaghi model is the most basic theory of soil mechanics, but it includes too many assumptions, such as soil is the linear elasticity, coefficient of consolidation remains constant in the process of consolidation, load should be imposed instantaneously and so on. Many of these assumptions are inconsistent with the actual situation, and does not well reflect the non-linear characteristics of consolidation of soil seepage. Therefore the calculation to consolidation and settlement of soil using this method is inaccurate. The amendment for Terzaghi model has been made from the law of non-linear seepage, the model of non-linear elastic stress-strain and the load changes with time and so on in the paper.In this dissertation the assumption that seepage is in conformity to the Darcy’s law has been modified using the model of non-linear seepage in Terzaghi theory, and numerical calculation procedure (NDFTERM) has been compiled which achieves one dimension linear numerical simulation of consolidation considering the nonlinear seepage. Simulation results show that the non-linear seepage has more significant impacts to the process of consolidation of cohesive soil presenting as more obvious lag dispersed phenomenon of super-static pore water pressure, which can give more reasonable explanation to some consolidation phenomenon.To the scope of non-linear seepage, numerical experiments have showed that the excess pore pressure intercepted by starting pressure (or planned to activate the pressure gradient) is the major factors to lead to be not full consolidation. When the excess pore pressure intercepted is much smaller than the largest excess pore water pressure in the process of consolidation, its impacts can be ignored.There is a big difference between the assumption of the linear elastic soil and the mechanical characteristics of cohesive soil in Terzaghi consolidation theory, so it does not well reflect the law of nonlinear consolidation of cohesive soil. Based on the study of Davis, Li Bingheand others, a numerical procedure (ODNLC) has been compiled to carry on numerical analysis of one-dimensional non-linear consolidation. The rusult is consistent with analytic solution of Davis and others which proves that there are some differences btween consolidation definited using excess pore pressure and that definited using settlement, the changes of permeability coefficient and lateral limits compressibility coefficient along with the effective stress and porosity satio and the size of load are the non-linear factors affecting soil consolidation, and it also indicates the effects of non-linear consolidation to soil settlement. In the dissertation, the non-linear seepage has been introduced to the model of one-dimensional nonl-inear consolidation, the model of one-dimensional nonl-inear consolidation has been advanced considering the non-linear seepage, a numerical calculation procedure (ODNLCNDF) has been compiled, and the simulation of one-dimensional non-linear consolidation has also been achieved considering nonlinear seepage for the first time.The load acted on the soil is changing with time in many practical situations. Based on the previous work of predecessors, consolidation analysis has been made considering the load changes with time which proves that there is a clear difference between consolidation rules of soil under the changed loads and Terzaghi theory. Instantaneous effect of consolidation of load obtained by calculation which can be looked as linear increase is not so clear, and this is also the main reason that forecast calculation is bigger in the practical issues. The cycle of load has a clear influence on the consolidation of soil for the load similar to the sine wave.For the load which has a significant variation, the effective stress of soil is variatied, so it does not only study the process of soil compression, but also take into account the differences between the process of resilience-compression and compression of soil when the effective stress has the attenuation. The dissertation points out limitations of the theory of one-dimensional non-linear consolidation considering the load changes advanced by Li Binghe, Geng Xueyu and others, the effective stress can be considered as indicators judging compression of soil and the process of rebound-compression, and the theoryof one-dimensional non-linear consolidation of changed load should be extended to that of arbitrary changes of load of one-dimensional non-linear consolidation. Through simple modifications, the theory can be extended to the theory of consolidation considering the greatest consolidation stress in advance.A numerical procedure (ODNLCTVL) has been developed to carry through the study on numerical simulation considering one-dimensional non-linear consolidation of changed load, and it has been found that the rules of the one-dimensional nonlinear consolidation of soil under the changed load have differences with that of instantaneous consolidation which includes linear load and the consolidation of fluctuated load. In addition, considering the influence of compression of soil to its consolidation and settlemen, it is very necessary to consider plastic deformation of soi.A numerical procedure (ODNLCNDFTVL) has also been developed to carry through thestudy on numerical simulation aimed at the model of one-dimensional non-linear consolidation based on non-linear seepage in the action of changed load, and it is found that there is a same great influence of non-linear seepage to one-dimensional nonlinear consolidation in the action of changed load which performs general lags in the process of consolidation and Darcy seepage. In the linear process of loading, the rules of consolidation is consistant with that of Darcy seepage. The hysteresis effect of nonlinear seepage is more significant, but it decreases rapidly in the process of cyclic loading.更多还原