摘要
高放废物地下处置、天然气水合物的开发、地热资源的利用、城市建设中的供热管道、埋地高压电缆等众多工程领域,都涉及到土体在应力、渗流、温度和化学等多场作用下的耦合问题。在多场耦合作用下,如何确定土体中土骨架的变形、孔隙水的渗流、热量的传递、组分物质或污染物的迁移与扩散、化学反应以及相变等多种过程,是目前国内外岩土工程研究领域一个迫切需要解决而又十分困难的问题。该问题的解决将为有效地解决许多工程问题,如土木工程的建设、地质灾害防治、环境保护、新能源高效开采等,提供必需的理论基础和分析方法。而建立在严格科学基础上的多场耦合理论却相对较少,传统的土体多场耦合理论大多数都是基于宏观现象学的认识,缺少严格和科学的理论基础。由此所建立的理论适用范围有限,也未能严格和有效地描述土体中多场和多过程耦合的现象,因此,无法满足解决上述实际工程问题的需要。尤其是在高放废物地下处置等一些新兴的岩土工程领域,温度对土体变形强度特性、渗流特性等基本性质的影响都不可忽略,而相关研究工作尚处于起步阶段,缺乏有价值的研究成果,更未形成完善的理论体系。
本文以多孔介质理论和热力学理论为基础,从系统的平衡方程、熵不等式以及一些本构假定出发,通过严密的理论推导建立了土体非线性多场耦合模型。然后,采用适当的自由能函数和耗散函数,建立了描述非饱和土变形-渗流-传热耦合过程的数学模型。此外,通过对新建立模型的适当简化,基于已有的试验研究成果,重点考虑非饱和土的温度效应,系统研究了温度对非饱和土变形、渗流特性的具体影响,建立了相应的本构模型,并编制计算程序对模型进行了验证。最后,为了更加直观和深入地研究温度对非饱和土基本性质的影响,还研制了温控非饱和土三轴试验装置,并基于此开展了温度对非饱和土土水特征曲线影响的试验研究。主要研究成果包括：
(1)将非饱和土视为由多组分的弹塑性固体骨架、粘性液体以及理想气体组成的混合物,根据多孔介质理论建立系统内各组分、各相及整体三个层次的平衡方程,在连续介质力学中的决定性原理、等存性原理、坐标不变性原理以及相容性原理等限制条件下进行了合理的本构假设,由此提出了三相土体在非平衡态以及平衡态时建立本构关系的理论框架,从而形成了闭合的场方程系统。其中的关键是提出了有效广义热力学力的概念以及近平衡态时系统内部各广义耗散力和广义流之间的非线性耦合本构关系。并以此为基础给出了固相热弹塑性本构关系、液相粘弹塑性本构关系、广义Fourier定律和广义Darcy定律四种特殊耦合关系的本构方程。在给出某一具体的耗散函数的基础上,还对广义Darcy定律的具体形式进行了推导；最后还指出了不考虑温度和其它场耦合作用时,这一非线性模型可退化为非饱和土的弹塑性本构模型。
(2)土体的变形-渗流-传热耦合作用是十分普遍的物理现象及工程问题。在已建立的非饱和土多场耦合理论框架基础上,选取适当的自由能函数和耗散函数,对其进行Taylor级数展开,从而得到耦合多种场作用的本构方程,并进一步得到非饱和土变形-渗流-传热耦合的数学模型。该模型统一地描述了变形-渗流-传热耦合作用下土体的弹塑性变形、流体的流动以及热量的传导等现象。与已有的研究土体多场耦合问题不同的是,所给出的守恒方程除增加了与其他场的耦合作用项以及各场之间的界面效应项外,更重要的是在变形-渗流-传热耦合作用时,对考虑各种场影响的非线性本构关系进行了推导。
(3)在(1)、(2)项研究成果的基础上,结合现有的试验研究成果,重点考察温度对非饱和土变形性质的影响,建立了热-水-力耦合作用下的非饱和土弹塑性本构模型,并通过适当的简化,建立了三轴应力条件下的本构模型。在此基础上利用Fortran语言编制计算程序,对各向同性条件下非饱和土受温度影响的弹塑性变形进行了预测,通过与这方面已有的试验数据的对比和分析,验证了所建立本构模型的适用性。
(4)基于热力学理论,利用van Genuchten土水特征曲线表达式,建立了一种能考虑温度影响的土水特征曲线方程。该方程综合考虑了温度对表面张力和浸润系数的影响。相对于完全根据试验数据拟合的表达式而言,所给出的方程具有更加坚实的理论基础以及更好的适用性和一般性。在此基础上,提出了一种预测不同温度下非饱和土相对渗透系数的间接方法。该方法适用于土水特征曲线的整个吸力范围,从而其应用范围也会更广。利用MX-80斑脱土和黄土土样的试验结果,验证了所建立的土水特征曲线方程的正确性,并对不同温度下相对渗透系数随吸力的变化进行了预测。
(5)基于GDS非饱和土三轴仪,开发和研制了全新的压力室系统,并实现了对试验过程中温度的自动控制。所研制的仪器对温度的控制操作简便,数据的测量和采集实现自动化,且所测数据精确。利用所研制的仪器,对取自北京地铁八号线二期某车站基坑的粉质粘土,进行了不同温度下土水特征曲线的试验研究,揭示了温度对土水特征曲线的影响规律。
With the development of modern geotechnical engineering such as the construction of high level radioactive waste repositories, exploitation of natural gas hy-drate and geothermal resources, heat-supply pipelines and high-voltage cables burial in city constructions, research into the multi-field coupled problems in soils including stress, seepage, temperature and chemical effect has become an important issue interna-tionally. Under the effect of multi-field coupling, soil behaviors are different from those under a single field, which including the deformation of soil skeleton, heat transfer, pore-water seepage, advection and diffusion of pollutants in soil pores, the chemical reaction and phase change, etc. And how to determine the soil response under these coupled fields has become an urgent but difficult problem in geotechnical engineering. The study of soil behaviors under multi-fields is of great demand in many applications, e.g., civil engineering construction, geo-disaster prevention, diffusion and migration of pollutants, and high-efficient exploitation of new energies. After several decades're-search on multi-field coupling theory, great achievements have been made. Most of them are based on intuition, experience, or macroscopic recognition, and are lack of a united and consistent scientific theoretical basis. These empirical theories normally have their own limitations and often fail to describe the behaviors of soils under multi-field coupling conditions strictly and effectively. Therefore, the solutions cannot meet the needs of engineering practice. Especially in some modern geotechnical and geoenvi-ronmental engineerings such as high level radioactive waste repositories, the influences of temperature on the deformation-strength and seepage characteristics of unsaturated soils are very significant. However, the related studies are still in its infancy, so valuable research achievement is fewer and the theoretical system has not been established.
In light of the thermodynamics-based porous media theory, a nonlinear multi-field coupled model is proposed in this paper. Following the balance equations, entropy in-equalities of the system and reasonable constitutive assumptions, rigorous theoretical derivation for the new model is presented. Based on the theoretical framework, a new mathematical model that describes the coupled skeleton deformation-fluid flow-heat transfer behavior in unsaturated soils is proposed via proper choices of free energy and dissipation function. In addition, a constitutive model that deals with the ther-mal-mechanical modeling of unsaturated soils is proposed based on simplification of the new coupled theoretical model and available experimental results. Temperature effects on volume change and seepage behavior of unsaturated soils is modeled and simulated by self-developed computer programs. Finally, a new temperature controlled triaxial test systerm for unsaturated soils has been developed to verify the proposed model. A series of SWCC tests are carried out on silt samples using the developed equipment at differ-ent temperatures, which show valuable results. The main achievements of this thesis are listed as follows:
(1) The balance equations with three levels (constituents, phases and the whole mixture soil) are set up under the assumption that soil is composed of multi-constituent elastic-plastic solid skeleton, viscous liquid and ideal gas. With reasonable constitutive assumptions in such restrictive conditions as the principles of determinism, equipre-sence, material frame-indifference and the compatible principle in continuum mechanics, a theoretical framework of constitutive relations modeling three-phase soil in both non-equilibrium and equilibrium states is established, thus the closed field equations are formed. In the theoretical framework, the concept of effective generalized thermody-namic forces is introduced, and the nonlinear coupling constitutive relations between generalized dissipation forces and generalized flows within the system at nonequili-brium state are also presented. On such a basis, four special coupling relations, i.e., sol-id thermal elastic-plastic constitutive relation, liquid visco-elastic-plastic constitutive relation, the generalized Fourier's law, and the generalized Darcy's law are put forward. Based on a specific dissipation function, the concrete form of generalized Darcy's law is deduced; without considering temperature and other coupling effects, the nonlinear coupled model in this thesis can degenerate into a soil elastic-plastic constitutive model.
(2) The coupled skeleton deformation-fluid flow-heat transfer behavior in unsatu-rated soils is very common physical phenomena and engineering problem. Based on the established theoretical framework, constitutive models and a new mathematical model that describe the coupled skeleton deformation-fluid flow-heat transfer behavior in un-saturated soils are proposed via proper choices of free energy and dissipation function. The difference between the proposed model and the existed models in literatures is the nonlinear constitutive equations that considering the effects from every physical field.
(3) Based on the nonlinear multi-field coupled model for soils and by using exist-ing experimental results, an elastic-plastic constitutive model of unsaturated soils under non-isothermal conditions is developed. The model is used to predict and analyze the influence of suction and temperature on the deformation properties of unsaturated soils under isotropic conditions. The proposed model is successfully verified by the compar-isons between the model predictions using Fortran-based computer programs and ex-isted experimental results.
(4) The thermodynamic based expression of suction for unsaturated soils is pre-sented. This expression can consider the temperature effects on suction for both surface tension and wetting coefficients. On contrast of expressions by experimental data fitting, its theoretical basis is more strict, and hence it has broader applicability. By adopting the van Genuchten expression of soil-water characteristic curve, a new model considering the temperature effects is established. On this basis, an indirect method for predicting permeability coefficients of unsaturated soils at different temperatures is presented. The new expressions are made for the entire suction range of SWCC; and hence it has a broader applicability. Based on the experiments of MX-80bentonite and loess, model predictions and the relative permeability coefficients at different temperatures with suc-tions are made.
(5) A new temperature controlled triaxial test systerm for unsaturated soils is de-veloped, which can be used to study the temperature effect on seepage and strength-deformation characteristics of unsaturated soils. With the organic combination of the existing static GDS triaxial test systerm and a new temperature controlled pres-sure chamber, the new test systerm can realize better control of temperature. Using the new temperature controlled triaxial test systerm, the soil-water characteristic curves of silty clay obtained from a foundation ditch of Beijing under different temperatures are tested, which reveal the variation law of the SWCC due to temperatures.
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