多孔介质失稳特性研究与化学—水力—力学耦合流形元分析
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摘要
近年来，多相多孔介质的材料失稳和物理-化学耦合非线性分析成为固体力学和工程力学界研究的热点问题之一。与单相材料的力学分析不同，多相多孔介质材料失稳问题和化学-力学耦合非线性分析属于耦合问题。相关研究工作具有广阔的工程应用背景，如与边坡失稳相联的饱和土壤面的破坏和石油开采中油层破裂、诱发地质沉降等问题以及工程土障的设计等。
本论文致力于以下三个方面的工作：1)引入各向异性本构关系，对多相多孔介质在拟静态和动力荷载条件下的失稳特性进行理论研究；2)提出饱和多孔介质动力非线性分析的数值流形元求解方法；3)提出非饱和多孔介质化学-水力-力学耦合本构模型并建立该模型的隐式积分一致性算法及其流形元模拟。
岩土材料作为在细观上由固、液两相(饱和的)或固、液、气三相(非饱和的)组成的多相多孔介质，具有非均匀的结构。而在宏观上一个基本和重要的假定是认为多相多孔介质是均匀连续介质且每相材料均充满全域。这样就可以在连续介质力学理论框架内对多相多孔介质的每点上建立两相或三相耦合模型。
大量对于岩土材料的实验研究结果表明岩土材料的破坏方式与其各向异性特性有关。实际上，这种各向异性行为与岩土材料的特殊的构造相关，比如节理面等，或者是由于应力的增长引起的。因此，在对多相多孔介质进行材料失稳研究中有必要考虑各向异性的材料本构。本文使用各向异性本构关系描述岩土材料的固体骨架的力学行为，基于不连续分叉方法研究了各向异性多孔介质在准静态以及动力荷载下的材料失稳(驻波间断与颤振失稳)问题，并考察了材料参数变化对材料失稳的影响。
饱和多孔介质动力问题的有限元求解存在一个困难，即u-p形式的有限元公式要求位移(或速度)和压力的有限元插值函数满足Babuska-Brezzi稳定性准则或者它的简单表达形式Zienkiewicz-Taylor分片试验条件。否则，计算所得的孔隙压力场会呈现不合理的空间振荡性分布。这些条件判定了使用u-p等阶插值单元(例如T3p3平面单元，即u-p均采用三节点线性插值)是不可靠的。基于数值流形方法的思想，本文提出了适合饱和多孔介质动力非线性分析的流形单元法。数值算例表明该单元能有效地解决孔隙压力场的数值振荡问题且可以被应用到饱和多孔介质非线性破坏的数值模拟中。
人们已经在实验中发现粘质土壤孔隙溶液中的某些化学污染物会对土壤的水力-力学性质产生不利的影响。实际上，环境化学荷载因素可以使土壤产生弹性和不可恢复的塑性变形。深入研究化学荷载对土壤的影响是工程土障、隧道开挖等岩土工程分析和设计中必须考虑的因素。本文在非饱和多孔介质水力-力学本构模型以及饱和多孔介质化学-塑性本构模型的基础上，提出了一个非饱和多孔介质的化学-水力-力学耦合本构模型。根据经典率无关弹塑性模型的Euler向后完全隐式积分算法提出了非饱和多孔介质化学-水力-力学耦合本构模型的隐式积分算法并推导了一致性切线刚度阵。该算法考虑了化学软化效应和非饱和吸力的影响。由于非饱和吸力的变化会产生应力的变化，所以在推导一致性切线刚度阵时考虑了由于吸力的变化所产生的在总体流形单元分析中的非平衡力。数值算例表明该算法在局部水平具有较好的精度和收敛性，并能应用到有化学荷载的岩土工程问题中。
In the recent years, material instabilities and coupled physico-chemical nonlinear analysis of multiphase porous media has been one of research focuses in solid mechanics and engineering mechanics. Unlike simple mechanical analysis for single phase materials, this subject is a coupled problem and has comprehensive engineering applications, such as landslide related to the failure of saturated soils, fracture of the reservoir and land subsidence in petroleum extraction and design of engineering clay barrier etc.
The emphases of this thesis focus on the following three aspects. Firstly, an anisotropic constitutive relation is introduced to the theoretical research of material instabilities for multiphase porous media under quasi-static and dynamic loading conditions. Secondly, numerical manifold element is presented for dynamic nonlinear analysis of saturated porous media. Thirdly, a chemo-hydro-mechanical constitutive model and the corresponding implicit integration algorithm are presented for numerical simulation of partially saturated porous media.
Modelled as the solid-liquid or solid-liquid-gas mixture, saturated or partially saturated geomaterials have non-homogeneous structures in space. A fundamental assumption is to model the non-homogeneous multiphase system as a porous-continuum in the macroscopic level, in which each phase is assumed to fill up the whole domain. Based on this assumption, the theory frame of continuum can be applied to porous media as two-phase or three-phase mixtures.
A great number of experiment investigations on geomaterials indicate that the failure mode of geomaterials is related to the anisotropic behavior. As a matter of fact, the anisotropic behavior is caused by the special structures of geomaterials, such as layering etc, or by stress growth. It is necessary to introduce anisotropic constitutive relations to material instability analysis of porous media. An anisotropic constitutive model developed for geomaterials is used to model the anisotropic mechanical behavior of the solid skeleton of saturated porous media. Conditions for static instability and dynamic instability (stationary discontinuity and flutter instability) of saturated porous media are derived based on strain rate discontinuous bifurcation analysis method. The effects of material parameters on material instability are investigated in detail by numerical computations.
There is a difficulty in finite element analysis for u-p mixed formulation of saturated porous media. Lots of previous works showed that the interpolation function for the displacement and the pore pressure must fulfill the so-called Babuska-Brezzi stability criteria or the Zienkiewicz-Taylor patch test. Otherwise, oscillations will appear in pore pressure field. These criteria preclude the use of finite elements with the same order of interpolation, such as T3p3 triangles (3-noded linear triangle for displacement and 3-noded linear triangle for pressure). Based on the idea of the numerical manifold method, the manifold elements for dynamic nonlinear analysis of saturated porous media are developed. Numerical examples indicate that the proposed manifold elements achieve the goal of avoiding oscillations in pressure field and can be applied in nonlinear failure analysis of saturated porous media.
It has been recognized from experiments that chemical concentration in pore fluid may have negative effect on the hydro-mechanical qualities of clayed soils. Chemical loading may cause elastic and elastoplastic deformation. Understanding of the chemical effect is essential for the design and analysis of civil engineering such as clay barriers and tunnels etc. A coupled chemo-hydro-mechanical constitutive model of partially porous media is developed on the basis of the existing hydro-mechanical constitutive model and chemo-plastic constitutive model. Based on the definition of implicit Euler backward integration scheme for standard plasticity, an implicit integration algorithm and the consistent tangent moduli are presented for the chemo-hydro-mechanical constitutive model. The chemical softening effect and variation of suction are taken into account in the present algorithm. The nonlinear terms arose by suction are also taken into account at global level of manifold element analysis. Numerical examples are presented to demonstrate accuracy and convergence property of the algorithm proposed at local level and the application to geotechnical engineering with chemical loading.
本论文致力于以下三个方面的工作：1)引入各向异性本构关系，对多相多孔介质在拟静态和动力荷载条件下的失稳特性进行理论研究；2)提出饱和多孔介质动力非线性分析的数值流形元求解方法；3)提出非饱和多孔介质化学-水力-力学耦合本构模型并建立该模型的隐式积分一致性算法及其流形元模拟。
岩土材料作为在细观上由固、液两相(饱和的)或固、液、气三相(非饱和的)组成的多相多孔介质，具有非均匀的结构。而在宏观上一个基本和重要的假定是认为多相多孔介质是均匀连续介质且每相材料均充满全域。这样就可以在连续介质力学理论框架内对多相多孔介质的每点上建立两相或三相耦合模型。
大量对于岩土材料的实验研究结果表明岩土材料的破坏方式与其各向异性特性有关。实际上，这种各向异性行为与岩土材料的特殊的构造相关，比如节理面等，或者是由于应力的增长引起的。因此，在对多相多孔介质进行材料失稳研究中有必要考虑各向异性的材料本构。本文使用各向异性本构关系描述岩土材料的固体骨架的力学行为，基于不连续分叉方法研究了各向异性多孔介质在准静态以及动力荷载下的材料失稳(驻波间断与颤振失稳)问题，并考察了材料参数变化对材料失稳的影响。
饱和多孔介质动力问题的有限元求解存在一个困难，即u-p形式的有限元公式要求位移(或速度)和压力的有限元插值函数满足Babuska-Brezzi稳定性准则或者它的简单表达形式Zienkiewicz-Taylor分片试验条件。否则，计算所得的孔隙压力场会呈现不合理的空间振荡性分布。这些条件判定了使用u-p等阶插值单元(例如T3p3平面单元，即u-p均采用三节点线性插值)是不可靠的。基于数值流形方法的思想，本文提出了适合饱和多孔介质动力非线性分析的流形单元法。数值算例表明该单元能有效地解决孔隙压力场的数值振荡问题且可以被应用到饱和多孔介质非线性破坏的数值模拟中。
人们已经在实验中发现粘质土壤孔隙溶液中的某些化学污染物会对土壤的水力-力学性质产生不利的影响。实际上，环境化学荷载因素可以使土壤产生弹性和不可恢复的塑性变形。深入研究化学荷载对土壤的影响是工程土障、隧道开挖等岩土工程分析和设计中必须考虑的因素。本文在非饱和多孔介质水力-力学本构模型以及饱和多孔介质化学-塑性本构模型的基础上，提出了一个非饱和多孔介质的化学-水力-力学耦合本构模型。根据经典率无关弹塑性模型的Euler向后完全隐式积分算法提出了非饱和多孔介质化学-水力-力学耦合本构模型的隐式积分算法并推导了一致性切线刚度阵。该算法考虑了化学软化效应和非饱和吸力的影响。由于非饱和吸力的变化会产生应力的变化，所以在推导一致性切线刚度阵时考虑了由于吸力的变化所产生的在总体流形单元分析中的非平衡力。数值算例表明该算法在局部水平具有较好的精度和收敛性，并能应用到有化学荷载的岩土工程问题中。
In the recent years, material instabilities and coupled physico-chemical nonlinear analysis of multiphase porous media has been one of research focuses in solid mechanics and engineering mechanics. Unlike simple mechanical analysis for single phase materials, this subject is a coupled problem and has comprehensive engineering applications, such as landslide related to the failure of saturated soils, fracture of the reservoir and land subsidence in petroleum extraction and design of engineering clay barrier etc.
The emphases of this thesis focus on the following three aspects. Firstly, an anisotropic constitutive relation is introduced to the theoretical research of material instabilities for multiphase porous media under quasi-static and dynamic loading conditions. Secondly, numerical manifold element is presented for dynamic nonlinear analysis of saturated porous media. Thirdly, a chemo-hydro-mechanical constitutive model and the corresponding implicit integration algorithm are presented for numerical simulation of partially saturated porous media.
Modelled as the solid-liquid or solid-liquid-gas mixture, saturated or partially saturated geomaterials have non-homogeneous structures in space. A fundamental assumption is to model the non-homogeneous multiphase system as a porous-continuum in the macroscopic level, in which each phase is assumed to fill up the whole domain. Based on this assumption, the theory frame of continuum can be applied to porous media as two-phase or three-phase mixtures.
A great number of experiment investigations on geomaterials indicate that the failure mode of geomaterials is related to the anisotropic behavior. As a matter of fact, the anisotropic behavior is caused by the special structures of geomaterials, such as layering etc, or by stress growth. It is necessary to introduce anisotropic constitutive relations to material instability analysis of porous media. An anisotropic constitutive model developed for geomaterials is used to model the anisotropic mechanical behavior of the solid skeleton of saturated porous media. Conditions for static instability and dynamic instability (stationary discontinuity and flutter instability) of saturated porous media are derived based on strain rate discontinuous bifurcation analysis method. The effects of material parameters on material instability are investigated in detail by numerical computations.
There is a difficulty in finite element analysis for u-p mixed formulation of saturated porous media. Lots of previous works showed that the interpolation function for the displacement and the pore pressure must fulfill the so-called Babuska-Brezzi stability criteria or the Zienkiewicz-Taylor patch test. Otherwise, oscillations will appear in pore pressure field. These criteria preclude the use of finite elements with the same order of interpolation, such as T3p3 triangles (3-noded linear triangle for displacement and 3-noded linear triangle for pressure). Based on the idea of the numerical manifold method, the manifold elements for dynamic nonlinear analysis of saturated porous media are developed. Numerical examples indicate that the proposed manifold elements achieve the goal of avoiding oscillations in pressure field and can be applied in nonlinear failure analysis of saturated porous media.
It has been recognized from experiments that chemical concentration in pore fluid may have negative effect on the hydro-mechanical qualities of clayed soils. Chemical loading may cause elastic and elastoplastic deformation. Understanding of the chemical effect is essential for the design and analysis of civil engineering such as clay barriers and tunnels etc. A coupled chemo-hydro-mechanical constitutive model of partially porous media is developed on the basis of the existing hydro-mechanical constitutive model and chemo-plastic constitutive model. Based on the definition of implicit Euler backward integration scheme for standard plasticity, an implicit integration algorithm and the consistent tangent moduli are presented for the chemo-hydro-mechanical constitutive model. The chemical softening effect and variation of suction are taken into account in the present algorithm. The nonlinear terms arose by suction are also taken into account at global level of manifold element analysis. Numerical examples are presented to demonstrate accuracy and convergence property of the algorithm proposed at local level and the application to geotechnical engineering with chemical loading.
引文
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