低孔隙度岩石细观本构模型及损伤—渗流耦合研究
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摘要
多场耦合问题的研究近年来成为现代岩石力学的一个重要分支，其原因是该领域的研究涉及到诸多工程应用，如核废料处置、石油二次开采、二氧化碳地下封存、高坝坝基安全性评估等等。目前该领域在数学模型、原位实验、计算程序三个方面取得了一定的进展，对岩石、结构面、岩体耦合机制的研究仍需进一步完善。就岩石而言，学者们致力寻求一个可以完全描述应力-应变全过程中渗透率种种变化规律的模型，尤其希望模型能够正确反映出岩石损伤引起的渗透率各向异性演化。本文选择低孔隙度岩石作为研究对象，采用细观力学作为研究工具，全面展开本构模型和渗透率演化模型的研究。论文的主要研究成果和研究工作归纳如下：
(1)对当前岩石力学中常用建模理论、荷载(变形)引起的渗透率演化模型、数值方法进行综述。对比损伤力学中的两个分支：连续损伤力学和细观损伤力学，陈述本文选用细观损伤力学建立本构模型和渗透率演化模型的因由。指出现有的岩石和岩体渗透率演化模型的不足之处，在此基础上提出本文的研究思路和研究方法。
(2)选用基于应变的数学格式建立岩石的细观本构模型。在归纳出低孔隙度岩石三轴试验各种现象的基础上，提出了建模的预期目标。叙述了建模的步骤、REV尺度的确定以及所采用的岩石概念模型：将岩石视为岩石基质和微裂纹系统组成的二元介质。把微裂纹分为张拉／压剪两类，建立了张拉／压剪微裂纹的判别准则，在应变空间中对判别准则进行表达。对张拉微裂纹进行细观力学分析，推导了张拉微裂纹扩展的判别准则和演化方程。应用能量原理推导了张拉微裂纹的四阶均匀化刚度张量和四阶切线均匀化刚度张量。
(3)在评述当前常用的微裂纹滑移准则的基础上，提出了本文的滑移准则，考虑了微裂纹滑移引起的裂纹面法向膨胀，以及由法向膨胀引起的微裂纹进一步扩展，阐明了滑移-扩展相互影响的细观力学机制。推导了压剪微裂纹的四阶切线均匀化刚度张量，通过球面积分推导了含微裂纹系统的增量本构表达式。编制了相应的程序模拟三轴拉伸试验以及三轴压缩试验，对模型的各个参数进行敏感性分析。从细观机理上对计算结果的进行详细的分析和解释。
(4)总结低孔隙度岩石三轴压缩过程中渗透率的变化规律，在此基础上提出岩石的4阶段渗透率演化概念模型，以此作为渗透率演化模型的建模目标。对影响岩石渗透率的两个因素：单条微裂隙开度和微裂隙系统的连通率展开讨论，将单裂隙隙宽的变化拆分为弹性压缩、剪切滑移引起的法向膨胀、裂隙扩展引起的法向膨胀三个部分，推导了应变空间描述的隙宽演化表达式；推导了损伤过程中连通度的演化方程。编制了相应的程序用对渗透率演化模型的参数进行敏感性分析，从微裂隙的细观运动机制上对数值模拟的结果做出详细的解释。
(5)通过试验验证提出的本构模型和渗透率演化模型。选取南京大理石试样进行三轴试验，采用提出细观本构模型对试验进行数值模拟，将模拟的结果和试验的结果进行对比，验证模型的正确性。对其他文献中的花岗岩、砂岩试验成果进行数值模拟，验证模型的普适性。分析两组深部花岗岩的渗透率演化试验成果，用提出的渗透率模型对试验成果进行模拟，并与Souley的数值模拟结果进行对比，给出两种渗透率模型的评述。定性分析洛古玄武岩三轴压塑过程中的渗透率演化的规律，采用本文的渗透率演化模型对其进行数值模拟，并给出评述。
(6)借助于ABAQUS的二次开发功能，将提出的细观模型和渗透率演化模型嵌入其中。用提出的模型模拟加拿大的地下原位试验室420m深处的3条峒室，对模拟的结果给出解释，并与现场观测的结果进行对比。
Coupled THM problem has become an important branch of modern rock mechanics, this issue related to many project applications, such as: disposal of nuclear waste, secondary exploitation of petroleum, underground sealing of carbon dioxide, and safety assessment of high dam foundation etc. Though certain advance has been made on mathematic model, in situ experiment and computer code at present, the coupling process of intact rock, fracture rockmass and signle fracture still need proceed. Scholars still work on the coupling model that could describe the deformation and permeability chang during triaxial compression especially hoped the model could describe the load induced permeability anisotropic chang. In this thesis, we study a special kind of rock: low porosity rock, the constitutive model and permeability change model is investigated by using micromechanical theory. The main research content and result is as follows:
(1) The constitutive modeling theory, permeability change model and numerical method in rock mechanics are summarized. Continue damage theory and micromechanical damge theory is compared; the reason of choosing micromechanical damage theory to establish constitutive model and permeability evolution model is stated. The deficiency in the current permeability change model is pointed out, then, the research thought and method in the thesis is put forward.
(2) The micromechanical model for low porosity rock is established in strain-based formulation. Firstly, the main character of rock deformation in triaxial compression is summaried and a explanation in micro structure level is given as a goal of micromechanical. The procedure of modeling, determination of REV scale and conceptual model of rock: low porosity rock composed of rock host and microcracks is represented. According to stress condition, the microcracks are divided into two classes: tensile microcrack and shear microcrack. The criterion of tensile/shear is established and expressed in the strain space. The criterion of tensile microcrack propagation and evolution equation is deduced based on micromechanics analysis. The fourth order homogeneous stiffness tensor and tagent homogeneous stiffness are deduced by using energy theory.
(3) A comment of criterions of microcrack sliding is given; then a new sliding criterion in this thesis is put forward. Crack sliding induced microcrack surface normal dilation and normal dilation induced microcrack further self-similar propagation are considered, the ineracting of sliding and propagation is clarified. The fourth-order tangent homogeneous stiffness tensor of shear microcrack is deduced, and at last the constitutive model of low porosity is expressed in increment formulation though unit sphere surface integral. The computer code that simulates the triaxial experiment of tension and compression is developed, and sensibility of each model parameter is analyzed, the computation result is analyzed and explained in detail.
(4) The regularity pheonomenon of permeability change in the triaxial compression process is generalized, and the conception model that describes the four stage of permeability evolution is presented, which is the goal of modeling. The two factor influencing rock permeability: aperture of micro fracture and connectivity of micro fracture system is discussed. The change fracture aperture is considered consis of three parts: elastic compression, shear sliding induced normal dilatation and fracture propagation induced normal dilatation. The evolution equation of fracture aperture in the strain space is deduced, and the evolution equation of connectivity in the damage process is derived. The code that analyzes the sensibility of model parameters in the permeability change model is programmed, and computation result is explained with micro fracure kinesis.
(5) The constitutive model and permeability change model is verified through rock sample experiment. Marble sample in Nanjing area is selected to triaxial test, and the test result is simulated by the micro constitutive model suggested in the thesis. The simulation confirms the correct of the model. The universality of the model is proved by simulation of test of granite and sandstone in other literatures. Experiment results of granite permeability in triaxial compression is analyzed and simulated by the permeability change model in the thesis. The simulation result is compared with the result of Souley, and the commentary is given. The experiment result of basalt in Luogu area during the triaxial compression is analyzed and simulated, and the commentary is given.
(6)Developed the calculation code of constitutive and permeability change model by using ABAQUS's user define material routine interface. Three tunnel's excavation about 420 meters below underground which located in URL Canada is simulated using promoted model. Results of simulation is discussed and compared with measured.
(1)对当前岩石力学中常用建模理论、荷载(变形)引起的渗透率演化模型、数值方法进行综述。对比损伤力学中的两个分支：连续损伤力学和细观损伤力学，陈述本文选用细观损伤力学建立本构模型和渗透率演化模型的因由。指出现有的岩石和岩体渗透率演化模型的不足之处，在此基础上提出本文的研究思路和研究方法。
(2)选用基于应变的数学格式建立岩石的细观本构模型。在归纳出低孔隙度岩石三轴试验各种现象的基础上，提出了建模的预期目标。叙述了建模的步骤、REV尺度的确定以及所采用的岩石概念模型：将岩石视为岩石基质和微裂纹系统组成的二元介质。把微裂纹分为张拉／压剪两类，建立了张拉／压剪微裂纹的判别准则，在应变空间中对判别准则进行表达。对张拉微裂纹进行细观力学分析，推导了张拉微裂纹扩展的判别准则和演化方程。应用能量原理推导了张拉微裂纹的四阶均匀化刚度张量和四阶切线均匀化刚度张量。
(3)在评述当前常用的微裂纹滑移准则的基础上，提出了本文的滑移准则，考虑了微裂纹滑移引起的裂纹面法向膨胀，以及由法向膨胀引起的微裂纹进一步扩展，阐明了滑移-扩展相互影响的细观力学机制。推导了压剪微裂纹的四阶切线均匀化刚度张量，通过球面积分推导了含微裂纹系统的增量本构表达式。编制了相应的程序模拟三轴拉伸试验以及三轴压缩试验，对模型的各个参数进行敏感性分析。从细观机理上对计算结果的进行详细的分析和解释。
(4)总结低孔隙度岩石三轴压缩过程中渗透率的变化规律，在此基础上提出岩石的4阶段渗透率演化概念模型，以此作为渗透率演化模型的建模目标。对影响岩石渗透率的两个因素：单条微裂隙开度和微裂隙系统的连通率展开讨论，将单裂隙隙宽的变化拆分为弹性压缩、剪切滑移引起的法向膨胀、裂隙扩展引起的法向膨胀三个部分，推导了应变空间描述的隙宽演化表达式；推导了损伤过程中连通度的演化方程。编制了相应的程序用对渗透率演化模型的参数进行敏感性分析，从微裂隙的细观运动机制上对数值模拟的结果做出详细的解释。
(5)通过试验验证提出的本构模型和渗透率演化模型。选取南京大理石试样进行三轴试验，采用提出细观本构模型对试验进行数值模拟，将模拟的结果和试验的结果进行对比，验证模型的正确性。对其他文献中的花岗岩、砂岩试验成果进行数值模拟，验证模型的普适性。分析两组深部花岗岩的渗透率演化试验成果，用提出的渗透率模型对试验成果进行模拟，并与Souley的数值模拟结果进行对比，给出两种渗透率模型的评述。定性分析洛古玄武岩三轴压塑过程中的渗透率演化的规律，采用本文的渗透率演化模型对其进行数值模拟，并给出评述。
(6)借助于ABAQUS的二次开发功能，将提出的细观模型和渗透率演化模型嵌入其中。用提出的模型模拟加拿大的地下原位试验室420m深处的3条峒室，对模拟的结果给出解释，并与现场观测的结果进行对比。
Coupled THM problem has become an important branch of modern rock mechanics, this issue related to many project applications, such as: disposal of nuclear waste, secondary exploitation of petroleum, underground sealing of carbon dioxide, and safety assessment of high dam foundation etc. Though certain advance has been made on mathematic model, in situ experiment and computer code at present, the coupling process of intact rock, fracture rockmass and signle fracture still need proceed. Scholars still work on the coupling model that could describe the deformation and permeability chang during triaxial compression especially hoped the model could describe the load induced permeability anisotropic chang. In this thesis, we study a special kind of rock: low porosity rock, the constitutive model and permeability change model is investigated by using micromechanical theory. The main research content and result is as follows:
(1) The constitutive modeling theory, permeability change model and numerical method in rock mechanics are summarized. Continue damage theory and micromechanical damge theory is compared; the reason of choosing micromechanical damage theory to establish constitutive model and permeability evolution model is stated. The deficiency in the current permeability change model is pointed out, then, the research thought and method in the thesis is put forward.
(2) The micromechanical model for low porosity rock is established in strain-based formulation. Firstly, the main character of rock deformation in triaxial compression is summaried and a explanation in micro structure level is given as a goal of micromechanical. The procedure of modeling, determination of REV scale and conceptual model of rock: low porosity rock composed of rock host and microcracks is represented. According to stress condition, the microcracks are divided into two classes: tensile microcrack and shear microcrack. The criterion of tensile/shear is established and expressed in the strain space. The criterion of tensile microcrack propagation and evolution equation is deduced based on micromechanics analysis. The fourth order homogeneous stiffness tensor and tagent homogeneous stiffness are deduced by using energy theory.
(3) A comment of criterions of microcrack sliding is given; then a new sliding criterion in this thesis is put forward. Crack sliding induced microcrack surface normal dilation and normal dilation induced microcrack further self-similar propagation are considered, the ineracting of sliding and propagation is clarified. The fourth-order tangent homogeneous stiffness tensor of shear microcrack is deduced, and at last the constitutive model of low porosity is expressed in increment formulation though unit sphere surface integral. The computer code that simulates the triaxial experiment of tension and compression is developed, and sensibility of each model parameter is analyzed, the computation result is analyzed and explained in detail.
(4) The regularity pheonomenon of permeability change in the triaxial compression process is generalized, and the conception model that describes the four stage of permeability evolution is presented, which is the goal of modeling. The two factor influencing rock permeability: aperture of micro fracture and connectivity of micro fracture system is discussed. The change fracture aperture is considered consis of three parts: elastic compression, shear sliding induced normal dilatation and fracture propagation induced normal dilatation. The evolution equation of fracture aperture in the strain space is deduced, and the evolution equation of connectivity in the damage process is derived. The code that analyzes the sensibility of model parameters in the permeability change model is programmed, and computation result is explained with micro fracure kinesis.
(5) The constitutive model and permeability change model is verified through rock sample experiment. Marble sample in Nanjing area is selected to triaxial test, and the test result is simulated by the micro constitutive model suggested in the thesis. The simulation confirms the correct of the model. The universality of the model is proved by simulation of test of granite and sandstone in other literatures. Experiment results of granite permeability in triaxial compression is analyzed and simulated by the permeability change model in the thesis. The simulation result is compared with the result of Souley, and the commentary is given. The experiment result of basalt in Luogu area during the triaxial compression is analyzed and simulated, and the commentary is given.
(6)Developed the calculation code of constitutive and permeability change model by using ABAQUS's user define material routine interface. Three tunnel's excavation about 420 meters below underground which located in URL Canada is simulated using promoted model. Results of simulation is discussed and compared with measured.
引文
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