干燥和饱水状态下炭质板岩流变力学特性与模型研究
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摘要
开展不同含水状态下岩石流变力学特性与模型研究，对于正确预测和有效控制岩石工程的安全与稳定具有重要的理论价值和工程实践意义。本文以兰渝铁路木寨岭隧道炭质板岩为研究对象，采用试验研究、理论分析相结合的方法，基于炭质板岩在干燥和饱水状态下的力学特性以及蠕变规律，建立适用于炭质板岩的非线性流变理论模型，结合粒子群算法(PSO)和非线性最小二乘法对流变参数进行辨识，并将建立的流变模型嵌入FLAC3D，完成数值程序的二次开发。本文主要研究工作如下：
(1)开展干燥和饱和状态下炭质板岩单轴和三轴试验、楔形剪切试验、巴西圆盘劈裂试验，以及单轴循环加卸载瞬时力学特性试验，掌握了两种状态下炭质板岩的瞬时力学特性，也为开展岩石蠕变试验提供了试验基础。试验结果表明：水对炭质板岩强度和变形的影响是显著的，而在单轴循环加卸载条件下的影响更为突出；
(2)采用全自动伺服流变仪，对干燥和饱和炭质板岩开展分级加载和分级增量循环加卸载蠕变试验，研究两种状态下炭质板岩的蠕变特点，以及水对岩石在各级压力下的蠕变量、蠕变速率的影响。在中、低应力水平下，岩石蠕变变形主要呈现出衰减蠕变和稳态蠕变2个阶段，当加载应力增加到较高应力水平时，岩石轴向变形急剧增长，表现出加速蠕变阶段；相同应力水平下的饱水岩样的蠕变量为干燥岩样的3倍以上；加卸载蠕变试验表明：水对岩石瞬时变形的影响主要表现在瞬时塑性变形方面，对瞬时弹性变形的影响不大，而对岩石蠕变变形的影响则主要体现在粘弹性应变方面；
(3)根据炭质板岩在干燥和饱水状态下的蠕变特点，在Burgers流变模型的基础上，结合一个非线性粘塑性体，和Burgers流变模型相串联，构建适于炭质板岩蠕变特点的改进Burgers非线性粘弹塑性流变模型，导出了模型的本构方程、蠕变方程、卸载方程以及蠕变模型的三维形式；
(4)在粒子群算法的基础上，将线性递减权重粒子群算法和Levenberg-Marqud非线性最小二乘法相结合，先采用线性递减粒子群算法对流变模型参数进行初步辨识，将其结果作为初始值，再采用L-M算法进行辨识，参数辨识后的相关系数均在0.94以上；
(5)针对目前建立的能反映蠕变加速阶段的流变模型元件和参数较多的问题，借鉴经典元件组合模型的建模思路，将含分数阶微积分的软体元件与弹簧元件串联，结合一个幂函数粘塑性体，提出一种新的四元件非线性粘弹塑性流变模型，并给出该模型的本构方程和蠕变方程。利用炭质板岩蠕变试验结果，将该模型与改进Burgers非线性流变模型进行对比拟合分析，表明该模型能够有效地描述岩石的三阶段蠕变特性，在满足拟合精度的前提下，能够减少组合模型中的元件个数和参数数量；
(6)岩石的蠕变过程是岩石内部应力不断调整，硬化和损伤效应不断发展并共同作用的结果。以经典元件模型为基础，将岩石的初始屈服强度作为蠕变硬化的应力阈值，岩石的长期强度作为损伤软化的应力阈值，引入能反映岩石蠕变硬化的硬化函数和损伤效应的损伤变量，建立了一个能够全面反映蠕变机制的岩石非线性蠕变模型。利用蠕变试验数据对所提出的模型进行辨识，结果表明该模型不仅能够很好地描述三阶段蠕变特性，而且可以全面反映岩石蠕变过程中的蠕变硬化和损伤软化机制；
(7)依据FLAC3D提供的内置本构模型源代码，在Burgers蠕变模型有限差分形式的基础上，导出了改进Burgers非线性蠕变模型的三维差分形式。借助C++语言将改进Burgers非线性蠕变模型的三维差分形式编译成动态链接库，嵌套到FLAC3D中，实现了本构模型的二次开发，并利用新开发的流变模型进行单轴压缩蠕变模拟试验，验证了程序二次开发的正确性。
It is very important theoretical value and practical significance is that carry out the rockrheological mechanical properties and models research for which correct prediction andeffective control of the security and stability of rock engineering under different waterconditions. carbonaceous slate in wooden village ridge tunnel of Lan-Yu railway were takenfor research object, the research methods combined with the experiment, theoretical analysisand numerical calculation are used, based on the mechanical properties and creep law in dryand saturated state of the carbonaceous slates, Nonlinear rheological constitutive model ofcarbonaceous slate rock were established, identified the rheological parameters combinedwith particle swarm optimization (PSO) and nonlinear least square method, and accomplishedsecondary development in the FLAC3Dnumerical program, all of these are vital for predictionlong-term stability of tunnel engineering. The paper mainly focused on the following:
(1) It is grasp the instantaneous mechanical properties of dry and saturated statecarbonaceous slate in which carry out uniaxial and triaxial compression test, wedge shear test,brazilian spilt test, as well as uniaxial cyclic loading and unloading instantaneous mechanicalproperties test. It is mainly focused on the mechanical property differences of two states ofrock, and also provide test base for creep test of rock; The test shows that water bring aboutsignificant influence to strength and deformation of carbonaceous slates, especially in uniaxialcyclic loading and unloading test conditions;
(2) It is launched step load and circular increment step load and unload creep test of thedry and saturated carbonaceous slates in automatic servo rheometer, the mainly researchedcreep characteristics of two conditions of carbonaceous slates, and the influence of watertowards on the creep value and creep rate under all levels of pressure.The test resultsindicated that creep deformation mainly presents attenuation creep and steady-state creep inmost stress level, and the deformation has increased dramatically, performance acceleratingcreep stage when the stress level is higher. The mainly influence of water towards on rock isthat instantaneous plastic value in instantaneous deformation and the visco-elastic strain increep deformation;
(3) According to the creep characteristics of carbonaceous slates in dry and saturatedstate, put forward a nonlinear viscoplastic body, combined with Burgers rheological model,established an improvement Burgers nonlinear viscoelastic-plastic rheological model, and thecreep equation, unloading equation and three dimensional form of creep model is deducedfrom the rheological constitutive model model;
(4) Considered the defect of parameter identification in rheological model, based on theimprovement particle swarm optimization (PSO), combined with linear decreasing weightparticle swarm optimization and Levenberg-Marqud nonlinear least squares method, a newparameter inversion method is proposed，which proceeds as:1) the model parmeters areinverted using PSO;2) L-M nonlinear least square is used to invert the model parameterswith initial values from step1). A case demonstrates that the PSO—L-M method could beeffectively used in inverting the parameters of rock creep models;
(5) By means of classic element combination modeling ideas, put forward a newnonlinear viscoelasto-plastic rheological model that contained component of fractionalcalculus and a nonlinear visco-plastic body of power function, and given constitutive equationand creep equation of the model. The fitted results of the test data showed that nonlinearrheological model that contained soft-matter element and nonlinear visco-plastic body can beeffectively depicted the creep properties of rocks, efficiently reduced the number ofcomponents and parameters of combination model;
(6) Rock creep process is the result that constantly adjusts internal stresses of rock,hardening and damage effect gradually growth and mutual affect. By means of classicelement combination modeling ideas, the rock initial yield strength is regarded as the stressthreshold of the creep hardening, and rock's long-term strength served as the stress thresholdof damage softening, introduced hardening function and damage variable that can reflectedthe effect of rock hardening and damage effect, established nonlinear creep model of rock thatcan comprehensively reflected the creep mechanism. The fitted results of the test data showedthat nonlinear rheological model not only can be effectively described the creep process ofrocks, but also can reflected creep hardening and damage softening mechanism in the creepprocess of rocks;
(7) On the basis of the constitutive model code and the finite difference form of Burgerscreep model in FLAC3D, deduced the three dimensional difference form of improvementBurgers nonlinear creep model,and compiled into the dynamic link library in FLAC3Dby C++language, finished secondary development of the constitutive model. Uniaxial compressioncreep simulation test is implemented, the simulation test manifested that it is fitted for theindoor creep test curves, verified the correctness of the secondary development.
(1)开展干燥和饱和状态下炭质板岩单轴和三轴试验、楔形剪切试验、巴西圆盘劈裂试验，以及单轴循环加卸载瞬时力学特性试验，掌握了两种状态下炭质板岩的瞬时力学特性，也为开展岩石蠕变试验提供了试验基础。试验结果表明：水对炭质板岩强度和变形的影响是显著的，而在单轴循环加卸载条件下的影响更为突出；
(2)采用全自动伺服流变仪，对干燥和饱和炭质板岩开展分级加载和分级增量循环加卸载蠕变试验，研究两种状态下炭质板岩的蠕变特点，以及水对岩石在各级压力下的蠕变量、蠕变速率的影响。在中、低应力水平下，岩石蠕变变形主要呈现出衰减蠕变和稳态蠕变2个阶段，当加载应力增加到较高应力水平时，岩石轴向变形急剧增长，表现出加速蠕变阶段；相同应力水平下的饱水岩样的蠕变量为干燥岩样的3倍以上；加卸载蠕变试验表明：水对岩石瞬时变形的影响主要表现在瞬时塑性变形方面，对瞬时弹性变形的影响不大，而对岩石蠕变变形的影响则主要体现在粘弹性应变方面；
(3)根据炭质板岩在干燥和饱水状态下的蠕变特点，在Burgers流变模型的基础上，结合一个非线性粘塑性体，和Burgers流变模型相串联，构建适于炭质板岩蠕变特点的改进Burgers非线性粘弹塑性流变模型，导出了模型的本构方程、蠕变方程、卸载方程以及蠕变模型的三维形式；
(4)在粒子群算法的基础上，将线性递减权重粒子群算法和Levenberg-Marqud非线性最小二乘法相结合，先采用线性递减粒子群算法对流变模型参数进行初步辨识，将其结果作为初始值，再采用L-M算法进行辨识，参数辨识后的相关系数均在0.94以上；
(5)针对目前建立的能反映蠕变加速阶段的流变模型元件和参数较多的问题，借鉴经典元件组合模型的建模思路，将含分数阶微积分的软体元件与弹簧元件串联，结合一个幂函数粘塑性体，提出一种新的四元件非线性粘弹塑性流变模型，并给出该模型的本构方程和蠕变方程。利用炭质板岩蠕变试验结果，将该模型与改进Burgers非线性流变模型进行对比拟合分析，表明该模型能够有效地描述岩石的三阶段蠕变特性，在满足拟合精度的前提下，能够减少组合模型中的元件个数和参数数量；
(6)岩石的蠕变过程是岩石内部应力不断调整，硬化和损伤效应不断发展并共同作用的结果。以经典元件模型为基础，将岩石的初始屈服强度作为蠕变硬化的应力阈值，岩石的长期强度作为损伤软化的应力阈值，引入能反映岩石蠕变硬化的硬化函数和损伤效应的损伤变量，建立了一个能够全面反映蠕变机制的岩石非线性蠕变模型。利用蠕变试验数据对所提出的模型进行辨识，结果表明该模型不仅能够很好地描述三阶段蠕变特性，而且可以全面反映岩石蠕变过程中的蠕变硬化和损伤软化机制；
(7)依据FLAC3D提供的内置本构模型源代码，在Burgers蠕变模型有限差分形式的基础上，导出了改进Burgers非线性蠕变模型的三维差分形式。借助C++语言将改进Burgers非线性蠕变模型的三维差分形式编译成动态链接库，嵌套到FLAC3D中，实现了本构模型的二次开发，并利用新开发的流变模型进行单轴压缩蠕变模拟试验，验证了程序二次开发的正确性。
It is very important theoretical value and practical significance is that carry out the rockrheological mechanical properties and models research for which correct prediction andeffective control of the security and stability of rock engineering under different waterconditions. carbonaceous slate in wooden village ridge tunnel of Lan-Yu railway were takenfor research object, the research methods combined with the experiment, theoretical analysisand numerical calculation are used, based on the mechanical properties and creep law in dryand saturated state of the carbonaceous slates, Nonlinear rheological constitutive model ofcarbonaceous slate rock were established, identified the rheological parameters combinedwith particle swarm optimization (PSO) and nonlinear least square method, and accomplishedsecondary development in the FLAC3Dnumerical program, all of these are vital for predictionlong-term stability of tunnel engineering. The paper mainly focused on the following:
(1) It is grasp the instantaneous mechanical properties of dry and saturated statecarbonaceous slate in which carry out uniaxial and triaxial compression test, wedge shear test,brazilian spilt test, as well as uniaxial cyclic loading and unloading instantaneous mechanicalproperties test. It is mainly focused on the mechanical property differences of two states ofrock, and also provide test base for creep test of rock; The test shows that water bring aboutsignificant influence to strength and deformation of carbonaceous slates, especially in uniaxialcyclic loading and unloading test conditions;
(2) It is launched step load and circular increment step load and unload creep test of thedry and saturated carbonaceous slates in automatic servo rheometer, the mainly researchedcreep characteristics of two conditions of carbonaceous slates, and the influence of watertowards on the creep value and creep rate under all levels of pressure.The test resultsindicated that creep deformation mainly presents attenuation creep and steady-state creep inmost stress level, and the deformation has increased dramatically, performance acceleratingcreep stage when the stress level is higher. The mainly influence of water towards on rock isthat instantaneous plastic value in instantaneous deformation and the visco-elastic strain increep deformation;
(3) According to the creep characteristics of carbonaceous slates in dry and saturatedstate, put forward a nonlinear viscoplastic body, combined with Burgers rheological model,established an improvement Burgers nonlinear viscoelastic-plastic rheological model, and thecreep equation, unloading equation and three dimensional form of creep model is deducedfrom the rheological constitutive model model;
(4) Considered the defect of parameter identification in rheological model, based on theimprovement particle swarm optimization (PSO), combined with linear decreasing weightparticle swarm optimization and Levenberg-Marqud nonlinear least squares method, a newparameter inversion method is proposed，which proceeds as:1) the model parmeters areinverted using PSO;2) L-M nonlinear least square is used to invert the model parameterswith initial values from step1). A case demonstrates that the PSO—L-M method could beeffectively used in inverting the parameters of rock creep models;
(5) By means of classic element combination modeling ideas, put forward a newnonlinear viscoelasto-plastic rheological model that contained component of fractionalcalculus and a nonlinear visco-plastic body of power function, and given constitutive equationand creep equation of the model. The fitted results of the test data showed that nonlinearrheological model that contained soft-matter element and nonlinear visco-plastic body can beeffectively depicted the creep properties of rocks, efficiently reduced the number ofcomponents and parameters of combination model;
(6) Rock creep process is the result that constantly adjusts internal stresses of rock,hardening and damage effect gradually growth and mutual affect. By means of classicelement combination modeling ideas, the rock initial yield strength is regarded as the stressthreshold of the creep hardening, and rock's long-term strength served as the stress thresholdof damage softening, introduced hardening function and damage variable that can reflectedthe effect of rock hardening and damage effect, established nonlinear creep model of rock thatcan comprehensively reflected the creep mechanism. The fitted results of the test data showedthat nonlinear rheological model not only can be effectively described the creep process ofrocks, but also can reflected creep hardening and damage softening mechanism in the creepprocess of rocks;
(7) On the basis of the constitutive model code and the finite difference form of Burgerscreep model in FLAC3D, deduced the three dimensional difference form of improvementBurgers nonlinear creep model,and compiled into the dynamic link library in FLAC3Dby C++language, finished secondary development of the constitutive model. Uniaxial compressioncreep simulation test is implemented, the simulation test manifested that it is fitted for theindoor creep test curves, verified the correctness of the secondary development.
引文
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