岩石类材料的动态性能研究
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摘要
岩石类材料动态力学特性的研究是岩石力学较为基础的研究分支，这方面的工作较早源于原子能设施安全防护以及地震工程的研究。随着工程爆破在岩矿开采、地下洞室的营造以及场平开挖等工程中的广泛应用，岩石类材料的动态力学特性的研究有了较大的发展。与岩石类材料的静力学相比，其动力学问题在实验研究和力学分析上要复杂得多，物理和数学处理上也困难得多，因此到目前为止岩石类材料在动态实验研究和动力学理论分析上还处于不成熟阶段，某些研究领域还仅仅处于起步阶段。虽然国内外研究人员对岩石类材料在动荷载作用下的强度和变形特性做了一些卓有成效的工作，但这些工作主要集中在实验研究方面，而且大部分限于中低应变率下简单应力作用的实验研究，因此对其进行实验与理论相结合的系统研究是十分必要的。
本文采用纯铜波形整形器改进后的分离式Hopkinson压杆装置(SHPB)，分别对新加坡地区的花岗岩和混凝土试件进行了中高应变率下的单轴冲击压缩和动态巴西圆盘实验。从动态实验研究出发，结合考虑多裂纹相互作用的滑移型裂纹模型、元件模型理论、反演分析以及数值计算等理论分析方法，将材料的微观特征与宏观现象相结合、理性与物性相结合，研究岩石类材料的内部微观结构与宏观动态力学特性的内在联系和规律，从宏观和微观两个角度对岩石类材料的动态力学特性进行充分地研究。旨在提出能为工程界所接受，便于数值分析的考虑损伤的岩石类材料动态本构模型及其研究方法。本文的研究内容和结果为：
(1)花岗岩和混凝土材料在动态单轴荷载作用下的实验研究。针对岩石类材料的特性采用黄铜波形整形器改进了SHPB装置，有效地避免了加载冲击荷载时，脆性材料在内部应力达到均衡之前过早的破坏，并且有效地降低了应力波的高频震荡给实验数据带来的波动。利用改进后的SHPB装置对新加坡地区的花岗岩和混凝土试件在不同应变率下进行了动态单轴压缩实验和动态巴西圆盘实验。研究表明在中高应变率下，花岗岩和混凝土材料的单轴冲击压缩强度、破坏程度、能量吸收以及冲击拉伸强度等动态力学性能有较强的应变率相关性，而材料的弹性模量、动态破坏应变、能量吸收率等参数可视为应变率无关量；
(2)花岗岩和混凝土材料的动态断裂性能研究。在实验的基础上，利用考虑多裂纹相互作用的滑移型裂纹模型，深入分析岩石类材料的微观内部缺陷对其宏观动态断裂特性的影响。分析表明裂纹面的摩擦系数决定了最易扩展的初始裂纹角度；正则化动态应力强度因子随着裂纹间距的增加而减小；动态应力强度因子与裂纹初始长度成正比；随着应变率的增加，临界裂纹初始长度有减小的趋势等；
(3)花岗岩和混凝土材料的动态本构模型研究。通过考虑应变率强化因子和损伤弱化因子修正静态线弹性和非弹性本构模型，建立岩石类材料的动态弹性损伤本构方程，并通过标准应力-应变曲线的几何特征初步确定出本构方程的部分参数；在总结现有元件模型以及岩石类材料力学特性的基础上，通过弹性元件、粘元件、塑性元件以及损伤元件的串并联组合，建立了岩石类材料的粘弹塑性损伤动态本构模型，并推导出其微分形式的本构方程；
(4)花岗岩和混凝土材料的动态力学特性反演分析。用计算机语言C++，编写基于下山法改进的自适应混合遗传算法的反演分析程序。结合SHPB实验结果，对花岗岩和混凝土材料的动态本构关系中的待定参数进行了反演分析。通过对再生应力-应变曲线与实验曲线的比较分析，证明该反演算法的参数识辨能力可以很好的满足SHPB实验的精度要求，并且验证了动态本构模型对于岩石类材料的适用性。
(5)花岗岩和混凝土材料的动态特性数值分析。结合岩石类材料动态本构模型，分别建立了应力波在考虑损伤的非线弹性和粘弹塑性细长杆件中的一维波动方程，以及基于损伤动态弹性本构模型的空间轴对称波动方程。利用有限差分法，在非线弹性波的传播理论研究的基础上，数值模拟从子弹撞击入射杆到试件破碎的整个加载过程中应力波在两压杆和试件中的传播，并与实验结果比较得到了可靠性验证。编制了可以考虑径向变形的岩石类材料的多维数值模拟程序，为材料动态特性研究提出了新的思路和方法。
Experiments of granite and concrete in high strain-rate unaxial compressive loading were produced in the modified split Hopkinson pressure bar (SHPB) with copper as the pulse shaper. It can be used to ensure the symmetrical stress in the specimens before fracture and avoid the fluctuation of test data due to input shaky stress pulse. Based on the results of the dynamical experiments and the theoretical analysis with the dynamic microcrack model and constitutive model theory, the relations and rule between the microcosmic frame and macroscopical mechanics characteristic of rock materials are discussed adequately. Furthermore, the optimization method based on the mixed genetic algorithmsand numerical analysis with the finite difference methods on rock materials are used to validate the results of the theory analysis. The research method can be applied to the other brittleness materials and laigh impedance materials. The main content in this thesis can be shown as follow:
The results of dynamic experiments on rock materials show that not only the compression strength of granite and concrete increase, but also the fragment size decrease and fragment numbers increase with the increasing strain rate. On the other hand, the results of experiments show also that the failure of the granite cylinder is typical tensile splitting failure mode by sudden splitting parallel with the direction of uniaxial compressive loading at different strain rates. Through analyzing contrastively the stress-strain curves, the energy absorbency-time curves and the energy absorptivity-time curves of granite with concrete, it is illuminated the brittleness, impedance, compression deformation capability of rock-like materials is crucial factor on the dynamic fracture.
The numerical calculation based on a dynamic interacting sliding microcrack model is adopted to investigate quantificationally the influence on the macro-mechanics properties of rock materials from microcracks included the different initial crack length, crack angle, crack space and friction coefficient under different strain rates. Accordingly, the strain-dependency of mechanics characteristic on rock materials can be explained reasonably.
Based on the statistical damage theory and constitutive model theory, the non-linear elastic and viscoelastoplastic dynamic constitutive relation of rock materials are constructed. The characteristic parameters of the dynamic constitutive model of rock materials are ascertained with the inverse analysis method with the adaptive hybrid genetic algorithms.
The non-linear elastic stress wave and viscoelastoplastic stress wave equation are derived with constitutive equation of rock materials and stress wave theory. Numerical simulation programs on the dynamic mechanics characteristic of rock materials based on the stress wave equation are programmed. Through contrastively analyzing the results of Numerical simulation and experiments, the correctness of the theory analysis on the dynamic mechanics characteristic of rock materials and the stress wave equations can be testified.
本文采用纯铜波形整形器改进后的分离式Hopkinson压杆装置(SHPB)，分别对新加坡地区的花岗岩和混凝土试件进行了中高应变率下的单轴冲击压缩和动态巴西圆盘实验。从动态实验研究出发，结合考虑多裂纹相互作用的滑移型裂纹模型、元件模型理论、反演分析以及数值计算等理论分析方法，将材料的微观特征与宏观现象相结合、理性与物性相结合，研究岩石类材料的内部微观结构与宏观动态力学特性的内在联系和规律，从宏观和微观两个角度对岩石类材料的动态力学特性进行充分地研究。旨在提出能为工程界所接受，便于数值分析的考虑损伤的岩石类材料动态本构模型及其研究方法。本文的研究内容和结果为：
(1)花岗岩和混凝土材料在动态单轴荷载作用下的实验研究。针对岩石类材料的特性采用黄铜波形整形器改进了SHPB装置，有效地避免了加载冲击荷载时，脆性材料在内部应力达到均衡之前过早的破坏，并且有效地降低了应力波的高频震荡给实验数据带来的波动。利用改进后的SHPB装置对新加坡地区的花岗岩和混凝土试件在不同应变率下进行了动态单轴压缩实验和动态巴西圆盘实验。研究表明在中高应变率下，花岗岩和混凝土材料的单轴冲击压缩强度、破坏程度、能量吸收以及冲击拉伸强度等动态力学性能有较强的应变率相关性，而材料的弹性模量、动态破坏应变、能量吸收率等参数可视为应变率无关量；
(2)花岗岩和混凝土材料的动态断裂性能研究。在实验的基础上，利用考虑多裂纹相互作用的滑移型裂纹模型，深入分析岩石类材料的微观内部缺陷对其宏观动态断裂特性的影响。分析表明裂纹面的摩擦系数决定了最易扩展的初始裂纹角度；正则化动态应力强度因子随着裂纹间距的增加而减小；动态应力强度因子与裂纹初始长度成正比；随着应变率的增加，临界裂纹初始长度有减小的趋势等；
(3)花岗岩和混凝土材料的动态本构模型研究。通过考虑应变率强化因子和损伤弱化因子修正静态线弹性和非弹性本构模型，建立岩石类材料的动态弹性损伤本构方程，并通过标准应力-应变曲线的几何特征初步确定出本构方程的部分参数；在总结现有元件模型以及岩石类材料力学特性的基础上，通过弹性元件、粘元件、塑性元件以及损伤元件的串并联组合，建立了岩石类材料的粘弹塑性损伤动态本构模型，并推导出其微分形式的本构方程；
(4)花岗岩和混凝土材料的动态力学特性反演分析。用计算机语言C++，编写基于下山法改进的自适应混合遗传算法的反演分析程序。结合SHPB实验结果，对花岗岩和混凝土材料的动态本构关系中的待定参数进行了反演分析。通过对再生应力-应变曲线与实验曲线的比较分析，证明该反演算法的参数识辨能力可以很好的满足SHPB实验的精度要求，并且验证了动态本构模型对于岩石类材料的适用性。
(5)花岗岩和混凝土材料的动态特性数值分析。结合岩石类材料动态本构模型，分别建立了应力波在考虑损伤的非线弹性和粘弹塑性细长杆件中的一维波动方程，以及基于损伤动态弹性本构模型的空间轴对称波动方程。利用有限差分法，在非线弹性波的传播理论研究的基础上，数值模拟从子弹撞击入射杆到试件破碎的整个加载过程中应力波在两压杆和试件中的传播，并与实验结果比较得到了可靠性验证。编制了可以考虑径向变形的岩石类材料的多维数值模拟程序，为材料动态特性研究提出了新的思路和方法。
Experiments of granite and concrete in high strain-rate unaxial compressive loading were produced in the modified split Hopkinson pressure bar (SHPB) with copper as the pulse shaper. It can be used to ensure the symmetrical stress in the specimens before fracture and avoid the fluctuation of test data due to input shaky stress pulse. Based on the results of the dynamical experiments and the theoretical analysis with the dynamic microcrack model and constitutive model theory, the relations and rule between the microcosmic frame and macroscopical mechanics characteristic of rock materials are discussed adequately. Furthermore, the optimization method based on the mixed genetic algorithmsand numerical analysis with the finite difference methods on rock materials are used to validate the results of the theory analysis. The research method can be applied to the other brittleness materials and laigh impedance materials. The main content in this thesis can be shown as follow:
The results of dynamic experiments on rock materials show that not only the compression strength of granite and concrete increase, but also the fragment size decrease and fragment numbers increase with the increasing strain rate. On the other hand, the results of experiments show also that the failure of the granite cylinder is typical tensile splitting failure mode by sudden splitting parallel with the direction of uniaxial compressive loading at different strain rates. Through analyzing contrastively the stress-strain curves, the energy absorbency-time curves and the energy absorptivity-time curves of granite with concrete, it is illuminated the brittleness, impedance, compression deformation capability of rock-like materials is crucial factor on the dynamic fracture.
The numerical calculation based on a dynamic interacting sliding microcrack model is adopted to investigate quantificationally the influence on the macro-mechanics properties of rock materials from microcracks included the different initial crack length, crack angle, crack space and friction coefficient under different strain rates. Accordingly, the strain-dependency of mechanics characteristic on rock materials can be explained reasonably.
Based on the statistical damage theory and constitutive model theory, the non-linear elastic and viscoelastoplastic dynamic constitutive relation of rock materials are constructed. The characteristic parameters of the dynamic constitutive model of rock materials are ascertained with the inverse analysis method with the adaptive hybrid genetic algorithms.
The non-linear elastic stress wave and viscoelastoplastic stress wave equation are derived with constitutive equation of rock materials and stress wave theory. Numerical simulation programs on the dynamic mechanics characteristic of rock materials based on the stress wave equation are programmed. Through contrastively analyzing the results of Numerical simulation and experiments, the correctness of the theory analysis on the dynamic mechanics characteristic of rock materials and the stress wave equations can be testified.
引文
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