Study of the nonlinear mechanical behavior of rock materials using the FFT numerical method based on the actual mesostructure
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摘要: 岩石的非均质性(矿物夹杂、微裂隙、微孔洞等细观结构)对其非线性力学行为和破坏过程有着显著影响。本文采用无需对复杂细观结构划分网格的快速傅立叶变换(FFT)数值方法，直接获取图像中的像素点作为材料点，准确得到非均质材料的细观结构特征和力学性质的特点，与数字图像处理(DIP)技术有机结合，建立了基于真实细观结构的FFT数值计算方法，模拟了非均质岩石在外荷载作用下的弹塑性变形过程，探究了岩石内部细观结构对非线性力学行为的影响规律与宏观力学性质的内在联系。研究结果表明：基于真实细观结构的FFT模型，能很好地预测不同埋深和不同围压条件下黏土岩的峰前非线性行为和峰值强度，细观结构的形状、大小和分布直接决定了黏土岩内部应力场的分布。研究结论为研究岩石细观结构特征及其非线性力学行为提供了一个重要手段。Abstract: Rock heterogeneity (such as mineral inclusions, micro-cracks, micro-voids and other microstructures) significantly affects its nonlinear mechanical behavior and failure process. This paper utilizes the Fast Fourier transform-based(FFT) numerical method which does not require meshing of complex microstructure but directly obtains the microstructure of heterogeneous materials through the pixels of the image. In addition, the method can be naturally combined with digital image processing (DIP). An actual-microstructure-based FFT method is thereby developed to simulate the elastoplastic behavior of the heterogeneous rocks under external load. The influence of microstructure on the nonlinear behavior is discussed as well as the internal relationship between the microstructure and the macroscopic mechanical properties. The results show that the real-microstructure-based FFT method can well predict the nonlinear behavior before and after the peak strength of the rocks under different depths and confining pressures. The shape, size and distribution of microstructure directly determine the distribution of stress field in clay rock. The actual-microstructure-based FFT method proposed in this paper can reasonably consider the rock heterogeneity, and provides an important tool for studying the influence of the rock microstructure characteristics on the nonlinear mechanical behavior.
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Key words:
- Fast Fourier Transforms (FFT) method /
- digital image process /
- rocks /
- micromechanics /
- heterogeneity
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图 2 基于COx黏土岩细观结构表征的流程
Figure 2. Flow chart based on microstructural characterization of COx clay rock
图 7 基于真实细观结构的FFT数值计算方法流程
Figure 7. Flow chart of the actual-mesostructure-based FFT numerical method
图 9 细观结构和局部本构模型的关系[12]
Figure 9. Relationship between microstructure and local constitutive model
图 11 数值模拟与三轴压缩实验数据的对比
Figure 11. Comparison of numerical simulation and experimental data
图 13 细观结构应力演化对宏观力学行为的影响
Figure 13. Influence of microstructure stress evolution on the macroscopic mechanical behavior
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