基于DIP-FFT数值方法的花岗岩多尺度力学特性研究

Study on multi-scale mechanical properties of granite based on DIP-FFT numerical method

为研究花岗岩的细观力学特性及其结构特征对宏观力学性质的影响,先利用X射线衍射和偏光显微镜获得花岗岩各矿物成分及比例和表面形貌,然后通过纳米压痕试验定性分析各相矿物的力学特性,并计算花岗岩的细观力学参数;最后,为了克服传统均匀化解析法求解等效参数时无法考虑细观结构的形状、大小和分布等特征的问题,将数字图像处理(DIP)技术和快速傅里叶变换法(FFT)有机结合,提出一种能直接利用岩石图像构建数值模型的DIP-FFT数值方法,基于真实细观结构计算等效弹性模量和泊松比,并与均匀化解析解和三轴压缩试验测定的宏观弹性模量和泊松比进行对比。研究结果表明:各相矿物在细观尺度上具有明显的异质性,石英强度高,力学性质稳定,长石次之,云母软弱变形大且内部存在孔隙结构;花岗岩的宏观弹性模量随围压的增加呈增大趋势并逐渐趋于稳定;DIP-FFT数值方法合理考虑了岩石细观结构特征的影响,建立了花岗岩宏细观力学参数的联系,其预测的等效弹性模量和泊松比与中围压下的测试结果吻合。该研究成果将为从微细观尺度确定岩石宏观力学性质提供一种更合理高效的方法,对于评价复杂工程环境下围岩的力学性质有着重要的工程实践意义。

In order to study the influence of the micromechanical property and microstructure on the macroscopic mechanical properties of granite,the composition and proportion of each mineral as well as the morphology of the granite are firstly obtained by the X-ray diffraction and the polarizing microscope tests.Then,the mechanical properties of each mineral are qualitatively analyzed by nanoindentation test and the micromechanical parameters are calculated.In order to overcome the difficulty of considering the internal microstructure characteristics of rocks by the traditional homogenization methods,a DIP-FFT numerical method is proposed based on the combination of the digital image processing(DIP)and the fast Fourier transforms(FFT)method which can directly use the actual image of rocks to generate the numerical model.The proposed method is applied to calculate the effective elastic modulus and Poisson’s ratio which are compared with the analytical homogenization solution and the triaxial compression tests.The research results show that the mineral phases are obviously heterogeneous at the microscopic scale.It is noted that the phase of quartz possesses high strength with stable mechanical properties,and followed by the feldspar.The phase of mica performs large deformation with internal pore structure.The macroscopic elastic modulus of granite increases with the growth of the confining pressure and tends to be stable.The proposed DIPFFT method reasonably considers the influence of microstructure characteristics and establishes the relationship between the microscopic and macroscopic properties of the studied granite.The predicted effective elastic modulus and Poisson’s ratio are well consistent with the experimental results under medium confining pressure.The results of this research provide a reasonable and efficient approach to determine the macroscopic mechanical properties of rock materials from the microscopic level.It is also important in engineering practice for evaluating the mechanical properties of surrounding rocks especially in complex engineering applications.