The movement and deformation of mineral grains in rocks control the failure behavior of rocks. However, at high resolution, the physical and mechanical behavior of three-dimensional microstructures in rocks under uniaxial compression has not been characterized. Here, in suit XCT (4.6 um) has been applied to investigate the behavior of mineral grains of sandstone -- movement, rotation deformation and the principle strains obtained by deformation gradient tensor constructed with three principle axial vector representation of grain, indicating that the behavior of grains between the fracture and the non-fracture zone are different. For further investigate the behavior of grain cluster, the material lines are used to obtain the Stokes local rotation, namely shear strain. The finding is that: 1. the shear strain is periodic in the radial direction. 2. on average sense, the positive shear strain and negative shear strain have local concentration features.
Deep Dive into Grain Deformation of Fractured Sandstone and Stokes Local-rotation of Material Line.
The movement and deformation of mineral grains in rocks control the failure behavior of rocks. However, at high resolution, the physical and mechanical behavior of three-dimensional microstructures in rocks under uniaxial compression has not been characterized. Here, in suit XCT (4.6 um) has been applied to investigate the behavior of mineral grains of sandstone – movement, rotation deformation and the principle strains obtained by deformation gradient tensor constructed with three principle axial vector representation of grain, indicating that the behavior of grains between the fracture and the non-fracture zone are different. For further investigate the behavior of grain cluster, the material lines are used to obtain the Stokes local rotation, namely shear strain. The finding is that: 1. the shear strain is periodic in the radial direction. 2. on average sense, the positive shear strain and negative shear strain have local concentration features.
The physical and mechanical behavior of rock is determined by the deformation behavior 1,2 , contact behavior [3][4][5] and interaction relationship of rock components 6,7 (pores, grains, cement). For example, the contact 8 and friction 9 phenomena between mineral grains are related to the formation, evolution and propagation mechanism of earthquakes 10 . At the same time, the geometric features of mineral grains affect the crack propagation 11 . For example, standard principle of local symmetry 12,13 and strain-energy density criterion 14 are applied to explain repulsive cracks 15 , but geometric conditions remain lacking. Liang et al. 16 studied the deformation and crack propagation path of mineral grains and found that there is a geometric correlation between crack path deflection and mineral grain motion. In addition, the deformation, movement behavior and stress evolution of mineral grains directly reflect the formation and evolution of local deformation zones and the propagation and expansion of cracks [17][18][19][20][21] . The above research shows that the properties of mineral grains are correlated with the stability of rock mass engineering.
However, due to technical limitation, the research on the physical and mechanical properties of mineral grains mainly focuses on numerical simulation and two-dimensional laboratory experiments on the surface of materials. Liu, Ting and Kock 22 use DEM to simulate the effects of mineral grains of different shapes and sizes under uniaxial compression on rock deformation, strength (crack initiation strength, damage strength and peak strength) 23 , and friction properties between mineral grains. Liang 16 used scanning electron microscope (SEM) to study the rock crack propagation path and mineral grain migration under the condition of medium and low strain rate loading, as well as the fine granulation and flow property of mineral grains. Sundaram 24 and his colleagues studied the deformation characteristics of granular matter around pre-cracked solids under dynamic loading by Digital Image Correlation technology (DIC), and obtained dynamic propagation patterns of different pre-cracks. Tan 25 obtained the interface separation characteristics of two-dimensional plane grains indirectly by digital speckle technique and micro-mechanics theory. Based on this, a cohesive law at the microscopic scale is established, and the cohesive strength and softening modulus of interfaces is analyzed. Maruyama 1,26 used the maker line to study the rotation and deformation properties of mineral grains on the rock surface, and found that the GBS-induced grain rotation and CPO behavior affect the seismic properties of the Earth’s mantle, and further revealed the stratum response characteristics and creep mechanism of the upper mantle during earthquakes. Studies have found that grain-scale microstructure controls macroscopic fracture patterns, and some fracture phenomena of rock have a strong correlation with the plastic behavior of the material microstructure, which can affect the macroscopic strength of the rock 20,27 . At the same time, Dong 28 found that the superplastic deformation behavior of feldspar and quartz reflects the deformation mechanism of the mantle on Earth.
The above studies show that the deformation and kinematics characteristics of mineral grains have a strong correlation with rock fracture and rock mass strength. However, the above research lacks a complete three-dimensional characterization of the physical and mechanical properties of mineral grains, and cannot overcome the errors caused by the out of plane displacement of mineral grains. Therefore, using the X-ray computed tomography technique, we study and characterize the deformation, movement, rotation and stress state of mineral grains after unloading, and discuss the difference between the physical and mechanical behavior of mineral grains in rock fracture zone and non-fracture zone. At the same time, material line is constructed based on rational mechanics theory, and shear strain of CT slices is calculated by measuring local rotation angle. The relationship between rock crack propagation and grain movement were studied.
The material considered in this research is poorly cemented sandstone, without removing any water for maintaining the microstructure of the sample, from Yunnan province in China. The diameter of sandstone grains is about 0.1mm, as shown in figure 1. Before the test, the sandstone with a 3.8 mm diameter by 7.4 mm long cylindrical sample manufactured by Focused Ion Beam (FIB), which eliminate the influence of end effect, extracted from a 50 mm diameter and 100mm long core. After the test, the mineral powder was analyzed by XRD diffraction, containing quartz, muscovite, calcite, albite and hematite, as shown in figure 2. The density, elastic modulus, and poisson’s ratio of mineral components are shown in table 1. The experiment was conducted by the Xradia 520 Versa (XCT) and Material Testing
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