MatDEM理论论文|脆性岩石的三维紧密堆积模型的力学性质和能量转换

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论文题目

Mechanical properties and energy conversion of 3D close-packed lattice model for brittle rocks

Liu et al., 2017, Computers & Geosciences

研究内容

Numerical simulations using the 3D discrete element method can yield mechanical and dynamic behaviors similar to rocks and grains. In the model, rock is represented by bonded elements, which are arranged on a tetrahedral lattice. The conversion formulas between inter-element parameters and rock mechanical properties were derived. By using the formulas, inter-element parameters can be determined according to mechanical properties of model, including Young's modulus, Poisson's ratio, tensile strength (Tu), compressive strength (Cu) and coeﬃcient of internal friction. The energy conversion rules of the model are proposed. Based on the methods, a Matlab code “MatDEM” was developed. Numerical models of quartzite were used to validate the formulas. The tested mechanical properties of a single unit correspond reasonably well with the values of quartzite. Tested Tu and Cu with multiple elements are lower than the values predicted by the formulas. In the simulation of rock failure processes, mechanical energy conversed between diﬀerent forms and heat is generated, but the mechanical energy plus heat always remains constant. Variations of breaking heat and frictional heat provide clues of the fracturing and slipping behaviors of the Tu and Cu tests. The model may be applied to a wide range of geological structures that involve breakage at multiple scales, heat generation and dynamic processes.

Fig. 1. Schematic of sliding distance used in the calculation of frictional heat. (a) The bond is broken and element is locked by static friction (i.e. FS < FSmax'). Although element center is moved to point O due to external force f, sliding distance along the contact surface is zero. (b) When the element slides, the eﬀective sliding distance is the length of P1P2, which equals the tangential relative displacement (O1O2) of element pair minus the reduction of spring length (Xs2-Xs1).

Fig. 2. Tested mechanical properties of close-packed models with diﬀerent element numbers. (a) Young's modulus; (b) Poisson's ratio; (c) Uniaxial tensile strength (Tu); (d) Uniaxial compressive strength (Cu).

Fig. 3. (a) Energy curves of compressive strength (Cu) test. Inset ﬁgure shows variation of kinetic energy when the model fails. (b) Energy curves of tensile strength (Tu) test. Inset ﬁgure shows energy conversion when the model fails. (c) Heat curves when the model fails at point A2 in Fig. 3a. (d) Heat curves when the model fails at point B1 in Fig. 3b

Liu C., Xu, Q., Shi, B., Deng, S., and Zhu, H. 2017. Mechanical properties and energy conversion of 3d close-packed lattice model for brittle rocks. Computers & Geosciences, 103, 12-20.

来源：矩阵离散元MatDEM