Brittleness is a crucial parameter of rock mass and the key indicator in rock engineerings, such as rockburst prediction, tunnelling machine borehole drilling, and hydraulic fracturing. To solve the problem of using present brittleness indexes, the existing rock brittleness indexes were firstly summarised in this paper. Then, a brittleness index (BL), which considers the ratio of stress drop rate and stress increase rate and the peak stress, was proposed. This new index has the advantage of simplifying the acquisition of key parameters and avoiding dimensional problems, as well as taking the complete stress-strain curves into account. While applying the BL, the peak strain is used to describe the difficulty of brittle failure before the peak point, and the ratio of stress drop to strain increase can reflect the stress drop rate without dimension problem. In order to verify the applicability of BL, through the PFC2D, the microparameters and confining pressure were changed to model different types of rock numerical specimens and different stress condition. The results show that the BL can well reflect and classify the brittleness characteristics of different rock types and characterise the constraint of confining pressure on rock brittleness. Moreover, the influence of microparameter on macroparameter was studied. In order to further verify the reliability of the brittleness index (BL), this study conducted uniaxial and triaxial compression tests (30 MPa) on marble, sandstone, limestone, and granite under different confining pressure.

The discrete element modelling (DEM) of triaxial tests plays a critical role in 2 unveiling fundamental properties of particulate materials, but the numerical 3 implementation of a flexible membrane boundary for the testing still imposes 4 problems. In this study, a robust algorithm was proposed to reproduce a flexible 5 membrane boundary in triaxial testing. The equivalence of strain energy enables the 6 particle-scale parameters representing the flexible membrane to be directly 7 determined from the real geometric and material parameters of the membrane. Then 8 the proposed flexible membrane boundary was implemented in the context of discrete 9 element simulation of triaxial testing and was validated with laboratory experiments. 10 Furthermore, comparisons of triaxial tests with flexible and rigid boundaries were 11 performed from macro-scale to meso-scale. The results show that the boundary 12 condition has limited influences on the stress-strain behaviour but a relatively large 13 impact on the volumetric change, the failure mode, the distribution of contact forces, 14 and the fabric evolution of particles in the specimen during triaxial testing. 15

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This paper presents a periodic boundary condition for the coupled discrete element and lattice Boltzmann method for simulating fluid-particle systems. Detailed implementation of this special boundary condition is given. Besides, the detailed procedure of immersed moving boundary scheme for fluid-solid coupling is proposed. The accuracy and applicability of the proposed periodic boundary condition are well demonstrated by two benchmark tests, i.e. single particle transport and multiple particle migration in an infinite tube filled with water. It is found that the novel periodic boundary condition proposed for discrete element and lattice Boltzmann method can greatly improve the computational efficiency of the later which is computationally expensive when thousands of particles are involved.

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