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The excavation in layered rocks is an issue for a number of geoengineering applications; these kinds of rocks all exhibit transverse isotropic features due to the process of metamorphic differentiation. This paper focuses on providing two methods, i.e., the 3D printing technology and the combined finite-discrete element method, to simulate the anisotropic characteristics of layered rocks. The results showed that both the 3D-printed samples and the FDEM numerical models are considered as a good match, and both revealed that as the inclined angle increased, the UCS of the sample first decreased and then increased, showing a U-shaped pattern. The results of this paper served as a reference to the promotion of the 3D printing technology and the combined finite-discrete element method in the geotechnical engineering field and laboratory test research. [ABSTRACT FROM AUTHOR]

The large deformation mechanisms and predictions of soft rock tunnels have always been important but difficult to solve problems in the field of geotechnical engineering. A combined finite–discrete element numerical simulation method (FDEM) was used to study large deformation mechanism, classification and prediction. The deformations or failure mechanisms of tunnel surrounding rock were revealed, and the failure modes and displacement value prediction of surrounding rock with different strength-stress ratios were also investigated. The following conclusions were obtained: (1) Critical hysteresis damping can be adopted to simulate the progressive large deformation process of soft rock tunnels, which can obtain the final deformation of unsupported tunnels and avoid a dynamic response. (2) Under concentrated tangential stress, the surrounding rock undergoes X-shaped conjugate shear fracture, and this type of fracture network continues to propagate toward the depth of the surrounding rock until the model reaches a stable state; the reduction in tunnel cross-section is mainly caused by the macroscopic movement and volume expansion of rock fragments, and the latter is due to the generation of a large number of macroscopic voids. (3) As the strength-stress ratio decreases, the deformation or failure modes of the surrounding rock can be divided into four categories: elastic–plastic deformation, closed fracturing, shear dilation and broken expansion. (4) Finally, a prediction equation for isotropic and homogeneous soft rock unsupported tunnel deformation with general size driven by hydrostatic in situ stress is obtained, which indicates that with an increasing strength-stress ratio, the surrounding rock displacement decreases as an exponential function, with a correlation coefficient of R 2 = 0.997. In addition, the robustness and reliability of the prediction equation is verified. [ABSTRACT FROM AUTHOR]

• A new constitutive model is proposed to eliminate the dependence of parameters on element size. • The influence laws of different parameters on the selection of fracture energy values are proposed, including E , ν , c , φ i , f t and h. • The reliability of the selection of fracture energy values is verified by uniaxial and triaxial compression simulations. The combined finite-discrete element method (FDEM) has been widely used in the numerical study of rock mechanics and geotechnical engineering. Selection of the correct parameter values is a prerequisite to ensure the accuracy of the simulation results. However, current calibration procedures are relatively cumbersome, and the parameters are strongly dependent on the element size. To eliminate the dependence of parameter values on the element size, this paper proposes a new constitutive model based on the stress–strain relationship. In addition, uniaxial compression and direct tension simulations are used to investigate the sensitivities of type II and type I fracture energies, i.e., G II and G I , including the influence of the G I (or G II) value on the simulation results of direct tension (or uniaxial compression) and the influence of different parameters (such as Young's modulus E , Poisson's ratio ν , cohesion c , internal friction angle φ i , tensile strength f t and element size h) on the selection of the values of G II and G I. The following results are obtained. (1) As G I or G II increases, the strength of the rock sample increases, and the plastic characteristics are more obvious, but the failure mode tends to be stable. (2) As the E value increases, the value of G I or G II decreases as a power function. As the value of f t or c increases, the value of G I or G II increases as a power function. However, other parameters, including ν , φ i and h , have no effect on the selection of the values of G II and G I. (3) Actual uniaxial compression and triaxial compression simulations prove that the calibrated G II and G I values are reasonable. In this study, only two fracture energies, G II and G I , must be calibrated; other macroparameters can be obtained through laboratory tests, and other microparameters can be obtained from previous empirical or theoretical values, which greatly improves the calibration efficiency of FDEM input parameters. [ABSTRACT FROM AUTHOR]

• A new calculation equation for normal contact stiffness is proposed. • The value of the coefficient in the new equation is proposed and the robustness of this value is verified. • The influence of different normal contact stiffness on uniaxial compression and tunnel excavation simulations are studied. The combined finite-discrete element method (FDEM) has been widely used in numerical studies in the fields of rock mechanics and geotechnical engineering. The normal contact stiffness between triangular elements is an important influencing parameter, but there is currently no effective method of measuring it. First, an equation for normal contact stiffness is proposed (P b = αP f , where P b is the basic stiffness, α is the coefficient, and P f is the joint penalty; the specific stiffness of each contact couple is determined by P b and the geometric sizes of the triangular elements together); then, the compression-shear failure of a single joint element is used to study the value range and robustness of α ; finally, uniaxial compression and tunnel excavation simulations are used to study the influence of different α values on rock crack propagation. The study results show that (1) an α value of 0.1448 is optimal and robust for a single joint element simulation and is therefore suitable for all simulation conditions; in other words, the value of α should not be too low to avoid decreasing the rock mass stiffness of existing natural fractures and deviating from the actual situation; in addition, the value of α should also not be too large to avoid the development of additional cracks, especially for hard rock simulation, in which the value of α is more sensitive; and (2) the crack topologies of the surrounding rock obtained by tunnel excavation simulation with a large α value deviate from the actual rock core (i.e., when α = 0.1448, the simulation results coincide well with the actual fractures). Through this study, the reliability of FDEM numerical simulation results is improved. [ABSTRACT FROM AUTHOR]

• A new phenomenological tensile failure criterion with an anisotropic coefficient was proposed. • Direct tensile test of the Kangding slate was carried out to verify the accuracy of the new criterion. • The tensile strength data of eight typical layered rocks were collected and compared with the other six typical tensile strength criteria to verify the universality and superiority of the new criterion. • Based on the sensitivity analysis of tensile rate, the loading rate of 0.01 m/s was recommended for the samples with various foliation angles. • Layer thickness has little effect on tensile strength, but a significant effect on tensile failure modes. The tensile strength is a key parameter for the design of many geotechnical engineerings such as tunnel support, slope support, and petroleum drilling. The tensile strength in layered rocks, however, is anisotropic due to the existence of bedding planes. In this paper, to study the anisotropic tensile behaviors, a series of direct tensile tests were conducted using Kangding slate with five different foliation angles (β = 0°, 30°, 45°, 60°, and 90°). Based on the N-Z criterion, a new tensile failure criterion with the anisotropic coefficient was proposed. The tensile strength data of nine typical layered rocks were collected to evaluate the prediction ability of seven anisotropic tensile failure criteria including the new criterion. Embedding the new criterion into FDEM, the loading rate-dependent and layer thickness-dependent tensile mechanism of layered rock under direct tensile test were simulated. The experimental and numerical simulation results showed that the foliation angle significantly affected the tensile strength and failure modes of the slate. With the increase of foliation angle (β), the tensile strength of nine typical layered rocks, including Kangding slate, presented a non-linear increase trend. Compared with the other six typical anisotropic tensile failure criteria, the new criterion has the best prediction capability on the tensile strength of rocks with four different anisotropic degrees, and therefore the new criterion was recommended. The new criterion was embedded in FDEM to carry out direct tensile simulation of slate with different β. The numerical simulation results were in good agreement with the experimental results, further verifying the accuracy of the new criterion. The loading rate sensitivity analysis indicated that a tensile rate of 0.01 m/s was recommended to assure quasi-static loading of the specimen. Through the sensitivity analysis of layer thickness, it is concluded that layer thickness has very little influence on tensile strength, but has a very significant influence on the final failure modes of the specimens. [ABSTRACT FROM AUTHOR]