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• The maximum mesh size and maximum loading rate that can be adopted for different specimens are proposed. • The maximum mesh size and calculation method for tunnel excavation simulation of different diameters are proposed. • The method for determining the critical kinetic energy of the system during excavation simulation is proposed. • The reduction function of the Young's modulus of the core material is proposed. The combined finite-discrete element method (FDEM) is extensively employed to model rocks and rock-like materials, in which calibration against the results from uniaxial/triaxial compression tests, Brazilian tests and shear tests have been widely carried out. However, since different element sizes and loading rates were used, it is difficult to assess the numerical results of these studies if the effects of the element size and loading rate are ignored. This paper discusses the effect of the element size, loading/unloading rate and unloading mode on the cracking processes in laboratory-scale (uniaxial compression tests and Brazilian tests) and field-scale (circle tunnel excavations). The results indicate that the element size and loading rate should not be less than 27–28 meshes in a diameter zone and larger than 0.5 m/s, respectively, in laboratory-scale. In field-scale models, four different tunnel diameters (3, 4, 5 and 6 m) are used in tunnel excavation simulations. The results reveal that the mesh number around the tunnel wall should not be less than 120, meanwhile the element size should not be longer than the length of fracture process zone (l FPZ). The unloading rate for the field-scale model is influenced by the model size and rock density. It cannot be determined directly but a new method is proposed to determine the unloading rate based on crack development curve. To compare the fracture patterns well to those observed from the tunnel simulations, the unloading mode of an exponential formula is apposite. [ABSTRACT FROM AUTHOR]

• A novel joint element calibration procedure is proposed for FDEM. • A fracture energy calculation method with different element sizes is proposed to realize cross-scale simulation. • More accurate results can be obtained for tunnel excavation simulation using the proposed joint element calibration technique. • More accurate values of the rock fracture energies G I and G II can be calibrated by the modified Brazilian disc model and variable-angle shear model. The combined finite–discrete element method (FDEM) has been widely used to simulate the fracture process of rock materials. The FDEM simulation requires many material parameters which should be calibrated through laboratory tests or directly cited from previous conclusions. However, it is difficult to obtain the joint element parameters, including the joint element penalty P f and the type I and type II fracture energies G I and G II. Therefore, a novel calibration method for the above three parameters must be proposed. First, P f can be obtained by uniaxial compression simulation, and P f = 30 E (E is Young's modulus) is applicable for homogeneous and isotropic rock materials. Second, an accurate G I value in the static loading state can be obtained by Brazilian disc simulation with a central preprepared failure path. Third, an accurate G II value can be calibrated by the modified variable-angle shear model. Finally, the G I and G II values with different element sizes can be calculated by the proposed linear equations. In addition, normal uniaxial and triaxial compression simulations can be used to verify the reliability of the calibrated G I and G II values. Moreover, the tunnel excavation simulation results show that the joint element parameters calibrated by the modified method can achieve cross-scale simulation, and the simulation results are more accurate. [ABSTRACT FROM AUTHOR]

• A novel joint element calibration procedure is proposed for FDEM. • A fracture energy calculation method with different element sizes is proposed to realize cross-scale simulation. • More accurate results can be obtained for tunnel excavation simulation using the proposed joint element calibration technique. • More accurate values of the rock fracture energies G I and G II can be calibrated by the modified Brazilian disc model and variable-angle shear model. The combined finite–discrete element method (FDEM) has been widely used to simulate the fracture process of rock materials. The FDEM simulation requires many material parameters which should be calibrated through laboratory tests or directly cited from previous conclusions. However, it is difficult to obtain the joint element parameters, including the joint element penalty P f and the type I and type II fracture energies G I and G II. Therefore, a novel calibration method for the above three parameters must be proposed. First, P f can be obtained by uniaxial compression simulation, and P f = 30 E (E is Young's modulus) is applicable for homogeneous and isotropic rock materials. Second, an accurate G I value in the static loading state can be obtained by Brazilian disc simulation with a central preprepared failure path. Third, an accurate G II value can be calibrated by the modified variable-angle shear model. Finally, the G I and G II values with different element sizes can be calculated by the proposed linear equations. In addition, normal uniaxial and triaxial compression simulations can be used to verify the reliability of the calibrated G I and G II values. Moreover, the tunnel excavation simulation results show that the joint element parameters calibrated by the modified method can achieve cross-scale simulation, and the simulation results are more accurate. [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]

• The long-term degradation behavior of rock strength was systematically summarized. • The long-term degeneration laws of cohesion and internal friction angle were proposed. • FDEM was used to study the long-term crack propagation of tunnel surrounding rock. • The conclusion of this paper was verified by engineering case. The time-dependence of rock strength is an issue that cannot be ignored in the rock engineering field. This paper summarizes previous study results on the degradation of the uniaxial compressive strength of rock (including component cohesion and internal friction angle), tensile strength and Young's modulus over time. Based on previous studies, the degeneracy formulas of intact rock cohesion and internal friction angle are derived. Taking circular tunnel excavation under hydrostatic pressure as an example, the surrounding rock response is studied under different degradation degrees of rock strength and stiffness, including the radius of the excavation damage zone, damage degree of surrounding rock, lining support pressure and tunnel boundary displacement. The results show that with the increasing degree of degradation of the surrounding rock compressive strength, the above four parameters increase in the form of an exponential function and that weakening of the tensile strength had little effect on the surrounding rock response. In addition, as the degradation degree of rock stiffness increases, the radius of the excavation damage zone remains unchanged, whereas the other three parameters values are reduced. An actual engineering case simulation using the combined finite-discrete element method shows that results consistent with field observations can be obtained if the rock strength degradation law proposed in this paper is adopted. [ABSTRACT FROM AUTHOR]