Technical note

Estimating Mohr-Coulomb friction and cohesion values from the Hoek-Brown failure criterion

The commonly used trial-and-error approach on selecting appropriate inter-particle parameters in DEM simulations incurs criticism such as user dependence and high computational cost. This study proposes a new framework based on a multi-fidelity residual neural network (MR-NN) as an alternative for calibrating inter-particle parameters in rock-like bonded granular materials. The model is first trained using low-fidelity data (LF) to focus on capturing the main underpinning correlations between macroscopic elastic and strength parameters with inter-particle parameters of contact models, where the LF data is generated from micro-macro quantitative relations. Subsequent training on sparser high-fidelity (HF) data is then used to calibrate and refine the model, in which the HF data is generated from DEM simulations for rock. Feedforward neural network (FNN) is considered as the baseline algorithm for training models. The trained MR-NN with the same LF data is finally used to predict the inter-particle parameters of calcarenite and granite in DEM simulations to examine its feasibility and generalization ability. Furthermore, the robustness of the framework is verified by discussing the effect of LF data on the performance of MR-NN. All results demonstrate that the proposed method can provide a fast and accurate determination of inter-particle parameters for DEM simulation.

In order to explore the freeze–thaw (FT) damage characteristics of fractured rock masses, FT cycle tests and uniaxial compression tests were conducted on intact and pre-cracked cyan sandstone samples, respectively. The degradation laws of physical and mechanical properties of samples under FT cycle conditions were analyzed, and the FT damage mechanism and failure mechanism were explored accordingly. The results indicate that as the number of FT cycles (N) increases, the saturation weight change rate and porosity of the sample continue to increase, while the P-wave velocity continues to decrease. The closure stress, initiation stress, damage stress, and peak stress decrease linearly with increasing FT cycles, and increase linearly with increasing crack inclination angle ($\beta$). Moreover, as FT cycles increase, the geological strength index GSI decreases linearly, while the damage factor (D) increases linearly. A Hoek Brown strength degradation model for fractured rocks subjected to FT damage under uniaxial compression was obtained, and its high reliability was verified using test results. The FT damage of cyan sandstone is mainly dominated by the frost heave force inside the rock, and the degree of FT damage of fractured samples is much higher than that of intact ones. The concentration of frost heave force at the crack tip leading to cracking is the key to exacerbating the FT damage in fractured rock masses. However, the crack initiation mechanism is still controlled by $\beta$. When$\beta$ = 90°, it exhibits tensile initiation mode, and when$\beta$ = 45°, it mainly exhibits shear initiation mode. Moreover, the fracture of the single crack sample conforms to the compression-shear fracture criterion. Taking the sample with pre-crack inclination angle of 45° as an example, the variation of $K_{\text{I}}$ and $K_{\text{II}}$, and the relationship between them are discussed accordingly. The results of this paper are beneficial to clarify the influence of FT cycles on the mechanical properties of cyan sandstone, and can provide reference for the study of related issues.

The face stability problem is a major concern for tunnels excavated in rock masses governed by the Hoek-Brown strength criterion. To provide an accurate prediction for the theoretical solution of the critical face pressure, this study adopts the piecewise linear method (PLM) to account for the nonlinearity of the strength envelope and proposes a new multi-horn rotational mechanism based on the Hoek-Brown strength criterion and the associative flow rule. The analytical solution of critical support pressure is derived from the energy-work balance equation in the framework of the plastic limit theorem; it is formulated as a multivariable nonlinear optimization problem relying on 2m dependent variables (m is the number of segments). Meanwhile, two classic linearized measures, the generalized tangential technique (GTT) and equivalent Mohr-Coulomb parameters method (EMM), are incorporated into the analysis for comparison. Surprisingly, the parametric study indicates a significant improvement in support pressure by up to 13% compared with the GTT, and as expected, the stability of the tunnel face is greatly influenced by the rock strength parameters. The stress distribution on the rupture surface is calculated to gain an intuitive understanding of the failure at the limit state. Although the limit analysis is incapable of calculating the true stress distribution in rock masses, a rough approximation of the stress vector on the rupture surface is permitted. In the end, sets of normalized face pressure are provided in the form of charts for a quick assessment of face stability in rock masses.

Epoxy-based polymer concretes (PCs) behave in a quasi-brittle manner and suffer from low tensile strength. Adding different kinds of fillers has been widely used to improve the ductility of these materials and change the failure mechanisms. In this study, we used polyethylene terephthalate (PET) fillers from recycled bottles to enhance the tensile strength and ductility of PCs and prevent sudden brittle failure. Two different sizes of fillers (i.e., fine and coarse) are considered and the Brazilian disk configuration is used to measure the indirect tensile strength of reinforced PCs. Experimental results showed that the addition of coarse PET fillers to the PC has more significant effects on tensile strength and failure mechanism than fine PET fillers. Then, micromechanical damage analyses are conducted via finite element simulations of two-dimensional representative volume elements. The effects of void content and recycled PET fillers on the tensile strength and ductility of reinforced PCs were studied in the micromechanical simulations. Since the Brazilian disk examines the indirect tensile behavior, a relationship was proposed between the direct micromechanical tensile strength and the indirect macro mechanical tensile strength. The new procedure is experimentally validated for the prediction of the tensile strength of both reinforced and unreinforced PCs.

This study investigates the ultimate bearing capacity of shallow foundations resting on rock masses under earthquakes using upper-bound limit analysis. A modified pseudodynamic method (MPD) that considers the influence of Rayleigh waves is initially used to characterize the spatiotemporal variation in earthquake acceleration. The strength of rock masses is governed by the generalized Hoek‒Brown criterion and the plastic flow at failure is assumed to respect the associated flow rule. The generalized tangential technique is introduced to provide a linear approximation of the strength envelope for capturing the equivalent Mohr‒Coulomb strength parameters. The classic nonsymmetrical multi-block translational mechanism, which is capable of assessing a rock-foundation system under asymmetrical load, is reconstructed to portray the velocity discontinuity of the plastic failure region. Based upon the energy equilibrium theorem of the limit analysis, an analytical solution of seismic bearing capacity is derived and then formulated as a multivariate optimization problem. Comparisons show good agreement with the literature and validate the correctness and rationality of this work. Parametric study indicates that the seismic foundation capacity obtained by MPD tends to be conservative compared to the pseudostatic method with the same seismic coefficients, and that the period of a Rayleigh wave has only a slight effect on the bearing capacity. The failure region is more sensitive to the disturbance coefficient than it is to the other rock strength parameters.

The use of gangue, cementitious materials, and water mixed to make cemented gangue backfill material (CGBM) can achieve solid waste recycling while reducing environmental problems caused by its accumulation. In this paper, the fractal dimension of particle size distribution (PSD) and the confining pressure were investigated on the compressive strength, elastic modulus, stress–strain behavior, dilatancy deformation, and failure mode of CGBM using uniaxial compression, conventional triaxial compression, and microscopic scanning tests. The mechanism of the PSD fractal dimension on the mechanical properties of CGBM was revealed from a microscopic perspective. The results demonstrate that the compressive strength and elastic modulus of CGBM are quadratic polynomial and positively linearly related to the PSD fractal dimension and confining pressure respectively, with the PSD fractal dimension characterizing the maximum compressive strength of CGBM ranging between 2.4150 and 2.6084. The volume strain variation of CGBM diminishes as the PSD fractal dimension grows and increases dramatically when the confining pressure rises. The PSD fractal dimension has a quadratic polynomial relationship with both the cohesive force and the internal friction angle of CGBM. A reasonable PSD fractal dimension can optimize the microstructure of CGBM, reduce the distribution of defects such as microcracks and micropores, and enable hydration products to effectively fill the defects, guaranteeing that the CGBM has sufficient load-bearing capacity.