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The microscopic parameters in the numerical method have an important influence on the results and computational efficiency of the models. The existing calibration methods of microscopic parameters in the finite-discrete element method (FDEM) are based on two-dimensional (2D) FDEM model, and there is a lack of calibration methods for microscopic parameters suitable for three-dimensional (3D) FDEM model. Therefore, this paper proposes a fast and convenient calibration method for the microscopic parameters of the 3D FDEM model. First, a tangential contact force calculation algorithm based on the total normal force is proposed and verified by the slider model. Subsequently, assuming that the penalty parameter of the solid element is equal to the penalty parameter of the joint element, the relationship between the normal penalty parameter and the tangential penalty parameter, and the relationship between the normal penalty parameter and the Young's modulus are studied using several numerical models. Moreover, the tensile strength and crack propagation path of the Brazilian disc model under different fracture energy parameter combinations are studied, and the fracture energy parameters are calibrated. Then, the triaxial compression model under different confining pressures is used to calibrate the cohesion c and the internal friction angle φ. In addition, the effects of loading rate, mesh size and time step on the model strength and calculation time are considered, respectively. Finally, the numerical simulation of dynamic Brazilian splitting test is carried out to verify the reliability of the parameter calibration method proposed in this paper. Although the calibration method of microscopic parameters is not unique, the microscopic parameter calibration method has important reference significance and is conducive to the application of 3D FDEM model. Highlights: A tangential contact force calculation algorithm based on the total normal contact force is proposed and verified by the slider model. The tangential penalty parameter in the 3D FDEM model needs to be greater than the normal penalty parameter, and the threshold of the normal penalty parameter is 50 times Young 's modulus. The tensile strength of the Brazilian disc model always begins to converge when the fracture energy GII is equal to 10GI, and the crack propagation path is along the central diameter direction. [ABSTRACT FROM AUTHOR]

Floor heave is a disaster that is frequently encountered in tunnel engineering. Existing explanations of floor heave mechanisms have many limitations, and the most important of which is that the stress concentration, release and transfer phenomena and the influences of the in-situ stress lateral coefficient and tensile strength are ignored. Therefore, the combined finite-discrete element method (FDEM) is used to study the failure process of floor rock masses and propose a new mechanical mechanism of floor heave that can consider the influences of the in-situ stress lateral coefficient and tensile strength. The type I fracture energy corresponding to different tensile strengths is calibrated using a direct tensile simulation test. Then, the floor heave mechanism is investigated under different lateral coefficients and tensile strengths, and five different floor heave modes are proposed under different in-situ stress lateral coefficients and tensile strengths. The floor heave modes controlled by the various in-situ stress lateral coefficients and tensile strengths are different, but they can all be explained by the maximum concentrated tangential stress. [ABSTRACT FROM AUTHOR]

A large amount of slates is distributed along Kangding No. 2 tunnel of Sichuan–Tibet Railway (China). The bedding of the Kangding slate is rich, showing apparent anisotropy of strength. For underground tunnels excavated in the anisotropic rock mass, the rock material is vulnerable to damage in tension because of its low tensile strength. Therefore, the tensile strength and fracture modes are important for the support design of layered surrounding-rock tunnel. In this study, first, a series of direct tensile tests were carried out on slate samples with five kinds of bedding dip angles. Second, the effect of bedding dip angle on the slate's tensile strength, failure modes, and acoustic emission characteristics was analyzed. Third, based on the Nova–Zaninetti criterion and the experiment results, a new phenomenological anisotropic criterion was proposed by introducing anisotropic coefficient, which could describe the nonlinear variation trend of tensile strength with foliation angles. Compared with four typical tensile strength criteria, the accuracy and universality of the new criterion were verified. Finally, the new criterion was implemented into the combined finite-discrete element method (FDEM) to conduct direct tensile simulation of slate with different foliation angles. The results indicated that the direct tensile strength followed an S-shaped increasing trend with the variation of foliation angles. The direct tensile failure modes of slate samples with different foliation angles could be divided into layer activation failure, mixed failure, and rock matrix failure. The acoustic emission process of slate with different bedding inclination under direct tension could be roughly divided into the following three stages: quiet period—stepped saltatory increase—drastic increase. The fitting effect of the new criterion was the highest among Kangding slate and other six typical layered rocks, which showed that the new criterion was suitable for predicting its Brazilian strength and direct tensile strength. At the same time, the numerical simulation results were in good agreement with the experimental results, which further verified the accuracy of the new criterion. Highlights: The acoustic emission characteristic parameters helped to reveal the direct tensile failure characteristics of layered rocks. A new phenomenological anisotropic tensile failure criterion was proposed. The direct tensile test data and the Brazilian splitting test data were used to study the accuracy and universality of the new anisotropic tensile failure criterion. FDEM was used to study the accuracy of the new anisotropic tensile failure criterion. [ABSTRACT FROM AUTHOR]

The anisotropic behavior of layered surrounding rock has always been a hot topic in underground engineering. This paper aims to investigate the deformation characteristics and crack evolution process of layered surrounding rock under excavation unloading conditions using the three-dimensional (3D) FDEM method. Firstly, the principle of 3D FDEM method is briefly introduced, and the transversely isotropic constitutive equation is embedded in the 3D FDEM method. At the same time, by implementing the GPU parallel algorithm based on CUDA, the code is optimized to improve the computational efficiency of the 3D FDEM method. Subsequently, the Brazilian splitting specimens and uniaxial compression specimens of layered rocks are numerically simulated to study the strength and deformation anisotropy characteristics of rock specimens with different bedding dip angles. The results indicate that the tensile strength of the model gradually decreases as the bedding dip angle increases. Moreover, the compressive strength of the model exhibits a U-shaped trend with an increase in the bedding dip angle. Notably, crack propagation within the model is significantly influenced by the bedding plane. Next, the 3D FDEM method is utilized to investigate the deformation and failure characteristics of horizontally layered surrounding rock in the Jiajinshan tunnel project. It is found that there are three types of failure cracks in the surrounding rock: conjugate shear cracks, shear cracks along the bedding plane, and tensile cracks perpendicular to the bedding plane. The deformation of surrounding rock is basically consistent with the field measurement value. Furthermore, a sensitivity analysis is conducted to examine the deformation and failure characteristics of the surrounding rock under different bedding angles. This research contributes to a comprehensive understanding of the anisotropic behavior of layered surrounding rock, especially for tunnel engineering, which is of great significance in adjusting the supporting measures for the surrounding rock. [ABSTRACT FROM AUTHOR]

The design of rock engineering projects requires an estimation of the strength of intact rock blocks. These blocks can be significantly larger than the typical laboratory test specimen; thus, understanding the specimen size effect on mechanical properties is essential. In this paper, a series of uniaxial compression tests and Brazilian disc tests were conducted on cylindrical samples with diameters varying from 20 to 150 mm, and direct shear tests were conducted on cubic samples with side lengths varying from 50 to 200 mm. The results showed that the uniaxial compressive strength (UCS), cohesion, and Young's modulus decrease with increasing specimen size, whereas the tensile strength initially increases and then decreases. Moreover, the applicability of different size effect models to experimental data was assessed. It was concluded that the fitting equations of UCS and cohesion are almost the same, whereas that of tensile strength is significantly different. The size effect law of rock mechanics parameters may be affected by the failure mode. [ABSTRACT FROM AUTHOR]

• An efficient Kriging-based calibration framework for FDEM is proposed. • A 3D FDEM numerical example validates the proposed method. • The proposed method employs fewer FDEM simulations to improve computational efficiency. The combined finite-discrete element method (FDEM) is a powerful numerical tool to simulate the transition of materials from continuous deformation to discontinuous fracturing and fragmentation. Calibrating parameters using laboratory data is crucial for applying FDEM to engineering-scale analysis. Considering the high computational costs in existing calibration schemes, this study proposes an effective FDEM calibration framework employing the Kriging surrogate model rooted in Uniaxial Compressive Strength (UCS) and Brazilian Tensile Strength (BTS) tests. The sensitivity analysis is first conducted on mesh size, loading rate, and numerical parameters to find a suitable set that balances computational efficiency and accuracy. Subsequently, an efficient mapping relationship between input fracture parameters and simulated strengths is established based on the Kriging surrogate model, replacing the expensive FDEM program for forward calculations. With the fracture parameters treated as unknown variables and experimental strengths available, the objective function is formulated and then solved to estimate fracture parameters. The effectiveness of the proposed method is validated through a numerical example. Compared to the conventional methods, the proposed approach requires fewer simulations of UCS and BTS, which highlights a significant computational efficiency advantage. [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]

In this study, a two-dimensional Voronoi element-based numerical manifold method (VE-NMM) is developed to analyze the granite fragmentation process by a single tunnel boring machine (TBM) cutter under different confining stresses. A Voronoi tessellation technique is adopted to generate the polygonal grain assemblage to approximate the microstructure of granite sample from the Gubei colliery of Huainan mining area in China. A modified interface contact model with cohesion and tensile strength is embedded into the numerical manifold method (NMM) to interpret the interactions between the rock grains. Numerical uniaxial compression and Brazilian splitting tests are first conducted to calibrate and validate the VE-NMM models based on the laboratory experiment results using a trial-and-error method. On this basis, numerical simulations of rock fragmentation by a single TBM cutter are conducted. The simulated crack initiation and propagation process as well as the indentation load-penetration depth behaviors in the numerical models accurately predict the laboratory indentation test results. The influence of confining stress on rock fragmentation is also investigated. Simulation results show that radial tensile cracks are more likely to be generated under a low confining stress, eventually coalescing into a major fracture along the loading axis. However, with the increase in confining stress, more side cracks initiate and coalesce, resulting in the formation of rock chips at the upper surface of the model. In addition, the peak indentation load also increases with the increasing confining stress, indicating that a higher thrust force is usually needed during the TBM boring process in deep tunnels. [ABSTRACT FROM AUTHOR]

• Rheological and mechanical properties of water-soluble epoxy resin modified grout were studied. • Water-soluble epoxy resin improved the rheological and mechanical properties of composite grout. • The uniform distribution of epoxy resin in the composite grouting promoted the hydration reaction of cement. • The modification mechanism of epoxy resin to cement-based grout was studied and the reaction mechanism model of the modification process was established. In order to improve the defects of conventional cement-based grout such as low strength, brittle failure, weak bonding, and poor stability, water-soluble epoxy resin was designed and used to modify cement-based grout. The purpose of this study is to investigate the feasibility of water-soluble epoxy resin as a high-performance tunnel grouting modifier through the rheological and mechanical properties analysis and chemical characterization of composite grout with different epoxy content and water-cement ratio. The results demonstrated that the fluidity of epoxy resin modified composite grout increased first and then decreased with the addition of epoxy resin. The addition of epoxy resin effectively reduced the bleeding ratio, and kept the grouting fluidity for a certain period of time after mixing. The average particle size of composite grout decreased. Epoxy resin particles and cement particles had opposite zeta potential, and electrostatic attraction occurred in the suspension. The absolute value of zeta potential first increased and then decreased with the increase of epoxy resin. The uniaxial compressive strength and splitting tensile strength of composite grout were observably improved by the modification of epoxy resin, and the ultimate strain was also significantly increased under high epoxy content, and the brittle failure characteristics of the material were improved. With the increase of the content of epoxy resin, the yield of calcium hydroxide in the hydration products increased while the content of calcium carbonate decreased. Epoxy resin contributed to the hydration reaction of cement, while excessive epoxy resin formed a film structure inside to restrict further hydration. The modification of epoxy resin significantly improved the bonding ability of composite grout, and the epoxy resin was uniformly distributed inside the composite grout. The core of the chemical reaction in the modification process was the reaction between free calcium ions and –OH in epoxy resin, and a complex cross-linking network structure was formed with calcium ions as the node. Compared with neat cement paste, epoxy resin modified composite grout had obvious advantages in strength, ultimate strain, fluidity, stability, and bonding ability, so it had broad research potential and application prospect. [ABSTRACT FROM AUTHOR]

Granite for hosting the deep geological repository (DGR) is subjected to thermo-hydro-mechanical (THM) treatment for decades of years, while the variations in the tensile strengths of mineral grain interfaces (MGIs) with THM treatment are still unknown. Served as an important parameter in determining the macro mechanical properties of granite, quantifying the tensile strength degradation of MGI with THM treatment is crucial for ensuring the long-term safety of DGR. In this study, the varied tensile strengths of MGIs in the granite after different THM treatments were first directly measured based on a self-developed single-MGI mechanical test system. Three-bending tests were conducted on six-hundred MGIs, which were submitted to various THM treatments with a temperature of 25–175 °C and a pore pressure of 0–15 MPa. The tensile strengths of the interfaces of quartz, feldspar and the interfaces between quartz and feldspar were derived based on the Dugdale–Barenblatt (D–B) model. Results show that the average tensile strength of the interfaces of quartz is 1.06 times larger than that of interfaces between quartz and feldspar, and 1.13 times larger than that of the interfaces of feldspar. Besides, the tensile strength of MGIs seems more susceptible to the pore pressure than to the temperature, and the degradation of tensile strength is the most obvious in the interfaces between quartz and feldspar, followed by the interfaces of feldspar and finally the interfaces of quartz after THM treatments. Based on the characteristics of the tensile strength distributions of different MGIs after THM treatments, the tensile strength degradation models of MGIs related to THM treatments were proposed in meso scale. • The tensile strength of MGI in granite was directly measured via self-developed single-MGI mechanical test system. • The discrepancies in the tensile strength degradations of different MGIs in the THM-treated granites were distinguished. • Tensile strength degradation models related to THM treatment were proposed based on tensile strength distributions of MGIs. [ABSTRACT FROM AUTHOR]