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As the weak structure and main seepage channel of rock mass, the discrete fracture network (DFN) has a significant influence on the physical and mechanical properties of rock mass. In this paper, based on the rectangular joint model, two algorithms are proposed to realize the precise modeling of the DFN in any polyhedron. First, the equivalence of DFN modeling with the rectangular joint model and the elliptical joint model is theoretically deduced. On this basis, the chain splicing algorithm suitable for the rectangular joint model is proposed, which can generate the DFN model according to the actual distribution of joint spacing, trace, and bridge length. Aiming at the concave boundary in the model domain, the segmentation‐stitching operation is put forward, and the continuity of the joint when passing through the interface is ensured. Finally, the effectiveness of the above algorithm is verified by several simple cases, and the relationship between the size of the geometrical representative elementary volume (REV) and discontinuity parameters is discussed. The results show that when the mean values of the joint distribution parameters are the same, even if the distribution rules are different, the number of joints generated in the same spatial region is approximately equal. The size of the geometrical REV is independent of the spacing and bridge length and is approximately three to five times the mean of the trace. The relevant algorithms and conclusions in this paper can be used as the basis for subsequent rock mass stability analysis and seepage calculation. [ABSTRACT FROM AUTHOR]

In order to study the deformation and stability of a fractured rock mass, existing research suggests that fracture deformation, which is usually obtained by evaluating the equivalent deformation modulus, dominates the deformation of a fractured rock mass. However, this parameter is difficult to obtain in theory and practice, which limits the application of rock mass deformation analysis methods. In order to calculate the deformation of fractured rock masses, the mass of the rock is regarded as a sponge-like material, and it is assumed that the deformation of a water-saturated fractured rock mass under external force load is approximately equal to the net flow of fracture water. Based on this assumption, firstly, the relationship between rock mass deformation and fracture flow is studied through a single-fracture rock mass model. The hydraulic properties of the fracture are characterized by the permeability coefficient, and the fracture deformation in the rock mass is equivalent to the fracture flow. The fracture deformation calculation formula is derived from the fracture hydraulics calculation formula, and this is compared with the measured data. The rationality of the calculation formula was verified. On this basis, the calculation formula for rock mass deformation, including multiple groups of fracture surfaces, is proposed, and the stress-strain constitutive relationship of a complex rock mass is established. The correctness of the calculation method was verified by comparing it with other theoretical calculation results. [ABSTRACT FROM AUTHOR]

As a typical heterogeneous material, the macroscopic mechanical properties of rocks are influenced by factors, such as the type, size, and spatial distribution of internal mineral particles. To study the influence of microscopic heterogeneity on the nonlinear mechanical behavior and fracture process of rocks, DIP (digital image processing) technology and FDEM (finite-discrete element method) are used to establish numerical models that characterize the microstructures of three types of gabbro: coarse-grained, medium-grained, and fine-grained. First, CT (Computed Tomography) scan images were segmented and vectorized. Then, the model was calibrated based on uniaxial compression experiment results. Finally, numerical tests of uniaxial compression were carried out on the three heterogeneous models to explore the deformation characteristics, crack propagation laws, and energy conversion effects of the micro-heterogeneous structures of the three gabbros. Combined numerical and laboratory uniaxial compression experiments results, the results showed that micro-cracks in gabbro appeared at the boundary between clinopyroxene and plagioclase, and propagated continuously along the mineral interface, and the final crack distribution was controlled by the spatial distribution of mineral particles. In addition, the particle size of gabbro had a significant impact on the micro-crack propagation and macroscopic mechanical properties of the model. The finer the particle size, the smaller the heterogeneity, the higher the UCS (uniaxial compression strength) and E (elastic modulus), the faster the energy dissipation, and the stronger the brittleness of the rock. The results of this study conclude the macroscopic mechanical behavior and micro-failure mechanism of gabbro in the compressed state, and also provide technical support for the study of similar rocks. Highlights: Based on the FDEM and digital image processing technology, a numerical model is being created that can represent the micro-heterogeneity of gabbro. Compared the results of numerical and laboratory experiments, the differences in mechanical behavior of different grain sizes gabbros were revealed. Compared the energy dissipation and crack propagation modes of gabbros, the impact of grain size on the rock fracturing process was revealed. [ABSTRACT FROM AUTHOR]

A reasonable prediction of the elastic modulus of rock and rock mass can provide sound basis for the design in tunnels and underground caverns. It is observed from the laboratory results that the elastic modulus not only depends on the confining pressure but also indicates certain sensitivity to the failure degree during the loading-fracturing process. This paper deduces a unified expression for the elastic modulus with the coupling effects of the plastic strain and confining stress, and fits the soft, moderate, hard rocks with different quality. In this paper, a method to determine the elastic modulus from the laboratory results is proposed. Through the method, the variation of the elastic modulus versus the plastic strain and confining stress for the soft, moderate, hard rocks is analysed. A unified deterioration model for the elastic modulus is developed by the nonlinear fitting regression method. This deterioration model can be employed in the analytical and numerical analysis of the tunnels and underground caverns, which enables to present a more realistic mechanical behaviour of rock mass. Highlights: Variation of elastic modulus versus plastic strain and confining stress for soft, moderate, hard rocks is analysed. A unified deterioration model for elastic modulus is developed by nonlinear fitting regression method. This deterioration model can be employed in analytical and numerical analysis of tunnels and underground caverns. [ABSTRACT FROM AUTHOR]

Highlights: The dynamic behaviors of rock under different seismic loads are numerically simulated. The properties of rock under different seismic loads are analyzed and compared. The main factors of seismic load for the deformation properties of rock are determined. [ABSTRACT FROM AUTHOR]

In the uniaxial compressive test, the strain energy density is expressed as follows: 2 HT ht Graph 3 HT ht Graph Graph: Fig. According to the strain equivalence hypothesis: 14 HT ht Graph 15 HT ht Graph Graph: Fig. [Extracted from the article]

Soil-rock mixture (SRM) shows complicated mechanical behaviors due to their complex compositions and structures, leading to challenging instability problems during the construction process. Typical SRM are composed of rocks with high strength and fine grained soils, and the mechanical characteristic is largely controlled by the rock block proportion (RBP) and component properties. It is noted that the rock sizes of natural SRM make it difficult for laboratory or in situ tests. There are few studies on empirical formulas to predict the mechanical characteristics of SRM. In this study, the nonlinear relationship between SRM shear strength and RBP was investigated, and an empirical formula predicting the shear strength of mixtures consisted of strong rocks and a weak soil matrix was proposed. For this purpose, a database of shear strength and uniaxial compressive strength (UCS) of SRM with different RBPs was built firstly on the basis of the laboratory test results from previous literatures. In order to focus on the interactions of rock blocks and soil matrix in SRM, a RBP range of 30–90% was set as the applicable range of the empirical formula and both of the compositions are held to provide shear resistance in the applicable range. Subsequently, a nonlinear equation to calculate the shear strength of SRM with RBP range of 30–90% was proposed using regression analysis considering the strengths of components and soil-rock contact faces. Several representative properties of rocks and soil matrix, such as RBP, UCS of the matrix (UCSm), and the friction angle of the blocks (φblock), were chosen as the input parameters based on the mechanical properties of SRM. An additional parameter "A" was used to describe the connect strengths of the soil-rock contact faces. In addition, uniaxial compression tests and large-scale direct shear tests were performed on the Taoyuan SRM samples. The test results and other measured data from the database were used to compare with the corresponding estimated values. The results demonstrated that the empirical approach could predict the shear strength with R2 = 0.75 and can be considered a practical tool in engineering designs when mechanical tests are not available. [ABSTRACT FROM AUTHOR]

It is not widely accepted that the dynamic strain rate experienced by a rock mass during an earthquake is lower than that during a high strain rate scenario such as an explosion or a rock burst. The present study investigated the problem of determining the mechanical properties of rock considering earthquake effects using experimental tests and empirical formulas. First, to obtain the most concentrated frequency band of earthquake energy, a statistical analysis was conducted to obtain the response spectra of ground motion records near the example projects. The mean response spectrum was then fitted with a design response spectrum formula. The most concentrated frequency band of earthquake energy was then determined with the flat segment of the design response spectrum. Based on this frequency range, cyclic loading–unloading testing that simulated the earthquake effect was conducted on rock samples. The strain rate range experienced by rocks during an earthquake was then obtained. This strain rate range is between the quasi-static and intermediate strain rate ranges and is significantly lower than the high strain rate range. Based on this strain rate range, dynamic triaxial compression tests were conducted on igneous rock specimens from the case study areas. It is confirmed that the fit of the dynamic compression test results with the Hoek–Brown (HB) criterion is more accurate than that with the Mohr–Coulomb criterion. The HB strength envelope under static conditions can be used to predict the seismic strength behaviors, requiring an update of only the intercept of the envelope. Thus, the HB strength criterion considering the seismic effect was obtained. Moreover, the seismic modulus of the intact rock can be estimated with the values of the uniaxial compressive strength (UCS) under different strain rates and the modulus ratio, which was found to be independent of the strain rate. Hence, it is practical to estimate the mechanical properties of rock masses in consideration of seismic effects with the seismic HB strength criterion and the Hoek and Diederichs equation based on the UCSs under various strain rates. Ultimately, the rock mechanical properties in consideration of seismic effects were estimated via the proposed approach for the Baihetan hydropower plant project as an example. [ABSTRACT FROM AUTHOR]

Knowledge from historical earthquake events indicates that a submarine tunnel crossing active strike-slip faults is prone to be damaged in an earthquake. Previous studies have demonstrated that the flexible joints are an effective measure for a submarine tunnel crossing a strike-slip fault. The background project of this paper is the second submarine tunnel of Jiaozhou bay. In this work, model tests and numerical simulations are conducted to investigate the deformation and failure mechanism of a submarine tunnel with flexible joints under a strike-slip fault dislocation. The influence of strike-slip faults on a tunnel with flexible joints has been investigated by examining the deformation of rock mass surface, analyzing lining stains, and crack propagation from model tests. Numerical simulations are conducted to study the effects of the design parameters of a tunnel with flexible joints on the mechanical response of the lining. The results showed that the 'articulated design' measure can improve the ability of the tunnel to resist the strike-slip faults. In terms of the mechanism of design parameters of a tunnel with flexible joints, this paper finds that increasing the lining thickness, decreasing the lining segment length, and decreasing the tunnel diameter to a reasonable extent could effectively improve the performance of this faulting resistance measure for a tunnel under the strike-slip fault zone dislocation. Compared with the horseshoe tunnel cross-section, the circular tunnel cross-section can improve the ability of the faulting resistance of a tunnel with flexible joints, while the optimal angle of the tunnel crossing the fault zone is 90º. It is concluded that the wider fault zone, smaller flexible joint width, and less stiffness of the flexible joint could make lining safer under a strike-slip fault dislocation. The above research results can serve as a necessary theoretical reference and technical support for the design of reinforcement measures for a submarine tunnel with flexible joints under strike-slip fault dislocation. [ABSTRACT FROM AUTHOR]

In engineering practice, it is a common that rocks are subjected to cyclic loading. The mechanical properties of rock materials under tiered, single-level, and multi-level cyclic load regimes (i.e., with different frequency, minimum stress, and amplitude) were numerically investigated by using a dynamic constitutive model for rock materials. A comparison between these loads from the aspects of stress-strain curve, modulus, damage, and strength was undertaken. The results indicate that the model can effectively reflect the different mechanical properties of rock materials under different cyclic load regimes. Under the action of tiered and multi-level cyclic loading, the area and width of the hysteresis loops become larger with increasing applied stress, but the slope of stress-strain curve, area and width of the hysteresis loops, maximum strain, and the irreversible deformation vary under different loads. The loading deformation modulus decreases with the increase of applied stress and the reductions therein are different when subjected to tiered, single-level, and multi-level cyclic loading. With increasing applied stress, the damage evolution in rock specimens subjected to tiered cyclic loading present an increasing trend and the trend likes an approximately inverted "s" -shape. Under multi-level cyclic loading, the damage variables increase rapidly at the first level, then become relatively stable and increase slowly as the applied stress increases. Furthermore, the peak strength of rock differs under different load regimes, and results indicate that cyclic loading has both strengthening and damaging effects on rock strength. • Simulated the behaviors of rock under tiered and multi-level cyclic loading. • The properties of rock under cyclic loading with different models were compared. • The properties of rock under tiered and multi-level cyclic loading were analysed. [ABSTRACT FROM AUTHOR]

• A new constitutive model able to reproduce the behavior of rock materials under triaxial cyclic loading was established. • The model can reproduce the cumulative plastic deformation, hysteretic loop, damage and the effect of confining stress. • A reasonable consistency is observed between the numerical and experimental results for two different rocks. Underground rock engineering projects are often subjected to cyclic loading such as earthquake, rock blasting. A suitable constitutive model for rock materials modeling the deformation failure characteristics of rock materials subjected to triaxial cyclic loading is significant when evaluating the long-term stability of the engineering. To date, however, there have been notably few studies on proposing constitutive models for rock materials under triaxial cyclic loading. The paper presents and validates the formulation of a new constitutive model able to reproduce the cyclic behavior of rock materials under triaxial cyclic loading. The constitutive model is based on the subloading surface theory and the modified cohesion weakening and frictional strengthening (CWFS) model. It contains kinematic hardening of the subloading surface, isotropic softening on the cohesion and isotropic hardening on the friction angle, and the effect of confining stress. Further, the model is numerically implemented in a self-developed finite element program using elastic prediction-plasticity correction method. In addition, the model is validated against two different rock materials (T 2b marble and crystalline marble) under triaxial damage-controlled and constant amplitude cyclic compression loading. A reasonable consistency is observed between the numerical and experimental results for the stress-strain curves, the evolution of residual strain with number of cycles, degradation of strength and the effect of confining stress. It shows that the model can effectively reproduce the cumulative plastic deformation, hysteretic loop, damage and the effect of confining stress of rock materials under triaxial cyclic loading. Therefore, the proposed model can provide a helpful method to describe the main deformation and strength properties of rock materials under triaxial cyclic loading, and lays a foundation for the accurate analysis of the response of underground rock engineering under cyclic loading. [ABSTRACT FROM AUTHOR]

Rock materials, which are involved in a myriad of engineering projects, are often subjected to cyclic loading, such as earthquakes. Understanding the dynamic deformation properties of rock materials under cyclic loading is necessary for evaluating the stability of rock engineering structures. This study numerically investigated the influence of cyclic loading conditions (e.g., waveform, frequency, maximum loading stress and amplitude) on the deformation properties of rock samples using the finite element method (FEM). On the basis of the Drucker–Prager (D-P) yield criterion and sub-loading surface theory, a dynamic constitutive model for reproducing the hysteresis loops and the accumulative plastic deformation of rock materials subjected to cyclic loading was established, numerically implemented using FEM, and validated through comparison with experimental results on basalt and granite model materials. Then, cyclic uniaxial loading tests were simulated with a range of loading parameters, and the deformation properties of rock samples were analyzed. The results indicated that the hysteresis loops and accumulated plastic deformation of rock materials during the cyclic process can be numerically reproduced in an effective manner. The loading parameters significantly affected dynamic deformation properties such as the maximum strain, irreversible strain and hysteresis loop. The simulation results were almost consistent with the experimental results in the published literature. Therefore, through the proposed dynamic constitutive model, FEM can be used to numerically simulate the influence of cyclic loading conditions on the deformation properties of rock materials. • A model for reproducing the deformation characteristic of rock materials subjected to cyclic loading was established. • Cyclic uniaxial loading tests for rock samples with distinct loading parameters were simulated by FEM. • The loading parameters significantly affect the dynamic deformation properties. [ABSTRACT FROM AUTHOR]

• A novel fracture modeling method considering the closed fractures. • The elastic-brittle-plastic constitutive model under the compressive condition. Since the consistency of the bond failure criterion in traditional bond-based peridynamics (BB-PD) theory, the crack-propagation pattern of rocks under tensile and compressive loads is almost the same, however in reality the mechanisms of fractures in tensile and compression state are totally different. To solve this problem, two extensions are conducted on the basis of the traditional BB-PD to form the improved bond-based peridynamics theory (iBB-PD). First, a novel fracture-modeling method considering the actual closed state of fractures in a rock mass is proposed, which can transfer stress or waves across closed fractures. Second, by introducing the elastic-brittle-plastic constitutive model, the traditional PMB model is extended to simulate bond failure under compressive conditions. Three benchmark examples are presented to illustrate the rationale of iBB-PD. The iBB-PD theory is used to simulate the crack initiation, propagation and coalescence in rock specimens with pre-existing closed fractures under uniaxial compression, and the numerical results are in good agreement with the experimental results. The iBB-PD method proposed in this paper could extend traditional peridynamics to capture the failure process of rocks under compressive-shear stress conditions. [ABSTRACT FROM AUTHOR]