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Crack initiation, propagation, and coalescence are important for the understanding of rock mass behavior. In this paper, we use an improved numerical manifold method (NMM) that can stimulate the initiation, propagation, and coalescence of many cracks simultaneously to model the continuous–discontinuous deformation of granite under uniaxial and confined compression. This new simulation method couples subcritical crack growth (SCG) theory and the Mohr–Coulomb strength criterion with tension cut-off to consider the propagation of virtual and real cracks, respectively, and uses a statistical Weibull distribution to study the influence of elastic modulus inhomogeneity on crack propagation and rock failure. The mechanical behavior and failure modes of the models are in good agreement with experimental data. Increasing elastic modulus inhomogeneity decreases strength and the strain required for macroscopic failure. The stress corrosion index (n) and crack growth constant (C) also have a strong influence on uniaxial compressive strength. Indeed, higher values of C and n result in faster virtual crack speeds, a lower uniaxial compressive strength, and a lower axial strain upon failure. Confining pressure also exerts an influence on crack propagation, compressive strength, and failure mode. Our study shows that the improved NMM code combined with the virtual crack model is therefore an effective and reliable method to simulate crack initiation, propagation, and coalescence in granite under uniaxial and confined compression. Highlights: A virtual crack approach combined with subcritical crack growth theory is implemented in numerical manifold method to simulate the initiation of multi-cracks. The Mohr–Coulomb criterion with tension cut-off coupled with subcritical crack growth theory is incorporated into numerical manifold method to simulate the propagation of micro-and macro-cracks. Three types of crack intersection are identified in numerical manifold method to allow the model to accurately simulate the propagation and coalescence of multi-cracks and large displacement. [ABSTRACT FROM AUTHOR]

During underground hard-rock mining, the drilling and blasting method currently remains the most economical excavation method, and the rock may experience a multistrain-rate spectrum under quasi-static, dynamic, and rheological loading conditions and their combination as well. The study on the damage mechanism of rock under multistrain-rate condition that induced by mining excavation is the fundamental issue for predicting the mining-induced hazards such as rockburst. In this study, the state of the art of rock damage and failure under different strain rates is reviewed first. Then, the numerical model for rock failure under multiple strain rates is formulated when the rock damage is taken as the main thread. Meanwhile, we summarize our work in this area over the past ten years, and the constitutive law for the damage and failure of rock under multistrain rates is presented. Finally, several numerical examples, i.e., rock damage and failure under combined static and dynamic load, rock damage and failure triggered by dynamic stress redistribution due to excavation, rock damage and failure induced by blasting, and rock damage and failure due to the combination of dynamic disturbance and rheological load, are presented. Based on these numerical simulations, the associated rock damage mechanism and failure behaviors under differently combined multiple strain rates are clarified, which may provide a theoretical basis for clarifying the rock failure mechanism during rockbursts and rock blasting. Also, further studies on the damage and failure of rock under multiple strain rates are suggested. [ABSTRACT FROM AUTHOR]

Rocks with microdefects exhibit viscoelastic behavior during stress wave propagation. The viscosity coefficient of the wave can be used to characterize the attenuation as the wave propagates in rock. In this study, a long artificial bar with a readily adjustable viscosity coefficient was fabricated to investigate stress wave attenuation. The viscoelastic behavior of the artificial bar under dynamic loading was investigated, and the initial viscoelastic coefficient was obtained based on the amplitude attenuation of the incident harmonic wave. A one-dimensional wave propagation program was compiled to reproduce the time history of the stress wave measured during the experiments, and the program was well fitted to the Kelvin-Voigt model. The attenuation and dispersion of the stress wave in long artificial viscoelastic bars were quantified to accurately determine the viscoelastic coefficient. Finally, the method used to determine the viscoelastic coefficient of a long artificial bar based on the experiments and numerical simulations was extended to determine the viscoelastic coefficient of a short rock bar. This study provides a new method of determining the viscosity coefficient of rock. [ABSTRACT FROM AUTHOR]

During the excavation of underground opening, the rock may experience a complex loading path that includes the highly confined compression before excavation, unloading of confining stress and further disturbance of dynamic loading after excavation. By using Rock Failure Process Analysis for Dynamics (RFPA-Dynamics), the failure of rock sequentially subjected to this complex loading path is numerically simulated, in order to examine the rock failure mechanism induced by excavation. The RFPA-Dynamics is firstly used to reproduce the failure of rock under confined compression, followed by unloading of confining pressure, and it is validated against with the existing experimental observation. Then, the failure characteristics of rock specimen sequentially subjected to the quasi-static triaxial loading, unloading of confining pressure and dynamic disturbance are numerically simulated, where the effect of magnitude of axial loading and confining pressure, and duration and amplitude of the dynamic disturbance on the final failure patterns of rock are examined. The numerical results indicate that the arc-shaped spalling damage zone is prone to develop with the increase in the axial pressure and lateral pressure coefficient. As for the effect of dynamic disturbance, the contribution of duration and amplitude of dynamic disturbance on the energy input are similar, where the area of damage zone increases with the energy input into the rock specimen. In this regard, the area of the damage zone is influenced by both the magnitude of in situ stress and waveform of dynamic disturbance. This study denotes that it is of great significance to trace the complex loading path induced by excavation in order to capture the rock failure mechanism induced by underground excavation. [ABSTRACT FROM AUTHOR]

Shirengou iron mine in Hebei Province, China is now under transition from open pit to underground mining. During this process, the unstable failure risk of crown pillar is growing as a result of underground mining, fault activation and water seepage. To monitor the stability of the crown pillar, a microseismic monitoring system was equipped in 2006. Based on temporal and spatial distribution of microseismic events and deformation mechanism, it was found that it is the propagation of the buried fault F15 that causes the failure of the crown pillar, resulting in increased water seeping into the underground drifts. By analyzing the temporal changes in multiple microseismic parameters during the fracture process of the crown pillar, it was found that several distinct abnormalities in the microseismic data such as a rapid decrease in the b value, a sharp increase in energy release, an abnormal increase in apparent stress and a low dominant frequency, could be judged as the signal of an increasing risk. Therefore, the microseismic monitoring has been proven to be a suitable method for understanding damage and fracture process of the crown pillar during the transition from open pit to underground mining. [ABSTRACT FROM AUTHOR]

Highlights: [•] Performances of coal permeability models were benchmarked against correct solutions. [•] Assumptions of uniaxial stress, constant overburden stress and local equilibrium were removed. [•] The effective stress transfer between matrix and fracture were included. [•] These three assumptions were identified as the reason of coal permeability model failures. [Copyright &y& Elsevier]

• A linear closed-form model is proposed for quasi-brittle fracture of sandstone. • 95 sandstone specimens with volume ratio close to 1000 were tested and analyzed. • One normal distribution considering scatters/reliability applies to all results. • The closed-form solution is a predictive model more suitable for design analysis. • Statistical analysis of discrete cracking removes the need of curve-fitting. Quasi-brittle fracture properties of a medium-grain sandstone with an average grain size G around 0.3–0.4 mm were investigated under three-point-bending (3-p-b) conditions. In total, 95 specimens were tested with the beam width W varying from 10 to 300 mm, or the specimen-size/grain-size ratio from 30 to 900. 45 medium-sized specimens (W = 30, 60, 100 mm) were tested first to determine the tensile strength f t , which was then used as a reference for tests of 8 large notched specimens (W = 300 mm) and 42 small un-notched specimens (W = 10 mm). Statistical fracture modelling, based on normal distributions and the characteristic microstructure measurement (the average grain size G in this study), was used to quantify the quasi-stable fictitious crack growth Δ a fic at the peak load P max and the characteristic crack length a ch * defined by the bulk toughness and strength properties. The statistics-assisted modelling has changed the previous curve-fitting boundary effect model (BEM) to a predictive closed-form solution, providing a useful option when large scatters in experimental data and reliability in design need to be focused. The well-known size effect law (SEL) proposed for geometrically similar specimens was also used to fit the sandstone results, and compared with the closed-form BEM with built-in statistical functions. Applications of SEL and BEM and their key differences were explained. [ABSTRACT FROM AUTHOR]