A Macro–Micro Damage Model for Rock under Compression Loading

Rock damage caused by its microcrack growth has a great influence on the deformation and strength properties of rock under compressive loading. Considering the interaction of wing cracks and the additional stress caused by rock bridge damage, a new calculation model for the mode-I stress intensity factor at wing crack tip was proposed in this study. The proposed calculation model for the stress intensity factor can not only accurately predict the cracking angle of wing crack, but can also simulate the whole range of variation of wing crack length from being extremely short to very long. Based on the modified stress intensity factor, a macro–micro damage model for rock materials was also established by combining the relationship between microcrack growth and macroscopic strain. The proposed damage model was verified with the results from the conventional triaxial compression test of sandstone sample. The results show that the proposed damage model can not only continuously simulate the stress-strain curves under different confining pressures, but also can better predict the peak strength. Furthermore, the sensitivities of initial crack size, crack friction coefficient, fracture toughness, initial damage and parameter m on the stress-strain relationship are discussed. The results can provide a theoretical reference for understanding the effect of microcrack growth on the progressive failure of rock under the compressive loading.

Research on Microscopic Evolution Laws of Sandstone Deformation and Failure Based on the Particle Discrete Element Method

The fracture of sandstone is closely related to the condition of internal microcracks and the fabric of micrograin. The macroscopic mechanical property depends on its microscopic structures. However, it is difficult to obtain the law of the microcrack growth under loading by experiments. A series of microscopic sandstone models were established with particle flow code 3D (PFC3D) and based on the triaxial experiment results on sandstones. The experimental and numerical simulations of natural and saturated sandstones under different confining pressures were implemented. We analyzed the evolution of rock deformation and the rock fracture development from a microscopic view. Results show that although the sandstones are under different confining pressures, the law of microcrack growth is the same. That is, the number of the microcracks increases slowly in the initial stage and then increases exponentially. The number of shear cracks is more than the tensile cracks, and the proportion of the shear cracks increases with the increase of confining pressure. The cracking strength of natural and saturated sandstones is 26% and 27% of the peak strength, respectively. Under low confining pressure, the total number of cracks in the saturated sample is 20% more than that of the natural sample and the strongly scattered chain is barely seen. With the increase of the confining pressure, the effect of water on the total number of cracks is reduced and the distribution of the strong chain is even more uniform. In other words, it is the confining pressure that mainly affects the distribution of the force chain, irrespective of the state of the rock, natural or saturated. The research results reveal that the control mechanism of shear crack friction under the different stress states of a rock slope in the reservoir area provides a basis for evaluating the stability of rock mass and predicting the occurrence of geological disasters.

Numerical Simulation-Based Damage Identification in Concrete

High costs for the repair of concrete structures can be prevented if damage at an early stage of degradation is detected and precautionary maintenance measures are applied. To this end, we use numerical wave propagation simulations to identify simulated damage in concrete using convolutional neural networks. Damage in concrete subjected to compression is modeled at the mesoscale using the discrete element method. Ultrasonic wave propagation simulation on the damaged concrete specimens is performed using the rotated staggered finite-difference grid method. The simulated ultrasonic signals are used to train a CNN-based classifier capable of classifying three different damage stages (microcrack initiation, microcrack growth and microcrack coalescence leading to macrocracks) with an overall accuracy of 77%. The performance of the classifier is improved by refining the dataset via an analysis of the averaged envelope of the signal. The classifier using the refined dataset has an overall accuracy of 90%.

Numerical Simulation Based Damage Identification in Concrete

High costs for the repair of concrete structures can be prevented if damage at an early stage of degradation is detected and precautionary maintenance measures are applied. To this end, we use numerical wave propagation simulations to identify simulated damage in concrete using convolutional neural networks (CNN). Damage in concrete subjected to compression is modeled at the mesoscale using the discrete element method. Ultrasonic wave propagation simulation on the damaged concrete specimens are performed using the rotated staggered finite-difference grid method. The simulated ultrasonic signals are used to train a CNN based classifier capable of classifying three different damage stages (microcrack initiation, microcrack growth and microcrack coalescence leading to macrocracks). The performance of the classifier is improved by refining the dataset via an analysis of the averaged envelope of the signal. The classifier using the refined dataset has an overall accuracy of 90%.

Thermal Activation and Ductile vs. Brittle Behavior of Microcracks in 3D BCC Iron Crystals under Biaxial Loading by Atomistic Simulations

We present the results of free 3D molecular dynamics (MD) simulations, focused on the influence of temperature on the ductile-brittle behavior of a pre-existing central Griffith through microcrack (1¯10)[110] (crack plane/crack front) under biaxial loading σA and σB in tension mode I. At temperatures of 300 K and 600 K, the MD results provide new information on the threshold values of the stress intensity factor K and the energy release rate G, needed for the emission of <111>{112} blunting dislocations that support crack stability. A simple procedure for the evaluation of thermal activation from MD results is proposed in the paper. 3D atomistic results are compared with continuum predictions on thermal activation of the crack induced dislocation generation. At elevated temperature T and biaxiality ratios σB/σA ≤ 0.8 dislocation emission in MD is observed, supported by thermal activation energy of about ~30 kBT. With increasing temperature, the ductile-brittle transition moves to a higher biaxiality ratios in comparison with the situation at temperature of ~0 K. Near the transition, dislocation emission occurs at lower loadings than expected by continuum predictions. For the ratios σB/σA ≥ 1, the elevated temperature facilitates (surprisingly) the microcrack growth below Griffith level.

An analytical model of multi-stress drops triggered by localized microcrack damage in brittle rocks during progressive failure

Stress drops in stress–strain constitutive curves of intact brittle rocks under high confining pressure have great significance for evaluating the earthquake mechanism and the safety of deep underground engineering. Microcrack growth in intact rock strongly influences the stress drops. However, the theoretical model of microcrack growth-dependent multi-stress drops rarely is proposed in stress–strain curves of intact rocks. In this study, a constitutive model depending on the damage variable relating to microcrack growth and strain increment is proposed to explain the multi-stress drops in stress–strain curves including strain hardening and softening phases of intact rocks. This model is formulated by combining the wing crack growth model, the suggested relationship between axial strain and wing crack growth, and the stepping function of damage relating to axial strain. This stepping function of damage relating to axial strain approximately is used to simulate the developing process of the small individual shear bands caused by the local microcrack accumulation and coalescence. The effects of parameters in the suggested stepping function of damage on the stress–strain curves containing stress drops are discussed. The theoretical model qualitatively explains the experimental phenomena of multi-stress drops in the stress–strain curves, which provides an important implication for evaluating the earthquake mechanism and the safety of deep underground engineering.

Microcrack Growth Properties of Granite under Ultrasonic High-Frequency Excitation

The failure of most rock materials is essentially a process of crack initiation and propagation. It is of great significance to study the microcrack growth characteristics of granite under ultrasonic high-frequency excitation for understanding the failure mechanism of rock under ultrasonic vibration. In this paper, the experimental and numerical simulation methods are used to study the propagation characteristics of rock cracks under ultrasonic vibration. Scanning electron microscopy (SEM) was used to observe the growth of microcracks in granite samples after ultrasonic vibration for 0 min, 2 min, and 4 min. A discrete element software PFC2D was used to simulate and solve the cracking mechanism of rock cracks under ultrasonic vibration. Also, it is found that the action of ultrasonic vibration can effectively promote the development of microcracks in the granite samples. The main three cracks causing the failure of quartz under the ultrasonic high frequency are intragranular cracks, transgranular cracks, and grain boundary cracks. The breakage of transgranular cracks usually contributes a shell-like fracture, that is, a regular curved surface with a concentric circular pattern appears on the fracture surface, which is a typical quartz brittle fracture mode. In addition, the feldspar grain failure is mainly caused by intragranular crack and transgranular crack. Microcracks are wavy expansion in feldspar grain. Mica failure is mainly caused by grain boundary crack, and the effect of lamellar cleavage on the failure of mica is significant. Moreover, it is also found that the mechanism of microcrack propagation is tensile failure. The failure of feldspar grains is mainly contributed to the failure of granite.