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Rock as a natural material is heterogeneous. Rock material consists of minerals, crystals, cement, grains, and microcracks. Each component of rock has a different mechanical behavior under applied loading condition. Therefore, rock component distribution has an important effect on rock mechanical behavior, especially in the postpeak region. In this...
Citations
... The results were able to capture the anisotropic nature of the samples but were unable to predict microscopic bond stresses based on macroscopic applied stresses in random pack systems. In another study, Molladavoodi and RahimiRezaei (2018) introduced a methodology that incorporated image processing, statistical techniques, and upscaling micro-mechanics to analyze the mechanical properties of rhyodacite, an igneous rock. They integrated the Mohr-Coulomb softening model into a DEM code and conducted numerical simulations. ...
Rocks can deform at varying scales (nano-, micro- and macro-scale) under different temperatures, pressures, stresses, and time conditions. Sub-core scale (nano- to micro-scale) changes in rock properties can influence local (fine-scale) and bulk scale (macro-scale) rock deformation. However, there is a lack of comprehensive knowledge on how rock deformation at sub-core scale (i.e., nano- to micro-scale) is assessed and its potential to accurately predict and estimate the macro-scale mechanical behavior of rocks. This study presents a comprehensive and forward-leaning review of the assessment of nano-scale and micro-scale rock mechanical parameters, their time-dependent behavior, and potential applications in rock engineering. Also, we highlighted the key findings based on experimental and numerical methods for evaluating rock mechanical parameters, and presented the limitations of these approaches. Further, we discussed the reliability of sub-core scale mechanical assessments in predicting macromechanical (larger-scale) properties and the behavior of rocks in geo-engineering. Finally, we offer recommendations to advance investigations focused on rock mechanical assessments at these smaller scales and provide a more accurate characterization at the sub-core scale.
... The second type is a rheological model based on creep tests and the Thermo-Viscoplastic theory [25,26]. The third type is the thermal damage constitutive model of rocks based on statistical distribution [27,28]. The statistical damage constitutive model can directly and accurately describe the evolution process of rock damage, so as to better describe the mechanism of rock damage. ...
Studying the mechanical behavior of rocks under real-time high-temperature conditions is of great significance for the development of energy caverns, nuclear waste disposal projects, and tunneling engineering. In this study, a real-time high-temperature impact compression test was conducted on Sejila Mountain granite to explore the effects of temperature and external load on its mechanical properties. Based on the concepts of damage mechanics and statistics, a coupled thermal-mechanical (T-M) damage constitutive model was established, which considers the temperature effect and uses the double-shear unified strength as the yield criterion. The parameter expressions were clarified, and the accuracy and applicability of the model were verified by experimental data. The research results indicated that high temperatures had an obvious damaging and deteriorating effect on the strength of the granite, while an increase in impact velocity had an enhancing effect on the strength of the granite. The established constitutive model theoretical curve and test curve showed a high degree of agreement, indicating that the coupled T-M model can objectively represent the evolution process of damage in rocks and the physical meaning of its parameters is clear.
... In statistical modeling, the Weibull distribution function is considered a suitable function to reflect the mesoheterogeneity of rock and is usually used to describe heterogeneous rock. In previous studies, some simulation methods can already simulate the rock heterogeneity, such as the RFPA, DEM, and DDA method [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Based on the assumption that the rock mesoelement parameters meet the Weibull distribution, Tang et al. [6,7] introduced the heterogeneity model in the RFPA method, which was proven to be feasible. ...
... Besides, Chen and Konietzky [10] introduced the heterogeneity model into the DEM method and analyzed the rock mechanical behavior effectively. Molladavoodi and Rahimirezaei [11] introduced a constitutive model based on the Weibull distribution into the DEM to study the influence of heterogeneity on rock mechanical behavior. Tang et al. [12][13][14][15] introduced a spatial correlation length factor into the traditional Weibull distribution and studied the heterogeneity character of concrete failure using an equivalent probabilistic model. ...
Heterogeneity is an important characteristic that affects the mechanical behavior of rock. In the present work, a statistical rock mesoheterogeneity model based on the Weibull distribution function is introduced into the discontinuous deformation analysis (DDA) method to simulate the mechanical failure of heterogeneous rock, in which the general heterogeneity degree is controlled by a heterogeneity index and the mechanical property of each subblock element is randomly assigned. Brazilian disc and uniaxial compressive rectangular specimens are simulated as examples. Results show that it is more reasonable to consider the heterogeneity of elasticity properties (the elastic modulus and Poisson’s ratio) and strength properties (the tensile strength, cohesion, and friction angle) simultaneously in the heterogeneity model. It is also shown that with a larger heterogeneity index, which means a lower degree of heterogeneity, the reproducibility of the macroscopic response curves of a specimen gets better, while the exact cracking always differs but with less scattered cracks, and the global fracturing failure pattern and mode are weakly influenced by the heterogeneity. Moreover, with the increase in the heterogeneity index, the macroscopic equivalent modulus and strength get larger and approach those of a homogeneous specimen. This work indicates the importance of heterogeneity for rock mechanical behaviors including the macroscopic equivalent response and the fracturing failure. By the subblock DDA method to simulate fracturing realistically, the fracturing failure process of heterogeneous rock can be successfully reproduced, which builds good foundation for the simulation study of heterogeneous rock fracturing in practical problems, e.g., coal and rock fracturing in fluidization mining in the future.
... Argillaceous siltstone is commonly known as 'problematic rock' in the geotechnical engineering [1][2][3] because it poses water-softening properties in a way that its strength is significantly reduced upon encountering water. It is now recognized that the properties are caused by interskeleton clay materials that are particularly rich in clay-like components such as kaolinite and illite. ...
... (a) Discrete element method (DEM) [2,[4][5][6][7]: this method is a promising numerical technique for the macroscopic and microscopic investigations on granular materials, which was originally developed by Cundall in 1971 for the analysis of rock mechanics problems and then applied to soils by Cundall and Strack [4]. Unlike the continuum-based numerical techniques such as finite element method, DEM treats the soils or rock as an assembly of interacted particles that are governed by Newton's laws of motion and the contact constitutive law. ...
... Molladavoodi and RahimiRezaei [2] successfully simulated the mechanical behaviors of rock and reproduced the experimental stress-strain curve. (b) Photoelastic experiments [8][9][10][11][12][13][14][15][16][17]: such experiments have been widely undertaken for a variety of stress analysis of an optical material under mechanic deformation since the discovery of the birefringent phenomenon of the optical material in 1816. ...
This paper aims at investigating mechanical behaviors of argillaceous siltstone through a photoelastic model test and DEM modelling. Both bonded and unbonded conditions were considered. The photoelastic model was fabricated in a controllable environment, and its scaled factor was 1 : 200 in length and 11.9 : 1 in Young’s modulus. The polariscope was designed to have an area-based LCD source and an automatic digital camera. A calibration test was carried out to obtain the relationship between the contact force and the average intensity gradient squared. A 2D DEM simulation is carried out for a 100 mm × 200 mm rectangular container filled with particles of 6 mm and 10 mm, in which the bonding effect is realized by adjusting the shear contact stiffness. The results show that both the photoelastic model and DEM modelling are able to capture the evolution of force chain network, effective contact number and stress concentration factor, and rheological behaviors when it is subjected to an increasing uniaxial load. The bonding effect plays an important role in the mechanical performance of argillaceous siltstone.
... DIP usually adopts an image segmentation approach to acquire the image information of microstructures in rock, and the information is then inputted into numerical software to realize the reconstruction of the microstructures. This technique is expected to be widely applied in the research of rock mechanics due to its merits including distinct theory and great applicability to instruments [26]. ...
Research on energy accumulation and releasing in the rock plays a key role on revealing its failure mechanism. This paper establishes a microscopic structure model of granite using Otsu digital image processing (DIP) technology and particle flow code software (PFC2D). A series of numerical compression tests under different confining pressures were conducted to investigate the macro and micro characteristics of energy evolution in granite. The results showed that the energy evolution of granite is divided into three stages: stable accumulation, slow dissipation, and rapid release. With increasing confining pressure, the strain energy accumulation ratio decreased exponentially and the peak value of strain energy increased linearly. It was found that the energy accumulation speed in the pre-peak stage increased as a linear function, while the energy release speed in the post-peak stage decreased as an exponential function. In addition, the feldspar is the main microstructure which played a major part in accumulating energy in granite. However, the unit mineral energy of mica particles was bigger than that of feldspar and quartz. When subjected to increasing confining pressure, the feldspar’s total energy growth rate was fastest. Meanwhile, the mica’s unit energy growth rate was fastest.
Rocks are a typical kind of heterogeneous material composed of differences in size, shape, type, and mineral particle distribution. The strength and deformation characteristics of rocks are controlled by their internal heterogeneous structures. A numerical model was built to analyse the strength and failure characteristics of sandstone samples with randomly distributed heterogeneous. The results revealed that heterogeneous structures induce local stress concentrations and accelerate sample failure. At a loading rate of 0.01 mm/s, the mechanical properties of sandstone samples with soft heterogeneous particles are uniformly smaller than those of standard sandstone samples, while those of sandstone samples with hard heterogeneous particles follow different variation rules, depending on the specific heterogeneous particle content. With the differences between heterogeneous particles and sandstone particles in properties, an increase is observed in the mechanical properties of samples with different heterogeneous particle contents. Soft heterogeneous structures determine the crack initiation position of the main crack and the development and propagation space of cracks through their distribution pattern, while hard heterogeneous structures are load-bearing and change crack propagation paths. When there are multiple structures with different properties in rocks, micro-cracks occur first between soft heterogeneous particles, and the distribution pattern of soft heterogeneous particles determines the ultimate failure mode of samples as well as the propagation paths and development space of cracks.
Combining the digital speckle correlation method (DSCM) with the finite element model updating (FEMU) method, a new inversion method of non-uniform distribution of rock material parameters is proposed to study the characteristics of non-uniform distribution of rock material parameters and its evolution with the loading process. The non-uniform displacement field of the specimen during experimental loading is calculated based on DSCM. Based on FEMU, the experimental loading process is simulated in finite element software ABAQUS. Under the initial conditions, different material parameters (elastic modulus and Poisson’s ratio) are given for each element according to Weibull distribution to calculate the non-uniform displacement field. The objective function is constructed by the difference between the experimental displacement field and the finite element simulation displacement field. The objective function is optimized and iterated by the genetic algorithm (GA) and the particle swarm optimization (PSO) algorithm to calculate the elastic modulus and Poisson’s ratio of the experimental specimen. The inversion method for non-uniform distribution of rock materials is applied to the uniaxial compression experiment of sandstone, and the non-uniform distribution of elastic modulus and Poisson’s ratio under different loading states is obtained. The inversion method for non-uniform distribution of rock material parameters proposed in this paper provides a basis for complex experiments or structural system parameter inversion.
The stress–strain curves and mechanical properties of Shuangjiangkou granite were obtained using five groups of conventional triaxial tests under various confining pressures using MTS815 rock test equipment. From the microscale, mesoscale, and macroscale perspectives, four types of mechanisms that contribute to energy dissipation during granite deformation were investigated. Based on the energy dissipation ratio, a new approach for estimating crack closure stress and damage stress is proposed. The energy dissipation ratio was substituted into the Weibull distribution function, and then a new nonlinear statistical damage constitutive model of granite based on the energy dissipation ratio was constructed after Biot’s theory was modified per the Lemaitre strain equivalence principle. By comparing experimental data with theoretical values estimated by the model, the model’s rationality and correctness were confirmed.
