Strength criteria are the basis for rock engineering stability assessment and structural optimization design. To predict the triaxial strength of various lithologies, a novel strength criterion is established based on the ultimate strength. A database consisting of over 1642 triaxial tests conducted on rocks is established to calibrate and validate the criterion. According to the measured and predicted results, the fitting accuracy of the criterion is analyzed and compared with several classical criteria, and the sensitivity of the criterion parameters is further discussed. Results indicate that the criterion exhibits high accuracy in fitting and performs better in sandstone but worse in gneiss. In most samples, the criterion underestimates the triaxial strength, which is beneficial for establishing safety redundancy in engineering. Compared to other classical strength criteria, this particular criterion demonstrates superior fitting accuracy and displays lower sensitivity to parameters that lack physical significance. In addition, a simplified criterion is proposed to predict the strength without triaxial test data. Although its fitting accuracy falls slightly below that of the original criterion, its predictive performance is acceptable. Consistent with the original criterion, the simplified criterion performed significantly better in sandstone than in gneiss, and the simplified criterion also underestimated the strength in most lithologies. Finally, the simplified criterion is applied in the Jinping II hydropower station, and the prediction results confirm its applicability of the simplified criterion on the strength prediction of rocks.

Polyurethane grouting is a commonly employed technique for seepage prevention and reinforcement during tunnel construction. Gaining insights into the propagation behavior of polyurethane grout within rock fractures holds importance in guiding grouting operations. To investigate the effects of fracture aperture on the propagation of self-expanding polyurethane grout, experimental studies were first conducted to examine the polyurethane propagation characteristics in homogenous fractures. Subsequently, propagation mechanisms of polyurethane grout and cement grout were compared and analyzed by numerical simulation. Finally, the scanning electron microscope (SEM) tests were performed to analyze the effect of fracture aperture on the microscopic characteristics of filled polyurethane grout. The experimental results demonstrate that, larger fracture apertures result in smaller maximum propagation distances and shorter propagation time. Besides, in fractures with a large aperture, a noticeable pressure drop occurs after grout gelation. The simulation results demonstrate that an increase in the aperture is inversely proportional to the polyurethane filling rate, whereas it is directly proportional to the cement filling rate. This disparity is attributed to different injection modes and driving force sources for these two grouting materials. In addition, the SEM test results show that larger fracture apertures correspond to greater microscopic pore diameters and fewer pore numbers in filled polyurethane grouts, which provides a microscopic explanation for the observed pressure drop during experimentation. The outcomes of this study offer valuable experimental and theoretical foundations for enhancing the understanding of self-expanding polyurethane grouting in rock fractures.

Cement grouting has been widely used in rock tunneling to reduce groundwater inflow by sealing rock fractures. However, the injected cement grout often encounters hydraulic erosion that affects the safety and sustainability of rock tunnels in the long term. Analysis of the long-term hydraulic erosion effect on cement grout in rock fractures is therefore important for the safety and sustainability development of rock tunnel engineering. In this work, a hydraulic erosion model for analyzing cement grout erosion in a homogeneous fracture is established and used to theoretically investigate the transmissivity evolution of the grouted fracture under longterm hydraulic erosion. In the present model, the fracture seepage characteristics, solid erosion theory and mass conversation for water-solid two-phase flow are considered, and the mathematical model as a set of partial differential equations is established. Based on laboratory tests, the key parameters (e.g., erosion coefficient) are calibrated and the erosion model is validated. Numerical simulations are conducted by numerically resolving the mathematical model. The results show that the erosion phenomenon first occurs in the edge areas of the grouted area near the fracture boundary; the erosion area gradually expands toward the center of the grouted area. The porosity and flow velocity significantly increase in the area with relatively strong erosion effects. During the erosion process, the concentration of cement grout gradually increases along the seepage path until a more uniform distribution of cement particle concentration is achieved. Due to the erosion process, the spatial distribution of hydraulic pressure along the fracture direction transforms from a linear distribution to a nonlinear distribution. The effective fracture transmissivity increases nonlinearly along the erosion process. The presented erosion model and analysis results are potentially useful for the safety and durability assessment of rock tunnels.

Co-exploitation of coal and geothermal energy through water-conducting structures is one of the most promising methods for harnessing renewable energy in some coal mines. A rock compression-erosion coupling test system is built to investigate the extraction efficiency of geothermal wells in the co-exploitation scheme. Compression-erosion tests are carried out to analyze the evolution of mechanics and hydraulic characteristics of broken rocks. The testing results show that the hydrothermal flow erodes the fine rock particles, and compressive deformation can be observed during the erosion process. The erosion effect in broken rocks intensifies with the decrease of axial stress and the increase of fractal dimension, water pressure, and inner radius. Meanwhile, the rock sample shows more significant deformation. Two permeability forecasting models are adopted to forecast permeability evolution during geothermal extraction. The forecasting results indicate that the Brinkman model is better than the Hazen model, and the accuracy of the Brinkman model is lower for the samples with stronger compression-erosion effects. In addition, strategies to improve the extraction efficiency are proposed, i.e., reinforcing the broken rocks above the geothermal well, locating geothermal wells in rocks with higher fragmentation, increasing pumping pressure, and expanding the geothermal well size.

Pre-existing fractures in rock engineering significantly affect the entire structural stability. To deepen the understanding of the fracture mechanism of fractured rocks under shear loading, a numerical study based on the distinct element method was conducted to investigate the shear behaviors of rock fractures. A discrete element model with fractures of Barton's ten standard profiles was established, and shear simulations under different normal stresses and joint roughness coefficient (JRC) were carried out. The simulation results show that the shear stress–displacement curve can be divided into three stages: elastic loading stage, inelastic stage and stress drop stage. The shear strength, internal friction angle and cohesion increase with the increase of normal stress and JRC. These macroscopic mechanical characteristics are consistent with the results of previous experimental studies. Most of the microcracks generated during the shearing process are tensile microcracks, which are first formed at the steep position of the fracture profile line, and the proportion of shear microcracks is less than 10%. In addition, the contact force between particles is mainly compressive stress, which is greater in magnitude and density than tensile stress. As the shear proceeds, the displacement of the particles gradually changes from non-uniform distribution to uniform distribution.

Hydraulic erosion may pose a threat to the safety and sustainability of geo-related infrastructure, yet quantifying the intricate process of hydraulic erosion still poses a significant scientific and technical challenge. One important step in meeting this challenge is the formulation of a hydraulic erosion model with the erosion coefficient as a central controlling parameter. Calibration of the erosion coefficient (or rate) remains one of the main obstacles to improving predictive modelling, particularly in scenarios lacking long-term laboratory test data. In this study, sensitivity analysis of the key erosion indicators on the parameters controlling hydraulic erosion is conducted. A novel calibration method for the erosion coefficient is presented based on sensitivity analysis. After validating against simulation results and laboratory test findings, the proposed calibration method is applied to a hypothetical long-term hydraulic erosion case. The results show that the maximum hydraulic erosion time is sensitive to all considered parameters (erosion coefficient, initial fraction of fluidized solid particle, initial porosity and maximum porosity), while the erosion curve shape is only sensitive to the initial porosity and the maximum porosity. The validation by existing simulation results shows that the proposed calibration method is robust and internally consistent. The validation by experimental results indicates that the proposed calibration method also has high external validity. Finally, the proposed calibration method is applied to hypothetical long-term erosion in a grouted area. The results show that the hydraulic erosion effect in the grouted area becomes increasingly severe over time. This study contributes toward a more efficient calibration of the erosion coefficient, especially for scenarios in the absence of testing porosity evolution data. The research outcome provides a theoretical foundation for the safety assessment and sustainability analysis of geotechnical structures that are subject to hydraulic erosion.

Research on the plastic shear deformation of rock discontinuities is essential to the structural design of rock engineering, and the yield point is an important indicator for plastic shear deformation. In this paper, a con-ceptual model based on renormalization group theory is proposed to qualitatively explain the evolution mode of shear deformation. Then, considering the stress transfer mechanism, the mathematical description of the critical failure point is derived. Subsequently, the criterion for yield shear displacement is obtained by combining the renormalization group model with the shear constitutive model. Finally, experimental results based on the ratio of yield stress to shear strength for different rock types are provided to verify the proposed criterion. The theoretical and mathematical analysis indicates that the yield point is the phase transition point during the shear deformation of rock discontinuities, which is equivalent to the critical failure point in the renormalization group theory. The relationship between the failure probability of n-order blocks and the basic failure probability can be obtained according to the stress transfer mechanism and the conditional probability, so that a mathematical description of the critical failure point can be established. The verification by both laboratory and in-situ tests shows that the results of the proposed criterion are consistent with those of classical methods. In addition, the determination of the parameters has little influence on the criterion's performance, which means the proposed criterion could eliminate the subjectiveness in determining the yield shear displacement.

In order to investigate the temporal-spatial evolution properties of the water inrush disaster process of weakly cemented fault rock mass, a creep-erosion coupling water inrush model of weakly cemented fault rock mass is established. This model expands the equivalent continuum seepage theory, and a creep submodel and an erosion submodel are established respectively. The proposed creep submodel fully considers the mass conversion among materials, stress-strain and strain-porosity relationships. The proposed erosion submodel fully considers the mass conservation, particle migration and non-Darcy flow laws. According to the superposition principle of the mass conservation equations and three influence relationships (i.e., porosity-effective stress, porosity-creep material coefficient and creep strain-porosity-permeability relationships), the coupling between the submodels is realized, and the governing equations of the one-dimensional radial seepage direction coupling model are given. The solution conditions of the water inrush model are set, and the numerical computation method of the model in the temporal-spatial domain is established based on the COMSOL Multiphysics. By comparing the laboratory experimental results and the model calculation results of porosity evolution, the validity of the creep-erosion coupling model of weakly cemented surrounding rock is verified. On this basis, the temporal-spatial evolution law of the creep-erosion characteristics of weakly cemented surrounding rocks of the roadway is solved and analyzed. The calculated results show that in terms of the creep characteristics evolution, the effective stress decreases and the creep strain increases with time, and the samples exhibit the accelerated creep characteristics. The inhomogeneity of the spatial distribution of effective stress and creep strain increases with the creep-erosion coupling process. As for the evolution of the erosion characteristics, in the initial stage of the creep-erosion coupling process, the fine rock particles migrate out continuously under the effect of water flow, the volume fraction of fluidized particles, the permeability and flow velocity continuously increase, and new water-conducting channels are constantly formed in the weakly cemented rock mass. Subsequently, the erosion effect is weakened and finally stagnates due to the increasing creep effect. The closer to the inner wall of the roadway, the stronger the erosion effect. The spatial distribution of porosity and permeability after the stagnation of erosion shows obvious inhomogeneous characteristics, and the spatial distribution of water pressure presents a nonlinear-linear-nonlinear trend in the creep-erosion coupling process.

The shear constitutive model is important for the analysis of the interface shear deformation mechanism. In this study, five statistical distributions, including four that have never been applied in interface shear deformation, are introduced to describe the damage evolution of the interface. The corresponding statistical damage constitutive models are developed, and they have been validated using a series of experimental data (both laboratory and in-situ tests) at the rock-concrete interface. The comparison results with laboratory data show that the Mitscherlich model has the lowest prediction accuracy. By comparing with in-situ data, the Weibull model shows the best-predicted performance. Based on the Akaike information criterion metric, the Morgan-Mercer-Flodin (MMF) model performs much better than the other models in the laboratory tests, which indicates the MMF model can be introduced for a comprehensive analysis of interface shear deformation. In addition, the similarities between the MMF model and the Weibull model are found through the canonical transformation of the MMF model. And the analysis of the two unknown parameters of the MMF model shows that they are related to the yield characteristics and strength characteristics of the interface, respectively. Based on the damage variable evolution, the shear deformation of the interface can be divided into three phases, i.e., damage initiation phase, damage acceleration phase and damage slowing phase. And the parameters of the MMF model have an important influence on the damage variable curves.

The shear strength of rock fractures serves as a crucial control on the strength and deformation behavior of engineering rock masses. To reduce the uncertainties in the shear strength evaluation, a hybrid machine learning model (GS-SVR model) of the support vector regression (SVR) underpinned by the grid search optimization algorithm (GS) was proposed. It achieves the prediction of shear strength by generalization and deduction of a large amount of data on rock fracture parameters, which avoids the complex derivation of theoretical equations. For practical application, a dataset comprising more than 134 shear tests on various rocks was compiled to collect the relevant three-dimensional morphological and mechanical parameters for training and prediction. Three classical shear strength models and the original SVR model were introduced for further comparison. Finally, sensitivity analysis was carried out to explore the relative importance of input variables to the shear strength. The results showed that the GS-SVR model (correlation coefficient R2 = 0.984, root mean squared error RMSE=0.383) outperformed the original SVR model (R2 = 0.936, RMSE=0.568). Moreover, compared with three classical shear strength models, the prediction results of the GS-SVR model were also most consistent with the experimental results (with the lowest RMSE and the highest R2). This machine learning model enhanced by GS can be used as a reliable and accurate shear strength prediction tool to partially replace laboratory tests to save costs.