The classical Mohr–Coulomb criterion has an extremely wide range of applications in the field of engineering geology, while it cannot accurately characterize rock failure under high confining stresses. Therefore, a nonlinear modification is implemented based on the Mohr–Coulomb criterion for achieving wider usage in all stress environments. The cohesion and internal friction angle are firstly calculated by regression based on the triaxial experiments of diorite and other typical rocks in different confining stress ranges, and the variation modes of cohesion and internal friction angle are then formalized and integrated into the classical Mohr–Coulomb criterion. Using the experimental results of 435 triaxial compression tests in existing publications, the predictions of the modified criterion are compared with those of the previous nonlinear criteria, which show that the predicted values of the modified criterion are in good agreement with the measured strength. Compared with the previous nonlinear criteria, the modified criterion has a wider application range and always maintains a higher accuracy.

Intermittent joints are widely found in slopes and the rock section (locking section) in intermittent joints is an important structure that prevents joints from interconnecting and maintains slope stability, but the exact shape of the locking section is not yet known. In this paper, based on the finite difference method (FDM), k-means algorithm, and alpha shape algorithm, a method is proposed to calculate the shape of locking sections and to quantitatively analyze the controlling effect of locking sections and non-locking sections areas on the stability of slopes. In addition, for slopes with high accuracy in the shape of the locking section, the original mesh in the FDM is reconstructed and a network of discrete points is arranged at the locking section at customised intervals and the maximum principal stresses at each discrete point are calculated by the inverse transformation method of the isoparametric elements. This method greatly reduces the influence of grid size on the shape of the locking section. Finally, eight working conditions were designed to investigate the effect of the position of the weak interlayer on the shape and area of the locking section. The results show that the shape of the locking section does not change much as the angle of the line connecting the end points of the weak interlayer increases, and the shape basically remains elliptical, while the area of the locking section changes by increasing and then decreasing.

Rock excavation is essentially an unloading behavior, and its mechanical properties are significantly different from those under loading conditions. In response to the current deficiencies in the peak strength prediction of rocks under unloading conditions, this study proposes a hybrid learning model for the intelligent prediction of the unloading strength of rocks using simple parameters in rock unloading tests. The XGBoost technique was used to construct a model, and the PSO-XGBoost hybrid model was developed by employing particle swarm optimization (PSO) to refine the XGBoost parameters for better prediction. In order to verify the validity and accuracy of the proposed hybrid model, 134 rock sample sets containing various common rock types in rock excavation were collected from international and Chinese publications for the purpose of modeling, and the rock unloading strength prediction results were compared with those obtained by the Random Forest (RF) model, the Support Vector Machine (SVM) model, the XGBoost (XGBoost) model, and the Grid Search Method-based XGBoost (GS-XGBoost) model. Meanwhile, five statistical indicators, including the coefficient of determination (R2), mean absolute error (MAE), mean absolute percentage error (MAPE), mean square error (MSE), and root mean square error (RMSE), were calculated to check the acceptability of these models from a quantitative perspective. A review of the comparison results revealed that the proposed PSO-XGBoost hybrid model provides a better performance than the others in predicting rock unloading strength. Finally, the importance of the effect of each input feature on the generalization performance of the hybrid model was assessed. The insights garnered from this research offer a substantial reference for tunnel excavation design and other representative projects.

The shear strength of discontinuities with different joint wall compressive strength (DDJCS) is an important mechanical property. In this paper, the prediction of shear strength of DDJCS is performed using a hybrid machine learning model of artificial neural network (ANN) model with particle swarm optimisation (PSO). To develop the proposed model, a total of 168 cases are collected. Two classical models are introduced, and four performance indexes (i.e. coefficient of determination R2, mean absolute error MAE, root mean square error RMSE, and variance account for VAF) are utilised to evaluate the comprehensive predictive performances of these models. Finally, a graphical user interface (GUI) for predicting the shear strength of DDJCS is developed. The comparison results demonstrate that compared to the remaining models, this hybrid model has a better predictive performance and generalisation capability, with R2, RMSE, VAF, and MAE values of 0.999, 0.02, 99.9%, and 0.01, respectively. GUI signifies that this novel model provides an intuitive, efficient, and visual production experience for researchers. These findings can provide valuable insights for developing accurate predictive models.

Rock bridges are important structures for maintaining rock mass stability, but their shapes are not well known. The researchers propose a method for determining the shape of rock bridges based on experiments, discrete element methods and machine learning, which is applicable to complex joints with arbitrary spatial distribution. Numerical models are constructed using the discrete element method, and parameter matching is performed based on experimental results. The particles were clustered using the k-means algorithm with the maximum principal stress (σ1) as an indicator and the selection of initial values was optimized. The density-based spatial clustering of applications with noise (DBSCAN) algorithm was used to delete the noise from the particles. Finally, the boundary lines of the particles were extracted by self-programming, and the shape of the rock bridges was determined. Twenty-four sets of simulations were used to analyze the effect of rock bridges on the specimens. The results show that the failure mode of the specimen changes from shear to tensile damage as the cohesive force of the rock bridges increases. The peak strength and peak strain of the specimens increased with the increase of cohesion in the rock bridge. Rock bridges are the fastest growing areas of stress in the specimen.

As a composite material, the stability of rock mass is usually controlled by a joint. During the process of excavation, the normal stress of the joint decreases continuously, and then the shear strength of the joint decreases, which may eventually lead to the instability and failure of rock mass. Previous studies have mainly focused on the shear behavior of joints under constant normal stress, but have rarely considered the unloading of normal stress. In this paper, a direct shear test of joints with different roughness was carried out, in which the shear stress remained unchanged while the normal stress decreased. The strength characteristics of joints were explored, and the deformation and acoustic emission-counting characteristics of joints were analyzed by digital image correlation (DIC) techniques and acoustic emission (AE). A new method for predicting the instability of joints under normal unloading was proposed based on the evolution law of normal deformation energy (Un), tangential deformation energy (Us) and total deformation energy (U0). The results show the following: (1) The unloading amount of normal stress was enlarged for greater initial normal stress and roughness, while it decreased with an increase in initial shear stress. (2) AE events reached their maximum when the normal stress was equal to the failure normal stress, and the b-value fluctuated more frequently in stable development periods under normal unloading conditions. (3) U0 would change with the loading and unloading of stress, and this may be used to predict the unloading instability of rock mass using the abrupt change of U0.

The rock or rock mass in engineering often contains joints, fractures, voids, and other defects, which are the root cause of local or overall failure. In response to most of the current constitutive models that fail to simulate the nonlinear fracture compaction deformation in the whole process of rock failure, especially brittle rocks, a piecewise constitutive model was proposed to represent the global constitutive relation of rocks in this study, which was composed of the fracture compaction empirical model and the damage statistical constitutive model. The fracture empirical compaction model was determined by fitting the expressions of fracture closure curves of various rocks, while the rock damage evolution equation was derived underpinned by the fracture growth. According to the effective stress concept and strain equivalence hypothesis, the rock damage constitutive model was deduced. The model parameters of the fracture compaction empirical model and damage statistical constitutive model were all calculated by the geometrical characteristics of the global axial stress–strain curve to guarantee that the models are continuous and smooth at the curve intersection, which is also simple and ready to program. Finally, the uniaxial compression test data and the triaxial compression test data of different rocks in previous studies were employed to validate the models, and the determination coefficient was used to measure the accuracy. The results showed great consistency between the model curves and test data, especially in the pre-peak stage.

Previous studies in the field of slope stability mostly concentrate on the calculation of the safety factor, while critical slip line recognition and extraction are rarely noticed. Since the popular strength reduction method can only provide an approximate slip region, an automatic recognition and rapid extraction method for the slip line of a slope was proposed. Its core lies in the separation of slip mass and stable mass, which was realized by the modified k-medoid clustering algorithm according to the horizontal displacement difference of nodes, and the boundary was regarded as the critical slip line of the slope. In particular, for slopes requiring high slip line accuracy, it is recommended that discrete point networks can be arranged at custom intervals in the slip region, and the horizontal displacement of each point is calculated by the inverse transformation method of isoparametric elements. On this basis, a more accurate slip line is identified and extracted by the modified k-medoid clustering algorithm. This method reduces the influence of grid size and avoids the subjectivity of defining the slip line artificially. Ultimately, based on the published slope cases, the slip lines extracted by the proposed method were compared with those obtained by previous methods, which verifies its validity and reflects the advantages.

The slip surface is an important structure for analyzing the landslide mechanism, and it will be deformed by the traction and shear of the slide mass. For the landslide accident without artificial monitoring, if the slip surface can be restored according to the slope morphology before and after the landslide, information such as the safety factor before the damage to the slope and the volume of the slide mass can be obtained by the position of slip surface, which helps engineers to analyze the cause of the landslide. In this paper, an automatic slide mass identification and landslide inversion analysis method based on discrete element simulation is proposed. The method combines Gaussian Mixture Model (GMM), alpha shape algorithm, discrete element simulation, and the morphology of the slope before and after the landslide to invert the slip surface of the slope. This method is suitable for two and three dimensional slope models. In addition, the effect of the slope angle on the deformation of the slip surface is analyzed.

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.

Retrogressive landslide is caused by the lower rock mass sliding, so that the upper part loses support, is deformed, and starts to slide. In the process of highway construction, the incised slope often leads to retrogressive landslide, and the determination of the damage range of retrogressive landslide is of great significance for the control of the slope. Taking a highway retrogressive landslide in Hunan Province as the research object, the particle flow discrete element is used to numerically simulate the entire failure process of the slope. According to the complex geological conditions of the slope, the rock mass of each part of the slope model is divided, the displacement of key parts of the landslide is monitored, the whole failure process of the retrogressive landslide is simulated, and the lateral length of traction instability is calculated through the stability theory of the sliding pull-crack failure slope. The research shows that the incised slope is the root cause of the retrogressive landslide, and the rainfall is the direct cause. When the retrogressive landslide is treated in engineering practice, the lateral length of traction instability can be obtained according to the stability theory of the sliding pull-crack failure slope, to realize the accurate judgment of the traction failure range of the sliding body.

As the strength parameters of rock mass degrade differently during slope instability, different factors should be considered in the strength reduction method. Previous nonlinear reduction methods were essentially implemented based on the Mohr–Coulomb criterion, which was reported not to reflect the nonlinear performance of rock mass. To address this deficiency, in this study, the Hoek–Brown criterion was combined with a nonlinear reduction technique for slope stability evaluation. Firstly, based on the classical definition of safety factors, the relationships that should be satisfied by each parameter of the critical slope were derived. The critical curve of the slope regarding the Hoek–Brown constant mb and the uniaxial compressive strength of rock mass σcmass was then obtained. On the assumption that the slope parameter deterioration conforms to the shortest path theory, the reduction ratio of σcmass to mb was determined. The more objective k-means algorithm was employed to automatically search the potential sliding surface, on which the slope safety factor was calculated as the ratio of sliding resistance to sliding force. Finally, the slopes in published literature were adopted for verification, and the calculated safety factors were compared with those by other methods, which showed better efficacy.

At present, the treatment of tailings is mostly carried out in the form of stacking in tailings ponds, resulting in a huge waste of mineral resources and a major threat to the environment and ecology. Using tailings instead of a part of the cement to make cementitious materials is an effective way to reduce the accumulation of tailings. In this paper, lead-zinc tailings-based cementitious materials were prepared by using lead-zinc tailings, fly ash, and ordinary Portland cement, and the effects of four factors on the mechanical properties of lead-zinc tailings, as well as fly ash content, cement content, and water-binder ratio were studied by orthogonal experiments. The corresponding relationship between the factors and the properties of cementitious materials was determined, and the optimization and prediction of the raw material ratio of lead-zinc tailings-based cementitious materials were realized. The test showed the ratio of raw materials to be at the lowest price ratio. Synchronously the ratio that meets the minimum strength requirements was predicted. When the proportion of fly ash:lead and zinc tailings:cement = 30:40:30 and the water-binder ratio was 0.4, the predicted compressive strength of the prepared cementitious material achieved 22.281 MPa, which meets the strength requirements, while the total content of lead-zinc tailings and fly ash was the highest at this time.

Rock mass usually contains cracks, joints and other defects with different density and spatial combination characteristics in the diagenetic process. Under the freeze-thaw effect, they continue to expand and connect, which continuously weakens the strength property and poses a serious threat to the stability of rock mass. Previous studies paid more attentions to the strength reduction of rock, failing to directly reflecting the freeze-thaw damage characteristics of rock mass. In this paper, the freeze-thaw failure characteristics and strength loss of non-penetrating fractured rock mass with different fracture densities were studied by means of theoretical derivation and laboratory tests. Firstly, non-penetrating fractured rock mass samples with different fracture conditions were prepared. Then the freeze-thaw samples were subjected to laboratory compression tests and the loss of uniaxial compressive strength was measured. On this basis, the theoretical values of geological strength index GSI was calculated for the samples, and the rough prediction empirical model of GSI for non -penetrating fractured rock mass treated with different freeze-thaw cycles was obtained through data fitting. Finally, by combining the apparent observation method with acoustic emission monitoring technique, the effects of freeze-thaw cycles and fracture density on the failure characteristics of non-penetrating fractured rock mass samples were analyzed comprehensively from both the macro and micro perspectives.

Frozen heaving failure of fractured rock mass is commonly encountered in engineering in cold regions, which is chiefly caused by the frost heaving pressure arising from the water–ice phase change in the crack. To explore the evolution of frost heaving pressure in penetrating elliptical crack considering water content and water migration, a new theoretical model embodying the frost heaving pressure evolutionary character was established by introducing freezing ratio function. The equivalent thermal expansion coefficient was used to analyze the evolution process of frost heaving pressure under the effect of water–ice phase change, which was then verified. It was found that the evolution process of frost heaving pressure can be divided into three stages: free expansion stage of water–ice phase change, rapid growth stage of frost heaving pressure, and stable stage of frost heaving pressure. Subsequently, the influences of rock thermal expansion effect, properties of rock and ice, and water content of crack on the frost heaving pressure were investigated. The results indicate that the impact of rock thermal expansion on frost heaving pressure is extremely slight, which is negligible. Comparing with the properties of rock, the properties of ice show significant effects on the frost heaving pressure, particularly the Poisson ratio of ice. In the case of identical water migration ratio, the peak frost heaving pressure increases linearly with the water content of crack.

Considering that a jointed rock mass in a cold area is often affected by periodic freeze-thaw cycles and shear failure, definitions for the mesoscopic and macroscopic damage to a jointed rock mass under the coupling of freeze-thaw and shear are proposed, and the damage mechanism is verified according to experimental results. The results show that: (1) the jointed rock specimens increase macro-joints and meso-defects, the mechanical properties deteriorate significantly under freeze-thaw cycles, and the damage degree becomes more and more significant with the increases in freeze-thaw cycles and joint persistency. (2) When the number of freeze-thaw cycles is constant, the total damage variable value gradually increases with the increase in joint persistency. The damage variable difference in specimens with different persistency is distinct, which is gradually reduced in the later cycles, indicating a weakening influence of persistency on the total damage variable. (3) The shear resistance of non-persistent jointed rock mass in a cold area is determined by the coupling effect of meso-damage and frost heaving macro-damage. The coupling damage variable can accurately describe the damage variation law of jointed rock mass under freeze-thaw cycles and shear load.

As an advanced spatial technology, topography-sensing technology is comprehensive, macroscopic, and intuitive. It shows unique advantages for rock structure interpretation and has important guiding significance for the research of the shear performances of rock–mortar interface under cyclic load in rock mass engineering. In this paper, cyclic shearing tests combined with the shear surface topography-sensing technology are employed to investigate the evolution characteristics of the interface morphology and the strength deterioration of the rock–mortar interface. Primarily, mortar and three types of rocks are used to prepare different rock–mortar interfaces, which are then applied to cyclic shear loading under two constant normal stresses. Subsequently, the shear strength degradation and dilatancy characteristics of rock–mortar interfaces with varying shear times are discussed. In addition, on the basis of the non-contact three-dimensional topography-sensing technology, the apparent three-dimensional point–cloud coordinate information of rock–mortar interface before and after each shear loading is obtained, and the apparent three-dimensional topography parameters of rock–mortar interface are calculated, according to which the influences of normal stress and lithology on the topography of interface subjected to cyclic shearing loading are analyzed.

The peak dilation angle is an important mechanical feature of rock discontinuities, which is significant in assessing the mechanical behaviour of rock masses. Previous studies have shown that the efficiency and accuracy of traditional experimental methods and analytical models in determining the shear dilation angle are not completely satisfactory. Machine learning methods are popular due to their efficient prediction of outcomes for multiple influencing factors. In this paper, a novel hybrid machine learning model is proposed for predicting the peak dilation angle. The model incorporates support vector regression (SVR) techniques as the primary prediction tools, augmented with the grid search optimization algorithm to enhance prediction performance and optimize hyperparameters. The proposed model was employed on eighty-nine datasets with six input variables encompassing morphology and mechanical property parameters. Comparative analysis is conducted between the proposed model, the original SVR model, and existing analytical models. The results show that the proposed model surpasses both the original SVR model and analytical models, with a coefficient of determination (R2) of 0.917 and a mean absolute percentage error (MAPE) of 4.5%. Additionally, the study also reveals that normal stress is the most influential mechanical property parameter affecting the peak dilation angle. Consequently, the proposed model was shown to be effective in predicting the peak dilation angle of rock discontinuities.

Parallel fractures, a kind of common geological defect in natural rock mass, show a variety of failure mechanism and increases the difficulty in the timely warning of geological disasters such as landslide. Therefore, studying the mechanical properties and failure mechanism of parallel-fractured rock mass occupies a vital position in the stability analysis and warning technology of disaster precursor. In response to this, the laboratorial efforts on micro fracture mode and macro strength prediction of parallel-fractured rock-like samples with different inclinations were made in this paper. Firstly, the parallel-fractured samples were prepared by changing the fracture parameters, and the uniaxial compression test was then carried out. According to the mechanical parameter variations of samples during axial loading, the multiple indexes affecting the uniaxial compressive strength of parallel-fractured samples was clarified, and the specific influence of fracture inclination was quantified by mathematical method. Finally, the progressive failure mechanism of samples was analyzed through strain field evolution in virtue of digital image correlation (DIC) technique, and the main failure modes of parallel-fractured samples were summarized. Meanwhile, the acoustic emission (AE) signals were collected and processed to further reveal the failure characteristics of parallel-fractured samples with different inclinations in a microscopical perspective.

The Hoek-Brown criterion can better depict the nonlinear failure characteristics of rock mass, which has been widely used in the fields of large-scaled slopes, deep-buried tunnels, foundations in complex geological condi-tions, hydropower dams, and energy mining. In view of the previous studies mostly focused on the property reduction of freeze-thaw rock, the deterioration study of Hoek-Brown parameters for freeze-thaw multi -fractured rock mass was investigated in this study. Firstly, Monte-Carlo method was used to generate two-dimensional discrete fracture network, according to which the multi-fractured rock-like samples were pre-pared. Freeze-thaw cycle experiments were subsequently designed and executed to observe the apparent damage of freeze-thaw effect on the samples. Then, laboratory direct shear tests on freeze-thaw samples under multi-stage normal loading were carried out. The shear performances of freeze-thaw rock mass were analyzed based on the shear stress-shear displacement curves of samples with different freeze-thawed cycles. Besides, considering the deficiencies of the existing Hoek-Brown parameter estimation methods such as complicated sample prepa-ration and strong subjectivity, a new estimation method based on shear test was proposed by deducing the shear expression of Hoek-Brown criterion, which was programmed in MATLAB and verified by direct shear test results. On this basis, the values of Hoek-Brown parameter of those samples under different freeze-thaw cycles were determined, and the variation law with freeze-thaw cycles was summarized. It turned out that the values of GSI and mi both decrease with the increase of freeze-thaw cycles, and the decreasing rate is also lowering, according with the negative exponential function model.