Mechanical Behavior Of Rock Mass Research Articles

Evaluating the Accuracy of Bonded Block Models for Prediction of Rockmass Analog Mechanical Behavior.

Large-scale rock formations, referred to as "rockmasses", consist of intact rock separated by pre-existing discontinuities (i.e., joints). The mechanical behavior of rockmasses is difficult to directly test in the laboratory due to the required specimen scale. Instead, Synthetic Rockmass Modeling (SRM) is often used to simulate field-scale rockmass behavior. SRM requires a calibrated discrete element model (DEM) of intact rock combined with a Discrete Fracture Network (DFN). While the SRM concept has been informally determined to provide reasonable results based on practitioner experience, detailed and peer-reviewed validation is lacking. The goal of this study was to evaluate the predictive capabilities of the SRM method. Previously available data on intact and rockmass analog laboratory specimens of Blanco Mera granite containing DFNs with two joint sets were used as a basis for the SRM created in this study. Specifically, the intact DEM was a Bonded Block Model (BBM), generated to match the grain structure and composition of Blanco Mera granite and the model's input parameters were calibrated so that the behavior of the BBM matched that of the intact laboratory specimens. The predictive capabilities of the model were evaluated by recreating the DFN from the jointed laboratory specimens within the intact BBM and comparing the behavior of the jointed models back to the jointed laboratory specimens, which has not been previously studied in the literature. The BBM was found capable of approximately predicting the behavior of rockmass analog specimens containing a pre-existing DFN without further calibration, which shows potential for the use of SRM in both industry and academia. Specifically, the BBM predicted the strength, dilatancy, and microfracturing behavior of the jointed laboratory specimens.

Numerical analysis of the influence of dissolution pore structure on mechanical behavior of rock mass

Numerical analysis of the influence of dissolution pore structure on mechanical behavior of rock mass

The effect of joint inclination angle on mechanical properties of rock mass studied by model test and DEM simulation

The joint inclination angle is a crucial factor influencing the mechanical behavior of rock masses and greatly affects the stability of rock mass engineering. The article utilizes cement mortar to fabricate jointed rock models with mechanical properties that closely resemble those of real rock formations. The compressive plate speed of the loading test machine is 0.005 mm/s, and the axial static loading rate ranges from 0.5 to 1.0 MPa/s. To investigate the influence of joint inclination angles on the macroscopic mechanical properties of the rock, the study initially employs indoor full-field observation and the non-contact technology known as Digital Image Correlation (DIC). Experiments are conducted on rock specimens with varying joint inclination angles of 30°, 45°, 60°and 90°. Following this, numerical simulations employing the Discrete Element Method (DEM) are conducted to analyze the microfracture process. The model test and numerical simulation results demonstrate good agreement, particularly regarding the failure modes. It is found that the most common failure mode for jointed rock is a composite form of shear and tension. As the joint inclination angle increases, tensile failure becomes more prominent. The Young’s modulus EJR/ER and peak strength σJR/σR ratios between jointed and jointless rock vary with the joint inclination angle, exhibiting a "V" shaped curve. A joint inclination angle of 45° results in minimum strength and modulus in the macro mechanical properties. The joint inclination angle has a negligible effect on the rock mass’s residual strength, maintaining an approximately constant ratio of 0.14 between residual and peak strength σr/σp .

Accurate prediction of indicators for engineering failures in complex mining environments

Due to seismic load, complex geological and geo-mechanical conditions of rock mass in Steeply Inclined and Extremely Thick Coal Seam (SIETCS) mines, the prediction and prevention of dynamic disasters remain quite challenging. Traditionally, physical models and numerical simulations are widely practiced for disaster prediction at shallow depths which becomes difficult in SIETCS mines. The drilling tests and above models are generally time-consuming and uneconomic providing miniature coverage. Whilst, rockburst driven disasters require detailed regional geological understanding and mechanical behavior of rock mass. For this purpose, a non-invasive and cost-effective geophysical workflow covering regional-scale geology is introduced for accurate identification and prediction of rockburst in a SIETCS mine of northwestern China. Passive seismological in-situ observations were made for a period of twenty-four months to compute the seismic source parameters, map fracturing process, identify regional lineaments and calculate important rockburst prediction indicators. The spatiotemporal distribution of induced-microseismicity, three-states stress theory, and mapped fractures helped in the identification of three rockbursts, several high-energy tremors, and the prediction of two new rockburst-prone regions. The mapped fractures through the novel ‘Seismo-Frac model’ showed that for the simultaneous excavation in B3 + 6 and B2 + 1 coal seams subjected to repetitive episodes of seismic deformation, the shear-displacement accumulation, prying effects of rock pillar and roof coupled with dynamic stress are the primary mode of deformation. The mapped fractures and lineaments are unevenly distributed in the minefield with a maximum density of the fractures concentrated in the B3 + 6 coal seam and rock pillar. Furthermore, through conditional probability analysis, the prediction efficiency of source parameter averages (E and N), seismological parameters (b-value and Δb), and maximum potential magnitude (Mm) was compared. A sharp-increase in source parameter averages while a sharp-decrease in the seismological parameters proved to be effective rockburst prediction indicators. This study also introduces decreasing occurrence frequency of fractures and lineaments as the new prediction indicators. This method, while a panacea for imaging the entire fracturing phenomenon, provides insights with widespread implications for academic researchers and industry practitioners to mitigate dynamic disasters in global underground engineering excavation.

Drone Photogrammetry for Accurate and Efficient Rock Joint Roughness Assessment on Steep and Inaccessible Slopes

The roughness of rock joints exerts a substantial influence on the mechanical behavior of rock masses. In order to identify potential failure mechanisms and to design effective protection measures, the accurate measurement of joint roughness is essential. Traditional methods, such as contact profilometry, laser scanning, and close-range photogrammetry, encounter difficulties when assessing steep and inaccessible slopes, thus hindering the safety and precision of data collection. This study aims to assess the feasibility of utilizing drone photogrammetry to quantify the roughness of rock joints on steep and inaccessible slopes. Field experiments were conducted, and the results were compared to those of 3D laser scanning in order to validate the approach’s procedural details, applicability, and measurement accuracy. Under a 3 m image capture distance using drone photogrammetry, the root mean square error of the multiscale model-to-model cloud comparison (M3C2) distance and the average roughness measurement error were less than 0.5 mm and 10%, respectively. The results demonstrate the feasibility and potential of drone photogrammetry for joint roughness measurement challenges, providing a useful tool for practitioners and researchers pursuing innovative solutions for assessing rock joint roughness on precipitous and hazardous slopes.

Hybrid Machine-Learning-Based Prediction Model for the Peak Dilation Angle of Rock Discontinuities.

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.

A general equivalent continuum model and elastic wave velocity analysis of jointed rock masses

The presence of joints dramatically affects the mechanical behavior of rock mass. For highly fractured jointed rock mass, it is more convenient to treat the jointed rock mass as equivalent continuum material. Consequently, several researchers have proposed continuum models to describe the mechanical behavior of jointed rock mass. These models are reviewed and their limitations are discussed. From the perspective of energy conservation, a general continuum model for jointed rock mass is proposed in this study, which incorporates a fourth-rank compliance tensor for joints. The stiffness, areas and orientations of joints are included in the compliance tensor. The proposed compliance tensor is in a general form, which is applicable for joints of arbitrary shape, such as penny-shaped joints and multi-sets of persistent/non-persistent joints etc. The directional modulus and Poisson's ratio of jointed rock mass are deduced from the proposed model. Besides, the elastic wave velocities of jointed rock mass are analyzed from the proposed model according to Christoffel equation. It is found that the square of longitudinal wave velocity is approximately proportional to directional modulus of jointed rock mass. Effectiveness of the proposed model is verified by comparisons with both in situ tests and numerical simulations.

A Damage Constitutive Model for a Jointed Rock Mass under Triaxial Compression

Due to the different structural characteristics and in situ environment, jointed rock masses encounter different failure mechanisms. Because of the joints, jointed rock masses show peculiar characteristics such as anisotropy and weakening. To describe the deformation and failure mechanism in jointed rock masses, a novel damage constitutive model of rock mass is proposed here considering the geometric parameters and mechanical properties of joints. A total damage variable is derived on the basis of the strain equivalence hypothesis, which combines the Weibull statistical damage theory for the strength of the rock elements and the fracture mechanics model for joints. This new damage variable reflects the coupled damage inflicted by two damage states, one is initial damage induced by prefabricated joints and the other is joint damage and rock mesoscopic damage under loading. The damage evolution path revealed by the new damage variable corresponds to the evolution of mechanical properties and behaviors induced by changes in the rock mass structure. Afterward, the computational formulation scheme for the model parameters is deduced using the extremum method. The model parameters, m and F0, have a clear physical meaning. The parameter m describes the ductility–brittleness characteristics of jointed rock masses, and F0 reflects the level of strength. This model describes the effect of joints and strain on the evolution of rock mass damage, model parameters, deformation, and failure characteristics. The mechanical behavior of rock mass described by the damage model and the change law of model parameters are consistent with the published experimental results.

Investigating the Influence of Joint Angles on Rock Mechanical Behavior of Rock Mass Using Two-Dimensional and Three-Dimensional Numerical Models

Numerical testing is an ideal testing method in the research on the mechanical behaviors of jointed rock. However, there are few systematic studies focused on the comparison between the two-dimensional (2D) and the three-dimensional (3D) simulation effects on rock mechanical behaviors, particularly those of jointed rock. In this paper, a particle flow model was established by utilizing PFC2D and PFC3D to represent the rock materials, and the rock (especially jointed rock) mechanical behaviors (uniaxial compressive strength UCS, tensile strength TS, crack initiation stress level Kσ, and the pattern of crack initiation) between 2D and 3D models were compared and analyzed. As expected, the result shows that the UCS and TS showed an increasing tendency with the increase in the joint angle (β) for both the 2D and the 3D models, and the strength of the 3D model was less than that of the 2D model under uniaxial compression but was greater than that of the 2D model under uniaxial tension. The crack initiation and Kσ of the specimens were essentially the same for the 2D and 3D models, and the tensile stresses are more concentrated than the compressive stresses before the failure of the specimen; the uniaxial tensile failure more closely approached abrupt failure than the uniaxial compression failure. The tensile cracks were often initiated at the tips of the joints for both the 2D and 3D models, but they were initiated in the middle of the joints when β was low (β = 0° and β = 15° in both the 2D and 3D models) under uniaxial compression and when β reached 90° under uniaxial tensile. The test results were validated and further analyzed with mathematical analysis. This study has relative referential value to experiments on jointed rock and to analysis of the instability fractures of engineering rock mass.

Analysis of Thermally Induced Strain Effects on a Jointed Rock Mass through Microseismic Monitoring at the Acuto Field Laboratory (Italy)

The study of the deformation of rock masses in response to near-surface thermal stresses is nowadays considered crucial in the field of geological risk mitigation. The superposition of heating and cooling cycles can influence the mechanical behavior of rock masses by inducing inelastic deformations that can trigger shallow slope instabilities, such as rockfalls and rock topples. This study reports the main outcomes obtained from the analysis of 20 month long microseismic monitoring at the Acuto field laboratory (Central Italy), where an integrated geotechnical and geophysical monitoring system has been operating since 2015. A preliminary event classification was performed through the analysis of time- and frequency-domain characteristic features of the extracted waveforms. Furthermore, the evolution of the local microseismicity was explored as a function of environmental factors (i.e., rock and air temperature, thermal gradients and ranges, and rainfalls) to highlight potential correlations. The here presented results highlight nontrivial insights into the role played by continuous near-surface temperature fluctuations and extreme thermal transients in influencing the stability of rock masses. In particular, the comparison of monitoring periods characterized by the most intense microseismic activity highlights a peculiar distribution of microseismicity during the heating and cooling phases of the rock mass in relation to different environmental conditions. These behaviors can be interpreted as the consequence of different driving mechanisms at the base of local failures.

Laboratory-Scale Investigation on Shear Behavior of Non-Persistent Joints and Joint Infill Using Lattice-Spring-Based Synthetic Rock Mass Model

Discontinuities mainly control the mechanical behavior of rock mass and cause a significant reduction in the rock mass strength. Joint persistency and joint infill conditions are considered the most significant joint parameters that control the mechanical response of rock mass. In this study, numerical and statistical analyses were performed on pre-cracked specimens with two flaws to investigate the effect of joint persistence parameters on shear strength. In addition, an extensive study was conducted to explore the effect of infilled mineral strength, infill thickness, and infill wall roughness on shear strength. The Lattice-Spring-Based Synthetic Rock Mass (LS-SRM) approach was utilized to perform the numerical models. The results showed that the tensile crack propagation is limited at higher normal stresses as tensile damage is largely suppressed. The increases in rock bridge angle slightly increased the shear strength and caused a change in the failure mechanisms of the rock bridge from tensile to shearing. The results of the models with infilled minerals revealed that infilled minerals mainly controlled the shear strength of specimens when the infill thickness was 4.0 mm or greater. The infill wall roughness had no apparent effect on the shear strength. In contrast, it governed the failure mechanisms; cracks initiated at the asperity of the rough filling wall and propagated through the hosted rock mass.

Dynamic responses and failure behavior of jointed rock masses considering pre-existing joints using a hybrid BPM-DFN approach

Numerous joints are often randomly distributed in strata, which can affect the mechanical behaviour of rock mass. The jointed rock mass at a large scale is modeled by the combined technology of the bonded particle model (BPM) and discrete fracture network (DFN). Then, the SHPB system is mimicked through the BPM to provide the dynamic disturbance. The effect of joint geometric parameters on the dynamic responses and failure behaviors of the jointed rock mass were symmetrically investigated. The numerical results exhibit that the dynamic strength decreases with the increase of joint intensity or joint length, however, with different functional relationships. Furthermore, when the average angle of the joints is an independent variable, the average angle will significantly affect the dynamic strength except for the case of deviation angle φ = 90°. When the deviation angle is an independent variable, the dynamic strength is also significantly affected except for the case of average angle θ = 45°. The failure modes are also closely related to the joint intensity, joint length and joint orientation, which are dominated by the X-shaped failure mode. A dynamic strength model is proposed based on the classical Hoek-Brown failure criterion, which is verified by the numerical results with different joint intensities.

Numerical simulating of pre-grouting in multi-jointed rock mass in deep coalmine roadway excavated via TBM

Tunnel Boring Machines (TBMs) have been used in many underground coal mines in China in recent years, most of which are open-type. The open-type TBM is unfavorable to advance in complex geological conditions, especially in heavily jointed rock mass. When the TBM advance in multi-jointed soft rock mass, the surrounding rock frequently damages and deforms around the tunneling face uncontrollably, which brings risk for the workers and reduces the advance rate. Pre-grouting the rock mass ahead before excavating is a common measure used to handle the above-mentioned condition. However, it is difficult to evaluate how the slurry diffuses and how it enhances the rock mass. Therefore, it is short of guidance to determine the parameters of the pre-grouting. In the present research, a 3D Ubiquitous-Multiple-Joint (UMJ) model was first proposed to simulate the mechanical behavior of rock mass affected by multiple sets of joints around the excavating face of TBM. Then, a seepage model with an equivalent anisotropic permeability tensor was proposed to simulate the diffusion of slurry in the jointed rock mass for pre-grouting. Following the in-situ action, the numerical model was first excavated using the UMJ model and then grouted according to the equivalent permeability tensor. After that, the grouted rock mass was enhanced by improving the mechanical parameters of joints. The effect of pre-grouting reinforcement could thus be simulated. Using the method, this paper studied the effect of grouting parameters and proposed some suggestions for TBM tunneling in multi-jointed rock mass.

Effect of reflected stress wave on dynamic crack propagation and arrest behavior of sandstone specimens under impact loading

The interaction of stress waves generated by blasting or excavation disturbance with cracks or joints significantly affects the mechanical behavior of rock masses with some pre-existing cracks. To better understand the dynamic damage evolution mechanism of fractured rock mass, the influence of stress waves on cracks in rock mass must be investigated. Thus, to study the effect of reflected stress wave on dynamic fracture behavior of fissured rock mass, a large-size arc-shape boundary single cleavage triangle (ABSCT) configuration sandstone specimen was proposed in the present study. A series of impact tests were performed on the specimen with 0°, 65°, 95°, and 125° ABSCT using the drop plate impact testing system to determine dynamic fracture properties. The test was numerically simulated using the modified finite difference software and the traditional finite element software. The effect of the reflected stress wave caused by the arc-shape boundary of the ABSCT specimen on the crack propagating speed, crack fracture toughness, and compressive stress along the crack trajectory under dynamic loads was analyzed and discussed. The results show that the ABSCT specimen has a crack arresting effect on a propagating crack. The average crack propagation speed of three specimens with arc-shape boundaries is almost 0.63 times that of the flat-bottom specimen, indicating that the arc boundary has an obvious effect on the crack propagating velocity. The average crack propagating speed decreases with the increase in arc boundary radian. The compressive stress on the crack path of three arc boundary specimens is found to be greater than that of the flat-bottom specimen. Furthermore, the crack arrest toughness is greater than the average crack propagating toughness at the arc-shape boundary specimen.

Application of Six Metaheuristic Optimization Algorithms and Random Forest in the uniaxial compressive strength of rock prediction

The uniaxial compressive strength (UCS) is one of the most important parameters for judging the mechanical behaviour of rock mass in rock engineering design and excavation such as tunnels, subways, drilling, slopes and mines stability. However, an obvious deficiency of traditional experimental operations to obtain UCS is that it suffers from a lack of efficiency and accuracy. Therefore, the prediction of the UCS of rock is of high practical significance in reducing evaluation time and improving the precision of results. At the same time, breaking the universality problem of traditional empirical models and improving the accuracy of artificial intelligence models need to absorb and accommodate more rock samples. Hence, a total of 226 rock samples with five properties were carried out from four published studies and selected to generate a dataset in this investigation, i.e., Granitic, Caliche, Schist, Sandstone and Grade III granitic. Five individual parameters of rock samples consisting of Schmidt hardness rebound number (SHR), P-wave velocity (Vp), point load strength (Is(50)), porosity (Pn), and density (D) were used to predict UCS. In this paper, six metaheuristic optimization algorithms were utilized to improve the performance of the Random Forest (RF) model, i.e., slime mould algorithm (SMA), chameleon swarm algorithm (CSA), transient search optimization (TSO), equilibrium optimizer (EO), social network search (SNS) and student psychology based optimization algorithm (SPBO). Four performance indices , the root mean square error (RMSE), the determination coefficient (R2), Willmott’s index (WI) and the variance accounted for (VAF) were utilized to evaluate the performance of all models in forecasting the UCS of rock. The results of the performance comparison demonstrated that the TSO-RF model has the highest values of R2 (train: 0.9923 and test: 0.9753), WI (train: 0.9980 and test: 0.9937), and VAF (train: 99.2272% and test: 97.6852%), the lowest values of RMSE (train: 3.8313 and test: 6.5968) compared to the other models. The research in this study provided an effective attempt to further improve the accuracy of UCS prediction.

Sensitivity Analysis of Fracture Geometry Parameters on the Mechanical Behavior of Rock Mass with an Embedded Three-Dimensional Fracture Network

The existence of fractures has a significant influence on the mechanical properties of a rock mass. The sensitivity of the rock mass’s mechanical properties to the fracture’s geometric parameters is conducive to improving the measurement accuracy of fractured rock mass engineering. Firstly, the fracture geometric parameters in the dam site area of Lianghekou Hydropower Station were counted using the ShapeMetriX3D system. Then, the effect of the fracture’s geometric parameters on the deformation characteristics, failure mode, and mechanical parameters of the rock mass were investigated based on the RFPA3D under the uniaxial compression test. The results showed that the stress–strain curves of the fractured rock mass mainly exhibited elastic-brittle characteristics. The failure pattern of the fractured rock mass was mainly defined by a compressive-shear composite. Additionally, the influence of the fracture’s geometric parameters on the uniaxial compressive strength (UCS) was greater than that of elastic modulus. The sensitivity of the UCS to fracture trace length was more significant.

Data-Driven Rock Strength Parameter Identification Using Artificial Bee Colony Algorithm

Rock strength parameters are essential to understanding the rock failure mechanism and safely constructing rock excavation. It is a challenging problem for determining the rock failure criterion and its parameters due to the complexity of rock media. This study adopts an artificial bee colony (ABC) algorithm to determine the Hoek-Brown failure criterion, widely used in rock engineering practice, based on experimental data. The ABC-based approach is presented in detail and applied to a collection of experimental data collected from the literature. The ABC-based approach successfully determines the Hoek-Brown failure criterion, and the determined failure envelope is in excellent agreement with the measured curve. The maximum relative error obtained by ABC is only 2.15% and is far less than the 12.24% obtained by the traditional method. Then, the developed approach is applied to the Goupitan Hydropower Station, China, and determines the rheological parameters of soft rock based on the Burgers model. The deformation of an experiment located in the Goupitan Hydropower Station is evaluated based on obtained parameters by the developed approach. The predicted deformation matches the monitored displacement in the field. The obtained parameters of the failure criterion characterize the mechanical behavior of rock mass well. Thus, the method used provides a reliable and robust approach to determining the mechanical parameters of the failure criterion.

Hydrothermally induced edifice destabilisation: The mechanical behaviour of rock mass surrounding a shallow intrusion in andesitic lavas, Pinnacle Ridge, Ruapehu, New Zealand

Volcanic edifices are composed of an assortment of materials with varying mechanical behaviours. The range in mechanical behaviours of these rock materials presents a critical unknown element to volcanic stability assessments. In this study, we explore the deformation behaviour (e.g. uniaxial, triaxial, and tensile deformation behaviour) of volcanic materials from seven geotechnical units associated with a small, shallow intrusion at Pinnacle Ridge, Ruapehu, New Zealand. First, we provide a complete characterisation of the rock masses using field (e.g. rock mass characterisation) and lab (compressive and tensile strength analyses) data for each geotechnical unit. The new data show a range of tensile and triaxial compressive strengths dependent largely on porosity, which is further modified by hydrothermal alteration. More altered rocks are generally weaker (with the exception of the brecciated lava margins) under triaxial conditions. Altered rocks generally transition from brittle to ductile behaviour at lower confining pressure, although this depends on the porosity.Using the stratigraphy and geomorphology of Pinnacle Ridge in conjunction with the rock property data we collect, we then use finite element modelling to depict the deformation behaviour of these units under different pore pressure and seismic conditions. The modelling shows that a relatively minor increase in pore pressure (e.g. < 3 MPa above hydrostatic conditions) is sufficient to change the slope failure type from deep-seated rotational sliding to extensional rupture. The presence of a low-permeability, low-rock mass strength material, even if very localised like a hydrothermal vein, can reduce slope stability by locally increasing pore pressure and providing a weakness plane that facilitates failure. The modelling also shows that a relatively minor increase in pore pressure (e.g. < 6 MPa above hydrostatic conditions) in a shallow hydrothermal system is sufficient to cause localised failure in the material, especially in the hydrothermal vein material. Additionally, the low-permeability hydrothermal vein material can cause pore pressure compartmentalisation, decreasing the strength factor in all materials in the compartment. While Pinnacle Ridge and its associated hydrothermal veins are >1 km from the currently active hydrothermal system, similar veins may be present near active parts of the hydrothermal system at Ruapehu and are an important consideration for future stability models at Ruapehu and other volcanoes.

Hydraulic Fracturing Mechanism of Rock Mass under Stress-Damage-Seepage Coupling Effect

According to the damage evolution model of rock mass under stress-seepage coupling effect, the representative element theory is employed to describe the change law of rock mesostructure. Based on the theory of elasticity and Weibull distribution, the statistical damage constitutive model of rock mass and the finite element numerical algorithm are established, by adopting the COMSOL Multiphysics numerical software and MATLAB program. Besides, the validity of the statistical damage constitutive model of rock mass is verified by the triaxial compression test. Besides, the hydraulic fracturing processes of rock mass under equal and unequal in situ stresses are numerically simulated, and the mechanical behavior of rock mass during hydraulic fracturing in complex underground environment is also studied. Under the condition of equal in situ stress, the stress distribution of surrounding rock of circular hole is annular, which is similar to the elastic stress distribution of surrounding rock. Under the condition of unequal in situ stress, the stress distribution tends to be circular with the increase of lateral pressure coefficient, and the stress distribution along the diagonal decreases. The simulation results are in good agreement with the theoretical results, which indicates that the damage mechanical model and the numerical model have correlation and certain accuracy. By analyzing the size and direction of horizontal in situ stress, the shape and extension direction of cracks are judged, which provides an important theoretical basis for water inrush prediction and engineering protection.

A theoretical method of mechanical analysis for a circular tunnel reinforced by fully grouted rock bolts

Analysis of the mechanical behavior of rock mass reinforced by fully grouted rock bolts is introduced based on the interaction between the rock mass and the bolts. The model is based on the following premises: (1) the elastic behavior of the rock mass and rock bolts; (2) the plane strain condition; (3) a deeply buried circular tunnel; (4) complete contact between the bolts and the surrounding rock, that is, they are bonded together; (5) the loads on the surrounding rock from the fully grouted rock bolts are replaced by innumerable concentrated forces along the longitudinal direction of the bolts. For this, the analytical radial displacement solution for a deeply buried circular tunnel subjected to concentrated forces at arbitrary points in surrounding rock is derived. As long as this displacement solution is integrated along the length direction of the bolt, the effect of the bolt on the surrounding rock can be obtained. According to the complete contact condition at the anchoring interface and the force balance condition of the bolts, under the action of the in situ stress, linear equations made up of shear stresses on the bolts are established, from which the distribution of shear stresses and axial forces along the bolts can be solved. Model simulations confirm the previous findings that each installed bolt has a pick-up length, an anchor length and a neutral point. Besides, the influence of the parameters of the rock bolts and the surrounding rock are discussed. The conclusion is consistent with the results of a practical project without adopting any empirical equations. The results of this method can provide a theoretical basis for the design and layout of rock bolts in underground caverns.