Hoek-Brown Failure Criterion Research Articles

Deformation behaviour of strain-softening rock mass in tunnels considering deterioration model of elastic modulus

By analyzing the composite effects of the plastic shear strain and confining stress according to the laboratory test results, a model adopting a deteriorating elastic modulus for the intact rock is proposed. Soft rock such as coal and the strong rock such as granite with different quality are investigated. Geological Strength Index (GSI) is adopted to represent the integrity of rock, to be specific, from intact rock to the rock mass. Specifically, for the strain-softening rock mass, the elastic modulus is gained by introducing GSI into the deterioration model. The strength parameters are obtained by fitting GSI into Hoek-Brown failure criterion. Then, the elastic modulus and strength parameters of the rock mass are employed in the numerical procedure for solving out the rock deformation, the radii of the plastic softening and residual zones of the tunnels. The rationality of the numerical procedure is verified with the existing semi-analytical and analytical procedures. In the discussion, the influences of the critical plastic parameters and GSI, on the elastic modulus, rock deformation, radii of the plastic softening and residual zones are investigated. Five models for the variation of the modulus including the proposed deterioration model are defined. The rock mass deformation behaviours of the five models are compared. The results indicate that, in the plastic softening zone that is far away from the tunnel periphery, the elastic modulus is more sensitive to the plastic shear strain, whereas near the tunnel periphery, the elastic modulus is primarily affected by the confining stress. Regarding a linear decrease of the elastic modulus versus the plastic shear strain overestimates the elastic modulus to some extent, especially for the soft rock mass.

Modeling Brittle-to-Ductile Transitions in Rock Masses: Integrating the Geological Strength Index with the Hoek–Brown Criterion

Many studies focus on brittle–ductile transition stress in intact rocks; however, in real life, we deal with rock mass which contains many discontinuities. To fill this gap, this research focuses on the brittle–ductile transition stress of rock mass by considering the influence of different Geological Strength Index (GSI) values on the brittle–ductile transition stress of rock mass. In other words, the Hoek–Brown failure criteria for rock mass were reformulated mathematically including the ductility parameter (d), which is defined as the ratio of differential stress to minor stress. Then, the results were analyzed and plotted between σ3*σc and GSI, considering different (d) and Hoek–Brown material constant (mi) values. The brittle–ductile transition stress, σ3*, was determined by intersecting the Hoek–Brown failure envelope with Mogi’s line, with ductility parameters d ranging from 3.4 (silicate rocks) to 5.0 (carbonate rocks). Numerical solutions were derived for σ3*σc as a function of GSI using Matlab, and the results were fitted with an exponential model. The analysis revealed an exponential relationship between σ3*σc and GSI for values above 32, with accuracy better than 3%. Increased ductility reduces rock mass strength, with higher d values leading to lower σ3*σc. The diminishing returns in confinement strength at higher GSI values suggest that rock masses with higher GSI can sustain more confinement but with reduced effectiveness as GSI increases. These findings provide a framework for predicting brittle–ductile transitions in rock engineering.

Explicit Analysis for the Ground Reaction of a Circular Tunnel Excavated in Anisotropic Stress Fields Based on Hoek–Brown Failure Criterion

Explicit Analysis for the Ground Reaction of a Circular Tunnel Excavated in Anisotropic Stress Fields Based on Hoek–Brown Failure Criterion

Analysis and Experimental Study on the Stability of Large-Span Caverns’ Surrounding Rock Based on the Progressive Collapse Mechanism

The collapse failure of rock surrounding caverns involves a progressive collapse process. Based on the nonlinear Hoek–Brown failure criterion and the upper limit theorem, the whole process curve of the progressive collapse of the surrounding rock of a large-span cavern is outlined in this paper. The progressive collapse process of the surrounding rock of the large-span cavern is experimentally studied using an independently developed visualized large-span-cavern geomechanical model test device with variable angles. The results show that, through theoretical calculation and model tests, the surrounding rock at the top of the large-span cavern undergoes three collapses. Under the condition of rock mass and the shape of the cavern, the larger the span of the cavern, the more times the surrounding rock collapses; with the increase in surrounding rock pressure, the first collapse occurs in the middle part of the arch roof. When the overlying load reaches a certain level, the arch foot becomes the weakest part, and the rock undergoes shear failure along the arch foot, gradually extending upwards, accompanied by multiple collapses, forming a progressive collapse process. The theoretical calculation results of this paper are basically consistent with the scope of the model test, and the research results can provide a basis for the construction and support design of the large-span cavern.

Pseudo-dynamic viscoelastic stability analysis of anti-dip bedding rock slopes

Earthquakes contribute to the failure of anti-dip bedding rock slopes (ABRSs) in seismically active regions. The pseudo-static method is commonly employed to assess the ABRSs stability. However, simplifying seismic effects as static loads often underestimates rock slope stability. The development of a practical stability analysis approach for ABRSs, particularly in slope engineering design, is imperative. This study proposes a stability evaluation model for ABRSs, incorporating the viscoelastic properties of rock, to quantitatively assess the safety factor and failure surface under seismic conditions. The mathematical description of the pseudo-dynamic method, derived in this study, accounts for the viscoelastic properties of ABRSs and integrates the Hoek–Brown failure criterion with the Kelvin-Voigt stress-strain relationship of rocks. Furthermore, to address concurrent translation-rotation failure in ABRSs, upper bound limit analysis is utilized to quantify the safety factor. Through a comparison with existing literature, the proposed method considers the effect of harmonic vibration on the stability of ABRSs. The obtained safety factor is lower than that of the quasi-static method, with the resulting percentage change exceeding 5%. The critical failure surface demonstrates superior positional accuracy compared to the Aydan and Adhikary basal planes, with minimal error observed between the physical model test and the numerical simulation test. The parameter sensitivity analysis reveals that the inclination of ABRSs exhibits the highest sensitivity (Sk) value across the three levels of horizontal seismic coefficient (kh). The study aims to devise an expeditious calculation approach for assessing the stability of ABRSs during seismic events, intending to offer theoretical guidance for their stability analysis.

Influences of bedding angle and soaking time on the mechanical behaviour of silty mudstone: laboratory testing and theoretical modelling

Silty mudstone is highly susceptible to the influence of hot and humid environments, leading to the deterioration of its mechanical properties presenting a geohazard and even resulting in geological disasters. Accurately characterizing the effects of bedding and water–rock interaction on the mechanical behaviour of silty mudstone is a crucial prerequisite for the protection and reinforcement of silty mudstone slopes. To this end, uniaxial compression tests and Brazilian splitting tests were conducted to examine the mechanical properties of bedded silty mudstone. Based on the test results, the effects of bedding angle and soaking time on mechanical properties such as tensile strength, uniaxial compressive strength and elastic modulus of bedded silty mudstone were revealed. The test results showed that the tensile strength increased exponentially with increasing bedding angle. The observed split failure patterns of bedded silty mudstone encompassed splitting–pulling damage, shear damage and splitting damage. The uniaxial compressive strength of silty mudstone exhibited a U-shaped variation with an increase in bedding angle. The specimen with a bedding angle of 45° had the lowest uniaxial compressive strength at 7.64 MPa. Furthermore, the elastic modulus of silty mudstone was positively correlated with the bedding angle. The failure patterns of bedded silty mudstone under uniaxial compression included splitting-tension damage, shear-slip damage and splitting-shear damage. The saturated tensile strength, uniaxial compressive strength and elastic modulus of bedded silty mudstone exhibited an exponential decrease with increasing soaking time. The test data confirmed the applicability of the Jaeger equation to the uniaxial compressive strength of bedded silty mudstone. Subsequently, a modified Hoek–Brown failure criterion was derived by combining fracture mechanics theory and test results and introducing a softening factor. The parameters A , D and m in the above failure criterion decreased exponentially with increasing soaking time and an empirical Hoek–Brown failure criterion considering the soaking time was established. Compared with previous theoretical models, this model is more adaptable to the actual engineering situation, which results in more accurate calculations.

A comparative slope stability analyses of heavily jointed open-pit slopes using 3D limit equilibrium and finite element methods: a case study from Bingöl, Türkiye

ABSTRACT This study investigates the slope stability of Bingöl open-pit iron mine slopes using 3D limit equilibrium and finite element methods. The pit benches are 3 m wide and 6 m high, with an overall slope angle of 38°. The geological composition comprises slightly to moderately weathered and heavily jointed phyllite, micaschist, and gneiss. Shear strength parameters were determined through back analyses of already failed sections using the Hoek-Brown failure criterion and Geological Strength Index (GSI). Factor of safety values for static and dynamic conditions were calculated using 3D limit equilibrium and 2D finite element analyses. Results show good agreement between the two methods, with benches in the northern section exhibiting a significant decrease in safety factor under dynamic conditions, indicating near-limit equilibrium slopes.

An enhanced micromechanical rock–pile interface model with application to rock‐socketed pile modeling

AbstractThe increasing use of rock‐socketed piles highlights the importance of developing a suitable design method for their bearing capacity. This study quantifies the shear behavior of the rock–pile interface, which generally dominates the bearing capacity of rock‐socketed piles under service load. A micromechanics‐based rock–pile interface model with idealized nonuniform profile is proposed with two enhancements: (1) the slip line method together with nonlinear Hoek–Brown failure criteria is integrated to identify the critical shear displacement of rock asperity; and (2) the residual stage of shear behavior is properly considered with the rounding progress of sheared rubbles. The enhanced interface model is first validated by the direct shear test results under constant normal stiffness. Then, the interface model is implemented via user‐defined FRIC into the finite element code ABAQUS without the need of explicitly building the rock–pile interface profile. Accordingly, the model is applied to simulate and analyze two field cases involving rock‐socketed piles. Comparison between the predictions and field observed results shows this method can well capture the axial load transfer behavior of pile socket into weak rock.

Experimental study on the punching failure model of soft red rock subgrade by BPT-BVM methods and it’s assessment of the load bearing capacity

The recommended bearing capacity of medium weathering mudstone foundation is less than the capacity of the rock structure to withstand loads in Southwest China. A comprehensive failure characterization of medium weathering mudstone in Chengdu has been performed including bearing plate test (BPT), binocular vision measurement (BVM) test, uniaxial compressive strength test, trial trench test of shallow rock surface and 3D imaging in this paper. Failure behavior of rock has been modeled with 3D imaging algorithm that utilizes Zhang’s calibration method in BVM system combination with trial trench test of shallow rock surface. The bearing capacity of medium weathering mudstone foundation were extracted from uniaxial experiments and BPT-BVM test by fitting relevant material properties to the data. The results revealed that: Bearing capacity of medium weathering mudstone of layered isotropic in Chengdu is undervalued. Specifically, the characteristic load carrying value is in the range 1500–2500 kP, that is 50% higher than in the local standard system. Failure process is different from Hoek–Brown Failure Criterion, presenting a wave peak transfer phenomenon of the increment displacement into the distance. Thus, it can be reduced to that of punching failures for thin bedded structures of Moudstone foundations. Compressive strength of soft rock proves to be main factor limiting the bearing capacity, a clear correlation between the uniaxial compressive strength reduction coefficient and the bearing capacity has been used to establish, leading to the proposal of a load bearing capacity prediction model.

Study of geomechanical properties of the Pimienta formation with undrained multi-stage triaxial tests, Central-Western Tampico Misantla Basin, Mexico

The Pimienta Formation (J-Pi) of the Tampico Misantla Basin (TMB) in Mexico is known for its potential as unconventional onshore hydrocarbon reserves. The area of interest in this study is located in the western-central part of the TMB, where no significant production has been established from unconventional resources. Given the low permeability and low porosity characteristics of the carbonaceous mudstone in the Pimienta formation, it is necessary to implement techniques to increase the area of flow from the reservoir to the borehole, achieving profitable oil and gas extraction.The geomechanical properties of rock strata are essential inputs for the design and implementation of shale oil and gas production engineering, such as horizontal drilling and hydraulic fracturing. Understanding the capabilities of the rock to yield and contain hydraulic fractures is essential to designing safe and efficient well stimulations. Likewise, the wellbore stability is of critical importance to the successful development of secondary and tertiary recovery systems.In this study, core samples from the Pimienta Formation in the TMB are analyzed through undrained multi-stage triaxial tests, emphasizing the estimated in-situ geo stresses and the effect of the mineral composition of the rock. The geomechanical parameters of compressional strength, Poisson ratio (PR), and Young's modulus of the Pimienta formation are obtained from the analysis of the experimental data and finding correlations to the mineral composition of the samples. A detailed characterization is completed under the conventional rock mechanics methodologies of Mohr-Coulomb and Hoek-Brown failure criterion, as well as Brittleness Index (BI).

Study on the Damage Evolution of Weathered Granite under Different Confining Pressure Based on Hoek-Brown Failure Criterion and Acoustic Emission Parameters

Abstract The stability of the mine construction is significantly impacted by weathered granite (WG), which presents a significant risk to the security of workers and equipment. In order to investigate the strength characteristics of WG under different confining pressures, acoustic emission (AE) and scanning electron microscopy (SEM) tests were performed on WG under triaxial compression. The relationship between strength evolution and different confining pressures of WG is studied. Under various confining pressures, the variation regularity of the AE parameters of rock samples was examined. Additionally, the microscopic morphology of rock samples is investigated using SEM. The results show that increased confining pressure suppresses WG damage development before the stress peak and switches to promoting damage development following the stress peak. The axial strength is quantitatively analyzed before the WG stress peak using the Hoek-Brown failure criterion, and the axial damage threshold stress under different confining pressures is obtained. Furthermore, the axial damage threshold stress point is clearly increased in the AE ring count rate and energy rate curves of WG at various confining pressures. The last effect of water on WG is microstructural weakening, which manifests itself in the swelling and erosion of the structure by water.

Rock slope stability analysis under Hoek–Brown failure criterion with different flow rules

The stability analysis of homogeneous rock slope following the Hoek–Brown failure criterion under the hypothesis of different flow rules is performed based on limit equilibrium and finite element methods. The applied failure criterion is the generalized Hoek–Brown that can be introduced as a shear/normal function in analysis applying different flow rules. The results are compared with those obtained by the application of equivalent shear strength parameters of the Mohr–Coulomb criterion, considering that this is still the most widely used criterion in rock slope stability analysis and is still the base for the shear strength reduction method applied in finite element modelling. Different proposals for estimating the equivalent strength parameters based on confining stress level are evaluated. The limitation of stress-dependent linear Mohr–Coulomb parameters is emphasized by analysing the vertical cut problem, for which, depending on the chosen stress level, different critical heights are obtained for the same material. Sensitivity analysis of geotechnical parameters used as input for failure criterion is performed to determine their influence on slope stability. Probabilistic analysis is conducted to determine the probability of failure when different flow rules are applied. If slope stability analysis is performed with an assumption of associative flow rule, the probability of failure is within the acceptable limits for the considered case study, while employing non-associative flow rule, the probability of failure is rather high. The chart is presented that could be readily used to estimate the combination of σci, GSI, and mi values that produce failure for the analysed case study.

Practical Methodology for Evaluating Mining Front Stability Based on the Diametrical Core Deformation Technique

The state of stress in a mining front constantly changes with mining activities. In a recent study, the authors developed and verified with laboratory measurements an analytical model for the calculation of mining-induced stresses based on measuring the deformations of a diamond drill rock core extracted perpendicular to the mining front or face. The method is called diametrical core deformation technique (DCDT). In this study, the DCDT is used in combination with 3D numerical modelling to develop a practical methodology for the assessment of mining face stability. To demonstrate the methodology, a diamond drill rock core was retrieved from an access drift face 530 m below the surface of an underground mine in northern Quebec. The state of stress in the mining front is estimated from the DCDT and used to adjust the orientation and principal stress magnitudes in the local area around the access drift in a 3D linear-elastic numerical model using an iterative approach. As the rock core is partially fractured due to previous face advance blasting, the numerical model is further adjusted to model the observed damage zone. The 3D model after adjustments is used to examine the mining front stability with the Hoek–Brown failure criterion. It is postulated that the proposed methodology is suitable for the stability assessment of any mining front with or without an observed damage zone.

Assessing stability of mine workings driven in stratified rock mass

Purpose.The research purpose is to assess the stability of mine workings driven in a stratified rock mass by studying the influence of the stratified rock bedding angle on the rock mass stress-strain state (SSS). Methods. The research uses both experimental and numerical methods. Experimental studies are carried out using rock samples with different angles of rock layer occurrence, while numerical modeling is performed using the RS2 (Geotechnical Finite Element Analysis) software based on the generalized Hoek-Brown failure criterion. The studies are carried out on models covering the border area of the mine workings driven in the mass with the angles of rock occurrence from 0 to 75°. Findings. Experimental and numerical studies have shown that when the rock layer inclination angle changes, significant changes occur in the stress concentration zones around the mine workings. An increased rock layer inclination angle is accompanied by a change in stress distribution, which is important for assessing the stability of mine workings. A particularly strong influence is observed at the angles of rock occurrence 30° and above. Originality. The research novelty is in revealing the patterns in the stress distribution in the stratified rock masses depen-ding on the rock layer inclination angle. Research results provide new data on the rock interaction mechanisms in difficult geological conditions. Practical implications. The results obtained can be used in the planning and operation of mine workings in difficult geological conditions. By taking into account the changes in stress zones caused by the rock layer inclination angle, it is possible to improve the safety and efficiency of mining operations.

A generalized nonlinear three-dimensional Hoek‒Brown failure criterion

To understand the strengths of rocks under complex stress states, a generalized nonlinear three-dimensional (3D) Hoek‒Brown failure (NGHB) criterion was proposed in this study. This criterion shares the same parameters with the generalized HB (GHB) criterion and inherits the parameter advantages of GHB. Two new parameters, β, and n, were introduced into the NGHB criterion that primarily controls the deviatoric plane shape of the NGHB criterion under triaxial tension and compression, respectively. The NGHB criterion can consider the influence of intermediate principal stress (IPS), where the deviatoric plane shape satisfies the smoothness requirements, while the HB criterion not. This criterion can degenerate into the two modified 3D HB criteria, the Priest criterion under triaxial compression condition and the HB criterion under triaxial compression and tension condition. This criterion was verified using true triaxial test data for different parameters, six types of rocks, and two kinds of in situ rock masses. For comparison, three existing 3D HB criteria were selected for performance comparison research. The result showed that the NGHB criterion gave better prediction performance than other criteria. The prediction errors of the strength of six types of rocks and two kinds of in situ rock masses were in the range of 2.0724%–3.5091% and 1.0144%–3.2321%, respectively. The proposed criterion lays a preliminary theoretical foundation for prediction of engineering rock mass strength under complex in situ stress conditions.

Three-dimensional limit variation analysis on the ultimate pullout capacity of the anchor cables based on the Hoek-Brown failure criterion

Three-dimensional limit variation analysis on the ultimate pullout capacity of the anchor cables based on the Hoek-Brown failure criterion

Study on potential collapse of deep-buried tunnel induced by local overbreak obeying Hoek-Brown failure criterion

Overbreak is an important cause of tunnel collapse. In order to study the influence of local overbreak on potential collapse of deep-buried tunnels, the upper bound method of limit analysis and functional theory are used to establish a tunnel collapse failure model with overbreak in the crown and surrounding rock conforming to Hoek-Brown criterion. The failure shape, collapse area and backfill area of tunnel collapse under overbreak are deduced based on the established model. The correctness of the method in the present study are verified by comparing with literature report. Finally, parameters from three aspects, namely, local overbreak geometry, surrounding rock properties and tunnel dimension, are investigated for its influence on collapse shape and area under local overbreak. The method raised in the present study provides a theoretical reference for evaluation and treatment of tunnel collapse caused by local overbreak in the crown.

Ultimate bearing capacity of strip footings on Hoek-Brown rock slopes – A stress characteristics solution

The present study addresses the ultimate bearing capacity of strip footings on rock slopes under seismic conditions. The stress characteristics method (SCM) is combined with the modified pseudo-dynamic (MPD) approach for the intended purpose. Unlike the solutions available in the literature, the generation of the stress characteristics network within the framework of the SCM automates the potential failure mechanism of the slope medium at the limiting state of collapse. The MPD approach enables the analysis to capture realistic earthquake inertia forces induced in the slope, considering the material damping properties of the slope. The non-linear nature of the rock mass strength is captured using the generalized Hoek-Brown failure criterion. The seismic ultimate bearing capacity of strip footings is reported as non-dimensional charts. Additionally, the impact of relevant dynamic characteristics of seismic waves and rock mass properties is thoroughly assessed by conducting a detailed parametric investigation. The results reveal a substantial reduction in the ultimate bearing capacity of footings resting on rock slopes under earthquake conditions. The efficacy of the proposed methodology is validated with the existing solutions reported by various researchers.

A conceptual three-dimensional frictional model to predict the effect of the intermediate principal stress based on the Mohr-Coulomb and Hoek-Brown failure criteria

The intermediate effective principal stress has a considerable influence on rock strength as shown by true-triaxial data on intact rock. Therefore, a failure criterion that incorporates all three principal stresses may provide an improved prediction of failure than one that considers only the major and minor effective principal stresses. This study introduces a generalisation method, which converts two-dimensional failure criteria (i.e., Mohr-Coulomb and Hoek-Brown failure criteria) to three-dimensional failure criteria, for the prediction of this true-triaxial data. This method is based on a physical mechanism, and it assumes that the potential failure surface of a material has roughness, which provides additional frictional resistance when the intermediate effective principal stress is greater than the minor effective principal stress. This roughness is introduced theoretically by assuming a repeating diamond-shaped element over the failure surface. These roughness elements have the same dip as predicted by the Mohr-Coulomb and Hoek-Brown failure criteria but are offset by the dip direction angle which is assumed similar to that calculated traditionally from the major effective principal stress direction to the failure surface. With this roughness, it is shown that the major effective principal stress at failure can be predicted using an explicit solution that uses the intermediate and minor effective principal stresses and the Mohr-Coulomb or Hoek-Brown parameters as inputs. This generalisation predicts the same strength as the Mohr-Coulomb or Hoek-Brown failure criteria under conventional triaxial loading conditions, when the intermediate and minor effective principal stresses are equal. Under general stress conditions, this generalisation produces results that are aligned closely with the true-triaxial data as well as other previous theoretical predictions. This method importantly gives a possible physical mechanism for the strengthening influence of the intermediate effective principal stress. This may lead to a more accurate prediction of the rock strength under general stress conditions.

Upper Bound Analysis of Ultimate Pullout Capacity for a Single Pile Using Hoek–Brown Failure Criterion

As a typical pullout foundation, the uplift pile has been widely used in ocean projects or geotechnical engineering, but the accurate prediction of its ultimate pullout capacity has always been a difficulty in engineering design. This study focused on a single pile in rock formation, and constructed a curved uplift failure mechanism in the case that the whole rock mass around the pile was damaged. In this mechanism, the rock mass failure was assumed to comply with the Hoek–Brown failure criterion. Then, the theoretical prediction formulas for the rock failure surface and the ultimate pullout capacity of the pile were derived by using the upper bound theorem. The influence laws of factors such as different rock mass parameters, pile parameters and additional surface load on the pile capacity and failure range were analyzed. Further, the proposed method was validated by comparing with the numerical simulation results. The results show that the ultimate pullout capacity of the pile increases with the increase in the length/diameter ratio, rock empirical parameter A, tensile strength, compressive strength, unit weight and additional surface load, but decreases with the increase in rock empirical parameter B. Empirical parameters A and B are key factors affecting the pile capacity and rock failure range, and should be attached importance to in engineering design. The research work in this study can provide some theoretical reference for the design of the uplift pile in rock formation.