Hoek-Brown Failure Criterion Research Articles

Numerical Study of Surrounding Rock Damage in Deep-Buried Tunnels for Building-Integrated Underground Structures

When deep-buried tunnels are excavated using the drill-and-blast method, the surrounding rock is subjected to combined cyclic blasting loads and excavation-induced stress unloading. Understanding the distribution characteristics of rock damage zones under these conditions is crucial for the design and safety of building-integrated underground structures. This study investigates the relationship between surrounding rock damage and in situ stress conditions through numerical simulation methods. A constitutive model suitable for simulating rock mass damage was developed and implemented in the LS-DYNA (version R12) code via a user-defined material model, with parameters determined using the Hoek–Brown failure criterion. A finite element model was established to analyze surrounding rock damage under cyclic blasting loads, and the model was validated using field data. Simulations were then carried out to explore the evolution of the damage zone under various stress conditions. The results show that with increasing hydrostatic pressure, the extent of the damage zone first decreases and then increases, with blasting-induced damage dominating under lower pressure and unloading-induced shear failure prevailing at higher pressure. When the hydrostatic pressure is less than 20 MPa, the surrounding rock stabilizes at a distance greater than 12.6 m from the tunnel face, whereas at hydrostatic pressures of 30 MPa and 40 MPa, this distance increases to 29.4 m. When the lateral pressure coefficient is low, tensile failure occurs mainly at the vault and floor, while shear failure dominates at the arch waist. As the lateral pressure coefficient increases, the failure mode at the vault shifts from tensile to shear. Additionally, when the horizontal stress perpendicular to the tunnel axis (σH) is less than the vertical stress (σv), variations in the axial horizontal stress (σh) have a significant effect on shear failure. Conversely, when σH exceeds σv, changes in σh have little impact on the extent of rock damage.

Probabilistic modelling of Copenhagen limestone mechanical behaviour with the Hoek–Brown failure criterion

Probabilistic modelling of Copenhagen limestone mechanical behaviour with the Hoek–Brown failure criterion

STRUCTURAL CHALLENGES IN ADVANCED ANALYTICAL TECHNIQUES FOR CHARACTERISING MODERN BUILT HERITAGE IN EGYPT

This paper presents a comprehensive structural evaluation of Sakakini Palace in Cairo. The investigation covers the physical properties and origins of the building materials, the geological context, damage assessment, petrographic analysis and the physical and mechanical characterisation of the stones and structural mortar. Advanced laboratory and in situ testing techniques, including three dimensional laser scanning microscopy, non-destructive X-ray fluorescence and porous media characterisation using a surface area analyser (which employs liquid nitrogen to measure surface area, micro-porosity, total pore volume and Brunauer-Emmett-Teller surface area) are utilised. Mechanical testing of the building materials is performed using uniaxial and triaxial compression tests (in combination with RocLab software to determine the strength parameters of the stones) based on the latest generalised Hoek-Brown failure criterion. The results are presented, discussed and analysed concerning potential risks to built heritage.

Tunnel stability modeling using finite element method: A case study of the inlet of diversion tunnel, Budong-Budong Dam, West Sulawesi, Indonesia

Abstract This article presents the results of the tunnel stability from the empirical design at the diversion tunnel of Budong-Budong Dam, West Sulawesi, Indonesia. The purpose of this study is to assess the effectiveness of the suggested support system using a numerical approach, taking into account the uncertainties in the design process and the use of face mapping during excavation. The tunnel support design is simulated using a two-dimensional finite element method and exposed to a seismic load derived from probabilistic seismic hazard analysis. Additionally, a numerical analysis is conducted with and without seismic load to serve as a comparison. Tunnel stability is analyzed using Phase-2 software. The input parameters used in the numerical analysis come from field investigations, which include surface engineering geological mapping, tunnel face mapping, core drilling evaluation, and laboratory tests. According to geological face mapping and drilling core data up to 25 meters deep, the diversion tunnel area consists of pyroclastic-epiclastic rocks. The Generalized Hoek-Brown Failure Criterion is selected to model rock strength. The horizontal seismic coefficient calculated for the pseudo-static tunnel stability analysis is 0.235. The recommended support designs include systematic rock bolts, steel ribs with wired mesh, and shotcrete installed at specific locations. Numerical modeling determines that implementing the suggested tunnel support system, as advised by empirical methods, results in a strength factor greater than 1.5 under static load and 1.1 under seismic load. The results confirm that the support system proposed by the empirical design methods provides a safe tunnel design under both static and seismic loads.

The effect of the intermediate principal stress on pillar strength

Room and pillar mining is an underground mining method that utilizes natural pillar support to control rock mass behavior, ensuring mine stability and a safe mine environment. This study specifically documents the influence of the intermediate principal stress component on the pillar behavior. So far only classical failure criteria ignoring the influence of the intermediate principal stress component were used for underground pillar design. By using an extended Hoek–Brown failure criterion in comparison with the classical Hoek–Brown failure criterion, the influence of the intermediate principal stress component is documented by indicating those areas where the failure criterion is violated. This study demonstrates, that depending on the rock type, the intermediate principal stress component can have a significant effect. Ignoring this influence can lead to uneconomic pillar design and incorrect determination of the factor of safety.

Numerical Analysis of Tunnel Displacement Profiles with Pipe Umbrella Support: Parametric Study of Selected Umbrella Parameters

Ensuring the stability of tunnels excavated in weak rock masses poses significant engineering challenges, particularly in controlling deformations of the excavated rock-mass. This research represents a conceptual analysis aimed at exploring the effectiveness of pipe umbrella support systems across various configurations, without being tied to a specific tunnel project. The study also investigates the possibility of using simplified Finite Element Method (FEM) modelling for such purpose. Specifically, analysis focuses on findin the correlation between selected design parameters and support system performance. A numerical model incorporating the Hoek-Brown failure criterion, was employed to simulate the interaction between the pipe umbrella and surrounding rock mass. Key parameters analyzed include the length of the pipe umbrella segments, overlap between segments, and the stiffness of the pipe umbrella material. The results demonstrate the potential in reducing both radial and axial displacements as the segment length of the pipe umbrella and overlap increase, with diminishing returns observed for higher umbrella’s stiffness values. This study despite being based on theoretical case scenario also highlights the practical advantages of a simplified axisymmetric FEM model for conducting parametric analyses, significantly reducing computational complexity while maintaining sufficient accuracy.

Impact of Rock Mass Strength Anisotropy with Depth on Slope Stability Under Excavation Disturbance

In open-pit excavations, overburden rock mass is disturbed by processes like blasting and mechanical excavation, leading to a reduction in mechanical properties. Accounting for this disturbance is essential for ensuring slope stability, optimizing costs, and maintaining feasibility. The Hoek–Brown failure criterion, a widely used empirical method in rock mechanics, incorporates the disturbance factor to reflect the reduction in rock mass strength after disturbance. This study reviews five approaches from the literature regarding the role of disturbance in rock mechanics, focusing on its impact on the factor of safety and the volume of rock mass above the potential failure surface. Additionally, an “S” shaped decay formulation was proposed as an alternative to existing equations. A key consideration is the transitional disturbance effect, which reflects the gradual change from a fully disturbed rock mass near the excavation surface to an undisturbed rock mass with increasing depth. Among the examined approaches, the “S” shaped decay equation, informed by insights from previous studies, appears to be the most realistic. One approach assumes the disturbance factor is highest at the surface due to the removal of blasted rock, leading to a fully disturbed rock mass in front of the excavation face. The disturbance then decreases with depth, transitioning to an undisturbed condition depending on the excavation method. Even when the rock mass is homogeneous and isotropic in joint properties, excavation induces anisotropy in mass strength, causing overall strength to increase with depth. This study also investigates the effect of anisotropic strength behavior resulting from the disturbance factor. For incorporating transitional disturbance in the design stage, both circular and combined failure mechanisms should be considered for a comprehensive understanding of slope stability.

Stability analysis of open stope #20 in sill pillar #2840 based on mining frame 134 using numerical, empirical, and analytical approaches at the Big Gossan Mine

Abstract Sill pillar #2840 has been identified as an economical reserve and is therefore planned to be mined. Stope #20 is one of 69 stopes in the sill pillar that will be mined. The stope is about 540m from surface. Mining activities that are far from the surface will cause stress redistribution. A geotechnical analysis was required to observe the stability condition of the open stope. The stability can be calculated by considering the induced stress around the open stope. The calculation of the Factor of Safety (FS) will be carried out using a numerical approach with Rocscience’s RS2 software using the Generalized Hoek-Brown failure criterion for hard rock and the Mohr-Coulomb failure criterion for paste fill, an empirical approach using a Modified Stability Number (N’) (Potvin, 1988) to calculate the stability of hard rock around the open stope, and an analytical approach using the Limit Equilibrium Equation (Mitchell, 1991) to calculate the stability of the paste fill around the open stope. The results of the approaches will be verified by the Sakurai chart. Based on the approaches, stope #20 in sill pillar #2840 is in stable condition to be mined.

Pseudo-dynamic stability analysis of 3D rock slopes considering tensile strength-modified Hoek–Brown failure criterion: Seismic UBLA implementations

Pseudo-dynamic stability analysis of 3D rock slopes considering tensile strength-modified Hoek–Brown failure criterion: Seismic UBLA implementations

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.

The Meaning of Average Compressive and Tensile Strength for Hoek-Brown mi Constant Determination

One of the most widely used failure criteria for rocks in the world is the Hoek-Brown failure criterion. For its use, the mi empirical parameter for a specific rock type is needed. The triaxial compression test is recommended for its determination; however, the full stress path for every rock comprises confined tension as well. This affects the course of the Hoek-Brown envelope, which is non-linear and starts at uniaxial tension. Fifty-one series of tests were carried out for three rock types: sandstone, claystone and limestone, to show the difference between the results of the mi determination, using two different approaches – so-called linear and non-linear. Moreover, the consistency between the developed simplified methods of constant determination and mi were checked. These comprised the UCS-based method, R-index method, TS-based method and advanced regression functions of compressive and tensile strength. The relationship between mi constant and the internal friction angle was checked as well. The analysis of the results showed that the consistency with the regression models developed by researchers depends on the chosen estimator. If it is derived from the triaxial test only, the results are closer to a linear determination of mi constant and have a good correlation with internal friction angle. If both tensile and compressive strength are used for its determination, the non-linear value correlates better with the advanced regression functions, but quite poor with the average compressive strength (R-index method) and tensile strength (TS-based method). Taking into account that every rock retained next to the geotechnical or mining object is not only compressed but also tensed, the non-linear mi interpretation seems to be more correct. The interlayers and discontinuities inside sedimentary rocks increase the scatter of lab results and reduce the accuracy of mi determination.

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

The study aims to utilize the convergence–confinement method (CCM) by considering non-hydrostatic stress assumptions in the analysis of the surrounding rock in a circular tunnel. The rock mass properties should adhere to the criteria of the non-linear Hoek–Brown failure criterion. Through a thorough theoretical analysis approach, an analytical solution was derived to determine the stress and displacement induced by tunnel excavation, particularly in the elastic and plastic zones. This solution, applicable under anisotropic stress conditions, involves accounting for confinement loss incrementally for computational feasibility. The implementation of this analytical solution, facilitated by a straightforward spreadsheet, was validated against existing data to evaluate the impact of non-linear failure criteria on ground reaction behavior. The study scrutinizes the mechanical response at the tunnel’s inner curve and assesses stress–displacement distribution across the tunnel cross-section. A comparison between the proposed solution and published results demonstrates a consistent and promising correlation.

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

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

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

Abstract The 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

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