Generalized Hoek Brown Failure Criterion Research Articles

Analyzing Support Stability of Deep Shaft Based on Plastic Softening and Dilatancy of Hard Rock Mass

To explore the stability analyses and control methods for surrounding rocks in deep hard rock shafts, this paper is based on field engineering geological surveys and laboratory rock mechanics tests and relies on the main shaft being constructed in the Shaling Gold Mine of China as the engineering background. The quality of the rock mass is evaluated by the Q system, rock mass rating (RMR) and geological strength index (GSI). The mechanical parameters of the surrounding rock mass of the shaft are calculated by using the generalized Hoek–Brown failure criterion, and the main support system is determined based on the rock mass classification system. Based on the finite element method, a two-dimensional plane strain model is constructed to analyze and evaluate the deformation and plastic region range of surrounding rocks for different support systems. On this basis, considering the dilatancy and plastic softening characteristics of hard rock masses, an analytical solution of the stress, strain and plastic region radius of hard rock around shafts in homogeneous media is proposed. Finally, the plastic region of the surrounding rock is measured by the P-wave velocity test method. The results show that after considering the dilatancy and plastic softening characteristics of the rock mass, the numerical simulation, theoretical analytical solution and measured results are basically consistent, and the proposed support system can effectively ensure the stability of the shaft.

Sandstone Slope Stability Analysis Under Wetting-Drying Cycles Based on Generalized Hoek-Brown Failure Criterion

The deterioration of rock strength due to cyclic fluctuations in the groundwater level in drawdown regions influences bank slope stability. Based on wetting–drying cycling and uniaxial compression tests of sandstone specimens, the intact rock strength deterioration characteristics were analyzed. Considering different types of rock mass discontinuities, the rock mass strength deterioration features were shown. The results of rock mass strength deterioration characteristics were then applied in sandstone slope stability analysis. Using the finite element method, the safety factors of the slope under different wetting–drying cycles were computed based on the generalized Hoek–Brown failure criterion. Meanwhile, statistical distribution features of strength parameters were considered, and safety factor distribution of studied slopes was obtained with Monte Carlo simulation. The results show that rock mass deformation modulus decreased during wetting–drying cycling. The mean safety factors of the slope with any type of discontinuities were reduced by wetting–drying cycling in probabilistic analyses. Wetting–drying cycling plays an important role in damaging slope stability at initial stages since the degree of rock mass strength deterioration is remarkable during initial wetting–drying cycles. However, the rock mass strength and safety factor of the slope are reduced gently after 10 wetting–drying cycles. This research presents the phases of the effect of wetting–drying cycles on sandstone slope stability in drawdown regions.

Investigation of Failed Slopes Based on a New Method of Back Analysis in Rock Masses: A Case Study

Small variation in shear strength parameters results in remarkable changes in the safety factor (SF) of a rock slope. In this regard, rock mass strength of a failed slope can be estimated with reasonable accuracy using back analysis approach. The conventional back analysis (BA) procedure is based on trial and error approach on the mb and s parameters of Hoek–Brown failure criterion in conjunction with the Geological Strength Index (GSI) classification system. A new BA procedure presented in this paper, a functional relationship, that indicted all possible combinations of mb and s constants, was derived using stability analysis of a slope assuming that the SF of the slope is equal to unity. Then, another relationship is established between mb and s based on the magnitude of GSI. Intersection of the two relationships when plotting on a graph, defines a unique value for mb and s. Finally, effect of the constant a in the generalized Hoek–Brown failure criterion on the GSI value obtained from the method BA is discussed and its effect is considered in the BA approach. The most advantage of the proposed method is that a reliable GSI is obtained in a relatively short time. For better explanation of the new BA procedure, this method is used for the back analysis of a failed slope along the national railway of Iran. Comparing results obtained from the new BA approach and the traditional back analysis method well-specified which the new proposed BA approach increases the accuracy of parameter estimation.

Stability Analysis of Deep Rectangular Tunnels Using Adaptive Finite Element Limit Analysis with Hoek–Brown Failure Criterion

The purpose of this study is to investigate the stability of deep rectangular tunnels excavated in a jointed rock mass using adaptive finite element limit analysis (AFELA) method. The rock mass is assumed to obey the generalized Hoek–Brown failure criterion. The numerical results from parametric studies are presented in the form of dimensionless tables and figures concerning stability numbers (Ns). Typical failure mechanisms are depicted and discussed based on visualized results from AFELA. The results demonstrate that Ns decreases with geological strength index (GSI), increases with disturbance factor (D), stays nearly unchanged with the intact rock yield parameter (mi) and is less sensitive to GSI as D decreases. Besides, an analytical upper bound limit analysis method is also applied to provide a check on the validity of the results from AFELA. The influence of the excavation-induced disturbance on the stability of deep rectangle tunnels is investigated by introducing a disturbance coefficient (ζ).

Linking earthquake-triggered paleolandslides to their seismic source and to the possible seismic event that originated them in a portion of the Argentine Precordillera (31°–33°S)

A total of 36 rock slides were selected for analysing a probable seismic source in the active Andean Precordillera (31°–33°S), the most seismic region of Argentina. Seven of these slope instabilities were selected for in-depth analysis in the field as a function of the most frequent class, lithological susceptibility and field accessibility. Reconstructing the topography previous to collapse and using geotechnical parameters extracted from field data in conjunction with geomechanical testing, the rock slides were modelled using pseudostatic limit equilibrium analyses for the obtention of the critical probabilistic acceleration ( $${a}_{c}$$ ) required to generate the instability under unsaturated conditions and considering both the horizontal and vertical seismic components. To perform a probabilistic estimation of $${a}_{c}$$ , the parameters in relation to the generalized Hoek–Brown failure criterion were selected to operate statistically using 2D SLIDE 8.0 software. Applying inversely Ground Motion Prediction Equations (GMPEs) and concerning the distance to the studied paleolandslide, a possible earthquake inducing a seismic coefficient ( $$k_{h}$$ ) ≥ $$a_{c}$$ was determined. Therefore, a near active fault(s) capable of generating an earthquake magnitude inducing a Peak Ground Acceleration (PGA) ≥ $${a}_{c}$$ at the paleolandslide location was designated as the possible seismogenic source of the slope instability. Intersecting these results, potential paleoseismic events which could have caused several slope instabilities were determined. Thus, a new methodology was developed, which allowed to determine the main seismogenic sources capable of inducing the modelled instabilities in each studied subarea in the Precordillera.

A Mathematical Model Based on Artificial Neural Networks to Predict the Stability of Rock Slopes Using the Generalized Hoek–Brown Failure Criterion

Stability of rock slopes is a critical issue in many mining and civil engineering projects. The current state of practice for slope stability analysis is based on obtaining the factor of safety (FOS). Stability charts are widely used by engineers to obtain a FOS for a quick assessment of the initial stability of slopes. The stability of rock slopes with vertical walls in urban areas adjacent to existing structures is another important issue in this regard. However, the stability of earth or rock slopes are usually analyzed ignoring surcharge loads. The effect of adjacent structures (as surcharge load) on slope stability (considering these loads) can be very useful in slope stability analyses in urban or even non-urban areas. In the present study, it is tried to investigate the effect of surcharge load on the stability of rock slopes based on the generalized Hoek–Brown failure criterion using a finite element numerical software and the related charts are presented. Since there is a stability chart for each slope angle, a comprehensive mathematical model utilizing artificial neural networks is proposed to predict the stability factor of rock slopes. The independent variables in this study were slope angles, slope height, the intensity of surcharge load, Geological Strength Index (GSI), and unconfined compressive strength of the intact rock. Sensitivity analysis showed that the changes in GSI, effect of surcharge and unconfined compressive strength of rock have the highest effect on the slope stability assurance coefficient.

Aplikasi Uji Kuat Geser Dalam Remediasi Lereng Tambang Aspal Di PT Karunia Alam Indonesia Kec. Lasalimu Kab. Buton, Provinsi Sulawesi Tenggara

Mining activities iscommonlyto work with the problem of deformation or rock movement, this is causingthe shift of rock mass and generated in the occurrence of landslides activity. Slope Stability Analysisrequired that the slope in stable condition. Therefore, stable bench is needed to prevent failure benchthat bring about interference either tool traffic or loading material during production process. Testing ofUCS value is done on 6 lithology that is on asphalt lithology, mudstone, siltstone, sandstone andclaystone. Based on the results of laboratory testing show that value of cohesion and friction angle togenerate by using Generalized Hoek Brown Failure Criterion method.The values of cohesion andfriction angle in asphalt are 0.080712 MPa and 26.3176 º. Asphalt Rock Mass Strength Value is0.145453 MPa. The values of cohesion and friction angle in mudstone are 0.075424 MPa and17.4773º. Rock Mass Value The mudstone rock is 0.220617 MPa. The values of cohesion and frictionangle in siltstone are 0,105107 MPa and 28,2864º. Rock Mass Strength siltstone rock is 0.311426MPa. The values of cohesion and friction angle in the sandstone are 0.180389 MPa And 38.9621º.Rock mass strength sandstone rock is 0.739092 MPa. The values of cohesion and friction angle insiltstone are 0.180389 MPa And 38.9621º. The Power of Mass The siltstone rock is 0.739092MPa.The values of cohesion and friction angle in mudstone are 0.180389 MPa And 38.9621º. RockMass Strength value The mudstone rock is 0.739092 MPa. Given that in Geological Strength Indexmethod only qualitative data will be more accurate using RMR method so it can get quantitative data.

Analytical representation of Mohr failure envelope approximating the generalized Hoek-Brown failure criterion

The latest version of the Hoek-Brown criterion, referred to as the generalized Hoek-Brown (GHB) criterion, is an empirical failure condition for rock mass that correlates the rock mass strength with the data collected from the laboratory tests and field observations by use of GSI values. A shortcoming of the GHB criterion is that it does not provide an explicit relation between the shear and normal stresses on the failure plane, which limits its application in many geotechnical design calculations. In order to extend the application of the GHB failure criterion to limit equilibrium analysis and/or the upper-bound approach of limit analysis, the analytical approximations of the Mohr failure envelope corresponding the GHB criterion are derived. At present, the exact formulation is not available except for a=0.5, i.e. for a rock mass with GSI=100. In the formulation proposed here, the 1st- and 2nd- order Taylor approximations are employed to define the relation between the dimensionless normal stress and the sine of the instantaneous friction angle. Given the latter, the corresponding shear stress at failure is calculated from the established explicit relationship between the shear stress and the instantaneous friction angle. The Taylor expansion is carried out by taking the sine of the instantaneous friction angle as the expansion variable. A series of examples are given which demonstrate that the approximated Mohr envelope, derived by invoking the 2nd-order Taylor approximation with the expansion center of 0.5, is nearly identical to the exact analytical form. Even the 1st-order Taylor approximation with the expansion center of 0.5 is proven to be satisfactory. Furthermore, it is shown that the formulation is valid for a broad range of values of GSI. The latter has been verified by simulating the conventional triaxial compression tests within the framework of the critical plane approach (CPA) adopting the proposed form of Mohr failure envelope as a failure function. The results confirm that the calculated axial stresses at failure and the orientation of the failure plane are almost identical to the values stipulated by the original GHB criterion.

An iterative method for the linearization of nonlinear failure criteria

Linearization of a nonlinear failure criterion may be required if a software incorporating the nonlinear failure criterion is not readily available or if an additional computational difficulty is encountered due to the nonlinearity of the failure criterion. In this paper, a novel method is proposed for the linearization of nonlinear failure criteria. The proposed method is based on an iterative procedure and the least-squares regression is used for the linearization. The material is assumed to be elastic-perfectly plastic. By conducting analytical and finite element analyses of stresses and displacements around underground openings in rock mass governed by the generalized Hoek–Brown failure criterion, it is shown that the proposed method is convergent, efficient and effective.

Solutions for Displacement and Stress in Strain-Softening Surrounding Rock Incorporating the Effects of Hydraulic–Mechanical Coupling and Rockbolts Effectiveness

This study focuses on the stress and displacement of a circular opening that is excavated in a strain-softening rock mass incorporating the effects of hydraulic–mechanical coupling and rockbolts effectiveness. It follows the generalized Hoek–Brown failure criterion. Moreover, an improved numerical approach and stepwise procedure are proposed. This approach considers the deterioration of the strength, deformation, and dilation angle and the variation of elastic strain in the plastic region considering the effect of the hydraulic–mechanical coupling and the rockbolts effectiveness. The presented solutions were validated by FLAC results. Several examples are conducted to demonstrate the validity and accuracy of the proposed solution through MATLAB programming. Parametric studies are also conducted to highlight the influences of hydraulic–mechanical coupling and rockbolts effectiveness on stress and displacement. Results show that stress and displacement, incorporating the effects of hydraulic–mechanical coupling and rockbolts effectiveness, are between those when hydraulic–mechanical coupling or rockbolts effectiveness is considered separately. However, this theory needs more verification from practical engineering.

Theoretical Solutions of a Circular Tunnel with the Influence of the Out-of-Plane Stress Based on the Generalized Hoek–Brown Failure Criterion

AbstractThe effect of out-of-plane stress on theoretical solutions of stress, displacement, and plastic radius for a circular tunnel were studied by using the generalized Hoek–Brown (HB) failure criterion and nonassociated flow rule in elastic–brittle–plastic rock masses. A technique of using equivalent Mohr–Coulomb and generalized HB strength parameters was adopted to compare results of the developed method and published results. The presented solution was validated by existing theory. The results of the developed method were found to be larger than those previously published, which were determined through programming.

Improved analytical solutions for the response of underground excavations in rock masses satisfying the generalized Hoek–Brown failure criterion

Analytical solutions for tunnel design are widely used in practical engineering, as they allow a quick analysis of design issues such as estimation of support requirement. In recent years, several papers analyzing the behavior of rock masses that obey the conventional or generalized Hoek–Brown criterion have been published. This article presents a complementary analysis that includes a new normalization of the generalized Hoek–Brown failure criterion, complete solutions for associated and non-associated flow rules, with some new closed-form solutions in the latter case, and in-depth considerations regarding intermediate stresses and edge effects. The results obtained show full agreement with existing solutions in the literature, when possible, and with numerical finite element models in cases that had not been treated previously.

Distinct element method simulation of an analogue for a highly interlocked, non-persistently jointed rockmass

A grain-based distinct element model is used to reproduce the laboratory response of both intact and granulated Wombeyan marble. The term “granulated” refers to a heat treated marble where the cohesion of grain boundaries has been destroyed. The unconfined compressive strength of granulated marble is less than 50% of that of intact marble, while the strength of the granulated marble increases to about 80% of that of the intact marble at higher confining stresses. An iterative calibration approach is developed to match the unconfined and confined strengths of the models to those of intact and granulated marble. The simulation test results of the models of intact and granulated marble including the transition in the failure mode, stress–strain response, and the evolution of inter- and intra-grain micro-cracks with increasing confinement are discussed. The observed rapid strengthening effect, in terms of increasing confinement, is interpreted to be due to the high degree of grain assembly geometric interlock, which arises from the tight fit geometric shape of the grains as well as the roughness of the grain boundaries. It is suggested that the granulated marble can be considered to be an analogue for a highly interlocked, non-persistently jointed rockmass. It is shown that when the generalized Hoek–Brown failure criterion and the Geological Strength Index (GSI) are used to match the strength of the granulated marble at zero confinement, the confined strength of the granulated marble is underestimated by as much as a factor of two. Therefore, the confined strength of a highly interlocked, non-persistently jointed rockmass, with strong, brittle rock blocks, could be significantly higher than that predicted by commonly adopted empirical approaches. This has practical implications for the design of highly confined pillars and abutments, which is discussed in this paper.

A New Elasto-Viscoplastic Damage Model Combined with the Generalized Hoek–Brown Failure Criterion for Bedded Rock Salt and its Application

According to the requirement of the West–East Gas Transmission Project in China, the solution-mined cavities located in the Jintan bedded salt formation of Jiangsu province will be utilized for natural gas storage. This task is more challenging than conventional salt dome cavern construction and operation due to the heterogeneous bedding layers of the bedded salt formation. A three-dimensional creep damage constitutive model combined with the generalized Hoek–Brown model is exclusively formulated and validated with a series of strength and creep tests for the bedded rock salt. The viscoplastic model, which takes the coupled creep damage and the failure behavior under various stress states into account, enables both the three creep phases and the deformation induced by vicious damage and plastic flow to be calculated. A further geomechanical analysis of the rapid gas withdrawal for the thin-bedded salt cavern was performed by implementing the proposed model in the finite difference software FLAC3D. The volume convergence, the damage and failure propagation of the cavern, as well as the strain rate of the salt around the cavern, were evaluated and discussed in detail. Finally, based on the simulation study, a 7-MPa minimum internal pressure is suggested to ensure the structural stability of the Jintan bedded salt cavern. The results obtained from these investigations provide the necessary input for the design and construction of the cavern project.

Closed-Form Solutions for a Circular Tunnel in Elastic-Brittle-Plastic Ground with the Original and Generalized Hoek–Brown Failure Criteria

The paper presents a closed-form solution for the convergence curve of a circular tunnel in an elasto-brittle-plastic rock mass with both the Hoek–Brown and generalized Hoek–Brown failure criteria, and a linear flow rule, i.e., the ratio between the minor and major plastic strain increments is constant. The improvement over the original solution of Brown et al. (J Geotech Eng ASCE 109(1):15–39, 1983) consists of taking into account the elastic strain variation in the plastic annulus, which was assumed to be fixed in the original solution by Brown et al. The improvement over Carranza-Torres’ solution (Int J Rock Mech Min Sci 41(Suppl 1):629–639, 2004) consists of providing a closed-form solution, rather than resorting to numerical integration of an ordinary differential equation. The presented solution, by rigorously following the theory of plasticity, takes into account that the elastic strain components change with radial and circumferential stress changes within the plastic annulus. For the original Hoek–Brown failure criterion, disregarding the elastic strain change leads to underestimate the convergence by up to 55%. For a rock mass failing according to the generalized Hoek–Brown failure criterion, using the original failure criterion leads to a high probability (97%) of underestimating the convergence by up to 100%. As a consequence, the onset or degree of squeezing may be underestimated, and the loading on the support/reinforcement calculated with the convergence/confinement method may be largely underestimated.

Post-failure behavior of two mine pillars confined with backfill

Researchers from the National Institute for Occupational Safety and Health used a series of instruments (borehole extensometers , earth pressure cells , and embedment strain gauges) to study the post-failure behavior of two pillars confined by backfill in a test section at the Buick Mine near Boss, MO, USA. Evaluation of these pillars was part of a research project to assess the safety of the test section when high-grade support pillars were mined. Data from borehole extensometers installed in several backfill-confined pillars and numerical modeling indicated that these pillars failed during extraction of the support pillars. Failure was corroborated by the post-yield pillar strain response in which the immediate elastic strain was negligible compared to the time-dependent strain component measured between blasting rounds. A three-dimensional, finite-element program with an elastic perfectly plastic material model was calibrated using extensometer data to estimate rock mass modulus and unconfined compressive strength . The resulting rock mass modulus was 45–60% of the average deformation modulus obtained from laboratory tests, and the calibrated compressive strength was 40% of average laboratory values. A rock mass modulus equal to 52% of the average laboratory deformation modulus was calculated using the rock mass rating (RMR) system. Rock mass strength was calculated with the generalized Hoek–Brown failure criterion for jointed rock and indicated that in situ strength was 33% of laboratory strength. Post-failure stresses calculated by the finite-element model were larger for confined pillars than post-failure stresses in unconfined pillars calculated using empirical plots. Data from the calibrated model provided a strain-hardening stress-versus-strain relationship. This knowledge is critical for the design of mines that use partially failed pillars to carry overburden load.