Generalized Hoek Brown Criterion Research Articles

Rock slope stability assessment based on the critical failure state curve for the generalized Hoek‒Brown criterion

Rock slope stability assessment based on the critical failure state curve for the generalized Hoek‒Brown criterion

A Stope Mining Design with Consideration of Hanging Wall When Transitioning from Open Pit Mining to Underground Mining for Sepon Gold Mine Deposit, Laos

This study investigates the transition from surface to underground mining at the Sepon Gold mine. The stability of surface slopes is assessed prior to commencing underground operations. Stope mining is adopted based on ore body characteristics and geological features. Finite element numerical analysis, employing the Generalized Hoek–Brown criterion, evaluates slope stability for surface slopes and opening stopes. The pit design comprises a 70° slope angle, 20 m height, and 10–15 m safety berm, meeting stability requirements with a factor of safety of 2.46. Underground mining design includes a 62° ore body dip, a 50 m thick crown pillar to prevent surface subsidence, and 5 m wide, 5 m high stopes. Sill pillars are left for support after each level of excavation. Rock bolts are employed in specific stope areas where necessary, with continuous monitoring for surface deformation. This study analyzes the influence of stope sizes on the pit wall and pit bottom stability, identifying slope failures near the hanging wall close to the pit bottom during underground mining. A slight increase in the displacement zone is observed on the upper crest of the top footwall. Overall, the findings demonstrate successful stability in the transition from surface to underground mining at the Sepon Gold mine.

Bearing capacity of foundations resting on rock masses subjected to Rayleigh waves

This study investigates the ultimate bearing capacity of shallow foundations resting on rock masses under earthquakes using upper-bound limit analysis. A modified pseudodynamic method (MPD) that considers the influence of Rayleigh waves is initially used to characterize the spatiotemporal variation in earthquake acceleration. The strength of rock masses is governed by the generalized Hoek‒Brown criterion and the plastic flow at failure is assumed to respect the associated flow rule. The generalized tangential technique is introduced to provide a linear approximation of the strength envelope for capturing the equivalent Mohr‒Coulomb strength parameters. The classic nonsymmetrical multi-block translational mechanism, which is capable of assessing a rock-foundation system under asymmetrical load, is reconstructed to portray the velocity discontinuity of the plastic failure region. Based upon the energy equilibrium theorem of the limit analysis, an analytical solution of seismic bearing capacity is derived and then formulated as a multivariate optimization problem. Comparisons show good agreement with the literature and validate the correctness and rationality of this work. Parametric study indicates that the seismic foundation capacity obtained by MPD tends to be conservative compared to the pseudostatic method with the same seismic coefficients, and that the period of a Rayleigh wave has only a slight effect on the bearing capacity. The failure region is more sensitive to the disturbance coefficient than it is to the other rock strength parameters.

A New Discrete Form of Hoek–Brown Criterion and Its Application to Limit Equilibrium Analysis of Rock Slope Stability

The generalized Hoek–Brown criterion (GHB) is recognized as one of the standard failure criteria in rock engineering and its validity extends to a wide range of rock mass quality. A drawback of this criterion is the difficulty of transforming it into an explicit form defining the Mohr failure envelope when its strength parameter a is not equal to 0.5. The information on the functional form of the Mohr envelope for the full range of rock mass conditions enables the implementation of classical engineering approaches, such as the limit equilibrium method and limit analysis, in the framework of the GHB criterion. Knowing that for a≠0.5 the exact closed-form representation of the Mohr envelope is not feasible, an alternative is to express it in an approximate analytical form. The main purpose of this study is to propose a new improved method to define an approximate Mohr envelope of the GHB criterion that is much more accurate compared with the recently published approximations. The idea behind the formulation is to expand the Balmer’s equation, which defines the relationship between the normal stress and minor principal stress at failure, by invoking the finite Taylor series centered at the known solution for a=0.5. The formulation is then completed by substituting this solution into another Balmer’s equation, defining the relationship between the shear strength and the minor principal stress. The Taylor polynomial approximations of up to third degree are considered in the formulation. The accuracy of the shear strength prediction is shown to be much better than that of the approximate formula of Lee and Pietruszczak proposed in 2021. An illustrative example of limit equilibrium analysis of rock slope stability, incorporating the new approximate expression for the Mohr envelope, is provided. The analysis incorporates a modified version of the Bishop approach, which is simpler and more rigorous than the original nonlinear expression. The study confirms that the new approximate representation of the Mohr failure envelope can facilitate the application of the GHB criterion to a range of practical rock engineering calculations.

Stability Assessment of the Slopes of an Oceanside Coral Limestone Quarry under Drawdown Condition of Semidiurnal Ocean Tides

Vipingo quarry in Kilifi county, Kenya, is one of the quarries supplying coral limestone for limestone manufacturing in the coastal region. Due to its close proximity to the Indian ocean, the semidiurnal ocean tides tend to have an influence on the stability of the quarry slopes adjacent to the shoreline. Finite element numerical analysis using the generalized Hoek–Brown criterion is conducted to assess the stability condition of the slopes followed by slope-angle optimization to determine the safest overall slope angle as well as analyzing the stability of the slopes due to action of varying ocean tides. The optimum overall slope angles for various excavation depths are found to be 52° for 20 m, 46° for 30 m, 42° for 40 m, and 39° for 50 m, which are the same even with varying distance of the slope face from the shoreline. A parametric analysis shows that there is no significant effect of the tides on slope stability for excavations above the water table, but as the quarry gets deeper, the slope stability is affected. A sensitivity factor (ζ) is introduced, being a measure of how much the slope safety factor is reduced as a result of the semidiurnal tidal action.

Elastoplastic semi-analytical investigation on a deep circular tunnel incorporating generalized Zhang–Zhu rock mass strength

The semi-analytical method based on finite difference method is widely used in the study of the mechanical response of surrounding rocks in a circular tunnel. The core of the three-dimensional (3D) mechanical analysis of the plastic zone is to solve nonlinear equations with a complex yield criterion, which leads to a long iterative solution time and low accuracy. In this study, a new 3D semi-analytical method is proposed for a circular tunnel excavation. The method is based on the finite difference method, wherein a linear equation is used to replace the complex yield surface equation. This significantly reduces the iterative solution process and effectively improves the calculation rate. The accuracy of the proposed method is verified using conventional and 3D numerical methods. The two-dimensional (2D) generalized Hoek–Brown criterion (GHB), 3D generalized Pan–Hudson criterion (GPH), and 3D generalized Zhang–Zhu criterion (GZZ) are used to analyze the applicability of the proposed method. The mechanical properties of a circular tunnel excavation are studied using these criteria. Our results show that the calculation rate of the plastic zone response of the proposed method (based on the GZZ criterion) is 12,000 times higher than that of the conventional iterative method. The overall calculation rate is increased by a factor of 65, and the calculation error is smaller than that of the conventional method. The GHB does not consider the intermediate principal stress, and the GPH cannot reflect the mechanical properties of rock masses with different tensile and compressive strengths, although it considers the intermediate principal stress. The convergence–constraint characteristics of the surrounding rock of the GHB and GPH are significantly different from those of the GZZ. There is an optimal initial axial stress value qopt that yields the smallest deformation of the surrounding rock and the best stability. The internal support pressure and residual strength of the rock mass have a significant effect on the mechanical response of the surrounding rock. The proposed method has acceptable applicability to elastic–brittle and elastic–perfectly plastic rock masses. Additionally, it can be used in the study of deep-buried tunnel excavation at high geo-stresses.

Calculation Method for the Critical Thickness of a Karst Cave Roof at the Bottom of a Socketed Pile

The thickness of a karst cave roof at the bottom of a socketed pile plays an important role in the vertical bearing capacity of the socketed pile in the karst region. In practice, its thickness is simply recommended to be not less than 3 times the diameter of the socketed pile, regardless of the geological conditions and the size of the cave itself. In this study, we present an approach for calculating the critical thickness-to-diameter ratio of a karst cave roof η (η = h/d, the ratio of karst cave roof thickness to pile diameter) based on the generalized Hoek–Brown criterion by virtue of the limit analysis method, which considers the pile tip load, hardness degree of the intact rock, and rock mass quality. The analysis results show that less load at the bottom of the pile, higher quality of rock mass, and more hard rock all lead to a smaller critical thickness-diameter ratio, whereas the critical thickness-to-diameter ratio is greater. The validity of the proposed method is verified through a physical model test.

Applications of an Innovative Strength Parameter Estimation Method of the SoilRock Mixture in Evaluating the Deposit Slope Stability Under Rainfall

Deposit landslides are one of the most representative geological hazards around the world, and the poor understanding of the mechanical characteristics of the soilrock mixture (S-RM) increases the difficulties in evaluating the stability of the deposit slope subjected to rainfall. This study attempted to propose an innovative strength parameter estimation method of the S-RM based on the concept and format of the generalized HoekBrown criterion. The system of “rock blocks–soil–contact surface” was considered the main source providing resistance to the external force, and the effect of the soil matrix, rock blocks, and the contact surface between them was taken into account. The verification of the estimation method was proved based on the abundant test data. A typical deposit slope located in the Taoyuan region of Yunnan Province, China, was selected as a case study, and the estimation method was applied to provide the shear parameters of the S-RM. The slope stability subjected to different types of rainfall was analyzed considering the parameter deteriorations, and the results show that the deposit landslide is more prone to the wave-type rainfall, which shows a deeper response depth of pore water pressure and a smaller safety factor. The present study suggests a simple estimation method for the shear parameters of the S-RM using a few parameters for the engineers and provides an understanding of the deposit slope stability during the rainfall process.

A stability analysis of rock slopes using a nonlinear strength reduction numerical manifold method

To investigate rock slope stability, a nonlinear strength-reduction numerical manifold method (NSRNMM) using a generalized Hoek-Brown (GHB) criterion is proposed. As it is difficult to implement the nonlinear strength reduction method (NSRM) with the use of the GHB criterion by directly reducing the GHB parameters, two equivalent Mohr-Coulomb (MC) criteria, namely, the instantaneous and average equivalent MC criteria that are derived from the GHB criterion, are adopted in the NSRNMM. The implementation details of the NSRNMM are discussed. The stability of two rock slopes, namely, a rock slope with a GHB material and a rock slope with a GHB material and two MC materials, is investigated using the NSRNMM. The numerical results indicate that 1) the proposed NSRNMM using the instantaneous equivalent MC criterion can accurately calculate the safety factor (Fs) of rock slopes and that 2) the Fs predicted with the NSRNMM using the average equivalent MC criterion is more conservative than that using the instantaneous equivalent MC criterion.

PROBABILISTIC ASSESSMENT OF ROCK SLOPE STABILITY IN OPEN PIT MINE CHAARAT USING THE GENERALIZED HOEK–BROWN CRITERION

The slope stability evaluation using the generalized Hoek–Brown criterion and regarding the scale effect has been implemented in terms of the Chaarat gold project. Furthermore, the probabilistic assessment and sensitivity analysis are performed. Slope failure probabilities are determined, and the slope stability factors are obtained as functions of the slope height and angle. The slope stability estimation based on classified approach considering the scale effect, including GSI rating and probabilistic analysis is tested in rock slopes. Slope stability is mainly governed by variability of the Geological Strength Index related with the scale effect.

Estimation of Rock Burst Grades Using Rock Mass Strength

The traditional rock burst estimation method is usually based on the σc (rock strength) in practice, while the actual occurrence of rock burst depends more on the structure and strength of the rock mass. In this work, the actual rock bursts occurred in a railway tunnel project in Western China, and the σcm (rock mass strength) was calculated by the generalized Hoek–Brown criterion. According to the actual situation of rock bursts, a modified rock burst estimation criterion using the ratio of σcm to σmax (maximum geostress) was proposed. The influence of randomness on the reliability of rock burst estimation criterion was considered. The estimation results based on the traditional and modified method were furthermore compared with those of the actual rock bursts. The results show that σcm calculated by the generalized Hoek–Brown criterion may be considered well in the rock type and strength, construction condition, and structure features of the rock mass; the estimation results of rock burst using the ratio of σc to σmax are quite different from the actual situation, while those using the ratio of the σcm to σmax coincided relatively with the actual rock bursts; the ratios of σcm to σmax, which are greater than 0.167, 0.066 to 0.167, 0.012 to 0.066, and less than 0.012, are corresponded to the slight, medium, strong, and violent grades of the rock bursts, respectively; the randomness of data selection has certain influence on the rock burst estimation criterion, but the variation range is small; the modified estimation criterion of rock burst proposed in this work has a good reliability. The results presented herein are important for tunnel construction and the prevention of rock burst in the high geostress areas.

A New Semi-Analytical Method for Elasto-Plastic Analysis of a Deep Circular Tunnel Reinforced by Fully Grouted Passive Bolts

The use of fully grouted passive bolts as a reinforcement technique has been widely applied to improve the stability of tunnels. To analyze the behaviors of passive bolts and rock mass in a deep circular tunnel, a new semi-analytical solution is presented in this work based on the finite difference method. The rock mass was assumed to experience elastic–brittle–plastic behavior, and the linear Mohr–Coulomb criterion and the nonlinear generalized Hoek–Brown criterion were employed to govern the yielding of the rock mass. The interaction and decoupling between the rock mass and bolts were considered by using the spring–slider model. To simplify the analysis process, a bolted tunnel was divided into a bolted region and an unbolted region, while the contact stress at the bolted–unbolted interface and the rigid displacement of the bolts were obtained using two boundary conditions in combination with the bisection method. Comparisons show that the results obtained using the proposed solution agree well with those from the commercial numerical software and the in situ test. Finally, parametric analyses were performed to examine the effects of various reinforcement parameters on the tunnel’s stability. The proposed solution provided a fast but accurate estimation of the behavior of a reinforced deep circular tunnel for preliminary design purposes.

Lower Bound Limit Analysis Using Power Cone Programming for Solving Stability Problems in Rock Mechanics for Generalized Hoek–Brown Criterion

This study introduces a methodology to solve plane strain stability problems in rock mechanics, following the generalized Hoek and Brown yield criterion, by employing the lower bound finite elements limit analysis in conjunction with the power cone programming. The efficacy of the proposed approach has been demonstrated by solving three different types of stability problems: (1) finding the bearing capacity of strip footings on rock media, (2) assessing the stability of finite rock slopes, and (3) the stability analysis of unlined rectangular tunnels in rock mass. In all the cases, the results obtained from the analysis have been compared thoroughly with that computed using (1) nonlinear programming, and (2) semi-definite programming technique. The present approach has been found to be computationally very robust and it generates very accurate solutions.

Theoretical and Experimental Study on Rock Resistance Coefficient of Soft Rock Tunnel Considering Creep Effect

Creep deformation properties of soft rock are studied based on the visco-elastoplastic model. Combining with the generalized Hoek–Brown criterion, the calculation formula for rock resistance coefficient (RRC) of soft rock tunnel is deduced based on the creep effect, and the formula is applied to Tianjiashan tunnel, which is a typical soft rock tunnel. Besides, the influences of creep effect and tunnel buried depth on RRC are discussed. As shown in the results, the RRC which takes creep effect into consideration is declined, and the RRC decreases with the increase of tunnel depth and in situ stress. After the creep effect of surrounding rock is fully developed, the values of RRC are from 140.92 to 24.09 MP m−1 at different buried depth, which indicates that although soft rock tunnels have poor stability, the surrounding rock still possess certain elastic resistance and self-bearing capacity.

Stability analysis of twin horse-shoe shaped tunnels in rock mass

This study examines the stability of a single and twin horse-shoe shaped unlined tunnels laid in rock media and loaded with surcharge pressure on ground surface. The tunnels are assumed to be sufficiently long so that the plane strain analysis remains applicable. The failure of rock mass is governed by the generalized Hoek-Brown (GHB) yield criterion. The analysis has been performed by using the lower bound finite elements limit analysis in conjunction with the power cone programming (PCP). No assumption needs to be associated with either the smoothing of the yield surface or fixing the value of the exponent in the GHB criterion. For a given cover to diameter ratio of the tunnels, the maximum permissible value of the surcharge pressure on ground has been computed ensuring the stability of the tunnels. Apart from the different basic material yield parameters (GSI, mi and σci), the effect of clear spacing (S) between the twin tunnels on the results has also been studied. Failure patterns have also been explored for a number of cases to identify the region of the plastic shear zone. The computations reveal that the optimal spacing (Sopt), beyond which the tunnels behave like isolated ones, remains almost independent with respect to the material parameters and increases continuously with an increase in H/B; the value of Sopt/B increases from 2.5–3.0 for H/B = 1 to 13.0–14.0 for H/B = 6. The computational results have been duly validated and even compared with the different available solutions for square and circular twin tunnels in rock media.

Comparative analyses of finite element and limit-equilibrium methods for heavily fractured rock slopes

Limit-equilibrium method (LEM) and finite element method (FEM) with shear strength reduction (SSR) technique are the most widely used analysis tools in slope stability assessment. Recently, researchers have reported that both factor of safety (FOS) values and failure surfaces obtained from LEM and FEM are generally in good agreement except in some particular cases. On the other hand, the consistency between two methods has not been adequately discussed for heavily fractured rock mass models by employing Generalized Hoek–Brown Criterion (GHBC). In this study, the FOS values and failure surfaces derived from LEM and FE-SSR based on GHBC were compared concerning static and pseudo-static conditions, various overall slope angles, geological strength index (GSI) values, and various water table levels. In this context, three homogeneous, highly fractured rock slope models with irregular geometry and different slope heights were generated by two-dimensional Slide and Phase2 software. Limit-equilibrium (LE) analyses were performed by Bishop, Fellenius, Morgenstern–Price, and Spencer techniques. The comparisons of global minimum FOS values for 431 cases and the effects of variables on two methods were investigated by statistical analyses. Consequently, it was determined that the difference between the FOS values are statistically significant. However, if the seismic coefficient is higher than 0.1 g, slope angle is higher than 34°, and the slope is assumed to be fully saturated, Morgenstern–Price is the most well-matched technique with FE-SSR than the others. For the same cases, the failure surfaces detected by Fellenius is more similar to the ones detected by FE-SSR.

Application of generalized Hoek–Brown criterion to selection and design of mine support systems for the Oktyabrsky copper–nickel deposit: Case study

Application of generalized Hoek–Brown criterion to selection and design of mine support systems for the Oktyabrsky copper–nickel deposit: Case study

A strength reduction method based on the Generalized Hoek-Brown (GHB) criterion for rock slope stability analysis

The strength reduction method (SRM) combining with the Generalized Hoek-Brown (GHB) criterion has become a widely used means to assess the stability of rock slopes. Therefore, various efforts have been made to establish a standard reduction strategy for strength parameters. This paper presents a new nonlinear SRM based on the GHB criterion, and the core novelty of the proposed method is to provide a reduction strategy with precise physical meaning to find an optimal set of parameters that trigger rock slope failure. To verify the validity of the proposed method, two illustrative examples are analyzed. The results show that the proposed method could lead to a reasonable safety factor, and the critical sliding surface obtained by the proposed method can reflect the tensile crack in the steep slope. Finally, to distinguish the computational results and efficiency among the proposed method and other preexisting reduction methods, other more 8 slopes selected from the literature are used for research objects. The results show that the safety factors resulted from the proposed method are very close to those acquired by the most accurate method available at present (Hammah’s method), however, its computational efficiency is comparatively higher than that of Hammah’s method.

Stability assessment of landslide-prone road cut rock slopes in Himalayan terrain: A finite element method based approach

Abstract Large-scale slope destabilization could be aggravated due to swift urbanization and ever-rising demands of geoengineering projects such as dams, tunnels, bridges and widening roads. National Highway-58 connects Delhi to Badrinath in India, which passes through complex geomorphological and geological terrain and often encounters cut slopes susceptible to slope failures. In the present investigation, a detailed geotechnical appraisal is conducted along the road cut slopes from Rishikesh to Devprayag in the Himalayas. Twenty vulnerable road cut slopes were demarcated for detailed slope stability analysis using Phase2D finite element modeling simulator. Nonlinear generalized Hoek-Brown (GHB) criterion was adopted for stability analyses. Out of 20 slopes, five slopes (S6, S7, S18, S19 and S20) are unstable with factor of safety (FoS) less than or equal to 1, and thus needs immediate attention. The FoS values of four slopes (S2, S9, S13 and S17) lie between 1 and 1.3, i.e. marginally stable, and slopes S1, S3, S4, S5, S8, S10, S11, S12, S14, S15 and S16 are stable. Mohr-Coulomb (MC) criterion was also adopted to compare the slope stability analysis with GHB criterion. The FoS calculated from GHB criterion is close to that using MC criterion for lower values of FoS whereas for higher values, the difference is marked. For the jointed rock in the Himalayan region, the nonlinear GHB criterion gives better results as compared to MC criterion and matches with the prevailing field conditions. Accordingly, some suggestions are proposed to strengthen the stability of cut slopes.

Practical Use of Modified Hoek–Brown Criterion for Soil Slope Stability Analysis

Many slopes are comprised of soils that exhibit a nonlinear shear strength or failure envelope, and multiple mathematical relationships have been developed to account for this nonlinearity. At the same time, the numerical shear strength reduction (SSR) method has become a common method for analyzing the stability of slopes. Despite these developments, a practical, commercially available method to include nonlinear shear strength in numerical analysis has not been established for soil. The Generalized Hoek–Brown (GHB) model provides a nonlinear failure criterion, but is formulated for use with rock. This paper proposes a Modified Hoek–Brown (MHB) criterion to make the model applicable to soil and leverage the GHB criterion present in many numerical analysis packages. Past applications of SSR to the GHB are discussed and a numerical method for reduction of the parameters in the context of soil slopes is proposed. A simple wedge analysis validates the MHB method for a linear envelope. Three examples of increasing complexity compare results of limit equilibrium with both finite element and finite difference SSR analyses. In general, the different numerical methods yield very similar results. The SSR method using MHB predicts critical strength reduction factors 2–5% lower than the limit equilibrium factors of safety. The approach presented in this paper allows practitioners to model nonlinear shear strength in finite element strength reduction analysis for cases where this nonlinearity is judged to be an important factor.