Hoek Brown Research Articles

Modification of rock failure criteria considering the RMR caused by joints

The aim of this study is to present a modification of the failure criteria of rock masses, separately considering the effect that the Bieniawski’s rock mass rating (RMR) has due to joints, as well as the RMR linked to compressive strength of the mass rock. This modification can be applied to three of the already existing criteria: that of Bieniawski–Yudhbir–Kalamaras, that of Sheorey, and that of Hoek–Brown, comparatively analysing the effects of the three modifications that have been proposed. The new, modified criterion will be validated with new data obtained in a marble mine exploited by means of rooms and pillars. The values observed and measured in the mine are compared to those obtained through numerical modelling of the pillars, using the Análisis Lagrangiano de Medios Continuos, Lagrangian Analysis of Continuous Media (ALMEC) program. Finally, several conclusions related to the application of these rock failure criteria to the analysis of mining excavation of rooms and pillars will be proposed.

Linear Mohr–Coulomb strength parameters from the non-linear Hoek–Brown rock masses

Most conventional computer codes, design practice and standards in rock engineering are formulated in terms of a linear Mohr–Coulomb (MC) failure criterion. However, experimental data shows that the failure of almost all types of rock masses follows a modified Hoek–Brown (HB) failure criterion that is non-linear. In order to avoid the difficulty resulting from the non-linearity of the strength envelope of rock masses in calculation of bearing capacity, the equivalent MC strength parameters from the modified HB failure criterion are developed for practical use in engineering. From the results, it is found that the equivalent strength parameters depend on not only the non-linear HB failure criterion but also the surcharge load and self-weight, which is different from the published results.

Limit analysis solutions for the bearing capacity of rock masses using the generalised Hoek–Brown criterion

This paper applies numerical limit analyses to evaluate the ultimate bearing capacity of a surface footing resting on a rock mass whose strength can be described by the generalised Hoek–Brown failure criterion [Hoek E, Carranza-Torres C, Corkum B. Hoek–Brown failure criterion—2002 edition. In: Proceedings of the North American rock mechanics society meeting in Toronto, 2002]. This criterion is applicable to intact rock or heavily jointed rock masses that can be considered homogeneous and isotropic. Rigorous bounds on the ultimate bearing capacity are obtained by employing finite elements in conjunction with the upper and lower bound limit theorems of classical plasticity. Results from the limit theorems are found to bracket the true collapse load to within approximately 2%, and have been presented in the form of bearing capacity factors for a range of material properties. Where possible, a comparison is made between existing numerical analyses, empirical and semi-empirical solutions.

Equivalent Mohr–Coulomb and generalized Hoek–Brown strength parameters for supported axisymmetric tunnels in plastic or brittle rock

The evaluation of equivalent Mohr–Coulomb (M–C) strength parameters to the prototype Hoek–Brown (H–B) ones for tunnels has been tackled in different ways for many years. The extension of the H–B criterion to the generalized one has made the challenge even greater. Most of the latest methods did not account for the effect of the support pressure and none gave formulae for equivalent parameters of supported or brittle rock. Here, an almost exact explicit solution for the evaluation of the critical pressure, of a tunnel in a rock mass satisfying the generalized H–B criterion, is initially investigated. Then, formulae are derived for the evaluation of equivalent parameters, of either elastoplastic or elastic–brittle plastic rock. They are based either on a best fitting procedure of the two envelopes or on the equation of selected responses of the models. Supported tunnels in equivalent M–C rock masses are then validated against those excavated in the prototype H–B rock masses.

Stability of highly fractured infinite rock slopes with nonlinear failure criteria and nonassociated flow laws

The effect of the dilatancy phenomenon on rock masses is not usually considered when calculating slope stability. A theoretical analysis has been conducted on the stability of infinite rock slopes, with varied hypotheses of simplified seepage flow nets. The calculations were made in the most general way possible, for any type of failure criterion and for linear-type flow laws. When the calculations were completed they were applied to the original and modified Hoek–Brown failure criteria and also to the associated flow and constant-dilatancy conditions. The study reveals the great importance of the dilatancy value and the "non-conservative" nature of an associated flow law hypothesis, which is the hypothesis that is generally used. The important effect of groundwater flow in the slope has also been enhanced. A quantitative estimation of the stability is provided for homogeneous and isotropic rock media under different angles of dilatancy and water flow nets. Lastly, the equilibrium is dependent on the following parameters: slope inclination angle (α), specific weight of the rock mass (γR*), type of rock (m0), unconfined compression strength (σc*), and geological strength index (GSI).Key words: infinite rock slope, Hoek Brown, dilatancy.

Effect of Rock Strength Criterion on the Predicted Onset of Sand Production

The variation of sanding onset prediction results with the selection of one or another rock strength criterion is investigated. In this paper, four commonly used rock strength criteria in sanding onset prediction and wellbore stability studies are presented. There are Mohr–Coulomb, Hoek–Brown, Drucker–Prager, and modified Lade criteria. In each of the criterion, there are two or more parameters involved. In the literature, a two-step procedure is applied to determine the parameters in the rock strength criterion. First, the Mohr–Coulomb parameters like cohesion So and internal friction angle ϕf , are regressed from the laboratory test data. Then, the parameters in other criteria are calculated using the regressed Mohr–Coulomb parameters. It is proposed that the best way to evaluate the parameters in a specific rock strength criterion is to perform direct regression of the laboratory test data using that criterion. Using this methodology, it is demonstrated that the effect of various rock strength criteria...

Stability analysis of rock slopes with a modified Hoek–Brown failure criterion

AbstractThe original Hoek–Brown (HB) failure criterion was used to analyse the stability of rock slopes. For highly fractured rock, the original HB failure criterion has been modified, but its effect on the stability of rock slopes has not been studied. Within the framework of the kinematical approach of limit analysis, this paper computes the rigorous upper bounds of stability factors of homogeneous rock slopes with the modified HB failure criterion under the plane strain condition, by employing a ‘generalized tangential’ technique. In such technique, instead of using the modified HB failure criterion, a series of linear failure surfaces tangent to the actual non‐linear failure surface are utilized to derive the upper bound solutions, incorporating a new parameter n ranging from 0.5 to 0.65. The numerical results are compared with other published solutions for the case of n=0.5. The effects of the n on the stability factors of rock slopes are discussed. Copyright © 2004 John Wiley & Sons, Ltd.

Influence of a nonlinear failure criterion on the bearing capacity of a strip footing resting on rock mass using a lower bound approach

The strength envelope of almost all geomaterials is nonlinear when one considers a wide range of stresses. Therefore, a nonlinear failure criterion needs to be used in stability analysis whenever the effects of nonlinearity are too significant to be neglected. This paper presents a lower bound solution to the bearing capacity calculation of a strip footing resting on a homogenous weightless rock mass using the nonlinear Hoek–Brown (HB) failure criterion. Two types of admissible stress fields are used to develop solutions. The first stress field has three stress legs. The second stress field has a spiral-like shape with n stress legs, where n may vary from 9 to 18 000 (even to infinity). Using two admissible stress fields, equations are derived and used for the calculation of lower bound bearing capacity values of a strip footing on rock mass. The influences of the admissible stress leg number n and the material parameter s in the nonlinear HB failure criterion are investigated. It is found that the lower bound bearing capacity calculated using the spiral-like shape admissible stress field approaches to the true optimum value as the stress leg number n increases, and the nonlinear material parameter s has a strong influence on the bearing capacity of the footing.Key words: HB failure criterion, bearing capacity, stress leg, lower bound theorem, rock.

Modelling of powder compaction using an endochronic plasticity model: A.R. Khoei et al. (Sharif University of Technology, Tehran, Iran.) J. Mater. Process. Technol., Vol 130–131, 2002, 175–180

The parameters of rock mass structures, strength and seismic effect are critical factors for the seismic stability analysis of rock slopes. This paper demonstrates the use of a new form of a chart-based slope stability method that satisfies the Hoek-Brown (HB) criterion. The limit equivalent method is used to assess the stability of rock slopes subjected to seismic inertial force. First, stability charts for calculating the factors of safety (FoS) with a slope angle of β = 30° in static and pseudo-static states were proposed by using Slide 6.0 software. Next, scaling factors of the horizontal seismic acceleration coefficient (fKh) and slope angle (fβ) were established to illustrate the influence of the horizontal seismic load and slope angle on the stability of rock slopes, respectively. Using regression analyses of fKh and fβ, a fast calculation model was proposed to solve the slope safety factors based on the stability charts. Finally, the stability charts analysis method (SCAM) was verified against the numerical solutions; the results showed that 70.63% of the data had discrepancies of less than ± 10%, and the data with discrepancies greater than ± 10% were associated with high values of geological strength index (GSI) and horizontal seismic acceleration coefficient (Kh). The proposed model calculating the FoS of rock slopes is simple and straightforward to use for seismic rock slope design and stability evaluation.

Modelling brittle failure of rock

Observations of brittle failure at the laboratory scale indicate that the brittle failure process involves the initiation, growth, and accumulation of micro-cracks. Around underground openings, observations have revealed that brittle failure is mainly a process of progressive slabbing resulting in a revised stable geometry that in many cases take the form of V-shaped notches. Continuum models with traditional failure criteria (e.g. Hoek–Brown or Mohr–Coulomb) based on the simultaneous mobilization of cohesive and frictional strength components have not been successful in predicting the extent and depth of brittle failure. This paper presents a continuum modelling approach that captures an essential component of brittle rock mass failure, that is, cohesion weakening and frictional strengthening (CWFS) as function of rock damage or plastic strain.

Shear failure envelope of Hoek-Brown criterion for rockmass

The Mohr-Coulomb (MC) criterion possesses a linear shear failure envelope and is widely used in geotechnical engineering calculations. However, the failure process in rockmass is more complex than that of soils, and it can be more adequately described by the Hoek-Brown (HB) failure criterion. This criterion has been updated as well as modified, but its effect on the shear failure envelope has not been studied. The shear failure envelope for the modified form of HB criterion is derived in this paper, which shows that a change in the value of parameter a from 0.5 to 0.6 affects the shear envelope more significantly for a rockmass characterized by a larger value of parameter m and high effective normal stress. The instantaneous friction angle is also affected by a change in the value of parameter a.

Slip zones around circular openings in a jointed Hoek-Brown medium

Abstract The regions of joint influence around a circular opening located in a Mohr-Coulomb (MC) medium can be easily estimated by the procedure described in the published literature. Such computations, although based on simplifying assumptions, are thought to be sufficiently accurate for several important practical applications, particularly because the input parameters may have large associated uncertainties which may not justify a more elaborate and accurate computation. However, a jointed rockmass can be more appropriately described by the Hoek-Brown strength criterion (HBSC). This paper presents the theory and computation procedure to estimate the region of joint influence around circular openings located in a Hoek-Brown (HB) medium. In addition to the disturbance caused by the excavation in the existing joint system (inherent anisotropy), the theory presented herein accounts for the possibility of formation of new joints at a new orientation (induced anisotropy). An approximate procedure to compute support pressure, in order to prevent slip along discontinuities is presented. Several results are given to illustrate the special features of the HB criterion, in particular the ability to account for the brokenness of the medium.

A viscoplastic model for soft rock

The aim of the model is to represent the main features of soft or brittle rock strata, using a small number of physically‐meaningful material parameters. The yield surface is based on either the Mohr—Coulomb or Hoek—Brown criterion, and a simple small‐dilation flow rule allows the implicit algorithm of elasto‐viscoplasticity to be used. Elastic—brittle plastic behaviour is modelled, resulting in stress discontinuities across the interface between intact and failed rock. The effects of lamination and jointing are taken into account. Results are presented for a tunnelling problem with axial symmetry.