Academic literature on the topic 'Generalized Hoek-Brown criterion'

This paper presents a further modification of the generalized three-dimensional (3D) Hoek-Brown criterion - the GZZ (generalized 3D Zhang-Zhu) criterion. Specifically, a modification was made by introducing a 3D version of effective mean stress to replace the original 2D version of effective mean stress in the GZZ criterion. The modification overcomes the non-smoothness and non-convexity problems of the GZZ criterion and maintains a simple form of the criterion expression. The modified GZZ criterion can also reduce to the two-dimensional (2D) Hoek-Brown criterion under both triaxial compression and extension conditions and thus inherits the advantages of and uses the same parameters as the Hoek-Brown criterion. Eleven sets of true triaxial test data were collected from publications to evaluate the newly modified GZZ criterion. The results indicate that the newly modified GZZ criterion has the highest or at least the same accuracy for strength prediction among the various 3D versions of the Hoek-Brown criterion that can reduce to the Hoek-Brown criterion and are smooth and convex. Moreover, of the various 3D versions of the Hoek-Brown criterion that can reduce to the Hoek-Brown criterion and are smooth and convex, only the newly modified GZZ criterion can be expressed explicitly.

In order to investigate the influence of the intermediate principal stress on the stress and displacement of surrounding rock, a novel approach based on 3D Hoek-Brown (H-B) failure criterion was proposed. Taking the strain-softening characteristic of rock mass into account, the potential plastic zone is subdivided into a finite number of concentric annulus and a numerical procedure for calculating the stress and displacement of each annulus was presented. Strains were obtained based on the nonassociated and associated flow rule and 3D plastic potential function. Stresses were achieved by the stress equilibrium equation and generalized Hoek-Brown failure criterion. Using the proposed approach, we can get the solutions of the stress and displacement of the surrounding rock considering the intermediate principal stress. Moreover, the proposed approach was validated with the published results. Compared with the results based on generalized Hoek-Brown failure criterion, it is shown that the plastic radius calculated by 3D Hoek-Brown failure criterion is smaller than those solved by generalized H-B failure criterion, and the influences of dilatancy effect on the results based on the generalized H-B failure criterion are greater than those based on 3D H-B failure criterion. The displacements considering the nonassociated flow rule are smaller than those considering associated flow rules.

The strength of massive jointed rock mass can be estimated based on Mohr-Coulomb criterion and Hoek-Brown criterion without making expensive experiment of massive jointed rock mass in site. Only using regression analysis, through transformation，Mohr-Coulomb criterion is compared with Hoek-Brown criterion, the strength of jointed rock mass can be economically obtained. In this paper, based on Geological Strength Index GSI and parameter Jv(Joint/m3), the strength of massive jointed rock mass can be obtained. As an example of GSI 24 for massive jointed rock mass is taken, generalized Hoek-Brown criterion is analyzed linearly and approximately using regression analysis, strength of jointed rock mass can be economically obtained That provide economical and effective method for practical engineering analysis

An analytical approach for the estimating of critical seismic acceleration of rock slopes was proposed in this study. Based on the 3D horn failure model, the critical seismic acceleration coefficient of rock slopes was conducted with the modified Hoek–Brown (MHB) failure criterion in the framework of upper-bound theory for the first time. The nonlinear Hoek–Brown failure criterion is incorporated into the three-dimensional rotational failure mechanism, and a generalized tangent technique is introduced and employed to convert the nonlinear Hoek–Brown failure criterion into a linear criterion. The critical seismic acceleration coefficients obtained from this study were validated by the numerical simulation results based on finite element limit analysis. The agreement showed that the proposed method is effective. Finally, design charts were provided for exceptional cases for practical use in rock engineering.

Generalized Hoek-Brown criterion is indicated as a dimensionless quantity, on this basis, elastic-plastic analytical method of circular underground chamber is presented based on generalized Hoek-Brown criterion in uniform stress field. Take into account a number of factors such as deep rock mass quality, rock strength, etc, surrounding rock mass plastic zone of deep underground chamber is analyzed by the analytical method. The results show that taking measures to improve the quality of rock mass can effectively control surrounding rock mass plastic zone for soft rock underground chamber, however, taking measures to improve the quality of rock mass can not appreciably control surrounding rock mass plastic zone for hard rock underground chamber.

Breakout is a shear failure due to compression that forms around the borehole due to stress concentration. In this paper, the breakout theory model is investigated by combining the equilibrium elasticity equations of stress around the borehole with two Hoek-Brown and Fairhurst generalized fracture criteria, both of which are based on the Griffith criterion. This theory model provides an explicit equation for the breakout failure width, but the depth of failure is obtained by solving a quartic equation. According to the results and in general, in situ stresses and rock strength characteristics are effective in developing the breakout failure area, As the ratio of in-situ stresses increases, the breakout area becomes deeper and wider. Because in the shear zone, the failure envelope of the Fairhurst criterion is lower than the Hoek-Brown failure criterion, the Fairhurst criterion provides more depth for breakout than the Hoek-Brown criterion. However, due to the same compressive strength of the rock in these two criteria, the same failure width for breakout is obtained from these two criteria. Also, the results obtained for the depth of failure from the theoretical model based on the Fairhurst criterion are in good agreement with the laboratory results on Westerly granite.

Design of rock slope is one of the major challenges at every stage of open pit mining operations. Providing an optimal excavation design based on a robust analysis in terms of safety, ore recovery and profit is the ultimate goal of any slope design. The rock slope stability is predominantly controlled by the strength and deformation of the rock mass which characteristically consists of intact rock materials and discontinuities. Initially, movement of the slope occurs due to stress relaxation as a result of removal of rocks which used to provide confinement. This behavior of slope can be attributed to linear elastic deformation. In addition to this, sliding along discontinuity surfaces and dilation in consequence of formation of cracks can occur. Ultimately all these instabilities lead to failure of the slopes. Therefore, formulation of slope designs plays critical role in the process of slope stability. In conventional approaches for assessing the stability of a homogeneous slope, such as the limit equilibrium method (LEM) and shear strength reduction (SSR) method, rock mass strength is usually expressed by the linear Mohr-Coulomb (MC) criterion. However, rock mass strength is a non-linear stress function. Therefore, the linear MC criterion generally do not agree with the rock mass failure envelope, especially for slope stability problems where the rock mass is in a state of low confining stresses that make the nonlinearity more dominant. With the aim of better understanding the fundamental rock slope failure mechanisms and improving the accuracy of the rock slope stability results, this research focuses on the application of the Hoek-Brown (HB) criterion, which can ideally represent the non-linear behavior of a rock mass, on the rock slope stability analysis. There, three major sections are available in the thesis. The first section, from Chapters 1 to 4, proposes new methods for estimating the intact rock and rock mass properties, which will be used for slope stability analysis. In the second section studied in Chapter 5, a new non-linear shear strength reduction technique is proposed for the analysis of three-dimensional (3D) slope modeling. In section three (Chapter 6), novel stability charts are proposed, which have the merit of estimating factor of safety (FOS) for a given slope directly from the HB parameters and rock mass properties. These charts can provide a quick and reliable assessment of rock slope stability. The major research contributions and outcomes of the overall researches are presented in six journal publications which are forming the thesis. The titles of Chapters 1 through 6 reflect the titles of the journal papers. In Chapter 1, laboratory tests conducted on Hawkesbury sandstone obtained from New South Wales are carried out to investigate the relationship between the HB constant mi and uniaxial compressive strength (UCS) of intact rock. Based on the analysis of the laboratory tests and the existing database, a new method that can estimate the HB constant mi values from UCS and rock types is proposed. The proposed method can reliably be used in the HB criterion for intact rock strength estimation when the triaxial tests are not available. In Chapter 2, an analytical solution for estimating the instantaneous MC shear strength from the HB failure criterion for highly fractured rock mass is presented. The proposed solution is based on the assumption that the HB parameter, s is equal to zero. The proposed solution has the merit of producing very accurate shear strength for highly fractured rock mass where the Geological Strength Index (GSI) is less than 40. In Chapter 3, an analytical solution, which can calculate the shear strength of rock masses accurately for the whole range GSI values, is proposed as an extension to the work in Chapter 2. The proposed approach is based on a symbolic regression analysis performed by genetic programming (GP). The proposed solution not only can be implemented into the LEM to calculate the instantaneous shear strength of each slice of a failure surface under a specified normal stress, but also can be implemented into finite element method performed by SSR approach to calculate the instantaneous shear strength of each element under different stress state of a slope. In Chapter 4, as a part of estimating rock mass strength and elastic properties in the first section, the most widely used empirical equations for the estimation of deformation modulus of rock masses (Em) are reviewed. Two simplified empirical equations for estimating of Em are also presented. The proposed empirical equations use the Rock Mass Rating classification system and the deformation modulus of intact rock (Ei) as input parameters. These equations can be used in the numerical modelling for slope stability analysis, which is conducted in Chapter 5. In Chapter 5, a new non-linear shear strength reduction technique is proposed to analysis the stability of 3D rock slopes satisfying the HB failure criterion. The method for estimating the instantaneous MC shear strength from the HB criterion described in Chapters 2 and 3 are used to estimate shear strength of elements in FLAC3D model. The proposed 3D slope model is used to analyse the influence of boundary condition on the calculation of FOS using 21 real open pit cases where the values of mi and Em values are calculated from the methods introduced in Chapters 1 and 4, respectively. Results show that the values of FOS for a given slope will be significantly influenced by the boundary condition, especially the case where the slope angle is less than 50°. In Chapter 6, extensive slope stability analyses using LEM are carried out. The calculation of FOS is based on estimating the instantaneous MC shear strength of slices of a slip surface from the HB criterion. Based on the analysis results, novel stability charts are proposed. The proposed charts are able to estimate the FOS for a given slope directly from the HB parameters, slope geometry and rock mass properties. It is suggested that the proposed chats can be used as useful tools for the preliminary rock slope stability assessment.
Thesis (Ph.D.) -- University of Adelaide, School of Civil, Environmental and Mining Engineering, 2013

博士
國立成功大學
資源工程學系碩博士班
95
The purpose of this study is to provide a new approach so that the deformation characters and non-linear strength properties of the geologic materials can be taken into account in a slope stability analysis method, which provides the answer of the minimum safety factor and the corresponding sliding plane. In other words, this method must uses a basic deformation method plus some additional function to calculate the safety factor and sliding planes just like the ordinary limit equilibrium method. This research uses the generalized Hoek-Brown failure criterion to define the non-linear strength property, and this failure criterion is incorporated in to the deformation analysis code, FLAC3D, by Fish. Two approaches are adapted to calculate the safety factor and sliding planes, the first one is so called “strength reduction method” and the second one is so called “dynamic programming method”. The basic idea of strength reduction method is to find the reduction ratio of the strength which produces the failure of the slope, then the safety factors can be calculated from the reduction ration, and the plastic zone at failure condition contains the sliding plane. The dynamic programming method, which is originated from operation research study, is to connect the grid points on the slopes with minimum passage (safety factor) to form the sliding plane, and the factor safety is calculated based on the stress and strength distribution of the slope, which is provided by the deformation method. The code of dynamic method is written by this research. After the completion of the computer codes, two published cases studies which are slopes with homogeneous materials are used to test the goodness of the computer codes, the result shows a very close answer, and the computer codes are accepted for further case studies. By comparison of the characteristics of dynamic programming and strength reduction methods, only the former method is adapted for further cases studies for its flexibility, convenience, and precise. Five more cases are studied. The first one is a homogeneous slope with heavy surcharge on its top, it shows the benefit of using non-linear strength criterion. The second case is a slope with two horizontal layers, the third case is a dip slope with a weathered layer, the fourth case is a dip slope with a soft inter-layer, and the fifth one is the third and fourth cases with a caped horizontal layer. These cases studies show that the adapted method can calculate the minimum safety factors of the complex geology slopes, and find the corresponding sliding planes. The merits of this approach combining dynamic programming method, non-linear strength criterion and deformation analysis are that (1) no more assumptions of slip surface are needed including the shape and locations (2) the safety factor and sliding planes of the slopes with complex geology, which are difficult to be analyzed by ordinary limit equilibrium method, can be easily done by this method. (3) the non-linear strength property of geologic materials are taken into account in this method.

ABSTRACT: The disturbance factor (D) is a parameter in the Generalized Hoek-Brown failure criterion for rock slopes in slope stability. It represents the subsurface damage to the rock material properties resulting from blasting and stress relaxation during excavations. Within the region of assumed damage, a number between zero (undisturbed) and unity (very disturbed) is prescribed as the value of the disturbance factor. Most commonly a uniform value of D is assumed within the entire region of damage, but little research has been done to study the impact of the variation in the D parameter on stability. Through use of an example, this paper examines the effect of various distribution functions of D through the damaged region, such namely, as constant, linearly varying, and exponentially varying. The failure surfaces and factors of safety for the slope as determined via limit equilibrium are also compared with finite element analyses. Varying the distribution of the damage function was found to significantly affect the failure surface and factor of safety. It is recommended that practitioners adopt care to select an appropriate distribution for slope stability analysis. 1. BACKGROUND The Generalized Hoek-Brown method (Hoek and Brown 2018) is widely used for determining rock mass strength in rock mechanics. One application of this method is in the design of open pits in rock masses which requires the evaluation of factor of safety against overall sliding. During excavation, subsurface damage can occur to the surrounding rock masses and cause fracturing. The damage can be caused by two sources: (a) blasting and (b) stress relaxation (Hoek et al. 2002), and can be quantified in the form of a disturbance factor, D, which ranges from a zero (undisturbed) to unity (disturbed) within the rock masses. For slope stability, the shear strength of the rock activated along the slip surface can be obtained by solving Eq. (1) to Eq. (4) (Hoek et al. 2018).