Hoek-Brown Media Research Articles

Seismic Bearing Capacity of Strip Footing Placed on Sand Layer Over Hoek–Brown Media using Finite Element Limit Analysis and Machine Learning Approach

Seismic Bearing Capacity of Strip Footing Placed on Sand Layer Over Hoek–Brown Media using Finite Element Limit Analysis and Machine Learning Approach

Three-dimensional face stability analysis of rock tunnels excavated in Hoek-Brown media with a novel multi-cone mechanism

In order to give a more accurate prediction of the required face pressure, this work revisits the three-dimensional (3D) face stability problems of rock tunnels excavated in Hoek-Brown media. The Piecewise Linear Method (PLM) is introduced to account for the nonlinearity of the rock strength rather than the simple linear substitution for the strength envelope. A novel multi-cone rotational mechanism consisting of n truncated curvilinear cones is generated respecting the plastic normality flow rule. Two typical linearized measures: Generalized Tangential Technique (GTT) and Equivalent Mohr-Coulomb parameters Method (EMM) are also included in this study for comparison and analysis. In terms of the energy-work balance equation, the required face pressure is formulated as an optimization problem depending on 2n variables and is resolved by a recently-proposed Marine Predators Algorithm (MPA). Parametric study implies that the solution of two-dimensional (2D) analysis is very conservative, despite being safe in engineering, it is uneconomical compared with 3D analysis. In 3D analysis, the required face pressure predicted by PLM is significantly improved by 9 % compared with that of GTT, and the results calculated from EMM show a good consistency with PLM and GTT for heavily fractured rock mass, while for high-quality rock masses, the diversity between the results of EMM and other two methods is distinct. To further extend the application of such modified mechanism, design charts of the normalized face pressure are calculated for a quick assessment of face stability in rock masses with different quality.

Pseudodynamic Approach for Rock Slopes in Hoek–Brown Media: Three-Dimensional Perspective

Pseudodynamic Approach for Rock Slopes in Hoek–Brown Media: Three-Dimensional Perspective

A Pseudo-dynamic Approach for Seismic Stability Analysis of Rock Slopes in Hoek–Brown Media

A Pseudo-dynamic Approach for Seismic Stability Analysis of Rock Slopes in Hoek–Brown Media

Probabilistic analysis for face stability of tunnels in Hoek-Brown media

A modified model combining Kriging and Monte Carlo method (MC) is proposed for probabilistic estimation of tunnel face stability in this paper. In the model, a novel uniform design is adopted to train the Kriging, instead of the existing active learning function. It has advantage of avoiding addition of new training points iteratively, and greatly saves the computational time in model training. The kinematic approach of limit analysis is employed to define the deterministic computational model of face failure, in which the Hoek-Brown failure criterion is introduced to account for the nonlinear behaviors of rock mass. The trained Kriging is used as a surrogate model to perform MC with dramatic reduction of calls to actual limit state function. The parameters in Hoek-Brown failure criterion are considered as random variables in the analysis. The failure probability is estimated by direct MC to test the accuracy and efficiency of the proposed probabilistic model. The influences of uncertainty level, correlation relationship and distribution type of random variables are further discussed using the proposed approach. In summary, the probabilistic model is an accurate and economical alternative to perform probabilistic stability analysis of tunnel face excavated in spatially random Hoek- Brown media.

Seismic stability analysis and charts of a 3D rock slope in Hoek–Brown media

Earthquakes act as a dominant trigger for failure of slopes in seismic active regions. In this study, a seismic stability analysis of a three-dimensional (3D) rock slope in Hoek–Brown media is conducted based on the limit analysis method. The energy balance equation is derived by equating the external work rate by rock mass weight and seismic forces to the internal energy dissipation rate, and an optimization code is then programmed to capture the optimized factor of safety (FoS) of a 3D rock slope based on the strength reduction technique. The validity of the equivalent Mohr–Coulomb parameters method and generalized tangent technique in conjunction with the limit analysis method to estimate FoS of a 3D rock slope is investigated. Subsequently, a quasi-static method is used to explore the effect of seismic forces on stability of a 3D rock slope. The results of the parametric analysis indicate that the seismic force exhibits significant negative effects on the stability of a 3D slope and that a significant difference exists between a 3D FoS solution and a solution obtained under two-dimensional (2D) plane strain. A stability chart analysis is performed to produce a set of seismic stability charts for preliminary design purposes. Finally, a case study is performed to apply stability charts in practical situations.

A methodology for lining design of circular mine shafts in different rock masses

In this study, the finite element numerical modelling of 2D shaft sections in a Hoek–Brown medium are carried out in a non-hydrostatic stress state in an attempt to predict pressures developing around mine shafts. An iterative process of applying support pressure until observing no failure zone around the shaft is used to simulate the required lining support pressure for different shaft models. Later, regression analysis is carried out to find a generic shaft pressure equation representing the rock mass and the stress state. Finally, the developed pressure equation which shows a good agreement with a case study is used in elastic “thick-walled cylinder” equation to calculate the lining thickness required to prevent the development of a failure zone around the shaft. At the end of the study, a user-friendly object-oriented computer program “Shaft 2D” is developed to simplify the rigorous shaft lining thickness calculation process.

Effect of seepage forces on circular openings excavated in Hoek–Brown rock mass based on a generalised effective stress principle

When an opening is excavated below groundwater table, the groundwater flows into the excavated zone and seepage forces apply to the rock mass surrounding the opening. Such seepage forces significantly affect the elasto-plastic responses of the rock mass based on effective stress law. In this regard, it is recognised that the failure criterion of a rock mass is a function of Terzaghi’s effective stress, while its elastic deformations are a function of Biot’s effective stress. Based on this generalised effective stress law, seepage forces arising from the groundwater flow into a cylindrical opening are estimated quantitatively, in the present study. An elastic–brittle–plastic analysis of deep circular openings in an infinite Hoek–Brown medium with consideration of the seepage forces under steady-state flow and the generalised effective stress law is derived. The proposed solution can be effectively used for the actual design of underwater openings below deep groundwater table. It is shown that, in openings below deep groundwater tables, the effect of seepage and pore pressure, and consequently, the effective stress law on mechanical analysis may be significant.

Influence of pore water pressure on upper bound analysis of collapse shape for square tunnel in Hoek-Brown media

To investigate the effective shape of collapsing block in square tunnel subjected to pore water pressure, the analytical solution of detaching curve was derived using upper bound theorem of limit analysis with Hoek-Brown failure criterion. The work rate of pore water pressure, which was regarded as an external rate of work, was taken into account in the framework of limit analysis. Taking advantages of variational calculation, the objective function with respect to detaching curve was optimized to obtain the effective shape of collapsing block for square tunnel. According to the numerical results, it is found that the varying pore water pressure coefficient only affects the height and width of the collapsing block, whereas the shape of collapsing block remains unchanged.

Elasto‐plastic analytical model for the design of grouted bolts in a Hoek–Brown medium

AbstractThis paper presents an elasto‐plastic analytical solution of an axi‐symmetrical problem for a circular tunnel reinforced by grouted bolts. Considered as the improved model of Indraratna and Kaiser (Int. J. Rock. Mech. Min. Sci. Geomech. Abstr. 1990; 27:269–281; Int. J. Numer. Anal. Meth. Geomech. 1990; 14:227–251), in proposed solution the rock mass obeys the non‐linear Hoek–Brown yield criterion (version 2002) in terms of its peak and residual strength parameters (the most spread strength criterion for the rock masses). The proposed approach considers a⩾0.5 for the rock mass and is based on the assumption that after the peak strength of the rock is reached, the material loses its strength, as dictated by a strength loss parameter. The strength loss parameter makes it possible to model either elastic–perfectly plastic or elastic–brittle–plastic behaviour. Because of the mathematical complexity, numerical treatments have been used to assist the solution in order to evaluate the equilibrium and compatibility equations. The concept of equivalent material for Hoek–Brown strength parameters is introduced to describe the rock mass improvement due to bolting effect. The results of the numerical analyses reveal a linear relation between the improved Hoek–Brown strength parameters and residual ones, taking into consideration the bolt density parameter (β). The proposed solution is able to analyse the stress and displacement state in the presence of a bolting intervention with the objective of improving the degree of stability of the rock around the tunnel. Descriptive applications of the derived elasto‐plastic solutions are also presented to explain the effectiveness of the grouted bolts in convergence reduction. Evidences obtained by numerical analysis verify the analytical solution. Copyright © 2009 John Wiley & Sons, Ltd.

Elastic–brittle–plastic analysis of circular openings in Hoek–Brown media

Abstract A closed-form solution is presented in this paper for the prediction of displacements around circular openings in a brittle rock mass subject to a hydrostatic stress field. The rock mass is assumed to be governed by Hoek–Brown yield criterion and a non-associated flow rule is used. For the elastic–brittle–plastic analysis of circular openings in an infinite Hoek–Brown medium, the existing analytical solutions were found to be incorrect. The present closed-form solution is based on a theoretically consistent method and the solution does not require the use of any numerical method. The present closed-form solution was validated by using the finite element method. In the finite element analysis, the infinite boundary was simulated “exactly” by using the newly developed elastic support method. Several cases were analyzed and the present closed-form solutions for stresses and displacements were found to be in an excellent agreement with those obtained by using the finite element method.

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.

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

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