Search Results (12)

In deep, geologically complex environments characterized by high in situ stress and elevated formation temperatures, the mechanical behavior of rocks often transitions from brittle to ductile, differing significantly from that of shallow formations. Traditional rock failure criteria frequently fail to accurately assess the strength of rocks under such deep conditions. To address this, a novel failure criterion suitable for high-temperature and high-pressure conditions has been developed by modifying the Mohr–Coulomb criterion. This criterion incorporates a quadratic function of confining pressure to account for the attenuation rate of strength increase under high confining pressure and a linear function of temperature to reflect the linear degradation of strength at elevated temperatures. This criterion has been used to predict the strength of granite, shale, and carbonate rocks, yielding results that align well with the experimental data. The average coefficient of determination (R²) reached 97.1%, and the mean relative error (MRE) was 5.25%. Compared with the Hoek–Brown and Bieniawski criteria, the criterion proposed in this study more accurately captures the strength characteristics of rocks under high-temperature and high-pressure conditions, with a prediction accuracy improvement of 1.70–4.09%, showing the best performance in the case of carbonate rock. A sensitivity analysis of the criterion parameters n and B revealed notable differences in how various rock types respond to these parameters. Among the three rock types studied, granite exhibited the lowest sensitivity to both parameters, indicating the highest stability in the prediction results. Additionally, the predictive outcomes were generally more sensitive to changes in parameter B than in n. These findings contribute to a deeper understanding of rock mechanical behavior under extreme conditions and offer valuable theoretical support for drilling, completion, and stimulation operations in deep hydrocarbon reservoirs. Full article

Slate typically possesses a pronounced layered structure and tends to soften when exposed to water, leading to numerous detrimental effects on the construction of related underground projects. In this study, X-ray diffraction (XRD) analysis was first performed to investigate the mineral composition of the typical slate from Changsha, China. Then, uniaxial and triaxial compression tests under varying bedding angles (i.e., 0°, 30°, 45°, 60°, and 90°) and moisture levels (i.e., dry state, natural state, and saturated state) were conducted to explore the anisotropy characteristics and susceptibility to water-induced softening of the slate. The results reveal that: (1) The exposure of slate to water exacerbates the deterioration of its layered structure, making it more prone to shear failure along the bedding planes. Furthermore, the energy released during shear-slip damage is reduced, which is macroscopically manifested by the decrease in slate brittleness and the increase in plasticity. (2) The slate’s compressive strength, elastic modulus, and cohesion vary in a U-shaped pattern with the increase in bedding angles. However, Poisson’s ratio and internal friction angle are slightly affected by the bedding angle and water content, which do not exhibit a clear variation pattern. (3) In addition, the formulations for strength and stiffness predictions of slate were also discussed in this study. The results show that the modified Hoek–Brown criterion characterizes the uniaxial and triaxial compressive strengths of slate more accurately, and the generalized Hooke’s Law more effectively predicts the elastic modulus. Full article

The present study performs a stability analysis of a three-dimensional (3D) rock slope in disturbed rock masses following the Generalized Hoek–Brown (GHB) failure criterion. The factor of safety (FoS) of the slope is derived and the optimal solution is captured combining the limit analysis method and the strength reduction technique. It is indicated by the parametric analysis that the 3D geometric characteristics have a significant impact on slope stability such that FoS decreases sharply with the increase in the width-to-height ratio $B/H$ within $0<B/H\le 2.0$ and thereafter reaches a constant value asymptotically. The FoS decreases more than 60% linearly when the disturbance factor D increases from 0 to 1.0. Stability charts and slope angle weight factor f_{β_3D} for 3D slopes are proposed to provide a convenient and straightforward approach to obtain the FoS solutions of 3D slopes. A case study was carried out to apply the stability charts on practical engineering cases, which showed that slope stability under two-dimensional (2D) plane strain will lead to conservative results, and a 3D stability analysis of slope is more appropriate, especially for a slope with a limited width. Full article

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. Full article

The direct application of the Hoek–Brown failure criterion to practical slope engineering is still an urgent problem. The slope geometries and earthquake effect need to be considered in the determination of linear Mohr–Coulomb (MC) strength parameters from the Hoek–Brown criteria for slope stability analysis. This study adopted the tangential method to construct a three-dimensional (3D) rotational failure mechanism using the Hoek–Brown failure criterion for homogeneous rock slopes undergoing earthquake. The quasi-static method was employed to treat the seismic action as an external seismic force in the work–energy equation of the limit analysis theory. Based on the numerical optimization, the least upper-bound solutions and equivalent MC strength parameters were derived with respect to different strength parameters and seismic loads. The influences of nonlinear strengths, geometric parameters and earthquake load on the equivalent MC strength parameters were thoroughly investigated. The results suggested that the nonlinear parameters have different influences on the equivalent MC parameters for general steep slopes and vertical slopes. The effects of nonlinear parameters on the equivalent MC parameters become obvious for vertical slopes. The disturbance factor D affects the equivalent MC parameters only for very steep slopes in fractured rock masses. Additionally, the effect of slope inclination on the equivalent MC parameters becomes obvious for slopes in fractured hard rock masses. The 3D effect of the rock slope on the equivalent MC parameters was found to be slight. Moreover, the impact of earthquakes on the approximate MC parameters becomes weaker for steeper rock slopes. The tables of approximate MC strength parameters were given for various slopes with different nonlinear strength parameters. The presented tables can provide certain references for practical slope engineering. Full article

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. Full article

The kinematic method of limit analysis theory was adopted in this paper to calculate the seismic bearing capacity of the shallow strip foundation on a rock mass obeying the non-linear modified Hoek-Brown failure criterion. The generalized Prandtl failure mechanism was chosen, which is different from the multi-wedge failure mechanism assumption commonly used in previous research. Three angle parameters were used to control the mechanism shapes, and the equivalent friction angle and equivalent cohesive were adopted to faithfully reflect the shape characteristics of the failure mechanism. The seismic action was considered using the pseudo-static method, which is simplified to the inertial force determined by the horizontal seismic coefficient. The validation of the present method was carried out by comparing with previous analytical results and the finite element model. Subsequently, the influences of the surface overload, the properties of the rock mass, and the seismic action on the shape and ultimate bearing capacity of the failure mechanism were investigated. For the convenience of practical engineering, this paper gives the ultimate bearing capacity of strip foundations on five representative rock foundations, and the variation trend of bearing capacity with the unit weight of rock mass, surface overload, and horizontal seismic coefficient. Full article

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 $a\ne 0.5$ 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. Full article

The generalized Hoek-Brown (GHB) failure criterion can estimate the rock mass parameters required for rock mechanics–related analyses such as numerical modeling in geomechanics. The determination of GHB parameters has been developed in the field of rock mechanics. Due to the wide use of the Mohr-Coulomb criterion and the lack of an existing relationship for determining its parameters for a rock mass, equivalent Mohr-Coulomb parameters (EMC) can be derived from the GHB. To determine the differences in the use of these two criteria, we analyzed the behavior of a deep circular tunnel in nine stress states for three metamorphic rocks recovered from the Canadian Shield from rock masses that present a very blocky structure. We carried out 241 simulations using the finite element code RS2 to assess the effect of the geological strength index (GSI), in situ stress, and rock type on the deviation of wall displacement, the number of yielded elements, and the differential stress obtained by the GHB and EMC parameters. A combination of low in situ stress and high GSI yielded similar results when using both failure criteria. Full article

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. Full article

Rock failure during tunnel excavation is still a matter of concern. The influence of groundwater is generally taken into account along discontinuities or in “soil-like” formations. However, brittle saturated porous rocks can be subject to undrained conditions during tunnel excavation. Negative effective stresses develop close to the tunnel boundary. This study aims at identifying a limit pore pressure in the rock around the tunnel, which induces failure in the tension zone. A discussion related to the strength parameters in the tension zone, with the Hoek and Brown criterion, is presented. A comparative analysis with different far-field stresses and rock properties indicates that the limit pore pressure decreases with the depth of the tunnel. The limit pore pressure is directly proportional to the uniaxial compressive strength and inversely proportional to the constant m. When the uniaxial compressive strength is close to the state of stress around the tunnel, the role of m reduces. Numerical models set up with FLAC indicate that the tension zone around the tunnel has a thickness of about 1 m. Due to uncertainties in the far-field stresses, hydro-mechanical behavior, and properties of the rock, the tension zone requires a careful investigation, in order to avoid stability problems. Full article

Serious borehole instability problems are often related to the presence of weakness planes in rock formations. In this study, we investigated the stability of wellbores drilled along a principal direction and parallel to the weakness planes. We used three different strength criteria (weakness plane model, Hoek and Brown and Nova and Zaninetti) to calculate the mud pressures to avoid slip and tensile failure along the weakness planes. We identified the orientation of the weakness planes that generate the most critical slip condition as a function of the friction angle of the planes. We also identified the range of orientations of the weakness planes that corresponds with the lower mud pressure window. We confirmed the validity of the proposed relationships with comparative stability analyses by using analytical solutions and numerical simulations (Ubiquitous Joint Model, FLAC). We found that the mud pressures calculated with the Hoek and Brown criterion show a particular trend, which cannot be predicted by the weakness plane model. We provided two normalized stability charts to predict mud pressures to prevent slip along the weakness planes in the critical slip condition. Finally, we corroborated our findings by simulating the stability of wellbores drilled in the Pedernales Field (Venezuela) and in oil fields located in Bohai Bay (China). Full article