Applying rock mass classifications to carbonate rocks for engineering purposes with a new approach using the rock engineering system

Classical rock mass classification systems are not applicable to carbonate rocks, especially when these are affected by karst processes. Their applications to such settings could therefore result in outcomes not representative of the real stress–strain behavior. In this study, we propose a new classification of carbonate rock masses for engineering purposes, by adapting the rock engineering system (RES) method by Hudson for fractured and karstified rock masses, in order to highlight the problems of implementation of geomechanical models to carbonate rocks. This new approach allows a less rigid classification for carbonate rock masses, taking into account the local properties of the outcrops, the site conditions and the type of engineering work as well.     

Numerical study on failure mechanism of tunnel in jointed rock mass

During underground excavation many surrounding rock failures have close relationship with joints. The stability study on tunnel in jointed rock mass is of importance to rock engineering, especially tunneling and underground space development. In this paper, a numerical code called RFPA was used to study the influence of different dip angle of layered joints and the lateral pressure coefficient on the stability of tunnel in jointed rock mass. Numerical analysis indicated that both the dip angle of joints and the lateral pressure coefficient have significant impacts on the failure mode and displacement characters of tunnel. The progressive failure processes of tunnel in jointed rock mass were presented and the mechanisms were discussed. The applicable condition of geographical method by Goodman is also discussed. These results offer a guideline in support design.     

The external water pressure on a deep buried tunnel in fractured rock

Underground tunnels are increasingly built at greater burial depths for water conservancy and hydropower projects. The safety of these tunnels is threatened by high external water pressure during construction and reservoir operations. In this research, external water pressure was considered to be a relative incremental water pressure, instead of an absolute value: it thus depended on several factors, such as the excavation, lining, and grouting zone of tunnel. The calculation thereof was deduced. Also, a coupled model was used to calculate the external water pressure. This model incorporated a fractured network model (DFN) into an equivalent continuous medium model (ECM). The results showed that calculated hydraulic heads matched measured values when using the coupled model, rather than the continuous model, in the areas where fractures and fault zones were well-developed. Furthermore, external water pressures were predicted using the verified coupled model during the emptying and filling of diversion tunnels with water.     

Influence of blasting load directions on tunnel stability in fractured rock mass

Tunnels in fractured rock masses are typically damaged by dynamic disturbances from various directions. To investigate the influence of blasting load directions on the stability of a tunnel with a pre-crack nearby, blasting tests were conducted on the physical models of an external crack around a tunnel (ECT) in this study. Failure modes of the tunnels were analysed based on stress wave theory. The Riedel–Hiermaier–Thoma (RHT) material model was employed to perform the numerical simulations on ECT models. Stress distribution around the tunnels and final failure patterns of the tunnels were characterised. The results show that, under blasting loads, the pre-crack propagates and then new cracks initiates on the incident side of the tunnel. These cracks extend towards each other and eventually coalesce. Blasting load directions significantly influence the ultimate failure mode of the tunnel in the fractured rock masses. The new cracks on the shadow side of the tunnel appear at different positions when the blasting stress waves come from various directions. The results are meaningful to the analysis of tunnel stability and optimisation of the tunnel support scheme.     

Numerical simulation of the rock fragmentation process induced by indenters

Rock fragmentation processes induced by single and double indenters were examined by a numerical method. The simulated results reproduce the progressive process of rock fragmentation in indentation. Rock deforms elastically at the initial loading stage. Then tensile cracks are initiated around the two corners of the truncated indenter and propagate in the well-known conical Hertzian manner. The rocks immediately under the indenter are in a highly tri-axial stress state, and some of them fail in the ductile cataclastic mode with the stress satisfying the ductile failure surface of the double elliptic strength criterion. With the tensile cone cracks and ductile cataclastic failure releasing the confining pressure, the rocks under the indenter are compressed into failure and the crushed zone gradually comes into being. With increasing loading displacement, the re-compaction behaviour of the crushed zone occurs. Side cracks initiated from the crushed zone or bifurcated from cone cracks are driven by tensile stress associated with the crushed zone to propagate in a curvilinear path and finally intersect with the free surface to form chips. It is pointed out that the curvilinear path is caused by heterogeneity. The simulated force-penetration curve is in fact the indication of the propagation of cracks, the crushing of microstructural grains and the formation of chips. It is found that the confining pressure has an important influence on the indentation results. With decreasing confining pressure, there is a decrease in the indentation strength and a change in the rock failure process from the formation of rock chips to a vertically axially splitting failure. The simulated fragmentation process in the double indenter test reproduces the side cracks, which are induced by two indenters, propagate, interact and finally coalesce, chipping the rock between the indenters. The line spacing is an important factor that affects the fragmentation efficiency in multiple indenter tests. It is pointed out that simultaneous loading with multiple indenters with an appropriate line spacing seems to provide a possibility of forming larger rock chips, controlling the direction of subsurface cracks and consuming a minimum total specific energy. According to the simulated results, it is believed that the numerical simulation method will contribute to an improved knowledge of rock fragmentation in indentation, which will in turn help to enhance mining and drilling efficiency through the improved design of mining tools and equipment.     

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.     

Overhanging rock slope by design: An integrated approach using rock mass strength characterisation,large-scale numerical modelling and limit equilibrium methods

Overhanging rock slopes(steeper than 90°) are typically avoided in rock engineering design, particularly where the scale of the slope exceeds the scale of fracturing present in the rock mass. This paper highlights an integrated approach of designing overhanging rock slopes where the relative dimensions of the slope exceed the scale of fracturing and the rock mass failure needs to be considered rather than kinematic release of individual blocks. The key to the method is a simplified limit equilibrium(LE) tool that was used for the support design and analysis of a multi-faceted overhanging rock slope. The overhanging slopes required complex geometries with constantly changing orientations. The overhanging rock varied in height from 30 m to 66 m. Geomechanical modelling combined with discrete fracture network(DFN)representation of the rock mass was used to validate the rock mass strength assumptions and the failure mechanism assumed in the LE model. The advantage of the simplified LE method is that buttress and support design iterations(along with sensitivity analysis of design parameters) can be completed for various cross-sections along the proposed overhanging rock sections in an efficient manner, compared to the more time-intensive, sophisticated methods that were used for the initial validation. The method described presents the development of this design tool and assumptions made for a specific overhanging rock slope design. Other locations will have different geological conditions that can control the potential behaviour of rock slopes, however, the approach presented can be applied as a general guiding design principle for overhanging rock cut slope.     

Experimental study of the hydro-mechanical behavior of rock joints using a parallel-plate model containing contact areas and artificial fractures

In recent years, geological disposal of radioactive wastes is considered to be the most promising option, which requires the understanding of the coupled mechanical, hydraulic and thermal properties of the host rock masses and rock fractures. The hydro-mechanical behavior and properties of rock fractures are usually determined by laboratory experiments on fracture specimens that serve as the basic building block of the constitutive models of fractured rock masses.Laboratory testing of rock fractures involve a number of technical issues that may have significant impacts on the reliability and applicability of the testing results, chief among them are the quantitative estimation of the evolutions of hydraulic transmissivity fields of fractures during shear under different normal constraint conditions, and the sealing techniques when fluid flow during shear is involved. In this study, a new shear-flow testing apparatus with specially designed fluid sealing techniques for rock fractures were developed, under constant normal load (CNL) or constant normal stiffness (CNS) constraint. The topographical data of all fracture specimens were measured before testing to constitute the geometrical models for simulating the change of mechanical aperture distributions during shearing. A number of shear-flow coupling tests were carried out on three kinds of rock fracture specimens to evaluate the influence of morphological properties of rock fractures on their hydro-mechanical behaviour. Some empirical relations were proposed to evaluate the effects of contact area and surface roughness on the behavior of fluid flow through rock fractures.     

Real-time prediction of rock mass classification based on TBM operation big data and stacking technique of ensemble learning

Real-time prediction of the rock mass class in front of the tunnel face is essential for the adaptive adjustment of tunnel boring machines(TBMs).During the TBM tunnelling process,a large number of operation data are generated,reflecting the interaction between the TBM system and surrounding rock,and these data can be used to evaluate the rock mass quality.This study proposed a stacking ensemble classifier for the real-time prediction of the rock mass classification using TBM operation data.Based on the Songhua River water conveyance project,a total of 7538 TBM tunnelling cycles and the corresponding rock mass classes are obtained after data preprocessing.Then,through the tree-based feature selection method,10 key TBM operation parameters are selected,and the mean values of the 10 selected features in the stable phase after removing outliers are calculated as the inputs of classifiers.The preprocessed data are randomly divided into the training set(90%)and test set(10%)using simple random sampling.Besides stacking ensemble classifier,seven individual classifiers are established as the comparison.These classifiers include support vector machine(SVM),k-nearest neighbors(KNN),random forest(RF),gradient boosting decision tree(GBDT),decision tree(DT),logistic regression(LR)and multilayer perceptron(MLP),where the hyper-parameters of each classifier are optimised using the grid search method.The prediction results show that the stacking ensemble classifier has a better performance than individual classifiers,and it shows a more powerful learning and generalisation ability for small and imbalanced samples.Additionally,a relative balance training set is obtained by the synthetic minority oversampling technique(SMOTE),and the influence of sample imbalance on the prediction performance is discussed.     

Influence of geometry and material properties on the axial vibration of a rock bolt

A continuous dynamic model for the axial vibration of a rock bolt system is presented. The model comprises three sections: the fixed length, bonded into the rock, the free length, which is not coupled to the rock, and the protruding length, which extends beyond the rock. The head assembly is modelled as a discrete mass and a spring, and a further discrete mass is included, representing a testing device that can be attached to the protruding end. Each section is modelled as a continuous elastic rod governed by the wave equation, with suitable compatibility conditions applied between the sections and boundary conditions, which also account for the effect of the discrete components, applied at the ends. Solutions in non-dimensional form are substituted into the boundary conditions to allow the natural frequencies to be calculated, and it is shown that two possible solutions for the mode shapes can be used for the fixed length—an exponential solution or the classical sinusoidal solution—depending on the stiffness of the grout relative to that of the bar. The conditions for which the two solutions are valid are developed, and changes in the frequency ratio with changes in length ratio, and the stiffness ratios of the grout and the anchor head relative to the stiffness of the fixed length of the anchorage are examined. Generally, the state of a bolt after installation is unknown and this does not provide proper assurance of the safety of the structure for which the bolts are used. The model provides a viable tool for helping to assess the condition of the bolt by using the natural frequencies associated with areas of the bolt of particular interest, e.g. the free length. The results show how the changes in the stiffness and/or length ratios affect the dynamics associated with fixed length of the bolt and the quality of the bonding installation. A case study is presented showing how the model can be used effectively to interpret real data.     

GPGPU-parallelised hybrid finite-discrete element modelling of rock chipping and fragmentation process in mechanical cutting

Mechanical cutting provides one of the most flexible and environmentally friendly excavation methods.It has attracted numerous efforts to model the rock chipping and fragmentation process,especially using the explicit finite element method(FEM) and bonded particle model(BPM),in order to improve cutting efficiency.This study investigates the application of a general-purpose graphic-processing-unit parallelised hybrid finite-discrete element method(FDEM) which enjoys the advantages of both explicit FEM and BPM,in modelling the rock chipping and fragmentation process in the rock scratch test of mechanical rock cutting.The input parameters of FDEM are determined through a calibration procedure of modelling conventional Brazilian tensile and uniaxial compressive tests of limestone,A series of scratch tests with various cutting velocities,cutter rake angles and cutting depths is then modelled using FDEM with calibrated input parameters.A few cycles of cutter/rock interactions,including their engagement and detachment process,are modelled for each case,which is conducted for the first time to the best knowledge of the authors,thanks to the general purpose graphic processing units(GPGPU) parallelisation.The failure mechanism,cutting force,chipping morphology and effect of various factors on them are discussed on the basis of the modelled results.Finally,it is concluded that GPGPU-parallelised FDEM provides a powerful tool to further study rock cutting and improve cutting efficiencies since it can explicitly capture different fracture mechanisms contributing to the rock chipping as well as chip formation and the separation process in mechanical cutting.Moreover,it is concluded that chipping is mostly owed to the mix-mode Ⅰ-Ⅱ fracture in all cases although mode Ⅱ cracks and mode Ⅰ cracks are the dominant failures in rock cutting with shallow and deep cutting depths,respectively.The chip morphology is found to be a function of cutter velocdty,cutting depth and cutter rake angle.     

Effect of rock mechanical properties on electromagnetic radiation mechanism of rock fracturing

The influence of rock mechanical properties on the electromagnetic radiation(EMR) mechanism of rock fracturing is an important research topic in solid mechanics and earthquake prediction.In this study,an EMR model of rock fracturing considering the fracture factor,elastic modulus,Poisson's ratio,radiation distance and crack length is derived based on the Hertz oscillator array assumption.An experimental system,including an electromagnetic shielding module,an EMR signal induction and transmission module,a signal recording module and a loading module,is developed to understand the EMR characteristics of four different rocks.The validity of the EMR theoretical model is verified and the relationships between the rock cracking morphology and the EMR waveform,amplitude and frequency are revealed.It is found that rock mechanical properties have obvious influences on the EMR waveform,amplitude and frequency during rock fracturing.This study provides a better understanding on the EMR mechanism of rock fracturing and can help to improve the accuracy of rock disaster prediction based on EMR.     

Numerical modeling of thermally-induced fractures in a large rock salt mass

Numerical modeling of thermally-induced fractures is a concern for many geo-structures including deep underground energy storage caverns. In this paper, we present the numerical simulation of a large-scale cooling experiment performed in an underground rock salt mine. The theory of fracture mechanics was embedded in the extended finite element code used. The results provide reliable information on fracture location and fracture geometry. Moreover, the timing of the fracture onset, as well as the stress redistribution due to fracture propagation, is highlighted. The conclusions of this numerical approach can be used to improve the design of rock salt caverns in order to guarantee their integrity in terms of both their tightness and stability.     

Experimental and numerical study of the geometrical and hydraulic characteristics of a single rock fracture during shear

Coupled shear-flow tests were conducted on two artificial rock fractures with natural rock fracture characteristics under constant normal loading boundary conditions. Numerical simulations using the 3-D Navier–Stokes equations taking account of the inertial effects of fluid were conducted using the void space geometry models obtained from the coupled shear-flow tests. The test and numerical simulation results show that the evolutions of geometrical and hydraulic characteristics of rock fracture exhibit a three-stage behavior. Transmissivity of a certain void space geometry within a fracture is related to the Reynolds number of fluid flow due to the inertial effects of fluid, which can be represented by the Navier–Stokes equations, but cannot be represented by some simplified equations, such as the cubic law, the Reynolds equation or the Stokes equations. The mechanical aperture is usually larger than the hydraulic aperture back-calculated from measured flow rate, and the difference between them is found strongly related to the geometrical characteristics of the fractures. A mathematical equation is proposed to describe the relation between hydraulic aperture and mechanical aperture by means of the ratio of the standard deviation of local mechanical aperture to its mean value, the standard deviation of local slope of fracture surface and Reynolds number.     

A state-of-the-art review of automated extraction of rock mass discontinuity characteristics using three-dimensional surface models

In the last two decades, significant research has been conducted in the field of automated extraction of rock mass discontinuity characteristics from three-dimensional (3D) models. This provides several methodologies for acquiring discontinuity measurements from 3D models, such as point clouds generated using laser scanning or photogrammetry. However, even with numerous automated and semi-automated methods presented in the literature, there is not one single method that can automatically characterize discontinuities accurately in a minimum of time. In this paper, we critically review all the existing methods proposed in the literature for the extraction of discontinuity characteristics such as joint sets and orientations, persistence, joint spacing, roughness and block size using point clouds, digital elevation maps, or meshes. As a result of this review, we identify the strengths and drawbacks of each method used for extracting those characteristics. We found that the approaches based on voxels and region growing are superior in extracting joint planes from 3D point clouds. Normal tensor voting with trace growth algorithm is a robust method for measuring joint trace length from 3D meshes. Spacing is estimated by calculating the perpendicular distance between joint planes. Several independent roughness indices are presented to quantify roughness from 3D surface models, but there is a need to incorporate these indices into automated methodologies. There is a lack of efficient algorithms for direct computation of block size from 3D rock mass surface models.     

Reliability analysis of tunnels using a metamodeling technique based on augmented radial basis functions

Metamodeling techniques have been developed and used for years in engineering reliability analysis involving expensive response simulations. In practical tunnel engineering problems where finite element (FE) simulations are required, the limited state/performance functions are in general implicit and nonlinear, and it is difficult to apply traditional gradient-based or sampling-based reliability methods, especially for large-scale problems. There is a need to develop accurate and efficient metamodels for practical tunnel engineering applications. In this paper, a metamodeling technique for reliability analysis of tunnels was studied based on augmented radial basis functions (RBFs). With a relatively small size of samples, the RBFs were used to create accurate approximate functions for different types of responses including linear and higher-order nonlinear functions. With the RBF-based metamodel constructed to express a limit state/performance function, Monte Carlo simulations (MCS) were applied to evaluate failure probability. The failure probability and reliability index obtained using the RBF-based metamodeling method were found to have good accuracy with a reasonable number of sample points. The reliability analyses of two existing tunnel examples showed that the augmented RBF metamodeling approach was efficient and effective for tunnel engineering problems.     

Effects of confinement on rock mass modulus: A synthetic rock mass modelling (SRM) study

The main objective of this paper is to examine the influence of the applied confining stress on the rock mass modulus of moderately jointed rocks (well interlocked undisturbed rock mass with blocks formed by three or less intersecting joints). A synthetic rock mass modelling (SRM) approach is employed to determine the mechanical properties of the rock mass. In this approach, the intact body of rock is represented by the discrete element method (DEM)-Voronoi grains with the ability of simulating the initiation and propagation of microcracks within the intact part of the model. The geometry of the pre-existing joints is generated by employing discrete fracture network (DFN) modelling based on field joint data collected from the Brockville Tunnel using LiDAR scanning. The geometrical characteristics of the simulated joints at a representative sample size are first validated against the field data, and then used to measure the rock quality designation (RQD), joint spacing, areal fracture intensity (P₂₁), and block volumes. These geometrical quantities are used to quantitatively determine a representative range of the geological strength index (GSI). The results show that estimating the GSI using the RQD tends to make a closer estimate of the degree of blockiness that leads to GSI values corresponding to those obtained from direct visual observations of the rock mass conditions in the field. The use of joint spacing and block volume in order to quantify the GSI value range for the studied rock mass suggests a lower range compared to that evaluated in situ. Based on numerical modelling results and laboratory data of rock testing reported in the literature, a semi-empirical equation is proposed that relates the rock mass modulus to confinement as a function of the areal fracture intensity and joint stiffness.     

Poroelastic solution of a wellbore in a swelling rock with non-hydrostatic stress field

The stress distribution around a circular borehole has been studied extensively. The existing analytical poroelastic solutions, however, often neglect the complex interactions between the solid and fluid that can significantly affect the stress solution. This is important in unconventional gas reservoirs such as coalbeds and shale formations. In order to address this limitation, this paper presents the development of a poroelastic solution that takes into account the effect of gas sorption-induced strain. The solution considers drainage of the reservoir fluid through a vertical wellbore in an isotropic, homogenous, poroelastic rock with non-hydrostatic in situ stress field. The sorption-induced shrinkage of coal is modelled using a Langmuir-type curve which relates the volumetric change to the gas pressure. The redistributed stress field around the wellbore after depletion is found by applying Biot's definition of effective stress and Airey's stress functions, which leads to a solution of the inhomogeneous Biharmonic equation. Two sets of boundary conditions were considered in order to simulate the unsupported cavity (open-hole) and supported cavity (lined-hole) cases. The implementation was verified against a numerical solution for both open-hole and lined-hole cases. A comparative study was then conducted to show the significance of the sorption-induced shrinkage in the stress distribution. Finally, a parametric study analysed the sensitivity of the solution to different poroelastic parameters. The results demonstrate that the developed solution is a useful tool that can be employed alongside complex flow models in order to conduct efficient, field-scale coupled hydro-mechanical simulations, especially when the stress-dependent permeability of the reservoir is of concern.     

A numerical study of THM effects on the near-field safety of a hypothetical nuclear waste repository—BMT1 of the DECOVALEX III project. Part 3: Effects of THM coupling in sparsely fractured rocks

As a part of the international DECOVALEX III project, and the European BENCHPAR project, the impact of thermal–hydrological–mechanical (THM) couplings on the performance of a bentonite-back-filled nuclear waste repository in near-field crystalline rocks is evaluated in a Bench-Mark Test problem (BMT1) and the results are presented in a series of three companion papers in this issue. This is the third paper with focuses on the effects of THM processes at a repository located in a sparsely fractured rock. Several independent coupled THM analyses presented in this paper show that THM couplings have the most significant impact on the mechanical stress evolution, which is important for repository design, construction and post-closure monitoring considerations. The results show that the stress evolution in the bentonite-back-filled excavations and the surrounding rock depends on the post-closure evolution of both fields of temperature and fluid pressure. It is further shown that the time required to full resaturation may play an important role for the mechanical integrity of the repository drifts. In this sense, the presence of hydraulically conducting fractures in the near-field rock might actually improve the mechanical performance of the repository. Hydraulically conducting fractures in the near-field rocks enhances the water supply to the buffers/back-fills, which promotes a more timely process of resaturation and development of swelling pressures in the back-fill, thus provides timely confining stress and support to the rock walls. In one particular case simulated in this study, it was shown that failure in the drift walls could be prevented if the compressive stresses in back-fill were fully developed within 50 yr, which is when thermally induced rock strain begins to create high differential (failure-prone) stresses in the near-field rocks.