Discontinuous Joints Research Articles

Numerical characterization for rock mass integrating GSI/Hoek-Brown system and synthetic rock mass method

Rock mass characterization is a key issue to derive mechanical properties of jointed rock mass. In this research, the strength, modulus and post-peak behaviour of rock masses with varied joint orientations and confining stresses are characterized by integrating an empirical geological strength index (GSI)/Hoek-Brown system and a synthetic rock mass (SRM) numerical method. The SRM model is a 3D distinct element model supporting explicit simulation of discontinuous joints and crack propagation in the rock mass. The rock mass structure as denoted by a discrete fracture network is correlated to the GSI system through a quantitative factor of rock block size. The strength and modulus are then derived from the GSI/Hoek-Brown system and used as references for a series of synthetic rock mass models. A comparative study shows that when the predominant joints are steeply inclined in the rock mass subjected to axial loading, the empirical GSI/Hoek-Brown system provides reliable mechanical properties. When the joints are less favorable to shear sliding, the GSI/Hoek-Brown system underestimates the rock mass strength. Cracking characteristics are also investigated in selected SRM models, where few cracks are simulated when inclined joints are inserted in the rock mass and low confining stresses are applied. This research finally shows the method to construct continuum rock mass models using the numerical parameters of the SRM models. The numerical results suggest that the global failure zone is thin when the post-peak is elasto-brittle, and the failure zone is much wider when the post-peak is elasto-plastic. The involvement of the additional failed zones is responsible for the post-peak ductility. The paper is meant to explore new methods to derive high quality geo-data for jointed rock mass.

Natural Frequency Characteristics of Rock Masses Containing a Complex Geological Structure and Their Effects on the Dynamic Stability of Slopes

The seismic failure of rock slopes is commonly a cumulative damage process; in particular, local slope damage usually occurs before the occurrence of landslides. The local damage in rock slopes is often caused by the high-frequency components of the waves. Special attention should be paid to the relationship between the local damage and the dynamic failure of landslides, which is of great significance to the study of the cumulative failure evolution of landslides. Based on a numerical modal analysis and dynamic characteristics determined using shaking-table tests, the relationship between the local damage and the dynamic failure of a rock slope with discontinuous joints and its failure mechanism is investigated in the frequency domain. The modal analysis clarifies the natural frequencies and vibration modes of the slope. The tests investigate the effects of the natural frequencies on the slope dynamic characteristics. The numerical and test results show that the high- and low-frequency components mainly induce local and overall deformation of the surface slope, respectively. The analyses of the peak Fourier spectrum amplitude (PFSA) suggest that the dynamic failure process of the slope includes a local damage stage ( 0.297 g). The high-frequency components play a major role in the slope cumulative deformation process, and the low-frequency components determine the failure mode of the landslide. The local damage induced by high-frequency components first occurs and progressively develops; then, when the damage is accumulated to a certain extent, the surface slope fails because of the low-frequency components.

Laboratory investigation of mechanical behavior of granite samples containing discontinuous joints through direct shear tests

The effect of the normal stress and joint persistency on the mechanical behavior of granite samples containing discontinuous joints was investigated in the laboratory through direct shear tests. The test results revealed three different failure modes occurring at the rock bridge: (a) shear failure, (b) compressive-shear failure, and (c) tensile failure. The failure mode depends on the joint persistency and normal stress level and influences the peak shear strength. Moreover, the joint persistency and normal stress level were also found to have a considerable influence on the post-failure behavior such as the fracture roughness and residual shear strength based on rock bridge area. The conducted investigation provided better understanding of the effect of a rock bridge on mechanical behavior of granitic discontinuous joints towards estimating the resistance capacity of rock bridges and hence to allow evaluation of stability of rock masses in both surface and underground excavations in rock engineering.

Cyclic behavior of hybrid RC columns using High-Performance Fiber-Reinforced Concrete and Ni-Ti SMA bars in critical regions

Thanks to their excellent deformation capacity and ductility, smart materials are now being increasingly used in the construction industry, one example being superelastic Shape Memory Alloys (SMA) such as Ni-Ti, which can recover from large strains without generating significant residual strains.The purpose of this work was to study the behavior under cyclic loading of hybrid-reinforced concrete columns containing super-elastic Ni-Ti bars and High-Performance Fiber-Reinforced Concrete (HPFRC) in their critical end regions, where plastic hinges may form (column ends). This critical region is a dissipative zone of the column where the most adverse combination of actions occurs.An experimental study was carried out to simulate inter-story columns in which the effects of the axial level and continuous or discontinuous beam-column joints were analyzed. The specimens with continuous joints were found to display greater lateral strength, ductility and energy dissipation, while those with discontinuous joints underwent smaller residual displacements and less damage in the critical regions of the columns.

Effect of Joint Geometrical Parameters on Hydraulic Fracture Network Propagation in Naturally Jointed Shale Reservoirs

The presence of a significant amount of discontinuous joints results in the inhomogeneous nature of the shale reservoirs. The geometrical parameters of these joints exert effects on the propagation of a hydraulic fracture network in the hydraulic fracturing process. Therefore, mechanisms of fluid injection-induced fracture initiation and propagation in jointed reservoirs should be well understood to unleash the full potential of hydraulic fracturing. In this paper, a coupled hydromechanical model based on the discrete element method is developed to explore the effect of the geometrical parameters of the joints on the breakdown pressure, the number and proportion of hydraulic fractures, and the hydraulic fracture network pattern generated in shale reservoirs. The microparameters of the matrix and joint used in the shale reservoir model are calibrated through the physical experiment. The hydraulic parameters used in the model are validated through comparing the breakdown pressure derived from numerical modeling against that calculated from the theoretical equation. Sensitivity analysis is performed on the geometrical parameters of the joints. Results demonstrate that the HFN pattern resulting from hydraulic fracturing can be roughly divided into four types, i.e., crossing mode, tip-to-tip mode, step path mode, and opening mode. As β (joint orientation with respect to horizontal principal stress in plane) increases from 0° to 15° or 30°, the hydraulic fracture network pattern changes from tip-to-tip mode to crossing mode, followed by a gradual decrease in the breakdown pressure and the number of cracks. In this case, the hydraulic fracture network pattern is controlled by both γ (joint step angle) and β. When β is 45° or 60°, the crossing mode gains dominance, and the breakdown pressure and the number of cracks reach the lowest level. In this case, the HFN pattern is essentially dependent on β and d (joint spacing). As β reaches 75° or 90°, the step path mode is ubiquitous in all shale reservoirs, and the breakdown pressure and the number of the cracks both increase. In this case, β has a direct effect on the HFN pattern. In shale reservoirs with the same β, either decrease in k (joint persistency) and e (joint aperture) or increase in d leads to the increase in the breakdown pressure and the number of cracks. It is also found that changes in d and e result in the variation in the proportion of different types of hydraulic fractures. The opening mode of the hydraulic fracture network pattern is observed when e increases to 1.2 × 10−2 m.

An improved approach for analysis of coupled structures in Energy Finite Element Analysis using the coupling loss factor

An alternative and improved approach for the analysis of coupled structures in Energy Finite Element Analysis (EFEA) is presented, which is termed as iEFEA in this paper. The conventional EFEA uses the power transfer coefficients (PTCs) to establish the power coupling relation on discontinuous joints, where PTCs are usually derived and processed by the wave transmission approach based on the diffuse wavefield assumption. However, the PTCs in conventional EFEA cannot capture wave filtering effects and only provide accurate predictions when the damping effect is weak. Inspired by the power coupling concept of Statistical Energy Analysis (SEA), an alternative approach using the coupling loss factors (CLFs) and considering the direct wavefield is developed. The present approach is implemented by Finite Element Method (FEM), and thus it inherits the advantages of FEM on handling geometrical complexity and material complexity. The applications of the present approach on coupled beams and coupled plates are demonstrated. The validation simulations show the accuracy and reliability of the present approach.

Numerical investigation of the shear behavior of granite materials containing discontinuous joints by utilizing the flat-joint model

In this paper, the shear behavior and failure mechanism of granite material bridges between discontinuous joints subjected to direct shearing were investigated using a flat-joint modeling approach. Through a comprehensive calibration and validation study, good agreement was successfully achieved considering the different normal stress levels, and three failure mechanisms were observed in both the numerical modeling and physical experiments. The joint persistency and UCS/Ts ratio were then meticulously investigated and found to have a pronounced effect on the failure mode, the peak shear strength and the shear deformation modulus of the granite samples containing discontinuous joints.

Effect of joint type on the shear behavior of synthetic rock

The shear behavior of the discontinuities of rock is important because it is closely related to the stability of a rock mass. The scientific challenge lies in the understanding of how different types of joint are related to the failure criterion. In the current study, direct shear tests are used to investigate the shear behavior of continuous planar joints, stepped joints, and discontinuous open joints. The joints were cast in a synthetic rock made of plaster, sand, and water and tested under normal stresses that ranged from 50 kPa to 3.5 MPa. The shear behavior of both the continuous and discontinuous joints has been found to be dependent on the normal stress. At normal stresses above the magnitude of the tensile strength, continuous and discontinuous joints displayed either strain weakening or brittle behavior. Results with the combination of all joint types indicated that the shear strength of the different types of joint increases sharply at low normal stress, and then approaches a lower bound residual strength envelope at high normal stress. At normal stresses of less than the tensile strength (1.84 MPa), the strength is dominated by cohesion, while at normal stresses greater than the tensile strength, friction appears to dominate the shear strength. For open joints, the shear stiffness is independent of the normal stress. For closed joints, the shear stiffness will increase as the normal stress increases, particularly evident below a normal stress of 1 MPa. Increasing the normal stress reduces the brittleness index of rock samples from 1 to 0. A primary reason for this non-unique failure envelope was the large dilation that occurred at high normal stresses. This dilation was attributed to grain crushing, and the roughness resulting from this crushing and gouge formation as shearing occurred.

Dynamic response characteristics of a rock slope with discontinuous joints under the combined action of earthquakes and rapid water drawdown

In order to study the dynamic response characteristics of a rock slope with discontinuities under the combined action of earthquakes and rapid water drawdown, a large-scale shaking table test was performed on a rock slope with discontinuous joints. Wenchuan earthquake (WE) seismic records were performed to investigate the horizontal and vertical acceleration response and displacement response. In particular, three-dimensional optical measurement techniques was used to obtain the slope surface displacements. A comparison was made on the seismic response according to the analysis of PGD (peak ground displacement) and M PGA (acceleration amplification coefficient) of the modeled slope. The results show that the experimental slope mainly underwent settlement and horizontal deformation when the WE records were applied in the z and x directions, respectively. The slope was first shaken by the P wave, which caused the differential settlement to occur at the surface slope; then, the slope was shaken more severely by the S wave, which led to a greater horizontal deformation. Moreover, analysis of the ΔPGD (increment of PGD) and ΔM PGA (increment of M PGA) under rapid drawdown suggests that the rapid water drawdown mainly impacts the deformation of the surface slope, particularly between the high and low water levels. The water infiltration through the cracks softened the material of the surface slope, and the rapid drawdown also enhanced the slope deformation. In addition, the damage evolution process of the slope can be identified, mainly including three stages: an elastic stage ( 0.336 g).

A Deep Catastrophic Failure Model of Hillslope for Numerical Manifold Method and Multiple Physics Computation

This study was aimed to create an analytical model for simulating deep catastrophic failure of hillslope (or deep-seated landslide) to help determining assessment criteria of potential risk based on numerical manifold method (NMM) and coupled multi-physics computation (MPC), in which the failure status is simulated by the NMM while the risk factors are studied by the MPC. The simulation delivers the landslide results that are compared with a laboratory test for approval. The proposed model includes a small-scale hillslope designed by two-dimensional geometry for the plane strain problem. Thus, the porous materials are considered for coupling fluid–structure interactions in hydraulic and geotechnical analyses. Meanwhile, discontinuous joints are assumed along the potential failure surfaces within the deep-seated layer to simulate collapse behaviors of hillslope once the risk factors, such as effective stress and friction angle, reach the thresholds. Furthermore, the model is initially setup as laboratory scale for comparing with a hydraulic experiment that practices the failure condition caused by seepage. The simulation hence explorers the criteria of potential failure risks due to variations of slope, friction angle, and groundwater level. This study performs feasibility of the proposed model that provides a reliable procedure based on both simulation and experiment to estimate the potential risks for deep catastrophic landslides. In the future, the study can be expanded for evaluating full-scale landslide in a variety of hillslope properties.

Strength Reduction Method for Stability Analysis of Local Discontinuous Rock Mass with Iterative Method of Partitioned Finite Element and Interface Boundary Element

SRM (strength reduction method) with iterative method of PFE (partitioned fnite element) and IBE (interface boundary element) is proposed to solve the safety factor of local discontinuous rock mass. Slope system is divided into several continuous bodies and local discontinuous interface boundaries. Each block is treated as a partition of the system and contacted by discontinuous joints. The displacements of blocks are chosen as basic variables and the rigid displacements in the centroid of blocks are chosen as motion variables. The contact forces on interface boundaries and the rigid displacements to the centroid of each body are chosen as mixed variables and solved iteratively using the interface boundary equations. Flexibility matrix is formed through PFE according to the contact states of nodal pairs and spring flexibility is used to reflect the influence of weak structural plane so that nonlinear iteration is only limited to the possible contact region. With cohesion and friction coefficient reduced gradually, the states of all nodal pairs at the open or slip state for the first time are regarded as failure criterion, which can decrease the effect of subjectivity in determining safety factor. Examples are used to verify the validity of the proposed method.

Distinct Element Modeling of the Effect of Joint Persistence on Dynamic Fracturing of Jointed Rock Masses

Rock masses consist of intact rock and discontinuities such as faults, joints and bedding planes. The presence of such discontinuities in rock masses dominates the response of jointed rock masses to static and dynamic loading. These structural weak planes seriously hinder and affect the propagation of stress waves in rock mass. The joints parameters such as persistence, orientation, distribution patterns, spacing and filling material have a significant effect on the response of rock masses against wave propagation. In most studies of blast induced wave propagation in jointed rock mass, it is assumed that joints are continuous. In many situations the rock mass consists of non-continuous joints and rock bridges. Rock bridges and discontinuous joints have a different effect on wave and fracture propagation in a blasting operation. With regard to complexities associated with rock blasting in particular in jointed media, numerical tools are viable alternatives for rock blasting analysis. In this study the DEM methods was employed to investigate the effects of rock bridges on the wave propagation process. A plain strain 2D scenario was assumed and a single blasthole explosion was simulated. Three models with different jointing orientation patterns including jointing pattern parallel to free face, perpendicular to free face and orientated at 45 degree with respect to free face were analyzed numerically to investigate rock mass fracturing while blast wave propagation. The discontinuous joints were considered to be filled with weak materials (open joints) and rock bridges are composed of intact rock. In order to allow material plastic failure, a Mohr-Coulomb material model was used. The analysis results show that the stress concentration at the rock bridge location leads to excessive fracturing. This effect is more visible at the free face where the stress wave reflection occurs. Moreover, the obtained results show that the pattern and orientation of non-continuous joint system has a pronounced effect on rock fragmentation.

The Research on the Calculation Methods and the Influential Factors Analysis of the Mechanical Joint Persistence Ratio of Jointed Rock Mass

The paper presents a method used to model rock as continuous media with discontinuous joints. The Monte-Carlo method is employed in simulating the joint network of jointed rock mass based on certain principles, and the calculation method on the mechanical persistence ratio is studied, furthermore, some research on the influential factors on the persistence ratio is performed, and the values of some empirical parameters are obtained, which assured the stability of the results.

Numerical Analysis on Failure Mechanism of Intermittent Joints

The mechanical characteristics of jointed rocks are mainly controlled by geometrical features of intermittent joints. The failure mechanism and shear behavior of discontinuous joints are simulated by series of direct shear tests using the particle flow code (PFC2D). The effects of joint persistence, separation and azimuth angle on the failure strength of jointed rock are studied in detail. The results shows that peak shear strength can be considered as a function of the geometrical parameters, which is in a reasonable accordance with other experimental results. Meanwhile, as for failure mechanism, joint separation and azimuth angle are especially discussed, and specific damage patterns are presented as well.

Safe rapid drifting – Support selection

Abstract Current drift advance rates in mining fall short of expectations with advances in drilling and blasting technologies. Quick access to orebodies improves their net present value (NPV). This is critical for block cave mining where several kilometers of drift network is initially required at high capital cost. Many mining companies are now planning block caving because of its long-term low production cost. This paper critically reviews the developments in tunnelling and mine drift development rates with advances in drilling and explosives technologies. Current drift support practice during development is also critically reviewed together with the rock mass classification systems. These reviews show that, while drilling and explosive technologies have drastically improved since 1850, current drift advance rates in the Canadian metalliferrous mining industry have either remained stagnant or dropped below the1960 advance rate levels and in comparison to advance rates in civil tunnelling. It is also established that a major cause for this stagnation is the use of long-term support in good ground conditions where only temporary support is required near-face for worker safety in the short-term. Long-term support takes up 46% of development cycle time. The paper presents a methodology for drift support design for underground hard rock conditions typically found in current mining practice in the Canadian Shield and discusses the rationale for optimizing ground support systems installed near-face during drift development. An improved Q-system called Q-star (Q∗) that accounts for discontinuous joints (rock bridges) and roughness of short joints in the rock mass is developed to more reliably estimate the self-support capacities of rock masses. It is recommended that construction damage be accounted for in the rock mass rating for safe support selection during development. A procedure is developed for the adjustment of Q∗ to account for construction damage. Perimeter blasting is recommended as pre-requisite for rapid drift development in order to minimize construction damage, reduce support demand and scaling and mucking times. A support matrix is presented based on rock mass quality and stress level for safe rapid drift development. Two case histories in active mines are presented to validate the procedure. The methodology is applicable to stress-induced damage and may not apply where complete relaxation occurs. While the procedures presented are focused on typical conditions in the Canadian Shield underground mines, they may be applicable in civil engineering tunneling and other underground mines where drill-and-blast is used as the excavation method.

Breakage and shear behaviour of intermittent rock joints

The breakage and shear behaviour of intermittent rock joints have been investigated in a series of direct shear tests with a new shear device, specifically designed for this purpose. The tests have been performed on specimens of rock-like material or hard rock, respectively, incorporating idealized non-persistent joints, made up of a number of short cracks in an en-échelon arrangement along the central shear axis. The shear behaviour of such a joint constellation has been found to be composed of different phases. The first phase of shearing is that of the actual rupture, initiated by the formation of wing cracks, starting from the existing cracks and growing into the material bridges, and concluded by the generation of additional new fractures connecting the initial cracks in the zone between the wing cracks. The second phase of shearing is characterized by friction processes and volume increase in the then continuous shear zone. Finally, the third phase of shearing, reached after large shear displacements, is determined by sliding processes inside the strongly fractured shear zone. In a large number of shear tests the geometrical parameters of the discontinuous joints as well as the loading conditions have been found to influence the activated shear resistance in each phase of shearing to a noticeably different extent. The orientation of the initial cracks and the normal stress, however, have been identified as the most influential parameters. Depending on the test conditions, an initially discontinuous rock joint can activate the largest shear resistance not just before rupture but in one of the two subsequent phases of shearing as well. The mechanisms which govern the different shear phases could be identified as (1) tensile rupturing, (2) rolling and sliding friction of dilatant joint zones and (3) sliding within the joint filling composed of brecciated material.

Viscoelastic Behavior of Granite and the Homogenization Analysis

Granite is a composite material of rock-forming minerals with discontinuous joints such as grain boundaries and microcracks. Studies of these microstructures are of increasing interest in geophysics and geotechnical engineering relating to underground space development. We first performed uniaxial compressive and relaxation tests for estimating physical properties of discontinuous joints by using three kinds of rocks that consist of quartz, quartz/feldspar and feldspar, respectively. Next a homogenization method is applied to analyze a viscoelastic behavior of granite including these joints.

Influence of discontinuous joints on permeability

Influence of discontinuous joints on permeability

Influence of Discontinuous Joints on Permeability

Extensive jointing is a fabric feature that is common to many fine-grained soils with high clay content. Both naturally occurring and recompacted soil deposits have been known to exhibit extensively jointed fabrics. Jointing has been shown to dramatically influence the nature of the flow of fluids through jointed soils. Field permeability tests have demonstrated permeabilities of several orders of magnitude higher than laboratory tests of intact samples of the same material. The purpose of this study is to investigate the influence of joints on permeability in a low-permeability matrix in which the joints are not necessarily continuously connected. This was accomplished by performing permeability tests on oriented samples of remolded fine-grained till that had been isotropically consolidated and by comparing these results with finite element models. The soil was obtained from the Lake Michigan shoreline in the state of Wisconsin. This soil has been found to be extensively jointed, perhaps due to post-glacial stress relief. A spherical sample of this soil was consolidated and tested at various orientations to obtain an intact matrix permeability. The specimen was then artificially jointed through the incorporation of a porous plate within the specimen. Additional permeability tests were performed at various orientations in order to investigate the influence of joint orientation on apparent permeability. The results indicated that the permeability in the direction parallel to the joint was significantly greater than the permeability perpendicular to the joint. The apparent permeability decreased rapidly as the applied gradient became more perpendicular to the joint, approaching that of the intact matrix. Similar results were obtained from a finite element model of the jointed spherical specimen.

Continuum characterization of jointed rock masses: Part I—The constitutive equations

Hill has proved that the average strain energy density in any region of an elastic and inhomogeneous material can be calculated from the average values of the stresses and strains within that region. This concept has been used to derive the general constitutive equations of a rock mass containing an orthogonal set of discontinuous joints intersecting an anisotropic rock material. The constants required for the continuum characterization of the jointed mass are the ‘joint stress concentration factors’ B N1 and B T1 (see Fig. 1 of this paper). These are defined as the ratio of stresses along the joint to the overall stresses in the rock. Exact expressions for the stress concentration factors have been obtained for the case of a rigid rock (i.e. the intact material between the joints) containing staggered compliant joints, and a correction is proposed for the case where the rock is (elastically) deformable. These results suggest that interlocking betweem blocks of rock may become significant even for a slight offset along the joints, such as may occur during shear deformation of a rock mass containing an initially continuous orthogonal joint set. Stress concentration factors computed independently from the results of a finite element program for a jointed mass compare excellently with the above-mentioned theoretical results. It is further shown that tensile stresses are developed inside a rock with staggered joints, and may be as high as twice the overall shear stresses or the overall compressive stresses. Typical stress distributions within a block are given in Fig 6(a) and 6(b) of this paper. It is concluded that a rock mass is rendered anisotropic by any joint set having a preferred orientation. Expressions from which the elastic moduli of the equivalent continuum anisotropic rock mass may be obtained are presented in Table 1.