Model For Jointed Rock Mass Research Articles

Analysis of EDZ Development of Columnar Jointed Rock Mass in the Baihetan Diversion Tunnel

Due to the time dependency of the crack propagation, columnar jointed rock masses exhibit marked time-dependent behaviour. In this study, in situ measurements, scanning electron microscope (SEM), back-analysis method and numerical simulations are presented to study the time-dependent development of the excavation damaged zone (EDZ) around underground diversion tunnels in a columnar jointed rock mass. Through in situ measurements of crack propagation and EDZ development, their extent is seen to have increased over time, despite the fact that the advancing face has passed. Similar to creep behaviour, the time-dependent EDZ development curve also consists of three stages: a deceleration stage, a stabilization stage, and an acceleration stage. A corresponding constitutive model of columnar jointed rock mass considering time-dependent behaviour is proposed. The time-dependent degradation coefficient of the roughness coefficient and residual friction angle in the Barton–Bandis strength criterion are taken into account. An intelligent back-analysis method is adopted to obtain the unknown time-dependent degradation coefficients for the proposed constitutive model. The numerical modelling results are in good agreement with the measured EDZ. Not only that, the failure pattern simulated by this time-dependent constitutive model is consistent with that observed in the scanning electron microscope (SEM) and in situ observation, indicating that this model could accurately simulate the failure pattern and time-dependent EDZ development of columnar joints. Moreover, the effects of the support system provided and the in situ stress on the time-dependent coefficients are studied. Finally, the long-term stability analysis of diversion tunnels excavated in columnar jointed rock masses is performed.

Study on the constitutive model for jointed rock mass.

A new elasto-plastic constitutive model for jointed rock mass, which can consider the persistence ratio in different visual angle and anisotropic increase of plastic strain, is proposed. The proposed the yield strength criterion, which is anisotropic, is not only related to friction angle and cohesion of jointed rock masses at the visual angle but also related to the intersection angle between the visual angle and the directions of the principal stresses. Some numerical examples are given to analyze and verify the proposed constitutive model. The results show the proposed constitutive model has high precision to calculate displacement, stress and plastic strain and can be applied in engineering analysis.

A dynamic damage constitutive model for a rock mass with persistent joints

The strength and deformability of a rock mass is one of the most important problems in the rock engineering. Rock masses are usually fractured as a result of many flaws of different scales through various geological processes. The joints and microcracks are the macroscopic and mesoscopic flaws, respectively. In this study, a dynamic damage constitutive model for jointed rock mass is proposed and applied to the rock mass models with many persistent joints. First, the mesoscopic damage variable and macroscopic damage tensor are introduced to describe the damage caused by microcracks and joints, respectively. Second, the coupled damage variable (tensor) is obtained with Lemaitre strain equivalence hypothesis. Finally, the dynamic damage constitutive model for the rock mass with persistent joints is proposed based on Taylor–Chen–Kuszmaul (TCK) model. The results show that the initial deformation stage of the samples coincides with each other under the different load strain rate. A further increase of strain increases the climax strength and the total strain of the materials. The parameter is studied further from the number of joints in rock mass, the climax strength gradually decreases with increase in joint number, but the reduction level gradually becomes less and tends to be a constant. The above conclusions agree well with the existing experimental and theoretical results.

A DEM analysis of step-path failure in jointed rock slopes

A numerical analysis of step-path failure mechanisms in rock slopes is provided based upon simulations performed using a discrete element method specifically enhanced for the modeling of jointed rock masses. Fracturing of the intact rock as well as yielding within discontinuities can be simulated to determine the failure surface without any a priori assumption on its location. For both coplanar and non-coplanar sets of discontinuities, failure is the result of the propagation of tensile microcracks that develop in the rock bridges from the tips of pre-existing discontinuity planes in a way similar to wing cracks extensions that can eventually coalesce to form extended step-path failure surfaces. Sensitivity analyses are performed to better understand the critical mechanisms that lead to slope failure and to discriminate between the respective roles played by intact rock and planes of weakness at the onset of failure. For a randomly distributed set of joints that share the same preferential orientation, failure is shown to be dependent on the frictional strength mobilized on the joint surfaces. The results confirm the critical need for a comprehensive and extensive characterization of both mechanical and geometrical properties of discontinuities when assessing the stability of a rock mass.

Microplane damage model for jointed rock masses

SUMMARYThe paper presents a new microplane constitutive model for the inelastic behavior of jointed rock masses that takes into account the mechanical behavior and geometric characteristics of cracks and joints. The basic idea is that the microplane modeling of rock masses under general triaxial loading, including compression, requires the isotropic rock matrix and the joints to be considered as two distinct phases coupled in parallel. A joint continuity factor is defined as a microplane damage variable to represent the stress‐carrying area fraction of the joint phase. Based on the assumption of parallel coupling between the rock joint and the rock matrix, the overall mechanical behavior of the rock is characterized by microplane constitutive laws for the rock matrix and for the rock joints, along with an evolution law for the microplane joint continuity factor. The inelastic response of the rock matrix and the rock joints is controlled on the microplane level by the stress–strain boundaries. Based on the arguments enunciated in developing the new microplane model M7 for concrete, the previously used volumetric–deviatoric splits of the elastic strains and of the tensile boundary are avoided. The boundaries are tensile normal, compressive normal, and shear. The numerical simulations demonstrate satisfactory fits of published triaxial test data on sandstone and on jointed plaster mortar, including quintessential features such as the strain softening and dilatancy under low confining pressure, as well as the brittle–ductile transition under higher confining pressure, and the decrease of jointed rock strength and Young's modulus with an increasing dip angle of the joint. Copyright © 2014 John Wiley & Sons, Ltd.

Reducing deformation effect of tunnel with Non-Deformable Support System by Jointed Rock Mass Model

Numerical modeling has been used widely in mining and construction industries in recent years. The most important issue in engineering projects designed with numerical modeling is accurate modeling of rock mass behavior. If the rock mass behavior is modeled accurately, fewer problems will be faced during field application of projects. Selection of the true material model is a very important issue in numerical modeling for the tunnel projects. Non-Deformable Support System (NDSS), which will be mentioned in the scope of this research, does not mean that it does not permit any deformation or is a very stiff system. NDSS is a support system that does not permit deformations exceeding specified deformation amounts which are calculated with determination of the accurate rock mass behavior by the true material model and it must be evaluated with support system and excavation advance specifically. The origin of the paper is that numerical modeling provides more comfortable results in tunneling in case one can determine rock mass deformation and failure behavior appropriately. In (NDSS), however, support system element can only be determined by proper numerical modeling analysis. Moreover, deformation values determined by NDSS analysis are accepted as limit values. Therefore, applied support system should be within deformation tolerance limits determined by NDSS analysis. Briefly, this paper is related to NDSS that should be determined by numerical modeling analysis.In this research, in regard to the excessive deformations in T-35 tunnel which is one of the 33 tunnels of Ankara–Istanbul High-Speed Railway Project, results of the in situ measurements in the tunnel excavated with the new developed NDSS and results of the numerical model made with Jointed Rock Mass Model have been compared. It is determined that the results of the numerical modeling and the in situ measurements are very consistent with each other.

Loading-unloading test analysis of anisotropic columnar jointed basalts

To evaluate the columnar jointed basalts in the dam site of Baihetan hydropower station in southwest China, we developed a basic conceptual model of single jointed rock mass. Considering that the rock mass deformation consists of rock block deformation and joints deformation, the linear mechanical characteristics of the cell (including the elastic joints and the nonlinear mechanical behaviors of the cell) with a combined frictional-elastic interface were analyzed. We developed formulas to calculate the rock block deformation, which can be adapted for multiple jointed rock mass and columnar jointed basalts. The formulas are effective in calculating the equivalent modulus of multiple jointed rock mass, and precisely reveal the anisotropic properties of columnar jointed basalts. Furthermore, the in situ rigid bearing plate tests were analyzed and calculated, and the types of loading-unloading curves and the equivalent modulus along different directions of columnar jointed basalts were obtained. The analytical results are in close compliance with the test results.

An Anisotropic Geomechanical Model for Jointed Rock Masses at Taishan Nuclear Power Station, Southern China

Abstract:An anisotropic geomechanical model for jointed rock mass is presented. Simultaneously with deriving the orthotropic anisotropy elastic parameters along the positive axis, the equivalent compliance matrix for the deflection axis orthotropic anisotropy was derived through a three‐dimensional coordinate transformation. In addition, Singh's analysis of the stress concentration effects of intermittent joints was adopted, based on two groups of intermittent joints and a set of cross‐cutting joints in the jointed rock mass. The stress concentration effects caused by intermittent joints and the coupling effect of cross‐cutting joints along the deflection‐axis are also considered. The proposed anisotropic mechanics parameters method is applied to determine the deformation parameters of jointed granite at the Taishan Nuclear Power Station. Combined with the deterministic mechanical parameters of rock blocks and joints, the deformation parameters and their variability in jointed rock masses are estimated quantitatively. The computed results show that jointed granite at the Taishan Nuclear Power Station exhibits typical anisotropic mechanical characteristics; the elastic moduli in the two horizontal directions were similar, but the elastic modulus in the vertical direction was much greater. Jointed rock elastic moduli in the two horizontal and vertical directions were respectively about 24% and 37% of the core of rock, showing weakly orthotropic anisotropy; the ratio of elastic moduli in the vertical and horizontal directions was 1.53, clearly indicating the transversely isotropic rock mass mechanical characteristics. The method can be popularized to solve other rock mechanics problems in nuclear power engineering.

A three-dimensional equivalent continuum constitutive model for jointed rock masses containing up to three random joint sets

A three dimensional constitutive model is formulated for deformation analysis of jointed rock masses containing up to three joint sets with arbitrary spatial configurations. A representative elementary volume (REV) that represents the deformational response of the rock mass is defined and the constitutive relationships are developed based on superposition of deformations of the REV components. By representing the constitutive relationships in a tensorial form, the model is able to implement deformation anisotropy of jointed rock masses. The Mohr-Coulomb failure criterion with tension cut-off is used for the intact rock and the joint sets. The model is implemented in FLAC3D and the deformations and strength values calculated by the model are compared with the results from a 3DEC model and analytical solutions. The model results are in good agreement with those obtained from 3DEC.

Investigation on strength and stability of jointed rock mass using three‐dimensional numerical manifold method

SUMMARYThis paper proposes a numerical model for jointed rock masses within the 3‐D numerical manifold method (NMM) framework equipped with a customized contact algorithm. The strength of rock sample containing a few sets of discontinuities is first investigated. The results of models with simple geometries are compared with the available analytical solutions to verify the developed computer code, whereas models with complex geometries are simulated to better understand the fundamental behavior and failure mechanism of jointed rock mass. Furthermore, the stability of jointed rock mass in an underground excavation is studied, where rock failure process is determined by the 3‐D NMM simulation. The simulation results provide valuable guidance on excavation process design and stabilization design in rock engineering practice. Copyright © 2012 John Wiley & Sons, Ltd.

New Constitutive Model for Two-Dimensional Jointed Rock Mass

Mechanical analysis for jointed rock mass is very significant in geotechnical engineering. In particular, the mechanical characteristics of jointed rock mass can result in nonlinear response of geotechnical engineering and in consequence mechanical analysis for the engineering is difficult. In order to simulate jointed rock mass, a new equivalent model is proposed for two-dimensional jointed rock mass based on strain energy equivalence principle. Firstly, the equivalent elastic modulus and Poisson's ratio for a horizontal joint in unit square is deduced. Then, the equivalent flexibility matrix for a joint of specified angle in unit square is given. Moreover, the equivalent flexibility matrix for multiple joints, which have different angles in unit square, is obtained. Finally, a numerical simulation is given to verify the model. Compared with other conventional algorithm, the proposed approach has some strong points: it is easy to implement in the finite element program. Furthermore, it provides a new model to compute the deformation of joints and rock and the precision is high.

The Responses of Jointed Rock Mass under Dynamic Loads

Joints can reflect and transmit stress waves, thus joints affect rock fracturing, and accordingly they could affect blasting efficiency. In this paper, numerical and experimental investigations have been implemented and the effect of joints on wave propagation and rock fracturing has been discussed. A dynamic numerical model of jointed rock mass has been established by using finite difference method. The simulation results show that as joints are parallel to wave propagation, the corresponding rock damage zones increase. Blasting experiments by using artificial joints have been carried out. Generally the experimental results agree with our numerical results.

A continuum model of jointed rock masses based on micromechanics and its integration algorithm

The paper is devoted to proposing a constitutive model based on micromechanics. The joints in rock masses are treated as penny-shaped inclusion in solid but not through structural planes by considering joint density, closure effect, joint geometry. The mechanical behavior of the joints is represented by an elasto-plastic constitutive law. Mori-Tanaka method is used to derive the relationship between the joint deformations and macroscopic strains. The incremental stress-strain relationship of rock masses is formulated by taking the volume average of the representative volume element. Meanwhile, the behavior of joints is obtained. By using implicit integration algorithms, the consistent tangent moduli are proposed and the method of updating stresses and joint displacements is presented. Some examples are calculated by ABAQUS user defined material subroutine based on this model.

Modeling strategy for jointed rock masses reinforced by rock bolts in tunneling practice

This paper deals with the modeling of jointed rock masses reinforced by rock bolts. It is well known that rock bolts are extremely effective in reinforcing jointed rocks. However, if a continuum approach is adopted for modeling jointed rock masses, it is often misleading to evaluate the effectiveness of the rock bolts by numerical analyses such as the finite element method. This may be due to the fact that since no more joints exist in the continuum, the effectiveness of the rock bolts in constraining the relative displacements along the joints cannot be evaluated properly. In order to investigate the reinforcement effect of rock bolts, physical model tests were performed in the laboratory. The test results revealed that jointed rock masses should be modeled as an equivalent continuum after the installation of rock bolts and that the mechanical parameters of the equivalent continuum should be evaluated by considering the reinforcement effect of the rock bolts. Therefore, the values of the mechanical parameters differ from place to place in accordance with the relation between joint orientation and rock bolt direction, even though joint systems are homogeneous. In conclusion, in the continuum approach for modeling jointed rock masses, it should be emphasized that rock bolts and jointed rock masses should not be modeled separately but should be modeled simultaneously by considering the reinforcement effect of the rock bolts in constraining joint movement. The modeling of shotcrete reinforced by steel ribs is also discussed in comparison to the modeling by rock bolts.

Generic strength model for dry jointed rock masses

A new nonlinear thermo-mechanical model for heavily jointed rock masses is presented. The model describes poroelasticity, shear-enhanced compaction and brittle–ductile transition in dry porous rocks. The key input parameters of the model, such as elastic moduli, tensile and compressive strength are expressed as functions of the reference porosity of the rock. These functions are based on empirical data for limestones and sandstones and assume that the medium is isotropic. The effect of joints is modeled by scaling down the key model parameters. The scaling rules are found with the help of explicit numerical modeling of randomly jointed media.

A Polyaxial System for Testing of Jointed Rock Mass Models

Abstract A polyaxial loading system was designed and developed at Indian Institute of Technology Delhi, India for laboratory testing of mechanical behavior of rock mass. The large-scale rock mass models of different joint geometry can be tested under polyaxial stress state simulating in situ stress conditions using this true-triaxial system. The system consists of a 1000 kN capacity vertical frame, a biaxial frame of 300 kN capacity fitted with two pairs of hydraulic jacks and platens, constant confining pressure unit for applying, monitoring, and maintaining horizontal stresses (σ2 and σ3) on specimen faces, eight-channel data acquisition system, and a personal computer to record all load and deformation data. Its working was verified by conducting true-triaxial testing on several models specimens of sand-lime blocks having three sets of orthogonal joints.

Finite element analysis of jointed rock masses reinforced by fully-grouted bolts and shotcrete lining

This paper presents the formulation of an equivalent constitutive model for jointed rock masses reinforced by fully-grouted bolt and shotcrete lining and its implementation in a finite element program. This model takes into consideration the elasto-viscoplastic behavior of the rock masses as well as the contribution of the bolt and lining to both the stiffness and shear resistance of the jointed rock masses. The equivalent model and corresponding software are verified by comparison to conventional numerical models which consider the individual contribution of the reinforcement. The relationship between the constitutive parameter “effective height” and the thickness of the lining is evaluated using the ANN approach. Finally, the interest of the proposed model is illustrated through its application for the analysis of the excavation of an underground cavern in a hydropower project.

Research on Fracture Damage Coupled with Crack Arrest by Anchorage Model of Discontinuous Jointed Rock Mass under the State of Complex Stress

Based on the hypothesis of equivalent strain energy and the theories of fracture mechanics and damage mechanics，the constitutive model and fracture damage mechanism of bolted discontinuous jointed rockmass are systematically studied under the state of complex stresses. Initially ， considering the equivalent strain energy ， the constitutive relation of anchored discontinuous jointed rockmass is derived under the state of compression-shear stresses. The constitutive relation under the state of tension-shear stresses is also developed according to the theory of self-consistence. Next，the damage evolution equations of discontinuous multi-crack rockmass under compression-shear and tension-shear are put forward according to the wing crack-initiating criterion. Finally，based on the above constitutive models and the damage evolution equations three-dimensional finite element procedures have been developed to evaluate the stability and deformability of the surrounding rock mass during excavation and supporting. The calculated results indicate that above-mentioned constitutive relation and the damage evolution equations are available.

A Study of Application about FLAC-3D in Damage of Rock Mass Slope

A damage mechanics model for jointed rock mass is established by the simulation of the multi-cleavage behaviour by introducing the damage tensor and by considering the jointed rock mass as continuous medium with damage. The data exchange technique with FLAC-3D is discussed by applying FISH Language that is inserted in FLAC-3D. The coupling analysis between the rock mass damage and FLAC-3D is realized by the computer program for damage mechanics analysis set up by Visual Basic, which is applied in the simulation analysis of the south slope of Yanqianshan Iron Mine.

き裂性岩盤モデルの比抵抗特性を用いた原位置岩盤の評価法

Before the underground structures such as tunnels are constructed, electrical prospecting is often applied, because of its sensitivity for the water included in the rock mass. However, the relationship between resistivity and the physical property of the rock mass has not quantitatively been clarified. Especially, in the jointed rock mass, it is important to grasp the influence of the joint on the resistivity. In this paper, two kinds of jointed rock mass model are used. One is the discontinuity model, which is made to change the open width of discontinuity by inserting various number of filter papers. The other is the porous model, in which micro opening cracks are generated inside the rock by heating with the electricity muffle furnace. Using these models, the characteristics of resistivity for the jointed rock mass are examined by comparing with the field data obtained by electrical prospecting. As the result, it is shown the possibility to evaluate the porosity of in-situ rock mass from the relationship between porosity and resistivity of the porous model.