Model For Jointed Rock Mass Research Articles

The investigation of seepage model for columnar jointed rock masses during cyclic loading and unloading of confining pressure

Columnar jointed rock masses (CJRM) as a type of jointed rock masses with the distinct structure are widely distributed in nature and have received considerable attention during the last few decades. In this paper, an approach, which is a combination of experiment and graphing method, is proposed to verify the existence of a representative elementary volume (REV) of CJRM during cyclic loading and unloading of confining pressure based on physical model permeability experiments. According to the experiment results, mathematical models for calculating permeability tensor of CJRM were established, and the major principal permeability component (PPC), the minor PPC, and the principal permeability angle (PPA) of CJRM during cyclic loading and unloading of confining pressure are calculated. It was concluded that the existence of a REV of CJRM during cyclic loading and unloading of confining pressure can be verified easily by using the proposed method. During cyclic loading and unloading of confining pressure, a REV does not always exist, especially at high confining pressure. The impacts of confining pressure on the major PPC, the minor PPC, and the PPA are large in the first cyclic loading phase.

Study on transient unloading loosening simulation test of excavation of jointed rock mass

Based on the abrupt displacement of a jointed surrounding rock mass during blasting excavation of deep underground caverns, a set of transient unloading loosening simulation tests was designed for multi-joint rock masses. Through the linear regression analysis of the unloading displacement of jointed rock masses, the opening displacement of a joint is determined to be proportional to the square of the initial unloading stress. The numerical simulation method is used to apply horizontal and vertical in situ stresses to the jointed rock mass model to study the opening displacement in the jointed rock mass at different lateral pressure coefficients of in situ stress. The results indicate that, with the unloading of the horizontal stress, a larger lateral pressure coefficient of the in situ stress leads to a larger opening displacement in the jointed rock mass. When the vertical stress is unloaded after the horizontal stress is totally unloaded, a lower lateral pressure coefficient of the in situ stress leads to a larger opening displacement. The influence of the stress lateral pressure coefficient on the open deformation of the jointed rock mass is obviously higher than that of the unloading rate on the rock mass.

Anisotropic Constitutive Model of Intermittent Columnar Jointed Rock Masses Based on the Cosserat Theory

In this work, an anisotropic constitutive model of hexagonal columnar jointed rock masses is established to describe the distribution law of deformation and the failure of columnar joint caverns under anisotropic conditions, and is implemented to study the columnar jointed rock mass at the dam site of the Baihetan Hydropower Station on the Jinsha River. The model is based on the Cosserat theory and considers the mesoscopic bending effect on the macroscopic mean. The influences of joint plane inclination on equivalent anisotropic elastic parameters are discussed via the introduction of an off-axis transformation matrix and the analysis of an example. It is also pointed out that the six-prism columnar jointed rock mass changes from transverse isotropy to anisotropy under the influence of the angle. A numerical calculation program of the Cosserat constitutive model is developed and is applied to the simulation calculation of a Baihetan diversion tunnel to compare and analyze the respective plastic zones and stress distributions after tunnel excavation under both isotropic and anisotropic conditions. The results reveal that, compared with the isotropic model, the proposed Cosserat anisotropic model better reflects the state of stress and asymmetric distribution of the plastic zone after tunnel excavation, and the actual deformation of the surrounding rock of the tunnel is greater than that calculated by the isotropic method. The results aid in a better understanding of the mechanical properties of rock masses.

Characterization, Modelling and Engineering of Rocks and Rockmasses

Rocks are heterogeneous materials usually associated with geological discontinuities making them weak for sustaining the loads due to civil and mining engineering structures. Characterization details of different isotropic, anisotropic and weathered rocks are presented along with the newly formulated classification system for weathered rockmass. Physical modelling of jointed rockmass under uniaxial, biaxial and polyaxial stress state through newly designed polyaxial system yielded significant results. Critical role of intermediate principal stress on strength and deformation for jointed rockmass is highlighted. New polyaxial failure criteria are proposed and compared. New observations on brittle fracture propagation and interlocking phenomena in crystalline rocks are modelled under polyaxial stress state. Extensive large-scale test results on rock joints under constant normal load and constant normal stiffness in static and cyclic modes were presented along with new predictive models. A new closed-form analytical solution is provided for circular openings in isotropic, homogeneous and elastoplastic rockmass for assessing the wellbore stability and openings. Results of physical modelling tests conducted on shallow tunnels subjected to impact loads and new predictive models developed for squeezing behaviour are also included in this paper. Understanding gained from the extensive characterization and physical modelling of materials in appropriate stress regime used effectively to solve real-time cases. The case studies included are: stability analysis of jointed rock slopes of Chenab bridge abutments, Subansiri power house slope stability, Tindharia landslide in Darjeeling, evaluation of bored tunnelling practices in rocks for Delhi metro and coupled hydromechanical modelling for the slopes in Beas catchment.

Coupling model of jointed rock mass and rock bolt in offshore LPG underground storage

AbstractMost of the surrounding rocks of offshore liquefied petroleum gas (LPG) reservoirs occur in jointed rock mass. This paper is aimed at the reinforcement of the layered composite rock masses. First, the structural mechanical model of the elastic deformation and completely plastic deformation for the bolt was constructed. Then, the equations of axial force, shear force, and bending moment in the cross section of the bolt were obtained by the force‐method canonical equation. The shear‐slip resistance effect of the bolt was decomposed into the friction effect and the dowel effect. In addition, the quantitative relationship between shear resistance and the characteristic angles (anchoring angle, friction angle, dilatancy angle, and deflection angle) and the geometrical and physical parameters of the bolt were derived. Finally, the influence of each characteristic angle on the mechanical properties of the bolt was analyzed in details and the model was verified. The analysis results showed that the laterally constrained load of the rock stratum on the bolt can be characterized by a power function, but the optimal power should be no less than 10. The dominant position of either the friction effect or the dowel effect was changed with the matching of different characteristic angles. The increase of the friction angle and dilatancy angle of the joint surface of the rock is beneficial to improve the lateral shear resistance of the bolt. The effect of the deflection angle on the lateral shear resistance of the bolt was affected by the anchoring angle. The optimal anchoring angle of the bolt should be in the range of 50°‐60°. The results in this study have important theoretical significance to guide the offshore anchoring engineering of layered composite rock masses.

Analysis of the deformation and fracture of underground mine roadway by joint rock mass numerical model

Joints in the rock mass and rheological properties are the main contributing factors in many engineering disasters. Using the user-defined visco-elastoplastic Nishihara constitutive model based on Particle Flow Code in three dimensions (PFC3D), a jointed rock mass numerical model was built to analyze rheological properties and failure behavior of a tunnel surrounded by jointed rock mass of the Zhangjiawa iron mine, Shandong Province, China. The joint distribution law was determined from a statistical analysis of joints on the tunnel walls. Based on the tunnel joint network constructed by the Monte-Carlo method, a jointed rock mass numerical model was established. The rheological properties of the jointed rock mass were separately analyzed by the Nishihara model and the linear elastic model. According to the result from the linear elastic model, the deformation of the tunnel roof and sides did not change with time and the model did not exhibit rheological properties. In contrast, the result of the user-defined Nishihara model showed obvious creep property. The bonds of the joint faces in the jointed rock mass model were primarily destroyed by shear failure. The failure modes and deformation data for the tunnel were generally consistent with field monitoring data.

Anisotropic constitutive model of pentagonal prism columnar jointed rock mass

The pentagonal prism is the dominant structural shape in the columnar jointed rock mass (CJRM) structure, and its anisotropic mechanical properties are crucial for engineering safety. In this paper, we propose an anisotropic constitutive model to accurately describe the anisotropic behavior of the CJRM. First, a generalized model of a pentagonal prism column with variable angle θ was established according to the basic structural features of the CJRM. Based on this model, the constitutive relationship space was derived in three dimensions and then improved through analysis of the influence of the inner disturbed belt and coordinate deflection. Subsequently, considering the CJRM at the Baihetan Hydropower Station in China, we determined the optimal value of θ using one set of in situ test results, thereby obtaining the constitutive relationship for this structure. Finally, the optimal constitutive model of the pentagonal prism was verified by the remaining test results, and its anisotropic characteristics were compared with the existing quadrangular and hexagonal prism constitutive models. The results revealed that the calculated elastic parameters of the pentagonal prism model are in good agreement with the test results and that the curve of the horizontal elastic modulus is approximately circular, which reflects the quasi-transverse isotropy of the proposed model. We found that the calculated results of the three models exhibit different deviations from the test results, owing to the different structural characteristics, and that the deviation in the pentagonal prism model is the smallest.

A Strain-Softening Constitutive Model of Heterogeneous Rock Mass Considering Statistical Damage and Its Application in Numerical Modeling of Deep Roadways

During the construction of underground caverns, the stability of deep underground cavern excavation, which affects the safety and sustainable development of such projects, is a hot issue. First, based on the mechanical properties of surrounding rock in deep tunnels, the strain-softening behavior, damage, and heterogeneity of rock masses are analyzed. Then, a strain-softening model of heterogeneous jointed rock mass that considers statistical damage (SSD) is developed and implemented through FLAC3D simulation software. Finally, the SSD is applied to a deep roadway in the Jinchuan mining area, and a comparative analysis of the computation results of the Mohr–Coulomb (MC) model and the strain-softening (SS) model are carried out. The numerical results are compared with the field-monitoring results, which show that the SSD model simulated the behavior of the surrounding rocks well. The results show that the deformations of the roof and floor are larger, which may serve as a reference for the support pattern of deep roadways.

Development of a damage rheological model and its application in the analysis of mechanical properties of jointed rock masses

AbstractFossil fuel resources (eg, coal, oil, and natural gas) exist in underground reservoirs, where discontinuities are widespread and influence the stability of rock structures. The mechanical behavior of jointed rock masses significantly affects the long‐term stability of rock engineering. A major challenge in this area is to link the time‐dependent deformation with damage influence induced by distribution of joints in rock masses. In this paper, a damage mechanical theory is adopted which deals with several groups of joints distributed in rock masses. Based on the geometrical distribution of joints, a damage model considering the influence of normal vector and area density of joints is used to describe the discontinuities. A damage rheological model for jointed rock masses is developed and programmed in the finite difference software FLAC3D, and an example of jointed rock masses is used to verify the validity of the model. The damage rheological model could predict the visco‐elastic strain which corresponds to primary creep property, visco‐plastic strain which corresponds to steady state creep property, and damage strain which reflects the damage effect of joints to rock masses. Finally, we use this model to predict the displacements and damage zones in the rock masses surrounding an underground opening.

Study on the equivalent mechanical parameter model of fractured rock mass based on the numerical test of particle flow code

In order to obtain accurately the equivalent mechanical parameter model of jointed rock mass, in this paper, the numerical test of particle flow code and Hoek-brown criterion are used to analyse the mechanical parameters of rock mass. First, based on rock sample indoor test, the PFC software is used to check rock block parameters and obtain rock block micromechanics parameters, and the joint elements are added for uniaxial compression and biaxial compression numerical experiments to obtain the mechanical strength parameters of rock mass. Then, these parameters obtained by numerical test are compared with those obtained by Hoek-Brown criterion to comprehensively determine mechanical parameters of rock mass. Finally, the equivalent mechanical parameter model of rock mass is established, and the microscopic parameters of it are obtained by checking the parameters. The research results have certain theoretical significance for joint rock mass modelling.

Generation of Numerical Models of Anisotropic Columnar Jointed Rock Mass Using Modified Centroidal Voronoi Diagrams

A columnar joint network is a natural fracture pattern with high symmetry, which leads to the anisotropy mechanical property of columnar basalt. For a better understanding the mechanical behavior, a novel modeling method for columnar jointed rock mass through field investigation is proposed in this paper. Natural columnar jointed networks lies between random and centroidal Voronoi tessellations. This heterogeneity of columnar cells in shape and area can be represented using the coefficient of variation, which can be easily estimated. Using the bisection method, a modified Lloyd’s algorithm is proposed to generate a Voronoi diagram with a specified coefficient of variation. Modelling of the columnar jointed rock mass using six parameters is then presented. A case study of columnar basalt at Baihetan Dam is performed to demonstrate the feasibility of this method. The results show that this method is applicable in the modeling of columnar jointed rock mass as well as similar polycrystalline materials.

Composite damage constitutive model of jointed rock mass considering crack propagation length and joint friction effect

In order to study the damage constitutive model of rock mass with non-persistent joints in engineering practice, the assumption that the rock mesoscopic elements strength obeys the Weibull distribution function of random, the Drucker–Prager criterion is used as a representation method to describe the strength of the mesoscopic elements, and mesoscopic damage variable is deduced. Combined with the energy principle and the fracture damage theory, the macroscopic damage variable formula is deduced considering the crack propagation length and the friction effect of joint closure in the rock mass. Finally, based on the strain equivalent hypothesis of Lemaitre and considering the coupling of macro and micro defects, the composite damage variables are derived. A macro–meso composite damage constitutive model of rock mass with non-persistent joints is established based on the Drucker–Prager criterion. The theoretical constitutive curves of the model are in good agreement with the experimental constitutive curves of the non-persistent jointed rock masses. The considering effects of crack propagation length and joint closure friction effect are compared with those without considering the crack propagation length and joint closure friction effect, which finds that the former is superior to the latter, and the rationality and validity of the model is verified.

Effect Mechanism of Fractures on the Mechanics Characteristics of Jointed Rock Mass Under Compression

Based on the theory of particle flow and the PFC2D program, a jointed rock mass model was constructed with a single-joint rock and angle joints of 0 $$^{\circ }$$ , 30 $$^{\circ }$$ , 45 $$^{\circ }$$ , 60 $$^{\circ }$$ , and 90 $$^{\circ }$$ . A universal testing machine was used for rock compression testing for an in-depth study of rock mechanical features during their destruction, allowing investigation into their macro- and micromechanical properties. Compressive tests were performed using numerical simulation to observe the generation and development of fissures and study their failure mechanics, so as to understand the entire process of crack generation, expansion, and penetration. The main findings are as follows: (1) Tension failure dominates the failure modes of specimens as showed by testing and numerical simulation; (2) The impact of the joints on rock mass strength depends strongly on their angle of inclination, which can destroy the original rock structure and result in major changes to rock mass strength; (3) No simple proportionality exists between joint angle and uniaxial compressive strength of specimen, but as the joint angle increases, uniaxial compressive strength increases and then decreases. (4) The forms of major fissures are highly similar and are mainly distributed near the ends of joints, with narrower fissure zones close to the end.

Modelling jointed rock mass as a continuum with an embedded cohesive-frictional model

The mechanical and hydraulic properties of a jointed rock mass are strongly affected by the characteristics of joints within the intact rock mass. In this study, a constitutive model for jointed rock masses is developed by incorporating the contributions of both the joint and its surrounding rock mass. The behaviour of the joint is represented by a new coupled damage-plasticity cohesive-frictional model taking into account its dilation evolution and the reduction of both strength and stiffness, while the surrounding rock behaviour is assumed to behave elastically. The interactions between the joint and the surrounding rock are described by a set of kinematic enhancements and internal equilibrium equations across the interface of the joint. The formulation of the proposed model is presented along with its implementation algorithms and validation with experimental data. The enhanced kinematics facilitates the incorporation of both behaviour and orientation of the joint, together with the size and behaviour of the surrounding rock, allowing capturing key characteristics of jointed rock mass responses under mixed-mode loading conditions at different spatial scales.

Investigation on jointed rock strength based on fractal theory

Strength of discontinuities with complex structure is an important topic in rock engineering. A large number of studies have shown that fractal is applicable in the description of this discontinuity. Using fractal interpolation method for the generation of rock joints, numerical experiments of shear tests of the jointed rock mass model were carried out using FLAC3D. The test results show that the real rock joints can be simulated by fractal curves obtained by fractal interpolation. The fractal dimension is an important factor for the characterization of jointed rock mass; test results show that the fractal dimension of rock joints can be related to the equivalent cohesion strength and shear strength of the rock mass. When the fractal dimension of the joint surface is less than critical dimension D c 1.404, the cohesion strength and shear strength of the rock mass increase as the fractal dimension increases; for larger fractal dimensions, all mechanical parameters decrease as the fractal dimension increases. Joint surfaces with different degrees of roughness were obtained by the fractal interpolation method. Three types of failure modes were observed in the tests: climbing slip failure, climbing gnawing fracture, and non-climbing gnawing fracture.

A Parametric Study Using Numerical Modelling to Assess the Stability of Marble Quarries

Marble quarries, are located at 3km southeast of the city of Afyon İscehisar. The marble bed is lens shaped has a thickness of 300 meters. İscehisar is on south of the city center and marble bed extends through NW-SE direction for 6km long and 1.5km wide. Present base elevation of İscehisar marble quarry is at 1020 m and it is planned to be excavated down to 980 m elevation. The aim of this study is to determine the stability deep slopes at maximum depth (> 90 m) using numerical modelling. In the finite element method, generalized Hoek-Brown and Mohr-Coulomb failure criteria together with a jointed rock mass model are used. In marble quarries, particularly in this locations, the rock mass is severely affected by sliding blocks, caused by four intersecting joint sets. Stability analysis were conducted under static and dynamic conditions using Phase2V.9.016 software. Shear Strength Reduction (SSR) technique that is built into the software used to determine the failure mechanisms and to suggest and the necessary controls to ensure the stability of the slopes.

Effect of parallel joint interaction on mechanical behavior of jointed rock mass models

To better understand the interaction of parallel joints and its effect on the mechanical behavior of jointed rock mass models, the results of a physical experiment program undertaken in the laboratory were present in this manuscript. The joint spacing and joint overlap are varied to alter the relative positions of parallel joints in geometry. Accordingly, four basic failure modes identified from the testing results are tensile failure across the joint plane, shear failure along the joint plane, tensile failure along the joint plane, and intact material failure. The wing cracks from tensile failure across the joint plane mode represent the interaction between parallel joints which depends on the joint dip angle, joint spacing and joint overlap. With the increment of parallel joint interaction, the corresponding normalized strength and maximum displacement at peak stress of jointed rock mass models reduced generally except at α=0°.

An elasto-plastic damage constitutive model for jointed rock mass with an application

A forked tunnel, as a special complicated underground structure, is composed of big-arch tunnel, multi-arch tunnel, neighborhood tunnels and separate tunnels according to the different distances between two separate tunnels. Due to the complicated process of design and construction, surrounding jointed rock mass stability of the big-arch tunnel which belongs to the forked tunnel during excavation is a hot issue that needs special attentions. In this paper, an elasto-plastic damage constitutive model for jointed rock mass is proposed based on the coupling method considering elasto-plastic and damage theories, and the irreversible thermodynamics theory. Based on this elasto-plastic damage constitutive model, a three dimensional elasto-plastic damage finite element code (D-FEM) is implemented using Visual Fortran language, which can numerically simulate the whole excavation process of underground project and perform the structural stability of the surrounding rock mass. Comparing with a popular commercial computer code, three dimensional fast Lagrangian analysis of continua (FLAC3D), this D-FEM has advantages in terms of rapid computing process, element grouping function and providing more material models. After that, FLAC3D and D-FEM are simultaneously used to perform the structural stability analysis of the surrounding rock mass in the forked tunnel considering three different computing schemes. The final numerical results behave almost consistent using both FLAC3D and D-FEM. But from the point of numerically obtained damage softening areas, the numerical results obtained by D-FEM more closely approach the practical behaviors of in-situ surrounding rock mass.

Discrete element modeling of strata and surface movement induced by mining under open-pit final slope

Ore mining under the open-pit final slope will result in caving and large displacement movement of rock-masses surrounding the goaf. It is difficult for numerical methods that equate jointed rock-masses to a continuum to simulate the aforementioned mechanical behavior of rock-masses. However, the placing of joints in a calculation model according to their actual distribution characteristics will result in an excess of model blocks, which renders the calculation impossible. To solve this problem, a numerical modeling method based on an Equivalent Jointed Rock-mass Model (EJRM) is proposed in this paper. First, the rock-masses in the research area are simplified as an EJRM; then, a back analysis method, combining orthogonal design and numerical simulation with Discrete Element Method (DEM), is used to invert the mechanical parameters of the model; lastly, the DEM is utilized to analyze the movement and failure of the strata and surface induced by mining under open-pit slope. The Yanqianshan iron ore mine was treated as an example in the present study. Mining under the eastern slope of the open pit of the mine was simulated by means of the aforementioned method. The patterns of the failure and movement of the strata and slope at different mining stages were obtained. This numerical modeling method proposed can be used to simulate complex mechanical behaviors of rock-masses induced by underground mining.

Forecast Jointed Rock Mass Compressive Strength Using a Numerical Model

The method of forecasting the strength of the jointed rock mass by numerical modeling of finite element method in ABAQUS was described. The paper presents advantages of this method to solve the problem of determining the mechanical characteristics of jointed rock mass and the basic steps of creating a numerical geomechanical model of jointed rock mass and numerical experiment. Numerical simulation was carried out with jointed rock mass in order to obtain the ratio of strain and stress while loading the numerical model, determining parameters of quantitative assessment of the impact of the discontinuities orientation on the value of the compressive strength, compressive strength anisotropy. The results of the numerical experiment are compared with the data of experimental studies investigations. Innovative materials and structures are analyzed in this paper. The results that were obtained by calculation show qualitative agreement with the results of laboratory experiments of jointed rock mass.