Numerical manifold method for thermo-mechanical coupling simulation of fractured rock mass

As a calculation method based on the Galerkin variation,the numerical manifold method(NMM)adopts a double covering system,which can easily deal with discontinuous deformation problems and has a high calculation accuracy.Aiming at the thermo-mechanical(TM)coupling problem of fractured rock masses,this study uses the NMM to simulate the processes of crack initiation and propagation in a rock mass under the influence of temperature field,deduces related system equations,and proposes a penalty function method to deal with boundary conditions.Numerical examples are employed to confirm the effectiveness and high accuracy of this method.By the thermal stress analysis of a thick-walled cylinder(TWC),the simulation of cracking in the TWC under heating and cooling conditions,and the simulation of thermal cracking of the SwedishÄspöPillar Stability Experiment(APSE)rock column,the thermal stress,and TM coupling are obtained.The numerical simulation results are in good agreement with the test data and other numerical results,thus verifying the effectiveness of the NMM in dealing with thermal stress and crack propagation problems of fractured rock masses.

Multi-domain equivalent method for prediction of elastic modulus of complex fractured rock mass

Reliable estimation of deformation and failure behaviors of fractured rock mass is important for practical engineering design.This study proposes a multi-domain equivalent method for fracture network to estimate the deformation properties of complex fractured rock mass.It comprehends both the advantages of the discrete fracture network model and the equivalent continuum model to capture the features of discontinuities explicitly while reducing computational intensity.The complex fracture network is stochastically split into a number of subfracture networks according to the domain,length or angle.An analytical solution is derived to infer theoretically the relationship between the elastic moduli of the original complex fractured rock mass and the split subfractured rock masses by introducing a correction term based on the deformation superposition principle.Numerical simulations are conducted to determine the elastic moduli of split subfractured rock masses using universal distinct element code(UDEC),while the elastic modulus of the original model is estimated based on the currently proposed analytical relationship.The results show that the estimation accuracy with the current domainbased splitting model is far superior compared to those with the other two splitting models.Thus,the estimation method of elastic modulus of complex fractured rock mass based on domain splitting mode of fracture network is identified as the multi-domain equivalent method proposed in this paper.The reliability of this method is evaluated,and its high computational efficiency is demonstrated through exemplification with regard to different geometric configurations for stochastically artificial discrete fracture network.The proposed multi-domain equivalent method constructs the theoretical framework except for the regression analysis hypothesis compared to the density-reduced model equivalent method.

Fracture behaviors of columnar jointed rock mass using interface mechanics theorem

For a special geological structure of columnar jointed rock mass(CJRM),its mechanical properties are strongly affected by the columnar joints.To describe the fracture behaviors of CJRM using the basic theories of interface mechanics for composite materials,the interface stresses of the vertical and horizontal joints,which are the two primary joints in the CJRM under triaxial compression,are studied,and their mathematical expressions are derived based on the superposition principle.Based on the obtained interface stresses of the vertical and horizontal joints in the CJRM,the crack initiation of the joint interface in the CJRM is studied using the maximum circumferential stress theory in fracture mechanics.Moreover,based on this investigation,the fracture behaviors of CJRM are analyzed.According to the results of similar material physical model tests for the CJRM,the theoretical study is verified.Finally,the influence of the mechanical parameters of the CJRM on the joint interface stress is discussed comprehensively.

Comprehensive assessment on dynamic roof instability under fractured rock mass conditions in the excavation disturbed zone

The damage process of fractured rock mass showed that the fracture in rocks induced roof collapse in Yangchangwan Coal Mine, China. The rock mass was particularly weak and fractured. There occurred 6 large-scale dynamical roof falls in the excavation disturbed zone （EDZ） with the collapsing volume of 216 m^3. First, the field detailed geological environment, regional seismic dynamics, and dynamic instability of roadways were generally investigated. Second, the field multiple-index monitoring measurements for detecting the deep delamination of the roof, convergence deformation, bolt-cable load, acoustic emission （AE） characteristic parameters, total AE events, AE energy-releasing rate, rock mass fracture, and damage were arranged. Finally, according to the time-space-strength relations, a quantitative assessment of the influence of rock-mass damage on the dynamic roof instability was accomplished.

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.

Determination of hydraulic conductivity of fractured rock masses:A case study for a rock cavern project in Singapore

In order to reduce the risk associated with water seepage in an underground rock cavern project inSingapore, a reliable hydro-geological model should be established based on the in situ investigationdata. The key challenging issue in the hydro-geological model building is how to integrate limitedgeological and hydro-geological data to determine the hydraulic conductivity of the fractured rockmasses. Based on the data obtained from different stages （feasibility investigation stage, constructionstage, and post-construction stage）, suitable models and methods are proposed to determine the hydraulicconductivities at different locations and depths, which will be used at other locations in thefuture. 2015 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Effects of fracture distribution and length scale on the equivalent continuum elastic compliance of fractured rock masses

Fracture systems have strong influence on the overall mechanical behavior of fractured rock masses dueto their relatively lower stiffness and shear strength than those of the rock matrix. Understanding theeffects of fracture geometrical distribution, such as length, spacing, persistence and orientation, isimportant for quantifying the mechanical behavior of fractured rock masses. The relation betweenfracture geometry and the mechanical characteristics of the fractured rock mass is complicated due tothe fact that the fracture geometry and mechanical behaviors of fractured rock mass are stronglydependent on the length scale. In this paper, a comprehensive study was conducted to determine theeffects of fracture distribution on the equivalent continuum elastic compliance of fractured rock massesover a wide range of fracture lengths. To account for the stochastic nature of fracture distributions, threedifferent simulation techniques involving Oda＇s elastic compliance tensor, Monte Carlo simulation （MCS）,and suitable probability density functions （PDFs） were employed to represent the elastic compliance offractured rock masses. To yield geologically realistic results, parameters for defining fracture distributionswere obtained from different geological fields. The influence of the key fracture parameters andtheir relations to the overall elastic behavior of the fractured rock mass were studied and discussed. Adetailed study was also carried out to investigate the validity of the use of a representative elementvolume （REV） in the equivalent continuum representation of fractured rock masses. A criterion was alsoproposed to determine the appropriate REV given the fracture distribution of the rock mass.

Some results of modeling D-D seismogenic pattern by the fracture model experiment of large-scale rock samples(I)

sing the natural limestone samples taken from the field with dimension of 500 mm×500 mm×1 000 mm, the D-D (dilatancy-diffusion) seismogeny pattern was modeled under the condition of water injection, which observes the time-space evolutionary features about the relative physics fields of the loaded samples from deformation, formation of microcracks to the occurrence of main rupture. The results of observed apparent resistivity show: ① The process of the deformation from microcrack to main rupture on the loaded rock sample could be characterized by the precursory spatial-temporal changes in the observation of apparent resistivity; ② The precursory temporal changes of observation in apparent resistivity could be divided into several stages, and its spatial distribution shows the difference in different parts of the rock sample; ③ Before the main rupture of the rock sample the obvious ″tendency anomaly′ and ′short-term anomaly″ were observed, and some of them could be likely considered as the ″impending earthquake ″anomaly precursor of apparent resistivity. The changes and distribution features of apparent resistivity show that they are intrinsically related to the dilatancy phenomenon of the loaded rock sample. Finally, this paper discusses the mechanism of resistivity change of loaded rock sample theoretically.

Model test study of frost heaving pressures in tunnels excavated in fractured rock mass in cold regions

Based on the similarity theory, taking the horseshoe, city-gate and round linings as examples, the value and distribution regularities of normal frost heaving pressures （hereinafter as frost heaving pressures） in tunnels excavated in fractured rock mass in cold regions under different constraints and freezing depths were studied by a test model. It was found that the larger the frozen depth, the larger the frost heaving pressure, and the stronger the top constraint, the larger the frost heaving pressure. For the horseshoe lining and city-gate lining, the top constraint has a greater effect on the frost heaving pressures on the arch and the inverted arch. For the round lining, the influences of the top constraint on the frost heaving pressure in all linings are almost the same. The frost heaving pressure is maximum on the city-gate lining and minimal on the round lining. The largest frost heaving pressure all occur near the foot of the inverted arch for the three kinds of lining. Thus, the test data basically coincide with the observed in situ data.

Coupled hydro-mechanical effect of a fractured rock mass under high water pressure

To explore the variation of permeability and deformation behaviors of a fractured rock mass in high water pressure,a high pressure permeability test（HPPT）,including measuring sensors of pore water pressure and displacement of the rock mass,was designed according to the hydrogeological condition of Heimifeng pumped storage power station.With the assumption of radial water flow pattern in the rock mass during the HPPT,a theoretical formula was presented to estimate the coefficient of permeability of the rock mass using water pressures in injection and measuring boreholes.The variation in permeability of the rock mass with the injected water pressure was studied according to the suggested formula.By fitting the relationship between the coefficient of permeability and the injected water pressure,a mathematical expression was obtained and used in the numerical simulations.For a better understanding of the relationship between the pore water pressure and the displacement of the rock mass,a 3D numerical method based on a coupled hydro-mechanical theory was employed to simulate the response of the rock mass during the test.By comparison of the calculated and measured data of pore water pressure and displacement,the deformation behaviors of the rock mass were analyzed.It is shown that the variation of displacement in the fractured rock mass is caused by water flow passing through it under high water pressure,and the rock deformation during the test could be calculated by using the coupled hydro-mechanical model.

In-situ observations of damage-fracture evolution in surrounding rock upon unloading in 2400-m-deep tunnels

The damage-fracture evolution of deep rock mass has obvious particularity,which is revealed in 2400-mdeep tunnels by field tests.The evolution of the excavation damaged zone depth is consistent with that of the fractured zone depth.The ratio of the excavation damaged zone depth to the excavation fractured zone depth is greater than 2.0 in a rock mass with both high strength and good integrity,but less than1.5 in a rock mass with lower strength or poor integrity.Zonal disintegration in a rock mass with high strength and fair integrity is more likely to occur when it contains more than two groups of primary fractures in damaged zones.Fractures develop outward in zonal disintegration but are totally different from the single-zone fracture,in which the fractures develop inward,and it is the starting position of the fractured zone when the excavation surface of the middle pilot is 7–9 m close to the pre-set borehole and it stops after the excavation surface of the baseplate is 11–14 m away.The most intense evolution occurs around 2–4 m from the pre-set borehole in the sidewall expansion stage.The research results provide a reference for the monitoring scheme and support design of CJPL-Ⅲin its future construction.

Application and prospects of 3D printing in physical experiments of rock mass mechanics and engineering:materials,methodologies and models

The existence of joints or other kinds of discontinuities has a dramatic efect on the stability of rock excavations and engineering.As a result,a great challenge in rock mass mechanics testing is to prepare rock or rock-like samples with defects.In recent years,3D printing technology has become a promising tool in the feld of rock mass mechanics and engineering.This study frst reviews and discusses the research status of traditional test methods in rock mass mechanics tests of making rock samples with defects.Then,based on the comprehensive analysis of previous research,the application of 3D printing technology in rock mass mechanics is expounded from the following three aspects.The frst is the printing material.Although there are many materials for 3D printing,it has been found that 3D printing materials that can be used for rock mass mechanics research are very limited.After research,we summarize and evaluate printing material that can be used for rock mass mechanics studies.The second is the printing methodology,which mainly introduces the current application forms of 3D printing technology in rock mass mechanics.This includes printed precise casting molds and one-time printed samples.The last one is the printing model,which includes small-scale samples for mechanical tests and large-scale physical models.Then,the benefts and drawbacks of using 3D printing samples in mechanical tests and the validity of their simulation of real rock are discussed.Compared with traditional rock samples collected in nature or synthetic rock-like samples,the samples made by 3D printing technology have unique advantages,such as higher test repeatability,visualization of rock internal structure and stress distribution.There is thus great potential for the use of 3D printing in the feld of rock mass mechanics.However,3D printing materials also have shortcomings,such as insufcient material strength and accuracy at this stage.Finally,the application prospect of 3D printing technology in rock mass mechanics research is proposed.

Application of laser scanning for rock mass characterization and discrete fracture network generation in an underground limestone mine

Terrestrial laser scanning(TLS) is a useful technology for rock mass characterization. A laser scanner produces a massive point cloud of a scanned area, such as an exposed rock surface in an underground tunnel,with millimeter precision. The density of the point cloud depends on several parameters from both the TLS operational conditions and the specifications of the project, such as the resolution and the quality of the laser scan, the section of the tunnel, the distance between scanning stations, and the purpose of the scans. One purpose of the scan can be to characterize the rock mass and statistically analyze the discontinuities that compose it for further discontinuous modeling. In these instances, additional data processing and a detailed analysis should be performed on the point cloud to extract the parameters to define a discrete fracture network(DFN) for each discontinuity set. I-site studio is a point cloud processing software that allows users to edit and process laser scans. This software contains a set of geotechnical analysis tools that assist engineers during the structural mapping process, allowing for greater and more representative data regarding the structural information of the rock mass, which may be used for generating DFNs. This paper presents the procedures used during a laser scan for characterizing discontinuities in an underground limestone mine and the results of the scan as applied to the generation of DFNs for further discontinuous modeling.

A discrete model for prediction of radon flux from fractured rocks

Prediction of radon flux from the fractured zone of a propagating cave mine is basically associated with uncertainty and complexity. For instance, there is restricted access to these zones for field measure- ments, and it is quite difficult to replicate the complex nature of both natural and induced fractures in these zones in laboratory studies. Hence, a technique for predicting radon flux from a fractured rock using a discrete fracture network （DFN） model is developed to address these difficulties. This model quantifies the contribution of fractures to the total radon flux, and estimates the fracture density from a measured radon flux considering the effects of advection, diffusion, as well as radon generation and decay. Radon generation and decay are classified as reaction processes. Therefore, the equation solved is termed as the advection-diffusion-reaction equation （ADRE）. Peclet number （Pe）, a conventional dimensionless parameter that indicates the ratio of mass transport by advection to diffusion, is used to classify the transport regimes. The results show that the proposed model effectively predicts radon flux from a fractured rock. An increase in fracture density for a rock sample with uniformly distributed radon generation rate can elevate radon flux significantly compared with another rock sample with an equivalent increase in radon generation rate. In addition to Pe, two other independent dimensionless parameters （derived for radon transport through fractures） significantly affect radon dimensionless flux. Findings provide insight into radon transport through fractured rocks and can be used to improve radon control measures for proactive mitigation.

Anisotropy of strength and deformability of fractured rocks

Anisotropy of the strength and deformation behaviors of fractured rock masses is a crucial issue for design and stability assessments of rock engineering structures, due mainly to the non-uniform and non- regular geometries of the fracture systems. However, no adequate efforts have been made to study this issue due to the current practical impossibility of laboratory tests with samples of large volumes con- taining many fractures, and the difficulty for controlling reliable initial and boundary conditions for large-scale in situ tests. Therefore, a reliable numerical predicting approach for evaluating anisotropy of fractured rock masses is needed. The objective of this study is to systematically investigate anisotropy of strength and deformability of fractured rocks, which has not been conducted in the past, using a nu- merical modeling method. A series of realistic two-dimensional （2D） discrete fracture network （DFN） models were established based on site investigation data, which were then loaded in different directions, using the code UDEC of discrete element method （DEM）, with changing confining pressures. Numerical results show that strength envelopes and elastic deformability parameters of tested numerical models are significantly anisotropic, and vary with changing axial loading and confining pressures. The results indicate that for design and safety assessments of rock engineering projects, the directional variations of strength and deformability of the fractured rock mass concerned must be treated properly with respect to the directions of in situ stresses. Traditional practice for simply positioning axial orientation of tunnels in association with principal stress directions only may not be adequate for safety requirements. Outstanding issues of the present study and su^zestions for future study are also oresented.

Estimation of Fracture Geometry Parameters and Characterization of Rock Mass Structure for the Beishan Area,China

The accurate estimation of fracture geometry parameters and the characterization of rock mass structure are two important topics in the geological disposal system of high-level radioactive waste(HLW).The Beishan area,as the current preselected area for China’s HLW disposal,has three subareas considered to be the key survey area at the stage of site selection.In this paper,a comprehensive survey method conducted on the outcrop is developed to estimate fracture geometry parameters.Results show that fracture occurrence obeys a Fisher distribution,fracture trace length obeys a normal distribution,and the distribution of spacing obeys a negative exponential distribution.An evaluation index,Rock Mass Structure Rating(RMSR),is proposed to characterize rock mass structure for the three subareas.The results show that the Xinchang area is more suitable to act as China’s HLW disposal repository site.At the same time,the index can also be applied to characterize surface rock mass structure and rock mass integrity at the site selection phase of HLW disposal.

A Study on Propagation Mechanism of Fracture Systems in Rock Masses by Discontinuity Displacement Method

The main task of fracture mechanics of rock masses is the study on the propagating mechanism of fractures in rock masses , which can be efficiently conducted by discontinuty displacement (DD) numerical evaluation . Firstly ,the element stress and displacement are analysed and the principle and steps of the numerical calculation of stress intensity factor and fracture extension force are introduced .The numerical results of parallel and echelon fracture systems ,which are compared with real field fractures .are presented. Finally . a simple engineering application example is presented .

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 preexisting 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.

A universal elliptical disc(UED)model to represent natural rock fractures

Since natural fractures are often non-equidimensional,the circular disc model still has great limitations.By contrast,the elliptical disc model is more applicable to representing natural fractures,especially for slender ones.This paper developed a universal elliptical disc(UED)model by incorporating the center point,size,and azimuth of fractures as variables.Specifically,with respect to the azimuth of elliptical fractures in three-dimensional(3D)space,we proposed a paradigm to construct its probability density function(PDF)by coupling the orientation and rotation angle of long axis based on three coordinate transformations.To illustrate the construction process of the PDF of the fracture azimuth,we took the orientation following the Fisher distribution and the rotation angle following Von Mises distribution as an example.A rock slope is used to show the use of the developed UED model,and the 3D DFNs for the slope rock mass are generated by Monte Carlo simulation.In addition,the DFNs for the rock mass are also generated based on the existing circular disc model and non-universal elliptical disc model.The comparison results from the three models clearly illustrate the superiority of the UED model over the existing circular and non-universal elliptical disc models.