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.

A new elastoplastic model for bolt-grouted fractured rock

Complexities in mechanical behaviours of rock masses mainly stem from inherent discontinuities,which calls for advanced bolt-grouting techniques for stability enhancement.Understanding the mechanical properties of bolt-grouted fractured rock mass(BGFR)and developing accurate prediction methods are crucial to optimize the BGFR support strategies.This paper establishes a new elastoplastic(E-P)model based on the orthotropic and the Mohr-Coulomb(M-C)plastic-yielding criteria.The elastic parameters of the model were derived through a meso-mechanical analysis of composite materials mechanics(CMM).Laboratory BGFR specimens were prepared and uniaxial compression test and variable-angle shear test considering different bolt arrangements were carried out to obtain the mechanical parameters of the specimens.Results showed that the anisotropy of BGFR mainly depends on the relative volume content of each component material in a certain direction.Moreover,the mechanical parameters deduced from the theory of composite materials which consider the short fibre effect are shown to be in good agreement with those determined by laboratory experiments,and the variation rules maintained good consistency.Last,a case study of a real tunnel project is provided to highlight the effectiveness,validity and robustness of the developed E-P model in prediction of stresses and deformations.

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.

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.

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.

Fracture behavior and mechanism of highly fragmented steel cylindrical shell under explosive loading

An in-depth understanding of the fracture behavior and mechanism of metallic shells under internal explosive loading can help develop material designs for warheads and regulate the quantity and mass distribution of the fragments formed.This study investigated the fragmentation performance of a new high-carbon silicon-manganese(HCSiMn)steel cylindrical shell through fragment recovery experiments.Compared with the conventional 45Cr steel shell,the number of small mass fragments produced by the HCSi Mn steel shell was significantly increased with a scale parameter of 0.57 g fitted by the Weibull distribution model.The fragmentation process of the HCSi Mn shell exhibited more brittle tensile fracture characteristics,with the microcrack damage zone on the outer surface being the direct cause of its high fragmentation.On the one hand,the doping of alloy elements resulted in grain refinement by forming metallographic structure of tempered sorbite,so that microscopic intergranular fracture reduces the characteristic mass of the fragments;on the other hand,the distribution of alloy carbides can exert a"pinning"effect on the substrate grains,causing more initial cracks to form and propagate along the brittle carbides,further improving the shell fragmentation.Although the killing power radius for light armored vehicles was slightly reduced by about 6%,the dense killing radius of HCSiMn steel projectile against personnel can be significantly increased by about 26%based on theoretical assessment.These results provided an experimental basis for high fragmentation warhead design,and to some extent,revealed the correlation mechanism between metallographic structure and shell fragmentation.

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.

Deformation analysis of transversely isotropic coal-rock mass with porous and cracks

Coal-rock as a typical sedimentary rock has obvious stratification,namely it has transversely isotropic feature.Meanwhile,deformation leads to coal-rock mass having the characteristics of different porous and crack structures as well as local anisotropy.Equivalent axial and circumferential strain' formulas of the pure coal-rock mass specimen with a single crack were derived through the establishment of equivalent mechanical model of standard cylindrical coal-rock specimen,and have been widely used to a variety of media combined different structures containing multiple cracks.The complete stress strain curve of a real coal-rock specimen was obtained by the CTC test.Additionally,according to the comparison with the theoretical value,the theoretical mechanical model could well explain the deformation characteristics of coal-rock mass and verify its validity.Further,following features were analyzed:strain normalized coefficient and elastic modulus(Poisson's ratio) in vertical and parallel direction to the stratification,stratification angle,porosity,pore radius,normal and tangential stiffness of crack,and the relationship of different crack width with different tangential stiffness of crack.Through the analysis above,it substantiate this claim that the theoretical model with better reliability reflects the transversely isotropic nature of the coal-rock and the local anisotropy caused by the porous and cracks.

Similarity model tests of movement and deformation of coal-rock mass below stopes

For a study of the movement and deformation of coal-rock mass and low protected seams below a stope,as well as for fracture developments and rules of evolution of permeability,we designed a plane strain model test stand to carry out model tests of similar materials in order to improve the effect of gas drainage from low protected seams and to measure the movement and deformation of coal-rock mass using a method of non-contact close-range photogrammetry.Our results show that 1) using paraffin melting to take the place of coal seam mining can satisfy the mining conditions of a protective seam;2) coal-rock mass under goafs has an upward movement after the protective seam has been mined,causing floor heaving;3) low protected seams become swollen and deformed,providing a good pressure-relief effect and causing the coal-rock mass under both sides of coal pillars to become deformed by compression and 4) the evolution of permeability of low protected seams follows the way of initial values→a slight decrease→a great increase→stability→final decrease.Simultaneously,the coefficient of air permeability increased at a decreasing rate with an increase in interlayer spacing.

Ultrasound diagnosis of fractures in mass casualty incidents

The role of point-of-care ultrasound in mass casualty incidents(MCIs)is still evolving.Occasionally,hospitals can be destroyed by disasters resulting in large number of trauma patients.CAVEAT and FASTER ultrasound protocols,which are used in MCIs,included extremity ultrasound examination as part of them.The literature supports the use of ultrasound in diagnosing extremity fractures both in hospitals and MCIs.The most recent systematic review which was reported by Douma-den Hamer et al in 2016 showed that the pooled ultrasound sensitivity and specificity for detecting distal forearm fractures was 97% and 95% respectively.Nevertheless,majority of these studies were in children and they had very high heterogeneity.The portability,safety,repeatability,and cost-effectiveness of ultrasound are great advantages when treating multiply injured patients in MCIs.Its potential in managing fractures in MCIs needs to be further defined.The operator should master the technique,understand its limitations,and most importantly correlate the sonographic findings with the clinical ones to be useful.This editorial critically reviews the literature on this topic,describes its principles and techniques,and includes the author’s personal learned lessons so that trauma surgeons will be encouraged to use ultrasound to diagnose fractures in their own clinical practice.

Numerical simulation on pressure-relief deformation characteristics of underlying coal-rock mass after upper protective layer excavation

Based on the occurrence features of Group B coal-seams at a coal mine in the Huainan coal mining area, the elasto-plastic mechanical damage constitutive functions and numerical model for the protective layer excavation were established. With the UDEC2D computer program, after the upper protective layer was mined, the stress field change trends, crack development, and expansion deformation trends of underlying coal rock seams in the floor of the working face were simulated and analyzed. The simulation results show the stress changes in coal rock seams, the evolution process of pre-cracks during the process of upper protective layer mining, the caved zone and fractured zone of the underlying coal rock seams. At the same time, the results from the actual investigation and analysis of protected layer deformation match the simulation values, which verifies the validity and accuracy of numerical simulation results. The study results have an important guiding significance for gas management in low permeability and high gas coal seams with similar mining conditions.

3-D fracture network dynamic simulation based on error analysis in rock mass of dam foundation

Accurate 3-D fracture network model for rock mass in dam foundation is of vital importance for stability,grouting and seepage analysis of dam foundation.With the aim of reducing deviation between fracture network model and measured data,a 3-D fracture network dynamic modeling method based on error analysis was proposed.Firstly,errors of four fracture volume density estimation methods(proposed by ODA,KULATILAKE,MAULDON,and SONG)and that of four fracture size estimation methods(proposed by EINSTEIN,SONG and TONON)were respectively compared,and the optimal methods were determined.Additionally,error index representing the deviation between fracture network model and measured data was established with integrated use of fractal dimension and relative absolute error(RAE).On this basis,the downhill simplex method was used to build the dynamic modeling method,which takes the minimum of error index as objective function and dynamically adjusts the fracture density and size parameters to correct the error index.Finally,the 3-D fracture network model could be obtained which meets the requirements.The proposed method was applied for 3-D fractures simulation in Miao Wei hydropower project in China for feasibility verification and the error index reduced from 2.618 to 0.337.

Mechanical properties and failure characteristics of fractured sandstone with grouting and anchorage

Based on uniaxial compression experimental results on fractured sandstone with grouting and anchorage, we studied the strength and deformation properties, the failure model, crack formation and evolution laws of fractured sandstone under different conditions of anchorage. The experimental results show that the strength and elastic modulus of fractured sandstone with different fracture angles are significantly lower than those of intact sandstone. Compared with the fractured samples without anchorage,the peak strength, residual strength, peak and ultimate axial strain of fractured sandstone under different anchorage increase by 64.5–320.0%, 62.8–493.0%, and 31.6–181.4%, respectively. The number of bolts and degree of pre-stress has certain effects on the peak strength and failure model of fractured sandstone. The peak strength of fractured sandstone under different anchorage increases to some extent, and the failure model of fractured sandstone also transforms from tensile failure to tensile–shear mixed failure with the number of bolts. The pre-stress can restrain the formation and evolution process of tensile cracks, delay the failure process of fractured sandstone under anchorage and impel the transformation of failure model from brittle failure to plastic failure.

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.