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.

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.

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.

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 .

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.

Effect of fissure water on mechanical characteristics of rock mass

In view of the effect of fissure water in fractured rock mass on the strength of rock mass in engineering projects, we pre-pared specimens of cement mortar to simulate saturated rock mass with continuous fractures of different slope angles. By exerting static and dynamic loads on the specimens, the mechanical characteristics of rock mass with fissure water under these loads can be analyzed. Our experimental results indicate that the static compressive strength of saturated fractured rock mass is related to the slope angle. The lowest compressive strength of fractured rock mass occurs when the slope angle is 45°, while the highest strength occurs when the specimen has no fractures. Fissure water can weaken the strength of rock mass. The softening coefficient does not vary with the slope angle and type of load. The hydrodynamic pressure of fractured rock mass gradually increases with an increase in dynamic load. For a 0° slope angle, the hydrodynamic pressure reaches its highest level. When the slope angle is 90°, the hydro-dynamic pressure is the lowest.

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.

Seepage-heat transfer coupling process of low temperature return water injected into geothermal reservoir in carbonate rocks in Xian County,China

Fracture seepage and heat transfer in the geothermal reservoir of carbonate rocks after the reinjection of low temperature geothermal return water is a complex coupling process,which is also the frontier of geothermal production and reinjection research.Based on the research of cascade comprehensive development of geothermal resources in Beijing-Tianjin-Hebei(Xian County),the carbonate geothermal reservoir of Wumishan formation in the geothermal field in Xian County is investigated.With the development of the discrete fracture network model and the coupling model of seepage and heat transfer,the numerical solution of seepage field and temperature field with known fracture network is reached using the finite element software COMSOL,and the coupling process of seepage flow and heat in carbonate rocks is revealed.The results show that the distribution of temperature field of fractured rocks in geothermal reservoir of carbonate rocks has strong non-uniformity and anisotropy.The fracture network is interpenetrated,which constitutes the dominant channel of water conduction,and along which the fissure water moves rapidly.Under the influence of convective heat transfer and conductive heat transfer,one of the main factors to be considered in the study of thermal breakthrough is to make the cold front move forward rapidly.When the reinjection and production process continues for a long time and the temperature of the geothermal reservoir on the pumping side drops to a low level,the temperature of bedrocks is still relatively high and continues to supply heat to the fissure water,so that the temperature of the thermal reservoir on the pumping side will not decrease rapidly to the water temperature at the inlet of reinjection,but will gradually decrease after a long period of time,showing an obvious long tail effect.The distribution of fractures will affect the process of seepage and heat transfer in carbonate reservoirs,which should be considered in the study of fluid thermal coupling in carbonate reservoirs.

Stress wave propagation and incompatible deformation mechanisms in rock discontinuity interfaces in deep-buried tunnels

Complex weak structural planes and fault zones induce significant heterogeneity,discontinuity,and nonlinear characteristics of a rock mass.When an earthquake occurs,these characteristics lead to extremely complex seismic wave propagation and vibrational behaviors and thus pose a huge threat to the safety and stability of deep buried tunnels.To investigate the wave propagation in a rock mass with different structural planes and fault zones,this study first introduced the theory of elastic wave propagation and elastodynamic principles and used the Zoeppritz equation to describe wave field decomposition and develop a seismic wave response model accordingly.Then,a physical wave propagation model was constructed to investigate seismic waves passing through a fault,and dynamic damage was analyzed by using shaking table tests.Finally,stress wave attenuation and dynamic incompatible deformation mechanisms in a rock mass with fault zones were explored.The results indicate that under the action of weak structural planes,stress waves appear as a complex wave field decomposition phenomenon.When a stress wave spreads to a weak structural plane,its scattering may transform into a tensile wave,generating tensile stress and destabilizing the rock mass;wave dynamic energy is absorbed by a low-strength rock through wave scattering,which significantly weakens the seismic load.Wave propagation accelerates the initiation and expansion of internal defects in the rock mass and leads to a dynamic incompatible deformation.This is one of the main causes for large deformation and even instability within rock masses.These findings provide an important reference and guide with respect to stability analysis of rock mass with weak structural planes and fault zones.

Key issues in water sealing performance of underground oil storage caverns: Advances and perspectives

Water sealing performance is important for underground water-sealed oil storage(UWSOS).The key issues concerning water sealing performance mainly include the permeability of fractured rock mass(FRM),water-sealed safety(WSS),water curtain performance,and prediction and control of water inflow.This paper reviews the progress of above four key issues on water sealing performances.First,the permeability of an FRM is the basis of water sealing performance,and several commonly used permeability test methods and spatial variation characteristics of permeability are outlined.Second,the current water sealing criteria are compared,and the evaluation methods of WSS are summarized.Third,the design parameters and efficiency evaluation of water curtain systems(WCSs)are introduced.The water inflow of oil storage caverns(OSCs)can reflect the water sealing effect,and the prediction methods and control measures of water inflow are also summarized.Finally,the advantages and disadvantages of the current research are discussed,and the potential research directions are pointed out,such as optimization of water sealing criteria and FRM model,quantitative evaluation of WCS efficiency,accurate prediction of water inflow,and improvement of grouting technology.

Examining the influence of the loading path on the cracking characteristics of a pre-fractured rock specimen with discrete element method simulation

Damage in a rock mass is heavily dependent on the existence and growth of joints,which are also influenced by the complex stress states induced by human activities(e.g.,tunneling and excavation).A proper representation of the loading path is essential for understanding the mechanical behaviors of rock masses.Based on the discrete element method(DEM),the influence of the loading path on the cracking process of a rock specimen containing an open flaw is examined.The effectiveness of the model is confirmed by comparing the simulation results under a uniaxial compression test to existing research findings,where wing crack initiates first and secondary cracks contribute to the failure of the specimen.Simulation results confirm that the cracking process is dependent upon both the confining pressure and the loading path.Under the axial loading test,a higher confining pressure suppresses the development of tensile wing cracks and forces the formation of secondary cracks in the form of shear bands perpendicular to the flaw.Increase of confining pressure also decreases the influence of the loading path on the cracking process.Reduction of confining pressure during an unloading test amplifies the concentration of tensile stress and ultimately promotes the appearance of a tensile splitting fracture at meso-scale.Confining pressure at the failure stage is well predicted by the Hoek-Brown failure criterion under quasi-static conditions.

Equivalent Continuum Model of Rock Mass with Arbitrary Fractures

The constitutive model and equivalent deformation modulus of an arbitrary column in representative elementary volume （REV） of fractured rock mass are derived. The deformation of fractured rock mass is com- posed of the rock part and the fracture part. The elasto-visco-plastic property is considered in this model. For the convenience in engineering practice, the complex elasto-visco-plastic model and its equivalent modulus are degraded, and tbe rock is taken as an elastic body. By statistical analysis of the geometric positions of the column and the fracture, the equivalent modulus of rock mass with arbitrary fractures is obtained.

Mechanism of progressive failure of a slope with a steep joint under the action of freezing and thawing:model test

The stability of slope rock masses is influenced by freeze-thaw cycles in cold region,and the mechanism of stability deterioration is not clear.In order to understand the damage and progressive failure characteristics of rock masses under the action of freezing and thawing,a model test was conducted on slope with steep joint in this study.The temperature,frost heaving pressure and deformation of slope rock mass were monitored in real-time during the test and the progressive failure mode was studied.The experimental results show that the temperature variations of cracking and the rock mass of a slope are different.There are obvious latent heat stages in the temperature-change plot in the crack,but not in the slope rock masses.The frost heaving effect in the fracture is closely related to the constraint conditions,which change with the deformation of the fracture.The frost heaving pressure fluctuates periodically during freezing and continues to decrease during thawing.The surface deformation of the rock mass increases during freezing,and the deformation is restored when it thaws.Freeze-thaw cycling results in residual deformation of the rock mass which cannot be fully restored.Analysis shows that the rock mass at the free side of the steep-dip joint rotates slightly under the frost heaving effect,causing fracture propagation.The fracture propagation pattern is a circular arc at the beginning,then extends to the possible sliding direction of the rock mass.Frost heaving force and fracture water pressure are the key factors for the failure of the slope,which can cause the crack to penetrate the rock mass,and a landslide ensues when the overall anti-sliding resistance of the rock mass is overcome.