Creep constitutive model considering nonlinear creep degradation of fractured rock

Stability analysis of underground constructions requires a model study of rock masses’ long-term performance. Creep tests under different stress conditions was conducted on intact granite and granite samples fractured at 30° and 45° angles. The experimental results indicate that the steady creep strain rates of intact and fractured rock present an exponential increase trend with the increase of stress level. A nonlinear creep model is developed based on the experimental results, in which the initial damage caused by fracture together with the damage caused by constant load have been taken into consideration. The fitting analysis results indicated that the model proposed is more accurate at identifying the full creep regions in fractured granite, especially the accelerated stage of creep deformation. The least-square fit error of the proposed creep model is significantly lower than that of Nishihara model by almost an order of magnitude. An analysis of the effects of elastic modulus, viscosity coefficient, and damage factors on fractured rock strain rate and creep strain is conducted. If no consideration is given to the effects of the damage, the proposed nonlinear creep model can degenerate into to the classical Nishihara model.

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.

Borehole stability in naturally fractured rocks with drilling mud intrusion and associated fracture strength weakening:A coupled DFN-DEM approach

Borehole instability in naturally fractured rocks poses significant challenges to drilling.Drilling mud invades the surrounding formations through natural fractures under the difference between the wellbore pressure(P w)and pore pressure(P p)during drilling,which may cause wellbore instability.However,the weakening of fracture strength due to mud intrusion is not considered in most existing borehole stability analyses,which may yield significant errors and misleading predictions.In addition,only limited factors were analyzed,and the fracture distribution was oversimplified.In this paper,the impacts of mud intrusion and associated fracture strength weakening on borehole stability in fractured rocks under both isotropic and anisotropic stress states are investigated using a coupled DEM(distinct element method)and DFN(discrete fracture network)method.It provides estimates of the effect of fracture strength weakening,wellbore pressure,in situ stresses,and sealing efficiency on borehole stability.The results show that mud intrusion and weakening of fracture strength can damage the borehole.This is demonstrated by the large displacement around the borehole,shear displacement on natural fractures,and the generation of fracture at shear limit.Mud intrusion reduces the shear strength of the fracture surface and leads to shear failure,which explains that the increase in mud weight may worsen borehole stability during overbalanced drilling in fractured formations.A higher in situ stress anisotropy exerts a significant influence on the mechanism of shear failure distribution around the wellbore.Moreover,the effect of sealing natural fractures on maintaining borehole stability is verified in this study,and the increase in sealing efficiency reduces the radial invasion distance of drilling mud.This study provides a directly quantitative prediction method of borehole instability in naturally fractured formations,which can consider the discrete fracture network,mud intrusion,and associated weakening of fracture strength.The information provided by the numerical approach(e.g.displacement around the borehole,shear displacement on fracture,and fracture at shear limit)is helpful for managing wellbore stability and designing wellbore-strengthening operations.

Identifying flow regime in the aquifer of fractured rock system in Germi Chai Basin,Iran

Considering the importance of fractured rock aquifers in the hydrogeologic process,this research aimed to analyze the flow regime,internal degree of karstification,and estimate storage volume in fractured rock aquifers of the Germi Chai Basin in northwest Iran,which is attributed to its active tectonics,erosion,and the lithological diversity.Given the geological setting,the hypothesis is that this basin is characterized by a high degree of karstification and diffuse or intermediate flow regime leading to variation in discharge flow rate.The hydrodynamic and hadrochemical analysis was conducted on 9 well distributed springs across the basin from 2019 to 2020.The maximum flow rate in most of the springs appeared in the early wet season despite their different levels of fluctuations on the monthly discharge time series.Analyzing the spring recession curve form revealed an aquifer containing multiple micro-regimes withαrecession coefficients and a degree of karstification ranging between 0.001 to 0.06 and 0.55 to 2.61,respectively.These findings indicated a dominant diffuse and intermediate flow system resulting from the development of a high density of fractures in this area.The electrical conductivity of the spring changes inversely proportional to the change in flow discharge,indicating the reasonable hydrological response of the aquifer to rainfall events.Hydrograph analysis revealed that the delay time of spring discharge after rainfall events mostly varies between 10 to 30 days.The total dynamic storage volume of the spring for a given period(2019-2020)was estimated to be approximately 1324 million cubic meters reflecting the long-term drainage potential and high perdurability of dynamic storage.Estimating the maximum and minimum ratio revealed that the springs recharging system in Germi Chai Basin comes under the slow aquifers category.This finding provides valuable insight into the hydrogeological properties of fractured rock aquifers contributing to effective water management strategy.

Grouting theories and technologies for the reinforcement of fractured rocks surrounding deep roadways

Grouting is an effective method to improve the integrity and stability of fractured rocks that surround deep roadways.After years of research and practice,various theories and a complete set of grouting technologies for deep roadways with fractured rocks have been developed and are widely applied in Chinese coal mining production.This paper systematically summarizes and analyzes the research results concerning the theory,design,materials,processes,and equipment for the grouting and reinforcement of fractured rocks surrounding deep roadways.Specifically,in terms of grouting methods,pregrouting,groutingwhile-excavation,and postgrouting methods are explored;in terms of grouting theory,backfill grouting,compaction grouting,infiltration grouting,and fracture grouting theories are studied.In addition,this paper also studies grouting borehole arrangement,water-cement ratio,grouting pressure,grouting volume,grout diffusion radius,and other grouting parameters and their determination methods.On this basis,this paper explores the physical and mechanical properties of organic and organic-inorganic composite grouting materials,and assess grouting reinforcement quality testing methods and instruments.Taken as the field cases,the application of pregrouting in front of heading faces,groutingwhile-excavation,and postgrouting in the Kouzidong coal mine are then introduced,and the effects of the grouting reinforcements are evaluated.This paper proposes a development direction for grouting technology based on problems existing in the grouting reinforcement of fractured rocks surrounding deep roadways.

Groundwater flow through fractured rocks and seepage control in geotechnical engineering: Theories and practices

Groundwater flow through fractured rocks has been recognized as an important issue in many geotechnical engineering practices.Several key aspects of fundamental mechanisms,numerical modeling and engineering applications of flow in fractured rocks are discussed.First,the microscopic mechanisms of fluid flow in fractured rocks,especially under the complex conditions of non-Darcian flow,multiphase flow,rock dissolution,and particle transport,have been revealed through a com-bined effort of visualized experiments and theoretical analysis.Then,laboratory and field methods of characterizing hydraulic properties(e.g.intrinsic permeability,inertial permeability,and unsaturated flow parameters)of fractured rocks in different flow regimes have been proposed.Subsequently,high-performance numerical simulation approaches for large-scale modeling of groundwater flow in frac-tured rocks and aquifers have been developed.Numerical procedures for optimization design of seepage control systems in various settings have also been proposed.Mechanisms of coupled hydro-mechanical processes and control of flow-induced deformation have been discussed.Finally,three case studies are presented to illustrate the applications of the improved theoretical understanding,characterization methods,modeling approaches,and seepage and deformation control strategies to geotechnical engi-neering projects.

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.

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.

Variation in hydraulic conductivity of fractured rocks at a dam foundation during operation

Characterizing the permeability variation in fractured rocks is important in various subsurface applications,but how the permeability evolves in the foundation rocks of high dams during operation remains poorly understood.This permeability change is commonly evidenced by a continuous decrease in the amount of discharge(especially for dams on sediment-laden rivers),and can be attributed to fracture clogging and/or hydromechanical coupling.In this study,the permeability evolution of fractured rocks at a high arch dam foundation during operationwas evaluated by inverse modeling based on the field timeseries data of both pore pressure and discharge.A procedure combining orthogonal design,transient flow modeling,artificial neural network,and genetic algorithm was adopted to efficiently estimate the hydraulic conductivity values in each annual cycle after initial reservoir filling.The inverse results show that the permeability of the dam foundation rocks follows an exponential decay annually during operation(i.e.K/K0=0.97e^(-0.59t)+0.03),with good agreement between field observations and numerical simulations.The significance of the obtained permeability decay function was manifested by an assessment of the long-term seepage control performance and groundwater flow behaviors at the dam site.The proposed formula is also of merit for characterizing the permeability change in riverbed rocks induced by sediment transport and deposition.

Modeling unsaturated flow in fractured rocks with scaling relationships between hydraulic parameters

Modeling unsaturated flow in fractured rocks is essential in various subsurface engineering applications,but it remains a great challenge due to the difficulties in determining the unsaturated hydraulic properties of rocks that contain various scales of fractures.It is generally accepted that the van Genuchten(VG)model can be applied to fractured rocks,provided that the hydraulic parameters could be representatively determined.In this study,scaling relationships between the VG parameters(a and n)and hydraulic conductivity(K)across 8 orders of magnitude,from 10^(-10)m/s to 10^(-2)m/s,were proposed by statistical analysis of data obtained from 1416 soil samples.The correlations were then generalized to predict the upper bounds of VG parameters for fractured rocks from the K data that could be obtained more easily under field conditions,and were validated against a limited set of data from cores,fractures and fractured rocks available in the literature.The upper bound estimates significantly narrow the ranges of VG parameters,and the representative values of a and n for fractured rocks at the field scale can then be determined with confidence by inverse modeling using groundwater observations in saturated zones.The proposed methodology was applied to saturated-unsaturated flow modeling in the right-bank slope at the Baihetan dam site with a continuum approach,showing that most of the flow behaviors in fractured rocks in this complex hydrogeological condition could be properly reproduced.The proposed method overcomes difficulties in suction measurement in fractured rocks with strong heterogeneity,and provides a feasible way for modeling of saturated-unsaturated flow in fractured rocks with acceptable engineering accuracy.

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.

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.

Numerical evaluation of strength and deformability of fractured rocks

Knowledge of the strength and deformability of fractured rocks is important for design, construction and stability evaluation of slopes, foundations and underground excavations in civil and mining engineering. However, laboratory tests of intact rock samples cannot provide information about the strength and deformation behaviors of fractured rock masses that include many fractures of varying sizes, orientations and locations. On the other hand, large-scale in situ tests of fractured rock masses are economically costly and often not practical in reality at present. Therefore, numerical modeling becomes necessary. Numerical predicting using discrete element methods(DEM) is a suitable approach for such modeling because of their advantages of explicit representations of both fractures system geometry and their constitutive behaviors of fractures, besides that of intact rock matrix. In this study, to generically determine the compressive strength of fractured rock masses, a series of numerical experiments were performed on two-dimensional discrete fracture network models based on the realistic geometrical and mechanical data of fracture systems from feld mapping. We used the UDEC code and a numerical servo-controlled program for controlling the progressive compressive loading process to avoid sudden violent failure of the models. The two loading conditions applied are similar to the standard laboratory testing for intact rock samples in order to check possible differences caused by such loading conditions. Numerical results show that the strength of fractured rocks increases with the increasing confning pressure, and that deformation behavior of fractured rocks follows elasto-plastic model with a trend of strain hardening. The stresses and strains obtained from these numerical experiments were used to ft the well-known Mohr-Coulomb(MC) and Hoek-Brown(H-B) failure criteria, represented by equivalent material properties defning these two criteria. The results show that both criteria can provide fair estimates of the compressive strengths for all tested numerical models. Parameters of the elastic deformability of fractured models during elastic deformation stages were also evaluated, and represented as equivalent Young’s modulus and Poisson’s ratio as functions of lateral confning pressure. It is the frst time that such systematic numerical predicting for strength of fractured rocks was performed considering different loading conditions, with important fndings for different behaviors of fractured rock masses, compared with testing intact rock samples under similar loading conditions.

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.

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.

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.

DarcyTools:A Computer Code for Hydrogeological Analysis of Nuclear Waste Repositories in Fractured Rock

A computer code for simulation of groundwater flow and transport is described. Both porous and fractured media are handled by the code. The main intended application is the analysis of a deep repository for nuclear waste and for this reason flow and transport in a sparsely fractured rock is in focus. The mathematical and numerical models are described in some detail. In short, one may say that the code is based on the traditional conservation and state laws, but also embodies a number of submodels (subgrid processes, permafrost, etc). An unstructured Cartesian grid and a finite volume approach are the key elements in the discretization of the basic equations. A multigrid solver is part of the code as well as a parallelization option based on the SPMD (Single-Program Multiple-Data) method. The main application areas are summarized and an application to a deep repository is discussed in some more detail.

Application of Stochastic Fracture Network with Numerical Fluid Flow Simulations to Groundwater Flow Modeling in Fractured Rocks

The continuum approach in fluid flow modeling is generally applied to porous geological media, but has limited applicability to fractured rocks. With the presence of a discrete fracture network relatively sparsely distributed in the matrix, it may be difficult or erroneous to use a porous medium fluid flow model with continuum assumptions to describe the fluid flow in fractured rocks at small or even large field scales. A discrete fracture fluid flow approach incorporating a stochastic fracture network with numerical fluid flow simulations could have the capability of capturing fluid flow behaviors such as inhomogeneity and anisotropy while reflecting the changes of hydraulic features at different scales. Moreover, this approach can be implemented to estimate the size of the representative elementary volume (REV) in order to find out the scales at which a porous medium flow model could be applied, and then to determine the hydraulic conductivity tensor for fractured rocks. The following topics are focused on in this study: (a) conceptual discrete fracture fluid flow modeling incorporating a stochastic fracture network with numerical flow simulations; (b) estimation of REV and hydraulic conductivity tensor for fractured rocks utilizing a stochastic fracture network with numerical fluid flow simulations; (c) investigation of the effect of fracture orientation and density on the hydraulic conductivity and REV by implementing a stochastic fracture network with numerical fluid flow simulations, and (d) fluid flow conceptual models accounting for major and minor fractures in the 2 D or 3 D flow fields incorporating a stochastic fracture network with numerical fluid flow simulations.

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.