On the calibration and verification of Voronoi-based discontinuous deformation analysis for modeling rock fracture

Since its introduction,discontinuous deformation analysis(DDA)has been widely used in different areas of rock mechanics.By dividing large blocks into subblocks and introducing artificial joints,DDA can be applied to rock fracture simulation.However,parameter calibration,a fundamental issue in discontinuum methods,has not received enough attention in DDA.In this study,the parameter calibration of DDA for intact rock is carefully studied.To this end,a subblock DDA with Voronoi tessellation is presented first.Then,a modified contact constitutive law is introduced,in which the tensile and shear meso-strengths are modified to be independent of the bond lengths.This improvement can prevent the unjustified preferential failure of short edges.A method for imposing confining pressure is also introduced.Thereafter,sensitivity analysis is performed to investigate the influence of the calculated parameters and meso-parameters on the mechanical properties of modeled rock.Based on the sensitivity analysis,a unified calibration procedure is suggested for both cases with and without confining pressure.Finally,the calibration procedure is applied to two examples,including a biaxial compression test.The results show that the proposed Voronoi-based DDA can simulate rock fracture with and without confining pressure very well after careful parameter calibration.

Unloading-induced permeability recovery in rock fractures

Underground space creation and energy extraction, which induce unloading on rock fractures, commonly occur in various rock engineering projects, and rock engineering projects are subjected to high temperatures with increasing depth. Fluid flow behavior of rock fractures is a critical issue in many subsurface rock engineering projects. Previous studies have extensively considered permeability evolution in rock fractures under loading phase, whereas changes in fracture permeability under unloading phase have not been fully understood. To examine the unloading-induced changes in fracture permeability under different temperatures, we performed water flow-through tests on fractured rock samples subjected to decreasing confining pressures and different temperatures. The experimental results show that the permeability of fracture increases with unloading of confining pressure but decreases with loading-unloading cycles. Temperature may affect fracture permeability when it is higher than a certain threshold. An empirical model of fracture hydraulic aperture including two material parameters of initial normal stiffness and maximum normal closure can well describe the permeability changes in rough rock fracture subjected to loading-unloading cycles and heating. A coupled thermo-mechanical model considering asperity damage is finally used to understand the influences of stress paths and temperatures on fracture permeability.

Deep-seated rock fracture of valley slopes in China:A review

Deep-seated rock fractures(referred to as DSRF hereafter)in valley slopes are uncommon geological phenomena that challenge our previous understanding of slope unloading processes.These fractures weaken the strength and integrity of the rock mass,potentially forming unstable block boundaries with significant volume,thereby affecting the stability of slopes,chambers,and dam abutments.DSRF has emerged as a critical environmental and engineering geological issue that hinders large-scale projects in deep canyon areas.Despite the attention and practical treatment given to DSRF in engineering practice,theoretical research on this topic still lags behind the demands of engineering applications.To garner widespread attention and promote the resolution of DSRF-related problems,this review aims to redefine DSRF through comprehensive data collection and analysis,engineering geological analogies,and field investigations,and provide a summary and analysis of the research progress on DSRF,along with future research directions.The study defines DSRF as the intermittent tension cracks or relaxation zones within a slightly weathered or fresh,and intact or relatively intact rock mass distributed below the surface unloading zones of a deep canyon slope,and should be distinguished from"loose rock mass"and"deep-seated gravitational slope deformations".The article provides an overview of the development and distribution,rupture characteristics,and genesis mechanism of DSRF.It proposes that DSRF is formed based on the fluvial deviation-undercutting evolution mode,wherein the energy accumulated in the rock mass is violently released when the river further down cuts the slope after the rock mass has undergone cyclical loadingunloading.However,further research is necessary to establish a comprehensive database for DSRF,refine exploration techniques,understand evolutionary processes,develop engineering evaluation methods,and predict the distribution of DSRF.

A model to determine hole spacing in the rock fracture process by non-explosive expansion material

The application of the non-explosive expansion material （NEEM） is widely used as the controlled fracture method in quarry min- ing, especially in hard rocks. The pressure of NEEM is an important parameter in causing rock fracture. An empirical model based on hole spacing was developed to determine the pressure of NEEM in the rock fracture process. Primarily, the empirical model was developed by the mathematical method, utilizing dimensional analysis. Then, the Phase2 code, which is based on the finite element method, was utilized to predict crack growth in rocks. The results of numerical analysis show slight deviations from the empirical model. Hence, the polynomial re- gression analysis was used to modify the model. Finally, the modified model shows a good agreement with the results gained from numerical modeling.

Coupled GIMP and CPDI material point method in modelling blast-induced three-dimensional rock fracture

Three-dimensional rock fracture induced by blasting is a highly complex problem and has received considerable attention in geotechnical engineering.The material point method is firstly applied to treat this challenging task.Some inherent weaknesses can be overcome by coupling the generalized interpolation material point(GIMP)and the convected particle domain interpolation technique(CPDI).For the media in the borehole,unchanged GIMP-type particles are used to guarantee a homogenous blast pressure.CPDITetrahedron type particles are employed to avoid the fake numerical fracture near the borehole for the rock material.A blasting experiment using three-dimensional single-borehole rock was simulated to examine the applicability of the coupled model under realistic loading and boundary conditions.A good agreement was achieved between the simulation and experimental results.Moreover,the mechanism of three-dimensional rock fracture was analyzed.It was concluded that rock particle size and material parameters play an important role in rock damage.The reflected tensile waves cause severe damage in the lower part of the model.Rayleigh waves occur on the top face of the rock model to induce a hoop failure band.

Permeability evaluation for artificial single rock fracture according to geometric aperture variation using electrical resistivity

A convenient approach was proposed by which to evaluate and monitor the permeability of a rock fracture by verifying the quantitative correlation between the electrical resistivity and permeability at laboratory scale.For this purpose,an electrical resistivity measurement system was applied to the laboratory experiments using artificial cells with the shape of a single rock fracture.Sixty experiments were conducted using rock fractures according to the geometry,aperture sizes,wavelengths,and roughness amplitudes.The overall negative relationship between the normalized electrical resistivity values and the aperture sizes directly linked with the permeability,was well fitted by the power-law function with a large determination coefficient(≈0.86).The effects of wavelength and roughness amplitude of the rock fracture on the electrical resistivity were also analyzed.Results showed that the electrical resistivity was slightly increased with decreasing wavelength and increasing roughness amplitude.An empirical model for evaluating the permeability of a rock fracture was proposed based on the experimental data.In the field,if the electrical resistivity of pore groundwater could be measured in advance,this empirical model could be applied effectively for simple,quick monitoring of the fracture permeability.Although uncertainty may be associated with the permeability estimation due to the limited control parameters considered in this research,this electrical resistivity approach could be helpful to monitor the rock permeability in deep underground facilities such as those used for radioactive waste repositories or forms of energy storage.

Study on the physical meaning of seismic inhomogeneous degree by rock fracture experiments

It is observed that the parameter of seismic inhomogeneous degree (GL value) calculated from the earthquake catalog shows obvious abnormal changes prior to strong earthquakes, indicating the state change of local seismic activity. This paper focuses on the mechanism for the abnormal changes of the GL values based on the sequences of acoustic emission for three types of rock samples containing macro-asperity fracture; compressional en-echelon fracture and model-III shear fracture. The results show that for the three types of rock samples, there are continuous abnormal changes of GL value (>1) just before the non-elastic deformation occurs or during the process of nucleation prior to the instability. Based on the experimental results, it seems that the process of creep sliding and resistance-uniformization along fault zone is the possible mechanism for the abnormal changes of GL value before rock fractures.

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.

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.

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.

Relationship between fracture spacing and bed thickness in sedimentary rocks:Approach by means of Michaelis-Menten equation

Fractures occur in nearly all rocks at the Earth’s surface and exert essential control on the mechanical strengths of rock masses and permeability.The fractures strongly impact the stability of geological or man-made structures and flow of water and hydrocarbons,CO_(2) and storing waste.For this,the dependence of opening mode fracture spacing(s)on bed thickness(t)in sedimentary basins(reservoirs)is studied in this context.This paper shows that the MichaeliseMenten equation can provide an algebraic expression for the nonlinear s-t relationship.The two parameters have clear geological meanings:a is the maximum fracture spacing which can no longer increase with increasing t,and b is the characteristic bed thickness when s=0.5a.The tensile fracture strength(C)of the brittle beds during the formation of tensile fractures can be estimated from the two parameters.For sandstones of 16 areas reported in the literature,C ranges from 2.7 MPa to 15.7 MPa with a mean value of 8 MPa,which lies reasonably within the range of tensile strengths determined experimentally.This field-based approach by means of MichaeliseMenten equation provides a new method for estimating the tensile fracture strength of rock layers under natural conditions.

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.

Advances in development of shear-flow testing apparatuses and methods for rock fractures:A review

Understanding the mechanical and hydraulic properties of fractured rocks and their coupled processes is of great significance for the exploration,design,construction,operation,and maintenance of many rock engineering projects such as hydropower development,oil and gas extraction,and underground waste disposal.With the rapid advancement of global and national strategies such as the“Paris Agreement”and the“Belt and Road Initiative”,more and more projects are developed in the complex geological environment with varying geological structures.Shear failure and rock instability are prone to occur in fractured rock masses under the coupled effects of high stress,high pore pressure,and engineering disturbance,which are main sources for engineering disasters such as roof collapse and caving,water and mud inrushes,and induced earthquakes.To solve these problems,extensive research on the coupled shear-flow behavior of fractures has been conducted.However,due to the complex mechanical,hydraulic and geometrical characteristics of single fractures and fracture networks,a large number of outstanding issues related to the impact of the coupled processes on the engineering characteristics of rock masses are still unsolved.The relevant experimental apparatuses and methods remain to be further developed.Therefore,in this review,we analyze and summarize the existing shear-flow experimental apparatuses,classify apparatus configurations,specimen shapes,and testing principles,and compare their advantages and disadvantages.We also summarize the main scientific findings obtained from various experimental apparatuses,aiming to provide a reference for developing new shear-flow experimental apparatuses and conducting related scientific research in the future.

The influencing factors and mechanisms of the electromagnetic radiation during rock fracture

Based on the laboratory experiments this paper presented that the primary influence factors about the electromagnetic radiation during rock fracture are the rock mechanics characters and mineral components. The brittle samples and samples contained quartz, pyrite, chalopyrite produce electromagnetic radiation easily. There are three fracture radiation effects. The crystal fracture effect produces the high frequency electromagnetic signals, the piezoelectric effect produces low frequency signals and the natural semiconductor effect produces middle frequency signals possessed distinct wave shapes.

Experimental study on the slip evolution of planar fractures subjected to cyclic normal stress

The frictional rupture mechanisms of rock discontinuities considering the dynamic load disturbance still remain unclear.This paper investigates the transitional behaviors of slip events happened on a planar granite fracture under cyclic normal stress with diferent oscillation amplitudes.The experimental results show that the activations of fast slips always correlate with unloading of normal stress.Besides,the intensive normal stress oscillation can weaken the shear strength which is recoverable when the normal stress return to constant.The rupture patterns are quantifed by stress drop,slip length and slip velocity.With the efect of small oscillation amplitudes,the slip events show chaotic shapes,compared to the regular and predictable style under constant normal stress.When the amplitude is large enough,the big and small slip events emerge alternately,showing a compound slip style.Large amplitude of the cyclic normal stress also widens the interval diferences of the slip events.This work provides experimental supports for a convincible link between the dynamic stress disturbance and the slip behavior of rock fractures.

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.