Master crack types and typical acoustic emission characteristics during rock failure

Acoustic emission(AE)signals contain substantial information about the internal fracture characteristics of rocks and are useful for revealing the laws governing the release of energy stored therein.Reported here is the evolution of rock failure with diferent master crack types as investigated using Brazilian splitting tests(BSTs),direct shear tests(DSTs),and uniaxial compression tests(UCTs).The AE parameters and typical modes of each fracture type were obtained,and the energy release characteristics of each fracture mechanism were discussed.From the observed changes in the AE parameters,the rock fracture process exhibits characteristics of staged intensifcation.The scale and energy level of crack activity in the BSTs were signifcantly lower than those in the DSTs and UCTs.The proportion of tensile cracks in the BSTs was 65%–75%,while the proportions of shear cracks in the DSTs and UCTs were 75%–85%and 70%–75%,respectively.During the rock loading process under diferent conditions,failure was accompanied by an increased number of shear cracks.The amplitude,duration,and rise time of the AE signal from rock failure were larger when the failure was dominated by shear cracks rather than tensile ones,and most of the medium-and high-energy signals had medium to low frequencies.After calculating the proposed energy amplitude ratio,the energy release of shear cracks was found to exceed that of tensile cracks at the same fracture scale.

Applications of rock failure process analysis (RFPA) method

Brittle failure of rocks is a classical rock mechanical problem. Rock failure not only involves initiation and propagation of single crack, but also is associated with initiation, propagation and coalescence of many cracks. The rock failure process analysis （RFPA） tool has been proposed since 1995. The heterogeneity of rocks at a mesoscopic level is considered by assuming that the material properties follow the Weibull distribution. Elastic damage mechanics is used for describing the constitutive law of the meso-level element. The finite element method （FEM） is employed as the basic stress analysis tool. The maximum tensile strain criterion and the Mohr-Coulomb criterion are utilized as the damage threshold. In order to solve the stability problem related to rock engineering structures, fundamental principles of strength reduction method （SRM） and gravity increase method （GIM） are integrated into the RFPA. And the acoustic emission （AE） event rate is employed as the criterion for rock engineering failure. The prominent feature of the RFPA-SRM and RFPA-GIM for stability analysis of rock engineering is that the factor of safety can be obtained without any presumption for the shape and location of the failure surface. In this paper, several geotechnical engineering applications that use the RFPA method to analyze their stability are presented to provide some references for relevant researches. The principles of the RFPA method in engineering are introduced firstly, and then the stability analysis of tunnel, slope and dam is focused on. The results indicate that the RFPA method is capable of capturing the mechanism of rock engineering stability and has the potential for application in a larger range of geo-engineering.

Disturbance failure mechanism of highly stressed rock in deep excavation:Current status and prospects

This article reviews the current status on the dynamic behavior of highly stressed rocks under disturbances.Firstly,the experimental apparatus,methods,and theories related to the disturbance dynamics of deep,high-stress rock are reviewed,followed by the introduction of scholars’research on deep rock deformation and failure from an energy perspective.Subsequently,with a backdrop of highstress phenomena in deep hard rock,such as rock bursts and core disking,we delve into the current state of research on rock microstructure analysis and residual stresses from the perspective of studying the energy storage mechanisms in rocks.Thereafter,the current state of research on the mechanical response and the energy dissipation of highly stressed rock formations is briefly retrospected.Finally,the insufficient aspects in the current research on the disturbance and failure mechanisms in deep,highly stressed rock formations are summarized,and prospects for future research are provided.This work provides new avenues for the research on the mechanical response and damage-fracture mechanisms of rocks under high-stress conditions.

Real-time arrival picking of rock microfracture signals based on convolutional-recurrent neural network and its engineering application

Accurately picking P-and S-wave arrivals of microseismic(MS)signals in real-time directly influences the early warning of rock mass failure.A common contradiction between accuracy and computation exists in the current arrival picking methods.Thus,a real-time arrival picking method of MS signals is constructed based on a convolutional-recurrent neural network(CRNN).This method fully utilizes the advantages of convolutional layers and gated recurrent units(GRU)in extracting short-and long-term features,in order to create a precise and lightweight arrival picking structure.Then,the synthetic signals with field noises are used to evaluate the hyperparameters of the CRNN model and obtain an optimal CRNN model.The actual operation on various devices indicates that compared with the U-Net method,the CRNN method achieves faster arrival picking with less performance consumption.An application of large underground caverns in the Yebatan hydropower station(YBT)project shows that compared with the short-term average/long-term average(STA/LTA),Akaike information criterion(AIC)and U-Net methods,the CRNN method has the highest accuracy within four sampling points,which is 87.44%for P-wave and 91.29%for S-wave,respectively.The sum of mean absolute errors(MAESUM)of the CRNN method is 4.22 sampling points,which is lower than that of the other methods.Among the four methods,the MS sources location calculated based on the CRNN method shows the best consistency with the actual failure,which occurs at the junction of the shaft and the second gallery.Thus,the proposed method can pick up P-and S-arrival accurately and rapidly,providing a reference for rock failure analysis and evaluation in engineering applications.

Failure mechanism and coupled static-dynamic loading theory in deep hard rock mining: A review

Rock failure phenomena,such as rockburst,slabbing(or spalling) and zonal disintegration,related to deep underground excavation of hard rocks are frequently reported and pose a great threat to deep mining.Currently,the explanation for these failure phenomena using existing dynamic or static rock mechanics theory is not straightforward.In this study,new theory and testing method for deep underground rock mass under coupled static-dynamic loading are introduced.Two types of coupled loading modes,i.e.'critical static stress + slight disturbance' and 'elastic static stress + impact disturbance',are proposed,and associated test devices are developed.Rockburst phenomena of hard rocks under coupled static-dynamic loading are successfully reproduced in the laboratory,and the rockburst mechanism and related criteria are demonstrated.The results of true triaxial unloading compression tests on granite and red sandstone indicate that the unloading can induce slabbing when the confining pressure exceeds a certain threshold,and the slabbing failure strength is lower than the shear failure strength according to the conventional Mohr-Column criterion.Numerical results indicate that the rock unloading failure response under different in situ stresses and unloading rates can be characterized by an equivalent strain energy density.In addition,we present a new microseismic source location method without premeasuring the sound wave velocity in rock mass,which can efficiently and accurately locate the rock failure in hard rock mines.Also,a new idea for deep hard rock mining using a non-explosive continuous mining method is briefly introduced.

A true triaxial strength criterion for rocks by gene expression programming

Rock strength is a crucial factor to consider when designing and constructing underground projects.This study utilizes a gene expression programming(GEP)algorithm-based model to predict the true triaxial strength of rocks,taking into account the influence of rock genesis on their mechanical behavior during the model building process.A true triaxial strength criterion based on the GEP model for igneous,metamorphic and magmatic rocks was obtained by training the model using collected data.Compared to the modified Weibols-Cook criterion,the modified Mohr-Coulomb criterion,and the modified Lade criterion,the strength criterion based on the GEP model exhibits superior prediction accuracy performance.The strength criterion based on the GEP model has better performance in R2,RMSE and MAPE for the data set used in this study.Furthermore,the strength criterion based on the GEP model shows greater stability in predicting the true triaxial strength of rocks across different types.Compared to the existing strength criterion based on the genetic programming(GP)model,the proposed criterion based on GEP model achieves more accurate predictions of the variation of true triaxial strength(s1)with intermediate principal stress(s2).Finally,based on the Sobol sensitivity analysis technique,the effects of the parameters of the three obtained strength criteria on the true triaxial strength of the rock are analysed.In general,the proposed strength criterion exhibits superior performance in terms of both accuracy and stability of prediction results.

UNCERTAINTY ANALYSIS OF ROCK FAILURE BEHAVIOUR USING AN INTEGRATION OF THE PROBABILISTIC COLLOCATION METHOD AND ELASTO-PLASTIC CELLULAR AUTOMATON

The Karhunen-Loeve （KL） expansion and probabilistic collocation method （PCM） are combined and applied to an uncertainty analysis of rock failure behavior by integrating a self- developed numerical method （i.e., the elastic-plastic cellular automaton （EPCA））. The results from the method developed are compared using the Monte Carlo Simulation （MCS） method. It is concluded that the method developed requires fewer collocations than MCS method to obtain very high accuracy and greatly reduces the computational cost. Based on the method, the elasto- plastic and elasto-brittle-plastic analyses of rocks under mechanical loadings are conducted to study the uncertainty in heterogeneous rock failure behaviour.

Numerical simulation of rock progressive failure on samples with a pre-existed weak zone during brittle failure

Considering the heterogeneity of geomechanical materials, seismicity during brittle rock failure under compressive loading on the sample with an original weak zone is simulated by using rock failure process analysis code (RFPA2D). The run-through process of weak zone, the forming of new fault and associated micro-seismicities are studied. The modeling demonstrates the total process of source development of earthquake from deformation, micro-failure to collapse and the behavior of temporal-spatial distribution of micro-seismicities. The stress, strain and the temporal-spatial distribution of micro-seismicities life-likely portrayed the phenomena of localization and temporal-spatial transitions, which is similar to those observed in our real crust. Also, the results obtained in simulations are in agreement with or similar to the reported experimental observations.

A modified failure criterion for transversely isotropic rocks

A modified failure criterion is proposed to determine the strength of transversely isotropic rocks. Me-chanical properties of some metamorphic and sedimentary rocks including gneiss, slate, marble, schist, shale, sandstone and limestone, which show transversely isotropic behavior, were taken into consider-ation. Afterward, introduced triaxial rock strength criterion was modified for transversely isotropic rocks. Through modification process an index was obtained that can be considered as a strength reduction parameter due to rock strength anisotropy. Comparison of the parameter with previous anisotropy in-dexes in literature showed reasonable results for the studied rock samples. The modified criterion was compared to modified Hoek-Brown and Ramamurthy criteria for different transversely isotropic rocks. It can be concluded that the modified failure criterion proposed in this study can be used for predicting the strength of transversely isotropic rocks.

Phenomena and theoretical analysis for the failure of brittle rocks

Rockburst, an unstable failure of brittle rocks, has been greatly concerned in rock mechanics and rock engineering for more than 100 years. The current understanding on the mechanical mechanism of rockburst is based on the Coulomb theory, i.e. compressive-shear failure theory. This paper illustrates a series of tensile and tensile-shear fracture phenomena of rockburst, and proposes a methodology for the analysis of fracture mode and its energy dissipation process based on Griffith theory. It is believed that: (1) the fracture modes of rockburst should include compressive-shear, tensile-shear and pure tensile failures; (2) the rupture angle of rock mass decreases with the occurrence of tensile stress; (3) the proportion of kinetic energy in the released strain energy from a rockburst may be much larger than that transferred into surface energy; and (4) the understanding on the tensile and tensile-shear failure modes of rockburst may change the basic thinking of rockburst control, i.e. from keeping the reduction in initial compressive stress σ3 to restricting the creation of secondary tensile stress.

Numerical study on rock failure around a tunnel destressed by a conceptualized notched technique

A destressing method for reducing the strainburst risk in burst-prone grounds is suggested.In this method,the rock is destressed by cutting notches at the excavation boundary.First,the concept of the proposed method is described both analytically and numerically.Then,the method is applied to a tunneling problem.Several numerical models are built to study the destressing process and the failure mechanism around a circular tunnel.Results show that when the notch is added to the model,the rock at the tunnel wall is destressed,and the stress concentration zones shift to a farther distance away from the wall.Also,the analysis of the failure zone around the tunnel and the velocity of the failed elements show that the failure in the notched tunnel is less violent compared to that in the tunnel without the notch.Finally,a parametric study is conducted to investigate the influences of the notch dimensions on the stress distribution,deformation,and failures around the tunnel.

A simplified approach to directly consider intact rock anisotropy in Hoek——Brown failure criterion

Many rock types have naturally occurring inherent anisotropic planes, such as bedding planes, foliation,or flow structures. Such characteristic induces directional features and anisotropy in rocks＇ strength anddeformational properties. The HoekeBrown （HeB） failure criterion is an empirical strength criterionwidely applied to rock mechanics and engineering. A direct modification to HeB failure criterion toaccount for rock anisotropy is considered as the base of the research. Such modification introduced a newdefinition of the anisotropy as direct parameter named the anisotropic parameter （Kb）. However, thecomputation of this parameter takes much experimental work and cannot be calculated in a simple way.The aim of this paper is to study the trend of the relation between the degree of anisotropy （Rc） and theminimum value of anisotropic parameter （Kmin）, and to predict the Kmin directly from the uniaxialcompression tests instead of triaxial tests, and also to decrease the amount of experimental work. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Failure behavior of highly stressed rocks under quasi-static and intensive unloading conditions

Unloading failure of rocks,especially highly stressed rocks,is one of the key issues in construction of underground structures.Based on this,analytical models for rocks under quasi-static and intensive unloading conditions are established to study the failure behavior of highly stressed rocks.In case of rock failure under quasi-static unloading,the rock mass ahead of working face is regarded as an elasto-brittle material,and the stress-displacement curves are used to characterize the tensile fracture of peak-stress area.It is observed that,when intensive unloading happens,there is an elastic unloading wave（perturbation wave） propagating in the rock mass.If the initial stress exceeds the critical stress,there will be a fracture wave,following the elastic unloading wave.To study the propagation feature of fracture wave,the conservation laws of mass,momentum and energy are employed.Results show that the post-peak deformation,strength and energy dissipation are essential to the failure process of highly stressed rocks.

Reply to Discussion on “A generalized three-dimensional failure criterion for rock masses”

General:Jaiswal and Shrivastva(2012)proposed the mathematical formulations,i.e.the J–S criterion for converting generalized H-B failure criterion into 3D smooth convex failure criterion at deviatoric plane.The J–S strength criterion is in two versions:uniform and variable extension ratio.It has been observed from the analysis that at uniform extension ratio,the required strength parameters are only UCS and m(other parameters such as Ls,a,b and c are related with m).In the case of variable extension ratio,extra parameter f is required along with UCS and m.Thus,it has minimal strength parameters compared to You strength criterion.Furthermore,You strength criterion does not obey the smooth convex condition at deviatoric plane.

Periodical zonal character of damage near the openings inhighly-stressed rock mass conditions

Rock mass damage at great depths near underground openings is often of a zonal character.However,the classical elastoplastic theory fails to explain sufficiently all properties of zonal failure structures.A new non-Euclidean mathematical model for highly-stressed rock mass was developed based on the principles of mechanics of defected material and non-equilibrium thermodynamics.Methods were developed to determine model parameters that provide satisfactory correspondence between the experimental findings concerning faulted zonal structures near openings at great depths and mathematical calculations.The mechanism of this phenomenon was discovered which consisted in a periodical character of stresses in the surrounding rock mass and development of tensile macrocracks at zones of maximal tangential stresses.Main relationships between the cracking zone width and rock mass strength were established.

New artificial neural networks for true triaxial stress state analysis and demonstration of intermediate principal stress effects on intact rock strength

Simulations are conducted using five new artificial neural networks developed herein to demonstrate and investigate the behavior of rock material under polyaxial loading. The effects of the intermediate principal stress on the intact rock strength are investigated and compared with laboratory results from the literature. To normalize differences in laboratory testing conditions, the stress state is used as the objective parameter in the artificial neural network model predictions. The variations of major principal stress of rock material with intermediate principal stress, minor principal stress and stress state are investigated. The artificial neural network simulations show that for the rock types examined, none were independent of intermediate principal stress effects. In addition, the results of the artificial neural network models, in general agreement with observations made by others, show （a） a general trend of strength increasing and reaching a peak at some intermediate stress state factor, followed by a decline in strength for most rock types; （b） a post-peak strength behavior dependent on the minor principal stress, with respect to rock type; （c） sensitivity to the stress state, and to the interaction between the stress state and uniaxial compressive strength of the test data by the artificial neural networks models （two-way analysis of variance; 95% confidence interval）. Artificial neural network modeling, a self-learning approach to polyaxial stress simulation, can thus complement the commonly observed difficult task of conducting true triaxial laboratory tests, and/or other methods that attempt to improve two-dimensional （2D） failure criteria by incorporating intermediate principal stress effects.

Two-and three-dimensional stability analysis of underground storage caverns in soft rock(Cappadocia, Turkey) by finite element method

Engineering design in soft rocks and its stability analysis exerts many challenges to rock engineers. Many engineering works in Turkey’s Cappadocia region must face and tackle the existing sites covered by the soft rocks. This study is aimed to examine the stability condition of a typical underground storage cavern(USC) excavated in a soft rock in this region. For this purpose, two-and threedimensional stability analyses of the USCs were performed using the finite element method(FEM).Because of the inherent difficulty in characterizing soft/weak rock masses in the region using traditional classification systems, the stability of a typical USC was evaluated by representing the rock mass condition with two distinct scenarios in FEM analysis.While these structures were unstable according to the 2D analysis conducted in RS2 software in the worstcase scenario, they were stable in the 3D analysis using RS3 software in both scenarios. Besides,feasible cover depths were examined to assess their possible effects on the factor of safety and deformation measurements. It was found that 15 m seems to be an optimal depth for excavating a typical USC in the soft rocks exposed in the region. The 3D FEM results provide valuable information to optimize the future planning and preliminary design of USCs.

Time-dependent dilatancy for brittle rocks

This paper presents a theoretical study on time-dependent dilatancy behaviors for brittle rocks. The theory employs a well-accepted postulation that macroscopically observed dilatancy originates from the expansion of microcracks. The mechanism and dynamic process that microcracks initiate from local stress concentration and grow due to localized tensile stress are analyzed. Then, by generalizing the results from the analysis of single cracks, a parameter and associated equations for its evolution are developed to describe the behaviors of the microcracks. In this circumstance, the relationship between microcracking and dilatancy can be established, and the theoretical equations for characterizing the process of rock dilatancy behaviors are derived. Triaxial compression and creep tests are conducted to validate the developed theory. With properly chosen model parameters, the theory yields a satisfactory accuracy in comparison with the experimental results.

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.

Integrated modeling of fracturing-flowback-production dynamics and calibration on field data:Optimum well startup scenarios

We aim at the development of a general modelling workflow for design and optimization of the well flowback and startup operation on hydraulically fractured wells.Fracture flowback model developed earlier by the authors is extended to take into account several new fluid mechanics factors accompanying flowback,namely,viscoplastic rheology of unbroken cross-linked gel and coupled“fracture-reservoir”numerical submodel for influx from rock formation.We also developed models and implemented new geomechanical factors,namely,(i)fracture closure in gaps between proppant pillars and in proppant-free cavity in the vicinity of the well taking into account formation creep;(ii)propagation of plastic deformations due to tensile rock failure from the fracture face into the fluid-saturated reservoir.We carried out parametric calculations to study the dynamics of fracture conductivity during flowback and its effect on well production for the set of parameters typical of oil wells in Achimov formation of Western Siberia,Russia.The first set of calculations is carried out using the flowback model in the reservoir linear flow regime.It is obtained that the typical length of hydraulic fracture zone,in which tensile rock failure at the fracture walls occurs,is insignificant.In the range of rock permeability in between 0.01 mD and 1 D,we studied the effect of non-dimensional governing parameters as well as bottomhole pressure drop dynamics on oil production.We obtained a map of pressure drop regimes(fast,moderate or slow)leading to maximum cumulative oil production.The second set of parametric calculations is carried out using integrated well production modelling workflow,in which the flowback model acts as a missing link in between hydraulic fracturing and reservoir commercial simulators.We evaluated quantitatively effects of initial fracture aperture,proppant diameter,yield stress of fracturing fluid,pressure drop rate and proppant material type(ceramic and sand)on long-term well production beyond formation linear regime.The third set of parametric calculations is carried out using the flowback model history-matched to field data related to production of four multistage hydraulically fractured oil wells in Achimov formation of Western Siberia,Russia.On the basis of the matched model we evaluated geomechanics effects on fracture conductivity degradation.We also performed sensitivity analysis in the framework of the history-matched model to study the impact of geomechanics and fluid rheology parameters on flowback efficiency.