Comparison of microwave- and thermal-assisted rock fragmentation methods at different temperatures and loading rates

Understanding the effects of microwave irradiation and thermal treatment on the dynamic compression and fragmentation properties of rocks is essential to quantify energy consumption in rock engineering.In this study,Fangshan granite(FG)specimens were exposed to microwave irradiation and heat treatment.The damage of FG specimens induced by these two methods was compared using X-ray CT scanning and ultrasonic wave method.The temperatures of FG after microwave irradiation and thermal treatment were effectively evaluated using a newly proposed technique.A novelty method for precisely determining the geometric features of fragments is developed to estimate the fragmentation energy.Thus,the dynamic uniaxial compressive strength(UCS),the dynamic fragmentation characteristics,and the fragmentation energy of FG after these two pretreatment methods can be reasonably compared.The noticeable distinction of loading rate effect on the dynamic UCS of FG between these two pretreatment methods is first observed.A relationship is established between the dynamic UCS and the damage induced by microwave irradiation and heat treatment.Moreover,fragmentation energy fan analysis is introduced to accurately compare the fragmentation properties of FG after two pretreatment methods in dynamic compression tests.

Effects of fracture evolution and non-Darcy flow on the thermal performance of enhanced geothermal system in 3D complex fractured rock

In fractured geothermal reservoirs,the fracture networks and internal fluid flow behaviors can significantly impact the thermal performance.In this study,we proposed a non-Darcy rough discrete fracture network(NR-DFN)model that can simultaneously consider the fracture evolution and non-Darcy flow dynamics in studying the thermo-hydro-mechanical(THM)coupling processes for heat extraction in geothermal reservoir.We further employed the model on the Habanero enhanced geothermal systems(EGS)project located in Australia.First,our findings illustrate a clear spatial-temporal variation in the thermal stress and pressure perturbations,as well as uneven spatial distribution of shear failure in 3D fracture networks.Activated shear failure is mainly concentrated in the first fracture cluster.Secondly,channeling flow have also been observed in DFNs during heat extraction and are further intensified by the expansion of fractures driven by thermal stresses.Moreover,the combined effect of non-Darcy flow and fracture evolution triggers a rapid decline in the resulting heat rate and temperature.The NR-DFN model framework and the Habanero EGS's results illustrate the importance of both fracture evolution and non-Darcy flow on the efficiency of EGS production and have the potential to promote the development of more sustainable and efficient EGS operations for stakeholders.

Effect of roughness on the shear behavior of rock joints subjected to impact loading

The shear behavior is regarded as the dominant property of rock joints and is dramatically affected by the joint surface roughness.To date,the effect of surface roughness on the shear behavior of rock joints under static or cyclic loading conditions has been extensively studied,but such effect under impact loading conditions keeps unclear.To address this issue,a series of impact shear tests was performed using a novel-designed dynamic experimental system combined with the digital image correlation(DIC)technique.The dynamic shear strength,deformability and failure mode of the jointed specimens with various joint roughness coefficients(JRC)are comprehensively analyzed.Results show that the shear strength and shear displacement characteristics of the rock joint under the impact loading keep consistent with those under static loading conditions.However,the temporal variations of shear stress,slip displacement and normal displacement under the impact loading conditions show obviously different behaviors.An elastic rebound of the slip displacement occurs during the impact shearing and its value increases with increasing joint roughness.Two identifiable stages(i.e.compression and dilation)are observed in the normal displacement curves for the rougher rock joints,whereas the joints with small roughness only manifest normal compression displacement.Besides,as the roughness increases,the maximum compression tends to decrease,while the maximum dilation gradually increases.More-over,the microstructural analysis based on scanning electron microscope(SEM)suggests that the roughness significantly affects the characteristics of the shear fractured zone enclosing the joint surface.

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.

Correction of dynamic Brazilian disc tensile strength of rocks under preloading conditions considering the overload phenomenon and invoking the Griffith criterion

Dynamic tensile failure is a common phenomenon in deep rock practices,and thus accurately evaluating the dynamic tensile responses of rocks under triaxial pressures is of great significance.The Brazilian disc(BD)test is the suggested method by the International Society for Rock Mechanics and Rock Engineering(ISRM)for measuring both the static and dynamic tensile strengths of rock-like materials.However,due to the overload phenomenon and the complex preloading conditions,the dynamic tensile strengths of rocks measured by the BD tests tend to be overestimated.To address this issue,the dynamic BD tensile strength(BTS)of Fangshan marble(FM)under different preloading conditions were measured through a triaxial split Hopkinson pressure bar(SHPB).The fracture onset in BD specimen was captured through a strain gage around the disc center.The discrepancy between the traditional tensile strength(TTS,determined by the peak load P_(f) of the BD specimen)and the nominal tensile strength(NTS,obtained from the load P_(i) when the diametral fracture commences in the tested BD specimen)was applied to quantitatively evaluating the overload phenomenon.The Griffith criterion was used to rectify the calculation of the tensile stress at the disc center under triaxial stress states.The results demonstrate that the overload ratio(s)increases with the loading rate(σ)and decreases with the hydrostatic pressure(σ_(s)).The TTS corrected by the Griffith criterion is independent of theσ_(s)due to the overload phenomenon,while the NTS corrected by the Griffith criterion is sensitive to both the andσ.Therefore,it is essential to modify the tensile stress in dynamic confined BD tests using both the overload correction and the Griffith criterion rectification to obtain the accurate dynamic BTS of rocks.

Dynamic responses and failure mechanisms of the existing tunnel under transient excavation unloading of an adjacent tunnel

Engineering disasters(e.g.rock slabbing and rockburst)of the tunnel groups induced by the transient excavation of an adjacent tunnel threaten the stability of the existing tunnel,especially for those excavated by using the drill and blast tunneling(D&B).However,the dynamic response and failure mechanism of surrounding rocks of the existing tunnel caused by adjacent transient excavation are not clear due to the difficulty in conducting field tests and laboratory experiments.Therefore,a novel transient unloading experimental system for deep tunnel excavation was proposed in this study.The real stress path and the unloading rate can be reproduced by using this proposed system.The experiments were conducted for observing the dynamic response of the existing tunnel induced by adjacent transient excavation under different lateral pressure coefficients l(?0.4,0.6,0.8,1,1.2,1.4,1.6,1.8)with a polymethyl methacrylate(PMMA)specimen.The propagation of the impact wave and unloading surface wave was detected through the digital image correlation(DIC)analysis.The reflection of the unloading surface wave on the incident side of the existing tunnel(tunnel-E)was observed and analyzed.Moreover,the dynamic characteristics of the stress redistribution,the particle displacement and vibration velocity of surrounding rocks of tunnel-E were analyzed and summarized.In addition,the Mohr-Coulomb(MeC)failure criterion with tension cut-off was adopted to evaluate the stability of the existing tunnel under adjacent transient excavation.The results indicate that the incident side of the existing tunnel under the dynamic disturbance of transient excavation of an adjacent tunnel was more prone to fail,followed by the shadow side and the top/bottom side.

Dynamic notched semi-circle bend(NSCB) method for measuring fracture properties of rocks:Fundamentals and applications

Rocks are increasingly used in extreme environments characterised by high loading rates and high confining pressures.Thus the fracture properties of rocks under dynamic loading and confinements are critical in various rock mechanics and rock engineering problems.Due to the transient nature of dynamic loading,the dynamic fracture tests of rocks are much more challenging than their static counterparts.Understanding the dynamic fracture behaviour of geomaterials relies significantly on suitable and reliable dynamic fracture testing methods.One of such methods is the notched semi-circle bend(NSCB)test combined with the advanced split Hopkinson pressure bar(SHPB)system,which has been recommended by the International Society for Rock Mechanics and Rock Engineering(ISRM)as the standard method for the determination of dynamic fracture toughness.The dynamic NSCB-SHPB method can provide detailed insights into dynamic fracture properties including initiation fracture toughness,fracture energy,propagation fracture toughness and fracture velocity.This review aims to fully describe the detailed principles and state-of-the-art applications of dynamic NSCB-SHPB techniques.The history and principles of dynamic NSCB-SHPB tests for rocks are outlined,and then the applications of dynamic NSCB-SHPB method(including the measurements of initiation and propagation fracture toughnesses and the limiting fracture velocity,the size effect and the digital image correlation(DIC)experiments)are discussed.Further,other applications of dynamic NSCB-SHPB techniques(i.e.the thermal,moisture and anisotropy effects on the dynamic fracture properties of geomaterials,and dynamic fracture toughness of geomaterials under pre-loading and hydrostatic pressures)are presented.

Dynamic mechanical behaviors of Fangshan marble

Dynamic strength parameters are extensively used in mining engineering and rock mechanics.However,there are no widely accepted dynamic failure models for rocks.In this study,the dynamic punching shear strength,uniaxial compressive strength(UCS) and tensile strength of fine-grained Fangshan marble(FM)are first measured by using a split Hopkinson pressure bar(SHPB) system.The pulse-shaping technique is then implemented to maintain the dynamic force balance in SHPB tests.Experimental results show that the dynamic punching shear strength,UCS and tensile strength increase with the loading rate.A recently developed dynamic Mohr-Coulomb theory is then used to interpret the testing data.In this model,the angle of internal friction φ is assumed to be independent of loading rate and is obtained using the static strength values.According to the dynamic Mohr-Coulomb theory,the dynamic UCS and the dynamic tensile strength are predicted from the dynamic punching shear strength.Furthermore,based on this dynamic theory,the dynamic UCS is predicted from the dynamic tensile strength.The consistency between the predicted and measured dynamic strengths demonstrates that the dynamic Mohr-Coulomb theory is applicable to FM.

Dynamic ModeⅡfracture behavior of rocks under hydrostatic pressure using the short core in compression(SCC)method

The shear failure of rocks under both a static triaxial stress and a dynamic disturbance is common in deep underground engineering and it is therefore essential for the design of underground engineering to quantitively estimate the dynamic ModeⅡfracture toughness KⅡCof rocks under a triaxial stress state.However,the method for determining the dynamic KⅡCof rocks under a triaxial stress has not been developed yet.With an optimal sample preparation,the short core in compression(SCC)method was designed and verified in this study to measure the dynamic KⅡCof Fangshan marble(FM)subjected to different hydrostatic pressures through a triaxial dynamic testing system.The formula for calculating the dynamic KⅡCof the rock SCC specimen under hydrostatic pressures was obtained by using the finite element method in combination with secondary cracks.The experimental results indicate that the failure mode of the rock SCC specimen under a hydrostatic pressure is the shear fracture and the KⅡCof FM increases as the loading rate.In addition,at a given loading rate the dynamic rock KⅡCis barely affected by hydrostatic pressures.Another important observation is that the dynamic fracture energy of FM enhances with loading rates and hydrostatic pressures.

Dynamic rock tensile strengths of Laurentian granite: Experimental observation and micromechanical model

Tensile strength is an important material property for rocks. In applications where rocks are subjected to dynamic loads, the dynamic tensile strength is the controlling parameter. Similar to the study of static tensile strength, there are various methods proposed to measure the dynamic tensile strength of rocks.Here we examine dynamic tensile strength values of Laurentian granite(LG) measured from three methods: dynamic direct tension, dynamic Brazilian disc(BD) test, and dynamic semi-circular bending(SCB). We found that the dynamic tensile strength from direct tension has the lowest value, and the dynamic SCB gives the highest strength at a given loading rate. Because the dynamic direct tension measures the intrinsic rock tensile strength, it is thus necessary to reconcile the differences in strength values between the direct tension and the other two methods. We attribute the difference between the dynamic BD results and the direct tension results to the overload and internal friction in BD tests. The difference between the dynamic SCB results and the direct tension results can be understood by invoking the non-local failure theory. It is shown that, after appropriate corrections, the dynamic tensile strengths from the two other tests can be reduced to those from direct tension.

Dynamic fragmentation of microwave irradiated rock

The microwave-assisted rock fragmentation has been proven to be a promising approach in reducing cutting tools wear and improving efficiency in rock crushing and excavation.Thus,understanding the influence of damage induced by microwave irradiation on rock fragmentation is necessary.In this context,cylindrical Fangshan granite(FG)specimens were exposed to microwave irradiation at a power of 6 kW for different durations up to 4.5 min.The damages of the specimens induced by irradiation were quantified by using both X-ray micro-CT scanning and ultrasonic wave measurement.The CT value and Pwave velocity decreased with increase of irradiation duration.The irradiated specimens were then tested using a split Hopkinson pressure bar(SHPB)system to simulate rock fragmentation.A momentum-trap technique was utilized to ensure single-pulse loading on the specimen in SHPB tests,enabling valid fragment size distribution(FSD)analysis.The dependence of dynamic uniaxial compressive strength(UCS)on the irradiation duration and loading rate was revealed.The dynamic UCS increased with increase of loading rate while decreased with increase of irradiation duration.Using the sieve analysis,three fragmentation types were proposed based on FSD,which were dictated by both loading rate and irradiation duration.In addition,an average fragment size was proposed to quantify FSD.The results showed that the average fragment size decreased with increase of loading rate.A loading rate range was identified,where a dramatic reduction of the average fragment size occurred.The dependence of fragmentation on the irradiation duration and loading rate was also discussed.

Numerical study on tensile failures of heterogeneous rocks

Many experimental results have demonstrated the apparent discrepancy of a rock material between its flexural tensile strength measured using various bending methods and its tensile strength measured using direct tension method or Brazil disc(BD)method.To understand the physical mechanism for such discrepancy,numerical simulation using the realistic failure process analysis(RFPA)is carried out in this work to simulate the tensile failure of heterogeneous rocks.Direct tension and semi-circular bend(SCB)tests are simulated using RFPA for rock materials with different levels of inhomogeneity,which is characterized by the homogeneity index of the Weibull distribution used in RFPA.The numerical results show that the discrepancy in the tensile strength values is caused by the inhomogeneity of the rock material.Furthermore,non-local failure criterion is adopted to calculate the characteristic length of the rock materials used in the simulation.It is shown that below a certain value of the homogeneity index,both the characteristic length and discrepancy between two types of tensile strengths of rock decrease with increase of the homogeneity index up to a critical value,at which the discrepancy disappears and the rock material is essentially homogeneous.

Dynamic rock tests using split Hopkinson （Kolsky） bar system - A review

Dynamic properties of rocks are important in a variety of rock mechanics and rock engineering problems. Due to the transient nature of the loading, dynamic tests of rock materials are very different from and much more challenging than their static counterparts. Dynamic tests are usually conducted using the split Hopkinson bar or Kolsl^j bar systems, which include both split Hopkinson pressure bar （SHPB） and split Hopkinson tension bar （SHTB） systems. Significant progress has been made on the quantification of various rock dynamic properties, owing to the advances in the experimental techniques of SHPB system. This review aims to fully describe and critically assess the detailed procedures and principles of tech- niques for dynamic rock tests using split Hopkinson bars. The history and principles of SHPB are outlined, followed by the key loading techniques that are useful for dynamic rock tests with SHPB （i.e. pulse shaping, momentum-trap and multi-axial loading techniques）. Various measurement techniques for rock tests in SHPB （i.e. X-ray micro computed tomography （CT）, laser gap gauge （LGG）, digital image corre- lation （DIC）, Moir~ method, caustics method, photoelastic coating method, dynamic infrared thermog- raphy） are then discussed. As the main objective of the review, various dynamic measurement techniques for rocks using SHPB are described, including dynamic rock strength measurements （i.e. dynamic compression, tension, bending and shear tests）, dynamic fracture measurements （i.e. dynamic imitation and propagation fracture toughness, dynamic fracture energy and fracture velocity）, and dy- namic techniques for studying the influences of temperature and pore water.

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.

Dynamic rock tests using split Hopkinson(Kolsky)bar system-A review

Dynamic properties of rocks are important in a variety of rock mechanics and rock engineering problems.Due to the transient nature of the loading, dynamic tests of rock materials are very different from and much more challenging than their static counterparts. Dynamic tests are usually conducted using the split Hopkinson bar or Kolsky bar systems, which include both split Hopkinson pressure bar(SHPB) and split Hopkinson tension bar(SHTB) systems. Signi fi cant progress has been made on the quanti fi cation of various rock dynamic properties, owing to the advances in the experimental techniques of SHPB system.This review aims to fully describe and critically assess the detailed procedures and principles of techniques for dynamic rock tests using split Hopkinson bars. The history and principles of SHPB are outlined,followed by the key loading techniques that are useful for dynamic rock tests with SHPB(i.e. pulse shaping, momentum-trap and multi-axial loading techniques). Various measurement techniques for rock tests in SHPB(i.e. X-ray micro computed tomography(CT), laser gap gauge(LGG), digital image correlation(DIC), Moiré method, caustics method, photoelastic coating method, dynamic infrared thermography) are then discussed. As the main objective of the review, various dynamic measurement techniques for rocks using SHPB are described, including dynamic rock strength measurements(i.e.dynamic compression, tension, bending and shear tests), dynamic fracture measurements(i.e. dynamic imitation and propagation fracture toughness, dynamic fracture energy and fracture velocity), and dynamic techniques for studying the in fl uences of temperature and pore water.

A stress-rifting origin of Grand Canyon

The Grand Canyon is a massive rift in the Colorado Plateau. How and when it developed has been debated for nearly 150 years. Most geologists believe the unusual landscape was primarily shaped by water erosion.Here we propose a stress-rifting model to provide an alternative explanation for the origin of Grand Canyon.This paper adopts a brittle–ductile double layer model to simulate the deformation and rifting of the plateau due to the mantle-melting-induced expansion. Our results show that the uplift induced by thermal expansion and its associated horizontal extension can cause open fractures that extend from the brittle surface to the underlying ductile layer in a top-down way. In addition, we find that episodic uplift can deepen and connect multiple fractures together to form a larger fracture network. Our findings suggest that the formation of the Grand Canyon might have been driven by plateau uplift and its associated rifting under crustal extension, wherein water erosion played only a minor role in shaping the course of the Colorado River. The new paradigm provides simpler explanations to some of the long-standing geological mysteries surrounding the canyon.