Strainburst is one type of rockburst that generally occurs in deep tunnel.In this study,the strainburst behaviors of marble specimens were investigated under tunnel-excavation-induced stress condition,and two stress p...Strainburst is one type of rockburst that generally occurs in deep tunnel.In this study,the strainburst behaviors of marble specimens were investigated under tunnel-excavation-induced stress condition,and two stress paths were designed,a commonly used stress path in true triaxial unloading rockburst tests and a new test path in which the intermediate principal stress was varied.During the tests,a high-speed camera was used to record the strainburst process,and an acoustic emission(AE)monitoring system was used to monitor the AE characteristics of failure.In these two stress paths,all the marble specimens exhibited strainbursts;however,when the intermediate principal stress was varied,the rockburst became more violent.The obtained results indicate that the intermediate principal stress has a significant effect on rockburst behavior of marble.Under a higher intermediate principal stress before the unloading,more elastic strain energy was accumulated in the specimen,and the cumulative AE energy was higher in the rockburst-induced failure,i.e.,more elastic strain energy was released during the failure.Therefore,more violent failure was observed:more rock fragments with a higher mass and larger size were ejected outward.展开更多
Investigation of unloading rock failure under differentσ_(2)facilitates the control mechanism of excavation surrounding rock.This study focused on single-sided unloading tests of granite specimens under true triaxial...Investigation of unloading rock failure under differentσ_(2)facilitates the control mechanism of excavation surrounding rock.This study focused on single-sided unloading tests of granite specimens under true triaxial conditions.The strength and failure characteristics were studied with micro-camera and acoustic emission(AE)monitoring.Furthermore,the choice of test path and the effect ofσ_(2)on fracture of unloading rock were discussed.Results show that the increasedσ_(2)can strengthen the stability of single-sided unloading rock.After unloading,the rock’s free surface underwent five phases,namely,inoculation,particle ejection,buckling rupture,stable failure,and unstable rockburst phases.Moreover,atσ_(2)≤30 MPa,the b value shows the following variation tendency:rising,dropping,significant fluctuation,and dropping,with dispersed damages signal.Atσ_(2)≥40 MPa,the tendency shows:a rise,a decrease,a slight fluctuation,and final drop,with concentrated damages signal.After unloading,AE energy is mainly concentrated in the micro-energy range.With the increasedσ_(2),the micro-energy ratio rises.In contrast,low,medium and large energy ratios drop gradually.The increased tensile fractures and decreased shear fractures indicate that the failure mode of the unloading rock gradually changes from tensile-shear mode to tensile-split one.The fractional dimension of the rock fragments first increases and then decreases with an inflection point at 20 MPa.The distribution of SIF on the planes changes asσ_(2)increases,resulting in strengthening and then weakening of the rock bearing capacity.展开更多
Precisely understanding the dynamic mechanical properties and failure modes of rocks subjected to true triaxial stress state(σ1>σ2>σ3,whereσ1,σ2,andσ3 are the major principal stress,intermediate principal ...Precisely understanding the dynamic mechanical properties and failure modes of rocks subjected to true triaxial stress state(σ1>σ2>σ3,whereσ1,σ2,andσ3 are the major principal stress,intermediate principal stress,and minor principal stress,respectively)is essential to the safety of underground engineering.However,in the laboratory,it is difficult to maintain the constant true triaxial stress state of rocks during the dynamic testing process.Herein,a numerical servo triaxial Hopkinson bar(NSTHB)was developed to study the dynamic responses of rocks confronted with a true triaxial stress state,in which lateral stresses can maintain constant.The results indicate that the dynamic strength and elastic modulus of rocks increase with the rise of intermediate principal stressσ2,while the dynamic elastic modulus is independent of the dynamic strain rate.Simulated acoustic emission distributions indicate that the intermediate principal stressσ2 dramatically affects dynamic failure modes of triaxial confined rocks.Asσ2 increases,the failure pattern switches from a single diagonal shear zone into two parallel shear zones with a small slant.Moreover,a recent triaxial Hopkinson bar experimental system using three bar pairs is also numerically established,and the measuring discrepancies are identified between the two numerical bar systems.The proposed NSTHB system provides a controllable tool for studying the dynamic triaxial behavior of rocks.展开更多
The overturning stability is vital for the retaining wall design of foundation pits, where the surrounding soils are usually unsaturated due to water draining. Moreover, the intermediate principal stress does affect t...The overturning stability is vital for the retaining wall design of foundation pits, where the surrounding soils are usually unsaturated due to water draining. Moreover, the intermediate principal stress does affect the unsaturated soil strength; meanwhile, the relationship between the unsaturated soil strength and matric suction is nonlinear. This work is to present closed-form equations of critical embedment depth for a rigid retaining wall against overturning by means of moment equilibrium. Matric suction is considered to be distributed uniformly and linearly with depth. The unified shear strength formulation for unsaturated soils under the plane strain condition is adopted to characterize the intermediate principal stress effect, and strength nonlinearity is described by a hyperbolic model of suction angle. The result obtained is orderly series solutions rather than one specific answer; thus, it has wide theoretical significance and good applicability. The validity of this present work is demonstrated by comparing it with a lower bound solution. The traditional overturning designs for rigid retaining walls, in which the saturated soil mechanics neglecting matric suction or the unsaturated soil mechanics based on the Mohr-Coulomb criterion are employed, are special cases of the proposed result. Parametric studies about the intermediate principal stress, matric suction and its distributions along with two strength nonlinearity methods on a new defined critical buried coefficient are discussed.展开更多
The significant differences between hard rocks(more brittle)and soft rocks(more ductile)may suggest the use of different failure criteria.A strength criterion for soft rocks that includes intermediate principal stress...The significant differences between hard rocks(more brittle)and soft rocks(more ductile)may suggest the use of different failure criteria.A strength criterion for soft rocks that includes intermediate principal stress was proposed.The new criterion includes two independent parameters:the uniaxial compressive strength(σ_(ci)),which can be obtained from common laboratory tests or indirectly estimated by alternative index tests in the laboratory or field;and f(joint),which is used to characterize the rock mass quality and can be easily estimated.The authors compared the predictive capabilities of the new criterion with other criteria using the database of soft rocks under two conditions:with and without triaxial data.For the estimation of triaxial and true-triaxial strengths,the new criterion generally produced a better fit.The proposed criterion is practical for an approximate first estimation of rock mass strength,even without triaxial data,as it balances accuracy(lower prediction error)and simplicity(fewer independent parameters).展开更多
Based on particle flow theory, the influences of the magnitude and direction of the intermediate principal stress on failure mechanism of hard rock with a pre-existing circular opening were studied by carrying out tru...Based on particle flow theory, the influences of the magnitude and direction of the intermediate principal stress on failure mechanism of hard rock with a pre-existing circular opening were studied by carrying out true triaxial tests on siltstone specimen. It is shown that peak strength of siltstone specimen increases firstly and subsequently decreases with the increase of the intermediate principal stress. And its turning point is related to the minimum principal stress and the direction of the intermediate principal stress. Failure characteristic(brittleness or ductility) of siltstone is determined by the minimum principal stress and the difference between the intermediate and minimum principal stress. The intermediate principal stress has a significant effect on the types and distributions of microcracks. The failure modes of the specimen are determined by the magnitude and direction of the intermediate principal stress, and related to weakening effect of the opening and inhibition effect of confining pressure in essence: when weakening effect of the opening is greater than inhibition effect of confining pressure, the failure surface is parallel to the x axis(such as σ2=σ3=0 MPa); conversely, the failure surface is parallel to the z axis(such as σ2=20 MPa, σ3=0 MPa).展开更多
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 stre...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.展开更多
A series of numerical simulations of conventional and true triaxial tests for soft rock materials using the three-dimensional finite difference code FLAC3D were presented. A hexahedral element and a strain hardening/s...A series of numerical simulations of conventional and true triaxial tests for soft rock materials using the three-dimensional finite difference code FLAC3D were presented. A hexahedral element and a strain hardening/softening constitutive model based on the unified strength theory(UST) were used to simulate both the consolidated-undrained(CU) triaxial and the consolidated-drained(CD) true triaxial tests. Based on the results of the true triaxial tests simulation, the effect of the intermediate principal stress on the strength of soft rock was investigated. Finally, an example of an axial compression test for a hard rock pillar with a soft rock interlayer was analyzed using the two-dimensional finite difference code FLAC. The CD true triaxial test simulations for diatomaceous soft rock suggest the peak and residual strengths increase by 30% when the effect of the intermediate principal stress is taken into account. The axial compression for a rock pillar indicated the peak and residual strengths increase six-fold when the soft rock interlayer approached the vertical and the effect of the intermediate principal stress is taken into account.展开更多
A series of true triaxial unloading tests are conducted on sandstone specimens with a single structural plane to investigate their mechanical behaviors and failure characteristics under different in situ stress states...A series of true triaxial unloading tests are conducted on sandstone specimens with a single structural plane to investigate their mechanical behaviors and failure characteristics under different in situ stress states.The experimental results indicate that the dip angle of structural plane(θ)and the intermediate principal stress(σ2)have an important influence on the peak strength,cracking mode,and rockburst severity.The peak strength exhibits a first increase and then decrease as a function ofσ2 for a constantθ.However,whenσ2 is constant,the maximum peak strength is obtained atθof 90°,and the minimum peak strength is obtained atθof 30°or 45°.For the case of an inclined structural plane,the crack type at the tips of structural plane transforms from a mix of wing and anti-wing cracks to wing cracks with an increase inσ2,while the crack type around the tips of structural plane is always anti-wing cracks for the vertical structural plane,accompanied by a series of tensile cracks besides.The specimens with structural plane do not undergo slabbing failure regardless ofθ,and always exhibit composite tensile-shear failure whatever theσ2 value is.With an increase inσ2 andθ,the intensity of the rockburst is consistent with the tendency of the peak strength.By analyzing the relationship between the cohesion(c),internal friction angle(φ),andθin sandstone specimens,we incorporateθinto the true triaxial unloading strength criterion,and propose a modified linear Mogi-Coulomb criterion.Moreover,the crack propagation mechanism at the tips of structural plane,and closure degree of the structural plane under true triaxial unloading conditions are also discussed and summarized.This study provides theoretical guidance for stability assessment of surrounding rocks containing geological structures in deep complex stress environments.展开更多
Fracture(fault)reactivation can lead to dynamic geological hazards including earthquakes,rock collapses,landslides,and rock bursts.True triaxial compression tests were conducted to analyze the fracture reactivation pr...Fracture(fault)reactivation can lead to dynamic geological hazards including earthquakes,rock collapses,landslides,and rock bursts.True triaxial compression tests were conducted to analyze the fracture reactivation process under two different orientations of σ_(2),i.e.σ_(2) parallel to the fracture plane(Scheme 2)and σ_(2) cutting through the fracture plane(Scheme 3),under varying σ_(3) from 10 MPa to 40 MPa.The peak or fracture reactivation strength,deformation,failure mode,and post-peak mechanical behavior of intact(Scheme 1)and pre-fractured(Schemes 2 and 3)specimens were also compared.Results show that for intact specimens,the stress remains nearly constant in the residual sliding stage with no stick-slip,and the newly formed fracture surface only propagates along the σ_(2) direction when σ_(3) ranges from 10 MPa to 30 MPa,while it extends along both σ_(2) and σ_(3) directions when σ_(3) increases to 40 MPa;for the pre-fractured specimens,the fractures are usually reactivated under all the σ_(3) levels in Scheme 2,but fracture reactivation only occurs when σ_(3) is greater than 25 MPa in Scheme 3,below which new faulting traversing the original macro fracture occurs.In all the test schemes,both ε_(2) and ε_(3) experience an accumulative process of elongation,after which an abrupt change occurs at the point of the final failure;the degree of this change is dependent on the orientation of the new faulting or the slip direction of the original fracture,and it is generally more than 10 times larger in the slip direction of the original fracture than in the non-slip direction.Besides,the differential stress(peak stress)required for reactivation and the post-peak stress drop increase with increasing σ_(3).Post-peak stress drop and residual strength in Scheme 3 are generally greater than those in Scheme 2 at the same σ_(3) value.Our study clearly shows that intermediate principal stress orientation not only affects the fracture reactivation strength but also influences the slip deformation and failure modes.These new findings facilitate the mitigation of dynamic geological hazards associated with fracture and fault slip.展开更多
Failure of mine pillars,especially in deep underground mines,significantly threatens the safety of miners and equipment.Previous studies on mine pillar stability design have used classical constitutive models that ign...Failure of mine pillars,especially in deep underground mines,significantly threatens the safety of miners and equipment.Previous studies on mine pillar stability design have used classical constitutive models that ignore the intermediate principal stress component when determining the factor of safety.In this study,we develop and implement a three-dimensional modified Hoek-Brown(HB)constitutive model that incorporates the intermediate principal stress component into the numerical simulation tool FLAC3D.Furthermore,we propose and apply a strength-reduction technique to determine a more accurate factor of safety for mine pillars.This novel approach provides a more comprehensive and realistic method for geomechanical analysis and pillar design,enhancing our understanding of pillar stability.Through numerical analysis,we illustrate the impact of the intermediate principal stress component on mine pillar plasticity.The factor of safety is calculated via the strength reduction method,revealing a substantial improvement from 1.7 with the classical HB model to 2.0 with the 3D HB model.Including the intermediate principal stress component reduces the evolution of plasticity in the mine pillar.For instance,the volume of plastic zones diminishes,and the factor of safety increases as the width-to-height ratio increases.Exemplary simulations show that ignoring the effect of the intermediate principal stress component,including underestimating safety levels,designing suboptimal pillar design,and misinterpreting in situ observations and measurements,can lead to severe consequences.展开更多
A series of monotonic and rotational shearing tests are carried out on reconstituted clay using a hollow cylinder apparatus under undrained condition. In the rotational shearing tests, the principal stress axes rotate...A series of monotonic and rotational shearing tests are carried out on reconstituted clay using a hollow cylinder apparatus under undrained condition. In the rotational shearing tests, the principal stress axes rotate cyclically with the magnitudes of the principal stresses keeping constant. The anisotropy of the reconstituted clay is analyzed from the monotonic shearing tests. Obvious pore pressure is induced by the principal stress rotation alone even with shear stress q0=5 k Pa. Strain components also accumulate with increasing the number of cycles and increases suddenly at the onset of failure. The deviatoric shear strain of 7.5% can be taken as the failure criterion for clay subjected to the pure cyclic principal stress rotation. The intermediate principal stress parameter b plays a significant role in the development of pore pressure and strain. Specimens are weakened by cyclic rotational shearing as the shear modulus decreases with increasing the number of cycles, and the shear modulus reduces more quickly with larger b. Clear deviation between the directions of the principal plastic strain increment and the principal stress is observed during pure principal stress rotation. Both the coaxial and non-coaxial plastic mechanisms should be taken into consideration to simulate the deformation behavior of clay under pure principal stress rotation. The mechanism of the soil response to the pure principal stress rotation is discussed based on the experimental observations.展开更多
A unified semi-analytical solution is presented for elastic-plastic stress of a deep circular hydraulic tunnel with support yielding under plane strain conditions.The rock mass is assumed to be elastic-perfectly plast...A unified semi-analytical solution is presented for elastic-plastic stress of a deep circular hydraulic tunnel with support yielding under plane strain conditions.The rock mass is assumed to be elastic-perfectly plastic and governed by the unified strength theory (UST).Different major principal stresses in different engineering situations and different support yielding conditions are both considered.The unified solution obtained in this work is a series of results,rather than one specific solution,hence it is suitable for a wide range of rock masses.In addition,parametric study is conducted to investigate the effect of intermediate principal stress.The result shows the major principal stress should be rationally chosen according to different engineering conditions.Finally,the applicability of the unified solution is discussed according to the critical pressures.展开更多
A series of directional shear tests on remolded frozen soil was carried out at 10°C by using a hollow cylinder apparatus to study failure criterion under a directional shear-stress path.Directional shear tests we...A series of directional shear tests on remolded frozen soil was carried out at 10°C by using a hollow cylinder apparatus to study failure criterion under a directional shear-stress path.Directional shear tests were conducted at five shear rates(10,20,30,40,and 50 kPa/min)and five intermediate principal stress coefficients(b=0,0.25,0.5,0.75,and 1),with the mean principal stress(p=4.5 MPa)kept constant.The results show that the torsional strength and the generalized strength both increase with the increase of the shear rates.According to the failure modes of frozen soil under different shear rates,the specimens present obvious plastic failure and shear band;and the torsional shear component dominates the failure modes of hollow cylindrical specimens.A shear rate of 30 kPa/min is chosen as the loading rate in the directional shear tests of frozen soil.The shape of the failure curve in theπplane is dependent on the directional anglesαof the major prin cipal stress.It is reasonable to use the strain-hardening curves to define the deviatoric stress value atγg=15%(generalized shear strain)as the failure criterion of frozen soil under a directional shear-stress path.展开更多
On the basis of the sufficient consideration of vectorial characteristics of stress, a new nonlinear constitutive model for cohesionless soil under plane strain and 3-D conditions was presented in a way that the actio...On the basis of the sufficient consideration of vectorial characteristics of stress, a new nonlinear constitutive model for cohesionless soil under plane strain and 3-D conditions was presented in a way that the action effects of stress vector are decomposed into the action effect of mean effective stress and that of the stress ratio vector (ratio of deviatoric stress vector to mean effective stress). The constitutive model can take account of the influence of both numerical and directional changes of stress vector on deformation of soil simultaneously, and is applicable of both static and dynamic loading.展开更多
To understand the strengths of rocks under complex stress states,a generalized nonlinear threedimensional(3D)Hoek‒Brown failure(NGHB)criterion was proposed in this study.This criterion shares the same parameters with ...To understand the strengths of rocks under complex stress states,a generalized nonlinear threedimensional(3D)Hoek‒Brown failure(NGHB)criterion was proposed in this study.This criterion shares the same parameters with the generalized HB(GHB)criterion and inherits the parameter advantages of GHB.Two new parameters,b,and n,were introduced into the NGHB criterion that primarily controls the deviatoric plane shape of the NGHB criterion under triaxial tension and compression,respectively.The NGHB criterion can consider the influence of intermediate principal stress(IPS),where the deviatoric plane shape satisfies the smoothness requirements,while the HB criterion not.This criterion can degenerate into the two modified 3D HB criteria,the Priest criterion under triaxial compression condition and the HB criterion under triaxial compression and tension condition.This criterion was verified using true triaxial test data for different parameters,six types of rocks,and two kinds of in situ rock masses.For comparison,three existing 3D HB criteria were selected for performance comparison research.The result showed that the NGHB criterion gave better prediction performance than other criteria.The prediction errors of the strength of six types of rocks and two kinds of in situ rock masses were in the range of 2.0724%-3.5091%and 1.0144%-3.2321%,respectively.The proposed criterion lays a preliminary theoretical foundation for prediction of engineering rock mass strength under complex in situ stress conditions.展开更多
Strength theory is the basic theory for calculating and designing the strength of engineering materials in civil,hydraulic,mechanical,aerospace,military,and other engineering disciplines.Therefore,the comprehensive st...Strength theory is the basic theory for calculating and designing the strength of engineering materials in civil,hydraulic,mechanical,aerospace,military,and other engineering disciplines.Therefore,the comprehensive study of the generalized nonlinear strength theory(GNST)of geomaterials has significance for the construction of engineering rock strength.This paper reviews the GNST of geomaterials to demonstrate the research status of nonlinear strength characteristics of geomaterials under complex stress paths.First,it systematically summarizes the research progress of GNST(classical and empirical criteria).Then,the latest research the authors conducted over the past five years on the GNST is introduced,and a generalized three-dimensional(3D)nonlinear Hoek‒Brown(HB)criterion(NGHB criterion)is proposed for practical applications.This criterion can be degenerated into the existing three modified HB criteria and has a better prediction performance.The strength prediction errors for six rocks and two in-situ rock masses are 2.0724%-3.5091%and 1.0144%-3.2321%,respectively.Finally,the development and outlook of the GNST are expounded,and a new topic about the building strength index of rock mass and determining the strength of in-situ engineering rock mass is proposed.The summarization of the GNST provides theoretical traceability and optimization for constructing in-situ engineering rock mass strength.展开更多
This paper aims to comprehensively analyze the influence of the principal stress angle rotation and intermediate principal stress on loess's strength and deformation characteristics. A hollow cylinder torsional sh...This paper aims to comprehensively analyze the influence of the principal stress angle rotation and intermediate principal stress on loess's strength and deformation characteristics. A hollow cylinder torsional shear apparatus was utilized to conduct tests on remolded samples under both normal and frozen conditions to investigate the mechanical properties and deformation behavior of loess under complex stress conditions. The results indicate significant differences in the internal changes of soil particles, unfrozen water, and relative positions in soil samples under normal and frozen conditions, leading to noticeable variations in strength and strain development.In frozen state, loess experiences primarily compressive failure with a slow growth of cracks, while at normal temperature, it predominantly exhibits shear failure. With the increase in the principal stress angle, the deformation patterns of the soil samples under different conditions become essentially consistent, gradually transitioning from compression to extension, accompanied by a reduction in axial strength. The gradual increase in the principal stress axis angle(α) reduces the strength of the generalized shear stress and shear strain curves.Under an increasing α, frozen soil exhibits strain-hardening characteristics, with the maximum shear strength occurring at α = 45°. The intermediate principal stress coefficient(b) also significantly impacts the strength of frozen soil, with an increasing b resulting in a gradual decrease in generalized shear stress strength. This study provides a reference for comprehensively exploring the mechanical properties of soil under traffic load and a reliable theoretical basis for the design and maintenance of roadbeds.展开更多
In this research,a series of biaxial compression and biaxial fatigue tests were conducted to investigate the mechanical behaviors of marble and sandstone under biaxial confinements.Experimental results demonstrate tha...In this research,a series of biaxial compression and biaxial fatigue tests were conducted to investigate the mechanical behaviors of marble and sandstone under biaxial confinements.Experimental results demonstrate that the biaxial compressive strength of rocks under biaxial compression increases firstly,and subsequently decreases with increase of the intermediate principal stress.The fatigue failure characteristics of the rocks in biaxial fatigue tests are functions of the peak value of fatigue loads,the intermediate principal stress and the rock lithology.With the increase of the peak values of fatigue loads,the fatigue lives of rocks decrease.The intermediate principal stress strengthens the resistance ability of rocks to fatigue loads except considering the strength increasing under biaxial confinements.The fatigue lives of rocks increase with the increase of the intermediate principal stress under the same ratio of the fatigue load and their biaxial compressive strength.The acoustic emission(AE)and fragments studies showed that the sandstone has higher ability to resist the fatigue loads compared to the marble,and the marble generated a greater number of smaller fragments after fatigue failure compared to the sandstone.So,it can be inferred that the rock breaking efficiency and rock burst is higher or severer induced by fatigue loading than that induced by monotonous quasi-static loading,especially for hard rocks.展开更多
The Hoek-Brown(HB)strength criterion has been applied widely in a large number of projects around the world.However,this criterion ignores the intermediate principal stress s2.Many evidences have demonstrated that the...The Hoek-Brown(HB)strength criterion has been applied widely in a large number of projects around the world.However,this criterion ignores the intermediate principal stress s2.Many evidences have demonstrated that the rock strength is dependent on s2.Thus it is necessary to extend the HB criterion into a three-dimensional(3D)form.In this study,the effect of s2 on the strength of rocks is identified by reviewing the true triaxial tests of various rock types reported in the literature.A simple 3D strength criterion is developed.The modified criterion is verified by the true triaxial tests of 13 rock types.The results indicate that the modified criterion can achieve a good fit to most of rock types.It can represent a series of criteria as b varies.For comparisons,several existing 3D versions of the HB criterion are selected to predict the strengths of these rock types.It is indicated that the proposed criterion works better than other criteria.A substantial relationship between parameter b and the unconfined compressive strength is established,which guarantees that the proposed criterion can still work well even in the absence of true triaxial test data.展开更多
基金Project(2016YFC0801403) supported by the National Key Research and Development Program of ChinaProject(2017RCJJ012) supported by the Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents,China+1 种基金Project(ZR2018MEE009) supported by the Shandong Provincial Natural Science Foundation,ChinaProject(MDPC2017ZR04) supported by the Open Project Fund for State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology of China
文摘Strainburst is one type of rockburst that generally occurs in deep tunnel.In this study,the strainburst behaviors of marble specimens were investigated under tunnel-excavation-induced stress condition,and two stress paths were designed,a commonly used stress path in true triaxial unloading rockburst tests and a new test path in which the intermediate principal stress was varied.During the tests,a high-speed camera was used to record the strainburst process,and an acoustic emission(AE)monitoring system was used to monitor the AE characteristics of failure.In these two stress paths,all the marble specimens exhibited strainbursts;however,when the intermediate principal stress was varied,the rockburst became more violent.The obtained results indicate that the intermediate principal stress has a significant effect on rockburst behavior of marble.Under a higher intermediate principal stress before the unloading,more elastic strain energy was accumulated in the specimen,and the cumulative AE energy was higher in the rockburst-induced failure,i.e.,more elastic strain energy was released during the failure.Therefore,more violent failure was observed:more rock fragments with a higher mass and larger size were ejected outward.
基金This work was supported by the Scientific Research Project of Anhui Province Universities,China(No.YJS20210388)the National Natural Science Foundation of China(Nos.51974009,52004006,and 52004005)+2 种基金the Major Science and Technology Special Project of Anhui Province,China(No.202203a07020011)the Collaborative Innovation Project of Anhui Province Universities,China(No.GXXT-2021-075)the Huaibei City Science and Technology Major Program(No.Z2020005).
文摘Investigation of unloading rock failure under differentσ_(2)facilitates the control mechanism of excavation surrounding rock.This study focused on single-sided unloading tests of granite specimens under true triaxial conditions.The strength and failure characteristics were studied with micro-camera and acoustic emission(AE)monitoring.Furthermore,the choice of test path and the effect ofσ_(2)on fracture of unloading rock were discussed.Results show that the increasedσ_(2)can strengthen the stability of single-sided unloading rock.After unloading,the rock’s free surface underwent five phases,namely,inoculation,particle ejection,buckling rupture,stable failure,and unstable rockburst phases.Moreover,atσ_(2)≤30 MPa,the b value shows the following variation tendency:rising,dropping,significant fluctuation,and dropping,with dispersed damages signal.Atσ_(2)≥40 MPa,the tendency shows:a rise,a decrease,a slight fluctuation,and final drop,with concentrated damages signal.After unloading,AE energy is mainly concentrated in the micro-energy range.With the increasedσ_(2),the micro-energy ratio rises.In contrast,low,medium and large energy ratios drop gradually.The increased tensile fractures and decreased shear fractures indicate that the failure mode of the unloading rock gradually changes from tensile-shear mode to tensile-split one.The fractional dimension of the rock fragments first increases and then decreases with an inflection point at 20 MPa.The distribution of SIF on the planes changes asσ_(2)increases,resulting in strengthening and then weakening of the rock bearing capacity.
基金the financial support from the National Natural Science Foundation of China(Nos.52039007 and 52009086)the Sichuan Province Youth Science and Technology Innovation Team(No.2020JDTD0001)。
文摘Precisely understanding the dynamic mechanical properties and failure modes of rocks subjected to true triaxial stress state(σ1>σ2>σ3,whereσ1,σ2,andσ3 are the major principal stress,intermediate principal stress,and minor principal stress,respectively)is essential to the safety of underground engineering.However,in the laboratory,it is difficult to maintain the constant true triaxial stress state of rocks during the dynamic testing process.Herein,a numerical servo triaxial Hopkinson bar(NSTHB)was developed to study the dynamic responses of rocks confronted with a true triaxial stress state,in which lateral stresses can maintain constant.The results indicate that the dynamic strength and elastic modulus of rocks increase with the rise of intermediate principal stressσ2,while the dynamic elastic modulus is independent of the dynamic strain rate.Simulated acoustic emission distributions indicate that the intermediate principal stressσ2 dramatically affects dynamic failure modes of triaxial confined rocks.Asσ2 increases,the failure pattern switches from a single diagonal shear zone into two parallel shear zones with a small slant.Moreover,a recent triaxial Hopkinson bar experimental system using three bar pairs is also numerically established,and the measuring discrepancies are identified between the two numerical bar systems.The proposed NSTHB system provides a controllable tool for studying the dynamic triaxial behavior of rocks.
基金Project(41202191)supported by the National Natural Science Foundation of ChinaProject(2015JM4146)supported by the Natural Science Foundation of Shaanxi Province,ChinaProject(2015)supported by the Postdoctoral Research Project of Shaanxi Province,China
文摘The overturning stability is vital for the retaining wall design of foundation pits, where the surrounding soils are usually unsaturated due to water draining. Moreover, the intermediate principal stress does affect the unsaturated soil strength; meanwhile, the relationship between the unsaturated soil strength and matric suction is nonlinear. This work is to present closed-form equations of critical embedment depth for a rigid retaining wall against overturning by means of moment equilibrium. Matric suction is considered to be distributed uniformly and linearly with depth. The unified shear strength formulation for unsaturated soils under the plane strain condition is adopted to characterize the intermediate principal stress effect, and strength nonlinearity is described by a hyperbolic model of suction angle. The result obtained is orderly series solutions rather than one specific answer; thus, it has wide theoretical significance and good applicability. The validity of this present work is demonstrated by comparing it with a lower bound solution. The traditional overturning designs for rigid retaining walls, in which the saturated soil mechanics neglecting matric suction or the unsaturated soil mechanics based on the Mohr-Coulomb criterion are employed, are special cases of the proposed result. Parametric studies about the intermediate principal stress, matric suction and its distributions along with two strength nonlinearity methods on a new defined critical buried coefficient are discussed.
基金This work was partly financially supported by the major special project of the National Natural Science Foundation of China(No.41941018),for which the authors are grateful.
文摘The significant differences between hard rocks(more brittle)and soft rocks(more ductile)may suggest the use of different failure criteria.A strength criterion for soft rocks that includes intermediate principal stress was proposed.The new criterion includes two independent parameters:the uniaxial compressive strength(σ_(ci)),which can be obtained from common laboratory tests or indirectly estimated by alternative index tests in the laboratory or field;and f(joint),which is used to characterize the rock mass quality and can be easily estimated.The authors compared the predictive capabilities of the new criterion with other criteria using the database of soft rocks under two conditions:with and without triaxial data.For the estimation of triaxial and true-triaxial strengths,the new criterion generally produced a better fit.The proposed criterion is practical for an approximate first estimation of rock mass strength,even without triaxial data,as it balances accuracy(lower prediction error)and simplicity(fewer independent parameters).
基金Project(51021004)supported by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China
文摘Based on particle flow theory, the influences of the magnitude and direction of the intermediate principal stress on failure mechanism of hard rock with a pre-existing circular opening were studied by carrying out true triaxial tests on siltstone specimen. It is shown that peak strength of siltstone specimen increases firstly and subsequently decreases with the increase of the intermediate principal stress. And its turning point is related to the minimum principal stress and the direction of the intermediate principal stress. Failure characteristic(brittleness or ductility) of siltstone is determined by the minimum principal stress and the difference between the intermediate and minimum principal stress. The intermediate principal stress has a significant effect on the types and distributions of microcracks. The failure modes of the specimen are determined by the magnitude and direction of the intermediate principal stress, and related to weakening effect of the opening and inhibition effect of confining pressure in essence: when weakening effect of the opening is greater than inhibition effect of confining pressure, the failure surface is parallel to the x axis(such as σ2=σ3=0 MPa); conversely, the failure surface is parallel to the z axis(such as σ2=20 MPa, σ3=0 MPa).
文摘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.
基金Projects(41172276,51279155)supported by the National Natural Science Foundation of ChinaProjects(106-00X101,106-5X1205)supported by the Central Financial Funds for the Development of Characteristic Key Disciplines in Local University,China
文摘A series of numerical simulations of conventional and true triaxial tests for soft rock materials using the three-dimensional finite difference code FLAC3D were presented. A hexahedral element and a strain hardening/softening constitutive model based on the unified strength theory(UST) were used to simulate both the consolidated-undrained(CU) triaxial and the consolidated-drained(CD) true triaxial tests. Based on the results of the true triaxial tests simulation, the effect of the intermediate principal stress on the strength of soft rock was investigated. Finally, an example of an axial compression test for a hard rock pillar with a soft rock interlayer was analyzed using the two-dimensional finite difference code FLAC. The CD true triaxial test simulations for diatomaceous soft rock suggest the peak and residual strengths increase by 30% when the effect of the intermediate principal stress is taken into account. The axial compression for a rock pillar indicated the peak and residual strengths increase six-fold when the soft rock interlayer approached the vertical and the effect of the intermediate principal stress is taken into account.
基金supports from the National Natural Science Foundation of China (Grant Nos.52004143 and 52374095)the open fund for the Laboratory of Mining Response and Disaster Prevention and Control in Deep Coal Mines (Grant No.SKLMRDPC21KF06).
文摘A series of true triaxial unloading tests are conducted on sandstone specimens with a single structural plane to investigate their mechanical behaviors and failure characteristics under different in situ stress states.The experimental results indicate that the dip angle of structural plane(θ)and the intermediate principal stress(σ2)have an important influence on the peak strength,cracking mode,and rockburst severity.The peak strength exhibits a first increase and then decrease as a function ofσ2 for a constantθ.However,whenσ2 is constant,the maximum peak strength is obtained atθof 90°,and the minimum peak strength is obtained atθof 30°or 45°.For the case of an inclined structural plane,the crack type at the tips of structural plane transforms from a mix of wing and anti-wing cracks to wing cracks with an increase inσ2,while the crack type around the tips of structural plane is always anti-wing cracks for the vertical structural plane,accompanied by a series of tensile cracks besides.The specimens with structural plane do not undergo slabbing failure regardless ofθ,and always exhibit composite tensile-shear failure whatever theσ2 value is.With an increase inσ2 andθ,the intensity of the rockburst is consistent with the tendency of the peak strength.By analyzing the relationship between the cohesion(c),internal friction angle(φ),andθin sandstone specimens,we incorporateθinto the true triaxial unloading strength criterion,and propose a modified linear Mogi-Coulomb criterion.Moreover,the crack propagation mechanism at the tips of structural plane,and closure degree of the structural plane under true triaxial unloading conditions are also discussed and summarized.This study provides theoretical guidance for stability assessment of surrounding rocks containing geological structures in deep complex stress environments.
基金funding support from the National Nature Science Foundation of China(Grant No.42272334)the National Key Research and Development Program of China(Grant No.2022YFE0137200)the Taishan Scholars Program(Grant No.2019RKB01083).
文摘Fracture(fault)reactivation can lead to dynamic geological hazards including earthquakes,rock collapses,landslides,and rock bursts.True triaxial compression tests were conducted to analyze the fracture reactivation process under two different orientations of σ_(2),i.e.σ_(2) parallel to the fracture plane(Scheme 2)and σ_(2) cutting through the fracture plane(Scheme 3),under varying σ_(3) from 10 MPa to 40 MPa.The peak or fracture reactivation strength,deformation,failure mode,and post-peak mechanical behavior of intact(Scheme 1)and pre-fractured(Schemes 2 and 3)specimens were also compared.Results show that for intact specimens,the stress remains nearly constant in the residual sliding stage with no stick-slip,and the newly formed fracture surface only propagates along the σ_(2) direction when σ_(3) ranges from 10 MPa to 30 MPa,while it extends along both σ_(2) and σ_(3) directions when σ_(3) increases to 40 MPa;for the pre-fractured specimens,the fractures are usually reactivated under all the σ_(3) levels in Scheme 2,but fracture reactivation only occurs when σ_(3) is greater than 25 MPa in Scheme 3,below which new faulting traversing the original macro fracture occurs.In all the test schemes,both ε_(2) and ε_(3) experience an accumulative process of elongation,after which an abrupt change occurs at the point of the final failure;the degree of this change is dependent on the orientation of the new faulting or the slip direction of the original fracture,and it is generally more than 10 times larger in the slip direction of the original fracture than in the non-slip direction.Besides,the differential stress(peak stress)required for reactivation and the post-peak stress drop increase with increasing σ_(3).Post-peak stress drop and residual strength in Scheme 3 are generally greater than those in Scheme 2 at the same σ_(3) value.Our study clearly shows that intermediate principal stress orientation not only affects the fracture reactivation strength but also influences the slip deformation and failure modes.These new findings facilitate the mitigation of dynamic geological hazards associated with fracture and fault slip.
文摘Failure of mine pillars,especially in deep underground mines,significantly threatens the safety of miners and equipment.Previous studies on mine pillar stability design have used classical constitutive models that ignore the intermediate principal stress component when determining the factor of safety.In this study,we develop and implement a three-dimensional modified Hoek-Brown(HB)constitutive model that incorporates the intermediate principal stress component into the numerical simulation tool FLAC3D.Furthermore,we propose and apply a strength-reduction technique to determine a more accurate factor of safety for mine pillars.This novel approach provides a more comprehensive and realistic method for geomechanical analysis and pillar design,enhancing our understanding of pillar stability.Through numerical analysis,we illustrate the impact of the intermediate principal stress component on mine pillar plasticity.The factor of safety is calculated via the strength reduction method,revealing a substantial improvement from 1.7 with the classical HB model to 2.0 with the 3D HB model.Including the intermediate principal stress component reduces the evolution of plasticity in the mine pillar.For instance,the volume of plastic zones diminishes,and the factor of safety increases as the width-to-height ratio increases.Exemplary simulations show that ignoring the effect of the intermediate principal stress component,including underestimating safety levels,designing suboptimal pillar design,and misinterpreting in situ observations and measurements,can lead to severe consequences.
基金Projects(51338009,51178422)supported by the National Natural Science Foundation of China
文摘A series of monotonic and rotational shearing tests are carried out on reconstituted clay using a hollow cylinder apparatus under undrained condition. In the rotational shearing tests, the principal stress axes rotate cyclically with the magnitudes of the principal stresses keeping constant. The anisotropy of the reconstituted clay is analyzed from the monotonic shearing tests. Obvious pore pressure is induced by the principal stress rotation alone even with shear stress q0=5 k Pa. Strain components also accumulate with increasing the number of cycles and increases suddenly at the onset of failure. The deviatoric shear strain of 7.5% can be taken as the failure criterion for clay subjected to the pure cyclic principal stress rotation. The intermediate principal stress parameter b plays a significant role in the development of pore pressure and strain. Specimens are weakened by cyclic rotational shearing as the shear modulus decreases with increasing the number of cycles, and the shear modulus reduces more quickly with larger b. Clear deviation between the directions of the principal plastic strain increment and the principal stress is observed during pure principal stress rotation. Both the coaxial and non-coaxial plastic mechanisms should be taken into consideration to simulate the deformation behavior of clay under pure principal stress rotation. The mechanism of the soil response to the pure principal stress rotation is discussed based on the experimental observations.
基金Project(50969007)supported by National Natural Science Foundation of ChinaProject(GJJ13753)supported by the Scientific and Technological Research Fund,Department of Education,Jiangxi Province,China
文摘A unified semi-analytical solution is presented for elastic-plastic stress of a deep circular hydraulic tunnel with support yielding under plane strain conditions.The rock mass is assumed to be elastic-perfectly plastic and governed by the unified strength theory (UST).Different major principal stresses in different engineering situations and different support yielding conditions are both considered.The unified solution obtained in this work is a series of results,rather than one specific solution,hence it is suitable for a wide range of rock masses.In addition,parametric study is conducted to investigate the effect of intermediate principal stress.The result shows the major principal stress should be rationally chosen according to different engineering conditions.Finally,the applicability of the unified solution is discussed according to the critical pressures.
基金supported by the National Natural Science Foundation of China(Nos.U1703244 and 41672310)the National Natural Science Foundation of China(No.41801038)+6 种基金the State Key Laboratory for Geo Mechanics and Deep Underground Engineering,the China University of Mining and Technology(SKLGDUEK1904)the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDA2003020102)the Major Program of Bureau of International Cooperation,the Chinese Academy of Sciences(131B62KYSB20170012)the National Key Research and Development Program(2017YFC0405101)the Research Project of the State Key Laboratory of Frozen Soils Engineering(Grant No.SKLFSE-ZY-16)the Science and Technology Major Project of Gansu Province(143GKDA007)the Science and Technology Planning Project of Gansu Province(No.18JR3RA376)
文摘A series of directional shear tests on remolded frozen soil was carried out at 10°C by using a hollow cylinder apparatus to study failure criterion under a directional shear-stress path.Directional shear tests were conducted at five shear rates(10,20,30,40,and 50 kPa/min)and five intermediate principal stress coefficients(b=0,0.25,0.5,0.75,and 1),with the mean principal stress(p=4.5 MPa)kept constant.The results show that the torsional strength and the generalized strength both increase with the increase of the shear rates.According to the failure modes of frozen soil under different shear rates,the specimens present obvious plastic failure and shear band;and the torsional shear component dominates the failure modes of hollow cylindrical specimens.A shear rate of 30 kPa/min is chosen as the loading rate in the directional shear tests of frozen soil.The shape of the failure curve in theπplane is dependent on the directional anglesαof the major prin cipal stress.It is reasonable to use the strain-hardening curves to define the deviatoric stress value atγg=15%(generalized shear strain)as the failure criterion of frozen soil under a directional shear-stress path.
文摘On the basis of the sufficient consideration of vectorial characteristics of stress, a new nonlinear constitutive model for cohesionless soil under plane strain and 3-D conditions was presented in a way that the action effects of stress vector are decomposed into the action effect of mean effective stress and that of the stress ratio vector (ratio of deviatoric stress vector to mean effective stress). The constitutive model can take account of the influence of both numerical and directional changes of stress vector on deformation of soil simultaneously, and is applicable of both static and dynamic loading.
基金supported by the National Natural Science Foundation of China(Grant Nos.51934003,52334004)Yunnan Major Scientific and Technological Projects(Grant No.202202AG050014)。
文摘To understand the strengths of rocks under complex stress states,a generalized nonlinear threedimensional(3D)Hoek‒Brown failure(NGHB)criterion was proposed in this study.This criterion shares the same parameters with the generalized HB(GHB)criterion and inherits the parameter advantages of GHB.Two new parameters,b,and n,were introduced into the NGHB criterion that primarily controls the deviatoric plane shape of the NGHB criterion under triaxial tension and compression,respectively.The NGHB criterion can consider the influence of intermediate principal stress(IPS),where the deviatoric plane shape satisfies the smoothness requirements,while the HB criterion not.This criterion can degenerate into the two modified 3D HB criteria,the Priest criterion under triaxial compression condition and the HB criterion under triaxial compression and tension condition.This criterion was verified using true triaxial test data for different parameters,six types of rocks,and two kinds of in situ rock masses.For comparison,three existing 3D HB criteria were selected for performance comparison research.The result showed that the NGHB criterion gave better prediction performance than other criteria.The prediction errors of the strength of six types of rocks and two kinds of in situ rock masses were in the range of 2.0724%-3.5091%and 1.0144%-3.2321%,respectively.The proposed criterion lays a preliminary theoretical foundation for prediction of engineering rock mass strength under complex in situ stress conditions.
基金This research was financially supported by the National Natural Science Foundation of China(Nos.51934003,52334004)Yunnan Innovation Team(No.202105AE 160023)+2 种基金Major Science and Technology Special Project of Yunnan Province,China(No.202102AF080001)Yunnan Major Scientific and Technological Projects,China(No.202202AG050014)Key Laboratory of Geohazard Forecast and Geoecological Restoration in Plateau Mountainous Area,MNR,and Yunnan Key Laboratory of Geohazard Forecast and Geoecological Restoration in Plateau Mountainous Area.
文摘Strength theory is the basic theory for calculating and designing the strength of engineering materials in civil,hydraulic,mechanical,aerospace,military,and other engineering disciplines.Therefore,the comprehensive study of the generalized nonlinear strength theory(GNST)of geomaterials has significance for the construction of engineering rock strength.This paper reviews the GNST of geomaterials to demonstrate the research status of nonlinear strength characteristics of geomaterials under complex stress paths.First,it systematically summarizes the research progress of GNST(classical and empirical criteria).Then,the latest research the authors conducted over the past five years on the GNST is introduced,and a generalized three-dimensional(3D)nonlinear Hoek‒Brown(HB)criterion(NGHB criterion)is proposed for practical applications.This criterion can be degenerated into the existing three modified HB criteria and has a better prediction performance.The strength prediction errors for six rocks and two in-situ rock masses are 2.0724%-3.5091%and 1.0144%-3.2321%,respectively.Finally,the development and outlook of the GNST are expounded,and a new topic about the building strength index of rock mass and determining the strength of in-situ engineering rock mass is proposed.The summarization of the GNST provides theoretical traceability and optimization for constructing in-situ engineering rock mass strength.
基金This work was supported by the National Natural Science Foundation of China(Nos.42161026&41801046)the Natural Science Foundation of Qinghai Province(No.2023-ZJ-934M)the Youth Research Foundation of Qinghai University(No.2022-QGY-5).
文摘This paper aims to comprehensively analyze the influence of the principal stress angle rotation and intermediate principal stress on loess's strength and deformation characteristics. A hollow cylinder torsional shear apparatus was utilized to conduct tests on remolded samples under both normal and frozen conditions to investigate the mechanical properties and deformation behavior of loess under complex stress conditions. The results indicate significant differences in the internal changes of soil particles, unfrozen water, and relative positions in soil samples under normal and frozen conditions, leading to noticeable variations in strength and strain development.In frozen state, loess experiences primarily compressive failure with a slow growth of cracks, while at normal temperature, it predominantly exhibits shear failure. With the increase in the principal stress angle, the deformation patterns of the soil samples under different conditions become essentially consistent, gradually transitioning from compression to extension, accompanied by a reduction in axial strength. The gradual increase in the principal stress axis angle(α) reduces the strength of the generalized shear stress and shear strain curves.Under an increasing α, frozen soil exhibits strain-hardening characteristics, with the maximum shear strength occurring at α = 45°. The intermediate principal stress coefficient(b) also significantly impacts the strength of frozen soil, with an increasing b resulting in a gradual decrease in generalized shear stress strength. This study provides a reference for comprehensively exploring the mechanical properties of soil under traffic load and a reliable theoretical basis for the design and maintenance of roadbeds.
基金Projects(51774326,41807259)supported by the National Natural Science Foundation of ChinaProject(MDPC201917)supported by Mining Disaster Prevention and Control Ministry Key Laboratory at Shandong University of Science and Technology,China。
文摘In this research,a series of biaxial compression and biaxial fatigue tests were conducted to investigate the mechanical behaviors of marble and sandstone under biaxial confinements.Experimental results demonstrate that the biaxial compressive strength of rocks under biaxial compression increases firstly,and subsequently decreases with increase of the intermediate principal stress.The fatigue failure characteristics of the rocks in biaxial fatigue tests are functions of the peak value of fatigue loads,the intermediate principal stress and the rock lithology.With the increase of the peak values of fatigue loads,the fatigue lives of rocks decrease.The intermediate principal stress strengthens the resistance ability of rocks to fatigue loads except considering the strength increasing under biaxial confinements.The fatigue lives of rocks increase with the increase of the intermediate principal stress under the same ratio of the fatigue load and their biaxial compressive strength.The acoustic emission(AE)and fragments studies showed that the sandstone has higher ability to resist the fatigue loads compared to the marble,and the marble generated a greater number of smaller fragments after fatigue failure compared to the sandstone.So,it can be inferred that the rock breaking efficiency and rock burst is higher or severer induced by fatigue loading than that induced by monotonous quasi-static loading,especially for hard rocks.
基金This work was supported by the Key Research and Development Programof Shaanxi,China(Grant Nos.2019SF-231and 2020SF-394)the Natural Science Foundation of China(Grant No.41630639).
文摘The Hoek-Brown(HB)strength criterion has been applied widely in a large number of projects around the world.However,this criterion ignores the intermediate principal stress s2.Many evidences have demonstrated that the rock strength is dependent on s2.Thus it is necessary to extend the HB criterion into a three-dimensional(3D)form.In this study,the effect of s2 on the strength of rocks is identified by reviewing the true triaxial tests of various rock types reported in the literature.A simple 3D strength criterion is developed.The modified criterion is verified by the true triaxial tests of 13 rock types.The results indicate that the modified criterion can achieve a good fit to most of rock types.It can represent a series of criteria as b varies.For comparisons,several existing 3D versions of the HB criterion are selected to predict the strengths of these rock types.It is indicated that the proposed criterion works better than other criteria.A substantial relationship between parameter b and the unconfined compressive strength is established,which guarantees that the proposed criterion can still work well even in the absence of true triaxial test data.
