Strainburst process of marble in tunnel-excavation-induced stress path considering intermediate principal stress

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.

Experimental study on failure characteristics of single-sided unloading rock under different intermediate principal stress conditions

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.

Investigation of the influence of intermediate principal stress on the dynamic responses of rocks subjected to true triaxial stress state

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.

Failure criterion for soft rocks considering 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).

Critical embedment depth of a rigid retaining wall against overturning in unsaturated soils considering intermediate principal stress and strength nonlinearity

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.

Effects of intermediate stress on deep rock strainbursts under true triaxial stresses

The effect of intermediate stress(in situ tunnel axial)on a strainburst is studied with a threedimensional(3D)bonded block distinct element method(DEM).A series of simulations of strainbursts under true triaxial in situ stress conditions(i.e.high tangential stress,moderate intermediate stress and low radial stress)of near-boundary rock masses are performed.Compared with the experimental results,the DEM model is able to capture the stress-strain response,failure pattern and energy balance of strainbursts.The fracturing processes of strainbursts are also numerically reproduced.Numerical results show that,as the intermediate stress increases:(1)The peak strain of strainbursts increases,the yield stress increases,the rock strength increases linearly,and the ratio of yield stress to rock strength decreases,indicating that the precursory information on strainbursts is enhanced;(2)Tensile and shear cracks increase significantly,and slabbing and bending of rock plates are more pronounced;and(3)The stored elastic strain energy and dissipated energy increase linearly,whereas the kinetic energy of the ejected rock fragments increases approximately exponentially,implying an increase in strainburst intensity.By comparing the experimental and numerical results,the effect of intermediate stress on the rock strength of strainbursts is discussed in order to address three key issues.Then,the Mogi criterion is applied to construct new strength criteria for strainbursts by converting the one-face free true triaxial stress state of a strainburst to its equivalent true triaxial stress state.In summary,the effect of intermediate stress on strainbursts is a double-edged sword that can enhance the rock strength and the precursory information of a strainburst,but also increase its intensity.

EFFECT OF HEAT TREATMENT ON INTERMEDIATE TEMPERATURE STRESS RUPTURE PROPERTIES OF ALLOY K403

The standard heat treatment of cast nickel base superalloy K403 is the solid solution treatment of 1210℃/4h, air cooling. It is very difficult to meet the requirements of Aviation Standard HB5155, in which the stress rupture life at 750℃ and 645MPa is longer than 50h. The results showed that the intermediate temperature stress rupture properties impaired by treatment of 1210℃/4h were due to precipitation of too small γ′ phase(<0.2μm) in grains and absence of the secondary carbides at grain boundaries. Microstructure containing the intergranular M6C carbides with envelope of γ′ and the residual coarse γ′ was obtained by means of 1180℃/4h treatment, therefore the stress rupture life was obviously increased to meet the demand of HB5155. The effect of γ′ size was also discussed from the view point of deformation mechanism in this paper.

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.

Influence of intermediate principal stress on failure mechanism of hard rock with a pre-existing circular opening

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).

Effect of intermediate principal stress on strength of soft rock under complex stress states

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.

Study on intermediate focus earthquake belt in Hindukush-Pamirs

According to the feature of Hindukush-Pamirs intermediate focus earthquake belt with a S-shaped pattern of dip direction reversion by using the data of earthquake catalogues obtained by seismic networks in Xinjiang and Mid-Asia area of the former Soviet Union, by means of focal mechanism solution and tectonic stress analysis, it is considered that the intermediate focus earthquake belt is possibly formed by the compression rupture which is caused by the collision between Indian and European Plates in the lithosphere of the upper mantle. Under the action of torsion moment, the continuous torsional break of reverse part of the earthquake belt might be the reason why the intermediate focus strong earthquakes occur repeatedly in the same place. In this paper, the boundary line between the intermediate focus earthquake belt and the shallow focus earthquake region of the western part of south Tianshan is also defined from the angle of seismicity division.

Influence of orientation of the intermediate principal stress on fracture reactivation in granite

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.

考虑中主应力影响的朗肯主动土压力研究

针对朗肯理论不能计算墙背倾斜、填土表面倾斜情况下的土压力,以及M-C准则未能考虑中主应力的问题,基于统一强度理论及朗肯理论,首先推导了墙背倾斜、填土表面倾斜情况下考虑中主应力的主动土压力计算公式;接着采用数值模拟对推得的理论公式进行验证;最后对中主应力系数、墙背倾角及填土倾角3类土压力影响因素进行分析。结果表明:理论解与模拟解在大部分区间内拟合较好,通过数值模拟验证了公式的合理性;随着中主应力系数的增大,主动土压力值呈非线性减小;墙背倾角一定时,随着填土面倾角增大,主动土压力呈非线性增大;填土表面倾角一定时,随着墙背倾角增大,主动土压力呈非线性增大。

Factor of safety analysis for mine pillar considering the influence of the intermediate principal stress component

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.

Unified semi-analytical solution for elastic-plastic stress of deep circular hydraulic tunnel with support yielding

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.

Definition of failure criterion for frozen soil under directional shear-stress path

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.

Undrained response of reconstituted clay to cyclic pure principal stress rotation

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.

A STRESS VECTOR-BASED CONSTITUTIVE MODEL FOR COHESIONLESS SOIL (Ⅰ)-THEORY

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.

Stress fractures in uncommon location:Six case reports and review of the literature

BACKGROUND Individuals’interest in sports activities has been increasing,contributing to more stress fracture occurrences in uncommon locations on the skeleton.In this study,several cases of stress fractures in atypical locations are presented,and the possibility of combining diagnostic methods to make accurate and quick diagnoses is explored.Additionally,different causes of stress fractures,as well as various modalities of treatment,are highlighted.Other potential factors of stress fractures were identified by a literature review.CASE SUMMARY Six cases of stress fractures in the calcaneus,intermediate cuneiform bone,sacrum,tibia(bilateral),navicular bone and femoral neck are presented,with different types of diagnostic imaging and treatments.All of the cases were associated with an aspect of mobility because all of the patients were physically active in various sport disciplines.CONCLUSION The type of therapeutic procedure selected should depend on the specific clinical case,i.e.,the patient’s condition and level of physical activity.

Stress analysis of single joint rock mass under triaxial compression

Based on the fundamental principle of rock mechanics, the stresses of single joint rock mass under three-dimensional compression were analyzed. The effect of the in-termediate principle stress on the strength of single joint rock mass were discussed in par-ticular. It is found that the strength of single joint rock are affected by the intermediate principal stress, which may be the main factor in some conditions.