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.

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.

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.

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.

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).

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).

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.

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.

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 generalized nonlinear three-dimensional Hoek‒Brown failure criterion

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.

Retrospective and prospective review of the generalized nonlinear strength theory for geomaterials

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.

Analysis of strength characteristics of loess before and after freezing using a hollow cylinder torsional shear apparatus

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.

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.

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.

A generalized nonlinear three-dimensional failure criterion based on fracture mechanics

Based on fracture mechanics theory and wing crack model,a three-dimensional strength criterion for hard rock was developed in detail in this paper.Although the basic expression is derived from initiation and propagation of a single crack,it can be extended to microcrack cluster so as to reflect the macroscopic failure characteristic.Besides,it can be derived as HoekeBrown criterion when the intermediate principal stress σ_(2) is equal to the minimum principal stress σ_(3)(Zuo et al.,2015).In addition,the opening direction of the microcrack cluster decreases with the increase of the intermediate principal stress coefficient,which could be described by an empirical function and verified by 10 kinds of hard rocks.Rock strength is influenced by the coupled effect of stress level and the opening direction of the microcrack clusters related to the stress level.As the effects of these two factors on the strength are opposite,the intermediate principal stress effect is induced.

A true triaxial strength criterion for rocks by gene expression programming

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

Experimental investigations on mechanical performance of rocks under fatigue loads and biaxial confinements

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.

A simplified three-dimensional extension of Hoek-Brown strength criterion

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.

Elasto-plastic analysis of the surrounding rock mass in circular tunnel based on the generalized nonlinear unified strength theory

The present paper aims to establish a versatile strength theory suitable for elasto-plastic analysis of underground tunnel surrounding rock. In order to analyze the effects of intermediate principal stress and the rock properties on its deformation and failure of rock mass, the generalized nonlinear unified strength theory and elasto-plastic mechanics are used to deduce analytic solution of the radius and stress of tunnel plastic zone and the periphery displacement of tunnel under uniform ground stress field. The results show that: intermediate principal stress coefficient b has significant effect on the plastic range,the magnitude of stress and surrounding rock pressure. Then, the results are compared with the unified strength criterion solution and Mohr–Coulomb criterion solution, and concluded that the generalized nonlinear unified strength criterion is more applicable to elasto-plastic analysis of underground tunnel surrounding rock.