3D DEM simulation of hard rock fracture in deep tunnel excavation induced by changes in principal stress magnitude and orientation

To achieve the loading of the stress path of hard rock,the spherical discrete element model(DEM)and the new flexible membrane technology were utilized to realize the transient loading of three principal stresses with arbitrary magnitudes and orientations.Furthermore,based on the deep tunnel of China Jinping Underground Laboratory II(CJPL-II),the deformation and fracture evolution characteristics of deep hard rock induced by excavation stress path were analyzed,and the mechanisms of transient loading-unloading and stress rotation-induced fractures were revealed from a mesoscopic perspective.The results indicated that the stressestrain curve exhibits different trends and degrees of sudden changes when subjected to transient changes in principal stress,accompanied by sudden changes in strain rate.Stress rotation induces spatially directional deformation,resulting in fractures of different degrees and orientations,and increasing the degree of deformation anisotropy.The correlation between the degree of induced fracture and the unloading magnitude of minimum principal stress,as well as its initial level is significant and positive.The process of mechanical response during transient unloading exhibits clear nonlinearity and directivity.After transient unloading,both the minimum principal stress and minimum principal strain rate decrease sharply and then tend to stabilize.This occurs from the edge to the interior and from the direction of the minimum principal stress to the direction of the maximum principal stress on theε1-ε3 plane.Transient unloading will induce a tensile stress wave.The ability to induce fractures due to changes in principal stress magnitude,orientation and rotation paths gradually increases.The analysis indicates a positive correlation between the abrupt change amplitude of strain rate and the maximum unloading magnitude,which is determined by the magnitude and rotation of principal stress.A high tensile strain rate is more likely to induce fractures under low minimum principal stress.

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.

Implications for identification of principal stress directions from acoustic emission characteristics of granite under biaxial compression experiments

The rock fracture characteristics and principal stress directions are crucial for prevention of geological disasters.In this study,we carried out biaxial compression tests on cubic granite samples of 100 mm in side length with different intermediate principal stress gradients in combination with acoustic emission(AE)technique.Results show that the fracture characteristics of granite samples change from‘sudden and aggregated’to‘continuous and dispersed’with the increase of the intermediate principal stress.The effect of increasing intermediate principal stress on AE amplitude is not significant,but it increases the proportions of high-frequency AE signals and shear cracks,which in turn increases the possibility of unstable rock failure.The difference of stress in different directions causes the anisotropy of rock fracture and thus leads to the obvious anisotropic characteristics of wave velocity variations.The anisotropy of wave velocity variations with stress difference is probable to identify the principal stress directions.The AE characteristics and the anisotropy of wave velocity variations of granite under two-dimensional stress are not only beneficial complements for rock fracture characteristic and principal stress direction identification,but also can provide a new analysis method for stability monitoring in practical rock engineering.

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.

Implications for rock instability precursors and principal stress direction from rock acoustic experiments

The characteristics of rock instability precursors and the principal stress direction are very crucial for the prevention of geological disasters.This study investigated the qualitative relationship between rock instability precursors and principal stress direction through wave velocity in rock acoustic emission(AE)experiments.Results show that the wave velocity variation exhibits obvious anisotropic characteristics in 0%–20%and 60%–90%of peak strength due to the differences of stress-induced microcrack types.The amplitude of wave velocity variation is related to the azimuth and position of wave propagation path,which indicates that the principal stress direction can be identified by the anisotropic characteristics of wave velocity variations.Furthermore,the experiments also demonstrate that the AE event rate and wave velocity show quiet and stable variations in the elastic stage of rock samples,while they present a trend of active and unstable variations in the plastic stage.It implies that both the AE event rate and wave velocity are effective monitoring parameters for rock instability.The anisotropic characteristics of the wave velocity variation and AE event rate are beneficial complements for identifying the rock instability precursors and determining the principal stress direction,which provides a new analysis method for stability monitoring in practical rock engineering.

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).

Influence of principal stress rotation of unequal tensile and compressive stress amplitudes on characteristics of soft clay

Soil behavior can reflect the characteristics of principal stress rotation under dynamic wave and traffic loads. Unequal amplitudes of tensile and compressive stresses applied to soils have complex effects on foundation soils in comparison with the pure principal stress rotation path. A series of undrained cyclic hollow torsional shear tests were performed on typical remolded soft clay from the Hexi area of Nanjing, China. The main control parameters were the tensile and compressive stress amplitude ratio(α) and the cyclic dynamic stress ratio(η). It was found that the critical η tended to remain constant at 0.13, when the value of the compressive stress amplitude was higher than the tensile stress amplitude. However, the influence of the tensile stress was limited by the dynamic stress level when α= 1.For obvious structural change in the soil, the corresponding numbers of cyclic vibration cycles were found to be independent of α at low stress levels and were only related to η. Finally, a new method for evaluating the failure of remolded soft clay was presented. It considers the influence of the tensile and compressive stresses which caused by complex stress paths of the principal stress rotation. This criterion can distinguish stable, critical, and destructive states based on the pore-water-pressure-strain coupling curve while also providing a range of failure strain and vibration cycles. These results provide the theoretical support for systematic studies of principal stress rotation using constitutive models.

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.

Dynamic strength characteristics and failure criteria of anisotropically consolidated silt under principal stress rotation

In order to identify the critical properties and failure criteria of in-situ silt under vehicle or wave loading, anisotropically consolidated silt under undrained cyclic principal stress rotation was studied with hollow cylinder dynamic tests. The results show that for the slightly anisotropically consolidated samples with consolidation ratios no larger than 1.5, the structure collapses and the deviator strain and pore pressure increase sharply to fail after collapse. For the highly anisotropically consolidated samples with consolidation ratios larger than 1.5, the strain increases steadily to high values, which shows characteristics of ductile failure. 4% is suggested to be the threshold value of deviator stain to determine the occurrence of collapse. The normalized relationship between pore pressure and deviator strain can be correlated by a power fimction for all the anisotropically consolidated samples. Based on it, for the highly anisotropically consolidated samples, the appearance of inflection point on the power function curve is suggested to sign the failure. It can be predicted through the convex pore pressure at this point, whose ratio to the ultimate pore pressure is around linear with the consolidation ratio in spite of the dynamic shear stress level. And the corresponding deviator strain is between 3% and 6%. The strain failure criterion can also be adopted, but the limited value of stain should be determined according to engineering practice. As for the slightly anisotropically consolidated samples, the turning points appear after collapse. So, the failure is suggested to be defined with the occurrence of collapse and the collapse pore pressure can be predicted with the ultimate pore pressure and consolidation ratio.

Evaluation of earthquake impact on magnitude of the minimum principal stress along a shotcrete lined pressure tunnel in Nepal

In situ stress condition in rock mass is influenced by both tectonic activity and geological environment such as faulting and shearing in the rock mass.This influence is of significance in the Himalayan region,where the tectonic movement is active,resulting in periodic dynamic earthquakes.Each large-scale earthquake causes both accumulation and sudden release of strain energy,instigating changes in the in situ stress environment in the rock mass.This paper first highlights the importance of the magnitude of the minimum principal stress in the design of unlined or shotcrete lined pressure tunnel as water conveyance system used for hydropower schemes.Then we evaluated the influence of local shear faults on the magnitude of the minimum principal stress along the shotcrete lined high pressure tunnel of Upper Tamakoshi Hydroelectric Project(UTHP)in Nepal.A detailed assessment of the in situ stress state is carried out using both measured data and three-dimensional(3D)numerical analyses with FLAC3D.Finally,analysis is carried out on the possible changes in the magnitude of the minimum principal stress in the rock mass caused by seismic movement(dynamic loading).A permanent change in the stress state at and nearby the area of shear zones along the tunnel alignment is found to be an eminent process.

Influence of maximum principal stress direction on the failure process and characteristics of D-shaped tunnels

To investigate the failure process and characteristics of D-shaped tunnels under different maximum principal stress directions θ, true-triaxial tests were conducted on cubic sandstone samples with a through D-shaped hole. The test results show that the failure process can be divided into 4 periods:calm, buckling deformation, gradual buckling and exfoliation of rock fragment, and formation of a Vshaped notch. With an increase in θ from 0° to 90°, the size of the rock fragments first decreases and then increases, whereas the fractal dimension of the rock fragments first increases and then decreases. Meanwhile, the failure position at the left side shifts from the sidewall to the corner and finally to the floor, whereas the failure position at the right side moves from the sidewall to the spandrel and finally to the roof, which is consistent with the failure position in underground engineering. In addition, the initial vertical failure stress first decreases and then increases. By comparing the results,the failure severities at different maximum principal stress directions can be ranked from high to low in the following order: 90°>60°>30°>45°>0°.

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.

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.

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.

Three-dimensional stress variation characteristics in deep hard rock of CJPL-Ⅱ project based on in-situ monitoring

In deep hard rock excavation, stress plays a pivotal role in inducing stress-controlled failure. While the impact of excavation-induced stress disturbance on rock failure and tunnel stability has undergone comprehensive examination through laboratory tests and numerical simulations, its validation through insitu stress tests remains unexplored. This study analyzes the three-dimensional stress changes in the surrounding rock at various depths, monitored during the excavation of B2 Lab in China Jinping Underground Laboratory Phase Ⅱ(CJPL-Ⅱ). The investigation delves into the three-dimensional stress variation characteristics in deep hard rock, encompassing stress components and principal stress. The results indicate changes in both the magnitude and direction of the principal stress during tunnel excavation. To quantitatively describe the degree of stress disturbance, a series of stress evaluation indexes are established based on the distances between stress tensors, including the stress disturbance index(SDI), the principal stress magnitude disturbance index(SDIm), and the principal stress direction disturbance index(SDId). The SDI indicates the greatest stress disturbance in the surrounding rock is 4.5 m from the tunnel wall in B2 Lab. SDIm shows that the principal stress magnitude disturbance peaks at2.5 m from the tunnel wall. SDId reveals that the largest change in principal stress direction does not necessarily occur near the tunnel wall but at a specific depth from it. The established relationship between SDI and the depth of the excavation damaged zone(EDZ) can serve as a criterion for determining the depth of the EDZ in deep hard rock engineering. Additionally, it provides a reference for future construction and support considerations.

Granular behaviour under bi-directional shear with constant vertical stress and constant volume

This paper aims to investigate the role of bi-directional shear in the mechanical behaviour of granular materials and macro-micro relations by conducting experiments and discrete element method(DEM)modelling.The bi-directional shear consists of a static shear consolidation and subsequent shear under constant vertical stress and constant volume conditions.A side wall node loading method is used to exert bi-directional shear of various angles.The results show that bi-directional shear can significantly influence the mechanical behaviour of granular materials.However,the relationship between bidirectional shear and mechanical responses relies on loading conditions,i.e.constant vertical stress or constant volume conditions.The stress states induced by static shear consolidation are affected by loading angles,which are enlarged by subsequent shear,consistent with the relationship between bidirectional shear and principal stresses.It provides evidence for the dissipation of stresses accompanying static liquefaction of granular materials.The presence of bi-directional principal stress rotation(PSR)is demonstrated,which evidences why the bi-directional shear of loading angles with components in two directions results in faster dissipations of stresses with static liquefaction.Contant volume shearing leads to cross-anisotropic stress and fabric at micro-contacts,but constant vertical stress shearing leads to complete anisotropic stress and fabric at micro-contacts.It explains the differentiating relationship between stress-strain responses and fabric anisotropy under these two conditions.Micromechanical signatures such as the slip state of micro-contacts and coordination number are also examined,providing further insights into understanding granular behaviour under bi-directional shear.

Dip2a regulates stress susceptibility in the basolateral amygdala

Dysregulation of neurotransmitter metabolism in the central nervous system contributes to mood disorders such as depression, anxiety, and post–traumatic stress disorder. Monoamines and amino acids are important types of neurotransmitters. Our previous results have shown that disco-interacting protein 2 homolog A(Dip2a) knockout mice exhibit brain development disorders and abnormal amino acid metabolism in serum. This suggests that DIP2A is involved in the metabolism of amino acid–associated neurotransmitters. Therefore, we performed targeted neurotransmitter metabolomics analysis and found that Dip2a deficiency caused abnormal metabolism of tryptophan and thyroxine in the basolateral amygdala and medial prefrontal cortex. In addition, acute restraint stress induced a decrease in 5-hydroxytryptamine in the basolateral amygdala. Additionally, Dip2a was abundantly expressed in excitatory neurons of the basolateral amygdala, and deletion of Dip2a in these neurons resulted in hopelessness-like behavior in the tail suspension test. Altogether, these findings demonstrate that DIP2A in the basolateral amygdala may be involved in the regulation of stress susceptibility. This provides critical evidence implicating a role of DIP2A in affective disorders.

Intact soft clay’s critical response to dynamic stress paths on different combinations of principal stress orientation

Comprehensive tests on Hangzhou intact soft clay were performed, which were used to obtain the soils' critical response to undrained dynamic stress paths under different combinations of principal stress orientation. The different combinations included cyclic principal stress rotation (CPSR for short), cyclic shear with abrupt change of principal stress orientation (CAPSO for short) and cyclic shear with fixed principal stress orientation (CFPSO for short). On one side, under all these stress paths, samples have obvious strain inflection points and shear bands, and the excess pore water pressure is far from the level of initial effective confining pressure at failure. Stress paths of major principal stress orientation (α) alternating from negative and positive have quite different influence on soil's properties with those in which α is kept negative or positive. On the other side, due to the soil's strongly initial anisotropy, samples under double-amplitudes CPSR and CAPSO (or single-amplitude CPSR and CFPSO) have similar properties on dynamic shear strength and pore water pressure development tendency when α is kept within ±45°, while have quite different properties when α oversteps ±45°.