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.

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.

Stress Path Analysis of Deep-Sea Sediments Under the Compression-Shear Coupling Load of Crawler Collectors

The mechanical properties of deep-sea sediments during the driving process of crawler collectors are essential factors in the design of mining systems.In this study,a crawler load is divided into a normal compression load and a horizontal shear load.Then,the internal stress state of sedimentary soil is examined through a theoretical calculation and finite element numerical simulation.Finally,the driving of crawlers is simulated by changing the relative spatial position between the load and stress unit,obtaining the stress path of the soil unit.Based on the calculation results,the effect of the horizontal shear load on the soil stress response is analyzed at different depths,and the spatial variation law of the soil stress path is examined.The results demonstrate that the horizontal shear load has a significant effect on the rotation of the principal stress,and the reverse rotation of the principal stress axis becomes obvious with the increase in the burial depth.The stress path curve of the soil is different at various depths.The spatial variation rule of the stress path of the shallow soil is complex,whereas the stress path curve of the deep soil tends to shrink as the depth increases.The stress path of the corresponding depth should be selected according to the actual research purpose and applied to the laboratory test.

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.

Modern tectonic stress field in the Chinese mainland inverted from focal mechanism solutions

The inversion of modern tectonic stress field in China is made by regions on the basis of focal mechanism data inthe period of 1920-1996. Results of the inversion show that the maximum principal compressive stress σ1 axisstrikes nearly north-south direction in the Tibet Plateau and western Chin4 east-west direction in North China Incentral China, its strikes show a radiate pattern, i.e., north-north east in north part, east-west in central part andnorth-north west in south part. The σ1 axes are often perpendicular to the minimum principal stress σ3 axes, exceptwestern China where the σ1 axes are oblique to the σ3 axes with an acute angle. R is defined by (σ2-σ1)/(σ3-σ1),has the higher values (0.60-0.90) in north part of central China and quickly changes into the lower values(0. 10-0.30) in the Tibet Plateau. Both of the observed and inverted fault planes have strikes varying with locations.Combining stress directions and R value, the stress configuration is divided into 7 groups. Most of the groups showstrike-slip faulting with intermediate R values, which occupies North China and the eastern part of China as well asinner Tibet Plateau. A few of them show reverse faulting with higher R values within western pod of China and thenorth edge of the Tibet Plateau. Normal faulting occurred on the south edge of the Tibet Plateau with smaller Rval nes.

Determination of stress intensity factor with direct stress approach using finite element analysis

In this article, a direct stress approach based on finite element analysis to determine the stress intensity factor is improved. Firstly, by comparing the rigorous solution against the asymptotic solution for a problem of an infinite plate embedded a central crack, we found that the stresses in a restrictive interval near the crack tip given by the rigorous solution can be used to determine the stress intensity factor, which is nearly equal to the stress intensity factor given by the asymptotic solution. Secondly, the crack problem is solved numerically by the finite element method. Depending on the modeling capability of the software, we designed an adaptive mesh model to simulate the stress singularity. Thus, the stress result in an appropriate interval near the crack tip is fairly approximated to the rigorous solution of the corresponding crack problem. Therefore, the stress intensity factor may be calculated from the stress distribution in the appropriate interval, with a high accuracy.

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°.

Cyclic behavior of reinforced sand under principal stress rotation

Although the cyclic rotation of the principal stress direction is important,its effect on the deformation behavior and dynamic properties of the reinforced soil has not been reported to date.Tests carried out on large-scale hollow cylinder samples reveal that the cyclic rotation of the principal stress direction results in significant variations of strain components(ε,ε,εand γ) with periodic characteristics despite the deviatoric stress being constant during tests.This oscillation can be related to the corresponding variations in the stress components and the anisotropic fabric that rotate continuously along the principal stress direction.Sand under rotation appears to develop a plastic strain.Similar trends are observed for reinforced sand,but the shear interaction,the interlocking between particles and reinforcement layer,and the confinement result in significant reductions in the induced strains and associated irrecoverable plastic strains.Most of the strains occur in the first cycle,and as the number of cycles increases,the presence of strains becomes very small,which is almost insignificant.This indicates that the soil has reached anisotropic critical state(ACS),where a stable structure is formed after continuous orientation,realignment and rearrangement of the particles accompanied with increasing cyclic rotation.Rotation in the range of 60°-135° produces more induced strains even in the presence of the reinforcement,when compared with other ranges.This relates to the extension mode of the test in this range in which σ>σand to the relative approach between the mobilized plane and the weakest horizontal plane.Reinforcement results in an increase in shear modulus while it appears to have no effect on the damping ratio.Continuous cycles of rotation result in an increase in shear modulus and lower damping ratio due to the densification that causes a decrease in shear strain and less dissipation of energy.

Pore Water Pressure Buildup Under Cyclic Rotation of Principal Stress and Stability Evaluation of Seabed Deposit

The cyclic rotation of principal stress direction with a constant amplitude is the characteristics of cyclic stress in seabed deposit induced by travelling waves. Presented in the paper are the results obtained from tests simulating the cyclic stress characteristics, with emphasis laid on the buildup of pore water pressure in soil samples. Regression analysis of test data shows that the pore water pressure can be expressed as the function of the number of cycles of cyclic loading, or as the function of generalized shear strain. Using the results thus obtained, the possibility of failure of seabed deposit under cyclic loading induced by travelling waves can be evaluated. The comparison with the results of conventional cyclic torsional shear tests shows that neglect of the effect of the cyclic rotation of the principal stress direction will result in considerable over-estimation of the stability of seabed deposit.

Fracture characteristics of the 1997 Jiashi,Xinjiang, China, earthquake swarm inferred from source spectra

Broadband P and S waves source spectra of 12 M_s≥5.0 earthquakes of the 1997 Jiashi, Xinjiang, China. earthquake swarm recorded at 13 GDSN stations have been analyzed. Rupture size and static stress drop of these earthquakes have been estimated through measuring the corner frequency of the source spectra. Direction of rupture propaga- tion of the earthquake faulting has also been inferred from the azimuthal variation of the comer frequency. The main results are as follows: ① The rupture size of M_s≥6.0 strong earthquakes is in the range of 10~20 km, while that of Ms_=5.0~5.5 earthquakes is 6~10 km. ② The static stress drop of the swarm earthquakes is rather low, being of the order of 0.1 MPa. This implies that the deformation release rate in the source region may be low. ③ Stress drop of the earthquakes appears to be proportional to their seismic moment, and also to be dependent on their focal mechanism. The stress drop of normal faulting earthquakes is usually lower than that of strike-slip type earth quakes. ④ For each M_s≥6.0 earthquake there exists an apparent azimuthal variation of the comer frequencies. Azimuthally variation pattern of comer frequencies of different earthquakes shows that the source rupture pattern of the Jiashi earthquake swarm is complex and no uniform rupture expanding direction exists.

Estimation of the horizontal in-situ stress magnitude and azimuth using previous drilling data

Oil exploration and production,well stability,sand production,geothermal drilling,waste-water or CO_(2) sequestration,geohazards assessment,and EOR processes such as hydraulic fracturing,require adequate information about in-situ stresses.There are several methods for analyzing the magnitude and direction of in-situ stresses.The evaluation of tensile fractures and shear fractures in vertical oil and gas wellbores using image logs is one of these methods.Furthermore,when image logs are run in boreholes,they can be extremely costly and possibly stop the drilling.The data for this study were gathered from seven directional wells drilled into a strike-slip fault reservoir in southern Iran.Vertical stress,minimum horizontal stress,pore pressure,Poisson's ratio of formations,and 233 mud loss reporting points make up the entire data.This is the first time maximum horizontal stress direction has been calculated without referring to image log data.In addition,the points of lost circulation were categorized into natural and induced fracture.The results revealed that,the maximum horizontal stress direction of the reservoir was calculated at 65northeast-southwest.The error rate is roughly 10when comparing the results of this investigation to those obtained from the image log.The maximum horizontal stress direction is calculated precisely.In terms of tensile fracture pressure,the in-situ stress ratio identifies the safest as well as the most critical inclination and azimuth for each well.

Determination of key soil characteristic parameters using angle of repose and direct shear stress test

Discrete element modelling(DEM)is a numerical method for examining the dynamic behavior of granular media.In order to build an accurate simulation model and provide more comprehensive soil characteristic parameters for the design and optimization of various soil contact machinery,in this paper,the discrete element simulation method(EDEM)combined with experimental approach is used to investigate the soil contact characteristic parameters in East Asia.In this study,Hertze-Mindlin(no slip)was used as a particle contact model by taking particle contact parameters and soil JKR(Johnson-Kendall-Roberts)surface energy as determinants,and repose angle,internal friction angle,and cohesive force as evaluation indexes.The method of Plackett-Burman,Stepest ascent,and Box-Behnken were used to gradually reduce the range of parameters needed for simulation until the most accurate value was determined.The results show that the restitution coefficient,static friction coefficient,and rolling friction coefficient between soil particles have significant effects on the DEM model,and their value of them are 0.596,0.725,and 0.16,respectively.Based on these parameters used for the repose angle test and direct shear stress test,the value of repose angle is 31.97°,the internal friction angle is 27.61°,and the cohesive force is 33.06 kPa.The relative errors with the actual measured values are 9.54%,1.87%,and 2.31%,respectively.In order to further test whether the simulation parameters of soil obtained by repose angle test and direct shear stress test are consistent with the real soil,comparison test between field test and discrete element simulation was used.The results show that the error in height of ridge between the simulated soil and the actual soil is 4.06%,which is within the acceptable range.It also indicates that the calibrated and optimized soil simulation model can accurately represent the real soil.The research provides theoretical basis and technical support for the study of soil contact parts by using the discrete element method,combined with repose angle test and direct shear stress test.

Three-Dimensional Stress and Stress Intensity for Tensioned Flat Plates with Edge Cracks

The stress in the thickness direction is an important factor influencing the fracture behavior of structural members. A stress σy tensioned flat plate with edge cracks is widely used as an analysis model. The stresses σx and σy for the plate model can be acquired from Neuber＇s solution. However, the solution is applicable only for a perfect plane stress or plane strain state. As a consequence of the thickness of the plate a three-dimensional （3-D） stress state will arise near the crack tip, resulting in a variation of the distribution of σx and σy stresses. A full analysis for the 3-D stress fields for a tensioned flat plate with edge cracks has been therefore carried out. The results show that the 3-D stress field near the crack tip is mainly determined by two factors： the thickness of the plate and the curvature radius at the crack tip. A further analysis has been carried out for the stress intensity near the crack tip. In this paper we give some equations matching to the 3-D stress and stress intensity, which describe precisely the stress state near the crack tip, and which can be applied effectively in engineering analysis.

Orbiting Optimization Model for Tracking Voltage Security Region Boundary in Bulk Power Grids

A voltage security region(VSR)is a powerful tool for monitoring the voltage security in bulk power grids with high penetration of renewables.It can prevent cascading failures in wind power integration areas caused by serious over or low voltage problems.The bottlenecks of a VSR for practical applications are computational efficiency and accuracy.To bridge these gaps,a general optimization model for tracking a voltage security region boundary(VSRB)in bulk power grids is developed in this paper in accordance with the topological characteristics of the VSRB.First,the initial VSRB point on the VSRB is examined with the traditional OPF by using the base case parameters as initial values.Then,the rest of the VSRB points on the VSRB are tracked one after another,with the proposed optimization model,by using the parameters of the tracked VSRB point as the initial value to explore its adjacent VSRB point.The proposed approach can significantly improve the computational efficiency of the VSRB tracking over the existing algorithms,and case studies,in the WECC 9-bus and the Polish 2736-bus test systems,demonstrate the high accuracy and efficiency of the proposed approach on exploring the VSRB.

Combination of direct-forcing fictitious domain method and sharp interface method for dielectrophoresis of particles

In this paper, we combine the direct-forcing fictitious domain （DF/FD） method and the sharp interface method to resolve the problem of particle dielectrophoresis in two dimensions. The flow field and the motion of particles are solved with the DF/FD method, the electric field is solved with the sharp inter- face method, and the electrostatic force on the particles is computed using the Maxwell stress tensor method. The proposed method is validated via three problems： effective conductivity of particle compos- ite between two planar plates, cell trapping in a channel, and motion of particles due to both conventional and traveling wave dielectrophoretic forces.