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.

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.

Reduction of Residual Stress in Low Alloy Steel with Magnetic Treatment in Different Directions

The behavior that different magnetic treatment directions induce various amounts of welding residual stress reductions in low alloy steel was studied. Reductions of 26%-28% in the longitudinal stress σ x were obtained when low frequency alternating magnetic treatment was applied perpendicularly to the welding bead, whereas reductions of 20%-21% in σ x were measured by using the same treatment parameters except that the field direction was applied parallel to the bead. It is proposed that different extent of stress reductions caused by the above two treatment directions is attributed primarily to the alteration of the energy absorbed by domains from the external magnetic field, which part of energy can arouse plastic deformation in microstructures by the motion of domain walls.

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.

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.

3D digital-image correlation insight into generalized relaxation behavior of sandstone under stress and pore pressure coupling

The occurrence of geological hazards and the instability of geotechnical engineering structures are closely related to the time-dependent behavior of rock.However,the idealization boundary condition for constant stress in creep or constant strain in relaxation is not usually attained in natural geological systems.Therefore,generalized relaxation tests that explore the simultaneous changes of stress and strain with time under different stress levels with constant pore-water pressure are conducted in this study.The results show that in area I,area II,and area III,the stress and strain both change synchronously with time and show similar evolutionary laws as the strain-time curve for creep or the stress-time curve for relaxation.When the applied stress level surpasses the sci or scd threshold,the variations in stress and strain and their respective rates of change exhibit a significant increase.The radial deformation and its rate of change exhibit greater sensitivity in response to stress levels.The apparent strain deforms homogeneously at the primary stage,and subsequently,gradually localizes due to the microcrack development at the secondary stage.Ultimately,interconnection of the microcracks causes the formation of a shear-localization zone at the tertiary stage.The strain-time responses inside and outside the localization zone are characterized by local strain accumulation and inelastic unloading during the secondary and tertiary stages,respectively.The width of the shear-localization zone is found to range from 4.43 mm to 7.08 mm and increased with a longer time-to-failure.Scanning electron microscopy(SEM)reveals a dominant coalescence of intergranular cracks on the fracture surface,and the degree of physiochemical deterioration caused by water-rock interaction is more severe under a longer lifetime.The brittle sandstone’s time-dependent deformation is essentially controlled by microcrack development during generalized relaxation,and its expectancy-life is determined by its initial microstructural state and the rheological path.

THEORETICAL STUDY ON ALEKSANDROWSKI′S METHOD OF THE GRAPHICAL DETERMINATION OF PRINCIPAL STRESS DIRECTIONS FROM THE FAULT SLIP DATA SETS

A graphical method for determining the principal stress distribution of a triaxial stress state from a fault slipstate was proposed by Aleksandrowski in 1985,based on Arthaud′s concept of plane movement,Alek-sandrowski′s method,however,is only valid for the cases in which the values of the stress ratios(C)are consid-ered 1o be ,10,2,1.1 and 1.Whether the method is applicable for general cases of all values of C has not yetbeen confirmed.In this paper.Aleksandrowskis′ method is tested using a numerical derivation from spatialgeometric analysis,and it is revealed that this method is correct for all values of stress ratios other than C=,10,2,1.1,and 1,i.c-【C【.

Effect of boron addition on the microstructure and stress-rupture properties of directionally solidified superalloys

This study is focused on the effect of boron addition, in the range of 0.0007wt% to 0.03wt%, on the microstructure and stress-rupture properties of a directionally solidified superalloy. With increasing boron content in the as-cast alloys, there is an increase in the fraction of the γ′/γ eutectic and block borides precipitate around the γ′/γ eutectic. At a high boron content of 0.03wt%, there is precipitation of lamellar borides. Upon heat treatment, fine block borides tend to precipitate at grain boundaries with increasing boron content. Overall, the rupture life of the directionally solidified superalloy is significantly improved with the addition of nominal content of boron. However, the rupture life decreases when the boron content exceeds 0.03wt%.

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°.

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.

Numerical study of AE and DRA methods in sandstone and granite in orthogonal loading directions

The directional dependency of the acoustic emission （AE） and deformation rate analysis （DRA） methods was analyzed, based on the contact bond model in the two-dimensional particle flow code （PFC2D） in two types of rocks, the coarse-grained sandstone and Aue granite. Each type of rocks had two shapes, the Brazilian disk and a square shape. The mechanical behaviors of the numerical model had already been verified to be in agreement with those of the physical specimens in previous research. Three loading protocols with different loading cycles in two orthogonal directions were specially designed in the numerical tests. The results show that no memory effect is observed in the second loading in the orthogonal direction. However, both the cumulative crack number of the second loading and the differential strain value at the inflection point are influenced by the first loading in the orthogonal direction.

Influence of seismic wave type and incident direction on the dynamic response of tall concrete-faced rockfill dams

Owing to the stochastic behavior of earthquakes and complex crustal structure,wave type and incident direction are uncertain when seismic waves arrive at a structure.In addition,because of the different types of the structures and terrains,the traveling wave effects have different influences on the dynamic response of the structures.For the tall concrete-faced rockfill dam(CFRD),it is not only built in the complex terrain such as river valley,but also its height has reached 300 m level,which puts forward higher requirements for the seismic safety of the anti-seepage system mainly comprising concrete face slabs,especially the accurate location of the weak area in seism.Considering the limitations of the traditional uniform vibration analysis method,we implemented an efficient dynamic interaction analysis between a tall CFRD and its foundation using a non-uniform wave input method with a viscous-spring artificial boundary and equivalent nodal loads.This method was then applied to investigate the dynamic stress distribution on the concrete face slabs for different seismic wave types and incident directions.The results indicate that dam-foundation interactions behave differently at different wave incident angles,and that the traveling wave effect becomes more evident in valley topography.Seismic wave type and incident direction dramatically influenced stress in the face slab,and the extreme stress values and distribution law will vary under oblique wave incidence.The influence of the incident direction on slab stress was particularly apparent when SH-waves arrived from the left bank.Specifically,the extreme stress values in the face slab increased with an increasing incident angle.Interestingly,the locations of the extreme stress values changed mainly along the axis of the dam,and did not exhibit large changes in height.The seismic safety of CFRDs is therefore lower at higher incident angles from an anti-seepage perspective.Therefore,it is necessary to consider both the seismic wave type and incident direction during seismic capacity evaluations of tall CFRDs.

Influence of Solution Temperature on Microstructure and Mechanical Properties of Directionally Solidified Superalloy DZ22

The microstructure changed markedly with increasing solution temperature, i.e eutectic γ' phases and coarse primary γ' phase are redissolved continuously into matrix, which was finished at 1250-1260℃, and more and finer γ' phases are reprecipitated. The grain boundary morphology changed gradually to 'fine line' form. The dendritic segregation of elements decreased. With raising solution temperature the longitudinal stress-rupture life at high and intermediate temperature were enhanced, but the transversal stress-rupture life at intermediate temperature decreased obviously. The incipient melting temperature of DZ22 alloy was measured to be 1230-1240℃ and may be increased by homogenization at 1150℃. In this paper the principle of determining solution temperature of DS alloys was discussed. It was suggested that the solution temperature of alloy DZ22 selected at 1200-1210℃ is appropri- ate.

Design of Measuring Instrument with Whole Direct Method for Bed Shear Stress Under Two-Dimensional Water-Flow Co-action

The present study aims at the design and making of measuring instrument of whole direct method for bed shear stress under two-dimensional water-flow co-action. The instrument combines the traditional strain gauge with a precise pressure gauge, and adopts the method directly measuring the difference between the lateral hydrodynamic pressure and different head pressures on both sides of the force plate. As a result, such an instrument solves a technical puzzle of the past strain gauge, i.e. the difficulty to set apart shear stress and lateral force. Static force test and sink test both prove that the instrument is precise, stable and applicable to the measurement of rough beds with different shear stresses.

Unified analytical stressstrain curve for quasibrittle geomaterial in uniaxial tension, direct shear and uniaxial compression

Considering strain localization in the form of a narrow band initiated just at peak stress, three analytical expressions for stressstrain curves of quasibrittle geomaterial (such as rock and concrete) in uniaxial tension, direct shear and uniaxial compression were presented, respectively. The three derived stressstrain curves were generalized as a unified formula. Beyond the onset of strain localization, a linear strain-softening constitutive relation for localized band was assigned. The size of the band was controlled by internal or characteristic length according to gradient-dependent plasticity. Elastic strain within the entire specimen was assumed to be uniform and decreased with the increase of plastic strain in localized band. Total strain of the specimen was decomposed into elastic and plastic parts. Plastic strain of the specimen was the average value of plastic strains in localized band over the entire specimen. For different heights, the predicted softening branches of the relative stressstrain curves in uniaxial compression are consistent with the previously experimental results for normal concrete specimens. The present expressions for the post-peak stressdeformation curves in uniaxial tension and direct shear agree with the previously numerical results based on gradient-dependent plasticity.

Influence of complicated faults on the differentiation and accumulation of in-situ stress in deep rock mass

High geostress will become a normality in the deep because in-situ stress rises linearly with depth.The geological structure grows immensely intricate as depth increases.Faults,small fractures,and joint fissures are widely developed.The objective of this paper is to identify geostress anomalies at a variety of locations near faults and to demonstrate their accumulation mechanism.Hydrofracturing tests were conducted in seven deep boreholes.We conducted a test at a drilling depth of over one thousand meters to reveal and quantify the influence of faults on in-situ stresses at the hanging wall,footwall,between faults,end of faults,junction of faults,and far-field of faults.The effect of fault sites and characteristics on the direction and magnitude of stresses has been investigated and compared to test boreholes.The accumulation heterogeneity of stresses near faults was illustrated by a three-dimensional numerical simulation,which is utilized to explain the effect of faults on the accumulation and differentiation of in-situ stress.Due to regional tectonics and faulting,the magnitude,direction,and stress regime are all extremely different.The concentration degree of geostress and direction change will vary with the location of faults near faults,but the magnitude and direction of in-situ stress conform to regional tectonic stress at a distance from the faults.The focal mechanism solution has been verified using historical seismic ground motion vectors.The results demonstrate that the degree of stress differentiation varies according to the fault attribute and its position.Changes in stress differentiation and its ratio from strong to weak occur between faults,intersection,footwall,end of faults,and hanging wall;along with the sequence of orientation is the footwall,between faults,the end of faults,intersection,and hanging wall.This work sheds new light on the fault-induced stress accumulation and orientation shift mechanisms across the entire cycle.

CREEP CRACK PROPAGATION IN CONVENTIONAL CAST AND DIRECTIONALLY SOLIDIFIED SUPERALLOY RENE 80

The creep crack propagation in superalloy René80 of two different microstructures,i.e., equiaxed grain structure by conventional casting and columnar grain by directional solidification,was investigated under static load at 1123 K.The creep crack growth rate, da/dt,seems to be correlated with the stress intensity factor,K.The creep crack growth rate in the directionally solidified alloy is lower than that in the conventional cast alloy,owing to the elimination of transverse grain boundaries.The effect of microstructure on creep crack propagation has also been discussed.

Mathematical Modeling of Shear Stress and Direct Shear Test for Compressible Soil: Case of Soil Bordering the Wouri River

This paper focuses on the development of the mathematical model of shear stress by direct shear test for compressible soil of the littoral region, which will be a great tool in the hand of geotechnical engineers. The most common use of a shear test is to determine the shear strength which is the maximum shear stress that a material can withstand before the failure occurs. This parameter is useful in many engineering designs such as foundations, roads and retaining walls. We carried out an experimental laboratory test of ten samples of undisturbed soil taken at different points of the border of Wouri river of Cameroon. The samples were collected at different depths and a direct shear test was conducted. The investigations have been performed under constant vertical stresses and constant sample volume with the aim to determine the frictional angle and the cohesion of the compressible soil which are so important to establish the conditions of buildings stability. Special care was taken to derive loading conditions actually existing in the ground and to duplicate them in the laboratory. Given that the buildings constructed in this area are subjected to settlement, landslide, and punch break or shear failure, the cohesion and the frictional angle are determined through the rupture line after assessed the mean values of the shear stress for the considered ten samples. The bearing capacity of the soil, which is the fundamental soil parameter, was calculated. From the laboratory experimental results, the least squared method was used to derive an approximated mathematical model of the shearing stress. Many optimizations methods were then considered to reach the best adjustment.

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.

Thermal-stress Simulation of Direct-chill Casting of AZ31 Magnesium Alloy Billets

Two-dimensional （2D） transient coupled finite element model was developed to compute the temperature and stress field in cast billets, so as to predict the defects of the I-type billets made from AZ31 magnesium alloy and find the causes and solutions for surface cracks and shrinkages during direct-chill （DC） casting process. Method of equivalent specific heat was used in the heat conduction equation. The boundary and initial conditions used for primary and secondary cooling were elucidated on the basis of the heat transfer during the solidification of the billet. The temperature and the thermal-stress fields were simulated with the thermal-structural coupled module of ANSYS software. The influences of casting parameters on the distributions of temperature and stress were studied, which helped optimize the parameters （at pouring temperature of 680 ℃, casting speed of 2 min/s, heat-transfer coefficient of the second cooling equals to 5 000 W/m^2.℃^-1）. The simulation results of thermal stress and strain fields reveal the formation mechanism of some casting defects, which is favourable for optimizing the casting parameters and obtain high quality billets. Some measures of controlling processes were taken to prevent the defects for direct-chill casting billets.