Effects of axial static stress on stress wave propagation in rock considering porosity compaction and damage evolution

A wave equation of rock under axial static stress is established using the equivalent medium method by modifying the Kelvin-Voigt model.The analytical formulas of longitudinal velocity,space and time attenuation coefficients and response frequency are obtained by solving the equation using the harmonic method.A series of experiments on stress wave propagation through rock under different axial static stresses have been conducted.The proposed models of stress wave propagation are then verified by comparing experimental results with theoretical solutions.Based on the verified theoretical models,the influences of axial static stress on longitudinal velocity,space and time attenuation coefficients and response frequency are investigated by detailed parametric studies.The results show that the proposed theoretical models can be used to effectively investigate the effects of axial static stress on the stress wave propagation in rock.The axial static stress influences stress wave propagation characteristics of porous rock by varying the level of rock porosity and damage.Moreover,the initial porosity,initial elastic modulus of the rock voids and skeleton,viscous coefficient and vibration frequency have significant effects on the P-wave velocity,attenuation characteristics and response frequency of the stress wave in porous rock under axial static stress.

Rock damage and fracturing induced by high static stress and slightly dynamic disturbance with acoustic emission and digital image correlation techniques

A series of coupled static-dynamic loading tests is carried out in this study to understand the effect of slightly dynamic disturbance on the rocks under high static stress.The acoustic emission(AE)and digital image correlation(DIC)techniques are combined to quantitatively characterize the damage and fracturing behaviors of rocks.The effects of three influencing factors,i.e.initial static stress,disturbance amplitude,and disturbance frequency,on the damage and fracturing evolution are analyzed.The experimental results reveal the great differences in AE characteristics and fracturing behaviors of rocks under static loads and coupled static-dynamic loads.Both the Kaiser effect and Felicity effect are observed during the disturbance loading process.The crack initiation,stable and unstable propagation in the highly-stressed rocks can be triggered by cyclic disturbance loads,and more local tensile splitting cracks are found in the rocks subjected to coupled static-dynamic loads.The damage and fracturing evolution of rocks during cyclic disturbances can be divided into two stages,i.e.steady and accelerated stages,and the increase rate and proportion of each stage are greatly affected by these influencing factors.High initial static stress,low disturbance frequency,and high disturbance amplitude are considered to be adverse factors to the stability of the rocks,which would induce a high increase rate of the steady stage and a high proportion of the accelerated stage within the whole disturbance period.Based on the two-stage damage evolution trend,a linear-exponential damage model is employed to predict the instability of the rocks under coupled static-dynamic loads.

Piezoelectric responses of brittle rock mass containing quartz to static stress and exploding stress wave respectively

The electromagnetic emission(EME) induced from the rock containing piezoelectric materials was investigated under both static stress and exploding stress wave in the view of piezoelectric effect. The results show that the intensity of the EME induced from the rock under static stress increases with increasing stress level and loading rate; the relationship between the amplitude of the EME from the rock under different modes of stress wave and elastic parameters and propagation distance was presented. The intensity of the EME relates not only to the strength and elastic moduli of rock masses,but also to the initial damage of the rock. The intensity of EME induced by stress wave reaches the highest at the explosion-center and attenuates with the propagation distance. The intensity of EME increases with increasing the elastic modulus and decreases with increasing initial damage. The results are in good agreement with the experimental results.

Three dimensional finite element analysis of acetabulum loaded by static stress and its biomechanical significance

Objective:To explore the mechanical behavior of acetabulum loaded by static stress and provide the mechanical basis for clinical analysis and judgement on acetabular mechanical distribution and effect of static stress.Methods:By means of computer simulation, acetabular three dimensional model was input into three dimensional finite element analysis software ANSYS7.0. The acetabular mechanical behavior was calculated and the main stress value, stress distribution and acetabular unit displacement in the direction of main stress were analyzed when anterior wall of acetabulum and acetabular crest were loaded by 1 000 N static stress. Results:When acetabular anterior wall loaded by X direction and Z direction composition force, the stress passed along 4 directions: (1)from acetabular anterior wall to pubic symphysis along superior branch of pubis firstly, (2)from acetabular anterior wall to cacroiliac joint along pelvic ring,(3)in the acetabulum,(4)from the suffered point to ischium. When acetabular crest loaded by X direction and Y direction composition force, the stress transmitted to 4 directions: (1)from acetabular crest to ilium firstly, (2)from suffered point to cacroiliac joint along pelvic ring,(3) in the acetabulum ,(4)along the pubic branch,but no stress transmitted to the ischium branch.Conclusion:Analyzing the stress distribution of acetabulum and units displacement when static stress loaded can provide internal fixation point for acetabular fracture treatment and help understand the stress distribution of acetabulum.

Static Stretching Combined with Conscious Slower Breathing May Increase Parasympathetic Activity and Reduce Stress in Adult Women

Background: Women are thought to be more susceptible to stress than men in a stressful society, and reducing stress is crucial for women to maintain their health. Static stretching (SST) is applied in various fields to not only increase muscle flexibility but also reduce stress. Additionally, conscious slower breathing (CSB) predominates parasympathetic activity, causing a relaxing effect. These results indicate that combining SST and CSB may be more useful in reducing stress. However, to the best of our knowledge, the effect of this combination remains unclear. Objective: This study aimed to elucidate the effects of the combination of SST and CSB on autonomic activity and stress in adult women. Methods: Eleven healthy Japanese adult female participants performed SST with nonconscious natural breathing for 20 min. The same participants performed SST in combination with CSB (2 s inspiratory and 4 s expiratory) for 20 min on another day. Salivary cortisol and chromogranin A levels were measured before and after stretching as stress markers of the hypothalamic-pituitary-adrenal axis and sympathetic nervous system. The coefficient of variation of the R-R interval (CVR-R) and high-frequency component (HF), which reflect parasympathetic nerve activity, and heart rate and low-frequency component (LF)/HF ratio, which reflect sympathetic nerve activity, were measured before, during, and after stretching. Results: SST decreased cortisol levels but with no significant changes in chromogranin A, heart rate, CVR-R, HF, or LF/HF ratio. The combination of SST and CSB increased CVR-R and HF levels in addition to decreasing cortisol levels but with no significant changes in chromogranin A, heart rate, or LF/HF levels. Conclusion: These results indicate that the combination of SST and CSB may increase parasympathetic activity and reduce stress. However, future randomized controlled trials with larger sample sizes should support this conclusion.

Static Stress Triggering Effects Related with M_s8.0 Wenchuan Earthquake

In this article, firstly, we calculated and analyzed the patterns of Coulomb stress changes induced by a sequence of strong earthquakes that occurred in Songpan （松藩）, Sichuan （四川） Province in 1973 and 1976, and discovered that the Ms8.0 Wenchuan （汶川） earthquake of 2008 was epicentered in a relevant Coulomb stress triggering zone. This suggests that the Coulomb stress on the middle and southern segments of the Longmenshan （龙门山） fault zone increased after the Songpan sequence of strong earthquakes, and the stress increment might cause the 2008 Wenchuan earthquake having al- ready occurred somewhat ahead of time. Further, we calculated and analyzed Coulomb stress changes coinduced by both the Songpan sequence and the Ms8.0 Wenchuan mainshock. The result shows that the Ms6.4 Qingchuan （青川） earthquake of May 25, 2008 on the northeastern segment of the Longmenshan fault zone was triggered by the Wenchuan mainshock, and that the southwestern segment of the fault zone is also in the stress triggering zone. Besides, the Maoxian （茂县）-Wenchuan fault （i.e., the back-range fault of the Longmenshan fault zone）, which extends parallel to the seismogenic fault of the Wenchuan earthquake, is in a shadow zone of the Coulomb stress changes, and therefore, its potential hazard for producing a strong or large earthquake in the near future could be reduced relatively.

Complete Coulomb stress changes induced by the Ms7.6 earthquake in Lancang-Gengma, Yunnan and triggering of aftershocks by dynamic and static stress

The spatiotemporal evolution patterns of complete Coulomb stress changes caused by 1988 Ms7.6 earthquake in Lancang-Gengma, Yunnan, are calculated and studied. And the triggering problems of Ms7.2 Gengma shock occurring 13 minutes after the main shock and of Ms5.0―6.9 aftershocks within 24 days after the main shock are discussed. The results show that the spatial distribution patterns of complete Coulomb stress changes of the Ms7.6 main shock are strongly asymmetric. The areas of positive dynamic and static Coulomb stress are both coincident well with the strong aftershocks' loca-tions. The Ms7.2 Gengma shock and most of strong aftershocks are subjected to the triggering effect of dynamic and static Coulomb stresses induced by the Ms7.6 Lancang earthquake.

Static Yield Stress of Cement-based Grouting Material under Different Rheological Modes

To quantitatively estimate the workability of cement-based grouting material,from the perspective of rheology,the result of the static yield stress evaluated using the rate-controlled and stress-controlled modes,respectively,was compared using the Rheowin rheometer.Also,the correlation of workability and solid concentration of slurry with static yield stress was studied.Results show that the static yield stress of cement-based grouting slurry relates to the established slurry structure,and is the shear stress corresponding to the transformation of elastics to plastics;In rate-controlled mode,the static yield stress of the slurry is related to the shear rate.The higher the shear rate,the greater the yield stress of the slurry.For the stress-controlled mode,the result is more accurate and suitable for testing static yield stress under different water-cement ratios.Since the water-cement ratio has a good correspondence with the static yield stress and the static yield stress has a good correspondence with the slump flow of the slurry,the static yield stress is the minimum stress to be overcome when the slurry begins to flow and it reflects the yield behavior and structural stability of the cement.

Residual Stress and Deformation Analysis of Static Bonding Multi-layer Pyrex7740 Glass and Aluminum

Residual stresses and deformation of static bonding multi-layer Pyrex7740 glass and aluminum have important effects on performances of bonding parts. The stress and strain finite element analysis of anodic bonding can optimize the structure and process design, reduce the workload of the experiments, shorten the production cycle, improve the bonding quality, and reduce the process costs. In this paper, residual stresses and deformation in the static bonding two-layer （glass/aluminum）, three-layer （glass/aluminum/ glass）,five-layer（glass/aluminum/glass/aluminum/glass）and seven-layer （glass/aluminum/glass/aluminum/glass/ aluminum/glass） samples have been analyzed using nonlinear finite element simulation software MARC. The simulation results show that the shear stress distribution and deformation distribution in different multi-layer glass and aluminum samples are similar. The stress distribution along thickness at different typical positions in all multi-layer samples has characteristics of pulse pattern, which has pulse peak at the position of transition layers and then decreases abruptly to the minimum value at the positions of glass and aluminum. The maximum shear stress is located in the outside surface area in the transition layer between the top unconstrained glass layer and aluminum layer. The displacement distribution along thickness in all multi-layer samples increases gradually fi＇om the constrained bottom glass layer to the top unconstrained glass layer with abrupt step increase in the aluminum layers, The maximum deformations occur in aluminum layers. It is found that the minimum deformation distortion and the minimum shear stress occur in the three-layer static bonding sample.

Static and Thermal Analysis of Aluminium (413,390,384 and 332) Piston Using Finite Element Method

The main objective of this research was to examine the suitability of aluminium alloy to design a piston of an internal combustion engine for improvement in weight and cost reduction. The piston was modelled using Autodesk Inventor 2017 software. The modelled piston was then imported into Ansys for further analysis. Static structural and thermal analysis were carried out on the pistons of the four different materials namely: Al 413 alloy, Al 384 alloy, Al 390 alloy and Al332 alloy to determine the total deformation, equivalent Von Mises stress, maximum shear stress, and the safety factor. The results of the study revealed that, aluminium 332 alloy piston deformed less compared to the deformations of aluminium 390 alloy piston, aluminium 384 alloy piston and aluminium 413 alloy piston. The induced Von Mises stresses in the pistons of the four different materials were found to be far lower than the yield strengths of all the materials. Hence, all the selected materials including the implementing material have equal properties to withstand the maximum gas load. All the selected materials were observed to have high thermal conductivity enough to be able to withstand the operating temperature in the engine cylinders.

Research on seismic stress triggering

This paper briefly reviews basic theory of seismic stress triggering. Recent development on seismic stress triggering has been reviewed in the views of seismic static and dynamic stress triggering, application of viscoelastic model in seismic stress triggering, the relation between earthquake triggering and volcanic eruption or explosion, other explanation of earthquake triggering, etc. And some suggestions for further study on seismic stress triggering in near future are given.

FEM Static Analysis of ITER Overall Gravity Support System

For the static structural of ITER overall gravity support are analyzed by the ANSYS software of finite element method （FEM）. All the maximum stress intensity and maximum displacement of overall gravity support system are within the allowable stress limit and displacement limit.

Nonlinearity analysis of piezoelectric micromachined ultrasonic transducers based on couple stress theory

This paper studies the static deformation behavior of a piezoelectric micromachined ultrasonic transducer （PMUT） actuated by a strong external electric field. The transducer membrane consists of a piezoelectric layer, a passive layer and two electrode layers. The nonlinearities of the piezoelectric layer caused by electrostriction under a strong electric field are analyzed. Because the thickness of the transducer membrane is on the microscale, the size dependence of the deformation behavior is evaluated using the couple stress theory. The results show that the optimal ratio of the top electrode diameter and the membrane diameter is around 0.674. It is also found that this optimal value does not depend on any other parameters if the thicknesses of the two electrodes are negligible compared with those of the piezo- electric and passive layers. In addition, the nonlinearities of the piezoelectric layer will become stronger along with the increase of the electric field, which means that softening of the membrane stiffness occurs when a strong external electric field is applied. Meanwhile, the optimal thickness ratio for the passive layer and the piezoelectric layer is not equal to 1.0 which is usually adopted by previous researchers. Because there exists size dependence of membrane deforma-tion, the optimal value of this thickness ratio needs to be greater than 1.0 on the microscale.

Static Recrystallization Behavior of SCM435 Steel

The static recrystallization behaviors in SCM435 steel were investigated by two-pass hot compression tests on MMS-200 thermosimulation machine. Effects of deformation temperature, strain rate,deformation degree and the initial austenite grain size on static softening were analyzed. The stress compensation method was used to calculate the static recrystallization. The kinetics model of the static recrystallization of SCM435 steel was established and the obtained activation energy for static recrystallization was 182. 8 kJ /mol. Results showed that within a certain time interval( 1-100 s),the static recrystallization fraction X of SCM435 steel increased as the deformation temperature,the deformation rate and the amount of deformation increased,and it decreased as the initial grain size increased and increased as the time interval increased.

Probabilistic estimate of rock mass static and dynamic demands for underground excavation stabilisation

Excavation damage under high in situ stress depends largely upon the potential block size associated with any violent ejection.The size and shape of the dynamic instability are largely controlled by the location,orientation and extent of the pre-existing geological discontinuities.A new methodology is presented in which the rock mass demand can be expressed in terms of the mass in tonnes of unstable rock that is ejected per unit area of the excavation surface where failure occurs.A probabilistic approach has been implemented to estimate the potential rock mass instabilities and their associated static and dynamic demands.The new methodology considers that the strain energy released by the rock mass during violent stress-driven failure is largely converted into kinetic energy of ejection for blocks.The estimated dynamic demand has been favourably compared with observations of rock mass damage in a number of underground excavations.

Study on Stress Triggering During the Activity Process of the Jiashi Strong Earthquake Swarm

The Bachu-Jiashi earthquake of MS6.8 occurred on February 24,2003,about 20km from the southeast of the 1997～1998 Jiashi seismic region in Xinjiang,and its aftershocks are rich and strong.Did the 1997～1998 Jiashi strong earthquake swarm trigger the Bachu-Jiashi MS6.8 earthquake? The Atushi earthquake of MS6.7 occurred in 1996,and the 1997～1998 Jiashi strong earthquake swarm occurred about 70km from the Atushi earthquake 10 months later.Did the Atushi earthquake of M-S6.7 encourage the 1997～1998 Jiashi strong earthquake swarm? There were 9 earthquakes with M-S6.0 from 1996 to 1997 in the Jiashi seismic region,how did they act on each other? To answer the above questions,the article studies the triggering effect of the activity process of the whole Jiashi earthquake swarm from the 1996 Atushi earthquake of M-S6.7,the 1997～1998 Jiashi strong swarm to the 2003 Bachu-Jiashi earthquake of M-S6.8,and analyzes the seismicity characteristics around the Jiashi region.The results show that the 1996 Atushi earthquake of M-S6.7 encouraged the 1997～1998 Jiashi strong swarm to some extent,the accumulative Coulomb stress change from the previous M-6.0 earthquakes of the Jiashi strong swarm had certain triggering effects on the following M-6.0 events,and the Coulomb stress change converted from the Jiashi strong swarm strongly encouraged the 2003 Bachu-Jiashi earthquake with M-S6.8.

Research on Frequency of the Aftershock Sequence of the Wenchuan Earthquake Based on Coseismic Coulomb Stress Change

By the aftershock frequency estimation method based on the calculation of coseismic static Coulomb stress changes and rate-and state-dependent fault constitutive law,we calculate the frequency of "direct "aftershocks of the Wenchuan earthquake related to coseismic static Coulomb stress changes in its aftershock zone and the areas nearby.It shows that the frequency is significantly lower than the truth in the main rupture zone,especially in the southern rupture zone,due to the decrease of stress level on the rupture plane of the main shock resulting from coseismic Coulomb stress change.The study also shows that the effect of the Coulomb stress change on the duration of aftershock activity is associated with the lower limit magnitude.The duration is about 15-16 months for aftershocks above ML4.0,and close to 60 months for aftershocks above ML3.5.In this period,the ratio of the"direct"aftershocks caused by coseismic Coulomb stress change ranges between 44.7% to48.6%,which suggests that,even in the "effective"period of coseismic Coulomb stress changes,about half of the aftershocks on the main shock rupture plane are independent of coseismic Coulomb stress changes.It is pointed out that those aftershocks may be related to the afterslip or the viscoelastic relaxation,which are time dependent cases.

静态应力扰动对走滑断层阶区附近地震破裂传播影响的二维数值模拟

动态破裂在走滑断裂带上阶区附近的传播能力控制了地震破裂的可能规模,而非均匀应力场对动态破裂的传播有显著影响。在本研究中,我们通过整合动态破裂模型和静态应力扰动模型,构建了走滑断层上的非均匀应力场,对走滑断层阶区附近前次动态破裂所产生的静态应力扰动对后续破裂传播行为的影响进行了二维动态破裂模型研究。模拟结果表明,当考虑到走滑断层上的地震复发行为时,即使前序地震破裂传播被阶区所阻挡,其所产生的静态应力扰动也可显著提升下次地震跨该阶区传播的能力。另外,不同的初始均匀应力使得动态破裂能够跨大致相同宽度的阶区传播。较大的应力降或者较小的断层强度比(S)能够使得动态破裂在相对较宽的阶区上传播。因此,在研究走滑断裂带不同分段的级联破裂模式时,需要考虑前序地震所造成的静态应力扰动影响。

Statically Determinate Equations of Equilibrium in Particulate Mechanics

Based on a model of two stress tensors possessing high fluidity, a statically determinate system of partial difference equations of equilibrium has been derived for use to particulate media of such nature. Through non dimensionalization of independent and dependent variables, the system passes into that of partial differential equations. Although the statically determinate system of partial differential equations is non linear, yet the two dimensional one falls apart into three separate groups which can be solved easily one after another.

STRESS FIELD AT A TIP OF A PREFABRICATED SPIRAL V-NOTCH

Based on the tranditional V-notched blasting, a technique of spirally V-notched blasting to loosen earth and rock was presented. Fracture mechanics and Westergaard stress function were adopted to build a complex stress function to derive the plane stress and strain fields at one tip of the crack under a quasi-static pressure. An expression was formulated to define the stress intensity factor of spiral V-notch loosen blasting. Factors that have effects on the stress intensity factor were studied. It is demonstrated that spiral V-notch loosen blasting is an extension of vertical V-notch blasting, straight cracking, and alike theories.