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.

Shear sliding of rough-walled fracture surfaces under unloading normal stress

Through high-precision engraving,self-affine sandstone joint surfaces with various joint roughness coefficients(JRC=3.21e12.16)were replicated and the shear sliding tests under unloading normal stress were conducted regarding various initial normal stresses(1e7 MPa)and numbers of shearing cycles(1 e5).The peak shear stress of fractures decreased with shear cycles due to progressively smooth surface morphologies,while increased with both JRC and initial normal stress and could be verified using the nonlinear Barton-Bandis failure criterion.The joint friction angle of fractures exponentially increased by 62.22%e64.87%with JRC while decreased by 22.1%e24.85%with shearing cycles.After unloading normal stress,the sliding initiation time of fractures increased with both JRC and initial normal stress due to more tortuous fracture morphologies and enhanced shearing resistance capacity.The surface resistance index(SRI)of fractures decreased by 4.35%e32.02%with increasing shearing cycles due to a more significant reduction of sliding initiation shear stress than that for sliding initiation normal stress,but increased by a factor of 0.41e1.64 with JRC.After sliding initiation,the shear displacement of fractures showed an increase in power function.By defining a sliding rate threshold of 5105 m/s,transition from“quasi-static”to“dynamic”sliding of fractures was identified,and the increase of sliding acceleration steepened with JRC while slowed down with shearing cycles.The normal displacement experienced a slight increase before shear sliding due to deformation recovery as the unloading stress was unloaded,and then enhanced shear dilation after sliding initiation due to climbing effects of surface asperities.Dilation was positively related to the shear sliding velocity of fractures.Wear characteristics of the fracture surfaces after shearing failure were evaluated using binary calculation,indicating an increasing shear area ratio by 45.24%e91.02%with normal stress.

Wellbore stability model in shale formation under the synergistic effect of stress unloading-hydration

According to the transversely isotropic theory and weak plane criterion, and considering the mechanical damages due to stress unloading and hydration during drilling, a shale wellbore stability model with the influence of stress unloading and hydration was established using triaxial test and shear test. Then, factors influencing the wellbore stability in shale were analyzed. The results indicate that stress unloading occurs during drilling in shale. The larger the confining pressure and axial stress, the more remarkable weakening of shale strength caused by stress unloading. The stress unloading range is positively correlated with the weakening degree of shale strength. Shale with a higher development degree of bedding is more prone to damage along bedding. In this case, during stress unloading, the synergistic effect of weak structural plane and stress unloading happens, leading to a higher weakening degree of shale strength and poorer mechanical stability, which brings a higher risk of wellbore instability. Fluid tends to invade shale through bedding, promoting the shale hydration. Hydration also can weaken shale mechanical stability, causing the decline of wellbore stability. Influence of stress unloading on collapse pressure of shale mainly occurs at the early stage of drilling, while the influence of hydration on wellbore stability mainly happens at the late stage of drilling. Bedding, stress unloading and hydration jointly affect the wellbore stability in shale. The presented shale wellbore stability model with the influence of stress unloading and hydration considers the influences of the three factors. Field application demonstrates that the prediction results of the model agree with the actual drilling results, verifying the reliability of the model.

Mechanical performances of shield tunnel segments under asymmetric unloading induced by pit excavation

To explore the stress and deformation responses,as well as the failure characteristics of the shield tunnel segment of Hangzhou Metro under the influences of pit excavation and other surrounding projects,a self-developed“shield tunnel segment hydraulic loading system”was used to carry out full-scale loading tests on the three-ring staggered assembled segments.The structural performances and failure process of the tunnel segment under step-by-step asymmetric unloading were studied.A safety index was proposed to describe the bearing capacity of the segment.Next,a finite element model(FEM)was established to analyze the bearing capacity of segment using the test results.Finally,the effect of reinforcement with a steel plate on the deformation and bearing capacity of the segment was analyzed.The results showed that under asymmetric unloading,the peak value and amplitude of the bending moment on the near unloading side converged with a greater value than those on the far side.The concrete internal force exhibited a directional transformation at different load stages.Cracks first appeared at the 180inner arc surface of the bottom standard block and then expanded to both sides,while the rate of crack propagation of the outer arc surface was relatively lower.The bearing capacity of the segments can be evaluated by the combination of the factors,e.g.the residual bearing capacity coefficient,moment transfer coefficient,and characterization coefficient.The segments approaching failure can facilitate the increase in the residual bearing capacity coefficient by more than 50%.This can provide guidance for the service assessment of metro tunnel operations.

Dynamic characteristics of high stressed red sandstone subjected to unloading and impact loads

In the process of deep projects excavation,deep rock often experiences a full stress process from high stress to unloading and then to impact disturbance failure.To study the dynamic characteristics of three-dimensional high stressed red sandstone subjected to unloading and impact loads,impact compression tests were conducted on red sandstone under confining pressure unloading conditions using a modified split Hopkinson pressure bar.Impact disturbance tests of uniaxial pre-stressed rock were also conducted(without considering confining pressure unloading effect).The results demonstrate that the impact compression strength of red sandstone shows an obvious strain rate effect.With an approximately equal strain rate,the dynamic strength of red sandstone under confining unloading conditions is less than that in the uniaxial pre-stressed impact compression test.Confining pressure unloading produces a strength-weakening effect,and the dynamic strength weakening factor(DSWF)is also defined.The results also indicate that the strain rate of the rock and the incident energy change in a logarithmic relation.With similar incident energies,unloading results in a higher strain rate in pre-stressed rock.According to the experimental analysis,unloading does not affect the failure mode,but reduces the dynamic strength of pre-stressed rock.The influence of confining pressure unloading on the shear strength parameters(cohesion and friction angle)is discussed.Under the same external energy impact compression,prestressed rock subjected to unloading is more likely to be destroyed.Thus,the effect of unloading on the rock mechanical characteristics should be considered in deep rock project excavation design.

Effect of fatigue loading-confining stress unloading rate on marble mechanical behaviors: An insight into fracture evolution analyses

Rocks in underground works usually experience rather complex stress disturbance.For this,their fracture mechanism is significantly different from rocks subjected to conventional triaxial compression conditions.The effects of stress disturbances on rock geomechanical behaviors under fatigue loading conditions and triaxial unloading conditions have been reported in previous studies.However,little is known about the dependence of the unloading rate on fatigue loading and confining stress unloading(FL-CSU)conditions that influence rock failure.In this paper,we aimed at investigating the fracture behaviors of marble under FL-CSU conditions using the post-test X-ray computed tomography(CT)scanning technique and the GCTS RTR 2000 rock mechanics system.Results show that damage accumulation at the fatigue stage can influence the final fracture behaviors of marble.The stored elastic energy for rock samples under FL-CSU tests is relatively larger compared to those under conventional triaxial tests,and the dissipated energy used to drive damage evolution and crack propagation is larger for FL-CSU tests.In FL-CSU tests,as the unloading rate increases,the dissipated energy grows and elastic energy reduces.CT scanning after the test reveals the impacts of the unloading rate on the crack pattern and a fracture degree index is therein defined in this context to represent the crack dimension.It shows that the crack pattern after FL-CSU tests depends on the unloading rate,and the fracture degree is in agreement with the analysis of both the energy dissipation and the amount of energy released.The effect of unloading rate on fracture evolution characteristics of marble is revealed by a series of FL-CSU tests.

Dynamic responses and failure mechanisms of the existing tunnel under transient excavation unloading of an adjacent tunnel

Engineering disasters(e.g.rock slabbing and rockburst)of the tunnel groups induced by the transient excavation of an adjacent tunnel threaten the stability of the existing tunnel,especially for those excavated by using the drill and blast tunneling(D&B).However,the dynamic response and failure mechanism of surrounding rocks of the existing tunnel caused by adjacent transient excavation are not clear due to the difficulty in conducting field tests and laboratory experiments.Therefore,a novel transient unloading experimental system for deep tunnel excavation was proposed in this study.The real stress path and the unloading rate can be reproduced by using this proposed system.The experiments were conducted for observing the dynamic response of the existing tunnel induced by adjacent transient excavation under different lateral pressure coefficients l(?0.4,0.6,0.8,1,1.2,1.4,1.6,1.8)with a polymethyl methacrylate(PMMA)specimen.The propagation of the impact wave and unloading surface wave was detected through the digital image correlation(DIC)analysis.The reflection of the unloading surface wave on the incident side of the existing tunnel(tunnel-E)was observed and analyzed.Moreover,the dynamic characteristics of the stress redistribution,the particle displacement and vibration velocity of surrounding rocks of tunnel-E were analyzed and summarized.In addition,the Mohr-Coulomb(MeC)failure criterion with tension cut-off was adopted to evaluate the stability of the existing tunnel under adjacent transient excavation.The results indicate that the incident side of the existing tunnel under the dynamic disturbance of transient excavation of an adjacent tunnel was more prone to fail,followed by the shadow side and the top/bottom side.

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.

Evolution of mechanical parameters of Shuangjiangkou granite under different loading cycles and stress paths

Surrounding rocks at different locations are generally subjected to different stress paths during the process of deep hard rock excavation.In this study,to reveal the mechanical parameters of deep surrounding rock under different stress paths,a new cyclic loading and unloading test method for controlled true triaxial loading and unloading and principal stress direction interchange was proposed,and the evolution of mechanical parameters of Shuangjiangkou granite under different stress paths was studied,including the deformation modulus,elastic deformation increment ratios,fracture degree,cohesion and internal friction angle.Additionally,stress path coefficient was defined to characterize different stress paths,and the functional relationships among the stress path coefficient,rock fracture degree difference coefficient,cohesion and internal friction angle were obtained.The results show that during the true triaxial cyclic loading and unloading process,the deformation modulus and cohesion gradually decrease,while the internal friction angle gradually increases with increasing equivalent crack strain.The stress path coefficient is exponentially related to the rock fracture degree difference coefficient.As the stress path coefficient increases,the degrees of cohesion weakening and internal friction angle strengthening decrease linearly.During cyclic loading and unloading under true triaxial principal stress direction interchange,the direction of crack development changes,and the deformation modulus increases,while the cohesion and internal friction angle decrease slightly,indicating that the principal stress direction interchange has a strengthening effect on the surrounding rocks.Finally,the influences of the principal stress interchange direction on the stabilities of deep engineering excavation projects are discussed.

Carbon unloading in roots in relation to root senescence in Cercis chinensis seedlings under drought stress

When Cercis chinensis seedlings suffered from drought treatment, net photosynthetic rates had been significantly reduced at the end of the drought treatment. Compared with the control, the activities of acid invertases in roots had increased 5 and 11 days after drought treatment. Seventeen days after drought treatment, the activities of acid invertases in roots were significantly decreased, while activities of alkaline invertases in roots had also been significantly reduced. As the moisture in culture media decreased, so the activities of sucrose synthases in leaves decreased slightly. In roots, their activities had significantly increased 5 and 11 days after drought treatment. The contents of fructose in roots reduced as the moisture in culture media decreased and 11 and 17 days after drought treatment the reduction was significant. The content of glucose in roots clearly did not change as drought stress occurred further, but was still less than that in the control seedlings. Similarly, the content of sucrose reduced as the moisture in culture media decreased. At the beginning of the drought stress, the content of sucrose was significantly higher than that in the control and afterwards there were no differences between drought-treated seedlings and the control. The gradient of the sucrose content between leaves and roots was 0.0982 mg.g^-1 FW 17 days after drought treatment, while the gradient of the seedlings under normal condition was 1.3832 mg.g^-1 FW. The sucrose concentration gradient reduced by 92.9%. The reduction in the sucrose content gradient under drought stress decreased the sucrose partitioning in roots. Therefore, our results support the hypothesis of‘shared control＇.

Experimental and Numerical Study on the Shear Strength and Strain Energy of Rock Under Constant Shear Stress and Unloading Normal Stress

Excavation and earth surface processes(e.g.,river incision)always induce the unloading of stress,which can cause the failure of rocks.To study the shear mechanical behavior of a rock sample under unloading normal stress conditions,a new stress path for direct shear tests was proposed to model the unloading of stress caused by excavation and other processes.The effects of the initial stresses(i.e.,the normal stress and shear stress before unloading)on the shear behavior and energy conversion were investigated using laboratory tests and numerical simulations.The shear strength of a rock under constant stress or under unloading normal stress conforms to the Mohr Coulomb criterion.As the initial normal stress increases,the cohesion decreases linearly and the tangent of the internal friction angle increases linearly.Compared with the results of the tests under constant normal stress,the cohesions of the rock samples under unloading normal stress are smaller and their internal friction angles are larger.A strength envelope surface can be used to describe the relationship between the initial stresses and the failure normal stress.Shear dilatancy can decrease the total energy of the direct shear test under constant normal stress or unloading normal stress,particularly when the stress levels(the initial stresses in the test under unloading normal stress or the normal stress in the test under constant normal stress)are high.The ratio of the dissipated energy to the total energy at the moment failure occurs decreases exponentially with increasing initial stresses.The direct shear test under constant normal stress can be considered to be a special case of a direct shear test under unloading normal stress with an unloading amount of zero.

The Effect of Unloading Positions and Times on Sheet Metal’s Stress-Strain Curve

The loading-unloading-reloading process could affect the tensile deformation of metals with the combined function of stress relaxation and work hardening, which has been reported in multiple experiments. Nevertheless, the effects of different unloading positions and unloading times have not been investigated. In this study, unloading-reloading tests on three materials (AL6061, HSLA and Q195) were conducted. The stress exhibits a rapid rise momentarily upon reloading and stabilizes afterward while the post stress-strain curve deviates up or down from the monotonic tensile curve. The ductility is enhanced by the unloading-reloading process in general. Different unloading positions and unloading times have different degrees of influence on the stretching of these metals. The effect of loading conditions on a medium manganese steel was further studied. The functions to modify the post stress-strain relationship after unloading-reloading were established.

Failure properties of rocks in true triaxial unloading compressive test

Slabbing failure often occurs in the surround rock near a deep underground excavation. The mechanism of slabbing failure is still unclear. In order to reveal the influence of the intermediate principal stress （σ2） on slabbing failure, true triaxial unloading compressive test was carried out based on the stress path of the underground engineering excavation, i.e., unloading the minimum principal stress （σ3）, keeping σ2, increasing the maximum principal stress （σ1）. The initiation and the propagation of slabbing fracture in rock specimens were identified by examining the acoustic emission （AE） and the infrared radiation characterization. The test results show that the failure modes of the granite and red sandstone specimens are changed from shear to slabbing with the increase of σ2. The AE characteristic of rock specimen under low σ2 is swarm type which is the main shock type under high σ2. The infrared radiation properties of rock specimen under different σ2 are also different. The temperature change area is just along the shear fracture such as the uniaxial compression. With the increase of σ2, the temperature change area is planar of rock specimen which proofs that the failure mode of rock specimen turns into slabbing.

ZONAL DISINTEGRATION MECHANISM OF DEEP CRACK-WEAKENED ROCK MASSES UNDER DYNAMIC UNLOADING

Size and quantity of fractured zone and non-fractured zone are controlled by cracks contained in deep rock masses. Zonal disintegration mechanism is strongly dependent on the interaction among cracks. The strong interaction among cracks is investigated using stress superposition principle and the Chebyshev polynomials expansion of the pseudo-traction. It is found from numerical results that crack nucleation, growth and coalescence lead to failure of deep crack- weakened rock masses. The stress redistribution around the surrounding rock mass induced by unloading excavation is studied. The effect of the excavation time on nucleation, growth, interaction and coalescence of cracks was analyzed. Moreover, the influence of the excavation time on the size and quantity of fractured zone and non-fractured zone was given. When the excavation time is short, zonal disintegration phenomenon may occur in deep rock masses. It is shown from numerical results that the size and quantity of fractured zone increase with decreasing excavation time, and the size and quantity of fractured zone increase with the increasing value of in-situ geostress.

Unloading responses of pre-flawed rock specimens under different unloading rates

Based on the stress redistribution analysis of rock mass during the deep underground excavation, the unloading process of pre-flawed rock material was simulated by distinct element method (DEM). The effects of unloading rate and flaw inclination angle on unloading strengths and cracking properties of pre-flawed rock specimens are numerically revealed. The results indicate that the unloading failure strength of pre-flawed specimen exhibits a power-function increase trend with the increase of unloading period. Moreover, combined with the stress state analysis on the flaws, it is found that the unloading failure strength increases with the increase of flaw inclination angle. The cracking distribution of pre-flawed specimens under the unloading condition closely depends on the flaw inclination angle, and three typical types of flaw coalescence are observed. Furthermore, at a faster unloading rate, the pre-flawed specimen experiences a sharper and quicker unloading failure process, resulting in more splitting cracks in the specimens.

Calculation of foundation pit deformation caused by deep excavation considering influence of loading and unloading

A new analytical solution for ground surface settlement induced by deep excavation is proposed based on the elastic half space Melan’s solution,and the analytical model is related to the physical and mechanical properties of soil with the loading and unloading action during excavation process.The change law of earth pressure of the normal consolidation soil after the foundation pit excavation was analyzed,and elastic displacement calculation methods of analytic solution were further established given the influence of excavation and unloading.According to the change of stress state in the excavation process of foundation pit,the planar mechanical analysis model of the foundation excavation problem was established.By combining this model with the physical equations and geometric equations of plane strain problem with consideration of the loading and unloading modulus of soil,constitutive equation of the plane strain problem was also established.The loading and unloading modulus formula was obtained by using the parameter calculation method in Duncan-Chang curve model.The constitutive equation obtained from the model was used to calculate the soil stress state of each point to determine its loading and unloading modulus.Finally,the foundation pit displacement change after excavation was calculated,and thus the soil pressure distribution after retaining structure deformation.The theoretical results calculated by making corresponding programs were applied to engineering practice.By comparing the conventional calculation results with monitoring results,the practicability and feasibility of the calculation model were verified,which should provide a theoretical basis for similar projects.

Characteristic stress and strain precursor information for fine-grained granite during failure process under triaxial loading and unloading conditions

The unloading effect by excavation may cause irreversible and severe damage to the surrounding rock masses in underground engineering.In this paper,both conventional triaxial compression(CTC)tests and triaxial unloading confining pressure(TUCP)tests were conducted on fine-grained granite to study its triaxial compression failure processes due to unloading.Based on the crack volumetric strain(CVS)method,the crack axial strain(CAS)method and crack radial area strain(CRAS)method were proposed to identify the failure precursor information(including stress thresholds and axial strain at the initiation point of crack connectivity stage)during the rock failure processes.The results of the CTC tests show that the stable crack development stressσsd,unstable crack development stressσusd,and crack connectivity stressσct identified by the CAS method are 6%,74%–84%,and 86%–97%of the peak stress,respectively.For the TUCP cases,as the confining pressure increases,the stress thresholds,axial pressure at failure and axial strain at the start of the crack connectivity stage increase,while the time ratio of the crack connectivity stage to the entire unloading stage decreases.This indicates that fine-grained granite is prone to generate more cracks and leads to fail suddenly under high confining pressure.Furthermore,this new method demonstrates that the point at which the derivative of the radial crack area strain transitions from stable to a sudden increase or decrease is defined as the precursor point of rock failure.The results of axial strain at the starting point of the crack connectivity stage are very close to those predicted by the AE method,withβ1 no more than 11%.

Lymphocyte reduction induced by hindlimb unloading: distinct mechanisms in the spleen and thymus

Hindlimb unloading(HU)in rodent is a well-accepted ground-based model used to simulate some of the conditions of space flight and reproduce its deleterious effects on the musculoskeletal,cardiovascular and immune systems.In this study,the effects of HU on lymphocyte homeostasis in the spleen and thymus of mice were examined.HU was found to drastically deplete various cell populations in the spleen and thymus.These changes are likely to be mediated by apoptosis,since DNA strand breaks indicative of apoptosis were detected by terminal deoxynucleotidyl transferase-mediated nick end-labeling in both splenocytes and thymocytes.Surprisingly,administration of opioid antagonists or interference with the Fas-FasL interaction was able to block HU-induced reductions of splenocytes,but not thymocytes.On the other hand,steroid receptor antagonists blocked the reduction of lymphocyte numbers in both spleen and thymus.Therefore,the effects of HU on the homeostasis of splenocytes and thymocytes must be exerted through distinct mechanisms.

THE CONSTITUTIVE RELATION OF CRACK-WEAKENED ROCK MASSES UNDER AXIAL-DIMENSIONAL UNLOADING

An accurate and efficient numerical method for solving the crack-crack interaction problem is presented. The method is mainly by means of the dislocation model, stress superposition principle and Chebyshev polynomial expansion of the pseudo-traction. This method can be applied to compute the stress intensity factors of multiple kinked cracks and multiple rows of periodic cracks as well as the overall strains of rock masses containing multiple kinked cracks under complex loads. Many complex computational examples are given. The dependence of the crack-crack interaction on the crack configuration, the geometrical and physical parameters, and loads pattern, is investigated. By comparison with numerical results under confining pressure unloading, it is shown that the crack-crack interaction under axial-dimensional unloading is weaker than those under confining pressure unloading. Numerical results for single faults and crossed faults show that the single faults are more unstable than the crossed faults. It is found from numerical results for different crack lengths and different crack spacing that the interaction among kinked cracks decreases with an increase in length of the kinked cracks and the crack spacing under axial-dimensional unloading.

An experimental study of the dynamic features of shadow areas of caustics in response to loading/unloading fracture

Using a plexiglass sample and by means of real-time holographic interferometry and shadow optical method of caustics, the different features of dynamic variation in stress (strain) field, plastic area and nucleation zone (shadow area) when the sample fractures during loading (loading-fracture) and unloading (unloading-fracture) are studied visually. The results show that the strain nuclei (zones with dense fringes) appear first at the tips of prefabricated cracks at low stress, and then the shadow areas of caustics form with the increase of load. These nuclei and shadow areas can become larger, or smaller, when the process of loading, or unloading, goes on. When the stress is kept within a certain range, the shadow areas of caustics can become larger and smaller alternatively with repeated loading and unloading (cyclic loading). However, when loading and unloading at high stress, in particular when the macrofracture is about to appear, the variations of the shadow areas of caustics are irreversible and quite different. The shadow areas of caustics expand rapidly at an increasing speed when loading-fracture appears. In contrast, the shadow areas of caustics expand at a lower speed when unloading-fracture appears; besides, there is a circular shadow in front of the sharp-angle shaped area.