A stability evaluation method for deep-seated toppling in the upper Lancang river,Southwestern China

Deep-seated toppling in the upper reaches of the Lancang River,southwest China involves deformations exceeding 100 m in depth.The slope deformation is initiated by river downcutting and evolves distinctive characteristics with a depth of river incision.In this study,we propose a system for evaluating the stability of deep-seated toppled slopes in different evolutionary stages.This system contains identification criteria for each evolutionary stage and provides the corresponding stability evaluation methods.Based on the mechanical and kinematic analysis of slope blocks,the specific stage of slope movement can be identified in the field through outcrop mapping,in situ tests,surface displacement monitoring,and adit and borehole explorations.The stability evaluation methods are established based on the limiting equilibrium theory and the strain compatibility between the undisturbed zone and the toppled zone.Finally,several sample slopes in different evolution stages have been investigated to verify the applicability and accuracy of the proposed stability evaluation system.The results indicate that intense tectonic activity and rapid river incision lead to a maximum principal stress ratio exceeding 10 near the slope surface,thus triggering widespread toppling deformations along the river valley.When considering the losses of joint cohesion during the further rotation process,the safety factor of the slope drops by 7%e28%.The self-stabilization of toppling deformation can be recognized by the layer symmetry configuration after the free rotation of the deflected layers.Intensely toppled rock blocks mainly suffer sliding failures beyond the layer symmetry condition.The factor of safety of the K73 rockslide decreased from 1.17 to 0.87 by considering the development of the potential sliding surface and the toesaturated zone.

Determining rock crack stress thresholds using ultrasonic through-transmission measurements

The crack initiation stress threshold is widely used in excavation industries as rock spalling strength when designing deep underground structures to avoid unwanted brittle failures.While various strain-based methods have been developed for the estimation of this critical design parameter,such methods are destructive and often requires subjective interpretations of the stress–strain curves,particularly in rocks with pre-existing microcracks or high porosity.This study explore the applicability of non-destructive ultrasonic through-transmission methods for determining rock damage levels by assessing the changes in transmitted signal characteristics during loading.The change in velocity,amplitude,dominant frequency,and root-mean-square voltage are investigated with four different rock types including marble,sandstone,granite,and basalt under various stress levels.Results suggest the rate of signal variations can be reliably used to estimate crack closure and crack initiation stress levels across the tested rocks before failure.Comparison of the results between the conventional techniques and the new proposed methods based on ultrasonic monitoring are further discussed.

Experimental study of the damage characteristics of rocks containing non-penetrating cracks under cyclic loading

The damage evolution process of non-penetrating cracks often causes some unexpected engineering disasters.Gypsum specimens containing non-penetrating crack(s)are used to study the damage evolution and characteristics under cyclic loading.The results show that under cyclic loading,the relationship between the number of non-penetrating crack(s)and the characteristic parameters(cyclic number,peak stress,peak strain,failure stress,and failure strain)of the pre-cracked specimens can be represented by a decreasing linear function.The damage evolution equation is fitted by calibrating the accumulative plastic strain for each cycle,and the damage constitutive equation is proposed by the concept of effective stress.Additionally,non-penetrating cracks are more likely to cause uneven stress distribution,damage accumulation,and local failure of specimen.The local failure can change the stress distribution and relieve the inhibition of non-penetrating crack extension and eventually cause a dramatic destruction of the specimen.Therefore,the evolution process caused by non-penetrating cracks can be regarded as one of the important reasons for inducing rockburst.These results are expected to improve the understanding of the process of spalling formation and rockburst and can be used to analyze the stability of rocks or rock structures.

Deep-seated large-scale toppling failure in metamorphic rocks：a case study of the Erguxi slope in southwest China

Deep-seated large-scale toppling failure presents unique challenges in the study of natural slope deformation process in mountainous regions.An active deep-seated toppling process was identified in the Erguxi slope located in southwest China,which affected a large area and damaged critical transportation infrastructure with the volume of the deforming rock mass exceeding 24×10~6 m^3.It poses significant risks to the downstream Shiziping Hydropower Station by damming the Zagunao River.Field investigation and monitoring results indicate that the deformation of the Erguxi slope is in the advanced stage of deep-seated toppling process,with the formation of a disturbed belt but no identifiable master failure surface.It was postulated that the alternating tensile and shear strength associated with the hard/soft laminated rock strata of metasandstone and phyllite layers preclude the development of either a tensile or shear failure surface,which resulted in the continuous deformation and displacement without a catastrophic mass movement.The slope movement is in close association with the unfavorable geological conditions of the study area in addition to the construction of transportation infrastructure and the increase of the reservoir level.On the basis of the mechanism and intensity of the ongoing toppling deformation,a qualitative grading system was proposed to describe the toppling process and toevaluate the slope stability.This paper summarized the field observation and monitoring data on the toppling deformation for better characterizing its effect on the stability of the Erguxi slope.The qualitative grading system intends to provide a basis for quantitative study of large-scale deep-seated toppling process in metamorphic rocks.

Surface crack evolution patterns in freeze-thaw damage of fissured rock bodies

To explore the effects of freeze‒thaw cycles on the mechanical properties and crack evolution of fissured sandstone,biaxial compression experiments were carried out on sandstone subjected to freeze‒thaw cycles to characterize the changes in the physical and mechanical properties of fissured sandstone caused by freeze‒thaw cycles.The crack evolution and crack change process on the surface of the fissured sandstone were recorded and analysed in detail via digital image technology(DIC).Numerical simulation was used to reveal the expansion process and damage mode of fine-scale cracks under the action of freeze‒thaw cycles,and the simulation results were compared and analysed with the experimental data to verify the reliability of the numerical model.The results show that the mass loss,porosity,peak stress and elastic modulus all increase with increasing number of freeze‒thaw cycles.With an increase in the number of freeze‒thaw cycles,a substantial change in displacement occurs around the prefabricated cracks,and a stress concentration appears at the crack tip.As new cracks continue to sprout at the tips of the prefabricated cracks until the microcracks gradually penetrate into the main cracks,the displacement cloud becomes obviously discontinuous,and the contours of the displacement field in the crack fracture damage area simply intersect with the prefabricated cracks to form an obvious fracture.The damage patterns of the fractured sandstone after freeze‒thaw cycles clearly differ,forming a symmetrical"L"-shaped damage pattern at zero freeze‒thaw cycles,a symmetrical"V"-shaped damage pattern at 10 freeze‒thaw cycles,and a"V"-shaped damage pattern at 20 freeze‒thaw cycles.After 20 freeze‒thaw cycles,a"V"-shaped destruction pattern and"L"-shaped destruction pattern are formed;after 30 freeze‒thaw cycles,an"N"-shaped destruction pattern is formed.This shows that the failure mode of fractured sandstone gradually becomes more complicated with an increasing number of freeze‒thaw cycles.The effects of freeze‒thaw cycles on the direction and rate of crack propagation are revealed through a temperature‒load coupled model,which provides an important reference for an in-depth understanding of the freeze‒thaw failure mechanisms of fractured rock masses.

Assessing the range of blasting-induced cracks in the surrounding rock of deeply buried tunnels based on the unified strength theory

Blasting-induced cracks in the rock surrounding deeply buried tunnels can result in water gushing and rock mass collapse,posing significant safety risks.However,previous theoretical studies on the range of blasting-induced cracks often ignore the impact of the in-situ stress,especially that of the intermediate principal stress.The particle displacement−crack radius relationship was established in this paper by utilizing the blasthole cavity expansion equation,and theoretical analytical formulas of the stress−displacement relationship and the crack radius were derived with unified strength theory to accurately assess the range of cracks in deep surrounding rock under a blasting load.Parameter analysis showed that the crushing zone size was positively correlated with in-situ stress,intermediate principal stress,and detonation pressure,whereas negatively correlated with Poisson ratio and decoupling coefficient.The dilatancy angle-crushing zone size relationship exhibited nonmonotonic behavior.The relationships in the crushing zone and the fracture zone exhibited opposite trends under the influence of only in-situ stress or intermediate principal stress.As the in-situ stress increased from 0 to 70 MPa,the rate of change in the crack range and the attenuation rate of the peak vibration velocity gradually slowed.

Extraction of the key infrared radiation temperature features concerning stress and crack evolution of loaded rocks

The infrared radiation temperature(IRT)variation concerning stress and crack evolution of rocks is a critical focus in rock mechanics domain and engineering disaster warning.In this paper,a methodology to extract the key IRT features related to stress and crack evolution of loaded rocks is proposed.Specifically,the wavelet denoising and reconstruction in thermal image sequence(WDRTIS)method is employed to eliminate temporal noise in thermal image sequences.Subsequently,the adaptive partition temperature drift correction(APTDC)method is introduced to alleviate temperature drift.On this basis,the spatial noise correction method based on threshold segmentation and adaptive median filtering(OTSU-AMF)is proposed to extract the key IRT features associated with microcracks of loaded rocks.Following temperature drift correction,IRT provides an estimation of the thermoelastic factor in rocks,typically around 5.29×10^(-5) MPa^(-1) for sandstones.Results reveal that the high-temperature concentrated region in cumulative thermal images of crack evolution(TICE)can elucidate the spatiotemporal evolution of localized damage.Additionally,heat dissipation of crack evolution(HDCE)acquired from TICE quantifies the progressive failure process of rocks.The proposed methodology enhances the reliability of IRT monitoring results and provides an innovative approach for conducting research in rock mechanics and monitoring engineering disasters.

Wmic-GMTS and Wmic-GMERR criteria for micron-scale crack propagation in red-bed soft rocks under hydraulic action

Micron-scale crack propagation in red-bed soft rocks under hydraulic action is a common cause of engineering disasters due to damage to the hard rockesoft rockewater interface.Previous studies have not provided a theoretical analysis of the length,inclination angle,and propagation angle of micron-scale cracks,nor have they established appropriate criteria to describe the crack propagation process.The propagation mechanism of micron-scale cracks in red-bed soft rocks under hydraulic action is not yet fully understood,which makes it challenging to prevent engineering disasters in these types of rocks.To address this issue,we have used the existing generalized maximum tangential stress(GMTS)and generalized maximum energy release rate(GMERR)criteria as the basis and introduced parameters related to micron-scale crack propagation and water action.The GMTS and GMERR criteria for micronscale crack propagation in red-bed soft rocks under hydraulic action(abbreviated as the Wmic-GMTS and Wmic-GMERR criteria,respectively)were established to evaluate micron-scale crack propagation in redbed soft rocks under hydraulic action.The influence of the parameters was also described.The process of micron-scale crack propagation under hydraulic action was monitored using uniaxial compression tests(UCTs)based on digital image correlation(DIC)technology.The study analyzed the length,propagation and inclination angles,and mechanical parameters of micron-scale crack propagation to confirm the reliability of the established criteria.The findings suggest that the Wmic-GMTS and Wmic-GMERR criteria are effective in describing the micron-scale crack propagation in red-bed soft rocks under hydraulic action.This study discusses the mechanism of micron-scale crack propagation and its effect on engineering disasters under hydraulic action.It covers topics such as the internal-external weakening of nano-scale particles,lateral propagation of micron-scale cracks,weakening of the mechanical properties of millimeter-scale soft rocks,and resulting interface damage at the engineering scale.The study provides a theoretical basis for the mechanism of disasters in red-bed soft-rock engineering under hydraulic action.

Geochemistry and origin of deep-seated cracked gas on the northern slope of the Dongying Sag, Shandong Province

Deep-seated cracked gas exploration was achieved great breakthrough in Es4L of the Minfeng area on the northern slope of the Dongying Sag. Carbon isotopic and molecular compositions studies revealed the characteristics of wet gas and a normal trend of carbon isotopic composition. Empirical cutoff points of δ13C2 and δ13C3 and light hydrocarbon compositions distinguished the cracking gas as sapropelic gas. Variations in i/nC5, i/nC4 and δ13C2 fur-ther confirmed that the gas was cracked from residual kerogen. Source characteristics indicated that the gas was de-rived from mature-highly mature source rocks of Es4 with kerogen type II being dominant mixed with some oil-cracking gas. Burial history modeling indicated that there were two hydrocarbon charging periods in Es4L reser-voirs. The first period refers to the Guantao-Minghuazhen stage dominated by oil charging, while the second period refers to the Minghuazhen stage and has been dominated by cracked gas charging till now.

Deep-seated rock fracture of valley slopes in China:A review

Deep-seated rock fractures(referred to as DSRF hereafter)in valley slopes are uncommon geological phenomena that challenge our previous understanding of slope unloading processes.These fractures weaken the strength and integrity of the rock mass,potentially forming unstable block boundaries with significant volume,thereby affecting the stability of slopes,chambers,and dam abutments.DSRF has emerged as a critical environmental and engineering geological issue that hinders large-scale projects in deep canyon areas.Despite the attention and practical treatment given to DSRF in engineering practice,theoretical research on this topic still lags behind the demands of engineering applications.To garner widespread attention and promote the resolution of DSRF-related problems,this review aims to redefine DSRF through comprehensive data collection and analysis,engineering geological analogies,and field investigations,and provide a summary and analysis of the research progress on DSRF,along with future research directions.The study defines DSRF as the intermittent tension cracks or relaxation zones within a slightly weathered or fresh,and intact or relatively intact rock mass distributed below the surface unloading zones of a deep canyon slope,and should be distinguished from"loose rock mass"and"deep-seated gravitational slope deformations".The article provides an overview of the development and distribution,rupture characteristics,and genesis mechanism of DSRF.It proposes that DSRF is formed based on the fluvial deviation-undercutting evolution mode,wherein the energy accumulated in the rock mass is violently released when the river further down cuts the slope after the rock mass has undergone cyclical loadingunloading.However,further research is necessary to establish a comprehensive database for DSRF,refine exploration techniques,understand evolutionary processes,develop engineering evaluation methods,and predict the distribution of DSRF.

Numerical analysis of confinement effect on crack propagation mechanism from a flaw in a pre-cracked rock under compression

In many situations rocks are subjected to biaxial loading and the failure process is controlled by the lateral confinement stresses. The importance of confinement stresses has been recognized in the literature by many researchers, in particular, its influence on strength and on the angle of fracture, but still there is not a clear description for the influence of confining stress on the crack propagation mechanism of rocks. This paper presents a numerical pro- cedure for the analysis of crack propagation in rock-like ma- terials under compressive biaxial loads. Several numerical simulations of biaxial tests on the rock specimen have been carried out by a bonded particle model （BPM） and the influ- ence of confinement on the mechanism of crack propagation from a single flaw in rock specimens is studied. For this purpose, several biaxial compressive tests on rectangular spec- imens under different confinement stresses were modeled in （2 dimensional particle flow code） PFC2D. The results show that wing cracks initiate perpendicular to the flaw and trend toward the direction of major stress, however, when the lat- eral stresses increase, this initiation angle gets wider. Also it is concluded that in addition to the material type, the initiation direction of the secondary cracks depends on confine- ment stresses, too. Besides, it is understood that secondary cracks may be produced from both tensile and shear mechanisms.

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.

Crack branching mechanism of rock-like quasi-brittle materials under dynamic stress

The cracking patterns of a thin sheet with a pre-existing crack subjected to dynamic loading are numerically simulated to investigate the mechanism of crack branching by using the FEM method.Six numerical models were set up to study the effects of load,tensile strength and heterogeneity on crack branching.The crack propagation is affected by the applied loads,tensile strength and heterogeneity.Before crack branching,the crack propagates by some distance along the direction of the pre-existing crack.For the materials with low heterogeneity,the higher the applied stress level is and the lower the tensile strength of the material is,the shorter the propagation distance is.Moreover,the branching angle becomes larger and the number of branching cracks increases.In the case of the materials with high heterogeneity,a lot of disordered voids and microcracks randomly occur along the main crack,so the former law is not obvious.The numerical results not only are in good agreement with the experimental observations in laboratory,but also can be extended to heterogeneity media.The work can provide a good approach to model the cracking and fracturing of heterogeneous quasi-brittle materials,such as rock,under dynamic loading.

Crack initiation stress and strain of jointed rock containing multi-cracks under uniaxial compressive loading: A particle flow code approach

The ratio of crack initiation stress to the uniaxial compressive strength(SCI,B/SUC,B) and the ratio of axial strain at the crack initiation stress to the axial strain at the uniaxial compressive strength(B,UCB,CI,A,A/SSSS) were studied by performing numerical stress analysis on blocks having multi flaws at close spacing's under uniaxial loading using PFC3 D. The following findings are obtained: SCI,B/SUC,B has an average value of about 0.5 with a variability of ± 0.1. This range agrees quite well with the values obtained by former research. For joint inclination angle, β=90°,B,UCB,CI,A,A/SSSS is found to be around 0.48 irrespective of the value of joint continuity factor, k. No particular relation is found betweenB,UCB,CI,A,A/SSSS and β; however, the average B,UCB,CI,A,A/SSSS seems to slightly decrease with increasing k. The variability ofB,UCB,CI,A,A/SSSS is found to increase with k.Based on the cases studied in this work,B,UCB,CI,A,A/SSSS ranges between 0.3 and 0.5. This range is quite close to the range of 0.4to 0.6 obtained for SCI,B/SUC,B. The highest variability of ± 0.12 forB,UCB,CI,A,A/SSSS is obtained for k=0.8. For the remaining k values the variability ofB,UCB,CI,A,A/SSSS can be expressed within ± 0.05. This finding is very similar to the finding obtained for the variability of SCI,B/SUC,B.

Cyclic constitutive equations of rock with coupled damage induced by compaction and cracking

In this paper,the cyclic constitutive equations were proposed to describe the constitutive behavior of cyclic loading and unloading.Firstly,a coupled damage variable was derived,which contains two parts,i.e.,the compaction-induced damage and the cracking-induced damage.The compaction-induced damage variable was derived from a nonlinear stress–strain relation of the initial compaction stage,and the cracking-induced damage variable was established based on the statistical damage theory.Secondly,based on the total damage variable,a damage constitutive equation was proposed to describe the constitutive relation of rock under the monotonic uniaxial compression conditions,whereafter,the application of this model is extended to cyclic loading and unloading conditions.To validate the proposed monotonic and cyclic constitutive equations,a series of mechanical tests for marble specimens were carried out,which contained the monotonic uniaxial compression(MUC)experiment,cyclic uniaxial compression experiments under the variable amplitude(CUC-VA)and constant amplitude(CUC-CA)conditions.The results show that the proposed total damage variable comprehensively reflects the damage evolution characteristic,i.e.,the damage variable firstly decreases,then increases no matter under the conditions of MUC,CUC-VA or CUC-CA.Then a reasonable consistency is observed between the experimental and theoretical curves.The proposed cyclic constitutive equations can simulate the whole cyclic loading and unloading behaviors,such as the initial compaction,the strain hardening and the strain softening.Furthermore,the shapes of the theoretical curves are controlled by the modified coefficient,compaction sensitivity coefficient and two Weibull distributed parameters.

Characteristics of acoustic emission signals in damp cracking coal rocks

A uniaxial load experiment on coal rocks at different stress rates was carried out, based on the characteristics of acoustic emission (AE) signals in cracking coal rocks, decomposition, de-noising and reconstruction for the AE signals through wavelet packet transform for solving the current problems created by the presence of noise in AE signals and the existing problems in AE signal processing. The results show that the various characteristics of AE signals in coal rocks cracking under different situations can be clearly reflected, after the AE signals are de-noised by the wavelet packet. Compared to dry coal rocks, the number of AE occurrences in damp coal rocks was significantly reduced, as well as the average amplitude. The number of AE occurrences in damp and dry coal rocks clearly increased with increases in the loading rate, but the largest amplitude of the AE signals in damp coal rocks has been reduced. There is no clear evidence of change in dry coal rocks.

A state-of-the-art review of mechanical characteristics and cracking processes of pre-cracked rocks under quasi-static compression

The mechanical characteristics and failure behavior of rocks containing flaws or discontinuities have received wide attention in the field of rock mechanics.When external loads are applied to rock materials,stress-induced cracks would initiate and propagate from the flaws,ultimately leading to the irreversible failure of rocks.To investigate the cracking behavior and the effect of flaw geometries on the mechanical properties of rock materials,a series of samples containing one,two and multiple flaws have been widely investigated in the laboratory.In this paper,the experimental results for pre-cracked rocks under quasistatic compression were systematically reviewed.The progressive failure process of intact rocks is briefly described to reveal the background for experiments on samples with flaws.Then,the nondestructive measurement techniques utilized in experiments,such as acoustic emission(AE),X-ray computed tomography(CT),and digital image correlation(DIC),are summarized.The mechanical characteristics of rocks with different flaw geometries and under different loading conditions,including the geometry of pre-existing flaws,flaw filling condition and confining pressure,are discussed.Furthermore,the cracking process is evaluated from the perspective of crack initiation,coalescence,and failure patterns.

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.

Visual representation and characterization of three-dimensional hydrofracturing cracks within heterogeneous rock through 3D printing and transparent models

The heterogeneity of unconventional reservoir rock tremendously affects its hydrofracturing behavior. A visual representation and accurate characterization of the three-dimensional （3D） growth and distribution of hydrofracturing cracks within heterogeneous rocks is of particular use to the design and implementation of hydrofracturing stimulation of unconventional reservoirs. However, because of the difficulties involved in visually representing and quantitatively characterizing a 3D hydrofracturing crack-network, this issue remains a challenge. In this paper, a novel method is proposed for physically visualizing and quantitatively characterizing the 3D hydrofracturing crack-network distributed through a heterogeneous structure based on a natural glutenite sample. This method incorporates X-ray microfocus computed tomography （μCT）, 3D printing models and hydrofracturing triaxial tests to represent visually the heterogeneous structure, and the 3D crack growth and distribution within a transparent rock model during hydrofracturing. The coupled effects of material heterogeneity and confining geostress on the 3D crack initiation and propagation were analyzed. The results indicate that the breakdown pressure of a heterogeneous rock model is significantly affected by material heterogeneity and confining geostress. The measured breakdown pressures of heterogeneous models are apparently different from those predicted by traditional theories. This study helps to elucidate the quantitative visualization and characterization of the mechanism and influencing factors that determine the hydrofracturing crack initiation and propagation in heterogeneous reservoir rocks.

Damage and failure characteristics of rock similar materials with pre-existing cracks

In order to further study the damage and failure mechanism for rock similar materials,this study investigated the mechanical properties and failure characteristics,law of damage space development,and damage evolution characteristics for rock similar materials with pre-existing cracks of varying length under uniaxial compression load.The equipment used in this study is the self-developed YYW-Ⅱ strain controlled unconfined compression apparatus and the PCIE-8 acoustic emission monitoring system.Results show that,as the length of pre-existing crack increases:(1) the peak and residual strength reduces,and the peak axial strain and the strain during the initial compression phase increases;(2) the major failure mode is changed from shear failure to tensile failure along a vertical plane that passes the middle of the pre-existing crack;(3) The damage increases during the stable and accelerated development stage,and the effect of the pre-existing cracks is more during the accelerated development stage than the stable development stage.