Geological characteristics and exploration breakthroughs of coal rock gas in Carboniferous Benxi Formation,Ordos Basin,NW China

To explore the geological characteristics and exploration potential of the Carboniferous Benxi Formation coal rock gas in the Ordos Basin,this paper presents a systematic research on the coal rock distribution,coal rock reservoirs,coal rock quality,and coal rock gas features,resources and enrichment.Coal rock gas is a high-quality resource distinct from coalbed methane,and it has unique features in terms of burial depth,gas source,reservoir,gas content,and carbon isotopic composition.The Benxi Formation coal rocks cover an area of 16×104km^(2),with thicknesses ranging from 2 m to 25 m,primarily consisting of bright and semi-bright coals with primitive structures and low volatile and ash contents,indicating a good coal quality.The medium-to-high rank coal rocks have the total organic carbon(TOC)content ranging from 33.49%to 86.11%,averaging75.16%.They have a high degree of thermal evolution(Roof 1.2%-2.8%),and a high gas-generating capacity.They also have high stable carbon isotopic values(δ13C1of-37.6‰to-16‰;δ13C2of-21.7‰to-14.3‰).Deep coal rocks develop matrix pores such as gas bubble pores,organic pores,and inorganic mineral pores,which,together with cleats and fractures,form good reservoir spaces.The coal rock reservoirs exhibit the porosity of 0.54%-10.67%(averaging 5.42%)and the permeability of(0.001-14.600)×10^(-3)μm^(2)(averaging 2.32×10^(-3)μm^(2)).Vertically,there are five types of coal rock gas accumulation and dissipation combinations,among which the coal rock-mudstone gas accumulation combination and the coal rock-limestone gas accumulation combination are the most important,with good sealing conditions and high peak values of total hydrocarbon in gas logging.A model of coal rock gas accumulation has been constructed,which includes widespread distribution of medium-to-high rank coal rocks continually generating gas,matrix pores and cleats/fractures in coal rocks acting as large-scale reservoir spaces,tight cap rocks providing sealing,source-reservoir integration,and five types of efficient enrichment patterns(lateral pinchout complex,lenses,low-amplitude structures,nose-like structures,and lithologically self-sealing).According to the geological characteristics of coal rock gas,the Benxi Formation is divided into 8 plays,and the estimated coal rock gas resources with a buried depth of more than 2000 m are more than 12.33×10^(12)m^(3).The above understandings guide the deployment of risk exploration.Two wells drilled accordingly obtained an industrial gas flow,driving the further deployment of exploratory and appraisal wells.Substantial breakthroughs have been achieved,with the possible reserves over a trillion cubic meters and the proved reserves over a hundred billion cubic meters,which is of great significance for the reserves increase and efficient development of natural gas in China.

Response characteristics of gas pressure under simultaneous static and dynamic load:Implication for coal and gas outburst mechanism

Coal and gas outbursts are dynamic disasters in which a large mass of gas and coal suddenly emerges in a mining space within a split second.The interaction between the gas pressure and stress environment is one of the key factors that induce coal and gas outbursts.In this study,first,the coupling relationship between the gas pressure in the coal body ahead of the working face and the dynamic load was investigated using experimental observations,numerical simulations,and mine-site investigations.It was observed that the impact rate of the dynamic load on the gas-bearing coal can significantly change the gas pressure.The faster the impact rate,the speedier the increase in gas pressure.Moreover,the gas pressure rise was faster closer to the impact interface.Subsequently,based on engineering background,we proposed three models of stress and gas pressure distribution in the coal body ahead of the working face:static load,stress disturbance,and dynamic load conditions.Finally,the gas pressure distribution and outburst mechanism were investigated.The high concentration of gas pressure appearing at the coal body ahead of the working face was caused by the dynamic load.The gas pressure first increased gradually to a peak value and then decreased with increasing distance from the working face.The increase in gas pressure plays a major role in outburst initiation by resulting in the ability to more easily reach the critical points needed for outburst initiation.Moreover,the stronger the dynamic load,the greater the outburst initiation risk.The results of this study provide practical guidance for the early warning and prevention of coal and gas outbursts.

Mechanism of gas pressure action during the initial failure of coal containing gas and its application for an outburst inoculation

Faced with the continuous occurrence of coal and gas outburst(hereinafter referred to as“outburst”)disasters,as a main controlling factor in the evolution process of an outburst,for gas pressure,it is still unclear about the phased characteristics of the coupling process with in situ stress,which induce coal damage and instability.Therefore,in the work based on the mining stress paths induced by typical outburst accidents,the gradual and sudden change of three-dimensional stress is taken as the background for the mechanical reconstruction of the disaster process.Then the true triaxial physical experiments are conducted on the damage and instability of coal containing gas under multiple stress paths.Finally,the response characterization between coal damage and gas pressure has been clarified,revealing the mechanism of action of gas pressure during the initial failure of coals.And the main controlling mechanism during the outburst process is elucidated in the coupling process of in situ stress with gas pressure.The results show that during the process of stress loading and unloading,the original gas pressure enters the processes of strengthening and weakening the action ability successively.And the strengthening effect continues to the period of large-scale destruction of coals.The mechanical process of gas pressure during the initial failure of coals can be divided into three stages:the enhancement of strengthening action ability,the decrease of strengthening action ability,and the weakening action ability.The entire process is implemented by changing the dominant action of in situ stress into the dominant action of gas pressure.The failure strength of coals is not only affected by its original mechanical strength,but also by the stress loading and unloading paths,showing a particularly significant effect.Three stages can be divided during outburst inoculation process.That is,firstly,the coals suffer from initial damage through the dominant action of in situ stress with synergy of gas pressure;secondly,the coals with spallation of structural division are generated through the dominant action of gas pressure with synergy of in situ stress,accompanied by further fragmentation;and finally,the fractured coals suffer from fragmentation and pulverization with the gas pressure action.Accordingly,the final broken coals are ejected out with the gas action,initiating an outburst.The research results can provide a new perspective for deepening the understanding of coal and gas outburst mechanism,laying a theoretical foundation for the innovation of outburst prevention and control technologies.

Elimination mechanism of coal and gas outburst based on geo‑dynamic system with stress–damage–seepage interactions

Coal and gas outburst is a complex dynamic disaster during coal underground mining.Revealing the disaster mechanism is of great signifcance for accurate prediction and prevention of coal and gas outburst.The geo-dynamic system of coal and gas outburst is proposed.The framework of geo-dynamic system is composed of gassy coal mass,geological dynamic environment and mining disturbance.Equations of stress–damage–seepage interaction for gassy coal mass is constructed to resolve the outburst elimination process by gas extraction with boreholes through layer in foor roadway.The results show the occurrence of outburst is divided into the evolution process of gestation,formation,development and termination of geo-dynamic system.The scale range of outburst occurrence is determined,which provides a spatial basis for the prevention and control of outburst.The formation criterion and instability criterion of coal and gas outburst are established.The formation criterion F1 is defned as the scale of the geo-dynamic system,and the instability criterion F2 is defned as the scale of the outburst geo-body.According to the geo-dynamic system,the elimination mechanism of coal and gas outburst—‘unloading+depressurization’is established,and the gas extraction by boreholes through layer in foor roadway for outburst elimination is given.For the research case,when the gas extraction is 120 days,the gas pressure of the coal seam is reduced to below 0.4 MPa,and the outburst danger is eliminated efectively.

In-situ gas contents of a multi-section coal seam in Sydney basin for coal and gas outburst management

The gas content is crucial for evaluating coal and gas outburst potential in underground coal mining. This study focuses on investigating the in-situ coal seam gas content and gas sorption capacity in a representative coal seam with multiple sections (A1, A2, and A3) in the Sydney basin, where the CO_(2) composition exceeds 90%. The fast direct desorption method and associated devices were described in detail and employed to measure the in-situ gas components (Q_(1), Q_(2), and Q_(3)) of the coal seam. The results show that in-situ total gas content (Q_(T)) ranges from 9.48 m^(3)/t for the A2 section to 14.80 m^(3)/t for the A3 section, surpassing the Level 2 outburst threshold limit value, thereby necessitating gas drainage measures. Among the gas components, Q_(2) demonstrates the highest contribution to Q_(T), ranging between 55% and 70%. Furthermore, high-pressure isothermal gas sorption experiments were conducted on coal samples from each seam section to explore their gas sorption capacity. The Langmuir model accurately characterizes CO_(2) sorption behavior, with ft coefcients (R^(2)) greater than 0.99. Strong positive correlations are observed between in-situ gas content and Langmuir volume, as well as between residual gas content (Q_(3)) and sorption hysteresis. Notably, the A3 seam section is proved to have a higher outburst propensity due to its higher Q_(1) and Q_(2) gas contents, lower sorption hysteresis, and reduced coal toughness f value. The insights derived from the study can contribute to the development of efective gas management strategies and enhance the safety and efciency of coal mining operations.

Experimental investigations on effects of gas pressure on mechanical behaviors and failure characteristic of coals

The mechanical behavior of coal is the key factor affecting underground coal mining and coalbed methane extraction.In this study,triaxial compression and seepage tests were carried out on coal at different gas pressures.The mechanical properties and failure process of coal were studied,as well as the acoustic emission(AE)and strain energy.The influence of gas pressure on the mechanical parameters of this coal was analyzed.Based on the conventional energy calculation formula,the pore pressure was introduced through the effective stress formula,and each energy component of coal containing gas was refined innovatively.The contribution of gas pressure to the total energy input and dissipation during loading was quantitatively described.Finally,the influence of gas pressure on coal strength was theo-retically analyzed from the perspectives of MohreCoulomb criterion and fracture mechanics.The results show that the total absorbed energy comprises the absorbed energy in the axial pressure direction(positive)and in the confining pressure direction(negative),as well as that induced by the pore pressure(initially negative and then positive).The absorbed energy in the axial pressure direction accounts for the main proportion of the total energy absorbed by coal.The quiet period of AE in the initial stage shortens,and AE activity increases during the pre-peak stage under high gas pressure.The fractal characteristics of AE in three stages are studied using the correlation dimension.The AE process has different forms of self-similarity in various deformation stages.

Multi-scale pore fractal characteristics of differently ranked coal and its impact on gas adsorption

Well-developed pores and cracks in coal reservoirs are the main venues for gas storage and migration.To investigate the multi-scale pore fractal characteristics,six coal samples of different rankings were studied using high-pressure mercury injection(HPMI),low-pressure nitrogen adsorption(LPGA-N2),and scanning electron microscopy(SEM)test methods.Based on the Frankel,Halsey and Hill(FHH)fractal theory,the Menger sponge model,Pores and Cracks Analysis System(PCAS),pore volume complexity(D_(v)),coal surface irregularity(Ds)and pore distribution heterogeneity(D_(p))were studied and evaluated,respectively.The effect of three fractal dimensions on the gas adsorption ability was also analyzed with high-pressure isothermal gas adsorption experiments.Results show that pore structures within these coal samples have obvious fractal characteristics.A noticeable segmentation effect appears in the Dv1and Dv2fitting process,with the boundary size ranging from 36.00 to 182.95 nm,which helps differentiate diffusion pores and seepage fractures.The D values show an asymmetric U-shaped trend as the coal metamorphism increases,demonstrating that coalification greatly affects the pore fractal dimensions.The three fractal dimensions can characterize the difference in coal microstructure and reflect their influence on gas adsorption ability.Langmuir volume(V_(L))has an evident and positive correlation with Dsvalues,whereas Langmuir pressure(P_(L))is mainly affected by the combined action of Dvand Dp.This study will provide valuable knowledge for the appraisal of coal seam gas reservoirs of differently ranked coals.

Three dimensional discrete element modelling of the conventional compression behavior of gas hydrate bearing coal

To analyze the relationship between macro and meso parameters of the gas hydrate bearing coal(GHBC)and to calibrate the meso-parameters,the numerical tests were conducted to simulate the laboratory triaxial compression tests by PFC3D,with the parallel bond model employed as the particle contact constitutive model.First,twenty simulation tests were conducted to quantify the relationship between the macro–meso parameters.Then,nine orthogonal simulation tests were performed using four meso-mechanical parameters in a three-level to evaluate the sensitivity of the meso-mechanical parameters.Furthermore,the calibration method of the meso-parameters were then proposed.Finally,the contact force chain,the contact force and the contact number were examined to investigate the saturation effect on the meso-mechanical behavior of GHBC.The results show that:(1)The elastic modulus linearly increases with the bonding stiffness ratio and the friction coefficient while exponentially increasing with the normal bonding strength and the bonding radius coefficient.The failure strength increases exponentially with the increase of the friction coefficient,the normal bonding strength and the bonding radius coefficient,and remains constant with the increase of bond stiffness ratio;(2)The friction coefficient and the bond radius coefficient are most sensitive to the elastic modulus and the failure strength;(3)The number of the force chains,the contact force,and the bond strength between particles will increase with the increase of the hydrate saturation,which leads to the larger failure strength.

Experimental and theoretical study on the dynamic effective stress of loaded gassy coal during gas release

In the process of mining coalbed methane(CBM),an unsteady state often arises due to the rapid extraction,release and pressure relief of CBM.In this case,the effective stress of coal changes dynamically,affecting the stability of the gassy coal seam.In this paper,gas release tests of gassy coal under conventional triaxial compression were performed,and the dynamic effective stress(DES)during gas release was obtained indirectly based on a constitutive equation and deformation of coal.The results show that the maximum increases in DES caused by the release of free gas and adsorbed gas under the stress of 1.1 MPa were 0.811 and 5.418 MPa,respectively,which seriously affected the stress state of the coal.During the gas release,the free gas pressure and the adsorbed gas volume were the parameters that directly affected the DES and showed a positive linear relationship with the DES with an intercept of zero.The DES of the coal sample increased exponentially with time,which was determined by the contents of free and adsorbed gas.Based on the experimental results and theoretical analysis,an effective stress model was obtained for loaded gassy coal during gas release.The results of verification indicated accuracy greater than 99%.

Dynamic behavior of outburst two-phase flow in a coal mine T-shaped roadway:The formation of impact airflow and its disaster-causing effect

The study of the dynamic disaster mechanism of coal and gas outburst two-phase flow is crucial for improving disaster reduction and rescue ability of coal mine outburst accidents.An outburst test in a T-shaped roadway was conducted using a self-developed large-scale outburst dynamic disaster test system.We investigated the release characteristics of main energy sources in coal seam,and obtained the dynamic characteristics of outburst two-phase flow in a roadway.Additionally,we established a formation model for outburst impact flow and a model for its flow in a bifurcated structure.The results indicate that the outburst process exhibits pulse characteristics,and the rapid destruction process of coal seam and the blocking state of gas flow are the main causes of the pulse phenomenon.The outburst energy is released in stages,and the elastic potential energy is released in the vertical direction before the horizontal direction.In a straight roadway,the impact force oscillates along the roadway.With an increase in the solid–gas ratio,the two-phase flow impact force gradually increases,and the disaster range extends from the middle of the roadway to the coal seam.In the area near the coal seam,the disaster caused by the two-phase flow impact is characterized by intermittent recovery.In a bifurcated roadway,the effect of impact airflow on impact dynamic disaster is much higher than that of two-phase flow,and the impact force tends to weaken with increasing solid-gas ratio.The impact force is asymmetrically distributed;it is higher on the left of the bifurcated roadway.With an increase in the solid-gas ratio,the static pressure rapidly decreases,and the bifurcated structure accelerates the attenuation of static pressure.Moreover,secondary acceleration is observed when the shock wave moves along the T-shaped roadway,indicating that the bifurcated structure increases the shock wave velocity.

Mechanism investigation on coal and gas outburst: An overview

Coal and gas outburst is a frequent dynamic disaster during underground coal mining activities.After about 150 years of exploration,the mechanisms of outbursts remain unclear to date.Studies on outburst mechanisms worldwide focused on the physicochemical and mechanical properties of outburst-prone coal,laboratory-scale outburst experiments and numerical modeling,mine-site investigations,and doctrines of outburst mechanisms.Outburst mechanisms are divided into two categories:single-factor and multi-factor mechanisms.The multi-factor mechanism is widely accepted,but all statistical phenomena during a single outburst cannot be explained using present knowledge.Additional topics about outburst mechanisms are proposed by summarizing the phenomena that need precise explanation.The most appealing research is the microscopic process of the interaction between coal and gas.Modern physical-chemical methods can help characterize the natural properties of outburst-prone coal.Outburst experiments can compensate for the deficiency of first-hand observation at the scene.Restoring the original outburst scene by constructing a geomechanical model or numerical model and reproducing the entire outburst process based on mining environment conditions,including stratigraphic distribution,gas occurrence,and geological structure,are important.Future studies can explore outburst mechanisms at the microscale.

Coal and gas outburst dynamic system

Coal and gas outburst is an extremely complex dynamic disaster in coal mine production process which will damage casualties and equipment facilities, and disorder the ventilation system by suddenly ejecting a great amount of coal and gas into roadway or working face. This paper analyzed the interaction among the three essential elements of coal and gas outburst dynamic system. A stress-seepage-damage coupling model was established which can be used to simulate the evolution of the dynamical system, and then the size scale of coal and gas outburst dynamical system was investigated. Results show that the dynam- ical system is consisted of three essential elements, coal-gas medium （material basis）, geology dynamic environment （internal motivation） and mining disturbance （external motivation）. On the case of CI 3 coal seam in Panyi Mine, the dynamical system exists in the range of 8-12 m in front of advancing face. The size scale will be larger where there are large geologic structures. This research plays an important guid- ing role for developing measures of coal and gas outburst prediction and prevention.

Similarity criteria and coal-like material in coal and gas outburst physical simulation

Coal and gas outburst is one of the main gas hazards in coal mines. However, due to the risks of the coal and gas outburst, the field test is difficult to complete. Therefore, an effective approach to studying the mechanism and development of outburst is to conduct the similar physical simulation. However, the similarity criteria and similar materials in outburst are the key factors which restrict the development of physical simulation. To solve those problems, this paper has established similarity criteria base on mechanics model, solid-fluid coupling model and energy model, and presented high similar materials. Combining with three groups of similar number, and considering similar mechanical parameters and deformation and failure regularity, the similarity criteria of outburst is determined on the basis of the energy model. According to those criteria, we put forward a similar material consists of pulverized coal, cement, sand, activated carbon, and water. The similar material has high compressive strength and the accordant characteristics with the raw coal, include density, porosity, adsorption, desorption. The new research is promising for preventing and controlling gas hazards in the future.

Preventing Coal and Gas Outburst Using Methane Hydration

According to the characteristics of the methane hydrate condensing and accumulating methane, authors put forward a new technique thought way to prevent the accident of coal and gas outburst by urging the methane in the coal seams to form hydrate. The paper analyzes the feasibility of forming the methane hydrate in the coal seam from the several sides, such as, temperature,pressure, and gas components, and the primary trial results indicate the problems should be settled before the industrialization appliance realized.

A coupled DEM and LBM model for simulation of outbursts of coal and gas

An outburst of coal and gas is a major hazard in underground coal mining. It is generally accepted that an outburst occurs when certain conditions of stress, coal gassiness and physical-mechanical properties of coal are met. Outbursting is recognized as a two-step process, i.e., initiation and development. In this paper, we present a fully-coupled solid and fluid code to model the entire process of an outburst. The deformation, failure and fracture of solid （coal） are modeled with the discrete element method, and the flow of fluid （gas and water） such as free flow and Darcy flow are modeled with the lattice Boltzmann method. These two methods are coupled in a two-way process, i.e., the solid part provides a moving boundary condition and transfers momentum to the fluid, while the fluid exerts a dragging force upon the solid. Gas desorption from coal occurs at the solid-fluid boundary, and gas diffusion is implemented in the solid code where particles are assumed to be porous. A simple 2D example to simulate the process of an outburst with the model is also presented in this paper to demonstrate the capability of the coupled model.

Application of the catastrophe progression method in predicting coal and gas outburst

Based on catastrophe theory,we used the catastrophe progression method to predict the risk of coal and gas outbursts in coal mines.According to the major factors affecting coal and gas outbursts,we built a comprehensive evaluation index system and a coal and gas outburst prediction model.In addition,we performed a standard transformation for each index system;based on the degree the various indices affect the risk of an outburst,to make the data dimensionless.Based on the outburst data from eight mines,we determined catastrophe progression values and verified these values.The results show that:1) converting multi-dimensional problems into one-dimensional problems using this catastrophe progression method can simplify the steps of predicting coal and gas outbursts;2) when pre-determined catastrophe progression values are used to predict coal and gas outbursts,the predicting accuracy rate can be as high as 87.5%;3) the various coal mines have different factors inducing outbursts with varying importance of these factors and 4) the catastrophe progression values,calculated based on these factors,can be used effectively to predict the risk of outbursts in coal mines.

Coal and gas outburst mechanism of the “Three Soft” coal seam in western Henan

Based on the particularities of gas outbursts,i.e.,low gas bearing capacity and low gas pressure in the "Three Soft" coal seam in western Henan,we applied the theories of plate tectonics and regional structural evolution to investigate the mechanism of this seam and its impact on the coal seam gas formation.Our investigation revealed that coal and gas outbursts are distributed in a strip in a NW direction,with a number of high-penetration mines scattered towards the south side and low-gas mines largely located on the north side.We analyzed the statistics of 38 gas explosions and the rock-coal sturdiness number coefficient f of 167 sampling sites in the region and found the gas outburst mechanism that features a "low indicator outburst phenomenon".The mechanism is characterized by structural coal as its core,a low gas bearing capacity,low gas pressure and sturdiness coefficient f mostly less than 0.3.Our research results provide a theoretical foundation for effective control of gas disasters.

Bayesian discriminant analysis for prediction of coal and gas outbursts and application

Based on the principle of Bayesian discriminant analysis, we established a model of Bayesian discriminant analysis for predicting coal and gas outbursts. We selected five major indices which affect outbursts, i.e., initial speed of methane diffusion, a consistent coal coefficient, gas pressure, destructive style of coal and mining depth, as discriminating factors of the model. In our model, we divided the type of coal and gas outbursts into four grades regarded as four normal populations. We then obtained the corresponding discriminant functions through training a set of data from engineering examples as learning samples and evaluated their criteria by a back substitution method to verify the optimal properties of the model. Finally, we applied the model to the prediction of coal and gas outbursts in the Yunnan Enhong Mine. Our results coincided completely with the actual situation. These results show that a model of Bayesian discriminant analysis has excellent recognition performance, high prediction accuracy and a low error rate and is an effective method to predict coal and gas outbursts.

Mechanical criterion for coal and gas outburst:a perspective from multiphysics coupling

Although a series of hypotheses have been proposed,the mechanism underlying coal and gas outburst remains unclear.Given the low-index outbursts encountered in mining practice,we attempt to explore this mechanism using a multiphysics coupling model considering the effects of coal strength and gas mass transfer on failure.Based on force analysis of coal ahead of the heading face,a risk identification index C_(m)and a critical criterion(C_(m)≥1)of coal instability are proposed.According to this criterion,the driving force of an outburst consists of stress and gas pressure gradients along the heading direction of the roadway,whereas resistance depends on the shear and tensile strengths of the coal.The results show that outburst risk decreases slightly,followed by a rapid increase,with increasing vertical stress,whereas it decreases with increasing coal strength and increases with gas pressure monotonically.Using the response surface method,a coupled multi-factor model for the risk identification index is developed.The results indicate strong interactions among the controlling factors.Moreover,the critical values of the factors corresponding to outburst change depending on the environment of the coal seams,rather than being constants.As the buried depth of a coal seam increases,the critical values of gas pressure and coal strength decrease slightly,followed by a rapid increase.According to its controlling factors,outburst can be divided into stress-dominated,coal-strength-dominated,gas-pressure-dominated,and multi-factor compound types.Based on this classification,a classified control method is proposed to enable more targeted outburst prevention.

Experimental study on evolution law for particle breakage during coal and gas outburst

Coal and gas outburst is a dynamic phenomenon in underground mining engineering that is often accompanied by the throwing and breakage of large amounts of coal.To study the crushing effect and its evolution during outbursts,coal samples with different initial particle sizes were evaluated using a coal and gas outburst testing device.Three basic particle sizes,5–10 mesh,10–40 mesh,and 40–80 mesh,as well as some mixed particle size coal samples were used in tests.The coal particles were pre-compacted at a pressure of 4 MPa before the tests.The vertical ground stress(4 MPa)and the horizontal ground stress(2.4 MPa)were initially simulated by the hydraulic system and maintained throughout.During the tests,the samples were first placed in a vacuum for 3 h,and the coal was filled with gas(CH4)for an adsorption time of approximately 5 h.Finally,the gas valve was shut off and the coal and gas outburst was induced by quickly opening the outburst hole.The coal particles that were thrown out by the outburst test device were collected and screened based on the particle size.The results show the following.(1)Smaller particle sizes have a worse crushing effect than larger sizes.Furthermore,the well-graded coal particles are weakly broken during the outburst process.(2)As the number of repeated tests increases,the relative breakage index grows;however,the increment of growth decreases after each test,showing that further fragmentation becomes increasingly difficult.