Dynamic Behavior and Fatigue Damage Evolution of Sandstone...

Research ArticleDynamic Behavior and Fatigue Damage Evolution ofSandstone under Uniaxial Cyclic Loading

Yidan Sun Yu Yang and Min Li

School of Civil Engineering Liaoning Technical University Fuxin 123000 China

Correspondence should be addressed to Yu Yang yangyu9300163com

Received 24 October 2019 Accepted 28 March 2020 Published 16 April 2020

Academic Editor Cristina Castejon

Copyright copy 2020 Yidan Sun et al +is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

+e mechanical response characteristics of sandstone specimens under different stress amplitudes and loading frequencies weretested by a TAW-2000 rock triaxial testing machine +e characteristics of the stress-strain curve and the evolution process ofstrain damage under cyclic loading are analyzed Based on creep theory and the disturbance state concept a theoretical modelbetween the axial compressive strain axial compressive stress and cycle number is established +e results show that there existsan upper threshold value of stress in cyclic loading above which the specimen will be damaged As peak stress increases the energyloss and irreversible deformation caused by damage gradually increase When loading to an unstable peak stress under cyclicloading the fatigue damage of sandstone under cyclic loading undergoes three characteristic stages the initial stage the stablestage and the accelerated failure stage +e parameters of the strain damage model based on the disturbance state concept ofsandstone are identified by test data and the rationality of the model is validated by comparing theoretical values withexperimental measurements

1 Introduction

In addition to static loads the surrounding rock nearroadways will also be disturbed by dynamic loads such asdrilling mechanical excavation or earthquakes fromminingprocesses [1]+emechanical properties of rock under cyclicloads are very different from those under static loads and itsmechanical behavior is more complex [2 3] +erefore it isof great significance to study the dynamic behavior andfatigue damage evolution laws of rock subjected to cyclicloading in order to assess the stability of rock formationssurrounding roadways

Laboratory testing is the primary method used tounderstand rock mechanical behavior In previous decadesscholars have little researched rock mechanical responsesunder cyclic loading +ere are some studies on the dy-namic response characteristics of various types of rockunder coupled static-dynamic loading and high-stressconditions [4ndash7] and the results have revealed themechanism of deep rock burst Song et al [8] carried outcyclic loading tests on salt rock samples and determined the

fatigue life of rock salt samples under different upper andlower stresses cyclic loading speeds temperatures andconfining pressures Fan [9] further quantified the fatiguelife and deformation evolution characteristics of salt rockby subjecting it to different stress amplitudes Wang et al[10] established the constitutive equation of cumulativedeformation of rock subjected to multiple disturbances andobtained the evolution law of the surrounding rock stressfield caused by a blasting disturbance Liu et al [11] studiedthe effects of confining pressure on the mechanicalproperties and fatigue damage evolution of sandstone byusing the MTS-815 rock test system Tang et al [12] carriedout uniaxial small-amplitude high-stress cyclic disturbancetests on deep marble and established a strain damage modelunder cyclic loading Based on the energy dissipationtheory Liu et al [13] established a new damage model todescribe the behavior of siltstone and sandy mudstonesubjected to cyclic loading and calculated the damageevolution equation of siltstone and sandy mudstone Liuet al [14] carried out cyclic loading tests on marble skarnand serpentine under different stress amplitudes and

HindawiShock and VibrationVolume 2020 Article ID 1452159 9 pageshttpsdoiorg10115520201452159

analyzed the evolution law of damage variables in responseto these variations Huang [15] studied the fatigue damagecharacteristics of gypsum under cyclic loading andestablished a creep damage constitutive model of gypsumSun et al [16] analyzed the damage evolution law andaccumulation mode of sandstone subjected to cyclicloading under different confining pressures Liu et al [17]studied the creep failure characteristics of soft rock underdynamic disturbance through a self-developed rock dis-turbance and creep experimental system and established adisturbance creep constitutive model of soft rock based ona disturbance factor Zhao et al [18] found that undershort-term cyclic loading of sandstone both the residualstrain and peak strain show the ldquodecay increaserdquo andldquosteady-state increaserdquo stages with the cyclic numberN andthey used a modified Burgers model to establish the re-lationship between the strain and cyclic number N underpeak stress (tensile or compressive stress) Wang et al [19]carried out uniaxial disturbance creep tests of gneiss underdifferent disturbance amplitudes and frequencies and ob-tained the influence of disturbance load on rock creepcharacteristics

+e above research results establish rock constitutiverelationships and rock damage characteristics based on theenergy and cyclic number or reveal the mechanical char-acteristics of disturbed rock from the angle of stress am-plitude and frequency +e methods seldom use the cyclicnumber and frequency in the same constitutive equation inorder to define the law of rock strain damage

2 Test Equipment and Scheme

21 Test Equipment and Specimen Preparation +e me-chanical properties of sandstone under cyclic loading arestudied by using a TAW-2000 rock triaxial testing machine(see Figure 1) Firstly the mechanical properties of sand-stone under different stress amplitudes are studied by fixingloading frequency +en the mechanical properties of rockunder different loading frequencies are studied by fixing thestress amplitude During the test the specimens are loadedaxially to a certain value σmax and then cyclically loaded instages +e loading process is shown in Figure 2

+e sandstone samples are taken from the roadway roofwith a buried depth of 800m in the West +ird mining areaof Hongyang No 2 Mine Sujiatun District Shenyang cityLiaoning Province China +e samples are a fine sandstonewith high hardness and homogeneity with a porosity of25 In compliance with the test procedures listed by In-ternational Society of Rock Mechanics [20] the shape of alltested sandstone specimens is cylindrical with 50mm indiameter and 100mm in length approximately In order toensure the consistency of physical and mechanical prop-erties of the specimens the specimens with rough unevenor defective surfaces are not used +e specimens are thentested for their propagation velocity in response to a P waveBased on these results the testing specimens with closepropagation velocities of the P wave are selected +especimens are divided into three groups Before the test theparameters such as the diameter circumference and weight

of specimens aremeasured and the density of each specimenis calculated +e grouping and physical parameters of thespecimens are shown in Table 1

22 Test Scheme In order to study the mechanical responsecharacteristics of sandstone under different stress ampli-tudes and loading frequencies the test process is divided intothree steps +e first group is used for uniaxial compressiontests to obtain the uniaxial compressive strength of sand-stone specimens in order to choose a reasonable upper limitσmax and lower limit value σmin +en the second group isused for fatigue damage tests under different cyclic stressamplitudes at a frequency of 05Hz +e third group is usedfor fatigue damage tests under different loading frequenciesat a stress amplitude of 5MPa

+e stress-velocity control method is adopted in the test+e specimen is loaded to the upper limit of cyclic loading ata speed of 05MPas under axial compression and then thecyclic test is carried out with 1000 cycles per stage

3 Test Results and Analysis

+e uniaxial compressive strength Rc yield strength σ0elastic modulus E and Poissonrsquos ratio μ of sandstone areobtained from averaging the results from the uniaxialcompressive tests as shown in Table 2

31 Influence of Stress Amplitude on Fatigue CharacteristicsDisturbance load is transmitted as a wave in the specimenDisturbance waves can cause damage and deformation ofrock and can be divided into two main cases One is thatdisturbance waves propagate as elastic waves in which therewill be no permanent deformation nor crack propagation

Figure 1 TAW-2000 rock triaxial testing machine

Tσmin

σmax

σm

Time t

Load

(MPa

)

0

Figure 2 Cyclic disturbance loading

2 Shock and Vibration

+e other is disturbance propagation in the form of plasticwaves In this case the original cracks propagate andpenetrate creating new cracks +e plastic deformationaccumulates gradually and the specimen eventually fails

In Figure 3 it can be seen that when the upper limit stress(peak stress) is 35 or 45MPa no fatigue damage occurs inthe specimens after 1000 cycles When peak stress is 55MPathe specimen fails after 297 cycles which verifies that there isan upper limit threshold in cyclic loading If the peak stress islower than this value no matter howmany cycles are loadedthe specimen will not be destroyed +e critical stress liesbetween 45 and 55MPa in which plastic deformation andfailure will result If the peak stress is higher than 55MPa thespecimen will be destroyed in 1000 cycles or less +is showsthat the fatigue life of sandstone is reduced with peak stressesgreater than 55MPa and is unaffected by peak stresses lessthan 45MPa Further testing is required in order to find thecritical peak failure stress in cyclic loading within the rangeof 45 to 55MPa

+e stress-strain hysteresis curves of the specimensunder cyclic loading are cusp-shaped rather than oval-shaped at the place of stress inversion which indicates thatthe elastic deformation response of the specimens is fasterthan the plastic deformation response As the stress am-plitude increases the hysteretic curve moves to the rightgradually the hysteretic loop area increases gradually thetransverse spacing of a single hysteretic loop widens and theaxial strain increases +is trajectory indicates the damageaccumulated and energy dissipated with the repeatedopening and closing of a microfracture +e energy loss andirreversible deformation caused by the damage increase withan increase in stress amplitude

Figure 4 shows the relationship between the axial peakstrain and the cycle numberN Under cyclic loading between25 and 35MPa the axial peak strain increases gradually andthen reaches a relative stability value of about 077 and it is

Table 1 Parameters for different specimens tested

Groups Specimen D(mm)

L(mm)

M(g)

ρ(gmiddotcmminus3)

Averagedensity(gmiddotcmminus3)

Loading mode σmax(MPa)

σmin(MPa)

f(Hz)

Failurestrength(MPa)

Cyclenumber

1

U1 5010 9984 5203 2645 2630 Uniaxialcompression mdash mdash mdash 656 mdash

U2 4942 10002 5021 2618 Uniaxialcompression mdash mdash mdash 675 mdash


2C-A1 4884 9864 4834 2617 2620 Cyclic loading 35 25 05 mdash 1000C-A2 4910 9943 4966 2639 Cyclic loading 45 25 05 mdash 1000C-A3 4830 10020 4784 2607 Cyclic loading 55 25 05 55 297

3CndashF1 4902 1003 4998 2642 2630 Cyclic loading 45 40 05 mdash 1000CndashF2 4824 9990 4749 2602 Cyclic loading 45 40 1 mdash 1000CndashF3 4844 1002 4872 2640 Cyclic loading 45 40 2 mdash 1000

Table 2 Static parameters of sandstone

Rc (MPa) σ0 (MPa) E (GPa) μ67 50 5 018 55MPa

45MPa

35MPa

Stre

ss (M

Pa)

Stre

ss (M

Pa)

0

10

20

30

40

50

60

05 10 15 20 2500Strain ()

07 08 09 10 11 12 1306Strain ()

25

30

35

40

45

50

55

Figure 3 Stress-strain curves under different stress amplitudes

Peak

stra

in (

)

04

06

08

10

12

14

200 400 600 800 10000Cycle number

σmax = 35MPaσmax = 45MPaσmax = 55MPa

Figure 4 Peak strain evolution curve

Shock and Vibration 3

still 077 for the remaining cycles For the cyclic loadingbetween 25 and 45MPa the axial peak strain increasesgradually and then reaches a stable value of 095 followingwhich it remains unchanged When cycling between 25 and55MPa the axial strain continues to increase with cyclenumber and does not reach a stable value +e fatiguedamage of sandstone under cyclic loading between 25 and55MPa undergoes three stages the first stage is the initialstage in which the strain rate decreases gradually the secondstage is the stable stage in which the strain rate remainsrelatively unchanged and the third stage is the acceleratedstage in which the strain rate increases rapidly

32 Effect of Loading Frequency on Fatigue Characteristics ofSandstone Figure 5 shows the stress-strain curves of thespecimens at frequencies of 05Hz 1Hz and 2Hz under astress amplitude of 5MPa As loading frequency increasesthe hysteresis loops become denser which indicates that thegrowth rate of plastic deformation is decreasing graduallyAfter the 2Hz cycling the specimens are not damaged andare in a fatigue stability stage but irreversible plastic de-formation occurs after unloading

As can be seen from Figure 6 as frequency increases thestrain remains unchanged which is different from previousresearch that showed strain of salt rock and gypsum rockdecreasing with increasing frequency [9 15] Hence duringcyclic loading the specimen enters the plastic deformationstage and remains in a stable fatigue stage with increasingloading frequency However to monitor the variation ofinternal cracks in rocks it is necessary to further observeinternal cracks through electron microscopy or CT

4 Establishment of Sandstone DamageConstitutive Model under Disturbance

41 Model Selection When rocks are subjected to repeateddisturbance loads internal structural distortion and crackevolution lead to cumulative damage and irreversible plasticdeformation At present the description of damage evolu-tion is mainly based on the evolution characteristics ofdamage variable D Kachanov [21] established the rela-tionship between the creep damage variable and creep timeof brittle rock

D 1 minus 1 minust

tR

1113888 1113889

(1r+1)

(1)

where tR is the creep life and r is the parameter of rockmaterial properties

In a cyclic loading test the rock fatigue life Nf is thenumber of cycles at the time of rock failure If T is the timefor one cycle then the cycle number and loading time satisfytNT and tR NfT and then (1) can be expressed as

D 1 minus 1 minusN

Nf

1113888 1113889

(1r+1)

(2)

It can be seen that this expression for damage undercyclic loading is similar to that of creep damage and the

essence of damage variable is the same For both cases underthe action of external load over a given cycle number or timeframe rock material properties will deteriorate due to in-ternal structure distortion crack initiation and propagationand continuous energy dissipation It can be seen fromFigure 4 that the peak strain curve under cyclic loading hasthe same evolution law as that under creep loading whichalso follows the three-stage characteristics listed in Section31 Based on the above two points it is considered that thedamage failure of specimens subjected to cyclic loading isessentially the rock creep under peak stress +erefore thispaper will study the damage characteristics of sandstoneunder cyclic loading based on creep theory

In view of the disturbance of geotechnical materialsunder external loads Desai an American scholar proposed

εpεe

Stre

ss (M

Pa)

0

10

20

30

40

50

02 04 06 08 10 12 1400Axial strain ()

05HZ1HZ2HZ

Stre

ss (M

Pa)

36

38

40

42

44

46

110 115 120 125 130105Strain ()

Figure 5 Stress-strain curves under different loading frequencies

Stra

in (

)

05HZ1HZ2HZ

01 02 03 04 05 0600Time t

00

02

04

06

08

10

12

14

Figure 6 Strain-time curves under different loading frequencies


the concept of disturbed state concept (DSC) [22] +e DSCholds that material structure is composed of an undisturbedrelative-integrity state (RI state) and completely destroyedfully adjusted state (FA state) +e material structure cantransform from RI state to FA state under external force+efunction describing the transformation process betweenthese two states is called the disturbed function (D) +eexpression of their relationship is

εij (1 minus D)εiij + Dεc

ij (3)

where εij εiji and εijc are observed strain values RI strainvalues and FA strain values respectively

Based on creep theory and the disturbance state conceptthe strain damage model of sandstone under different peakstresses is established in this paper According to the straincurves of sandstone under different peak stresses thespecimen exhibits elastic deformation at the moment ofloading As the cycle number increases the specimencontinues to deform and the deformation rate graduallydecreases showing viscous characteristics +en irreversibleplastic deformation occurs ultimately rupturing the rockspecimen +erefore the selected model should contain theelastic viscous and plastic elements in order to reflect thecomplete process of strain damage evolution

(a) Sandstone in an RI state is considered to have vis-coelastic deformation under external disturbance Inorder to simplify the model and reduce the pa-rameters the Kelvin model is used to representsandstone in RI state +e equation is as follows

ε σE1

1 minus eminus E1η1( )t( )1113874 1113875 (4)

where E1 and η1 are elastic fatigue coefficient andviscous coefficient of the Kelvin body respectively

(b) After entering FA state the material in RI stateencloses and restricts the material in FA state duringdeformation which locally hardens the material inFA state However after continuous disturbance thespecimen eventually breaks down so it can berepresented by a model with a critical state Huang[15] considered that the sudden change of fatiguerate will be triggered if the disturbance force exceedsa certain critical value A nonlinear disturbancecreep element (NDCE) is introduced (see Figure 7)+e nonlinear disturbance creep element satisfies

σ minus σs η3

tnminus1 middotdεdt

1113888 1113889

m

σ gt σs (5)

where η3 is viscous coefficient of the nonlinear claybody n is rheological coefficient t is rheological timem is the parameter of rock property (0lemle 1) and σsis threshold stress which is considered as yieldstrengthWhen ε (0) 0 (5) can be transformed using theseparation of variables method such that

ε(t) σ minus σs

η31113888 1113889

(1m)m

m + n minus 1t(m+nminus 1m)

σ gt σs (6)

+e FA state model is obtained by connecting theNDCE in series with the traditional Maxwell creepmodel (see Figure 8)+e state equation of the improved Maxwell model

σ1 E2ε1

σ2 η2 _ε2

σ3 σs +η3


1113888 1113889

m

σ σ1 σ2 σ3

ε ε1 + ε2 + ε3

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(7)

Combining (6) and (7) we obtain the disturbancemodel

ε

σE2

+ση2

t σ gt σs( 1113857

σE2

+ση2

t +σ1 minus σs

η31113888 1113889

(1m)m


σ gt σs( 1113857

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(8)

where E2 and η2 are elastic fatigue coefficient andviscous coefficient of the Maxwell body respectively

(c) According to Guo [23] the disturbance function D isa function with plastic cumulative strain value εp asan independent variable Assuming that the distur-bance function D is in the form of a Weibullfunction we obtain

D D εp( 1113857 Du 1 minus exp minusαεp

( 1113857β

1113876 11138771113882 1113883 (9)

where α and β are the scale and shape parameters ofrocks Du is the disturbance limit 0 leDule 1 and Du 1generally and εp is the plastic cumulative strain value+e total strain can be divided into two parts elasticstrain and plastic strain According to the Man-sonndashCoffin empirical formula [24 25] the total strain isexpressed using the cycle number and loading fre-quency as

σs

η3 n

σ σ

Figure 7 Nonlinear disturbance creep element


ε εe+ εp

c1 Nfk1minus 1

1113872 1113873minus β1

+ c2 Nfk2minus 1

1113872 1113873minus β2

(10)

where f is loading frequency c1 c2 k1 k2 β1 and β2 arematerial constants εe and εp are the elastic strain andplastic strain respectively and N is cycle numberHence the relationship between loading frequency andplastic strain εp is as follows

εp c2 Nf

k2minus 11113872 1113873

minus β2 (11)

(d) +e cycle number and loading time satisfy tNTCombining Equations (3) (4) (8) (9) and (11) wecan obtain the expression of one-dimensionalsandstone strain damage

ε(N)

1 minus eminus ANminusBfC( )1113960 1113961 middotσE1

1 minus eminus E1η1( )NT( )1113874 11138751113890 1113891 + eminus ANminusBfC( ) middot

σE2

+ση2

NT1113890 1113891 σ lt σs( 1113857



σE2

+ση2

NT +σ minus σs

η31113888 1113889

(1m)(NT)G

G⎡⎣ ⎤⎦ σ gt σs( 1113857

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

A α middot c2( 1113857β

B β middot β2

C 1 minus k2( 1113857 middot β middot β2

G m + n minus 1

m1113874 1113875

(12)

where σ is stress ε is strain N is cycle number f isloading frequency T is loading period T1f σs isthreshold stress which is considered as yield strengthE1 and E2 are elastic fatigue coefficients of the Kelvinbody and Maxwell body respectively η1 and η2 areviscous coefficients of the Kelvin body and Maxwellbody respectively η3 is viscous coefficient of thenonlinear clay body and A B C G are materialconstants related to c1 c2 k1 k2 β1 and β2+e modified strain damage model of sandstone isshown in Figure 9

42 Parameter Identification of Model According to thepeak strain of sandstone under uniaxial cyclic loading thestrain damage equation is fitted using Origin software and

the least squares principle and the parameters of the straindamage model are obtained as shown in Table 3 Whencycling to a peak stress of 55MPa both E2 and η2 in theMaxwell body increase significantly which may be due tothe hardening of the specimen before failure

+e strain damage model of sandstone based on theconcept of a disturbance state is compared with the ex-perimental results as shown in Figure 10 +e experimentalresults under different stress amplitudes are represented bysymbols of different shapes and the theoretical calculatedvalues are expressed by solid lines +e derived constitutivemodel is in good agreement with the experimental resultsand reflects the characteristic three stages of sandstonedamage failure under cyclic loading which verifies thepresented strain damage model of sandstone based ondisturbance state

σ σσs

η3 nη2E2

ε2ε1 ε3

Figure 8 Improved Maxwell model


Figure 11 shows the variation of the strain damage curvewith rheological coefficient n when the peak stress is fixed at55MPa +e acceleration phenomenon becomes more andmore obvious as coefficient n increases +e change of nmainly affects the accelerated failure stage and has nomeasurable effect on the first and second stages of strainevolution +is shows that the nonlinear clay body cansimulate the accelerated damage stage of sandstone well andverify the rationality of the model

Figure 12 shows the variation curve of disturbancefunction D with the cycle number under different peakstresses When the peak stress is 35 or 45MPa the slope ofthe curve increases gradually with 35MPa showing asharper initial slope increase in early cyclesWhile cycling upto 1000 cycles the disturbance function value tends to bestable and less than 1 for both cases which indicates that thespecimens were not damaged +is is similar to the variationrule of the peak strain curve When peak stress increases to

D

Maxwell NDCE

1 ndash D

Kelvin

σ σE1

E2η2

η1

σs

η3 n

Figure 9 Strain damage model of sandstone

Table 3 Strain damage model parameters of sandstone under disturbance state concept

σmax (MPa)Model parameter Fitting effect

A B C E1 (MPa) E2 (MPa) η1 (MPamiddotN) η2 (MPamiddotN) η3 (MPamiddotN) n m R2

35 074 036 031 4510 5217 642 6199851 099245 009 069 060 4639 5695 382 7031199 099155 8400 004 946 1255 2193055 228 2866247 510 89 057 0962

Stra

in (

)

06

08

10

12

14

200 400 600 800 10000Cycle number

35MPa45MPa

55MPaTheoretical curve

Figure 10 Comparison of strain damage model values with testcurves

Peak

stra

in (

)

09

10

11

12

13

14

100 200 300 400 5000Cycle number

n = 2n = 1

n = 4n = 3

Figure 11 Influence of rheological parameter n on the mode

Dist

urba

nce f

unct

ion

D

00

02

04

06

08

10

100 200 300 400 500 600 700 800 900 10000Cycle number

35MPa45MPa55MPa

Figure 12 Change curve of disturbance function


55MPa the second derivate of the slope is initially positivebefore inverting around 150 cycles For this case D con-tinues to sharply increase until reaching a value of 1 at 297cycles when the rupture of the rock specimen takes place+e 55MPa peak stress cycling process reflects the trans-formation from RI state to FA state controlled by thedisturbance function

5 Conclusion

(1) +ere exists an upper threshold value for the axialstress of sandstone under cyclic loading When theloading frequency is constant with the increase ofstress amplitude the area of hysteresis loop increasesgradually the transverse spacing of a single hys-teresis curve widens and the energy loss and irre-versible deformation of rock caused by damageincrease gradually When the stress amplitude isconstant (mean stress value of 425MPa and am-plitude of 5MPa) an increase in loading frequencydid not change the axial strain

(2) +e unstable fatigue damage of sandstone subjectedto cyclic loading generally goes through three stagesthe initial stage in which the strain rate decreasesgradually the stable stage in which the strain rateremains unchanged and the accelerated failure stagein which the strain rate increases rapidly

(3) On the basis of creep theory and the disturbance stateconcept a strain damage model of sandstone isestablished +e parameters of the model are solvedbyOrigin software+e rationality and correctness ofthe strain damage model are validated by comparingthe calculated results with the experimental data

Data Availability

+e test data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is study was supported by the National Key RampD Programof China (grant no 2018YFC0604705) National NaturalScience Foundation of China (grant no 51774167) andScience and Technology Innovation Leading Talent Projectof Liaoning Province (grant no XLYC1802063)

References

[1] A Taheri A Royle Z Yang and Y Zhou ldquoStudy on vari-ations of peak strength of a sandstone during cyclic loadingrdquoGeomechanics and Geophysics for Geo-Energy and Geo-Re-sources vol 2 pp 1ndash10 2016

[2] G-L Feng X-T Feng B-R Chen and Y-X Xiao ldquoMi-croseismic sequences associated with rockbursts in the tun-nels of the Jinping II hydropower stationrdquo International

Journal of Rock Mechanics and Mining Sciences vol 80pp 89ndash100 2015

[3] A Momeni M Karakus G R Khanlari and M HeidarildquoEffects of cyclic loading on the mechanical properties of agraniterdquo International Journal of Rock Mechanics and MiningSciences vol 77 pp 89ndash96 2015

[4] X Li Z Zhou T-S Lok L Hong and T Yin ldquoInnovativetesting technique of rock subjected to coupled static anddynamic loadsrdquo International Journal of Rock Mechanics andMining Sciences vol 45 no 5 pp 739ndash748 2008

[5] F J Zhao X B Li and T Feng ldquoResearch on experiments ofbrittle rock fragmentation by combined dynamic and staticloadsrdquo Rock and Soil Mechanics vol 2005 no 7 pp 1038ndash1042 2005

[6] Y J Zuo X B Li C A Tang Y P Zhang C D Ma andC B Yan ldquoExperimental investigation on failure of rocksubjected to 2D dynamic-static coupling loadingrdquo ChineseJournal of Rock Mechanics and Engineering vol 2006 no 9pp 1809ndash1820 2006

[7] Y-j Zuo X-b Li Z-l Zhou C-d Ma Y-p Zhang andW-h Wang ldquoDamage and failure rule of rock undergoinguniaxial compressive load and dynamic loadrdquo Journal ofCentral South University of Technology vol 12 no 6pp 742ndash748 2005

[8] R Song B Yue-ming Z Jing-Peng J De-yi and Y Chun-heldquoExperimental investigation of the fatigue properties of saltrockrdquo International Journal of Rock Mechanics and MiningSciences vol 64 pp 68ndash72 2013

[9] J Y Fan Fatigue damage and dilatancy properties for salt rockunder discontinuous cyclic loading PhD thesis ChongqingUniversity Chongqing China 2017

[10] B Wang Y F Gao and J Wang ldquoEvolution law analysis onsurrounding rock stress field by rheology disturbed effectsrdquoJournal of China Coal Society vol 35 no 9 pp 1446ndash14502010

[11] E Liu and S He ldquoEffects of cyclic dynamic loading on themechanical properties of intact rock samples under confiningpressure conditionsrdquo Engineering Geology vol 125 pp 81ndash912012

[12] L Z Tang J L Wu T Liu J Zhu and J B Shu ldquoMechanicalexperiments of marble under high stress and cyclic dynamicdisturbance of small amplituderdquo Journal Of Central SouthUniversity (Science And Technology) vol 45 no 12pp 4300ndash4307 2014

[13] X S Liu J G Ning Y L Tan and Q H Gu ldquoDamageconstitutive model based on energy dissipation for intact rocksubjected to cyclic loadingrdquo International Journal of RockMechanics and Mining Sciences vol 85 pp 27ndash32 2016

[14] T Liu P Yang W S Lv and K Du ldquoRock mechanicalproperties experiments with low-frequency circulation dis-turbance under different stress amplitudesrdquo Journal of ChinaCoal Society vol 42 no 9 pp 2280ndash2286 2017

[15] X Huang ldquoFatigue damage characteristics and constitutivemodel of gypsum rock under cyclic loadingrdquo Master thesisChangrsquoan University Xirsquoan China 2017

[16] B Sun Z Zhu C Shi and Z Luo ldquoDynamic mechanicalbehavior and fatigue damage evolution of sandstone undercyclic loadingrdquo International Journal of Rock Mechanics andMining Sciences vol 94 pp 82ndash89 2017

[17] F Liu Y J Yu L Z Cao W Zhang and G N ZhangldquoConstitutive model of soft rock disturbance creep based ondisturbance factorrdquo Journal of China Coal Society vol 43no 10 pp 2758ndash2764 2018


[18] B Y Zhao D Y Liu and W Liu ldquoMechanical behavior ofsandstone under uniaxial constant cyclical compressive andtensile loadingrdquo Arabian Journal of Geosciences vol 11no 17 p 490 2018

[19] J G Wang B Liang and P J Yang ldquoCreep experiment andnonlinear disturbance creep model of gneiss under dynamicand static loadsrdquo Journal of China Coal Society vol 44 no 1pp 192ndash198 2019

[20] ISRM ldquoSuggested methods for determining the strength ofrock material in triaxial compressionrdquo International Journalof Rock Mechanics and Mining Sciences and GeomechanicsAbstracts vol 15 no 2 pp 47ndash51 1978

[21] M Kachanov ldquoEffective elastic properties of cracked solidscritical review of some basic conceptsrdquo Applied MechanicsReviews vol 45 no 8 pp 304ndash335 1992

[22] C S Desai and A Gens ldquoMechanics of materials and in-terfaces the disturbed state conceptrdquo Journal of ElectronicPackaging vol 123 no 4 p 406 2001

[23] Z K Guo ldquoStudy on models and solution of fem basicformulation of theory of duality disturbancerdquo Master thesisShenyang Jianzhu University Shengyang China 2011

[24] L F Coffin ldquo+e effect of frequency on the cyclic strain andlow cycle fatigue behavior of cast Udimet 500 at elevatedtemperaturerdquo Metallurgical and Materials Transactions Bvol 2 no 11 pp 3105ndash3113 1971

[25] Y Wang L Ma P Fan and Y Chen ldquoA fatigue damagemodel for rock salt considering the effects of loading fre-quency and amplituderdquo International Journal of MiningScience and Technology vol 26 no 5 pp 955ndash958 2016


analyzed the evolution law of damage variables in responseto these variations Huang [15] studied the fatigue damagecharacteristics of gypsum under cyclic loading andestablished a creep damage constitutive model of gypsumSun et al [16] analyzed the damage evolution law andaccumulation mode of sandstone subjected to cyclicloading under different confining pressures Liu et al [17]studied the creep failure characteristics of soft rock underdynamic disturbance through a self-developed rock dis-turbance and creep experimental system and established adisturbance creep constitutive model of soft rock based ona disturbance factor Zhao et al [18] found that undershort-term cyclic loading of sandstone both the residualstrain and peak strain show the ldquodecay increaserdquo andldquosteady-state increaserdquo stages with the cyclic numberN andthey used a modified Burgers model to establish the re-lationship between the strain and cyclic number N underpeak stress (tensile or compressive stress) Wang et al [19]carried out uniaxial disturbance creep tests of gneiss underdifferent disturbance amplitudes and frequencies and ob-tained the influence of disturbance load on rock creepcharacteristics

+e above research results establish rock constitutiverelationships and rock damage characteristics based on theenergy and cyclic number or reveal the mechanical char-acteristics of disturbed rock from the angle of stress am-plitude and frequency +e methods seldom use the cyclicnumber and frequency in the same constitutive equation inorder to define the law of rock strain damage

2 Test Equipment and Scheme

21 Test Equipment and Specimen Preparation +e me-chanical properties of sandstone under cyclic loading arestudied by using a TAW-2000 rock triaxial testing machine(see Figure 1) Firstly the mechanical properties of sand-stone under different stress amplitudes are studied by fixingloading frequency +en the mechanical properties of rockunder different loading frequencies are studied by fixing thestress amplitude During the test the specimens are loadedaxially to a certain value σmax and then cyclically loaded instages +e loading process is shown in Figure 2

+e sandstone samples are taken from the roadway roofwith a buried depth of 800m in the West +ird mining areaof Hongyang No 2 Mine Sujiatun District Shenyang cityLiaoning Province China +e samples are a fine sandstonewith high hardness and homogeneity with a porosity of25 In compliance with the test procedures listed by In-ternational Society of Rock Mechanics [20] the shape of alltested sandstone specimens is cylindrical with 50mm indiameter and 100mm in length approximately In order toensure the consistency of physical and mechanical prop-erties of the specimens the specimens with rough unevenor defective surfaces are not used +e specimens are thentested for their propagation velocity in response to a P waveBased on these results the testing specimens with closepropagation velocities of the P wave are selected +especimens are divided into three groups Before the test theparameters such as the diameter circumference and weight

of specimens aremeasured and the density of each specimenis calculated +e grouping and physical parameters of thespecimens are shown in Table 1

22 Test Scheme In order to study the mechanical responsecharacteristics of sandstone under different stress ampli-tudes and loading frequencies the test process is divided intothree steps +e first group is used for uniaxial compressiontests to obtain the uniaxial compressive strength of sand-stone specimens in order to choose a reasonable upper limitσmax and lower limit value σmin +en the second group isused for fatigue damage tests under different cyclic stressamplitudes at a frequency of 05Hz +e third group is usedfor fatigue damage tests under different loading frequenciesat a stress amplitude of 5MPa

+e stress-velocity control method is adopted in the test+e specimen is loaded to the upper limit of cyclic loading ata speed of 05MPas under axial compression and then thecyclic test is carried out with 1000 cycles per stage

3 Test Results and Analysis

+e uniaxial compressive strength Rc yield strength σ0elastic modulus E and Poissonrsquos ratio μ of sandstone areobtained from averaging the results from the uniaxialcompressive tests as shown in Table 2

31 Influence of Stress Amplitude on Fatigue CharacteristicsDisturbance load is transmitted as a wave in the specimenDisturbance waves can cause damage and deformation ofrock and can be divided into two main cases One is thatdisturbance waves propagate as elastic waves in which therewill be no permanent deformation nor crack propagation

Figure 1 TAW-2000 rock triaxial testing machine

Tσmin

σmax

σm

Time t

Load

(MPa

)

0

Figure 2 Cyclic disturbance loading








L(mm)

M(g)

ρ(gmiddotcmminus3)



σmin(MPa)

f(Hz)


Cyclenumber

1








45MPa

35MPa

Stre

ss (M

Pa)

Stre

ss (M

Pa)

0

10

20

30

40

50

60

05 10 15 20 2500Strain ()

07 08 09 10 11 12 1306Strain ()

25

30

35

40

45

50

55


Peak

stra

in (

)

04

06

08

10

12

14

200 400 600 800 10000Cycle number









D 1 minus 1 minust

tR

1113888 1113889

(1r+1)

(1)



D 1 minus 1 minusN

Nf

1113888 1113889

(1r+1)

(2)




εpεe

Stre

ss (M

Pa)

0

10

20

30

40

50

02 04 06 08 10 12 1400Axial strain ()

05HZ1HZ2HZ

Stre

ss (M

Pa)

36

38

40

42

44

46

110 115 120 125 130105Strain ()


Stra

in (

)

05HZ1HZ2HZ

01 02 03 04 05 0600Time t

00

02

04

06

08

10

12

14





ij (3)




ε σE1

1 minus eminus E1η1( )t( )1113874 1113875 (4)



σ minus σs η3


1113888 1113889

m

σ gt σs (5)


ε(t) σ minus σs

η31113888 1113889

(1m)m


σ gt σs (6)


σ1 E2ε1

σ2 η2 _ε2

σ3 σs +η3


1113888 1113889

m

σ σ1 σ2 σ3

ε ε1 + ε2 + ε3

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(7)


ε

σE2

+ση2

t σ gt σs( 1113857

σE2

+ση2

t +σ1 minus σs

η31113888 1113889

(1m)m


σ gt σs( 1113857

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(8)




( 1113857β

1113876 11138771113882 1113883 (9)


σs

η3 n

σ σ



ε εe+ εp

c1 Nfk1minus 1

1113872 1113873minus β1

+ c2 Nfk2minus 1

1113872 1113873minus β2

(10)


εp c2 Nf

k2minus 11113872 1113873

minus β2 (11)


ε(N)



σE2

+ση2

NT1113890 1113891 σ lt σs( 1113857



σE2

+ση2

NT +σ minus σs

η31113888 1113889

(1m)(NT)G

G⎡⎣ ⎤⎦ σ gt σs( 1113857

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩


B β middot β2


G m + n minus 1

m1113874 1113875

(12)





σ σσs

η3 nη2E2

ε2ε1 ε3





D

Maxwell NDCE

1 ndash D

Kelvin

σ σE1

E2η2

η1

σs

η3 n





35 074 036 031 4510 5217 642 6199851 099245 009 069 060 4639 5695 382 7031199 099155 8400 004 946 1255 2193055 228 2866247 510 89 057 0962

Stra

in (

)

06

08

10

12

14

200 400 600 800 10000Cycle number

35MPa45MPa



Peak

stra

in (

)

09

10

11

12

13

14

100 200 300 400 5000Cycle number

n = 2n = 1

n = 4n = 3


Dist

urba

nce f

unct

ion

D

00

02

04

06

08

10

100 200 300 400 500 600 700 800 900 10000Cycle number

35MPa45MPa55MPa




5 Conclusion




Data Availability




Acknowledgments


References



































L(mm)

M(g)

ρ(gmiddotcmminus3)



σmin(MPa)

f(Hz)


Cyclenumber

1








45MPa

35MPa

Stre

ss (M

Pa)

Stre

ss (M

Pa)

0

10

20

30

40

50

60

05 10 15 20 2500Strain ()

07 08 09 10 11 12 1306Strain ()

25

30

35

40

45

50

55


Peak

stra

in (

)

04

06

08

10

12

14

200 400 600 800 10000Cycle number









D 1 minus 1 minust

tR

1113888 1113889

(1r+1)

(1)



D 1 minus 1 minusN

Nf

1113888 1113889

(1r+1)

(2)




εpεe

Stre

ss (M

Pa)

0

10

20

30

40

50

02 04 06 08 10 12 1400Axial strain ()

05HZ1HZ2HZ

Stre

ss (M

Pa)

36

38

40

42

44

46

110 115 120 125 130105Strain ()


Stra

in (

)

05HZ1HZ2HZ

01 02 03 04 05 0600Time t

00

02

04

06

08

10

12

14





ij (3)




ε σE1

1 minus eminus E1η1( )t( )1113874 1113875 (4)



σ minus σs η3


1113888 1113889

m

σ gt σs (5)


ε(t) σ minus σs

η31113888 1113889

(1m)m


σ gt σs (6)


σ1 E2ε1

σ2 η2 _ε2

σ3 σs +η3


1113888 1113889

m

σ σ1 σ2 σ3

ε ε1 + ε2 + ε3

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(7)


ε

σE2

+ση2

t σ gt σs( 1113857

σE2

+ση2

t +σ1 minus σs

η31113888 1113889

(1m)m


σ gt σs( 1113857

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(8)




( 1113857β

1113876 11138771113882 1113883 (9)


σs

η3 n

σ σ



ε εe+ εp

c1 Nfk1minus 1

1113872 1113873minus β1

+ c2 Nfk2minus 1

1113872 1113873minus β2

(10)


εp c2 Nf

k2minus 11113872 1113873

minus β2 (11)


ε(N)



σE2

+ση2

NT1113890 1113891 σ lt σs( 1113857



σE2

+ση2

NT +σ minus σs

η31113888 1113889

(1m)(NT)G

G⎡⎣ ⎤⎦ σ gt σs( 1113857

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩


B β middot β2


G m + n minus 1

m1113874 1113875

(12)





σ σσs

η3 nη2E2

ε2ε1 ε3





D

Maxwell NDCE

1 ndash D

Kelvin

σ σE1

E2η2

η1

σs

η3 n





35 074 036 031 4510 5217 642 6199851 099245 009 069 060 4639 5695 382 7031199 099155 8400 004 946 1255 2193055 228 2866247 510 89 057 0962

Stra

in (

)

06

08

10

12

14

200 400 600 800 10000Cycle number

35MPa45MPa



Peak

stra

in (

)

09

10

11

12

13

14

100 200 300 400 5000Cycle number

n = 2n = 1

n = 4n = 3


Dist

urba

nce f

unct

ion

D

00

02

04

06

08

10

100 200 300 400 500 600 700 800 900 10000Cycle number

35MPa45MPa55MPa




5 Conclusion




Data Availability




Acknowledgments


References


































D 1 minus 1 minust

tR

1113888 1113889

(1r+1)

(1)



D 1 minus 1 minusN

Nf

1113888 1113889

(1r+1)

(2)




εpεe

Stre

ss (M

Pa)

0

10

20

30

40

50

02 04 06 08 10 12 1400Axial strain ()

05HZ1HZ2HZ

Stre

ss (M

Pa)

36

38

40

42

44

46

110 115 120 125 130105Strain ()


Stra

in (

)

05HZ1HZ2HZ

01 02 03 04 05 0600Time t

00

02

04

06

08

10

12

14





ij (3)




ε σE1

1 minus eminus E1η1( )t( )1113874 1113875 (4)



σ minus σs η3


1113888 1113889

m

σ gt σs (5)


ε(t) σ minus σs

η31113888 1113889

(1m)m


σ gt σs (6)


σ1 E2ε1

σ2 η2 _ε2

σ3 σs +η3


1113888 1113889

m

σ σ1 σ2 σ3

ε ε1 + ε2 + ε3

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(7)


ε

σE2

+ση2

t σ gt σs( 1113857

σE2

+ση2

t +σ1 minus σs

η31113888 1113889

(1m)m


σ gt σs( 1113857

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(8)




( 1113857β

1113876 11138771113882 1113883 (9)


σs

η3 n

σ σ



ε εe+ εp

c1 Nfk1minus 1

1113872 1113873minus β1

+ c2 Nfk2minus 1

1113872 1113873minus β2

(10)


εp c2 Nf

k2minus 11113872 1113873

minus β2 (11)


ε(N)



σE2

+ση2

NT1113890 1113891 σ lt σs( 1113857



σE2

+ση2

NT +σ minus σs

η31113888 1113889

(1m)(NT)G

G⎡⎣ ⎤⎦ σ gt σs( 1113857

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩


B β middot β2


G m + n minus 1

m1113874 1113875

(12)





σ σσs

η3 nη2E2

ε2ε1 ε3





D

Maxwell NDCE

1 ndash D

Kelvin

σ σE1

E2η2

η1

σs

η3 n





35 074 036 031 4510 5217 642 6199851 099245 009 069 060 4639 5695 382 7031199 099155 8400 004 946 1255 2193055 228 2866247 510 89 057 0962

Stra

in (

)

06

08

10

12

14

200 400 600 800 10000Cycle number

35MPa45MPa



Peak

stra

in (

)

09

10

11

12

13

14

100 200 300 400 5000Cycle number

n = 2n = 1

n = 4n = 3


Dist

urba

nce f

unct

ion

D

00

02

04

06

08

10

100 200 300 400 500 600 700 800 900 10000Cycle number

35MPa45MPa55MPa




5 Conclusion




Data Availability




Acknowledgments


References































ij (3)




ε σE1

1 minus eminus E1η1( )t( )1113874 1113875 (4)



σ minus σs η3


1113888 1113889

m

σ gt σs (5)


ε(t) σ minus σs

η31113888 1113889

(1m)m


σ gt σs (6)


σ1 E2ε1

σ2 η2 _ε2

σ3 σs +η3


1113888 1113889

m

σ σ1 σ2 σ3

ε ε1 + ε2 + ε3

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(7)


ε

σE2

+ση2

t σ gt σs( 1113857

σE2

+ση2

t +σ1 minus σs

η31113888 1113889

(1m)m


σ gt σs( 1113857

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(8)




( 1113857β

1113876 11138771113882 1113883 (9)


σs

η3 n

σ σ



ε εe+ εp

c1 Nfk1minus 1

1113872 1113873minus β1

+ c2 Nfk2minus 1

1113872 1113873minus β2

(10)


εp c2 Nf

k2minus 11113872 1113873

minus β2 (11)


ε(N)



σE2

+ση2

NT1113890 1113891 σ lt σs( 1113857



σE2

+ση2

NT +σ minus σs

η31113888 1113889

(1m)(NT)G

G⎡⎣ ⎤⎦ σ gt σs( 1113857

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩


B β middot β2


G m + n minus 1

m1113874 1113875

(12)





σ σσs

η3 nη2E2

ε2ε1 ε3





D

Maxwell NDCE

1 ndash D

Kelvin

σ σE1

E2η2

η1

σs

η3 n





35 074 036 031 4510 5217 642 6199851 099245 009 069 060 4639 5695 382 7031199 099155 8400 004 946 1255 2193055 228 2866247 510 89 057 0962

Stra

in (

)

06

08

10

12

14

200 400 600 800 10000Cycle number

35MPa45MPa



Peak

stra

in (

)

09

10

11

12

13

14

100 200 300 400 5000Cycle number

n = 2n = 1

n = 4n = 3


Dist

urba

nce f

unct

ion

D

00

02

04

06

08

10

100 200 300 400 500 600 700 800 900 10000Cycle number

35MPa45MPa55MPa




5 Conclusion




Data Availability




Acknowledgments


References





























ε εe+ εp

c1 Nfk1minus 1

1113872 1113873minus β1

+ c2 Nfk2minus 1

1113872 1113873minus β2

(10)


εp c2 Nf

k2minus 11113872 1113873

minus β2 (11)


ε(N)



σE2

+ση2

NT1113890 1113891 σ lt σs( 1113857



σE2

+ση2

NT +σ minus σs

η31113888 1113889

(1m)(NT)G

G⎡⎣ ⎤⎦ σ gt σs( 1113857

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩


B β middot β2


G m + n minus 1

m1113874 1113875

(12)





σ σσs

η3 nη2E2

ε2ε1 ε3





D

Maxwell NDCE

1 ndash D

Kelvin

σ σE1

E2η2

η1

σs

η3 n





35 074 036 031 4510 5217 642 6199851 099245 009 069 060 4639 5695 382 7031199 099155 8400 004 946 1255 2193055 228 2866247 510 89 057 0962

Stra

in (

)

06

08

10

12

14

200 400 600 800 10000Cycle number

35MPa45MPa



Peak

stra

in (

)

09

10

11

12

13

14

100 200 300 400 5000Cycle number

n = 2n = 1

n = 4n = 3


Dist

urba

nce f

unct

ion

D

00

02

04

06

08

10

100 200 300 400 500 600 700 800 900 10000Cycle number

35MPa45MPa55MPa




5 Conclusion




Data Availability




Acknowledgments


References































D

Maxwell NDCE

1 ndash D

Kelvin

σ σE1

E2η2

η1

σs

η3 n





35 074 036 031 4510 5217 642 6199851 099245 009 069 060 4639 5695 382 7031199 099155 8400 004 946 1255 2193055 228 2866247 510 89 057 0962

Stra

in (

)

06

08

10

12

14

200 400 600 800 10000Cycle number

35MPa45MPa



Peak

stra

in (

)

09

10

11

12

13

14

100 200 300 400 5000Cycle number

n = 2n = 1

n = 4n = 3


Dist

urba

nce f

unct

ion

D

00

02

04

06

08

10

100 200 300 400 500 600 700 800 900 10000Cycle number

35MPa45MPa55MPa




5 Conclusion




Data Availability




Acknowledgments


References






























5 Conclusion




Data Availability




Acknowledgments


References





























Dynamic Behavior and Fatigue Damage Evolution of Sandstone...

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Transcript of Dynamic Behavior and Fatigue Damage Evolution of Sandstone...