Research ArticleAnalysis of the Dynamic Impact Mechanical Characteristics ofPrestressed Saturated Fractured Coal and Rock

Wen Wang 123 Shiwei Zhang1 Huamin Li13 Shuang Gong1 and Zhumeng Liu1

1School of Energy Science Engineering Henan Polytechnic University Jiaozuo 454003 China2Shanxi Coal Import and Export Group CoLtd Taiyuan Shanxi 030006 China3Collaborative Innovation Center of Coal Work Safety Henan 454003 China

Correspondence should be addressed to Wen Wang wwang306foxmailcom

Received 10 May 2018 Revised 25 August 2018 Accepted 9 December 2018 Published 1 January 2019

Guest Editor Gaofeng Zhao

Copyright copy 2019 Wen Wang 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 natural and water-saturated states of coal samples under static and static-dynamic loads were tested using the Split-Hopkinson pressure bar (SHPB) method and RMT-150 system respectively -e differences in the strength reduction coefficientand elastic modulus reduction coefficient of water-saturated coal samples under static and static-dynamic loads were discussed-e experimental results for coal were compared with the corresponding characteristics of typical sandstone samples under staticand static-dynamic loads Furthermore a fracture model of a hydrous wing branch fracture under static-dynamic loading wasestablished based on the theory of fracture damage mechanics -e difference in dynamic strength between coal and sandstonesamples for both the natural state and water-saturated state was analyzed On this basis the effect of water on the fracture surfaceof coal and the tensile strength and shear strength of the branch fracture surface were fully considered In addition criteria of thebranch fracture surface for crack initiation and crack arrest were also established Finally the phenomenon of increasing elasticmodulus in saturated coal samples was explained with this criterion

1 Introduction

Coal is a heterogeneous natural medium that contains a largenumber of pores and microcracks In the water-saturatedstate the large amount of free water in the pores andfractures of coal has an important influence on its physicalchemical and mechanical properties Owing to rock-waterchemical interactions and the impact of pore water pressurethe decrease in stored water and reduction of the strength ofcoal rockmaterials under the condition of static loading is anindisputable fact in geologic engineering [1ndash3] Howeverowing to differences in the properties and internal structureof coal and rockmaterials under dynamic loads the dynamicstrength of a water-saturated coal specimen can exhibiteither strengthening or weakening compared to the naturalstate specimen Pu and Ma [4 5] analyzed Split-Hopkinsonpressure bar (SHPB) experimental results for sandstone in acoalmine with different moisture contents and concludedthat the dynamic uniaxial compressive strength of sandstone

increased as a power function with increasing moisturecontent of the specimens Wang et al [6 7] carried outstatic-dynamic load experiments on coal specimens withdifferent moisture contents using the improved SHPBmethod and the RMT-150 test system -ey found that thedynamic peak strength of the coal specimens decreases withincreasing water-saturation time under static-dynamic loads(intermediate strain rate) Ding et al [8] performed dynamicexperiments on clay with four different moisture contentsusing the SHPBmethod-e results showed that the uniaxialcompressive strength of the specimens gradually decreasedwith increasing moisture content and the water in thesurface of unsaturated clay has a significant effect on itsmechanical properties Ding et al [9] studied the effect offree water content on the dynamic mechanical properties ofcement mortar under high strain rates and determined thatthe dynamic compressive strength of cement mortar de-creases with increasing water content -e dynamic com-pressive strength of saturated cement mortar specimens was

HindawiAdvances in Civil EngineeringVolume 2019 Article ID 5125923 10 pageshttpsdoiorg10115520195125923

23 lower than that of completely dry cement mortarspecimens Dynamic impact tests of argillaceous siltstonewere conducted by Zhan and Zhang [10] Zhao et al [11]studied the saturated specimens have stronger loading ratedependence than the dry specimens Saturated coal speci-mens have higher indirect tensile strength than dry onesPetrov et al [12] discovered that the temporal dependence ofthe dynamic compressive and split tensile strengths of dryand saturated limestone samples can be predicted by theincubation time criterion

-e results showed that the peak strength of specimensdecreases with increasing water content It can be seen thatunder the intermediate strain rates the dynamic strength ofdifferent coal and rock materials varies from the natural towater-saturated state However this difference is difficult toexplain from macroscopic mechanics experiments or the-oretical analyses Furthermore coal and rock are made up ofmany types of mineral grains -ere are many fractures andmicrostructures between these grains which will expandunder water-rock interaction particularly for low strengthmaterials

At present the mechanism for strength improvementof water-saturated coal and rock specimens has beendiscussed under dynamic impact However the mecha-nism for coal and rock strength reduction and the criteriafor coal and rock strength reduction and improvementhave not been addressed -e study of the mesomechanicalproperties of saturated rock under dynamic impact istypically based on fracture mechanics -e mesostructureof water-saturated rock was analyzed by using a micro-fracture model [13] During the analysis the effect ofvarying stress on the main fracture surface is primarilyconsidered At the same time the hydration corrosion ofcoal materials and stress distribution at the branch fracturesurface which have a significant impact on water-saturated low strength materials are rarely taken intoaccount -erefore integrating the above factors for coalmaterials analyses of the strength properties of water-saturated coal and rock under static-dynamic loads havetheoretical and practical significance

2 Methods

21 Testing Equipment -e tests include two loadingmodels static load and static-dynamic load-e static load iscarried out on a RMT-150 rock mechanics test systemwhich uses a displacement sensor (range 5mm) andpressure sensors measure axial deformation and axialloading respectively -e loading process is displacement-controlled and the load speed is 0002mms -e static-dynamic load test is conducted with amodified SHPB testingsystem as shown in Figure 1 [14 15] -is system uses half-sine stress wave loading

In these experiments the features of a one-dimensionalelastic wave are invariant as it propagates in a slender rod-e stress strain and strain rate of the specimen are cal-culated from the voltage values measured by a strain gaugeon the pressure bar -e relationships can be expressed bythe following equation

σ(t) AeEe

2AsεI(t) + εR(t) + εT(t)1113858 1113859

ε(t) Ce

Ls1113946

t

0εI(t)minus εR(t)minus εT(t)( 1113857 dt

_ε(t) Ce

LsεI(t)minus εR(t)minus εT(t)1113858 1113859

(1)

where As and Ae are the specimen area and cross-sectionalarea of the pressure bar respectively Ee is the elasticmodulus of the pressure bar εI εR and εT are the incidentstrain reflection strain and transmission strain re-spectively which are measured on the incident bar andtransmission bar and Ce and le are the wave velocity andlength of the stress bar respectively

22 Preparation of Specimens To reduce variation in theresults caused by differences in the coal specimens the coalspecimens for the static-dynamic load tests were collected asa relatively homogeneous lump coal in the bottom of the coalseam -e specimens were then drilled to form φ50mm times

30mm cylinders and the surface flatness of both ends of thespecimens was lt002mm on a certain structural surface-ese specimen parameters satisfied the requirements forthe static and static-dynamic load tests For preparation ofthe coal specimens (Figure 2) the specimens were randomlydivided into two states the natural state and the water-saturated state Natural state specimens were prepared byplacing the specimens on a dryerwater separator and keptfor 24 h after which the specimens were sealed with ref-erence to the 60ndash70 relative humidity in the coalmineWater-saturated state specimens were prepared by the freewater absorption method in accordance with methods fordetermining the physical and mechanical properties of coaland rock [16] In this specific method the surface of water is1-2 cm above the surface of the natural coal specimens in thevessel -e specimens were then weighed every 24 h and theweight of the coal specimens changed by le001 g betweentwo successive weighings after immersion for 7 d -especimens were thus in the water-saturated state -e rangeof moisture contents in the saturated-state specimens was32ndash61

Figure 1 SHPB test apparatus with bar

2 Advances in Civil Engineering

23 Test Scheme Static load testing was conducted on thenatural state and water-saturated coal specimens Figure 3shows the stress-strain curves for specimens under staticloads Static-dynamic load tests were performed on an im-proved SHPB testing system During the tests the specimenswere subjected to prestatic loads with a load stress of 12MPa(approximately 30 of the specimen peak strength in thenatural state) Dynamic loads were then applied to thespecimens -e inflation pressure was used to control thespeed of the bullet impact To obtain similar strain rates forthe specimens natural state specimens (D1-1 to D1-3 andD3-2 to D3-4) and water-saturated specimens (D1-4 to D2-2 andD2-3 toD3-1) were used for the static and static-dynamic loadtests respectively In these tests coal specimens in each statewere tested three times with each loading method -e ex-perimental results are shown in Figure 4

24 Static and Static-DynamicTest Results According to thestress-strain curve for the uniaxial compression test(Figure 3) the natural state specimens have uniaxialcompressive strengths of 4207ndash4311MPa with an aver-age of 4271MPa the elastic modulus is 190ndash211 GPawith an average of 265 GPa -e uniaxial compressivestrength of water-saturated coal specimens is 2040ndash2530MPa with an average of 2217MPa the elasticmodulus is 128ndash166 GPa with an average of 152 GPa-e physical parameters of the uniaxial compression testare summarized in Table 1-e water absorption of naturalspecimens is 32ndash61 -e average uniaxial compressivestrength reduction coefficient for the water-saturatedspecimens is 052 and the average elastic modulus re-duction coefficient is 066

-e compressive strength of sandstone is higher [17] -ewater absorption rate of the saturated sandstone is 0343ndash0771 with an average of 0434 Figure 5 shows the staticstress-strain curves for natural (A21ndashA23) andwater-saturated(A214ndashA216) sandstone specimens under uniaxial compres-sion-e elastic modulus of natural state sandstone specimensis 326ndash359GPa with an average of 342GPa the peakstrength is 1295ndash1624MPa with an average of 1431MPaFor saturated sandstone specimens the elastic modulus is295ndash364GPa with an average of 324GPa the peak strengthis 977ndash1300MPa with an average of 1129MPa -us thecompressive strength reduction coefficient for water-saturated

sandstone is 079 the elastic modulus reduction coefficientis 094

In the static-dynamic load tests a static load of 12MPa isapplied as preloading after which the impact loads areapplied -e dynamic strength characteristics of coal spec-imens in different moisture states are tested -e dynamicstrain rate range is 90ndash155 sminus1 and three samples for eachmoisture content are tested Dynamic stress-strain curves fordifferent aqueous coal specimens under static-dynamic loadsare shown in Figure 4

-e results show that the dynamic strength of coalspecimens varies with different moisture states Within thesame moisture state there is also some variation in the coalspecimens Figure 4(a) shows the stress-strain curves for coalspecimens in the natural state -e dynamic compressivestrength is 322ndash406MPa with an average of 372MPa theelastic modulus is 714ndash789GPa with an average of764GPa Figure 4(b) shows the stress-strain curves forsaturated coal specimens-e dynamic compressive strengthis 2808ndash3382MPa with an average of 3153MPa the elasticmodulus is 875ndash911GPa with an average of 898GPa -eaverage dynamic strength reduction coefficient of water-saturated coal specimens is 085 and the dynamic elasticmodulus is increased by 17

Pu and Ma [5] carried out uniaxial impact compressiontests for two coalmines with sandstone having four differentmoisture states -e results are shown in Figure 6 Under themedium strain rate the dynamic uniaxial compressivestrength of sandstone increases with the moisture contentof specimens -e dynamic compressive strength of thespecimens is highest for the forced water saturation andnatural saturation states Additionally their compressivestrengths are similar -e dynamic uniaxial compressivestrength of sandstone is second in the water-saturated stateand is the lowest in the dry state When the two types ofsandstone reached a maximum with the natural water ab-sorptionmethod the dynamic uniaxial compressive strengthof the saturated sandstone was increased by 18 and 29respectively compared to the dry state -is is contrary tothe trend reported by Chang for the peak strength of coal

50

40

30

20

10

0

σ (M

Pa)

0 10 20 30 40ε (10ndash3)

D1-1

D1-2D1-3

D2-1

D2-2

D1-4

Figure 3 Static stress-strain curves for water-saturated coalspecimens

Figure 2 Coal specimens for testing

Advances in Civil Engineering 3

Wang and Li [13 18] concluded that water-saturated con-crete and granite have similar mechanical properties

3 Mechanism and Discussion

-e analysis shows that in addition to the influence ofmineral composition structure and type of cementation rockmechanical properties are also influenced by the water en-vironment [19 20] Ogata et al [21] show that the tensilestrength of rocks with high porosity on the water saturationcondition was decreased on both static and dynamic con-dition Huang et al [22] found that the tensile strengthsoftening factor decreases with the loading rate Moreoverstatic and dynamic loading strength tests of sandstone underwater-bearing conditions were carried out by Zhou et al[23 24] revealing that the static and dynamic sandstonestrengths decreased by 2988 and 4055 following satu-ration -e permeability of coal and rock specimens is pri-marily determined by the presence of fractures and themineral components of these fractures -e presence of avariety of mineral components directly affects the physical

and chemical properties of coal and rock Coal and rockmaterials contain pores and fractures of varying numbers andshapes -e fractures contain a variety of minerals such assulfides oxides carbonates and silicates As a type of solventwater has a small corrosive effect on high strength materialsbut a highly corrosive effect on low strength materials -ecorrosive effect of water can readily create small weak parts inthe fractures resulting in the holes continuing to expandunder stress Erosion by corrosive molecules leads to thefractures and holes continuously increasing and enlargingMoreover water can dissolve some minerals in the coal androck causing water absorption expansion of montmorillonitein the mineral -is results in generation of uneven stress inthe interior of coal and rock specimens In addition becausethe cementing material in the fractures and a portion of thecement between particles are dissolved the cohesion forcebetween particles and cement decreases Furthermore themicrocomposition of coal and rock is changed and theoriginal microstructure can be broken causing the strength ofcoal and rock materials to decrease

D3-2

D3-4

D3-3

00 2 4 6 8 10 12

5

15

10

20

25

30

35

40

σ (M

Pa)

ε (10ndash3)

(a)

0 2 4 6 8 10 12 140

5

10

15

20

25

30

35

D3-1

D2-3

D2-4

σ (M

Pa)

ε (10ndash3)

(b)

Figure 4 Dynamic stress-strain curves for coal specimens with different moisture states (a) Natural state (b) Water-saturated state

180

90

150

120

60

30

00 1 2 3 4 5 6 7

A23

A215A21

A216

A214 A22

ε (10ndash3)

σ (M

Pa)

Figure 5 Static stress-strain curves for natural and water-saturatedsandstone specimens

Table 1 Physicomechanical parameters of natural and water-saturated specimens under uniaxial compression

Specimennumber State RC (MPa) w () P (kgmiddotmminus3) E (GPa)

D1-1 Natural 4311 mdash 133 211D1-2 Natural 4207 mdash 135 190D1-3 Natural 4292 mdash 134 194D1-4 Saturated 2530 32 137 173D2-1 Saturated 2081 61 145 128D2-2 Saturated 204 45 136 166A21 Natural 1373 mdash 261 343A22 Natural 1295 mdash 2606 326A23 Natural 1624 mdash 2625 359A214 Saturated 1112 023 2623 315A215 Saturated 1300 077 2608 364A216 Saturated 977 040 2603 295

4 Advances in Civil Engineering

Comparing Figures 3 and 4 leads to the followingconclusions the strength reduction coefficient and elasticmodulus reduction coefficient of the saturated coal speci-mens with a high water absorption rate are 052 and 077respectively However sandstone is relatively dense and thestrength reduction coefficient and elastic modulus reductioncoefficient of the saturated sandstone specimens with a lowwater absorption rate are 079 and 094 respectively

315e Force between Particles Compared to coal there arefew fractures and pores in the sandstone Additionallysandstone has a denser structure greater content of highstrength materials and weaker water-rock interaction thancoal -erefore the strength and antideformation ability ofcoal decreases significantly under static loads but the waterhas little effect on the strength and antideformation ability ofsandstone A comparison of the natural state and water-saturated state of a coal specimen is shown in Figure 7

Furthermore before the coal and rock specimens aresoaked in water some water is contained internally oc-curring on the surface of particles in the form of crystalwater pore water and fracture water -us an attractiveeffect will occur between the water and particles at thesame time capillary pressure will also be produced Underthe action of capillary stress a bridge of water moleculescan be formed and a concave surface appears between theparticles -is effect will bond the particles together andconstitutes the internal bond strength of the rock as shownin Figure 8

-e attractive force F between particles includes thesurface tension and capillary pressure -e capillary pres-sure Pc can be expressed as follows

Pc cos(ϕ + θ)

1minus cosϕσR

(2)

where R is the particle radius σ is the surface tension ofwater in the air and θ is the contact angle With decreasingparticle radius Pc approaches infinity and the attractiveforce between particles can be expressed as follows

F 2πRσ sinϕ sin(ϕ + θ) + πR2mpc (3)

where Rm is the radius of the concave water droplet whichcan be calculated geometrically -e reaction force betweenthe particles is expressed as follows

F sinϕ sin(ϕ + θ) +[sin(ϕ + θ) + cosϕminus 1minus sin θ]2

2(1minus cos θ)cos(ϕ + θ)11138971113896

middot 2πRσ

(4)

Equation (4) indicates that after the specimen is water-saturated water molecules enter the pores between particlescausing Rm to increase F gradually decreases and the co-hesion force between particles in the rock decreases Fur-thermore the strength also decreases

Owing to the high pore density of coal the cement strengthbetween particles is lower Coal also has a higher water ab-sorption rate (Table 1) resulting in a larger Rm for the coalspecimens than of the sandstone In the saturated state theforces acting among particles in the coal specimens are weakerthan in sandstone and the strength is decreased observably

32 Fracture Propagation Characteristics under DynamicLoad -e propagation and aggregation of microfractureswithin coal and rock is the fundamental cause of macro-damage to the coal and rock under external loading Toanalyze the effect of free water in the fractures of saturatedcoal and rock on crack propagation under static-dynamic

200

160

120

80

40

0

σ (M

Pa)

0000 0004 0008 0012 0016 0020ε

Natural moisture stateDry stateMandatory saturated state

Natural saturated state

(a)

200

160

120

80

40

0

σ (M

Pa)

0000 0004 0008 0012 0016 0020ε

Natural moisture stateDry stateMandatory saturated state

Natural saturated state

(b)

Figure 6 Dynamic stress-strain curves for sandstone specimens (a) Yangzhuang coalmine (_ε 198 sminus1) (b) Hengyuan north auxiliary shaft(_ε 200 sminus1)

Advances in Civil Engineering 5

loading this study simplifies the three-dimensional hydrousfracture to a plane fracture and a single fracture is taken asan example For the parameters of the hydrous singlefracture the static load is σs dynamic load is σd fracturelength is 2a and angle is β as shown in Figure 9

321 Fracture Propagation Characteristics of Saturated Coaland Rock under Static-Dynamic Loads During staticloading wing fractures will occur with increasing static load-e fracture propagation velocity is faster than the staticloading speed In addition the fracture tip will fill with freewater due to occurrence of a siphon phenomenon in thefracture tip

-is results in a decrease in the friction coefficient of thefracture contact surface increase in the microrupture ac-tivity of the coal and rock specimens acceleration of fracturepropagation and concatenation and transfixion betweenfractures Furthermore the macrodestructive force of the

specimens decreases and the compressive strength of thespecimens is also reduced Wang and Li [13] investigated theforce of free water in fracture propagation in coal and rockunder static loads

-e fracture growth characteristics of coal and rock arebasically consistent under static loads In the natural state thenumber of fractures further increases as the coal and rockspecimens absorb water -is occurs because of the low in-tensity of coal and its dense fractures coupled with thecorrosive effects of water At the same time the reaction forcebetween particles decreases significantly [13] -is leads thevelocity of the new fracture to grow faster in coal specimensunder static loads than in the saturated sandstone -estrength reduction coefficient and elastic modulus reductioncoefficient of the coal and rock specimens are smaller

322 Fracture Propagation Characteristics of Saturated Coaland Rock under Dynamic Loads -e propagation charac-teristics of coal and rock fractures under static-dynamicloading can be obtained from the mesomechanical analyticalmethod of concrete and rock mechanics [25 26] Understatic-dynamic loads a cohesive force F is formed from thesurface tension of free water in the fractures and resistanceand Fprime result from the Stefan effect and impede the fracturegrowth and further fracturing -e force that hindersfracture propagation pdw can be expressed as follows

pdw F + Fprime( 1113857

A

VR 2δ2 cosφ1113872 11138731113872 1113873 + 3ηr42πh3( 1113857(dudt)( 11138571113872 1113873

A

(5)

where V is the liquid volume R is the surface energy φ is thewetting angle δ is the radius of the water meniscus η is theliquid viscosity r is the radius of two parallel circular platesfilled with incompressible viscous fluids u is the relativedisplacement corresponding to the separation of the twocircular plates h is the space between the two circular platesand A is the area of the fracture containing water

θ

φ

Rm

R

Figure 8 Model of grain-water molecule interactions

(a) (b) (c)

Figure 7 Sketch of the coal specimen in the natural state and water-saturated state (a) Coal specimen D1-2 (b) Natural state (c) Water-saturated state

6 Advances in Civil Engineering

323 Stress Balance on Both Ends of the Specimen duringDynamic Impact Processes -e stress state under static-dynamic loading is shown in Figure 10 In the image σIis the incident stress σR is the reflected stress σT is thetransmission stress and σs is the prestatic load

-e stress balance on both ends of the specimen is aprecondition for a reasonable equivalent of the dynamicload Zncker and Closer proposed applying an equilibriumfactor μ to measure the stress equilibrium state of speci-mens μ was defined as the ratio of the stress differencebetween the two ends to the average stress in the specimenas given by Equation (6) As the equilibrium factor ap-proaches zero the stress in the specimens becomes moreuniform -e equilibrium factor is calculated as follows

μ 2 σSI minus σST( 1113857

σSI + σST (6)

where σSI is the incident end stress and σST is the trans-mission end stress

During the impact process the small size of the specimenand the complicated transient change in the stress mean thatthe present technique cannot achieve direct measurement ofthe stress distribution on both ends According to the theoryof SHPB tests for the equivalent stress on both ends of thespecimen the equivalent formula is as follows

σST σT

σSI σI + σR(7)

-e trend in the equilibrium factor during the dynamicshock process for a specimen under prestatic loads is shownin Figure 11

-e reflection wave σT is a platform which indicatesthat the experiment has achieved loading at a constant strainrate During the whole impact loading process the stress atthe incident and transmission ends are almost equal -e

equilibrium factor μ tends to approximately zero by 30 μsafter loading and is maintained to 140 μs -erefore thedynamic impact force of coal specimens is a reasonableequivalent for the quasi-static stress σd coupled with theprestatic load σs

During the static-dynamic loads a prestatic load σs isfirst applied followed by the dynamic load σd σsminusd is thecomposite failure strength of the coal specimen hydrousfracture under a combination load-e friction coefficient ofthe branch fracture is divided by the dynamic load factor fdof the branch fracture surface that is not in contact withwater and the dynamic load factor fdw of the branchfracture surface in contact with water owing to the lowstrength of natural saturated coal specimens at the fracturesurface and the uneven distribution of water in the branchfracture -erefore considering the difference in stressbetween the areas in the branch fracture surface that are incontact with water and those that are not in contact withwater is necessary

As shown in Figure 9 surface abndashcd is the free waterinterface and a mechanical analysis of the stress structure of awing branch fracture was carried out under static-dynamicloading -e compressive stress is assumed to be positive inthis analysis -us the shear stress τ(dminuss)w and normal stressσ(dminuss)w of the wing branch fracture surface in contact withfree water and the shear stress τ(dminuss) and normal stressσ(dminuss) of the wing branch fracture not in contact with water

XG1 X1 X2 XG2

Straingauge G1

σI

σR

σT

σR

σIσT σSσS

Incident bar Sample Transmission barStrain gauge G2

Figure 10 Loading diagram of a specimen under static-dynamicload

125100

755025

0ndash25ndash50ndash75

ndash100ndash125ndash150

0 20 40 60 80T (μs)

100 120 140 160

543210ndash1ndash2ndash3ndash4ndash5ndash6

σ (M

Pa)

μ

σR

σT

σSIμ

σR + σI σI

σRσST

σI

μ

Figure 11 Balance factor for specimens under static-dynamicloads

σdσs σdσs

σdσs σdσs

L

β

τ(s-d)w

τs

PswPdwa

bσ(s-d)w

σ(s-d)

PswPdw

cd

σ(s-d)w

PdwPsw

τ(s-d)w

τ(s-d)

σ(s-d)PdwPsw

Psw

Psw

Pdw

Pdw

Void

Void

2a

θ

Figure 9 Pressure at the crack surface caused by free water undercoupled static-dynamic loads

Advances in Civil Engineering 7

(out of the abndashcd surface) can be obtained -e above pa-rameters can be expressed by equations (8)ndash(11) as follows

τ(sminusd)w 12σsminusd sin 2(β + θ)

minusfdw σsminusd cos2(β + θ)minus psw minuspdw( 11138571113960 1113961

(8)

τ(sminusd) 12σsminusd sin 2(β + θ)minusfdσsminusd cos

2(β + θ) (9)

σ(sminusd)w σsminusd cos2(β + θ)minus psw minuspdw( 1113857 (10)

σ(sminusd) σsminusd cos2(β + θ) (11)

wheref(dminuss)w is the friction coefficient of the hydrous fracturein contact with free water under dynamic load fd is thefriction coefficient of the hydrous fracture not in contact withfree water under dynamic load pdw is the stress that inhibitsfracture extension and psw is the outward extrusion stress offree water on an airfoil fracture Numerically pdw is far largerthan psw in the dynamic impact process Both of these areinvolved in fracture development and breakthrough

From Equations (8)ndash(11) Equations (12) and (13) can beobtained for the relative shear stress τl generated normal tosurface abndashcd and the relative normal stress σl

τl τ(sminusd) minus τ(sminusd)w fdσsminusd cos2(β + θ)

minusfdw σsminusd cos2(β + θ)minus psw minuspdw( 11138571113960 1113961

(12)

τa σ(sminusd) minus σ(sminusd)w psw minuspdw (13)

where τl is the tensile stress at the branch fracture surfacenear the abndashcd interface and τa is the shear stress at thebranch fracture surface near the abndashcd interface

At the coal and rock branch fracture surface the settingtensile strength is τb and the shear strength is τf When thebranch fracture surface of saturated coal and rock meets oneof the conditions τb lt τl or τf lt τa the branch fracturesurface will be damaged and a new fracture will form -ebranch fracture surface of saturated coal and rock canproduce resistance due to the Stefan effect under static-dynamic loads -e extension of the fracture at the branchfracture surface in contact with water will result in a pressuredifference at the branch fracture surface -us the newfracture will generate owing to the low strength of thematerial In other words when the material meets one of thetwo conditions above destruction of the fracture will resultin more energy for generation and extension of the newfracture -us the elastic energy storage in the tip of theinitial fracture will decrease and the coal and rock materialstrength will also decrease During dynamic loading thestress inhomogeneity causes the extension of the initialfracture to lag behind the new fracture With breakthroughof the initial fracture and generation of the new fracturefragments will be formed At the same time a stress wave willprovide kinetic energy to the fragments resulting inthrowing and flying of fragments

When the branch fracture surface of saturated coal androck simultaneously meets both τb gt τl and τf gt τa a new

fracture will not be formed on the fracture surface underdynamic load conditions -e propagation velocity of thedynamic fracture is faster than the static and the propa-gation velocity of the fracture is much lower than theload -erefore fracture water cannot diffuse into thefracture tip in a relatively short time Under the action of thesurface tension of free water the water on the fracturesurface will produce a cohesion force (pdw minuspsw) Underdynamic loading because the materials simultaneously meetτb gt τl and τf gt τa the branch fracture surface will notgenerate new fractures -us the entire branch fractureextension will be hampered which increases the strength ofthe saturated coal and rock

As mentioned above coal has low intensity more de-veloped fractures a small strength reduction coefficientwhen saturated and the reaction force between particles isalso lower -us under static-dynamic loads the relativetensile stress and shear stress generated on the branchfracture surface of a saturated coal specimen is much higherthan the tensile strength and shear strength of the fracturesurface ie τb lt τl and τf lt τa -is can cause branchfracture tensile failure and shear failure -e damage of thecoal specimen and the expansion of fractures are acceleratedand the dynamic strength of the coal specimen is weakenedIn contrast the effect of water-rock interactions on sand-stone is smaller the strength reduction coefficient is largerand it has a high strength and relatively low fracture densityUnder the same conditions the relative tensile stress andshear stress generated in the fracture surface of saturatedsandstone under static-dynamic loads are much higher thantensile strength and shear strength of the fracture surfaceie τb gt τl and τf gt τa -erefore the extension of wholebranch fracture of naturally saturated sandstone will behampered due to the cohesion force generated from theStefan effect Additionally generation of new fractures onthe branch fracture surface of sandstone is also suppressed-e dynamic peak strength of the specimen is improved

Furthermore during dynamic impact the diffusion offree water lags behind the expansion of the new fracturebecause of generation of new fractures in the branch fracturesurface of saturated coal specimens -us the diffusionspeed of free water is largely determined by the growth speedof the new fracture which means that each primary and newfracture will contain free water -e area of the branchfracture surface in contact with water will produce a cohesiveforce hindering the branch fracture from growing -isreduces the compressibility of free water and the ability ofthe coal specimen to resist deformation is enhanced At thistime the greater the fracture area in contact with water thehigher the stiffness of the water-rock common loads will be-is provides a reason for the increase in the deformationmodulus of coal specimens with moisture content undermedium strain rate conditions

4 Conclusion

(1) Under static loading conditions the saturatedstrength reduction coefficient and elastic modulusreduction coefficient of coal samples are lower than

8 Advances in Civil Engineering

those of sandstone Under dynamic loading condi-tions the strength of naturally saturated coal samplesdecreases and the elastic modulus increases -isis the same strength variation trend and oppositeelastic modulus variation trend as observed forsandstone

(2) -e water-saturated coal specimens have greaterwater-rock interactions and strength reductioneffect its reduction in the ability to resist defor-mation is also very significant compared to saturatedsandstone

(3) Under static-dynamic loads owing to intensitydifferences in the saturated coal and rock materials astress difference results from the Stefan effect in thebranch fracture surface which is the main reasonthat the strength of coal and rock materials increasesor decreases Meanwhile fracture propagation atsaturated branch fracture surfaces can effectivelyexplain the increase in the deformation modulus ofcoal with increasing moisture content

(4) According to a sliding model of wing branch frac-ture the criteria for microfracture tensile stress andshear stress produced at the branch fracture surfacewere established If the branch fracture surface si-multaneously satisfies both τb gt τl and τf gt τa thebranch fracture surface will not break down -edynamic strength of water-saturated coal and rockwill increase If the branch fracture surface meetsonly one of the conditions τb lt τl or τf lt τa thebranch fracture surface will break down and thedynamic strength of water-saturated coal and rockwill decrease

Data Availability

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

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-e work was supported by the National Natural ScienceFoundation of China (51604093 and 51474096) NationalKey RampD Program of China (2018YFC0604502) Programfor Innovative Research Team at the University of Ministryof Education of China (IRT_16R22) Scientific and Tech-nological Key Project of Henan province (172107000016)and the Doctoral Research Fund Project of Henan Poly-technic University China (B2017-42)

References

[1] B Vasarhelyi and P Van ldquoInfluence of water content on thestrength of rockrdquo Engineering Geology vol 84 no 1-2pp 70ndash74 2006

[2] L S Tang P C Zhang and Y Wang ldquoOn fractures strengthof rocks with cracks under water actionrdquo Chinese Journal ofRock Mechanics and Engineering vol 23 no 19 pp 3337ndash3341 2004

[3] Z Zhu and D Hu ldquo-e effect of intestitial water pressure onrock mass strengthrdquo Rock and Soil Mechanics vol 21 no 1pp 64ndash67 2000

[4] Y Pu and Q Y Ma ldquoSplit Hopkinson pressure bar tests onsandstone in coalmine under cyclic wetting and dryingrdquo Rockand Soil Mechanics vol 9 pp 2557ndash2562 2013

[5] Y Pu and R Ma ldquoSplit Hopkinson pressure bar tests andanalysis of coalmine sandstone with various moisture con-tentsrdquo Chinese Journal of Rock Mechanics and Engineeringvol 34 no 1 pp 2888ndash2893 2015

[6] W Wang H Li and H Gu ldquoMicromechanics analysis andmechanical characteristics of water-saturated coal specimensunder coupled static-dynamic loadsrdquo Journal of China CoalSociety vol 3 pp 611ndash617 2016

[7] W Wang H Wang D Li H Li and Z Liu ldquoStrength andfailure characteristics of natural and water-saturated coalspecimens under static and dynamic loadsrdquo Shock and Vi-bration vol 2018 Article ID 3526121 15 pages 2018

[8] Y Q Ding W H Tang and X Xu ldquoExperimental studyof dynamic mechanical behaviors of unsaturated clay sub-jected touniaxial loadingrdquo Rock and Soil Mechanics vol 9pp 2546ndash2550 2013

[9] N Ding L Jin and J Zhang ldquoEffect of free water content onthe dynamic mechanical behavior of cement mortar underhigh strain raterdquo Concrete vol 10 pp 128ndash132 2013

[10] J Zhan and N Zhang ldquoStudy on the damage feature ofwater-bearing argillaceous siltstone under the impact loadrdquoNon-Ferrous Metal vol 6 pp 44ndash77 2015

[11] Y Zhao S Liu Y Jiang K Wang and Y Huang ldquoDynamictensile strength of coal under dry and saturated conditionsrdquoRock Mechanics and Rock Engineering vol 49 no 5pp 1709ndash1720 2015

[12] Y V Petrov I V Smirnov G A Volkov A K AbramianA M Bragov and S N Verichev ldquoDynamic failure of dryand fully saturated limestone samples based on incubationtime conceptrdquo Journal of Rock Mechanics and GeotechnicalEngineering vol 9 no 1 pp 125ndash134 2017

[13] B Wang and X Li ldquoMesomechanics analysis of static com-pressive strength and dynamic compressive strength of water-saturated rock under uniaxial loadrdquo Explosion and ShockWaves vol 32 no 4 pp 423ndash431 2014

[14] F Gong X Li X Liu et al ldquoExperimental study of dynamiccharacteristics of sandstone under one-dimensional coupledstatic and dynamic loadsrdquo Chinese Journal of Rock Mechanicsand Engineering vol 29 no 10 pp 2076ndash2085 2010

[15] F Q Gong and G F Zhao ldquoDynamic indirect tensile strengthof sandstone under different loading ratesrdquo Rock Mechanicsand Rock Engineering vol 47 no 6 pp 2271ndash2278 2013

[16] -e National Standard Compilation Groups of Peoplersquos Re-public of China GBT 235615-2009 Methods for Determiningthe Physical and Mechanical Properties of Coal and RockStandards Press of China Beijing China 2009 in Chinese

[17] D Xiong Z Zhao and C Su ldquoExperimental study of effect ofwater-sturated state on mechanical properties of rock in coalmeasure stratardquo Chinese Journal of Rock Mechanics andEngineering vol 5 pp 998ndash1006 2011

[18] H Wang and Q Li ldquoSaturated concrete mesoscopic me-chanics mechanism of the static and dynamic compressivestrengthrdquo Journal of Hydraulic Engineering vol 8 pp 958ndash962 2006

Advances in Civil Engineering 9

[19] M Tao H T Zhao X B Li and W Z Cao ldquoFailurecharacteristics of pre-stressed rock with a circular hole sub-jected to dynamic loadingrdquo Tunnelling and UndergroundSpace Technology vol 81 pp 1ndash15 2018

[20] M Tao A Ma W Cao X Li and F Gong ldquoDynamicresponse of pre-stressed rock with a circular cavity subject totransient loadingrdquo International Journal of Rock Mechanicsand Mining Sciences vol 99 pp 1ndash8 2017

[21] Y Ogata W J Jung S Kubota and Y Wada ldquoEffect of thestrain rate and water saturation for the dynamic tensilestrength of rocksrdquo Materials Science Forum vol 465-466pp 361ndash366 2004

[22] S Huang K Xia F Yan and X Feng ldquoAn experimental studyof the rate dependence of tensile strength softening ofLongyou sandstonerdquo Rock Mechanics and Rock Engineeringvol 43 no 6 pp 677ndash683 2010

[23] Z Zhou X Cai W Cao X Li and C Xiong ldquoInfluence ofwater content on mechanical properties of rock in bothsaturation and drying processesrdquo Rock Mechanics and RockEngineering vol 49 no 8 pp 3009ndash3025 2016

[24] Z Zhou X Cai L Chen W Cao Y Zhao and C XiongldquoInfluence of cyclic wetting and drying on physical and dy-namic compressive properties of sandstonerdquo EngineeringGeology vol 220 pp 1ndash12 2017

[25] D Zheng and Q Li ldquoAn explanation for rate effect of concretestrength based on fracture toughness including free waterviscosityrdquo Engineering Fracture Mechanics vol 71 no 16-17pp 2319ndash2327 2004

[26] P Rossi J G M van Mier C Boulay and F Le Maou ldquo-edynamic behaviour of concrete influence of free waterrdquoMaterials and Structures vol 25 no 9 pp 509ndash514 1992

10 Advances in Civil Engineering

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23 Test Scheme Static load testing was conducted on thenatural state and water-saturated coal specimens Figure 3shows the stress-strain curves for specimens under staticloads Static-dynamic load tests were performed on an im-proved SHPB testing system During the tests the specimenswere subjected to prestatic loads with a load stress of 12MPa(approximately 30 of the specimen peak strength in thenatural state) Dynamic loads were then applied to thespecimens -e inflation pressure was used to control thespeed of the bullet impact To obtain similar strain rates forthe specimens natural state specimens (D1-1 to D1-3 andD3-2 to D3-4) and water-saturated specimens (D1-4 to D2-2 andD2-3 toD3-1) were used for the static and static-dynamic loadtests respectively In these tests coal specimens in each statewere tested three times with each loading method -e ex-perimental results are shown in Figure 4

24 Static and Static-DynamicTest Results According to thestress-strain curve for the uniaxial compression test(Figure 3) the natural state specimens have uniaxialcompressive strengths of 4207ndash4311MPa with an aver-age of 4271MPa the elastic modulus is 190ndash211 GPawith an average of 265 GPa -e uniaxial compressivestrength of water-saturated coal specimens is 2040ndash2530MPa with an average of 2217MPa the elasticmodulus is 128ndash166 GPa with an average of 152 GPa-e physical parameters of the uniaxial compression testare summarized in Table 1-e water absorption of naturalspecimens is 32ndash61 -e average uniaxial compressivestrength reduction coefficient for the water-saturatedspecimens is 052 and the average elastic modulus re-duction coefficient is 066

-e compressive strength of sandstone is higher [17] -ewater absorption rate of the saturated sandstone is 0343ndash0771 with an average of 0434 Figure 5 shows the staticstress-strain curves for natural (A21ndashA23) andwater-saturated(A214ndashA216) sandstone specimens under uniaxial compres-sion-e elastic modulus of natural state sandstone specimensis 326ndash359GPa with an average of 342GPa the peakstrength is 1295ndash1624MPa with an average of 1431MPaFor saturated sandstone specimens the elastic modulus is295ndash364GPa with an average of 324GPa the peak strengthis 977ndash1300MPa with an average of 1129MPa -us thecompressive strength reduction coefficient for water-saturated

sandstone is 079 the elastic modulus reduction coefficientis 094

In the static-dynamic load tests a static load of 12MPa isapplied as preloading after which the impact loads areapplied -e dynamic strength characteristics of coal spec-imens in different moisture states are tested -e dynamicstrain rate range is 90ndash155 sminus1 and three samples for eachmoisture content are tested Dynamic stress-strain curves fordifferent aqueous coal specimens under static-dynamic loadsare shown in Figure 4

-e results show that the dynamic strength of coalspecimens varies with different moisture states Within thesame moisture state there is also some variation in the coalspecimens Figure 4(a) shows the stress-strain curves for coalspecimens in the natural state -e dynamic compressivestrength is 322ndash406MPa with an average of 372MPa theelastic modulus is 714ndash789GPa with an average of764GPa Figure 4(b) shows the stress-strain curves forsaturated coal specimens-e dynamic compressive strengthis 2808ndash3382MPa with an average of 3153MPa the elasticmodulus is 875ndash911GPa with an average of 898GPa -eaverage dynamic strength reduction coefficient of water-saturated coal specimens is 085 and the dynamic elasticmodulus is increased by 17

Pu and Ma [5] carried out uniaxial impact compressiontests for two coalmines with sandstone having four differentmoisture states -e results are shown in Figure 6 Under themedium strain rate the dynamic uniaxial compressivestrength of sandstone increases with the moisture contentof specimens -e dynamic compressive strength of thespecimens is highest for the forced water saturation andnatural saturation states Additionally their compressivestrengths are similar -e dynamic uniaxial compressivestrength of sandstone is second in the water-saturated stateand is the lowest in the dry state When the two types ofsandstone reached a maximum with the natural water ab-sorptionmethod the dynamic uniaxial compressive strengthof the saturated sandstone was increased by 18 and 29respectively compared to the dry state -is is contrary tothe trend reported by Chang for the peak strength of coal

50

40

30

20

10

0

σ (M

Pa)

0 10 20 30 40ε (10ndash3)

D1-1

D1-2D1-3

D2-1

D2-2

D1-4

Figure 3 Static stress-strain curves for water-saturated coalspecimens

Figure 2 Coal specimens for testing

Advances in Civil Engineering 3

Wang and Li [13 18] concluded that water-saturated con-crete and granite have similar mechanical properties

3 Mechanism and Discussion

-e analysis shows that in addition to the influence ofmineral composition structure and type of cementation rockmechanical properties are also influenced by the water en-vironment [19 20] Ogata et al [21] show that the tensilestrength of rocks with high porosity on the water saturationcondition was decreased on both static and dynamic con-dition Huang et al [22] found that the tensile strengthsoftening factor decreases with the loading rate Moreoverstatic and dynamic loading strength tests of sandstone underwater-bearing conditions were carried out by Zhou et al[23 24] revealing that the static and dynamic sandstonestrengths decreased by 2988 and 4055 following satu-ration -e permeability of coal and rock specimens is pri-marily determined by the presence of fractures and themineral components of these fractures -e presence of avariety of mineral components directly affects the physical

and chemical properties of coal and rock Coal and rockmaterials contain pores and fractures of varying numbers andshapes -e fractures contain a variety of minerals such assulfides oxides carbonates and silicates As a type of solventwater has a small corrosive effect on high strength materialsbut a highly corrosive effect on low strength materials -ecorrosive effect of water can readily create small weak parts inthe fractures resulting in the holes continuing to expandunder stress Erosion by corrosive molecules leads to thefractures and holes continuously increasing and enlargingMoreover water can dissolve some minerals in the coal androck causing water absorption expansion of montmorillonitein the mineral -is results in generation of uneven stress inthe interior of coal and rock specimens In addition becausethe cementing material in the fractures and a portion of thecement between particles are dissolved the cohesion forcebetween particles and cement decreases Furthermore themicrocomposition of coal and rock is changed and theoriginal microstructure can be broken causing the strength ofcoal and rock materials to decrease

D3-2

D3-4

D3-3

00 2 4 6 8 10 12

5

15

10

20

25

30

35

40

σ (M

Pa)

ε (10ndash3)

(a)

0 2 4 6 8 10 12 140

5

10

15

20

25

30

35

D3-1

D2-3

D2-4

σ (M

Pa)

ε (10ndash3)

(b)

Figure 4 Dynamic stress-strain curves for coal specimens with different moisture states (a) Natural state (b) Water-saturated state

180

90

150

120

60

30

00 1 2 3 4 5 6 7

A23

A215A21

A216

A214 A22

ε (10ndash3)

σ (M

Pa)

Figure 5 Static stress-strain curves for natural and water-saturatedsandstone specimens

Table 1 Physicomechanical parameters of natural and water-saturated specimens under uniaxial compression

Specimennumber State RC (MPa) w () P (kgmiddotmminus3) E (GPa)

D1-1 Natural 4311 mdash 133 211D1-2 Natural 4207 mdash 135 190D1-3 Natural 4292 mdash 134 194D1-4 Saturated 2530 32 137 173D2-1 Saturated 2081 61 145 128D2-2 Saturated 204 45 136 166A21 Natural 1373 mdash 261 343A22 Natural 1295 mdash 2606 326A23 Natural 1624 mdash 2625 359A214 Saturated 1112 023 2623 315A215 Saturated 1300 077 2608 364A216 Saturated 977 040 2603 295

4 Advances in Civil Engineering

Comparing Figures 3 and 4 leads to the followingconclusions the strength reduction coefficient and elasticmodulus reduction coefficient of the saturated coal speci-mens with a high water absorption rate are 052 and 077respectively However sandstone is relatively dense and thestrength reduction coefficient and elastic modulus reductioncoefficient of the saturated sandstone specimens with a lowwater absorption rate are 079 and 094 respectively

315e Force between Particles Compared to coal there arefew fractures and pores in the sandstone Additionallysandstone has a denser structure greater content of highstrength materials and weaker water-rock interaction thancoal -erefore the strength and antideformation ability ofcoal decreases significantly under static loads but the waterhas little effect on the strength and antideformation ability ofsandstone A comparison of the natural state and water-saturated state of a coal specimen is shown in Figure 7

Furthermore before the coal and rock specimens aresoaked in water some water is contained internally oc-curring on the surface of particles in the form of crystalwater pore water and fracture water -us an attractiveeffect will occur between the water and particles at thesame time capillary pressure will also be produced Underthe action of capillary stress a bridge of water moleculescan be formed and a concave surface appears between theparticles -is effect will bond the particles together andconstitutes the internal bond strength of the rock as shownin Figure 8

-e attractive force F between particles includes thesurface tension and capillary pressure -e capillary pres-sure Pc can be expressed as follows

Pc cos(ϕ + θ)

1minus cosϕσR

(2)

where R is the particle radius σ is the surface tension ofwater in the air and θ is the contact angle With decreasingparticle radius Pc approaches infinity and the attractiveforce between particles can be expressed as follows

F 2πRσ sinϕ sin(ϕ + θ) + πR2mpc (3)

where Rm is the radius of the concave water droplet whichcan be calculated geometrically -e reaction force betweenthe particles is expressed as follows

F sinϕ sin(ϕ + θ) +[sin(ϕ + θ) + cosϕminus 1minus sin θ]2

2(1minus cos θ)cos(ϕ + θ)11138971113896

middot 2πRσ

(4)

Equation (4) indicates that after the specimen is water-saturated water molecules enter the pores between particlescausing Rm to increase F gradually decreases and the co-hesion force between particles in the rock decreases Fur-thermore the strength also decreases

Owing to the high pore density of coal the cement strengthbetween particles is lower Coal also has a higher water ab-sorption rate (Table 1) resulting in a larger Rm for the coalspecimens than of the sandstone In the saturated state theforces acting among particles in the coal specimens are weakerthan in sandstone and the strength is decreased observably

32 Fracture Propagation Characteristics under DynamicLoad -e propagation and aggregation of microfractureswithin coal and rock is the fundamental cause of macro-damage to the coal and rock under external loading Toanalyze the effect of free water in the fractures of saturatedcoal and rock on crack propagation under static-dynamic

200

160

120

80

40

0

σ (M

Pa)

0000 0004 0008 0012 0016 0020ε

Natural moisture stateDry stateMandatory saturated state

Natural saturated state

(a)

200

160

120

80

40

0

σ (M

Pa)

0000 0004 0008 0012 0016 0020ε

Natural moisture stateDry stateMandatory saturated state

Natural saturated state

(b)

Figure 6 Dynamic stress-strain curves for sandstone specimens (a) Yangzhuang coalmine (_ε 198 sminus1) (b) Hengyuan north auxiliary shaft(_ε 200 sminus1)

Advances in Civil Engineering 5

loading this study simplifies the three-dimensional hydrousfracture to a plane fracture and a single fracture is taken asan example For the parameters of the hydrous singlefracture the static load is σs dynamic load is σd fracturelength is 2a and angle is β as shown in Figure 9

321 Fracture Propagation Characteristics of Saturated Coaland Rock under Static-Dynamic Loads During staticloading wing fractures will occur with increasing static load-e fracture propagation velocity is faster than the staticloading speed In addition the fracture tip will fill with freewater due to occurrence of a siphon phenomenon in thefracture tip

-is results in a decrease in the friction coefficient of thefracture contact surface increase in the microrupture ac-tivity of the coal and rock specimens acceleration of fracturepropagation and concatenation and transfixion betweenfractures Furthermore the macrodestructive force of the

specimens decreases and the compressive strength of thespecimens is also reduced Wang and Li [13] investigated theforce of free water in fracture propagation in coal and rockunder static loads

-e fracture growth characteristics of coal and rock arebasically consistent under static loads In the natural state thenumber of fractures further increases as the coal and rockspecimens absorb water -is occurs because of the low in-tensity of coal and its dense fractures coupled with thecorrosive effects of water At the same time the reaction forcebetween particles decreases significantly [13] -is leads thevelocity of the new fracture to grow faster in coal specimensunder static loads than in the saturated sandstone -estrength reduction coefficient and elastic modulus reductioncoefficient of the coal and rock specimens are smaller

322 Fracture Propagation Characteristics of Saturated Coaland Rock under Dynamic Loads -e propagation charac-teristics of coal and rock fractures under static-dynamicloading can be obtained from the mesomechanical analyticalmethod of concrete and rock mechanics [25 26] Understatic-dynamic loads a cohesive force F is formed from thesurface tension of free water in the fractures and resistanceand Fprime result from the Stefan effect and impede the fracturegrowth and further fracturing -e force that hindersfracture propagation pdw can be expressed as follows

pdw F + Fprime( 1113857

A

VR 2δ2 cosφ1113872 11138731113872 1113873 + 3ηr42πh3( 1113857(dudt)( 11138571113872 1113873

A

(5)

where V is the liquid volume R is the surface energy φ is thewetting angle δ is the radius of the water meniscus η is theliquid viscosity r is the radius of two parallel circular platesfilled with incompressible viscous fluids u is the relativedisplacement corresponding to the separation of the twocircular plates h is the space between the two circular platesand A is the area of the fracture containing water

θ

φ

Rm

R

Figure 8 Model of grain-water molecule interactions

(a) (b) (c)

Figure 7 Sketch of the coal specimen in the natural state and water-saturated state (a) Coal specimen D1-2 (b) Natural state (c) Water-saturated state

6 Advances in Civil Engineering

323 Stress Balance on Both Ends of the Specimen duringDynamic Impact Processes -e stress state under static-dynamic loading is shown in Figure 10 In the image σIis the incident stress σR is the reflected stress σT is thetransmission stress and σs is the prestatic load

-e stress balance on both ends of the specimen is aprecondition for a reasonable equivalent of the dynamicload Zncker and Closer proposed applying an equilibriumfactor μ to measure the stress equilibrium state of speci-mens μ was defined as the ratio of the stress differencebetween the two ends to the average stress in the specimenas given by Equation (6) As the equilibrium factor ap-proaches zero the stress in the specimens becomes moreuniform -e equilibrium factor is calculated as follows

μ 2 σSI minus σST( 1113857

σSI + σST (6)

where σSI is the incident end stress and σST is the trans-mission end stress

During the impact process the small size of the specimenand the complicated transient change in the stress mean thatthe present technique cannot achieve direct measurement ofthe stress distribution on both ends According to the theoryof SHPB tests for the equivalent stress on both ends of thespecimen the equivalent formula is as follows

σST σT

σSI σI + σR(7)

-e trend in the equilibrium factor during the dynamicshock process for a specimen under prestatic loads is shownin Figure 11

-e reflection wave σT is a platform which indicatesthat the experiment has achieved loading at a constant strainrate During the whole impact loading process the stress atthe incident and transmission ends are almost equal -e

equilibrium factor μ tends to approximately zero by 30 μsafter loading and is maintained to 140 μs -erefore thedynamic impact force of coal specimens is a reasonableequivalent for the quasi-static stress σd coupled with theprestatic load σs

During the static-dynamic loads a prestatic load σs isfirst applied followed by the dynamic load σd σsminusd is thecomposite failure strength of the coal specimen hydrousfracture under a combination load-e friction coefficient ofthe branch fracture is divided by the dynamic load factor fdof the branch fracture surface that is not in contact withwater and the dynamic load factor fdw of the branchfracture surface in contact with water owing to the lowstrength of natural saturated coal specimens at the fracturesurface and the uneven distribution of water in the branchfracture -erefore considering the difference in stressbetween the areas in the branch fracture surface that are incontact with water and those that are not in contact withwater is necessary

As shown in Figure 9 surface abndashcd is the free waterinterface and a mechanical analysis of the stress structure of awing branch fracture was carried out under static-dynamicloading -e compressive stress is assumed to be positive inthis analysis -us the shear stress τ(dminuss)w and normal stressσ(dminuss)w of the wing branch fracture surface in contact withfree water and the shear stress τ(dminuss) and normal stressσ(dminuss) of the wing branch fracture not in contact with water

XG1 X1 X2 XG2

Straingauge G1

σI

σR

σT

σR

σIσT σSσS

Incident bar Sample Transmission barStrain gauge G2

Figure 10 Loading diagram of a specimen under static-dynamicload

125100

755025

0ndash25ndash50ndash75

ndash100ndash125ndash150

0 20 40 60 80T (μs)

100 120 140 160

543210ndash1ndash2ndash3ndash4ndash5ndash6

σ (M

Pa)

μ

σR

σT

σSIμ

σR + σI σI

σRσST

σI

μ

Figure 11 Balance factor for specimens under static-dynamicloads

σdσs σdσs

σdσs σdσs

L

β

τ(s-d)w

τs

PswPdwa

bσ(s-d)w

σ(s-d)

PswPdw

cd

σ(s-d)w

PdwPsw

τ(s-d)w

τ(s-d)

σ(s-d)PdwPsw

Psw

Psw

Pdw

Pdw

Void

Void

2a

θ

Figure 9 Pressure at the crack surface caused by free water undercoupled static-dynamic loads

Advances in Civil Engineering 7

(out of the abndashcd surface) can be obtained -e above pa-rameters can be expressed by equations (8)ndash(11) as follows

τ(sminusd)w 12σsminusd sin 2(β + θ)

minusfdw σsminusd cos2(β + θ)minus psw minuspdw( 11138571113960 1113961

(8)

τ(sminusd) 12σsminusd sin 2(β + θ)minusfdσsminusd cos

2(β + θ) (9)

σ(sminusd)w σsminusd cos2(β + θ)minus psw minuspdw( 1113857 (10)

σ(sminusd) σsminusd cos2(β + θ) (11)

wheref(dminuss)w is the friction coefficient of the hydrous fracturein contact with free water under dynamic load fd is thefriction coefficient of the hydrous fracture not in contact withfree water under dynamic load pdw is the stress that inhibitsfracture extension and psw is the outward extrusion stress offree water on an airfoil fracture Numerically pdw is far largerthan psw in the dynamic impact process Both of these areinvolved in fracture development and breakthrough

From Equations (8)ndash(11) Equations (12) and (13) can beobtained for the relative shear stress τl generated normal tosurface abndashcd and the relative normal stress σl

τl τ(sminusd) minus τ(sminusd)w fdσsminusd cos2(β + θ)

minusfdw σsminusd cos2(β + θ)minus psw minuspdw( 11138571113960 1113961

(12)

τa σ(sminusd) minus σ(sminusd)w psw minuspdw (13)

where τl is the tensile stress at the branch fracture surfacenear the abndashcd interface and τa is the shear stress at thebranch fracture surface near the abndashcd interface

At the coal and rock branch fracture surface the settingtensile strength is τb and the shear strength is τf When thebranch fracture surface of saturated coal and rock meets oneof the conditions τb lt τl or τf lt τa the branch fracturesurface will be damaged and a new fracture will form -ebranch fracture surface of saturated coal and rock canproduce resistance due to the Stefan effect under static-dynamic loads -e extension of the fracture at the branchfracture surface in contact with water will result in a pressuredifference at the branch fracture surface -us the newfracture will generate owing to the low strength of thematerial In other words when the material meets one of thetwo conditions above destruction of the fracture will resultin more energy for generation and extension of the newfracture -us the elastic energy storage in the tip of theinitial fracture will decrease and the coal and rock materialstrength will also decrease During dynamic loading thestress inhomogeneity causes the extension of the initialfracture to lag behind the new fracture With breakthroughof the initial fracture and generation of the new fracturefragments will be formed At the same time a stress wave willprovide kinetic energy to the fragments resulting inthrowing and flying of fragments

When the branch fracture surface of saturated coal androck simultaneously meets both τb gt τl and τf gt τa a new

fracture will not be formed on the fracture surface underdynamic load conditions -e propagation velocity of thedynamic fracture is faster than the static and the propa-gation velocity of the fracture is much lower than theload -erefore fracture water cannot diffuse into thefracture tip in a relatively short time Under the action of thesurface tension of free water the water on the fracturesurface will produce a cohesion force (pdw minuspsw) Underdynamic loading because the materials simultaneously meetτb gt τl and τf gt τa the branch fracture surface will notgenerate new fractures -us the entire branch fractureextension will be hampered which increases the strength ofthe saturated coal and rock

As mentioned above coal has low intensity more de-veloped fractures a small strength reduction coefficientwhen saturated and the reaction force between particles isalso lower -us under static-dynamic loads the relativetensile stress and shear stress generated on the branchfracture surface of a saturated coal specimen is much higherthan the tensile strength and shear strength of the fracturesurface ie τb lt τl and τf lt τa -is can cause branchfracture tensile failure and shear failure -e damage of thecoal specimen and the expansion of fractures are acceleratedand the dynamic strength of the coal specimen is weakenedIn contrast the effect of water-rock interactions on sand-stone is smaller the strength reduction coefficient is largerand it has a high strength and relatively low fracture densityUnder the same conditions the relative tensile stress andshear stress generated in the fracture surface of saturatedsandstone under static-dynamic loads are much higher thantensile strength and shear strength of the fracture surfaceie τb gt τl and τf gt τa -erefore the extension of wholebranch fracture of naturally saturated sandstone will behampered due to the cohesion force generated from theStefan effect Additionally generation of new fractures onthe branch fracture surface of sandstone is also suppressed-e dynamic peak strength of the specimen is improved

Furthermore during dynamic impact the diffusion offree water lags behind the expansion of the new fracturebecause of generation of new fractures in the branch fracturesurface of saturated coal specimens -us the diffusionspeed of free water is largely determined by the growth speedof the new fracture which means that each primary and newfracture will contain free water -e area of the branchfracture surface in contact with water will produce a cohesiveforce hindering the branch fracture from growing -isreduces the compressibility of free water and the ability ofthe coal specimen to resist deformation is enhanced At thistime the greater the fracture area in contact with water thehigher the stiffness of the water-rock common loads will be-is provides a reason for the increase in the deformationmodulus of coal specimens with moisture content undermedium strain rate conditions

4 Conclusion

(1) Under static loading conditions the saturatedstrength reduction coefficient and elastic modulusreduction coefficient of coal samples are lower than

8 Advances in Civil Engineering

those of sandstone Under dynamic loading condi-tions the strength of naturally saturated coal samplesdecreases and the elastic modulus increases -isis the same strength variation trend and oppositeelastic modulus variation trend as observed forsandstone

(2) -e water-saturated coal specimens have greaterwater-rock interactions and strength reductioneffect its reduction in the ability to resist defor-mation is also very significant compared to saturatedsandstone

(3) Under static-dynamic loads owing to intensitydifferences in the saturated coal and rock materials astress difference results from the Stefan effect in thebranch fracture surface which is the main reasonthat the strength of coal and rock materials increasesor decreases Meanwhile fracture propagation atsaturated branch fracture surfaces can effectivelyexplain the increase in the deformation modulus ofcoal with increasing moisture content

(4) According to a sliding model of wing branch frac-ture the criteria for microfracture tensile stress andshear stress produced at the branch fracture surfacewere established If the branch fracture surface si-multaneously satisfies both τb gt τl and τf gt τa thebranch fracture surface will not break down -edynamic strength of water-saturated coal and rockwill increase If the branch fracture surface meetsonly one of the conditions τb lt τl or τf lt τa thebranch fracture surface will break down and thedynamic strength of water-saturated coal and rockwill decrease

Data Availability

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

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-e work was supported by the National Natural ScienceFoundation of China (51604093 and 51474096) NationalKey RampD Program of China (2018YFC0604502) Programfor Innovative Research Team at the University of Ministryof Education of China (IRT_16R22) Scientific and Tech-nological Key Project of Henan province (172107000016)and the Doctoral Research Fund Project of Henan Poly-technic University China (B2017-42)

References

[1] B Vasarhelyi and P Van ldquoInfluence of water content on thestrength of rockrdquo Engineering Geology vol 84 no 1-2pp 70ndash74 2006

[2] L S Tang P C Zhang and Y Wang ldquoOn fractures strengthof rocks with cracks under water actionrdquo Chinese Journal ofRock Mechanics and Engineering vol 23 no 19 pp 3337ndash3341 2004

[3] Z Zhu and D Hu ldquo-e effect of intestitial water pressure onrock mass strengthrdquo Rock and Soil Mechanics vol 21 no 1pp 64ndash67 2000

[4] Y Pu and Q Y Ma ldquoSplit Hopkinson pressure bar tests onsandstone in coalmine under cyclic wetting and dryingrdquo Rockand Soil Mechanics vol 9 pp 2557ndash2562 2013

[5] Y Pu and R Ma ldquoSplit Hopkinson pressure bar tests andanalysis of coalmine sandstone with various moisture con-tentsrdquo Chinese Journal of Rock Mechanics and Engineeringvol 34 no 1 pp 2888ndash2893 2015

[6] W Wang H Li and H Gu ldquoMicromechanics analysis andmechanical characteristics of water-saturated coal specimensunder coupled static-dynamic loadsrdquo Journal of China CoalSociety vol 3 pp 611ndash617 2016

[7] W Wang H Wang D Li H Li and Z Liu ldquoStrength andfailure characteristics of natural and water-saturated coalspecimens under static and dynamic loadsrdquo Shock and Vi-bration vol 2018 Article ID 3526121 15 pages 2018

[8] Y Q Ding W H Tang and X Xu ldquoExperimental studyof dynamic mechanical behaviors of unsaturated clay sub-jected touniaxial loadingrdquo Rock and Soil Mechanics vol 9pp 2546ndash2550 2013

[9] N Ding L Jin and J Zhang ldquoEffect of free water content onthe dynamic mechanical behavior of cement mortar underhigh strain raterdquo Concrete vol 10 pp 128ndash132 2013

[10] J Zhan and N Zhang ldquoStudy on the damage feature ofwater-bearing argillaceous siltstone under the impact loadrdquoNon-Ferrous Metal vol 6 pp 44ndash77 2015

[11] Y Zhao S Liu Y Jiang K Wang and Y Huang ldquoDynamictensile strength of coal under dry and saturated conditionsrdquoRock Mechanics and Rock Engineering vol 49 no 5pp 1709ndash1720 2015

[12] Y V Petrov I V Smirnov G A Volkov A K AbramianA M Bragov and S N Verichev ldquoDynamic failure of dryand fully saturated limestone samples based on incubationtime conceptrdquo Journal of Rock Mechanics and GeotechnicalEngineering vol 9 no 1 pp 125ndash134 2017

[13] B Wang and X Li ldquoMesomechanics analysis of static com-pressive strength and dynamic compressive strength of water-saturated rock under uniaxial loadrdquo Explosion and ShockWaves vol 32 no 4 pp 423ndash431 2014

[14] F Gong X Li X Liu et al ldquoExperimental study of dynamiccharacteristics of sandstone under one-dimensional coupledstatic and dynamic loadsrdquo Chinese Journal of Rock Mechanicsand Engineering vol 29 no 10 pp 2076ndash2085 2010

[15] F Q Gong and G F Zhao ldquoDynamic indirect tensile strengthof sandstone under different loading ratesrdquo Rock Mechanicsand Rock Engineering vol 47 no 6 pp 2271ndash2278 2013

[16] -e National Standard Compilation Groups of Peoplersquos Re-public of China GBT 235615-2009 Methods for Determiningthe Physical and Mechanical Properties of Coal and RockStandards Press of China Beijing China 2009 in Chinese

[17] D Xiong Z Zhao and C Su ldquoExperimental study of effect ofwater-sturated state on mechanical properties of rock in coalmeasure stratardquo Chinese Journal of Rock Mechanics andEngineering vol 5 pp 998ndash1006 2011

[18] H Wang and Q Li ldquoSaturated concrete mesoscopic me-chanics mechanism of the static and dynamic compressivestrengthrdquo Journal of Hydraulic Engineering vol 8 pp 958ndash962 2006

Advances in Civil Engineering 9

[19] M Tao H T Zhao X B Li and W Z Cao ldquoFailurecharacteristics of pre-stressed rock with a circular hole sub-jected to dynamic loadingrdquo Tunnelling and UndergroundSpace Technology vol 81 pp 1ndash15 2018

[20] M Tao A Ma W Cao X Li and F Gong ldquoDynamicresponse of pre-stressed rock with a circular cavity subject totransient loadingrdquo International Journal of Rock Mechanicsand Mining Sciences vol 99 pp 1ndash8 2017

[21] Y Ogata W J Jung S Kubota and Y Wada ldquoEffect of thestrain rate and water saturation for the dynamic tensilestrength of rocksrdquo Materials Science Forum vol 465-466pp 361ndash366 2004

[22] S Huang K Xia F Yan and X Feng ldquoAn experimental studyof the rate dependence of tensile strength softening ofLongyou sandstonerdquo Rock Mechanics and Rock Engineeringvol 43 no 6 pp 677ndash683 2010

[23] Z Zhou X Cai W Cao X Li and C Xiong ldquoInfluence ofwater content on mechanical properties of rock in bothsaturation and drying processesrdquo Rock Mechanics and RockEngineering vol 49 no 8 pp 3009ndash3025 2016

[24] Z Zhou X Cai L Chen W Cao Y Zhao and C XiongldquoInfluence of cyclic wetting and drying on physical and dy-namic compressive properties of sandstonerdquo EngineeringGeology vol 220 pp 1ndash12 2017

[25] D Zheng and Q Li ldquoAn explanation for rate effect of concretestrength based on fracture toughness including free waterviscosityrdquo Engineering Fracture Mechanics vol 71 no 16-17pp 2319ndash2327 2004

[26] P Rossi J G M van Mier C Boulay and F Le Maou ldquo-edynamic behaviour of concrete influence of free waterrdquoMaterials and Structures vol 25 no 9 pp 509ndash514 1992

10 Advances in Civil Engineering

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Wang and Li [13 18] concluded that water-saturated con-crete and granite have similar mechanical properties

3 Mechanism and Discussion

-e analysis shows that in addition to the influence ofmineral composition structure and type of cementation rockmechanical properties are also influenced by the water en-vironment [19 20] Ogata et al [21] show that the tensilestrength of rocks with high porosity on the water saturationcondition was decreased on both static and dynamic con-dition Huang et al [22] found that the tensile strengthsoftening factor decreases with the loading rate Moreoverstatic and dynamic loading strength tests of sandstone underwater-bearing conditions were carried out by Zhou et al[23 24] revealing that the static and dynamic sandstonestrengths decreased by 2988 and 4055 following satu-ration -e permeability of coal and rock specimens is pri-marily determined by the presence of fractures and themineral components of these fractures -e presence of avariety of mineral components directly affects the physical

and chemical properties of coal and rock Coal and rockmaterials contain pores and fractures of varying numbers andshapes -e fractures contain a variety of minerals such assulfides oxides carbonates and silicates As a type of solventwater has a small corrosive effect on high strength materialsbut a highly corrosive effect on low strength materials -ecorrosive effect of water can readily create small weak parts inthe fractures resulting in the holes continuing to expandunder stress Erosion by corrosive molecules leads to thefractures and holes continuously increasing and enlargingMoreover water can dissolve some minerals in the coal androck causing water absorption expansion of montmorillonitein the mineral -is results in generation of uneven stress inthe interior of coal and rock specimens In addition becausethe cementing material in the fractures and a portion of thecement between particles are dissolved the cohesion forcebetween particles and cement decreases Furthermore themicrocomposition of coal and rock is changed and theoriginal microstructure can be broken causing the strength ofcoal and rock materials to decrease

D3-2

D3-4

D3-3

00 2 4 6 8 10 12

5

15

10

20

25

30

35

40

σ (M

Pa)

ε (10ndash3)

(a)

0 2 4 6 8 10 12 140

5

10

15

20

25

30

35

D3-1

D2-3

D2-4

σ (M

Pa)

ε (10ndash3)

(b)

Figure 4 Dynamic stress-strain curves for coal specimens with different moisture states (a) Natural state (b) Water-saturated state

180

90

150

120

60

30

00 1 2 3 4 5 6 7

A23

A215A21

A216

A214 A22

ε (10ndash3)

σ (M

Pa)

Figure 5 Static stress-strain curves for natural and water-saturatedsandstone specimens

Table 1 Physicomechanical parameters of natural and water-saturated specimens under uniaxial compression

Specimennumber State RC (MPa) w () P (kgmiddotmminus3) E (GPa)

D1-1 Natural 4311 mdash 133 211D1-2 Natural 4207 mdash 135 190D1-3 Natural 4292 mdash 134 194D1-4 Saturated 2530 32 137 173D2-1 Saturated 2081 61 145 128D2-2 Saturated 204 45 136 166A21 Natural 1373 mdash 261 343A22 Natural 1295 mdash 2606 326A23 Natural 1624 mdash 2625 359A214 Saturated 1112 023 2623 315A215 Saturated 1300 077 2608 364A216 Saturated 977 040 2603 295

4 Advances in Civil Engineering

Comparing Figures 3 and 4 leads to the followingconclusions the strength reduction coefficient and elasticmodulus reduction coefficient of the saturated coal speci-mens with a high water absorption rate are 052 and 077respectively However sandstone is relatively dense and thestrength reduction coefficient and elastic modulus reductioncoefficient of the saturated sandstone specimens with a lowwater absorption rate are 079 and 094 respectively

315e Force between Particles Compared to coal there arefew fractures and pores in the sandstone Additionallysandstone has a denser structure greater content of highstrength materials and weaker water-rock interaction thancoal -erefore the strength and antideformation ability ofcoal decreases significantly under static loads but the waterhas little effect on the strength and antideformation ability ofsandstone A comparison of the natural state and water-saturated state of a coal specimen is shown in Figure 7

Furthermore before the coal and rock specimens aresoaked in water some water is contained internally oc-curring on the surface of particles in the form of crystalwater pore water and fracture water -us an attractiveeffect will occur between the water and particles at thesame time capillary pressure will also be produced Underthe action of capillary stress a bridge of water moleculescan be formed and a concave surface appears between theparticles -is effect will bond the particles together andconstitutes the internal bond strength of the rock as shownin Figure 8

-e attractive force F between particles includes thesurface tension and capillary pressure -e capillary pres-sure Pc can be expressed as follows

Pc cos(ϕ + θ)

1minus cosϕσR

(2)

where R is the particle radius σ is the surface tension ofwater in the air and θ is the contact angle With decreasingparticle radius Pc approaches infinity and the attractiveforce between particles can be expressed as follows

F 2πRσ sinϕ sin(ϕ + θ) + πR2mpc (3)

where Rm is the radius of the concave water droplet whichcan be calculated geometrically -e reaction force betweenthe particles is expressed as follows

F sinϕ sin(ϕ + θ) +[sin(ϕ + θ) + cosϕminus 1minus sin θ]2

2(1minus cos θ)cos(ϕ + θ)11138971113896

middot 2πRσ

(4)

Equation (4) indicates that after the specimen is water-saturated water molecules enter the pores between particlescausing Rm to increase F gradually decreases and the co-hesion force between particles in the rock decreases Fur-thermore the strength also decreases

Owing to the high pore density of coal the cement strengthbetween particles is lower Coal also has a higher water ab-sorption rate (Table 1) resulting in a larger Rm for the coalspecimens than of the sandstone In the saturated state theforces acting among particles in the coal specimens are weakerthan in sandstone and the strength is decreased observably

32 Fracture Propagation Characteristics under DynamicLoad -e propagation and aggregation of microfractureswithin coal and rock is the fundamental cause of macro-damage to the coal and rock under external loading Toanalyze the effect of free water in the fractures of saturatedcoal and rock on crack propagation under static-dynamic

200

160

120

80

40

0

σ (M

Pa)

0000 0004 0008 0012 0016 0020ε

Natural moisture stateDry stateMandatory saturated state

Natural saturated state

(a)

200

160

120

80

40

0

σ (M

Pa)

0000 0004 0008 0012 0016 0020ε

Natural moisture stateDry stateMandatory saturated state

Natural saturated state

(b)

Figure 6 Dynamic stress-strain curves for sandstone specimens (a) Yangzhuang coalmine (_ε 198 sminus1) (b) Hengyuan north auxiliary shaft(_ε 200 sminus1)

Advances in Civil Engineering 5

loading this study simplifies the three-dimensional hydrousfracture to a plane fracture and a single fracture is taken asan example For the parameters of the hydrous singlefracture the static load is σs dynamic load is σd fracturelength is 2a and angle is β as shown in Figure 9

321 Fracture Propagation Characteristics of Saturated Coaland Rock under Static-Dynamic Loads During staticloading wing fractures will occur with increasing static load-e fracture propagation velocity is faster than the staticloading speed In addition the fracture tip will fill with freewater due to occurrence of a siphon phenomenon in thefracture tip

-is results in a decrease in the friction coefficient of thefracture contact surface increase in the microrupture ac-tivity of the coal and rock specimens acceleration of fracturepropagation and concatenation and transfixion betweenfractures Furthermore the macrodestructive force of the

specimens decreases and the compressive strength of thespecimens is also reduced Wang and Li [13] investigated theforce of free water in fracture propagation in coal and rockunder static loads

-e fracture growth characteristics of coal and rock arebasically consistent under static loads In the natural state thenumber of fractures further increases as the coal and rockspecimens absorb water -is occurs because of the low in-tensity of coal and its dense fractures coupled with thecorrosive effects of water At the same time the reaction forcebetween particles decreases significantly [13] -is leads thevelocity of the new fracture to grow faster in coal specimensunder static loads than in the saturated sandstone -estrength reduction coefficient and elastic modulus reductioncoefficient of the coal and rock specimens are smaller

322 Fracture Propagation Characteristics of Saturated Coaland Rock under Dynamic Loads -e propagation charac-teristics of coal and rock fractures under static-dynamicloading can be obtained from the mesomechanical analyticalmethod of concrete and rock mechanics [25 26] Understatic-dynamic loads a cohesive force F is formed from thesurface tension of free water in the fractures and resistanceand Fprime result from the Stefan effect and impede the fracturegrowth and further fracturing -e force that hindersfracture propagation pdw can be expressed as follows

pdw F + Fprime( 1113857

A

VR 2δ2 cosφ1113872 11138731113872 1113873 + 3ηr42πh3( 1113857(dudt)( 11138571113872 1113873

A

(5)

where V is the liquid volume R is the surface energy φ is thewetting angle δ is the radius of the water meniscus η is theliquid viscosity r is the radius of two parallel circular platesfilled with incompressible viscous fluids u is the relativedisplacement corresponding to the separation of the twocircular plates h is the space between the two circular platesand A is the area of the fracture containing water

θ

φ

Rm

R

Figure 8 Model of grain-water molecule interactions

(a) (b) (c)

Figure 7 Sketch of the coal specimen in the natural state and water-saturated state (a) Coal specimen D1-2 (b) Natural state (c) Water-saturated state

6 Advances in Civil Engineering

323 Stress Balance on Both Ends of the Specimen duringDynamic Impact Processes -e stress state under static-dynamic loading is shown in Figure 10 In the image σIis the incident stress σR is the reflected stress σT is thetransmission stress and σs is the prestatic load

-e stress balance on both ends of the specimen is aprecondition for a reasonable equivalent of the dynamicload Zncker and Closer proposed applying an equilibriumfactor μ to measure the stress equilibrium state of speci-mens μ was defined as the ratio of the stress differencebetween the two ends to the average stress in the specimenas given by Equation (6) As the equilibrium factor ap-proaches zero the stress in the specimens becomes moreuniform -e equilibrium factor is calculated as follows

μ 2 σSI minus σST( 1113857

σSI + σST (6)

where σSI is the incident end stress and σST is the trans-mission end stress

During the impact process the small size of the specimenand the complicated transient change in the stress mean thatthe present technique cannot achieve direct measurement ofthe stress distribution on both ends According to the theoryof SHPB tests for the equivalent stress on both ends of thespecimen the equivalent formula is as follows

σST σT

σSI σI + σR(7)

-e trend in the equilibrium factor during the dynamicshock process for a specimen under prestatic loads is shownin Figure 11

-e reflection wave σT is a platform which indicatesthat the experiment has achieved loading at a constant strainrate During the whole impact loading process the stress atthe incident and transmission ends are almost equal -e

equilibrium factor μ tends to approximately zero by 30 μsafter loading and is maintained to 140 μs -erefore thedynamic impact force of coal specimens is a reasonableequivalent for the quasi-static stress σd coupled with theprestatic load σs

During the static-dynamic loads a prestatic load σs isfirst applied followed by the dynamic load σd σsminusd is thecomposite failure strength of the coal specimen hydrousfracture under a combination load-e friction coefficient ofthe branch fracture is divided by the dynamic load factor fdof the branch fracture surface that is not in contact withwater and the dynamic load factor fdw of the branchfracture surface in contact with water owing to the lowstrength of natural saturated coal specimens at the fracturesurface and the uneven distribution of water in the branchfracture -erefore considering the difference in stressbetween the areas in the branch fracture surface that are incontact with water and those that are not in contact withwater is necessary

As shown in Figure 9 surface abndashcd is the free waterinterface and a mechanical analysis of the stress structure of awing branch fracture was carried out under static-dynamicloading -e compressive stress is assumed to be positive inthis analysis -us the shear stress τ(dminuss)w and normal stressσ(dminuss)w of the wing branch fracture surface in contact withfree water and the shear stress τ(dminuss) and normal stressσ(dminuss) of the wing branch fracture not in contact with water

XG1 X1 X2 XG2

Straingauge G1

σI

σR

σT

σR

σIσT σSσS

Incident bar Sample Transmission barStrain gauge G2

Figure 10 Loading diagram of a specimen under static-dynamicload

125100

755025

0ndash25ndash50ndash75

ndash100ndash125ndash150

0 20 40 60 80T (μs)

100 120 140 160

543210ndash1ndash2ndash3ndash4ndash5ndash6

σ (M

Pa)

μ

σR

σT

σSIμ

σR + σI σI

σRσST

σI

μ

Figure 11 Balance factor for specimens under static-dynamicloads

σdσs σdσs

σdσs σdσs

L

β

τ(s-d)w

τs

PswPdwa

bσ(s-d)w

σ(s-d)

PswPdw

cd

σ(s-d)w

PdwPsw

τ(s-d)w

τ(s-d)

σ(s-d)PdwPsw

Psw

Psw

Pdw

Pdw

Void

Void

2a

θ

Figure 9 Pressure at the crack surface caused by free water undercoupled static-dynamic loads

Advances in Civil Engineering 7

(out of the abndashcd surface) can be obtained -e above pa-rameters can be expressed by equations (8)ndash(11) as follows

τ(sminusd)w 12σsminusd sin 2(β + θ)

minusfdw σsminusd cos2(β + θ)minus psw minuspdw( 11138571113960 1113961

(8)

τ(sminusd) 12σsminusd sin 2(β + θ)minusfdσsminusd cos

2(β + θ) (9)

σ(sminusd)w σsminusd cos2(β + θ)minus psw minuspdw( 1113857 (10)

σ(sminusd) σsminusd cos2(β + θ) (11)

wheref(dminuss)w is the friction coefficient of the hydrous fracturein contact with free water under dynamic load fd is thefriction coefficient of the hydrous fracture not in contact withfree water under dynamic load pdw is the stress that inhibitsfracture extension and psw is the outward extrusion stress offree water on an airfoil fracture Numerically pdw is far largerthan psw in the dynamic impact process Both of these areinvolved in fracture development and breakthrough

From Equations (8)ndash(11) Equations (12) and (13) can beobtained for the relative shear stress τl generated normal tosurface abndashcd and the relative normal stress σl

τl τ(sminusd) minus τ(sminusd)w fdσsminusd cos2(β + θ)

minusfdw σsminusd cos2(β + θ)minus psw minuspdw( 11138571113960 1113961

(12)

τa σ(sminusd) minus σ(sminusd)w psw minuspdw (13)

where τl is the tensile stress at the branch fracture surfacenear the abndashcd interface and τa is the shear stress at thebranch fracture surface near the abndashcd interface

At the coal and rock branch fracture surface the settingtensile strength is τb and the shear strength is τf When thebranch fracture surface of saturated coal and rock meets oneof the conditions τb lt τl or τf lt τa the branch fracturesurface will be damaged and a new fracture will form -ebranch fracture surface of saturated coal and rock canproduce resistance due to the Stefan effect under static-dynamic loads -e extension of the fracture at the branchfracture surface in contact with water will result in a pressuredifference at the branch fracture surface -us the newfracture will generate owing to the low strength of thematerial In other words when the material meets one of thetwo conditions above destruction of the fracture will resultin more energy for generation and extension of the newfracture -us the elastic energy storage in the tip of theinitial fracture will decrease and the coal and rock materialstrength will also decrease During dynamic loading thestress inhomogeneity causes the extension of the initialfracture to lag behind the new fracture With breakthroughof the initial fracture and generation of the new fracturefragments will be formed At the same time a stress wave willprovide kinetic energy to the fragments resulting inthrowing and flying of fragments

When the branch fracture surface of saturated coal androck simultaneously meets both τb gt τl and τf gt τa a new

fracture will not be formed on the fracture surface underdynamic load conditions -e propagation velocity of thedynamic fracture is faster than the static and the propa-gation velocity of the fracture is much lower than theload -erefore fracture water cannot diffuse into thefracture tip in a relatively short time Under the action of thesurface tension of free water the water on the fracturesurface will produce a cohesion force (pdw minuspsw) Underdynamic loading because the materials simultaneously meetτb gt τl and τf gt τa the branch fracture surface will notgenerate new fractures -us the entire branch fractureextension will be hampered which increases the strength ofthe saturated coal and rock

As mentioned above coal has low intensity more de-veloped fractures a small strength reduction coefficientwhen saturated and the reaction force between particles isalso lower -us under static-dynamic loads the relativetensile stress and shear stress generated on the branchfracture surface of a saturated coal specimen is much higherthan the tensile strength and shear strength of the fracturesurface ie τb lt τl and τf lt τa -is can cause branchfracture tensile failure and shear failure -e damage of thecoal specimen and the expansion of fractures are acceleratedand the dynamic strength of the coal specimen is weakenedIn contrast the effect of water-rock interactions on sand-stone is smaller the strength reduction coefficient is largerand it has a high strength and relatively low fracture densityUnder the same conditions the relative tensile stress andshear stress generated in the fracture surface of saturatedsandstone under static-dynamic loads are much higher thantensile strength and shear strength of the fracture surfaceie τb gt τl and τf gt τa -erefore the extension of wholebranch fracture of naturally saturated sandstone will behampered due to the cohesion force generated from theStefan effect Additionally generation of new fractures onthe branch fracture surface of sandstone is also suppressed-e dynamic peak strength of the specimen is improved

Furthermore during dynamic impact the diffusion offree water lags behind the expansion of the new fracturebecause of generation of new fractures in the branch fracturesurface of saturated coal specimens -us the diffusionspeed of free water is largely determined by the growth speedof the new fracture which means that each primary and newfracture will contain free water -e area of the branchfracture surface in contact with water will produce a cohesiveforce hindering the branch fracture from growing -isreduces the compressibility of free water and the ability ofthe coal specimen to resist deformation is enhanced At thistime the greater the fracture area in contact with water thehigher the stiffness of the water-rock common loads will be-is provides a reason for the increase in the deformationmodulus of coal specimens with moisture content undermedium strain rate conditions

4 Conclusion

(1) Under static loading conditions the saturatedstrength reduction coefficient and elastic modulusreduction coefficient of coal samples are lower than

8 Advances in Civil Engineering

those of sandstone Under dynamic loading condi-tions the strength of naturally saturated coal samplesdecreases and the elastic modulus increases -isis the same strength variation trend and oppositeelastic modulus variation trend as observed forsandstone

(2) -e water-saturated coal specimens have greaterwater-rock interactions and strength reductioneffect its reduction in the ability to resist defor-mation is also very significant compared to saturatedsandstone

(3) Under static-dynamic loads owing to intensitydifferences in the saturated coal and rock materials astress difference results from the Stefan effect in thebranch fracture surface which is the main reasonthat the strength of coal and rock materials increasesor decreases Meanwhile fracture propagation atsaturated branch fracture surfaces can effectivelyexplain the increase in the deformation modulus ofcoal with increasing moisture content

(4) According to a sliding model of wing branch frac-ture the criteria for microfracture tensile stress andshear stress produced at the branch fracture surfacewere established If the branch fracture surface si-multaneously satisfies both τb gt τl and τf gt τa thebranch fracture surface will not break down -edynamic strength of water-saturated coal and rockwill increase If the branch fracture surface meetsonly one of the conditions τb lt τl or τf lt τa thebranch fracture surface will break down and thedynamic strength of water-saturated coal and rockwill decrease

Data Availability

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

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-e work was supported by the National Natural ScienceFoundation of China (51604093 and 51474096) NationalKey RampD Program of China (2018YFC0604502) Programfor Innovative Research Team at the University of Ministryof Education of China (IRT_16R22) Scientific and Tech-nological Key Project of Henan province (172107000016)and the Doctoral Research Fund Project of Henan Poly-technic University China (B2017-42)

References

[1] B Vasarhelyi and P Van ldquoInfluence of water content on thestrength of rockrdquo Engineering Geology vol 84 no 1-2pp 70ndash74 2006

[2] L S Tang P C Zhang and Y Wang ldquoOn fractures strengthof rocks with cracks under water actionrdquo Chinese Journal ofRock Mechanics and Engineering vol 23 no 19 pp 3337ndash3341 2004

[3] Z Zhu and D Hu ldquo-e effect of intestitial water pressure onrock mass strengthrdquo Rock and Soil Mechanics vol 21 no 1pp 64ndash67 2000

[4] Y Pu and Q Y Ma ldquoSplit Hopkinson pressure bar tests onsandstone in coalmine under cyclic wetting and dryingrdquo Rockand Soil Mechanics vol 9 pp 2557ndash2562 2013

[5] Y Pu and R Ma ldquoSplit Hopkinson pressure bar tests andanalysis of coalmine sandstone with various moisture con-tentsrdquo Chinese Journal of Rock Mechanics and Engineeringvol 34 no 1 pp 2888ndash2893 2015

[6] W Wang H Li and H Gu ldquoMicromechanics analysis andmechanical characteristics of water-saturated coal specimensunder coupled static-dynamic loadsrdquo Journal of China CoalSociety vol 3 pp 611ndash617 2016

[7] W Wang H Wang D Li H Li and Z Liu ldquoStrength andfailure characteristics of natural and water-saturated coalspecimens under static and dynamic loadsrdquo Shock and Vi-bration vol 2018 Article ID 3526121 15 pages 2018

[8] Y Q Ding W H Tang and X Xu ldquoExperimental studyof dynamic mechanical behaviors of unsaturated clay sub-jected touniaxial loadingrdquo Rock and Soil Mechanics vol 9pp 2546ndash2550 2013

[9] N Ding L Jin and J Zhang ldquoEffect of free water content onthe dynamic mechanical behavior of cement mortar underhigh strain raterdquo Concrete vol 10 pp 128ndash132 2013

[10] J Zhan and N Zhang ldquoStudy on the damage feature ofwater-bearing argillaceous siltstone under the impact loadrdquoNon-Ferrous Metal vol 6 pp 44ndash77 2015

[11] Y Zhao S Liu Y Jiang K Wang and Y Huang ldquoDynamictensile strength of coal under dry and saturated conditionsrdquoRock Mechanics and Rock Engineering vol 49 no 5pp 1709ndash1720 2015

[12] Y V Petrov I V Smirnov G A Volkov A K AbramianA M Bragov and S N Verichev ldquoDynamic failure of dryand fully saturated limestone samples based on incubationtime conceptrdquo Journal of Rock Mechanics and GeotechnicalEngineering vol 9 no 1 pp 125ndash134 2017

[13] B Wang and X Li ldquoMesomechanics analysis of static com-pressive strength and dynamic compressive strength of water-saturated rock under uniaxial loadrdquo Explosion and ShockWaves vol 32 no 4 pp 423ndash431 2014

[14] F Gong X Li X Liu et al ldquoExperimental study of dynamiccharacteristics of sandstone under one-dimensional coupledstatic and dynamic loadsrdquo Chinese Journal of Rock Mechanicsand Engineering vol 29 no 10 pp 2076ndash2085 2010

[15] F Q Gong and G F Zhao ldquoDynamic indirect tensile strengthof sandstone under different loading ratesrdquo Rock Mechanicsand Rock Engineering vol 47 no 6 pp 2271ndash2278 2013

[16] -e National Standard Compilation Groups of Peoplersquos Re-public of China GBT 235615-2009 Methods for Determiningthe Physical and Mechanical Properties of Coal and RockStandards Press of China Beijing China 2009 in Chinese

[17] D Xiong Z Zhao and C Su ldquoExperimental study of effect ofwater-sturated state on mechanical properties of rock in coalmeasure stratardquo Chinese Journal of Rock Mechanics andEngineering vol 5 pp 998ndash1006 2011

[18] H Wang and Q Li ldquoSaturated concrete mesoscopic me-chanics mechanism of the static and dynamic compressivestrengthrdquo Journal of Hydraulic Engineering vol 8 pp 958ndash962 2006

Advances in Civil Engineering 9

[19] M Tao H T Zhao X B Li and W Z Cao ldquoFailurecharacteristics of pre-stressed rock with a circular hole sub-jected to dynamic loadingrdquo Tunnelling and UndergroundSpace Technology vol 81 pp 1ndash15 2018

[20] M Tao A Ma W Cao X Li and F Gong ldquoDynamicresponse of pre-stressed rock with a circular cavity subject totransient loadingrdquo International Journal of Rock Mechanicsand Mining Sciences vol 99 pp 1ndash8 2017

[21] Y Ogata W J Jung S Kubota and Y Wada ldquoEffect of thestrain rate and water saturation for the dynamic tensilestrength of rocksrdquo Materials Science Forum vol 465-466pp 361ndash366 2004

[22] S Huang K Xia F Yan and X Feng ldquoAn experimental studyof the rate dependence of tensile strength softening ofLongyou sandstonerdquo Rock Mechanics and Rock Engineeringvol 43 no 6 pp 677ndash683 2010

[23] Z Zhou X Cai W Cao X Li and C Xiong ldquoInfluence ofwater content on mechanical properties of rock in bothsaturation and drying processesrdquo Rock Mechanics and RockEngineering vol 49 no 8 pp 3009ndash3025 2016

[24] Z Zhou X Cai L Chen W Cao Y Zhao and C XiongldquoInfluence of cyclic wetting and drying on physical and dy-namic compressive properties of sandstonerdquo EngineeringGeology vol 220 pp 1ndash12 2017

[25] D Zheng and Q Li ldquoAn explanation for rate effect of concretestrength based on fracture toughness including free waterviscosityrdquo Engineering Fracture Mechanics vol 71 no 16-17pp 2319ndash2327 2004

[26] P Rossi J G M van Mier C Boulay and F Le Maou ldquo-edynamic behaviour of concrete influence of free waterrdquoMaterials and Structures vol 25 no 9 pp 509ndash514 1992

10 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Comparing Figures 3 and 4 leads to the followingconclusions the strength reduction coefficient and elasticmodulus reduction coefficient of the saturated coal speci-mens with a high water absorption rate are 052 and 077respectively However sandstone is relatively dense and thestrength reduction coefficient and elastic modulus reductioncoefficient of the saturated sandstone specimens with a lowwater absorption rate are 079 and 094 respectively

315e Force between Particles Compared to coal there arefew fractures and pores in the sandstone Additionallysandstone has a denser structure greater content of highstrength materials and weaker water-rock interaction thancoal -erefore the strength and antideformation ability ofcoal decreases significantly under static loads but the waterhas little effect on the strength and antideformation ability ofsandstone A comparison of the natural state and water-saturated state of a coal specimen is shown in Figure 7

Furthermore before the coal and rock specimens aresoaked in water some water is contained internally oc-curring on the surface of particles in the form of crystalwater pore water and fracture water -us an attractiveeffect will occur between the water and particles at thesame time capillary pressure will also be produced Underthe action of capillary stress a bridge of water moleculescan be formed and a concave surface appears between theparticles -is effect will bond the particles together andconstitutes the internal bond strength of the rock as shownin Figure 8

-e attractive force F between particles includes thesurface tension and capillary pressure -e capillary pres-sure Pc can be expressed as follows

Pc cos(ϕ + θ)

1minus cosϕσR

(2)

where R is the particle radius σ is the surface tension ofwater in the air and θ is the contact angle With decreasingparticle radius Pc approaches infinity and the attractiveforce between particles can be expressed as follows

F 2πRσ sinϕ sin(ϕ + θ) + πR2mpc (3)

where Rm is the radius of the concave water droplet whichcan be calculated geometrically -e reaction force betweenthe particles is expressed as follows

F sinϕ sin(ϕ + θ) +[sin(ϕ + θ) + cosϕminus 1minus sin θ]2

2(1minus cos θ)cos(ϕ + θ)11138971113896

middot 2πRσ

(4)

Equation (4) indicates that after the specimen is water-saturated water molecules enter the pores between particlescausing Rm to increase F gradually decreases and the co-hesion force between particles in the rock decreases Fur-thermore the strength also decreases

Owing to the high pore density of coal the cement strengthbetween particles is lower Coal also has a higher water ab-sorption rate (Table 1) resulting in a larger Rm for the coalspecimens than of the sandstone In the saturated state theforces acting among particles in the coal specimens are weakerthan in sandstone and the strength is decreased observably

32 Fracture Propagation Characteristics under DynamicLoad -e propagation and aggregation of microfractureswithin coal and rock is the fundamental cause of macro-damage to the coal and rock under external loading Toanalyze the effect of free water in the fractures of saturatedcoal and rock on crack propagation under static-dynamic

200

160

120

80

40

0

σ (M

Pa)

0000 0004 0008 0012 0016 0020ε

Natural moisture stateDry stateMandatory saturated state

Natural saturated state

(a)

200

160

120

80

40

0

σ (M

Pa)

0000 0004 0008 0012 0016 0020ε

Natural moisture stateDry stateMandatory saturated state

Natural saturated state

(b)

Figure 6 Dynamic stress-strain curves for sandstone specimens (a) Yangzhuang coalmine (_ε 198 sminus1) (b) Hengyuan north auxiliary shaft(_ε 200 sminus1)

Advances in Civil Engineering 5

loading this study simplifies the three-dimensional hydrousfracture to a plane fracture and a single fracture is taken asan example For the parameters of the hydrous singlefracture the static load is σs dynamic load is σd fracturelength is 2a and angle is β as shown in Figure 9

321 Fracture Propagation Characteristics of Saturated Coaland Rock under Static-Dynamic Loads During staticloading wing fractures will occur with increasing static load-e fracture propagation velocity is faster than the staticloading speed In addition the fracture tip will fill with freewater due to occurrence of a siphon phenomenon in thefracture tip

-is results in a decrease in the friction coefficient of thefracture contact surface increase in the microrupture ac-tivity of the coal and rock specimens acceleration of fracturepropagation and concatenation and transfixion betweenfractures Furthermore the macrodestructive force of the

specimens decreases and the compressive strength of thespecimens is also reduced Wang and Li [13] investigated theforce of free water in fracture propagation in coal and rockunder static loads

-e fracture growth characteristics of coal and rock arebasically consistent under static loads In the natural state thenumber of fractures further increases as the coal and rockspecimens absorb water -is occurs because of the low in-tensity of coal and its dense fractures coupled with thecorrosive effects of water At the same time the reaction forcebetween particles decreases significantly [13] -is leads thevelocity of the new fracture to grow faster in coal specimensunder static loads than in the saturated sandstone -estrength reduction coefficient and elastic modulus reductioncoefficient of the coal and rock specimens are smaller

322 Fracture Propagation Characteristics of Saturated Coaland Rock under Dynamic Loads -e propagation charac-teristics of coal and rock fractures under static-dynamicloading can be obtained from the mesomechanical analyticalmethod of concrete and rock mechanics [25 26] Understatic-dynamic loads a cohesive force F is formed from thesurface tension of free water in the fractures and resistanceand Fprime result from the Stefan effect and impede the fracturegrowth and further fracturing -e force that hindersfracture propagation pdw can be expressed as follows

pdw F + Fprime( 1113857

A

VR 2δ2 cosφ1113872 11138731113872 1113873 + 3ηr42πh3( 1113857(dudt)( 11138571113872 1113873

A

(5)

where V is the liquid volume R is the surface energy φ is thewetting angle δ is the radius of the water meniscus η is theliquid viscosity r is the radius of two parallel circular platesfilled with incompressible viscous fluids u is the relativedisplacement corresponding to the separation of the twocircular plates h is the space between the two circular platesand A is the area of the fracture containing water

θ

φ

Rm

R

Figure 8 Model of grain-water molecule interactions

(a) (b) (c)

Figure 7 Sketch of the coal specimen in the natural state and water-saturated state (a) Coal specimen D1-2 (b) Natural state (c) Water-saturated state

6 Advances in Civil Engineering

323 Stress Balance on Both Ends of the Specimen duringDynamic Impact Processes -e stress state under static-dynamic loading is shown in Figure 10 In the image σIis the incident stress σR is the reflected stress σT is thetransmission stress and σs is the prestatic load

-e stress balance on both ends of the specimen is aprecondition for a reasonable equivalent of the dynamicload Zncker and Closer proposed applying an equilibriumfactor μ to measure the stress equilibrium state of speci-mens μ was defined as the ratio of the stress differencebetween the two ends to the average stress in the specimenas given by Equation (6) As the equilibrium factor ap-proaches zero the stress in the specimens becomes moreuniform -e equilibrium factor is calculated as follows

μ 2 σSI minus σST( 1113857

σSI + σST (6)

where σSI is the incident end stress and σST is the trans-mission end stress

During the impact process the small size of the specimenand the complicated transient change in the stress mean thatthe present technique cannot achieve direct measurement ofthe stress distribution on both ends According to the theoryof SHPB tests for the equivalent stress on both ends of thespecimen the equivalent formula is as follows

σST σT

σSI σI + σR(7)

-e trend in the equilibrium factor during the dynamicshock process for a specimen under prestatic loads is shownin Figure 11

-e reflection wave σT is a platform which indicatesthat the experiment has achieved loading at a constant strainrate During the whole impact loading process the stress atthe incident and transmission ends are almost equal -e

equilibrium factor μ tends to approximately zero by 30 μsafter loading and is maintained to 140 μs -erefore thedynamic impact force of coal specimens is a reasonableequivalent for the quasi-static stress σd coupled with theprestatic load σs

During the static-dynamic loads a prestatic load σs isfirst applied followed by the dynamic load σd σsminusd is thecomposite failure strength of the coal specimen hydrousfracture under a combination load-e friction coefficient ofthe branch fracture is divided by the dynamic load factor fdof the branch fracture surface that is not in contact withwater and the dynamic load factor fdw of the branchfracture surface in contact with water owing to the lowstrength of natural saturated coal specimens at the fracturesurface and the uneven distribution of water in the branchfracture -erefore considering the difference in stressbetween the areas in the branch fracture surface that are incontact with water and those that are not in contact withwater is necessary

As shown in Figure 9 surface abndashcd is the free waterinterface and a mechanical analysis of the stress structure of awing branch fracture was carried out under static-dynamicloading -e compressive stress is assumed to be positive inthis analysis -us the shear stress τ(dminuss)w and normal stressσ(dminuss)w of the wing branch fracture surface in contact withfree water and the shear stress τ(dminuss) and normal stressσ(dminuss) of the wing branch fracture not in contact with water

XG1 X1 X2 XG2

Straingauge G1

σI

σR

σT

σR

σIσT σSσS

Incident bar Sample Transmission barStrain gauge G2

Figure 10 Loading diagram of a specimen under static-dynamicload

125100

755025

0ndash25ndash50ndash75

ndash100ndash125ndash150

0 20 40 60 80T (μs)

100 120 140 160

543210ndash1ndash2ndash3ndash4ndash5ndash6

σ (M

Pa)

μ

σR

σT

σSIμ

σR + σI σI

σRσST

σI

μ

Figure 11 Balance factor for specimens under static-dynamicloads

σdσs σdσs

σdσs σdσs

L

β

τ(s-d)w

τs

PswPdwa

bσ(s-d)w

σ(s-d)

PswPdw

cd

σ(s-d)w

PdwPsw

τ(s-d)w

τ(s-d)

σ(s-d)PdwPsw

Psw

Psw

Pdw

Pdw

Void

Void

2a

θ

Figure 9 Pressure at the crack surface caused by free water undercoupled static-dynamic loads

Advances in Civil Engineering 7

(out of the abndashcd surface) can be obtained -e above pa-rameters can be expressed by equations (8)ndash(11) as follows

τ(sminusd)w 12σsminusd sin 2(β + θ)

minusfdw σsminusd cos2(β + θ)minus psw minuspdw( 11138571113960 1113961

(8)

τ(sminusd) 12σsminusd sin 2(β + θ)minusfdσsminusd cos

2(β + θ) (9)

σ(sminusd)w σsminusd cos2(β + θ)minus psw minuspdw( 1113857 (10)

σ(sminusd) σsminusd cos2(β + θ) (11)

wheref(dminuss)w is the friction coefficient of the hydrous fracturein contact with free water under dynamic load fd is thefriction coefficient of the hydrous fracture not in contact withfree water under dynamic load pdw is the stress that inhibitsfracture extension and psw is the outward extrusion stress offree water on an airfoil fracture Numerically pdw is far largerthan psw in the dynamic impact process Both of these areinvolved in fracture development and breakthrough

From Equations (8)ndash(11) Equations (12) and (13) can beobtained for the relative shear stress τl generated normal tosurface abndashcd and the relative normal stress σl

τl τ(sminusd) minus τ(sminusd)w fdσsminusd cos2(β + θ)

minusfdw σsminusd cos2(β + θ)minus psw minuspdw( 11138571113960 1113961

(12)

τa σ(sminusd) minus σ(sminusd)w psw minuspdw (13)

where τl is the tensile stress at the branch fracture surfacenear the abndashcd interface and τa is the shear stress at thebranch fracture surface near the abndashcd interface

At the coal and rock branch fracture surface the settingtensile strength is τb and the shear strength is τf When thebranch fracture surface of saturated coal and rock meets oneof the conditions τb lt τl or τf lt τa the branch fracturesurface will be damaged and a new fracture will form -ebranch fracture surface of saturated coal and rock canproduce resistance due to the Stefan effect under static-dynamic loads -e extension of the fracture at the branchfracture surface in contact with water will result in a pressuredifference at the branch fracture surface -us the newfracture will generate owing to the low strength of thematerial In other words when the material meets one of thetwo conditions above destruction of the fracture will resultin more energy for generation and extension of the newfracture -us the elastic energy storage in the tip of theinitial fracture will decrease and the coal and rock materialstrength will also decrease During dynamic loading thestress inhomogeneity causes the extension of the initialfracture to lag behind the new fracture With breakthroughof the initial fracture and generation of the new fracturefragments will be formed At the same time a stress wave willprovide kinetic energy to the fragments resulting inthrowing and flying of fragments

When the branch fracture surface of saturated coal androck simultaneously meets both τb gt τl and τf gt τa a new

fracture will not be formed on the fracture surface underdynamic load conditions -e propagation velocity of thedynamic fracture is faster than the static and the propa-gation velocity of the fracture is much lower than theload -erefore fracture water cannot diffuse into thefracture tip in a relatively short time Under the action of thesurface tension of free water the water on the fracturesurface will produce a cohesion force (pdw minuspsw) Underdynamic loading because the materials simultaneously meetτb gt τl and τf gt τa the branch fracture surface will notgenerate new fractures -us the entire branch fractureextension will be hampered which increases the strength ofthe saturated coal and rock

As mentioned above coal has low intensity more de-veloped fractures a small strength reduction coefficientwhen saturated and the reaction force between particles isalso lower -us under static-dynamic loads the relativetensile stress and shear stress generated on the branchfracture surface of a saturated coal specimen is much higherthan the tensile strength and shear strength of the fracturesurface ie τb lt τl and τf lt τa -is can cause branchfracture tensile failure and shear failure -e damage of thecoal specimen and the expansion of fractures are acceleratedand the dynamic strength of the coal specimen is weakenedIn contrast the effect of water-rock interactions on sand-stone is smaller the strength reduction coefficient is largerand it has a high strength and relatively low fracture densityUnder the same conditions the relative tensile stress andshear stress generated in the fracture surface of saturatedsandstone under static-dynamic loads are much higher thantensile strength and shear strength of the fracture surfaceie τb gt τl and τf gt τa -erefore the extension of wholebranch fracture of naturally saturated sandstone will behampered due to the cohesion force generated from theStefan effect Additionally generation of new fractures onthe branch fracture surface of sandstone is also suppressed-e dynamic peak strength of the specimen is improved

Furthermore during dynamic impact the diffusion offree water lags behind the expansion of the new fracturebecause of generation of new fractures in the branch fracturesurface of saturated coal specimens -us the diffusionspeed of free water is largely determined by the growth speedof the new fracture which means that each primary and newfracture will contain free water -e area of the branchfracture surface in contact with water will produce a cohesiveforce hindering the branch fracture from growing -isreduces the compressibility of free water and the ability ofthe coal specimen to resist deformation is enhanced At thistime the greater the fracture area in contact with water thehigher the stiffness of the water-rock common loads will be-is provides a reason for the increase in the deformationmodulus of coal specimens with moisture content undermedium strain rate conditions

4 Conclusion

(1) Under static loading conditions the saturatedstrength reduction coefficient and elastic modulusreduction coefficient of coal samples are lower than

8 Advances in Civil Engineering

those of sandstone Under dynamic loading condi-tions the strength of naturally saturated coal samplesdecreases and the elastic modulus increases -isis the same strength variation trend and oppositeelastic modulus variation trend as observed forsandstone

(2) -e water-saturated coal specimens have greaterwater-rock interactions and strength reductioneffect its reduction in the ability to resist defor-mation is also very significant compared to saturatedsandstone

(3) Under static-dynamic loads owing to intensitydifferences in the saturated coal and rock materials astress difference results from the Stefan effect in thebranch fracture surface which is the main reasonthat the strength of coal and rock materials increasesor decreases Meanwhile fracture propagation atsaturated branch fracture surfaces can effectivelyexplain the increase in the deformation modulus ofcoal with increasing moisture content

(4) According to a sliding model of wing branch frac-ture the criteria for microfracture tensile stress andshear stress produced at the branch fracture surfacewere established If the branch fracture surface si-multaneously satisfies both τb gt τl and τf gt τa thebranch fracture surface will not break down -edynamic strength of water-saturated coal and rockwill increase If the branch fracture surface meetsonly one of the conditions τb lt τl or τf lt τa thebranch fracture surface will break down and thedynamic strength of water-saturated coal and rockwill decrease

Data Availability

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

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-e work was supported by the National Natural ScienceFoundation of China (51604093 and 51474096) NationalKey RampD Program of China (2018YFC0604502) Programfor Innovative Research Team at the University of Ministryof Education of China (IRT_16R22) Scientific and Tech-nological Key Project of Henan province (172107000016)and the Doctoral Research Fund Project of Henan Poly-technic University China (B2017-42)

References

[1] B Vasarhelyi and P Van ldquoInfluence of water content on thestrength of rockrdquo Engineering Geology vol 84 no 1-2pp 70ndash74 2006

[2] L S Tang P C Zhang and Y Wang ldquoOn fractures strengthof rocks with cracks under water actionrdquo Chinese Journal ofRock Mechanics and Engineering vol 23 no 19 pp 3337ndash3341 2004

[3] Z Zhu and D Hu ldquo-e effect of intestitial water pressure onrock mass strengthrdquo Rock and Soil Mechanics vol 21 no 1pp 64ndash67 2000

[4] Y Pu and Q Y Ma ldquoSplit Hopkinson pressure bar tests onsandstone in coalmine under cyclic wetting and dryingrdquo Rockand Soil Mechanics vol 9 pp 2557ndash2562 2013

[5] Y Pu and R Ma ldquoSplit Hopkinson pressure bar tests andanalysis of coalmine sandstone with various moisture con-tentsrdquo Chinese Journal of Rock Mechanics and Engineeringvol 34 no 1 pp 2888ndash2893 2015

[6] W Wang H Li and H Gu ldquoMicromechanics analysis andmechanical characteristics of water-saturated coal specimensunder coupled static-dynamic loadsrdquo Journal of China CoalSociety vol 3 pp 611ndash617 2016

[7] W Wang H Wang D Li H Li and Z Liu ldquoStrength andfailure characteristics of natural and water-saturated coalspecimens under static and dynamic loadsrdquo Shock and Vi-bration vol 2018 Article ID 3526121 15 pages 2018

[8] Y Q Ding W H Tang and X Xu ldquoExperimental studyof dynamic mechanical behaviors of unsaturated clay sub-jected touniaxial loadingrdquo Rock and Soil Mechanics vol 9pp 2546ndash2550 2013

[9] N Ding L Jin and J Zhang ldquoEffect of free water content onthe dynamic mechanical behavior of cement mortar underhigh strain raterdquo Concrete vol 10 pp 128ndash132 2013

[10] J Zhan and N Zhang ldquoStudy on the damage feature ofwater-bearing argillaceous siltstone under the impact loadrdquoNon-Ferrous Metal vol 6 pp 44ndash77 2015

[11] Y Zhao S Liu Y Jiang K Wang and Y Huang ldquoDynamictensile strength of coal under dry and saturated conditionsrdquoRock Mechanics and Rock Engineering vol 49 no 5pp 1709ndash1720 2015

[12] Y V Petrov I V Smirnov G A Volkov A K AbramianA M Bragov and S N Verichev ldquoDynamic failure of dryand fully saturated limestone samples based on incubationtime conceptrdquo Journal of Rock Mechanics and GeotechnicalEngineering vol 9 no 1 pp 125ndash134 2017

[13] B Wang and X Li ldquoMesomechanics analysis of static com-pressive strength and dynamic compressive strength of water-saturated rock under uniaxial loadrdquo Explosion and ShockWaves vol 32 no 4 pp 423ndash431 2014

[14] F Gong X Li X Liu et al ldquoExperimental study of dynamiccharacteristics of sandstone under one-dimensional coupledstatic and dynamic loadsrdquo Chinese Journal of Rock Mechanicsand Engineering vol 29 no 10 pp 2076ndash2085 2010

[15] F Q Gong and G F Zhao ldquoDynamic indirect tensile strengthof sandstone under different loading ratesrdquo Rock Mechanicsand Rock Engineering vol 47 no 6 pp 2271ndash2278 2013

[16] -e National Standard Compilation Groups of Peoplersquos Re-public of China GBT 235615-2009 Methods for Determiningthe Physical and Mechanical Properties of Coal and RockStandards Press of China Beijing China 2009 in Chinese

[17] D Xiong Z Zhao and C Su ldquoExperimental study of effect ofwater-sturated state on mechanical properties of rock in coalmeasure stratardquo Chinese Journal of Rock Mechanics andEngineering vol 5 pp 998ndash1006 2011

[18] H Wang and Q Li ldquoSaturated concrete mesoscopic me-chanics mechanism of the static and dynamic compressivestrengthrdquo Journal of Hydraulic Engineering vol 8 pp 958ndash962 2006

Advances in Civil Engineering 9

[19] M Tao H T Zhao X B Li and W Z Cao ldquoFailurecharacteristics of pre-stressed rock with a circular hole sub-jected to dynamic loadingrdquo Tunnelling and UndergroundSpace Technology vol 81 pp 1ndash15 2018

[20] M Tao A Ma W Cao X Li and F Gong ldquoDynamicresponse of pre-stressed rock with a circular cavity subject totransient loadingrdquo International Journal of Rock Mechanicsand Mining Sciences vol 99 pp 1ndash8 2017

[21] Y Ogata W J Jung S Kubota and Y Wada ldquoEffect of thestrain rate and water saturation for the dynamic tensilestrength of rocksrdquo Materials Science Forum vol 465-466pp 361ndash366 2004

[22] S Huang K Xia F Yan and X Feng ldquoAn experimental studyof the rate dependence of tensile strength softening ofLongyou sandstonerdquo Rock Mechanics and Rock Engineeringvol 43 no 6 pp 677ndash683 2010

[23] Z Zhou X Cai W Cao X Li and C Xiong ldquoInfluence ofwater content on mechanical properties of rock in bothsaturation and drying processesrdquo Rock Mechanics and RockEngineering vol 49 no 8 pp 3009ndash3025 2016

[24] Z Zhou X Cai L Chen W Cao Y Zhao and C XiongldquoInfluence of cyclic wetting and drying on physical and dy-namic compressive properties of sandstonerdquo EngineeringGeology vol 220 pp 1ndash12 2017

[25] D Zheng and Q Li ldquoAn explanation for rate effect of concretestrength based on fracture toughness including free waterviscosityrdquo Engineering Fracture Mechanics vol 71 no 16-17pp 2319ndash2327 2004

[26] P Rossi J G M van Mier C Boulay and F Le Maou ldquo-edynamic behaviour of concrete influence of free waterrdquoMaterials and Structures vol 25 no 9 pp 509ndash514 1992

10 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

loading this study simplifies the three-dimensional hydrousfracture to a plane fracture and a single fracture is taken asan example For the parameters of the hydrous singlefracture the static load is σs dynamic load is σd fracturelength is 2a and angle is β as shown in Figure 9

321 Fracture Propagation Characteristics of Saturated Coaland Rock under Static-Dynamic Loads During staticloading wing fractures will occur with increasing static load-e fracture propagation velocity is faster than the staticloading speed In addition the fracture tip will fill with freewater due to occurrence of a siphon phenomenon in thefracture tip

-is results in a decrease in the friction coefficient of thefracture contact surface increase in the microrupture ac-tivity of the coal and rock specimens acceleration of fracturepropagation and concatenation and transfixion betweenfractures Furthermore the macrodestructive force of the

specimens decreases and the compressive strength of thespecimens is also reduced Wang and Li [13] investigated theforce of free water in fracture propagation in coal and rockunder static loads

-e fracture growth characteristics of coal and rock arebasically consistent under static loads In the natural state thenumber of fractures further increases as the coal and rockspecimens absorb water -is occurs because of the low in-tensity of coal and its dense fractures coupled with thecorrosive effects of water At the same time the reaction forcebetween particles decreases significantly [13] -is leads thevelocity of the new fracture to grow faster in coal specimensunder static loads than in the saturated sandstone -estrength reduction coefficient and elastic modulus reductioncoefficient of the coal and rock specimens are smaller

322 Fracture Propagation Characteristics of Saturated Coaland Rock under Dynamic Loads -e propagation charac-teristics of coal and rock fractures under static-dynamicloading can be obtained from the mesomechanical analyticalmethod of concrete and rock mechanics [25 26] Understatic-dynamic loads a cohesive force F is formed from thesurface tension of free water in the fractures and resistanceand Fprime result from the Stefan effect and impede the fracturegrowth and further fracturing -e force that hindersfracture propagation pdw can be expressed as follows

pdw F + Fprime( 1113857

A

VR 2δ2 cosφ1113872 11138731113872 1113873 + 3ηr42πh3( 1113857(dudt)( 11138571113872 1113873

A

(5)

where V is the liquid volume R is the surface energy φ is thewetting angle δ is the radius of the water meniscus η is theliquid viscosity r is the radius of two parallel circular platesfilled with incompressible viscous fluids u is the relativedisplacement corresponding to the separation of the twocircular plates h is the space between the two circular platesand A is the area of the fracture containing water

θ

φ

Rm

R

Figure 8 Model of grain-water molecule interactions

(a) (b) (c)

Figure 7 Sketch of the coal specimen in the natural state and water-saturated state (a) Coal specimen D1-2 (b) Natural state (c) Water-saturated state

6 Advances in Civil Engineering

323 Stress Balance on Both Ends of the Specimen duringDynamic Impact Processes -e stress state under static-dynamic loading is shown in Figure 10 In the image σIis the incident stress σR is the reflected stress σT is thetransmission stress and σs is the prestatic load

-e stress balance on both ends of the specimen is aprecondition for a reasonable equivalent of the dynamicload Zncker and Closer proposed applying an equilibriumfactor μ to measure the stress equilibrium state of speci-mens μ was defined as the ratio of the stress differencebetween the two ends to the average stress in the specimenas given by Equation (6) As the equilibrium factor ap-proaches zero the stress in the specimens becomes moreuniform -e equilibrium factor is calculated as follows

μ 2 σSI minus σST( 1113857

σSI + σST (6)

where σSI is the incident end stress and σST is the trans-mission end stress

During the impact process the small size of the specimenand the complicated transient change in the stress mean thatthe present technique cannot achieve direct measurement ofthe stress distribution on both ends According to the theoryof SHPB tests for the equivalent stress on both ends of thespecimen the equivalent formula is as follows

σST σT

σSI σI + σR(7)

-e trend in the equilibrium factor during the dynamicshock process for a specimen under prestatic loads is shownin Figure 11

-e reflection wave σT is a platform which indicatesthat the experiment has achieved loading at a constant strainrate During the whole impact loading process the stress atthe incident and transmission ends are almost equal -e

equilibrium factor μ tends to approximately zero by 30 μsafter loading and is maintained to 140 μs -erefore thedynamic impact force of coal specimens is a reasonableequivalent for the quasi-static stress σd coupled with theprestatic load σs

During the static-dynamic loads a prestatic load σs isfirst applied followed by the dynamic load σd σsminusd is thecomposite failure strength of the coal specimen hydrousfracture under a combination load-e friction coefficient ofthe branch fracture is divided by the dynamic load factor fdof the branch fracture surface that is not in contact withwater and the dynamic load factor fdw of the branchfracture surface in contact with water owing to the lowstrength of natural saturated coal specimens at the fracturesurface and the uneven distribution of water in the branchfracture -erefore considering the difference in stressbetween the areas in the branch fracture surface that are incontact with water and those that are not in contact withwater is necessary

As shown in Figure 9 surface abndashcd is the free waterinterface and a mechanical analysis of the stress structure of awing branch fracture was carried out under static-dynamicloading -e compressive stress is assumed to be positive inthis analysis -us the shear stress τ(dminuss)w and normal stressσ(dminuss)w of the wing branch fracture surface in contact withfree water and the shear stress τ(dminuss) and normal stressσ(dminuss) of the wing branch fracture not in contact with water

XG1 X1 X2 XG2

Straingauge G1

σI

σR

σT

σR

σIσT σSσS

Incident bar Sample Transmission barStrain gauge G2

Figure 10 Loading diagram of a specimen under static-dynamicload

125100

755025

0ndash25ndash50ndash75

ndash100ndash125ndash150

0 20 40 60 80T (μs)

100 120 140 160

543210ndash1ndash2ndash3ndash4ndash5ndash6

σ (M

Pa)

μ

σR

σT

σSIμ

σR + σI σI

σRσST

σI

μ

Figure 11 Balance factor for specimens under static-dynamicloads

σdσs σdσs

σdσs σdσs

L

β

τ(s-d)w

τs

PswPdwa

bσ(s-d)w

σ(s-d)

PswPdw

cd

σ(s-d)w

PdwPsw

τ(s-d)w

τ(s-d)

σ(s-d)PdwPsw

Psw

Psw

Pdw

Pdw

Void

Void

2a

θ

Figure 9 Pressure at the crack surface caused by free water undercoupled static-dynamic loads

Advances in Civil Engineering 7

(out of the abndashcd surface) can be obtained -e above pa-rameters can be expressed by equations (8)ndash(11) as follows

τ(sminusd)w 12σsminusd sin 2(β + θ)

minusfdw σsminusd cos2(β + θ)minus psw minuspdw( 11138571113960 1113961

(8)

τ(sminusd) 12σsminusd sin 2(β + θ)minusfdσsminusd cos

2(β + θ) (9)

σ(sminusd)w σsminusd cos2(β + θ)minus psw minuspdw( 1113857 (10)

σ(sminusd) σsminusd cos2(β + θ) (11)

wheref(dminuss)w is the friction coefficient of the hydrous fracturein contact with free water under dynamic load fd is thefriction coefficient of the hydrous fracture not in contact withfree water under dynamic load pdw is the stress that inhibitsfracture extension and psw is the outward extrusion stress offree water on an airfoil fracture Numerically pdw is far largerthan psw in the dynamic impact process Both of these areinvolved in fracture development and breakthrough

From Equations (8)ndash(11) Equations (12) and (13) can beobtained for the relative shear stress τl generated normal tosurface abndashcd and the relative normal stress σl

τl τ(sminusd) minus τ(sminusd)w fdσsminusd cos2(β + θ)

minusfdw σsminusd cos2(β + θ)minus psw minuspdw( 11138571113960 1113961

(12)

τa σ(sminusd) minus σ(sminusd)w psw minuspdw (13)

where τl is the tensile stress at the branch fracture surfacenear the abndashcd interface and τa is the shear stress at thebranch fracture surface near the abndashcd interface

At the coal and rock branch fracture surface the settingtensile strength is τb and the shear strength is τf When thebranch fracture surface of saturated coal and rock meets oneof the conditions τb lt τl or τf lt τa the branch fracturesurface will be damaged and a new fracture will form -ebranch fracture surface of saturated coal and rock canproduce resistance due to the Stefan effect under static-dynamic loads -e extension of the fracture at the branchfracture surface in contact with water will result in a pressuredifference at the branch fracture surface -us the newfracture will generate owing to the low strength of thematerial In other words when the material meets one of thetwo conditions above destruction of the fracture will resultin more energy for generation and extension of the newfracture -us the elastic energy storage in the tip of theinitial fracture will decrease and the coal and rock materialstrength will also decrease During dynamic loading thestress inhomogeneity causes the extension of the initialfracture to lag behind the new fracture With breakthroughof the initial fracture and generation of the new fracturefragments will be formed At the same time a stress wave willprovide kinetic energy to the fragments resulting inthrowing and flying of fragments

When the branch fracture surface of saturated coal androck simultaneously meets both τb gt τl and τf gt τa a new

fracture will not be formed on the fracture surface underdynamic load conditions -e propagation velocity of thedynamic fracture is faster than the static and the propa-gation velocity of the fracture is much lower than theload -erefore fracture water cannot diffuse into thefracture tip in a relatively short time Under the action of thesurface tension of free water the water on the fracturesurface will produce a cohesion force (pdw minuspsw) Underdynamic loading because the materials simultaneously meetτb gt τl and τf gt τa the branch fracture surface will notgenerate new fractures -us the entire branch fractureextension will be hampered which increases the strength ofthe saturated coal and rock

As mentioned above coal has low intensity more de-veloped fractures a small strength reduction coefficientwhen saturated and the reaction force between particles isalso lower -us under static-dynamic loads the relativetensile stress and shear stress generated on the branchfracture surface of a saturated coal specimen is much higherthan the tensile strength and shear strength of the fracturesurface ie τb lt τl and τf lt τa -is can cause branchfracture tensile failure and shear failure -e damage of thecoal specimen and the expansion of fractures are acceleratedand the dynamic strength of the coal specimen is weakenedIn contrast the effect of water-rock interactions on sand-stone is smaller the strength reduction coefficient is largerand it has a high strength and relatively low fracture densityUnder the same conditions the relative tensile stress andshear stress generated in the fracture surface of saturatedsandstone under static-dynamic loads are much higher thantensile strength and shear strength of the fracture surfaceie τb gt τl and τf gt τa -erefore the extension of wholebranch fracture of naturally saturated sandstone will behampered due to the cohesion force generated from theStefan effect Additionally generation of new fractures onthe branch fracture surface of sandstone is also suppressed-e dynamic peak strength of the specimen is improved

Furthermore during dynamic impact the diffusion offree water lags behind the expansion of the new fracturebecause of generation of new fractures in the branch fracturesurface of saturated coal specimens -us the diffusionspeed of free water is largely determined by the growth speedof the new fracture which means that each primary and newfracture will contain free water -e area of the branchfracture surface in contact with water will produce a cohesiveforce hindering the branch fracture from growing -isreduces the compressibility of free water and the ability ofthe coal specimen to resist deformation is enhanced At thistime the greater the fracture area in contact with water thehigher the stiffness of the water-rock common loads will be-is provides a reason for the increase in the deformationmodulus of coal specimens with moisture content undermedium strain rate conditions

4 Conclusion

(1) Under static loading conditions the saturatedstrength reduction coefficient and elastic modulusreduction coefficient of coal samples are lower than

8 Advances in Civil Engineering

those of sandstone Under dynamic loading condi-tions the strength of naturally saturated coal samplesdecreases and the elastic modulus increases -isis the same strength variation trend and oppositeelastic modulus variation trend as observed forsandstone

(2) -e water-saturated coal specimens have greaterwater-rock interactions and strength reductioneffect its reduction in the ability to resist defor-mation is also very significant compared to saturatedsandstone

(3) Under static-dynamic loads owing to intensitydifferences in the saturated coal and rock materials astress difference results from the Stefan effect in thebranch fracture surface which is the main reasonthat the strength of coal and rock materials increasesor decreases Meanwhile fracture propagation atsaturated branch fracture surfaces can effectivelyexplain the increase in the deformation modulus ofcoal with increasing moisture content

(4) According to a sliding model of wing branch frac-ture the criteria for microfracture tensile stress andshear stress produced at the branch fracture surfacewere established If the branch fracture surface si-multaneously satisfies both τb gt τl and τf gt τa thebranch fracture surface will not break down -edynamic strength of water-saturated coal and rockwill increase If the branch fracture surface meetsonly one of the conditions τb lt τl or τf lt τa thebranch fracture surface will break down and thedynamic strength of water-saturated coal and rockwill decrease

Data Availability

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

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-e work was supported by the National Natural ScienceFoundation of China (51604093 and 51474096) NationalKey RampD Program of China (2018YFC0604502) Programfor Innovative Research Team at the University of Ministryof Education of China (IRT_16R22) Scientific and Tech-nological Key Project of Henan province (172107000016)and the Doctoral Research Fund Project of Henan Poly-technic University China (B2017-42)

References

[1] B Vasarhelyi and P Van ldquoInfluence of water content on thestrength of rockrdquo Engineering Geology vol 84 no 1-2pp 70ndash74 2006

[2] L S Tang P C Zhang and Y Wang ldquoOn fractures strengthof rocks with cracks under water actionrdquo Chinese Journal ofRock Mechanics and Engineering vol 23 no 19 pp 3337ndash3341 2004

[3] Z Zhu and D Hu ldquo-e effect of intestitial water pressure onrock mass strengthrdquo Rock and Soil Mechanics vol 21 no 1pp 64ndash67 2000

[4] Y Pu and Q Y Ma ldquoSplit Hopkinson pressure bar tests onsandstone in coalmine under cyclic wetting and dryingrdquo Rockand Soil Mechanics vol 9 pp 2557ndash2562 2013

[5] Y Pu and R Ma ldquoSplit Hopkinson pressure bar tests andanalysis of coalmine sandstone with various moisture con-tentsrdquo Chinese Journal of Rock Mechanics and Engineeringvol 34 no 1 pp 2888ndash2893 2015

[6] W Wang H Li and H Gu ldquoMicromechanics analysis andmechanical characteristics of water-saturated coal specimensunder coupled static-dynamic loadsrdquo Journal of China CoalSociety vol 3 pp 611ndash617 2016

[7] W Wang H Wang D Li H Li and Z Liu ldquoStrength andfailure characteristics of natural and water-saturated coalspecimens under static and dynamic loadsrdquo Shock and Vi-bration vol 2018 Article ID 3526121 15 pages 2018

[8] Y Q Ding W H Tang and X Xu ldquoExperimental studyof dynamic mechanical behaviors of unsaturated clay sub-jected touniaxial loadingrdquo Rock and Soil Mechanics vol 9pp 2546ndash2550 2013

[9] N Ding L Jin and J Zhang ldquoEffect of free water content onthe dynamic mechanical behavior of cement mortar underhigh strain raterdquo Concrete vol 10 pp 128ndash132 2013

[10] J Zhan and N Zhang ldquoStudy on the damage feature ofwater-bearing argillaceous siltstone under the impact loadrdquoNon-Ferrous Metal vol 6 pp 44ndash77 2015

[11] Y Zhao S Liu Y Jiang K Wang and Y Huang ldquoDynamictensile strength of coal under dry and saturated conditionsrdquoRock Mechanics and Rock Engineering vol 49 no 5pp 1709ndash1720 2015

[12] Y V Petrov I V Smirnov G A Volkov A K AbramianA M Bragov and S N Verichev ldquoDynamic failure of dryand fully saturated limestone samples based on incubationtime conceptrdquo Journal of Rock Mechanics and GeotechnicalEngineering vol 9 no 1 pp 125ndash134 2017

[13] B Wang and X Li ldquoMesomechanics analysis of static com-pressive strength and dynamic compressive strength of water-saturated rock under uniaxial loadrdquo Explosion and ShockWaves vol 32 no 4 pp 423ndash431 2014

[14] F Gong X Li X Liu et al ldquoExperimental study of dynamiccharacteristics of sandstone under one-dimensional coupledstatic and dynamic loadsrdquo Chinese Journal of Rock Mechanicsand Engineering vol 29 no 10 pp 2076ndash2085 2010

[15] F Q Gong and G F Zhao ldquoDynamic indirect tensile strengthof sandstone under different loading ratesrdquo Rock Mechanicsand Rock Engineering vol 47 no 6 pp 2271ndash2278 2013

[16] -e National Standard Compilation Groups of Peoplersquos Re-public of China GBT 235615-2009 Methods for Determiningthe Physical and Mechanical Properties of Coal and RockStandards Press of China Beijing China 2009 in Chinese

[17] D Xiong Z Zhao and C Su ldquoExperimental study of effect ofwater-sturated state on mechanical properties of rock in coalmeasure stratardquo Chinese Journal of Rock Mechanics andEngineering vol 5 pp 998ndash1006 2011

[18] H Wang and Q Li ldquoSaturated concrete mesoscopic me-chanics mechanism of the static and dynamic compressivestrengthrdquo Journal of Hydraulic Engineering vol 8 pp 958ndash962 2006

Advances in Civil Engineering 9

[19] M Tao H T Zhao X B Li and W Z Cao ldquoFailurecharacteristics of pre-stressed rock with a circular hole sub-jected to dynamic loadingrdquo Tunnelling and UndergroundSpace Technology vol 81 pp 1ndash15 2018

[20] M Tao A Ma W Cao X Li and F Gong ldquoDynamicresponse of pre-stressed rock with a circular cavity subject totransient loadingrdquo International Journal of Rock Mechanicsand Mining Sciences vol 99 pp 1ndash8 2017

[21] Y Ogata W J Jung S Kubota and Y Wada ldquoEffect of thestrain rate and water saturation for the dynamic tensilestrength of rocksrdquo Materials Science Forum vol 465-466pp 361ndash366 2004

[22] S Huang K Xia F Yan and X Feng ldquoAn experimental studyof the rate dependence of tensile strength softening ofLongyou sandstonerdquo Rock Mechanics and Rock Engineeringvol 43 no 6 pp 677ndash683 2010

[23] Z Zhou X Cai W Cao X Li and C Xiong ldquoInfluence ofwater content on mechanical properties of rock in bothsaturation and drying processesrdquo Rock Mechanics and RockEngineering vol 49 no 8 pp 3009ndash3025 2016

[24] Z Zhou X Cai L Chen W Cao Y Zhao and C XiongldquoInfluence of cyclic wetting and drying on physical and dy-namic compressive properties of sandstonerdquo EngineeringGeology vol 220 pp 1ndash12 2017

[25] D Zheng and Q Li ldquoAn explanation for rate effect of concretestrength based on fracture toughness including free waterviscosityrdquo Engineering Fracture Mechanics vol 71 no 16-17pp 2319ndash2327 2004

[26] P Rossi J G M van Mier C Boulay and F Le Maou ldquo-edynamic behaviour of concrete influence of free waterrdquoMaterials and Structures vol 25 no 9 pp 509ndash514 1992

10 Advances in Civil Engineering

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RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

323 Stress Balance on Both Ends of the Specimen duringDynamic Impact Processes -e stress state under static-dynamic loading is shown in Figure 10 In the image σIis the incident stress σR is the reflected stress σT is thetransmission stress and σs is the prestatic load

-e stress balance on both ends of the specimen is aprecondition for a reasonable equivalent of the dynamicload Zncker and Closer proposed applying an equilibriumfactor μ to measure the stress equilibrium state of speci-mens μ was defined as the ratio of the stress differencebetween the two ends to the average stress in the specimenas given by Equation (6) As the equilibrium factor ap-proaches zero the stress in the specimens becomes moreuniform -e equilibrium factor is calculated as follows

μ 2 σSI minus σST( 1113857

σSI + σST (6)

where σSI is the incident end stress and σST is the trans-mission end stress

During the impact process the small size of the specimenand the complicated transient change in the stress mean thatthe present technique cannot achieve direct measurement ofthe stress distribution on both ends According to the theoryof SHPB tests for the equivalent stress on both ends of thespecimen the equivalent formula is as follows

σST σT

σSI σI + σR(7)

-e trend in the equilibrium factor during the dynamicshock process for a specimen under prestatic loads is shownin Figure 11

-e reflection wave σT is a platform which indicatesthat the experiment has achieved loading at a constant strainrate During the whole impact loading process the stress atthe incident and transmission ends are almost equal -e

equilibrium factor μ tends to approximately zero by 30 μsafter loading and is maintained to 140 μs -erefore thedynamic impact force of coal specimens is a reasonableequivalent for the quasi-static stress σd coupled with theprestatic load σs

During the static-dynamic loads a prestatic load σs isfirst applied followed by the dynamic load σd σsminusd is thecomposite failure strength of the coal specimen hydrousfracture under a combination load-e friction coefficient ofthe branch fracture is divided by the dynamic load factor fdof the branch fracture surface that is not in contact withwater and the dynamic load factor fdw of the branchfracture surface in contact with water owing to the lowstrength of natural saturated coal specimens at the fracturesurface and the uneven distribution of water in the branchfracture -erefore considering the difference in stressbetween the areas in the branch fracture surface that are incontact with water and those that are not in contact withwater is necessary

As shown in Figure 9 surface abndashcd is the free waterinterface and a mechanical analysis of the stress structure of awing branch fracture was carried out under static-dynamicloading -e compressive stress is assumed to be positive inthis analysis -us the shear stress τ(dminuss)w and normal stressσ(dminuss)w of the wing branch fracture surface in contact withfree water and the shear stress τ(dminuss) and normal stressσ(dminuss) of the wing branch fracture not in contact with water

XG1 X1 X2 XG2

Straingauge G1

σI

σR

σT

σR

σIσT σSσS

Incident bar Sample Transmission barStrain gauge G2

Figure 10 Loading diagram of a specimen under static-dynamicload

125100

755025

0ndash25ndash50ndash75

ndash100ndash125ndash150

0 20 40 60 80T (μs)

100 120 140 160

543210ndash1ndash2ndash3ndash4ndash5ndash6

σ (M

Pa)

μ

σR

σT

σSIμ

σR + σI σI

σRσST

σI

μ

Figure 11 Balance factor for specimens under static-dynamicloads

σdσs σdσs

σdσs σdσs

L

β

τ(s-d)w

τs

PswPdwa

bσ(s-d)w

σ(s-d)

PswPdw

cd

σ(s-d)w

PdwPsw

τ(s-d)w

τ(s-d)

σ(s-d)PdwPsw

Psw

Psw

Pdw

Pdw

Void

Void

2a

θ

Figure 9 Pressure at the crack surface caused by free water undercoupled static-dynamic loads

Advances in Civil Engineering 7

(out of the abndashcd surface) can be obtained -e above pa-rameters can be expressed by equations (8)ndash(11) as follows

τ(sminusd)w 12σsminusd sin 2(β + θ)

minusfdw σsminusd cos2(β + θ)minus psw minuspdw( 11138571113960 1113961

(8)

τ(sminusd) 12σsminusd sin 2(β + θ)minusfdσsminusd cos

2(β + θ) (9)

σ(sminusd)w σsminusd cos2(β + θ)minus psw minuspdw( 1113857 (10)

σ(sminusd) σsminusd cos2(β + θ) (11)

wheref(dminuss)w is the friction coefficient of the hydrous fracturein contact with free water under dynamic load fd is thefriction coefficient of the hydrous fracture not in contact withfree water under dynamic load pdw is the stress that inhibitsfracture extension and psw is the outward extrusion stress offree water on an airfoil fracture Numerically pdw is far largerthan psw in the dynamic impact process Both of these areinvolved in fracture development and breakthrough

From Equations (8)ndash(11) Equations (12) and (13) can beobtained for the relative shear stress τl generated normal tosurface abndashcd and the relative normal stress σl

τl τ(sminusd) minus τ(sminusd)w fdσsminusd cos2(β + θ)

minusfdw σsminusd cos2(β + θ)minus psw minuspdw( 11138571113960 1113961

(12)

τa σ(sminusd) minus σ(sminusd)w psw minuspdw (13)

where τl is the tensile stress at the branch fracture surfacenear the abndashcd interface and τa is the shear stress at thebranch fracture surface near the abndashcd interface

At the coal and rock branch fracture surface the settingtensile strength is τb and the shear strength is τf When thebranch fracture surface of saturated coal and rock meets oneof the conditions τb lt τl or τf lt τa the branch fracturesurface will be damaged and a new fracture will form -ebranch fracture surface of saturated coal and rock canproduce resistance due to the Stefan effect under static-dynamic loads -e extension of the fracture at the branchfracture surface in contact with water will result in a pressuredifference at the branch fracture surface -us the newfracture will generate owing to the low strength of thematerial In other words when the material meets one of thetwo conditions above destruction of the fracture will resultin more energy for generation and extension of the newfracture -us the elastic energy storage in the tip of theinitial fracture will decrease and the coal and rock materialstrength will also decrease During dynamic loading thestress inhomogeneity causes the extension of the initialfracture to lag behind the new fracture With breakthroughof the initial fracture and generation of the new fracturefragments will be formed At the same time a stress wave willprovide kinetic energy to the fragments resulting inthrowing and flying of fragments

When the branch fracture surface of saturated coal androck simultaneously meets both τb gt τl and τf gt τa a new

fracture will not be formed on the fracture surface underdynamic load conditions -e propagation velocity of thedynamic fracture is faster than the static and the propa-gation velocity of the fracture is much lower than theload -erefore fracture water cannot diffuse into thefracture tip in a relatively short time Under the action of thesurface tension of free water the water on the fracturesurface will produce a cohesion force (pdw minuspsw) Underdynamic loading because the materials simultaneously meetτb gt τl and τf gt τa the branch fracture surface will notgenerate new fractures -us the entire branch fractureextension will be hampered which increases the strength ofthe saturated coal and rock

As mentioned above coal has low intensity more de-veloped fractures a small strength reduction coefficientwhen saturated and the reaction force between particles isalso lower -us under static-dynamic loads the relativetensile stress and shear stress generated on the branchfracture surface of a saturated coal specimen is much higherthan the tensile strength and shear strength of the fracturesurface ie τb lt τl and τf lt τa -is can cause branchfracture tensile failure and shear failure -e damage of thecoal specimen and the expansion of fractures are acceleratedand the dynamic strength of the coal specimen is weakenedIn contrast the effect of water-rock interactions on sand-stone is smaller the strength reduction coefficient is largerand it has a high strength and relatively low fracture densityUnder the same conditions the relative tensile stress andshear stress generated in the fracture surface of saturatedsandstone under static-dynamic loads are much higher thantensile strength and shear strength of the fracture surfaceie τb gt τl and τf gt τa -erefore the extension of wholebranch fracture of naturally saturated sandstone will behampered due to the cohesion force generated from theStefan effect Additionally generation of new fractures onthe branch fracture surface of sandstone is also suppressed-e dynamic peak strength of the specimen is improved

Furthermore during dynamic impact the diffusion offree water lags behind the expansion of the new fracturebecause of generation of new fractures in the branch fracturesurface of saturated coal specimens -us the diffusionspeed of free water is largely determined by the growth speedof the new fracture which means that each primary and newfracture will contain free water -e area of the branchfracture surface in contact with water will produce a cohesiveforce hindering the branch fracture from growing -isreduces the compressibility of free water and the ability ofthe coal specimen to resist deformation is enhanced At thistime the greater the fracture area in contact with water thehigher the stiffness of the water-rock common loads will be-is provides a reason for the increase in the deformationmodulus of coal specimens with moisture content undermedium strain rate conditions

4 Conclusion

(1) Under static loading conditions the saturatedstrength reduction coefficient and elastic modulusreduction coefficient of coal samples are lower than

8 Advances in Civil Engineering

those of sandstone Under dynamic loading condi-tions the strength of naturally saturated coal samplesdecreases and the elastic modulus increases -isis the same strength variation trend and oppositeelastic modulus variation trend as observed forsandstone

(2) -e water-saturated coal specimens have greaterwater-rock interactions and strength reductioneffect its reduction in the ability to resist defor-mation is also very significant compared to saturatedsandstone

(3) Under static-dynamic loads owing to intensitydifferences in the saturated coal and rock materials astress difference results from the Stefan effect in thebranch fracture surface which is the main reasonthat the strength of coal and rock materials increasesor decreases Meanwhile fracture propagation atsaturated branch fracture surfaces can effectivelyexplain the increase in the deformation modulus ofcoal with increasing moisture content

(4) According to a sliding model of wing branch frac-ture the criteria for microfracture tensile stress andshear stress produced at the branch fracture surfacewere established If the branch fracture surface si-multaneously satisfies both τb gt τl and τf gt τa thebranch fracture surface will not break down -edynamic strength of water-saturated coal and rockwill increase If the branch fracture surface meetsonly one of the conditions τb lt τl or τf lt τa thebranch fracture surface will break down and thedynamic strength of water-saturated coal and rockwill decrease

Data Availability

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

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-e work was supported by the National Natural ScienceFoundation of China (51604093 and 51474096) NationalKey RampD Program of China (2018YFC0604502) Programfor Innovative Research Team at the University of Ministryof Education of China (IRT_16R22) Scientific and Tech-nological Key Project of Henan province (172107000016)and the Doctoral Research Fund Project of Henan Poly-technic University China (B2017-42)

References

[1] B Vasarhelyi and P Van ldquoInfluence of water content on thestrength of rockrdquo Engineering Geology vol 84 no 1-2pp 70ndash74 2006

[2] L S Tang P C Zhang and Y Wang ldquoOn fractures strengthof rocks with cracks under water actionrdquo Chinese Journal ofRock Mechanics and Engineering vol 23 no 19 pp 3337ndash3341 2004

[3] Z Zhu and D Hu ldquo-e effect of intestitial water pressure onrock mass strengthrdquo Rock and Soil Mechanics vol 21 no 1pp 64ndash67 2000

[4] Y Pu and Q Y Ma ldquoSplit Hopkinson pressure bar tests onsandstone in coalmine under cyclic wetting and dryingrdquo Rockand Soil Mechanics vol 9 pp 2557ndash2562 2013

[5] Y Pu and R Ma ldquoSplit Hopkinson pressure bar tests andanalysis of coalmine sandstone with various moisture con-tentsrdquo Chinese Journal of Rock Mechanics and Engineeringvol 34 no 1 pp 2888ndash2893 2015

[6] W Wang H Li and H Gu ldquoMicromechanics analysis andmechanical characteristics of water-saturated coal specimensunder coupled static-dynamic loadsrdquo Journal of China CoalSociety vol 3 pp 611ndash617 2016

[7] W Wang H Wang D Li H Li and Z Liu ldquoStrength andfailure characteristics of natural and water-saturated coalspecimens under static and dynamic loadsrdquo Shock and Vi-bration vol 2018 Article ID 3526121 15 pages 2018

[8] Y Q Ding W H Tang and X Xu ldquoExperimental studyof dynamic mechanical behaviors of unsaturated clay sub-jected touniaxial loadingrdquo Rock and Soil Mechanics vol 9pp 2546ndash2550 2013

[9] N Ding L Jin and J Zhang ldquoEffect of free water content onthe dynamic mechanical behavior of cement mortar underhigh strain raterdquo Concrete vol 10 pp 128ndash132 2013

[10] J Zhan and N Zhang ldquoStudy on the damage feature ofwater-bearing argillaceous siltstone under the impact loadrdquoNon-Ferrous Metal vol 6 pp 44ndash77 2015

[11] Y Zhao S Liu Y Jiang K Wang and Y Huang ldquoDynamictensile strength of coal under dry and saturated conditionsrdquoRock Mechanics and Rock Engineering vol 49 no 5pp 1709ndash1720 2015

[12] Y V Petrov I V Smirnov G A Volkov A K AbramianA M Bragov and S N Verichev ldquoDynamic failure of dryand fully saturated limestone samples based on incubationtime conceptrdquo Journal of Rock Mechanics and GeotechnicalEngineering vol 9 no 1 pp 125ndash134 2017

[13] B Wang and X Li ldquoMesomechanics analysis of static com-pressive strength and dynamic compressive strength of water-saturated rock under uniaxial loadrdquo Explosion and ShockWaves vol 32 no 4 pp 423ndash431 2014

[14] F Gong X Li X Liu et al ldquoExperimental study of dynamiccharacteristics of sandstone under one-dimensional coupledstatic and dynamic loadsrdquo Chinese Journal of Rock Mechanicsand Engineering vol 29 no 10 pp 2076ndash2085 2010

[15] F Q Gong and G F Zhao ldquoDynamic indirect tensile strengthof sandstone under different loading ratesrdquo Rock Mechanicsand Rock Engineering vol 47 no 6 pp 2271ndash2278 2013

[16] -e National Standard Compilation Groups of Peoplersquos Re-public of China GBT 235615-2009 Methods for Determiningthe Physical and Mechanical Properties of Coal and RockStandards Press of China Beijing China 2009 in Chinese

[17] D Xiong Z Zhao and C Su ldquoExperimental study of effect ofwater-sturated state on mechanical properties of rock in coalmeasure stratardquo Chinese Journal of Rock Mechanics andEngineering vol 5 pp 998ndash1006 2011

[18] H Wang and Q Li ldquoSaturated concrete mesoscopic me-chanics mechanism of the static and dynamic compressivestrengthrdquo Journal of Hydraulic Engineering vol 8 pp 958ndash962 2006

Advances in Civil Engineering 9

[19] M Tao H T Zhao X B Li and W Z Cao ldquoFailurecharacteristics of pre-stressed rock with a circular hole sub-jected to dynamic loadingrdquo Tunnelling and UndergroundSpace Technology vol 81 pp 1ndash15 2018

[20] M Tao A Ma W Cao X Li and F Gong ldquoDynamicresponse of pre-stressed rock with a circular cavity subject totransient loadingrdquo International Journal of Rock Mechanicsand Mining Sciences vol 99 pp 1ndash8 2017

[21] Y Ogata W J Jung S Kubota and Y Wada ldquoEffect of thestrain rate and water saturation for the dynamic tensilestrength of rocksrdquo Materials Science Forum vol 465-466pp 361ndash366 2004

[22] S Huang K Xia F Yan and X Feng ldquoAn experimental studyof the rate dependence of tensile strength softening ofLongyou sandstonerdquo Rock Mechanics and Rock Engineeringvol 43 no 6 pp 677ndash683 2010

[23] Z Zhou X Cai W Cao X Li and C Xiong ldquoInfluence ofwater content on mechanical properties of rock in bothsaturation and drying processesrdquo Rock Mechanics and RockEngineering vol 49 no 8 pp 3009ndash3025 2016

[24] Z Zhou X Cai L Chen W Cao Y Zhao and C XiongldquoInfluence of cyclic wetting and drying on physical and dy-namic compressive properties of sandstonerdquo EngineeringGeology vol 220 pp 1ndash12 2017

[25] D Zheng and Q Li ldquoAn explanation for rate effect of concretestrength based on fracture toughness including free waterviscosityrdquo Engineering Fracture Mechanics vol 71 no 16-17pp 2319ndash2327 2004

[26] P Rossi J G M van Mier C Boulay and F Le Maou ldquo-edynamic behaviour of concrete influence of free waterrdquoMaterials and Structures vol 25 no 9 pp 509ndash514 1992

10 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

(out of the abndashcd surface) can be obtained -e above pa-rameters can be expressed by equations (8)ndash(11) as follows

τ(sminusd)w 12σsminusd sin 2(β + θ)

minusfdw σsminusd cos2(β + θ)minus psw minuspdw( 11138571113960 1113961

(8)

τ(sminusd) 12σsminusd sin 2(β + θ)minusfdσsminusd cos

2(β + θ) (9)

σ(sminusd)w σsminusd cos2(β + θ)minus psw minuspdw( 1113857 (10)

σ(sminusd) σsminusd cos2(β + θ) (11)

wheref(dminuss)w is the friction coefficient of the hydrous fracturein contact with free water under dynamic load fd is thefriction coefficient of the hydrous fracture not in contact withfree water under dynamic load pdw is the stress that inhibitsfracture extension and psw is the outward extrusion stress offree water on an airfoil fracture Numerically pdw is far largerthan psw in the dynamic impact process Both of these areinvolved in fracture development and breakthrough

From Equations (8)ndash(11) Equations (12) and (13) can beobtained for the relative shear stress τl generated normal tosurface abndashcd and the relative normal stress σl

τl τ(sminusd) minus τ(sminusd)w fdσsminusd cos2(β + θ)

minusfdw σsminusd cos2(β + θ)minus psw minuspdw( 11138571113960 1113961

(12)

τa σ(sminusd) minus σ(sminusd)w psw minuspdw (13)

where τl is the tensile stress at the branch fracture surfacenear the abndashcd interface and τa is the shear stress at thebranch fracture surface near the abndashcd interface

At the coal and rock branch fracture surface the settingtensile strength is τb and the shear strength is τf When thebranch fracture surface of saturated coal and rock meets oneof the conditions τb lt τl or τf lt τa the branch fracturesurface will be damaged and a new fracture will form -ebranch fracture surface of saturated coal and rock canproduce resistance due to the Stefan effect under static-dynamic loads -e extension of the fracture at the branchfracture surface in contact with water will result in a pressuredifference at the branch fracture surface -us the newfracture will generate owing to the low strength of thematerial In other words when the material meets one of thetwo conditions above destruction of the fracture will resultin more energy for generation and extension of the newfracture -us the elastic energy storage in the tip of theinitial fracture will decrease and the coal and rock materialstrength will also decrease During dynamic loading thestress inhomogeneity causes the extension of the initialfracture to lag behind the new fracture With breakthroughof the initial fracture and generation of the new fracturefragments will be formed At the same time a stress wave willprovide kinetic energy to the fragments resulting inthrowing and flying of fragments

When the branch fracture surface of saturated coal androck simultaneously meets both τb gt τl and τf gt τa a new

fracture will not be formed on the fracture surface underdynamic load conditions -e propagation velocity of thedynamic fracture is faster than the static and the propa-gation velocity of the fracture is much lower than theload -erefore fracture water cannot diffuse into thefracture tip in a relatively short time Under the action of thesurface tension of free water the water on the fracturesurface will produce a cohesion force (pdw minuspsw) Underdynamic loading because the materials simultaneously meetτb gt τl and τf gt τa the branch fracture surface will notgenerate new fractures -us the entire branch fractureextension will be hampered which increases the strength ofthe saturated coal and rock

As mentioned above coal has low intensity more de-veloped fractures a small strength reduction coefficientwhen saturated and the reaction force between particles isalso lower -us under static-dynamic loads the relativetensile stress and shear stress generated on the branchfracture surface of a saturated coal specimen is much higherthan the tensile strength and shear strength of the fracturesurface ie τb lt τl and τf lt τa -is can cause branchfracture tensile failure and shear failure -e damage of thecoal specimen and the expansion of fractures are acceleratedand the dynamic strength of the coal specimen is weakenedIn contrast the effect of water-rock interactions on sand-stone is smaller the strength reduction coefficient is largerand it has a high strength and relatively low fracture densityUnder the same conditions the relative tensile stress andshear stress generated in the fracture surface of saturatedsandstone under static-dynamic loads are much higher thantensile strength and shear strength of the fracture surfaceie τb gt τl and τf gt τa -erefore the extension of wholebranch fracture of naturally saturated sandstone will behampered due to the cohesion force generated from theStefan effect Additionally generation of new fractures onthe branch fracture surface of sandstone is also suppressed-e dynamic peak strength of the specimen is improved

Furthermore during dynamic impact the diffusion offree water lags behind the expansion of the new fracturebecause of generation of new fractures in the branch fracturesurface of saturated coal specimens -us the diffusionspeed of free water is largely determined by the growth speedof the new fracture which means that each primary and newfracture will contain free water -e area of the branchfracture surface in contact with water will produce a cohesiveforce hindering the branch fracture from growing -isreduces the compressibility of free water and the ability ofthe coal specimen to resist deformation is enhanced At thistime the greater the fracture area in contact with water thehigher the stiffness of the water-rock common loads will be-is provides a reason for the increase in the deformationmodulus of coal specimens with moisture content undermedium strain rate conditions

4 Conclusion

(1) Under static loading conditions the saturatedstrength reduction coefficient and elastic modulusreduction coefficient of coal samples are lower than

8 Advances in Civil Engineering

those of sandstone Under dynamic loading condi-tions the strength of naturally saturated coal samplesdecreases and the elastic modulus increases -isis the same strength variation trend and oppositeelastic modulus variation trend as observed forsandstone

(2) -e water-saturated coal specimens have greaterwater-rock interactions and strength reductioneffect its reduction in the ability to resist defor-mation is also very significant compared to saturatedsandstone

(3) Under static-dynamic loads owing to intensitydifferences in the saturated coal and rock materials astress difference results from the Stefan effect in thebranch fracture surface which is the main reasonthat the strength of coal and rock materials increasesor decreases Meanwhile fracture propagation atsaturated branch fracture surfaces can effectivelyexplain the increase in the deformation modulus ofcoal with increasing moisture content

(4) According to a sliding model of wing branch frac-ture the criteria for microfracture tensile stress andshear stress produced at the branch fracture surfacewere established If the branch fracture surface si-multaneously satisfies both τb gt τl and τf gt τa thebranch fracture surface will not break down -edynamic strength of water-saturated coal and rockwill increase If the branch fracture surface meetsonly one of the conditions τb lt τl or τf lt τa thebranch fracture surface will break down and thedynamic strength of water-saturated coal and rockwill decrease

Data Availability

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

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-e work was supported by the National Natural ScienceFoundation of China (51604093 and 51474096) NationalKey RampD Program of China (2018YFC0604502) Programfor Innovative Research Team at the University of Ministryof Education of China (IRT_16R22) Scientific and Tech-nological Key Project of Henan province (172107000016)and the Doctoral Research Fund Project of Henan Poly-technic University China (B2017-42)

References

[1] B Vasarhelyi and P Van ldquoInfluence of water content on thestrength of rockrdquo Engineering Geology vol 84 no 1-2pp 70ndash74 2006

[2] L S Tang P C Zhang and Y Wang ldquoOn fractures strengthof rocks with cracks under water actionrdquo Chinese Journal ofRock Mechanics and Engineering vol 23 no 19 pp 3337ndash3341 2004

[3] Z Zhu and D Hu ldquo-e effect of intestitial water pressure onrock mass strengthrdquo Rock and Soil Mechanics vol 21 no 1pp 64ndash67 2000

[4] Y Pu and Q Y Ma ldquoSplit Hopkinson pressure bar tests onsandstone in coalmine under cyclic wetting and dryingrdquo Rockand Soil Mechanics vol 9 pp 2557ndash2562 2013

[5] Y Pu and R Ma ldquoSplit Hopkinson pressure bar tests andanalysis of coalmine sandstone with various moisture con-tentsrdquo Chinese Journal of Rock Mechanics and Engineeringvol 34 no 1 pp 2888ndash2893 2015

[6] W Wang H Li and H Gu ldquoMicromechanics analysis andmechanical characteristics of water-saturated coal specimensunder coupled static-dynamic loadsrdquo Journal of China CoalSociety vol 3 pp 611ndash617 2016

[7] W Wang H Wang D Li H Li and Z Liu ldquoStrength andfailure characteristics of natural and water-saturated coalspecimens under static and dynamic loadsrdquo Shock and Vi-bration vol 2018 Article ID 3526121 15 pages 2018

[8] Y Q Ding W H Tang and X Xu ldquoExperimental studyof dynamic mechanical behaviors of unsaturated clay sub-jected touniaxial loadingrdquo Rock and Soil Mechanics vol 9pp 2546ndash2550 2013

[9] N Ding L Jin and J Zhang ldquoEffect of free water content onthe dynamic mechanical behavior of cement mortar underhigh strain raterdquo Concrete vol 10 pp 128ndash132 2013

[10] J Zhan and N Zhang ldquoStudy on the damage feature ofwater-bearing argillaceous siltstone under the impact loadrdquoNon-Ferrous Metal vol 6 pp 44ndash77 2015

[11] Y Zhao S Liu Y Jiang K Wang and Y Huang ldquoDynamictensile strength of coal under dry and saturated conditionsrdquoRock Mechanics and Rock Engineering vol 49 no 5pp 1709ndash1720 2015

[12] Y V Petrov I V Smirnov G A Volkov A K AbramianA M Bragov and S N Verichev ldquoDynamic failure of dryand fully saturated limestone samples based on incubationtime conceptrdquo Journal of Rock Mechanics and GeotechnicalEngineering vol 9 no 1 pp 125ndash134 2017

[13] B Wang and X Li ldquoMesomechanics analysis of static com-pressive strength and dynamic compressive strength of water-saturated rock under uniaxial loadrdquo Explosion and ShockWaves vol 32 no 4 pp 423ndash431 2014

[14] F Gong X Li X Liu et al ldquoExperimental study of dynamiccharacteristics of sandstone under one-dimensional coupledstatic and dynamic loadsrdquo Chinese Journal of Rock Mechanicsand Engineering vol 29 no 10 pp 2076ndash2085 2010

[15] F Q Gong and G F Zhao ldquoDynamic indirect tensile strengthof sandstone under different loading ratesrdquo Rock Mechanicsand Rock Engineering vol 47 no 6 pp 2271ndash2278 2013

[16] -e National Standard Compilation Groups of Peoplersquos Re-public of China GBT 235615-2009 Methods for Determiningthe Physical and Mechanical Properties of Coal and RockStandards Press of China Beijing China 2009 in Chinese

[17] D Xiong Z Zhao and C Su ldquoExperimental study of effect ofwater-sturated state on mechanical properties of rock in coalmeasure stratardquo Chinese Journal of Rock Mechanics andEngineering vol 5 pp 998ndash1006 2011

[18] H Wang and Q Li ldquoSaturated concrete mesoscopic me-chanics mechanism of the static and dynamic compressivestrengthrdquo Journal of Hydraulic Engineering vol 8 pp 958ndash962 2006

Advances in Civil Engineering 9

[19] M Tao H T Zhao X B Li and W Z Cao ldquoFailurecharacteristics of pre-stressed rock with a circular hole sub-jected to dynamic loadingrdquo Tunnelling and UndergroundSpace Technology vol 81 pp 1ndash15 2018

[20] M Tao A Ma W Cao X Li and F Gong ldquoDynamicresponse of pre-stressed rock with a circular cavity subject totransient loadingrdquo International Journal of Rock Mechanicsand Mining Sciences vol 99 pp 1ndash8 2017

[21] Y Ogata W J Jung S Kubota and Y Wada ldquoEffect of thestrain rate and water saturation for the dynamic tensilestrength of rocksrdquo Materials Science Forum vol 465-466pp 361ndash366 2004

[22] S Huang K Xia F Yan and X Feng ldquoAn experimental studyof the rate dependence of tensile strength softening ofLongyou sandstonerdquo Rock Mechanics and Rock Engineeringvol 43 no 6 pp 677ndash683 2010

[23] Z Zhou X Cai W Cao X Li and C Xiong ldquoInfluence ofwater content on mechanical properties of rock in bothsaturation and drying processesrdquo Rock Mechanics and RockEngineering vol 49 no 8 pp 3009ndash3025 2016

[24] Z Zhou X Cai L Chen W Cao Y Zhao and C XiongldquoInfluence of cyclic wetting and drying on physical and dy-namic compressive properties of sandstonerdquo EngineeringGeology vol 220 pp 1ndash12 2017

[25] D Zheng and Q Li ldquoAn explanation for rate effect of concretestrength based on fracture toughness including free waterviscosityrdquo Engineering Fracture Mechanics vol 71 no 16-17pp 2319ndash2327 2004

[26] P Rossi J G M van Mier C Boulay and F Le Maou ldquo-edynamic behaviour of concrete influence of free waterrdquoMaterials and Structures vol 25 no 9 pp 509ndash514 1992

10 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

those of sandstone Under dynamic loading condi-tions the strength of naturally saturated coal samplesdecreases and the elastic modulus increases -isis the same strength variation trend and oppositeelastic modulus variation trend as observed forsandstone

(2) -e water-saturated coal specimens have greaterwater-rock interactions and strength reductioneffect its reduction in the ability to resist defor-mation is also very significant compared to saturatedsandstone

(3) Under static-dynamic loads owing to intensitydifferences in the saturated coal and rock materials astress difference results from the Stefan effect in thebranch fracture surface which is the main reasonthat the strength of coal and rock materials increasesor decreases Meanwhile fracture propagation atsaturated branch fracture surfaces can effectivelyexplain the increase in the deformation modulus ofcoal with increasing moisture content

(4) According to a sliding model of wing branch frac-ture the criteria for microfracture tensile stress andshear stress produced at the branch fracture surfacewere established If the branch fracture surface si-multaneously satisfies both τb gt τl and τf gt τa thebranch fracture surface will not break down -edynamic strength of water-saturated coal and rockwill increase If the branch fracture surface meetsonly one of the conditions τb lt τl or τf lt τa thebranch fracture surface will break down and thedynamic strength of water-saturated coal and rockwill decrease

Data Availability

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

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-e work was supported by the National Natural ScienceFoundation of China (51604093 and 51474096) NationalKey RampD Program of China (2018YFC0604502) Programfor Innovative Research Team at the University of Ministryof Education of China (IRT_16R22) Scientific and Tech-nological Key Project of Henan province (172107000016)and the Doctoral Research Fund Project of Henan Poly-technic University China (B2017-42)

References

[1] B Vasarhelyi and P Van ldquoInfluence of water content on thestrength of rockrdquo Engineering Geology vol 84 no 1-2pp 70ndash74 2006

[2] L S Tang P C Zhang and Y Wang ldquoOn fractures strengthof rocks with cracks under water actionrdquo Chinese Journal ofRock Mechanics and Engineering vol 23 no 19 pp 3337ndash3341 2004

[3] Z Zhu and D Hu ldquo-e effect of intestitial water pressure onrock mass strengthrdquo Rock and Soil Mechanics vol 21 no 1pp 64ndash67 2000

[4] Y Pu and Q Y Ma ldquoSplit Hopkinson pressure bar tests onsandstone in coalmine under cyclic wetting and dryingrdquo Rockand Soil Mechanics vol 9 pp 2557ndash2562 2013

[5] Y Pu and R Ma ldquoSplit Hopkinson pressure bar tests andanalysis of coalmine sandstone with various moisture con-tentsrdquo Chinese Journal of Rock Mechanics and Engineeringvol 34 no 1 pp 2888ndash2893 2015

[6] W Wang H Li and H Gu ldquoMicromechanics analysis andmechanical characteristics of water-saturated coal specimensunder coupled static-dynamic loadsrdquo Journal of China CoalSociety vol 3 pp 611ndash617 2016

[7] W Wang H Wang D Li H Li and Z Liu ldquoStrength andfailure characteristics of natural and water-saturated coalspecimens under static and dynamic loadsrdquo Shock and Vi-bration vol 2018 Article ID 3526121 15 pages 2018

[8] Y Q Ding W H Tang and X Xu ldquoExperimental studyof dynamic mechanical behaviors of unsaturated clay sub-jected touniaxial loadingrdquo Rock and Soil Mechanics vol 9pp 2546ndash2550 2013

[9] N Ding L Jin and J Zhang ldquoEffect of free water content onthe dynamic mechanical behavior of cement mortar underhigh strain raterdquo Concrete vol 10 pp 128ndash132 2013

[10] J Zhan and N Zhang ldquoStudy on the damage feature ofwater-bearing argillaceous siltstone under the impact loadrdquoNon-Ferrous Metal vol 6 pp 44ndash77 2015

[11] Y Zhao S Liu Y Jiang K Wang and Y Huang ldquoDynamictensile strength of coal under dry and saturated conditionsrdquoRock Mechanics and Rock Engineering vol 49 no 5pp 1709ndash1720 2015

[12] Y V Petrov I V Smirnov G A Volkov A K AbramianA M Bragov and S N Verichev ldquoDynamic failure of dryand fully saturated limestone samples based on incubationtime conceptrdquo Journal of Rock Mechanics and GeotechnicalEngineering vol 9 no 1 pp 125ndash134 2017

[13] B Wang and X Li ldquoMesomechanics analysis of static com-pressive strength and dynamic compressive strength of water-saturated rock under uniaxial loadrdquo Explosion and ShockWaves vol 32 no 4 pp 423ndash431 2014

[14] F Gong X Li X Liu et al ldquoExperimental study of dynamiccharacteristics of sandstone under one-dimensional coupledstatic and dynamic loadsrdquo Chinese Journal of Rock Mechanicsand Engineering vol 29 no 10 pp 2076ndash2085 2010

[15] F Q Gong and G F Zhao ldquoDynamic indirect tensile strengthof sandstone under different loading ratesrdquo Rock Mechanicsand Rock Engineering vol 47 no 6 pp 2271ndash2278 2013

[16] -e National Standard Compilation Groups of Peoplersquos Re-public of China GBT 235615-2009 Methods for Determiningthe Physical and Mechanical Properties of Coal and RockStandards Press of China Beijing China 2009 in Chinese

[17] D Xiong Z Zhao and C Su ldquoExperimental study of effect ofwater-sturated state on mechanical properties of rock in coalmeasure stratardquo Chinese Journal of Rock Mechanics andEngineering vol 5 pp 998ndash1006 2011

[18] H Wang and Q Li ldquoSaturated concrete mesoscopic me-chanics mechanism of the static and dynamic compressivestrengthrdquo Journal of Hydraulic Engineering vol 8 pp 958ndash962 2006

Advances in Civil Engineering 9

[19] M Tao H T Zhao X B Li and W Z Cao ldquoFailurecharacteristics of pre-stressed rock with a circular hole sub-jected to dynamic loadingrdquo Tunnelling and UndergroundSpace Technology vol 81 pp 1ndash15 2018

[20] M Tao A Ma W Cao X Li and F Gong ldquoDynamicresponse of pre-stressed rock with a circular cavity subject totransient loadingrdquo International Journal of Rock Mechanicsand Mining Sciences vol 99 pp 1ndash8 2017

[21] Y Ogata W J Jung S Kubota and Y Wada ldquoEffect of thestrain rate and water saturation for the dynamic tensilestrength of rocksrdquo Materials Science Forum vol 465-466pp 361ndash366 2004

[22] S Huang K Xia F Yan and X Feng ldquoAn experimental studyof the rate dependence of tensile strength softening ofLongyou sandstonerdquo Rock Mechanics and Rock Engineeringvol 43 no 6 pp 677ndash683 2010

[23] Z Zhou X Cai W Cao X Li and C Xiong ldquoInfluence ofwater content on mechanical properties of rock in bothsaturation and drying processesrdquo Rock Mechanics and RockEngineering vol 49 no 8 pp 3009ndash3025 2016

[24] Z Zhou X Cai L Chen W Cao Y Zhao and C XiongldquoInfluence of cyclic wetting and drying on physical and dy-namic compressive properties of sandstonerdquo EngineeringGeology vol 220 pp 1ndash12 2017

[25] D Zheng and Q Li ldquoAn explanation for rate effect of concretestrength based on fracture toughness including free waterviscosityrdquo Engineering Fracture Mechanics vol 71 no 16-17pp 2319ndash2327 2004

[26] P Rossi J G M van Mier C Boulay and F Le Maou ldquo-edynamic behaviour of concrete influence of free waterrdquoMaterials and Structures vol 25 no 9 pp 509ndash514 1992

10 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

[19] M Tao H T Zhao X B Li and W Z Cao ldquoFailurecharacteristics of pre-stressed rock with a circular hole sub-jected to dynamic loadingrdquo Tunnelling and UndergroundSpace Technology vol 81 pp 1ndash15 2018

[20] M Tao A Ma W Cao X Li and F Gong ldquoDynamicresponse of pre-stressed rock with a circular cavity subject totransient loadingrdquo International Journal of Rock Mechanicsand Mining Sciences vol 99 pp 1ndash8 2017

[21] Y Ogata W J Jung S Kubota and Y Wada ldquoEffect of thestrain rate and water saturation for the dynamic tensilestrength of rocksrdquo Materials Science Forum vol 465-466pp 361ndash366 2004

[22] S Huang K Xia F Yan and X Feng ldquoAn experimental studyof the rate dependence of tensile strength softening ofLongyou sandstonerdquo Rock Mechanics and Rock Engineeringvol 43 no 6 pp 677ndash683 2010

[23] Z Zhou X Cai W Cao X Li and C Xiong ldquoInfluence ofwater content on mechanical properties of rock in bothsaturation and drying processesrdquo Rock Mechanics and RockEngineering vol 49 no 8 pp 3009ndash3025 2016

[24] Z Zhou X Cai L Chen W Cao Y Zhao and C XiongldquoInfluence of cyclic wetting and drying on physical and dy-namic compressive properties of sandstonerdquo EngineeringGeology vol 220 pp 1ndash12 2017

[25] D Zheng and Q Li ldquoAn explanation for rate effect of concretestrength based on fracture toughness including free waterviscosityrdquo Engineering Fracture Mechanics vol 71 no 16-17pp 2319ndash2327 2004

[26] P Rossi J G M van Mier C Boulay and F Le Maou ldquo-edynamic behaviour of concrete influence of free waterrdquoMaterials and Structures vol 25 no 9 pp 509ndash514 1992

10 Advances in Civil Engineering

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Hindawiwwwhindawicom Volume 2018

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Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom