mgapo

Keywords:

Rock mass damage

rock

in

ing

gro

eme

the data obtained from a eld blast test. A fully coupled numerical analysis, incorporating the explosion

process, has been performed, where the large deformation zone near the charge is solved by the

rounddamagcommeth

and phenomena were recorded. Empirical damage criterion,

argel. [5]el ofm/s.coal

Fourie and Green [7] reported that no signicant damage was

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Contents lists availab

.els

al&

International Journal of Rock Mechanics & Mining Sciences 46 (2009) 12061213damage, were classied according to the PPV damage criterion.Most empirical formulae available in the literature usually workusually based on peak particle velocity (PPV), was obtained fromthese observations and measurements. For example, the US ArmyCorps of Engineers conducted some large explosion tests between

found when the PPV reaches 110mm/s. Singh [8] investigated thethreshold value of PPV for the safety of underground workingsbased on rock mass rating (RMR) of the roof rock, and threegroups of damage, i.e., major damage, minor damage and no

well for certain specic types of rock mass and do not include theCorresponding author. Tel.: +6567905255.

E-mail address: czzhao@ntu.edu.sg (Z.Y. Zhao).1365-16

doi:10.1i.e. the empirical method and the numerical simulation. Someeld blast tests have been carried out and the experimental data

mine openings may occur when PPV lies in the range of50100mm/s and large roof falls at the PPV of 100200mm/s.analysis because the problem involves many complicated physicalprocesses, such as the explosion of the charge, the damageinitiation and propagation. Some attempts have been made toinvestigate the damage of rock mass under the blast loading, andgenerally the analysis can be characterized by two main methods,

hole while the crush zone will extend to 1.94.5 times the chhole for a fully coupled TNT charge in granite. Jensen et afound that no roof failure occurs even at vibration lev0.445m/s, and only a few loose stones are observed at 0.127Kidybinski [6] reported that small roof falls of a undergroundA reliable estimation of the damage zone in the rock mass underblast loads is the rst step in design and stability assessment ofunderground structures. The amount of damage in rock mass willdepend on the distance from the explosive charge, the weight ofthe charge, the rock mass properties and the joint distribution.However, it is quite difcult to include all those factors in the

Colorado. It was reported by Rupert and Clark [3] that only minordamage in the form of localized thin spalls and collapse ofpreviously fractured coal ribs resulted from blast vibrationexceeding 0.05m/s. Siskind and Fumanti [4] concluded that theblast induced cracks are a function of rock type, and that thecracking zone will extend to 4.920 times the radius of the chargePeak particle velocity

Damage criterion

1. Introduction

The safety and stability of undergare often affected by blast inducedsource of the blast loading mayexplosion, the drill/blast excavation09/$ - see front matter & 2009 Elsevier Ltd. A

016/j.ijrmms.2009.02.007mass of granite are estimated by the RMR system. The peak particle velocity (PPV) damage criterion and

the plastic strain criterion were adopted to study the damage zone around the charge hole, and an

empirical formula considering the effects of loading density, RMR and weight of charge was obtained to

estimate the damage zone in granite based on the numerical results.

& 2009 Elsevier Ltd. All rights reserved.

rock caverns or tunnelses and vibrations. Thee from an accidentalod or weapon attacks.

1948 and 1952 near unlined tunnels in sandstone [1]. Four zonesof failure were categorized in terms of the PPV. They found thatthe threshold PPV corresponding to an intermittent failure is0.46m/s. Kendorski et al. [2] reported that cracks in the shotcreteliner of a tunnel start to develop when the PPV reachesapproximately 1.22m/s in an experiment conducted at the Cimax,Explosion

Loading density

Arbitrary LagrangeEuler (ALE) method. The deformable modulus and compressive strength of rockNumerical simulations of rock mass daexplosion

X.Y. Wei a,b, Z.Y. Zhao a,, J. Gu a

a School of Civil and Environmental Engineering, Nanyang Technological University, Sinb School of Civil Engineering, Chang An University, Xian 710061, China

a r t i c l e i n f o

Article history:

Received 7 August 2008

Received in revised form

3 February 2009

Accepted 13 February 2009Available online 21 March 2009

a b s t r a c t

The damage prediction of

weapon attacks is crucial

evaluate the effect of load

damage induced by under

transient dynamic nite el

journal homepage: www

InternationRock Mechanicsll rights reserved.age induced by underground

re 639798, Singapore

mass under blast loads induced by accidental explosions, rock bursts or

rock engineering. In this paper, parametric studies are conducted to

density, rock mass rating (RMR) and weight of charge on the rock mass

und explosions. The numerical simulations are carried out based on the

nt program ANSYS-LSDYNA. The numerical model was calibrated against

le at ScienceDirect

evier.com/locate/ijrmms

Journal ofMining Sciences

charge is solved by the Arbitrary LagrangeEuler (ALE) method.

2.1. Material models

The material models used in this problem include explosive(TNT), air and rock mass.

2.1.1. TNT

Material Type 8 of LS-DYNA (*MAT_HIGH_EXPLOSIVE_BURN)is used for TNT and the JonesWilkensLee (JWL) equation of state(EOS) is used to calculate the pressure generated by the expansionof the detonation products of the chemical explosive. The JWL EOSdenes the pressure as

p A 1 oR1V

eR1V B 1 o

R2V

eR2V oE

V(3)

where A, B, R1, R2 and o are the material constants, p is thepressure, V is the relative volume of detonation product, E is thespecic energy with an initial value of E0. The material parametersfor TNT used in the present study are as follows: A 3.738102GPa, B 3.747GPa, R1 4.15, R2 0.9,o 0.35, E0 6.0GPa. Thedetonation velocity and mass density of TNT is 6.93103m/s and1.63103 kg/m3, respectively.

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0

Target in rock mass

y

A

6m

2.5m

2.5m2.5m

2.5m

5m

Concrete

Explosive

15m 25mAir

0.8m

Fig. 1. Conguration of measurements.

echThe deformable modulus and compressive strength of rock massof granite are estimated by the RMR system. The numerical modelis calibrated by comparing the PPV from the numerical results andthe experimental data. Parametric studies are performed tond out the most inuential factors on the damage of rock mass,such as the RMR of rock mass and the loading density. The PPVdamage criterion related to the RMR of rock mass was chosenaccording to the test data available in the literature. The empiricalformula for the damage depth into rock under blast loading wasderived based on the numerical results. The effect of loadingdensity, weight of charge and RMR of rock mass was considered inthe formula.

2. Numerical model and calibration

A series of eld blast tests at a site of Bukit Timah granite wasconducted in the previous study [11,12]. The detailed geologicalinvestigation and intensive laboratory tests on the granite werealso carried out. Fig. 1 shows the eld layout of the test. Thecharge hole has the following dimensions: total depth is 11m, andthe diameters of the charge hole are 1.5m and 0.8m for the upper6m and bottom 5m, respectively. Measurement points werelocated on three lines on the ground surface, i.e., the predominantrock joint direction, the perpendicular direction and the 451direction. Nine measurement points were on the parallel line withdistance of 2.5, 5, 10, 25 and 50m from the center of charge holeon the ground surface and 8.5m below the surface. Eight testswere carried out with equivalent TNT charge weights rangingfrom 5 to 50kg [12]. In each test, explosive was placed at thecenter of the charge hole. The recorded data were used to deriveempirical attenuation relations for PPV and peak particle accel-eration (PPA). The best tted empirical attenuation relations aregiven in the following [12]:

PPA 1928:2R=Q1=31:4531 g (1)

PPV 0:396R=Q1=31:1455 m=s (2)effects of loading density, the chamber geometry and theexplosive distribution.

With the rapid development of computer technology andadvanced numerical techniques, more detail and reliable predic-tions of rock mass damage under blast loading through numericalsimulations have become available. Various numerical methodshave been proposed to estimate the rock mass damage induced bythe blast loading. Yang et al. [9] developed an isotropic cumulativedamage model and calibrated the model by comparing thenumerical results with the blasting experiments. Wu et al. [10]presented an anisotropic damage model to predict the damagezone around the charge hole. Some attempts have been made toestablish an empirical formula to estimate the damage zone ofrock mass including the loading density and chamber geometry[10], where various loading densities, chamber geometries andexplosive distribution patterns are considered in their numericalmodels, and the obtained formula is established based on the PPVcriterion and the damage index criterion.

In this paper, a numerical method has been used to predict thedamage depth into rock mass induced by underground explosion.The numerical simulations are carried out based on the transientdynamic nite element program ANSYS-LSDYNA. A fully couplednumerical analysis, which includes the explosion process, hasbeen performed, where the large deformation zone near the

X.Y. Wei et al. / International Journal of Rock Mwhere R is distance in meter measured from the charge center; Qis equivalent TNT charge weight in kilogram.Plane View

Target on rock surface

Z

1.5mSensor

45Charge hole

Predominantrock joint set

90x

25.0m

15.0m

5.0m2.5m2.5manics & Mining Sciences 46 (2009) 12061213 12072.1.2. Air

Material Type 9 of LS-DYNA(*MAT_NULL) is used for the air.This material model must be used with an EOS. The polynomial

The compressive failure is governed by J2 ow. The detailed

numerical model. An ALE zone is dened for the area around

3. PPV damage criterion

As stated in a previous study [10], it is very difcult to obtain auniversally accepted damage criterion since it involves manyfactors. For practical applications, the PPV damage criteria arewidely used because it can be easily recorded at a site. Adhikariet al. [16] reported the range of PPV and the correspondingdamage in two operating mines as shown in Table 1. Persson [17]reported the PPV damage criterion for Swedish hard rock asshown in Table 2. Li and Huang [18] reported the PPV damage

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0.01

peak

scaled distance (m/kg1/3)

Test results [12]

1 10

Fig. 2. Peak particle velocity versus scaled distance.

100

1000

peak

par

ticle

acc

eler

atio

n (g

)

scaled distance (m/kg1/3)

Numerical resultsTest results [12]

1 10

Fig. 3. Peak particle acceleration versus scaled distance.

Table 1Threshold value of PPV (mm/s) for underground structures [16].

Type of damage Fair rock (RMR 60) Poor rock (RMR 38)

No damage o153 o52Opening of joints 153217 52195

Falling of loose pieces 217367 195297

Induced cracking 367604 297557

Excessive damage 4604 4557

echthe charge. The smallest size elements are used in the region nearthe charge, while larger elements are used for the other region.There are a total of 424752 elements in the mesh, with thesmallest element being 50mm50mm50mm. The cylindricalcharge with equivalent TNT weight 40 kg is used in the model. Thediameter and the height of the cylindrical charge are 0.358 and0.245m, respectively.

The PPV and the PPA obtained from the numerical simulationsare compared with experimental results, as shown in Figs. 2 and 3.It can be found that the PPV from the numerical results agree wellwith the eld test results when the scaled distance is less thandescription of this model is given in [13].Laboratory tests were conducted on the Bukit Timah granite at

the eld site. It was found that the granite at the site is of goodquality. The average density of the rock is 2650kg/m3, Poissonsratio is 0.16 [12], Youngs modulus of intact granite is 73.9GPa, theuniaxial compressive strength is 186MPa, and the tensile strengthis 16.1MPa [14]. The previous study also found that the initialdamage in three directions in the rock mass is 0.162, 0.124, 0.222,respectively [15]. The mean initial damage 0.169 is adopted in thisstudy. Thus, the equivalent elastic modulus, compressive strengthand tensile strength for the granite can be determined as61.41GPa, 154.57MPa and 13.38MPa, respectively. There is noavailable test data for the fracture toughness gc and viscosity Z forrock mass, so a parameter study is carried out to adjust the propervalues for granite by comparing the numerical results with thetest data.

2.2. Numerical results

Only a quarter of the eld is modeled owing to the symmetryabout the yz and xz planes as shown in Fig. 1. The non-reectionboundaries are applied to minimize the stress wave reection atthese computational boundaries. The computational modelshould be large enough to minimize the effect of the boundaryreection. The model with size of 60m60m35m are usedhere. In order to minimize the effect of mesh size on thenumerical results, three different meshes are tried for theEOS is used in the present study. It has the form

P C0 C1m C2m2 C3m3 C4 C5m C6m2e (4)where e is the internal energy per volume. The compression of thematerial is dened by the parameter m (r/r0)1 with r and r0being the current and initial density of the material, respectively.

The air is often modeled as the ideal gas by settingC0 C1 C2 C3 C6 0 and C4 C5 g1 with g is the ratioof specic heat. In the present study, the standard materialconstants of air g 1.4, r 1.225kg/m3 are used.

2.1.3. Rock mass

There are several material models for concrete and rockimplemented in LS-DYNA, designed for special purposes to takeinto account the erosion, effect of strain rate, cracking, etc. In thepresent study, the Mat_brittle_damage in LS-DYNA library is used.This anisotropic damage model is suitable for brittle failure ofrock and concrete and contains a minimal set of materialconstants, which can be determined from the standard tests. Itadmits progressive degradation of tensile and shear strengthacross smeared cracks that are initiated under tensile loadings.

X.Y. Wei et al. / International Journal of Rock M12084.0m/kg1/3, while a slightly larger difference can be observedwhen the scaled distance is larger than 4.0. The similar trend forthe PPA can be found, as shown in Fig. 3.0.1

1

parti

cle

velo

city

(m/s

)

Numerical results

anics & Mining Sciences 46 (2009) 12061213criterion for hard rock and soft rock as shown in Table 3 with thefollowing denition: slight damageinitial damage; mediumdamagepartial collapse; serious damagelarge area tunnel

collapse. The threshold values of PPV at different RMR of roof rockof seven coal mines are reported by Singh [8], as shown in Table 4.The damage is classied into three groups, i.e. major damage,minor damage and no damage. The vibration levels in no damagezone are taken as safe level of vibration, and the threshold value ofvibration for the safety of underground workings is recom-mended. A comprehensive study of tunnel damage for sandstoneis carried by the US Armys Underground Explosion Tests (UET), asreported by Hendron [1]. In this report, the damage is classiedinto four groups: intermittent failure, local failure, general failureand tight closure. Table 5 shows that tunnel PPV damage criterionfor different damage zones. The intermittent damage is observedwhen random spalling of loose rocks occurs.

It can be observed from the literature that the threshold PPVvalue under no damage condition is quite different because thequality of intact rock and rock mass is different from site to site.The PPV damage criteria for various rock masses were predictedusing articial neural network by Zhao et al. [19]. The tensilestrength, compressive strength of the intact rock and the RMR areused as the input data to predict the threshold value of PPV. Based

to investigate the effect of loading density on the pressure aroundthe wall of the charge hole and the corresponding damage zone.

obtained by varying the weight of TNT as 311.9, 559.9, 808.0,1056.0 and 5216kg while keeping the volume of charge hole3.2m3 unchanged.

The damage zone is measured from the wall of the charge holeaccording to the PPV damage criterion as stated in Section 3. Aplastic strain damage criterion is also used and the damage zone ismeasure from the wall of the charge hole to the location withplastic strain. The results are compared with that of PPV damagecriterion.

Fig. 4 shows an element pressure around the charge hole forvarious loading densities. It can be noted that the peak pressure of

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gth

Table 4Threshold value of PPV for the safety of underground workings [8].

RMR of roof rock Threshold value of PPV (mm/s)

2030 50

3040 5070

4050 70100

5060 100120

6080 120

Table 5UET tests, sandstone [1].

Damage zone Damage PPV (m/s)

1 Tight closure NA

2 General failure 12

3 Local failure 4

4 Intermittent failure 0.91.8

0.0000-500

0

500

1000

1500

2000

2500

pres

sure

(MP

a)

Time (s)

loading density=1630 (kg/m3)

loading density=407.5 (kg/m3)

loading density=83.2 (kg/m3)

loading density=20 (kg/m3)

0.0005 0.0010 0.0015 0.0020

X.Y. Wei et al. / International Journal of Rock Mechanics & Mining Sciences 46 (2009) 12061213 1209The loading densities 20.0, 83.2 and 407.5 kg/m3 are obtained bydening the length of the charge hole as 5.00, 1.20 and 0.245mwhile keeping the weight of TNT as 64 kg. The loading densities of97.5, 175.0, 252.5, 330.0 and 1630kg/m3 (fully coupled) are

Table 2Damage criterion for Scandinavian bed rocks [17].

Typical effect PPV (m/s)

Incipient swelling 0.7

Incipient damage 1.0

Fragmentation 2.5

Good fragmentation 5.0

Crushing 15.0

Table 3Tunnel damage criterion for unlined rock tunnels [18].

Rock type Rock parameter

Unit weight

(g/cm3)

Compressive

strength (MPa)

Tensile stren

(MPa)

Hard rock I 2.62.7 75110 2.13.4

Hard rock II 2.72.9 110180 3.45.1on the results of the articial neural network, the threshold valueof PPV corresponding to incipient damage is chosen as: 0.5m/swhen RMR is smaller than 60, 0.7m/s when RMR lies between 60and 80, 0.9m/s when RMR is larger than 80.

4. Effect of loading density and RMR on blast loading and rockmass damage

4.1. Effect of loading density

The dimension of the cubic charge hole is 0.8m0.8m5m.The loading density can be obtained by two ways: (1) varying thelength of the charge hole while keeping the weight of TNTunchanged and (2) varying the weight of TNT while keeping thevolume of charge hole unchanged. These two methods are all usedHard rock III 2.72.9 180200 5.15.7

Soft rock I 2.02.5 40100 1.13.1

Soft rock II 2.02.5 100160 3.44.5Threshold value of PPV (m/s)

No damage Slight

damage

Medium

damage

Serious

damage

0.27 0.54 0.82 1.53

0.31 0.62 0.96 1.78

Fig. 4. Pressure around the charge hole of various loading density.0.36 0.72 1.11 2.09

0.29 0.58 0.90 1.67

0.35 0.70 1.07 1.99

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echX.Y. Wei et al. / International Journal of Rock M1210the fully coupled charge is about 8 times that of the loadingdensity 20kg/m3, and the peak pressure decreases very quicklyand reaches a negative value. The pressure around the charge holeis not uniform and the location where the maximum pressureoccurs is different for different loading density. The maximumpressure around the charge hole for fully coupled charge is about5.5GPa.

Fig. 5 shows the plastic contour of different loading density at acertain time step. It indicates that the plastic zone of fully coupledcharge is much larger than that of smaller loading density.

For a very good quality of rock mass (RMR 95), the PPVdamage criterion 0.9m/s is adopted, the damage depth atdifferent loading density is obtained as

RPPV 0:306W0:257Q1=3 (5)

where RPPV is the depth of the damage zone into the rock massmeasured from the wall of charge hole where the particle velocityreaches the threshold PPV,W (kg/m3) is the loading density, Q (kg)is the weight of the equivalent TNT.

The damage zone is obtained according to the plastic straincriterion in a similar manner, and the empirical relation fordamage depth at different loading density can be obtained as

Rplastic strain 0:359W0:172Q1=3 (6)

Wu and Hao [10] investigated the loading density effect andalso gave an empirical equation based on their numerical results.Two damage criteria have been adopted in their study, i.e., PPV

Fig. 5. Plastic strain contour around the charge hole of various loading densities: (a) fu83.2 kg/m3 and (d) loading density 20 kg/m3.anics & Mining Sciences 46 (2009) 12061213damage criterion (PPVX0.9m/s) and damage index criterion(DX0.71). The rock mass is granite and has the same propertiesas in this study.

Fig. 6 compares the results from Eqs. (5) and (6) and that of Wuand Hao [10] for TNT weight of 64kg. The damage depth based onthe PPV criterion in this study is slightly larger than the results ofWu [10]. Obviously the damage depth based on the PPV damagecriterion is larger than that of the damage index criterion and theplastic strain criterion. It indicates that even for the locationwhere no plastic strain occurs, the PPV already reaches thethreshold value.

4.2. Effects of RMR

In this section, the inuence of rock mass properties on thepressure along the wall of charge hole and the damage zone areinvestigated. It is necessary to estimate the rock mass propertiessuch as deformation modulus and strength parameters fornumerical modeling. Although such parameters can ultimatelybe determined from the in-situ tests, at the preliminary stage,where access to the underground is limited, the practical way toobtain these parameters is to apply a rock mass classicationsystem, such as RQD, RMR, Q and Geological Strength Index (GSI)system.

The effect of rock mass properties on the damage zone wasconducted based on the RMR system in this study. The uniaxialcompressive strength and elastic modulus are evaluated based on

lly coupled charge 1630kg/m3, (b) loading density 407.5 kg/m3, (c) loading density

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ion criterion)age Index)

echanics & Mining Sciences 46 (2009) 12061213 12114

6

8

10

12

14

Dam

age

dept

h in

to ro

ck (m

)

PPV criterion Plastic strain criter Results of Wu(PPV Results of Wu(Dam

X.Y. Wei et al. / International Journal of Rock Mthe RMR system. Kalamaras and Bieniawski [20] suggested thefollowing relations

scj=sci expRMR 100=24 (7)

Ej=Ei expRMR 100=17:4 (8)where scj is the compressive strength of rock mass, sci is thecompressive strength of intact rock, Ej is the elastic modulus ofrock mass and Ei is the elastic modulus of intact rock.

Fig. 7 shows the pressure along the wall of the charge holewhen loading density is 83.2 kg/m3. It indicates that the effects ofthe RMR on the peak pressure are very small while it has obviousinuence on the gas pressure. The larger the RMR is, the larger thepressure is. It has very little effects on the peak pressure becauseof the very short arising time while the gas pressure will last for arelatively longer time.

The effect of RMR, loading density and the weight of TNT are allincluded in the numerical simulation to investigate their effectson the damage depth into rock mass. Four types of RMR (95, 80,

0.000

0

40

80

120

160

200

pres

sure

(MP

a)

time (s)

element 81862RMR=95RMR=80RMR=60RMR=40RMR=20RMR=0

0.002 0.004 0.006 0.008 0.010

Fig. 7. Effect of RMR on the blast loading along the charge hole.

0 200 400 600 800 1000 1200 1400 1600 18000

2

Loading density (kg/m3)

Fig. 6. Comparison of damage depth according to different damage criterion.

02

4

6

8

10

12

14

16

Dam

age

dept

h in

to ro

ck (m

)

Loading density (kg/m3)

Q=64kgRMR=95RMR=80RMR=60RMR=40

200 400 600 800 1000 1200 1400 1600 1800

02

4

6

8

10

12

14

16

Dam

age

dept

h in

to ro

ck (m

)

Loading density (kg/m3)

Q=64kgRMR=95RMR=80RMR=60RMR=40

200 400 600 800 1000 1200 1400 1600

Fig. 8. Damage depth into rock versus loading density and RMR: (a) according toPPV damage criterion and (b) according to plastic strain criterion.

60, 40), eight loading densities and six different weight of TNT asstated in Section 4.1 are considered in this study. Similarly, thedamage depth into rock mass under blast loading including theeffect of RMR, loading density and weight of charge can beobtained. All the obtained numerical results were used to derivethe empirical relations for damage depth. The best tted empiricalrelation is as follows:

RPPV 3:907W0:257RMR0:578Q1=3 (9)

Usually the scaled distance is often used to include the effect ofweight of charge and distance. If we dened the threshold scaleddistance as Z R/Q1/3, then the above equation can be expressedas

ZPPV RPPV=Q1=3 3:907W0:257RMR0:578 (10)

Similarly, the damage zone can be obtained according to theplastic strain damage criterion. The damage depth and thecorresponding threshold scaled distance at different loadingdensity are obtained as

Rplastic strain 5:598W0:172RMR0:534Q1=3 (11)

contract RPTJ0275030 for US Bureau of Mines; 1979. p. 99 .

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1

2

3

4

Thre

shol

d sc

aled

dis

tanc

e (m

/kg1

/3)

RMR=95RMR=80RMR=60RMR=40

X.Y. Wei et al. / International Journal of Rock Mech12120

Loading density (kg/m3)

-200

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Thre

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aled

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/kg1

/3)

Loading density (kg/m3)

RMR=95RMR=80RMR=60RMR=40

200 400 600 800 1000 1200 1400 1600

0 200 400 600 800 1000 1200 1400 1600Fig. 9. Threshold scaled distance versus loading density and RMR: (a) according toPPV damage criterion and (b) according to plastic strain criterion.[6] Kidybinski A. Design criteria for roadway supports to resist dynamic loads. IntJ Min Geol Eng 1986;4:91109.

[7] Fourie AB, Green RW. Damage to underground coal mines caused by surfaceblasting. Int J Surf Min 1993;7:116.

[8] Singh PK. Blast vibration damage to underground coal mines from adjacentopen-pit blasting. Int J Rock Mech Min Sci 2002;39(8):95973.

[9] Yang R, Bawden WF, Katsabanis PD. A new constitutive model for blastdamage. Int J Rock Mech Min Sci 1996;33(3):24554.

[10] Wu C, Hao H. Numerical prediction of rock mass damage due to accidentalexplosions in an underground ammunition storage chamber. Shock Waves2006;15(1):4354.

[11] Wu YK, Hao H, Zhou YX. Propagation characteristics of blast-induced shockwaves in a jointed rock mass. Soil Dyn Earthquake Eng 1998;17(6):40712.

[12] Hao H, Wu C, Zhou Y. Numerical analysis of blast-induced stress waves in arock mass with anisotropic continum damage models. Part 1: equivalentmaterial property approach. Rock Mech Rock Eng 2002;35(2):7994.

[13] Govindjee S, Kay GJ, Simo JC. Anisotropic modeling and numerical simulationof brittle damage in concrete. Int J Numer Methods Eng 1995;38(21):361133.

[14] Hao H, Wu YK, Ma GW, Zhou YX. Characteristics of surface ground motionsinduced by blasts in jointed rock mass. Soil Dyn Earthquake EngZplastic strain Rplastic strain=Q1=3 5:598W0:172RMR0:534 (12)Figs. 8a and b show the relationship between the damage depth

and the loading density and RMR based on PPV criterion andplastic strain criterion, respectively, when the weight of TNT is64 kg. Obviously the loading density and RMR all have signicantinuences on the damage zone. The larger the loading density, thelarge the damage zone is. It is straightforward to estimate thedamage depth under various loading density with different RMRfrom those gures.

The relationship between the threshold scaled distance,loading density and RMR are shown in Figs. 9a and b. The resultscan be used to estimate the safe scaled distance with variousloading density and the RMR. The damage zone can then beestimated if the weight of charge is given.

5. Conclusions

The damage of rock mass under blast loading was investigatedthrough numerical simulations in this study. The fully coupledmethod has been used, in which the large deformation zone nearthe charge is solved by the Arbitrary LagrangeEuler (ALE)method. A new PPV damage criterion was proposed includingthe effect of RMR of rock mass. The empirical formula for damagedepth including the effect of loading density, RMR and weight ofcharge, was derived based on the numerical results. It indicatesthat the loading density, RMR and weight of charge signicantlyinuence the damage depth. By introducing the scaled distance,the formula of safe scaled distance can be obtained. The safescaled distance for RMR 40 is about 1.7 times that of RMR 95under the fully coupled charge condition. It should be noted thatthe study is based on one type of rockgranite, so the PPVdamage criterion for other rocks should be different as they mayhave different rock mass properties but with the same RMR.

References

[1] Hendron AJ. Engineering of rock blasting on civil projects. In: Hall WJ, editor.Structural and geotechnical mechanics, a volume honoring NM Newmark.Englewood Cliffs, NJ: Prentice-Hall; 1977. p. 2427.

[2] Kendorski FS, Jude CV, Duncan WM. Effect of blasting on shortcrete driftlinings. Min Eng 1973;25(12):3841.

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ARTICLE IN PRESS

X.Y. Wei et al. / International Journal of Rock Mechanics & Mining Sciences 46 (2009) 12061213 1213

Numerical simulations of rock mass damage induced by underground explosionIntroductionNumerical model and calibrationMaterial modelsTNTAirRock mass

Numerical results

PPV damage criterionEffect of loading density and RMR on blast loading and rock mass damageEffect of loading densityEffects of RMR

ConclusionsReferences