An Alternative Approach to Determine the Holmberg-Persson (Onederra, Esen-Fragblast)

1

An alternative approach to determine the Holmberg-Perssonconstants for modelling near field peak particle velocityattenuation

I. Onederra1 & S. Esen1

1 Julius Kruttschnitt Mineral Research Centre, The University of Queensland, Brisbane, Qld, Australia

Italo Onederra BE(Hons) MEngSc.Senior Research Engineer - Mining ResearchJulius Kruttschnitt Mineral Research Centre (JKMRC)Isles Rd. IndooroopillyQLD. Australia 4068Phone: +61 7 3365 5888Fax: +61 7 3365 5999e-mail: [email protected]

2

An alternative approach to determine the Holmberg-Perssonconstants for modelling near field peak particle velocityattenuation

I. Onederra1 & S. Esen1

1 Julius Kruttschnitt Mineral Research Centre, The University of Queensland, Brisbane, Qld, Australia

ABSTRACT

A new approach to determine the Holmberg and Persson site specific constants (K andα) for modelling near field peak particle velocity (PPV) attenuation due to blasting ispresented. Currently the Holmberg-Persson approach requires the measurement ofpeak particle velocity at several locations resulting from a known explosive source.The objective is the determination of the attenuation characteristics of the rock massin a specified direction and for a given explosive type. The new alternative approachsignificantly reduces instrumentation and monitoring requirements. It uses ananalytical method to predict the peak particle velocity at the point at which rockcrushing ceases and combines this with a known value of PPV measured at a pre-defined location. Four case studies which include both model scale and full scaleblasting conditions are used to demonstrate and validate this alternative approach.

1 INTRODUCTION

Our understanding of blast induced rock mass damage has been significantlyenhanced by the application of both experimental research and numerical modelling(Wedmaier 1992, Blair & Minchinton 1996, Yang et al. 1996, Kouzniak &Rossmanith 1998, Uenishi & Rossmanith 1998). Numerical methods have allowed thefurther development of theories that describe the mechanisms of blast wavepropagation and have provided us with a better insight into what the rock mass maybe experiencing during the blasting process.

There is however still many issues to be resolved before numerical methods can beroutinely applied as engineering design tools. They include the development ofmechanisms that can accurately model the impact of important factors such as thestructural characteristics of the rock mass and the non-ideal detonation behaviour ofexplosives. Advances in this field are currently under way by combining advancednumerical methods with both ideal and non-ideal detonation codes as discussed byUenishi & Rossmanith (1998) and Chitombo (2002a).

Whilst advances in numerical models continue, due to the complex nature of theexplosive/rock interaction process, engineering solutions in the form of semi-mechanistic or empirical models still dominate the blast design engineering process.Wagner (2001) in a recent keynote address has noted that experience based designcriteria have and continue to give the most reliable results in mining applications.

One of the most widely used engineering methods to model the site specificattenuation of blast waves in the rock mass is the Holmberg-Persson approach

3

(Holmberg & Persson 1980). This approach models blast wave attenuation bydefining two site specific constants (K and α).

It is widely accepted that the Holmberg-Persson approach does not attempt to conveythe fundamentals of blast wave propagation theory nor does it represent a modelattempting to describe the underlying mechanisms of blast wave propagation as is thecase with the more fundamental numerical methods. This approach is akin to fitting aspecific relationship to a set of experimental data, with the main difference being thatthe data is collected in conditions where not all factors are controllable or can bethoroughly defined (i.e. rock mass characteristics, in situ stresses, non-idealdetonation behaviour of explosive, etc.). Understandably, by conducting fieldmeasurements the impact of the above factors are indirectly taken into account.

The Holmberg-Persson model is essentially a static approach as it is time independent.It does not consider the influence of explosive VOD, and thus, it must be calibratedseparately if two significantly different explosive types are being compared.Questions regarding the accuracy of this empirical approach have been raised in theliterature based on comparisons made with dynamic numerical approaches such asdynamic finite element modelling (DFEM) (Blair & Minchinton 1996, 1997). It canhowever be argued that comparisons of this nature are not strictly appropriate as bothapproaches are fundamentally different (i.e. static versus dynamic) and hence arebound to produce incompatible results.

Despite its limitations arising from its inherent assumptions, the Holmberg-Perssonmodel provides a unique practical methodology for blasting engineering applicationswhich include the development of site specific indices for damage prediction, damagecontrol and recently expanded as a tool to empirically model breakage andfragmentation (Andrieux et al. 1994, LeBlanc et al. 1995, McKenzie et al. 1995, Liu& Proulx 1996, Meyer & Dunn 1996, Onederra 2001).

The aim of the present work is to offer an alternative technique to determine theHolmberg and Persson site specific constants to model near field peak particlevelocity attenuation. The new approach uses an analytical method to predict the peakparticle velocity at the point at which rock crushing ceases and combines this with aknown value of PPV measured at a pre-defined location.

2 A BRIEF DESCRIPTION OF THE HOLMBERG-PERSSON APPROACH

The Holmberg and Persson (1980) approach makes the following assumptions:

• A radiating blast wave obeys charge weight scaling laws.• The peak particle velocity due to each small element of charge within the blast

hole is numerically additive.• For practical purposes, the velocity of detonation (VOD) of the explosive charge is

neglected.• The effect of free face boundaries is also neglected• For damage assessment purposes, it assumes that PPV is proportional to the

dynamic strain experienced by the rock mass.

4

The above assumptions allowed the derivation of a simple non linear relationship todescribe peak particle velocity (PPV) attenuation in the near field (Holmberg andPersson, 1980):

( )[ ]

α

αβ

−+= ∫

+Hx

xo

s

s xxr

dxKPPV

220

2

l (1)

where l is the linear charge concentration (kg/m), dx is the element of chargecontributing to the PPV at point P and ro, x and xo are geometric parameters (seeFigure 1). The above equation is simplified by assuming β = 2α, which yields:

α

−+

−+

=

o

so

o

os

o r

xx

r

xxH

rKPPV arctanarctan

l(2)

PPV = K [a]α (3)

where a is here defined as the Holmberg-Persson term and K and α are the sitespecific attenuation constants.

P(ro,xo)ro

H

xr

xo

xs

x

xs+H

dx

x-xo

xo-xs

( )[ ]R r x xo o= + −2 21

2

Figure 1. Schematic diagram of the Holmberg-Persson parameters to model peak particle velocityattenuation.

As mentioned earlier, due to the assumptions of the Holmberg-Persson approach, itsapplication requires site specific calibration. This calibration work entails theimplementation of a somewhat involved and costly vibration monitoring programwhich is discussed in the following section.

5

3 NEAR FIELD VIBRATION MONITORING TO DETERMINE THE SITESPECIFIC CONSTANTS

The site specific constants (K and α) are determined from the implementation of avibration monitoring program requiring the installation of an array of triaxialgeophones. Figure 2 illustrates the most commonly used layout which includesmeasurements taken at a minimum of three locations for a known explosive charge.Experimental layouts vary depending upon the characteristics of the rock mass, accessto the site, mining method and blast design parameters. Monitoring requirements canincrease substantially if the rock mass is anisotropic in nature as attenuation will bedependent upon the orientation of major discontinuities (e.g., bedded strata). Inaddition and as discussed earlier, because the Holmberg-Persson approach does notconsider the influence of velocity of detonation (VOD), different explosives should becalibrated separately within the same domain.

Explosive charge

Triaxial arrangement

Array #2 Array #3

Grout

Rock mass

VerticalGeophone

RadialGeophone

TransverseGeophone

DataCable

Array #1

To data acquisition system

Figure 2. Typical instrumentation layout for near field vibration attenuation monitoring in a predefineddirection.

In addition to peak particle velocity measurements, other information collected in thistype of monitoring program include geotechnical information such as rock materialproperties, rock mass characteristics (orientation of discontinuities) and designinformation such as charge configuration and location.

To determine the constants K and α, measured peak particle velocity (vector sum)records and design parameters are graphically resolved in the Holmberg and Perssonrelationship by fitting the linear relationship (Figure 3),

Log(PPV) =αLog(a) + Log(K) (4)

6

y = 1.0868x + 2.6742

R2 = 0.7289

0

0.5

1

1.5

2

2.5

3

-1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2

log (a )

log

(P

PV

)

Figure 3. Example data set of PPV records from a typical monitoring program.

4 NEW APPROACH TO DETERMINE THE SITE SPECIFIC CONSTANTS

The new approach differs from current practice in that it reduces the amount ofinstrumentation and monitoring required. This significantly reduces the costsassociated with near field vibration monitoring. The proposed method only requiresone monitoring point in the near field (e.g., in full scale production environments,from within 1/2 to 1 charge length). The approach uses an analytical method to predictthe peak particle velocity at the point at which rock crushing ceases and combines thiswith a known value of PPV measured at a pre-defined location. This is illustrated inFigure 4.

Explosive charge

Grout

Rock mass

Array #1

To data acquisition system

Log(a)

Log(PPV)

Radius ofcrushing, rc

Calculated maximumPPV at distance rc

Measured PPV at distance dd

Log(PPV) = Log(K) + α Log(a)

Figure 4. Schematic diagram of new approach required to define the Holmberg-Persson attenuationconstants

7

The following sections give a step by step description of the proposed approach whichinclude: a method to predict the maximum PPV at the end of crushing and thecalculation required to determine the attenuation constants K and α.

4.1 PPV at the end of the crushing zone

To calculate the PPV at the end of crushing, the simple equation for the stress in aplane sinusoidal stress wave is adopted (Persson et al. 1994),

d

peqc E

VPPPV = (5)

Where Peq is the equilibrium pressure at the end of crushing (Pa), Vp is thecompressional wave velocity (m/s) and Ed the dynamic Young's modulus (Pa). ThePPVc value at this point is independent of charge length and it is assumed to occur atthe mid point of the charge.

The calculation of equilibrium pressure Peq which is the pressure experienced at theend of the crushing zone is illustrated in Figure 5. The peak pressure attenuationfunction adopted in this case is based on the work by Liu & Katsabanis (1993) and isgiven by,

φ

=

o

cbeq r

rPP (6)

where Peq is the pressure at a distance rc from the centre of the blasthole (Pa); Pb is theborehole pressure (Pa), ro is the blasthole radius (m) and φ is the pressure decayfactor. This factor is a function of rock and explosive properties and is given by (Liu& Katsabanis 1993),

33.0

54.1−

−=

D

Vpφ (7)

where Vp is the compressional wave velocity (m/s) of the rock and D is the explosive'svelocity of detonation (m/s).

8

Distance

Pre

ssu

re

Pb

Peq

rc

rorc

Pd= Detonation pressurePb= Borehole pressurePeq= Equilibrium pressurerc= Crushing zone radiusro= Borehole radius

Pd

Figure 5. Diagram describing pressure attenuation with distance.

4.2 Predicting the radius of crushing (rc)

In order to predict the maximum extent of crushing around a blasthole, a new modelhas been developed (Esen et al. 2002).

The model is based on the back-analysis of a comprehensive experimental programthat included the direct measurement of the zone of crushing from 92 concrete blockblasting tests using two commercial explosives. The properties of the concrete blocksvaried from low, medium to high strength and measured 1.5 m in length, 1.0 m inwidth and 1.0 m in height.

In the proposed model, the extent or radius of crushing denoted as rc shown in Figure6 is assumed to be a function of explosive type, material properties and boreholediameter.

rc

ro

rc = f (ro,Pb,K,σσσσc)

Figure 6. Parameters influencing the extent of crushing.

9

As shown by Figure 6, ro is the original borehole radius (mm), Pb is the boreholepressure (Pa) calculated using non-ideal detonation theory, K is the rock stiffness (Pa)and σc is the uniaxial compressive strength (Pa). Rock stiffness K is defined assumingthat the material within the crushing zone is homogeneous and isotropic and is givenby,

d

dEK

υ+=

1(8)

where Ed is the dynamic Young’s modulus and νd is the dynamic Poisson’s ratio.

From the experimental work, a non-linear relationship defined by two dimensionlessindices has been derived and is given by:

( ) 219.0231.1 −= CZIr

r

c

o (9)

( )( ) 2

3

c

b

K

PCZI

σ×= or crushing zone index (CZI) (10)

where CZI is defined as the crushing zone index. This is a dimensionless index thatidentifies the crushing potential of a charged blasthole. Borehole pressure is computedfrom the non-ideal detonation model developed by Esen (2001).

Because it is physically impossible for the ratio between ro and rc to be greater than 1,the above relationship is constrained to 1 for very small values of CZI. In this case forvalues of CZI less than 2.6. These small values of CZI will generally correspond tosmall borehole pressures (i.e. decoupled charges).

Further details of the proposed model are discussed by Esen et al (2002), including thevalidation and comparison of this model with other approaches and its applicability tofull scale production blasting environments.

4.3 Calculation of the K and α constants

For a given explosive type and rock material, the radius of crushing is estimated byapplying the model described above, this allows the calculation of the equilibriumpressure at this distance which in turn allows for the estimation of peak particlevelocity (PPVc). At this point the influence of charge length can be neglected and it isassumed that this value occurs at the centre of the charge. By combining thiscalculated value of PPV with a measured value from a known explosive charge, thenthe linear relationship described by Equation 4 can be used to determine the constantsK and α.

10

5 VALIDATION OF THE PROPOSED APPROACH

Four case studies which include model scale tests and full scale vibration monitoringstudies have been used to validate the proposed approach. In each case study, acomparison is made by modelling PPV attenuation given by the Holmberg & Perssonrelationship (Equation 2) and by estimating the likely maximum extent of damagedefined by a threshold of critical peak particle velocity given by (Persson et al. 1994),

E

TVPPV p

crit = (11)

where T is the tensile strength of the rock (Pa), E is the Young's Modulus (Pa) and Vp

is the compressional wave velocity (m/s).

Table 1 gives a brief description of the case studies and summarises the physical andmechanical properties of the investigated domains. In addition, the properties of theexplosive products used in each case study are summarised in Table 2.

Table 1. Physical and mechanical properties of materials.

Casestudy

Description Domain σc,MPa

T,MPa

ρ,kg/m3

Vp, m/s

Es,GPa

Ed,GPa

νd PPVcrit,mm/s

1 Model scale tests Fosroc grout 58.3 4.7 2167 3716 9.6 14.2 0.199 18192 Vibration monitoring

in bench stopingUrquhart

Shales- Hilton130.0 11.7 2850 5800 80.0 97.9 0.315 848

3 Vibration monitoringin SLC mining

Volcanics-Ridgeway

131.0 15.8 2770 5180 67.0 79.9 0.296 1221

4 Vibration monitoringin VCR mining

Quartz diorite 240.0 19.3 2800 6103 87.0 110.7 0.329 1353

Table 2. Explosive properties.

Casestudy

Explosive ExplosiveDensity,

g/cm3

Heat ofReaction

q,MJ/kg

CJVOD,km/s

HoleDiameter,

mm

ChargeRadius

re,mm

BoreholePressure

Pb,GPa

1 Booster 1.540 4.830 7.022 25 11 5.6472 ANFO 0.800 3.858 4.835 89 44.5 1.6303 Emulsion 1.100 3.991 5.640 102 51 6.5534 Watergel 1.300 3.222 5.693 102 51 5.676

5.1 Case study 1 - Model scale tests in fosroc

Fosroc grout was cast into steel drums (Figure 7) to obtain the test samples at theJKMRC, Australia. During the casting process, two shock accelerometers (PCBPiezotronics Model U350B21) capable of measuring 100000 g (980 000 m/s2) were

11

installed in each drum at the distances shown in Figure 7. The distances chosen werebased upon preliminary estimates of the likely acceleration levels to be experienced sothat the capacity of the accelerometers was not exceeded (i.e. to avoid saturation). A25mm steel pipe was placed at the centre of the drum and later retrieved to form theblasthole. The physical and mechanical properties of the Fosroc grout used in theseexperiments are summarised in Table 1. The charge configuration consisted of a25mm blasthole charged with a 22mm UEE booster (26 g) composed of 60%TNT and40% PETN (see Table 2).

After each test, sections of the steel drum were cut to reveal the radial cracking andthe size of the crushing zone. Figure 8 shows the results of one of the two testsconducted. The radius of crushing (rc) for both experiments was measured as 37.5mm.

DrumDiameter = 600mmHeight = 840mm

Test 1a = 180mmb = 240mm

Test 2a = 150mmb = 240mm

Figure 7. Experimental set up (La Rosa & Onederra 2001).

Figure 8. Radial cracks and crushed zone measurement for Test #2 (La Rosa & Onederra 2001).

12

Accelerometer signals were acquired with a Tektronix oscilloscope with a samplingrate of 1 MHz, record length of 5000 points and 10% pretrigger. These settings gave arecord length of 5 ms with a pre-trigger of 500 µs. A typical signature captured duringone of the experiments is shown in Figure 9. Table 3 summarises the results obtainedfrom these experiments. Values of peak particle velocity (PPV) were calculated fromthe integration of the respective acceleration signals.

-100000

-80000

-60000

-40000

-20000

0

20000

40000

3020 3030 3040 3050 3060 3070 3080

Time (µµµµs)

g

16 µs = 3750 m/s

69933 g (@ 167.5mm*)

44333 g (@ 227.5 mm*)

* distance from borehole wall

Figure 9. An example of a typical acceleration signal from Test #1 (La Rosa & Onederra 2001).

Table 3. Summary of experimental results - measured accelerations and computed PPVs (La Rosa &Onederra 2001).

Test#

Distance from centreof charge (mm)

Acceleration(g)

PPV(mm/s)

1 180 69933 36701 240 44333 30302 150 94459 60902 240 42844 2750

5.1.1 Determination of K and α using the conventional approach

PPV measurements were used to determine the Holmberg-Persson constants K and αfollowing the conventional approach described in section 3. Table 4 summarises themeasured and calculated parameters that define the linear equation of the logarithmicterms.

Table 4. Parameters used to determine K and α using the conventional approach.

PPV(mm/s)

Distance(m)

LinearCharge(kg/m)

LN(a) LN(PPV)

6090 0.15 0.585 0.253906 8.7144033670 0.18 0.585 -0.10796 8.2079472890* 0.24 0.585 -0.68055 7.969012

* average of two tests

13

The line of best fit for this data set is given by LN(PPV) = 0.7632LN(a) + 8.433. Thiscorresponds to a K value of 4596 and α of 0.76.

5.1.2 Determination of K and α using the proposed approach

The new approach described in section 4 is applied by calculating the value ofequilibrium pressure (Peq) and the maximum PPV at the end of crushing (i.e. 37.5mmmeasured from the centre of the charge). The values are 0.725GPa and 189,787 mm/srespectively. The booster is assumed to detonate ideally. The CHEETAH idealdetonation code is used to determine the ideal detonation properties of the explosive(Table 2). Borehole pressure is computed by taking into account the decouplingeffect.

The average measured PPV value of 2890mm/s recorded 240 mm from the centre ofthe charge is combined with the calculated value to determine the K and α constants.The parameters that define the linear equation of logarithmic terms to determine Kand α are summarised in Table 5.

Table 5. Parameters used to determine K and α with the new approach.

PPV(mm/s)

Distance(m)

LinearCharge(kg/m)

LN(a) LN(PPV)

2890 0.24 0.585 -0.68055 7.969012189787 0.0375 0.585 2.910085 12.15366

The linear relationship between these two data points is given by LN(PPV) =1.1654LN(a) + 8.7621. This corresponds to a K value of 6387 and α of 1.17.

5.1.3 Comparison between the two methods

The resulting K and α values given by both methods are compared by plotting PPVattenuation shown in Figure 10 using the Holmberg-Persson relationship (Equation 2).Figure 10 shows the validity of the Holmberg-Persson approach as the model closelymatches the measured conditions (i.e. PPV value at 150mm from the centre of thecharge).

The threshold of critical peak particle velocity (PPVcrit) for the fosroc is also shown inFigure 10. As a way of comparison, the extent of damage given by the attenuationconstants determined with the current and new approach is 0.31 m and 0.29 mrespectively. This is in agreement with the observed extension of radial cracks for the600mm diameter drums (La Rosa & Onederra 2001).

The sharp attenuation described by the calculated constants was expected from thistype of soft/plastic material. The energy absorption characteristics of soft and mediumstrength rocks has been recognised and documented in theory and practice (Uenishi &Rossmanith 1998, Chitombo 2002b).

14

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

0 0.1 0.2 0.3 0.4

Distance (m)

PP

V (

mm

/s)

K=4596, alpha=0.76 -current approach K=6387, alpha=1.17 - New approach Measured

PR

50mm

25mm - Booster at 1.54 g/cc

PPVcrit

Figure 10. Comparison between PPV attenuation - model scale tests.

5.2 Case study 2. Blast monitoring study in bench stoping

This blast monitoring study was carried out at the Hilton operation, locatedapproximately 20 km North of Mt Isa in North-West Queensland, Australia (Scott1997, Villaescusa et al. 1997). The study aimed at measuring and modelling the extentof hangingwall damage from blasting. The location of monitoring stations and atypical cross section of the instrumentation array is shown in Figure 11. Triaxialgeophone arrangements were located at distances of 5, 9 and 13 metres from thehangingwall to determine the blast wave attenuation characteristics across bedding.Extensometers were used to measure hangingwall deformations. Observation holeswere drilled parallel and approximately 1 metre from geophone holes. A section ofthese were diamond drilled to provide information for core logging and also for rockmass characterisation purposes. Observation holes were surveyed before and aftereach blasting event. These observations helped in defining the zone of pre-conditioning or “damage”.

Production rings were drilled with 89mm holes using top hammer technology(Tamrock SOLO rig). The typical pattern used was approximately 3m between rings,in conjunction with an intermediate easer (1.5m burden). Blasthole lengths wereapproximately 30m. As a standard practice all hangingwall holes were charged withISANOL and the footwall holes with ANFO with a density of 0.8 g/cm3.

15

Cross-Section

AB

C

A - Geophone HoleB - Observation HoleC - Extensometer Hole

Drilling Drive

Mucking Drive

Station 1

Station 2

Station 3

Prod

uctio

n st

ope

Plan View

Instrumentation Drive

Figure 11. Schematic Diagram of Stope Instrumentation at Hilton/MIM.

Analysis of the Hilton vibration data across bedding planes enabled the determinationof the Holmberg and Persson site specific constants K and α (Scott 1997, Villaescusaet al. 2002). Results for the case of ANFO are summarised in Table 6

Table 6. Results from vibration attenuation study at Hilton (Scott 1997, Villaescusa et al. 2002).

Explosivetype

K α Number ofmeasurements

Correlationcoefficient

(R2)ANFO 456 1.12 78 0.71


Following the approach described in Section 4, the radius of crushing (rc), theequilibrium pressure (Peq) and the maximum PPV are: 47mm, 1.509 GPa and89,396mm/s respectively. A measured PPV value of 254 mm/s was recorded at adistance of 17.3m from the source. The source corresponded to an 89mm diameterfootwall hole having a 1.5m burden and charged with 29m of poured ANFO at 0.8g/cm3.

The parameters that define the linear equation of logarithmic terms are summarised inTable 7.


PPV(mm/s)

Distance(m)

Linear(kg/m)

LN(a) LN(PPV)

254 17.3 4.98 -0.9129 5.53733489396 0.047 4.98 5.805081 11.40083

16

The linear relationship between these two data points is given by Ln(PPV) =0.8728LN(a) + 6.3341 which gives K and α values of 563 and 0.87 respectively.


A comparison between the K and α constants calculated using the current and newapproach are given in Figure 12. These curves are for a 29m ANFO charge.

The threshold of critical peak particle velocity (PPVcrit) for this domain is also shownin Figure 12. For the attenuation constants determined with the current and newapproach, the PPV attenuation indicates a maximum extent of damage ofapproximately 6.5m and 6.8m respectively from the centre of the charge. For theHilton case study this corresponds to a zone of pre-conditioning/damage extending toapproximately 3.6m into the stope hangingwall. This is in agreement withobservations backed by borehole camera surveys and extensometers which confirmedthat the combined effect of blasting and stress redistribution affected the rock mass toapproximately 5m into the stope hangingwall (Villaescusa et al. 2002).

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

3000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Distance (m)

PP

V (

mm

/s)

K=456, alpha= 1.12 - current approach K=563, alpha= 0.87 - new approach

PR

29m

1.5m burden89mm - ANFO at 0.8 g/cc

PPVcrit

Figure 12. Comparison between PPV attenuation - case study 2.

5.3 Case study 3. Vibration monitoring study in SLC ring blasting

The aims of this study were to conduct a preliminary assessment of blast performancebased on vibration waveform analysis and to determine the near field Holmberg-Persson rock attenuation parameters specific to the volcanics domain at the Ridgewayoperation. This operation uses the Sublevel caving (SLC) mining method.

17

The monitoring program was designed to allow for normal production blastingconditions to be carried out. As shown in Figure 13, a system of three fully groutedtriaxial geophone arrangements was installed in one cross cut within the volcanicsdomain at approximately 5 m intervals (i.e. XC11 of the 5305 level undercut). Thearrangement consisted of 14Hz Omni directional OYO geophones. The dataacquisition system consisted of three synchronised µmx/blastronics monitors. Theµmx monitors were programmed to wake up for recording at production blastingtimes (i.e. end and start of shifts). The battery powered system allowed for continualmonitoring without the need for daily downloading.

5305-XC11

A

B

C

Directionof ringretreat

N

GEOPHONE ID Easting Northing RLA 10978.87 22751.10 5317.93B 10978.98 22745.89 5318.13C 10979.00 22740.70 5317.91

R27

R29

R31

Figure 13. Schematic diagram of monitoring layout.

Analysis of the Ridgeway vibration data enabled the determination of the Holmbergand Persson site specific constants K and α (Onederra 2001). Results are summarisedin Table 8.

Table 8. Results for vibration attenuation study at Ridgeway (Onederra 2001).

Explosivetype



(R2)EMULSION 470 0.94 10 0.74


Following the approach described in section 4, the radius of crushing (rc), theequilibrium pressure (Peq) and the maximum PPV are 140mm, 1.362 GPa and88,198mm/s respectively. A measured PPV value of 551 mm/s was recorded at a

18

distance of 15.6m from the source. The source corresponded to two adjacent 102mmdiameter blastholes charged with 25m of Emulsion at 1.1 g/cm3.



PPV(mm/s)

Distance(m)

Linear(kg/m)

LN(a) LN(PPV)

551 15.58 8.99 0.156497 6.31173588198 0.14 8.99 5.303207 11.38734



A comparison between the K and α constants calculated using the current and newapproach are given in Figure 14. These curves are for a 25m EMULSION charge.

The threshold of critical peak particle velocity (PPVcrit) for this domain is also shownin Figure 14. As a way of comparison, the extent of damage given by the attenuationconstants determined with the current and new approach is 7.0m and 7.1mrespectively.


0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 1 2 3 4 5 6 7 8 9 10

Distance (m)

PP

V (

mm

/s)

K=470, alpha= 0.94 - current approach K=472, alpha= 0.99 - new approach

PR25m

102mm - EMUL at 1.1 g/cc

PPVcrit

19

5.4 Case study 4. Damage study in vertical crater retreat mining (VCR)

As discussed by LeBlanc et al. (1995) the objectives of this particular study includedthe determination of the extent of damage caused by the detonation of over-confinedcharges and the establishment of a relationship between charge diameter and extentof induced damage in different domains using different explosive types and chargegeometries. A comprehensive near field blast monitoring program was conducted toachieve the above aims.

The measurement of vibration levels from each test blast was undertaken using fourarrays of non-retrievable triaxial geophone sensors. These sensor arrays were locatedat distance between 2m and 52m from blast holes, and fixed in place using non-shrinking grout. A plan view of the test layout is shown in Figure 15.

Figure 15. Plan view of test site layout (LeBlanc et al. 1995).

Analysis of vibration data enabled the determination of the Holmberg and Persson sitespecific constants K and α (LeBlanc et al. 1995). Results are summarised in Table10.

Table 10. Results for vibration attenuation (LeBlanc et al. 1995).

Explosivetype



(R2)Water-Gel 150 0.87 16 0.86


Following the approach described in Section 4, the radius of crushing (rc), theequilibrium pressure (Peq) and the maximum PPV are 92mm, 2.489 GPa and137,122mm/s respectively. A measured PPV value of 450 mm/s was recorded at adistance of 2.04m from the source. The source corresponded to a 102mm diameterblasthole charged with 0.9m of a Watergel explosive at 1.3 g/cm3.

20



PPV(mm/s)

Distance(m)

Linear(kg/m)

LN(a) LN(PPV)

450 2.04 10.62 0.815842 6.109914137122 0.092 10.62 5.75628 11.82863



A comparison between the K and α constants calculated using the current and newapproach are given in Figure 16. These curves are for a 0.9m watergel charge.

The threshold of critical peak particle velocity (PPVcrit) for this domain is also shownin Figure 16. As a way of comparison, the extent of damage given by the attenuationconstants determined with the current and new approach is 0.8m and 1.25mrespectively.

In this particular case study there is a greater discrepancy between the two approachesused to determine the constants K and α. This discrepancy can be explained by thelevel of scatter of the measured peak particle velocities associated with theinstrumentation layout. As shown in Figure 15, PPV measurements taken frommultiple orientations were grouped and analysed. This inherently introduced theinfluence of the anisotropic characteristics of the rock mass (e.g., influence ofdiscontinuities). In anisotropic environments, the K and α constants are expected to beaffected by the orientation of discontinuities with respect to the direction ofmonitoring.

21

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 0.5 1 1.5 2 2.5 3 3.5 4

Distance (m)

PP

V (

mm

/s)

K=150, alpha=0.87 -current approach K=175, alpha=1.16 - New approach

PPVcrit

PR0.9m

102mm - WatergeL at 1.3 g/cc


6 DISCUSSION

As summarised in Table 12, there is good agreement between the current andproposed methods in four case studies. Site specific constants and incipient damagevalues determined by the two methods generally agree well. The discrepancy in thefirst case study is more pronounced because of the assumptions made regarding idealdetonation and decoupling. In fourth case study, the discrepancy may be explained bythe degree of scatter due to the measurement locations (i.e. multiple monitoringdirections). Therefore , the proposed method is dependent on the direction ofmonitoring and explosive performance predictions.

Table 12. Summary of case studies used to demonstrate the validity of the alternative approach.

Casestudy

Explosive K, α(current)

K, α(alternative)

Incipientdamage, m(current)

Incipientdamage, m

(alternative)1 Booster 4596, 0.76 6387, 1.17 0.31 0.292 ANFO 456, 1.12 563,0.87 6.5 6.83 Emulsion 470, 0.94 472,0.99 7.0 7.14 Watergel 150, 0.87 175, 1.16 0.8 1.25

The proposed approach differs from current practice in that it reduces the amount ofinstrumentation and monitoring required, significantly reducing the costs associatedwith near field vibration monitoring studies. Savings are not only associated with areduction in the instrumentation required but also with a reduction in indirect costsincurred by the operation during installation and monitoring (e.g., drilling, grouting,cabling, supervision, etc.)

22

7 CONCLUSIONS

An alternative approach to determine the Holmberg and Persson site specificconstants (K and α) for modelling near field peak particle velocity (PPV) attenuationhas been presented. The approach uses an analytical method to predict the peakparticle velocity at the point at which rock crushing ceases and combines this with aknown value of PPV measured at a pre-defined location

Four case studies were used to show the validity of this alternative approach. It isshown that the proposed approach predicts the site specific constants within areasonable error range which can be accepted in practical applications. Case studies atthe JKMRC and the Hilton operation show that there is a close agreement betweenmeasured and predicted incipient damage based on field observations.

The proposed approach strongly relies on a proper definition of explosive propertiesand the physical and mechanical properties of the intact rock, as these parameters areused as direct input to estimate the zone of crushing and the PPV at the end of thiszone. Poor or unreliable explosive and rock material information can affect thevalidity and application of the approach. It should be also noted that the proposedapproach is dependent on the direction of monitoring and therefore should beconducted in the directions of interest.

ACKNOWLEDGEMENTS

The authors would like to thank the mining group staff at the JKMRC particularly KaiRiihioja for his suggestions. The authors would also like to thank the Hilton andRidgeway operations for their support in this research.

REFERENCES

Andrieux, P., McKenzie, C., Heilig J. & Drolet, A. 1994. The impact of blasting onexcavation design - A geomechanics approach. Proc. of the 10th Symp. onExplosives and Blasting Research. ISEE, Austin, USA: 107-119.

Blair, D. & Minchinton, A. 1996. On the damage zone surrounding a single blasthole.In Mohanty (ed.), Proc. of the Fifth International Symposium on RockFragmentation by Blasting-Fragblast-5. Montreal, Quebec, Canada: 121-130.

Blair, D. & Minchinton, A. 1997. On the damage zone surrounding a single blasthole.FRAGBLAST – International Journal of Blasting and Fragmentation 1: 59-72.

Chitombo, G. 2002a. Development of the Hybrid Stress Blast Model (HSBM). AJKMRC Internal (HSBM) Report, JKMRC, Australia.

Chitombo, G. 2002b. Personal communication.

Esen, S. 2001. Modelling non-ideal detonation behaviour of commercial explosives.Internal Report, JKMRC, Australia.

23

Esen, S., Onederra, I. & Bilgin, H. 2002. Modelling the size of the crushing zonearound a blasthole. Paper submitted to the Int. J. Rock Mech. Min. Sci.Geomech. Abstr. under review.

Holmberg, R. & Persson, P.A. 1980. Design of tunnel perimeter blast hole patterns toprevent rock damage. Transactions of the Institute of Mining and Metallurgy 89:A37-A40.

Kouzniak, N. & Rossmanith, H.P. 1998. Supersonic detonation in rock mass -Analytical solutions and validation of numerical models - Part 1: Stress analysis.FRAGBLAST – International Journal of Blasting and Fragmentation 2: 449-486.

La Rosa, D. & Onederra, I. 2001. Acceleration measurements from a small diameterexplosive charge. Confidential Internal Report, JKMRC, Australia.

LeBlanc, T., Heilig, J. & Ryan, J. 1995. Predicting the envelope of damage from thedetonation of a confined charge. Proc. of the Sixth High-Tech Seminar on theState of the Art in Blasting Technology Instrumentation and ExplosivesApplications. Massachusetts, USA: 225-291.

Liu, Q. & Katsabanis, P.D. 1993. A theoretical approach to the stress waves around aborehole and their effect on rock crushing. Fourth International Symposium onRock Fragmentation by Blasting-Fragblast-4. Vienna, Austria: 9-16.

Liu, Q. & Proulx, R. 1996. The mechanisms of rock damage in blasthole open stopemining: Blast induced versus stress induced. NARMS 1996 - Rock MechanicsTools and Techniques: 599-608.

McKenzie, C., Scherpenisse, C., Arriagada, J. & Jones, J. 1995. Application ofComputer Assisted Modelling to Final Wall Blast Design. EXPLO 95 - Aconference exploring the role of rock breakage in mining and quarrying.Brisbane, Australia: 285-292.

Meyer, T. & Dunn, P.G. 1996. Fragmentation and rock mass damage assessment -Sunburst excavator and drill and blast. NARMS 1996 - Rock Mechanics Toolsand Techniques: 609-617.

Onederra I. 2001. Near field vibration monitoring of SLC ring blasting in XC11 of the5305 level undercut. JKMRC BART II internal project report, Brisbane,Australia.

Persson, P-A., Holmberg, R. & Lee, J. 1994. Rock blasting and explosivesengineering. CRC Press. p. 247.

Raina, A.K., Chakraborty, A.K., Ramulu, M. & Jethwa, J.L. 2000. Rock mass damagefrom underground blasting, a literature review, and lab- and full scale tests toestimate crack depth by ultrasonic method. FRAGBLAST – InternationalJournal of Blasting and Fragmentation 4: 103-125.

24

Scott, C. 1997. The effect of blasting on the stability of underground excavations inbedded strata. M.Sc. Thesis. University of Queensland, Australia.

Uenishi, K. & Rossmanith, H.P. 1998. Blast wave propagation in rock mass - Part II:layered media. FRAGBLAST – International Journal of Blasting andFragmentation 2: 39-77.

Villaescusa, E., Onederra, I. & Scott, C. 2002. Blast induced damage and dynamicbehaviour of hangingwalls in bench stoping. Paper under review.

Wagner, H. 2001. The rock mechanics challenge in mining. Proceedings ofEUROCK 2001, Rock mechanics - a challenge for society. Finland: XIX-XXVIII.

Wedmaier, R. 1992. An investigation of failure criteria and a blast wave propagationmodel for a description of the rock breakage problem. Ph.D. Thesis. Universityof Queensland, Australia.

Yang, R., Bawden, W. F. & Katsabanis, P. D. 1996. A new constitutive model forblast damage. Int. J. Rock Mech. Min. Sci. 33 (3): 245-254.

Documents

An Alternative Approach to Determine the Holmberg-Persson (Onederra, Esen-Fragblast)