development of an assessment system for the blast ability of rock

Development of an assessment system for the blastability of rockmasses

J.-P. Latham, Ping Lu

Geomaterials Unit, Queen Mary and West®eld College, London E1 4NS, U.K.

Accepted 13 September 1998

Abstract

Intact rock properties and the discontinuity structure of a rock mass are among the most important variables in¯uencing

blasting results. This in¯uence is considered to be a composite intrinsic property of a rock mass and is referred to as theblastability of a rock mass. It represents the ease with which a rock mass can be fragmented by blasting. This paper outlines anenergy-block-transition model, recently proposed by the authors for characterising the blast process. A preliminary validation of

this model using two sets of ®eld data from the literature is brie¯y outlined. The model is comparable or better than Bond'scomminution theory at predicting blasting results for cases where intrinsic rock properties are relatively constant. To generate apredictive capability for the model, a blastability designation BD, is designed which re¯ects the intrinsic resistance of the rock

mass to blasting. The quanti®cation of BD, based on rock engineering systems approaches and consideration of acomprehensive range of intact rock properties and discontinuity structures is illustrated. A case study is given which applies themodel and the associated assessment system to a highway cutting site. Con®dence as to the potential value of the assessment

system and the model is obtained since re®nement and improvement on pre-existing models can be seen from the newpreliminary results. # 1999. Published by Elsevier Science Ltd. All rights reserved.

1. Introduction

Blasting is the most frequently used means for quar-

rying, mining and highway rock excavation. A blasting

operation can be comprehensively described by: intact

rock and rock mass properties (the concern of this

paper), explosive properties, blasting geometry or pat-

tern and initiation sequences, etc.

The in¯uence of intact rock and rock mass proper-

ties on blasting operations has long been studied [1±

12]. This in¯uence has been mentioned and incorpor-

ated in various ways, such as Bond's work index [13],

Hino's blastability coe�cient [14], rock factor [15] and

blastability index [16]. However, little attempt has been

made to develop a quantitative parameter or system to

de®ne the ease of fragmentation of rock by blasting, in

spite of the fact that this kind of development was

suggested long ago [2] and was recently

reemphasised [10, 17].

Selecting one or more parameters for the rock prop-

erties that will re¯ect the resistance of the rock mass to

fragmentation by blasting has been a major obstacle to

the description of the ease of fragmentation. The

e�ect, until recent times, has been that blasting design

has relied on rules of thumb obtained by precedent

practice [10]. The failure to promote blast design tools

beyond rules of thumb might have resulted from the

fact that the in¯uence of in-situ rock properties, dis-

continuity structures and their interactions are often

too di�cult to be quantitatively isolated and identi®ed.

The rock engineering systems methodology developed

by Hudson [18], aims to provide both a useful check-

list for the in¯uential factors of rock engineering pro-

jects and a logical framework for the complete design

procedure. As such, it has potential for coping with

complex rock engineering problems, such as the re-

sponse to blasting.

It was noted from ®ndings reported by di�erent

researches [4±6, 16, 19] and the present authors [9, 20±

22] that in-situ rock mass properties are among the

most important contributory factors in fragmentation

and that the characterisation of the blastability has

become a pressing task for blasting operations. It was

also found that a coherent but essentially empirical

rock blastability system which incorporates the mech-

anical properties of a rock mass, the in-situ block size

International Journal of Rock Mechanics and Mining Sciences 36 (1999) 41±55

0148-9062/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved.

PII: S0148-9062(98 )00175 -2

PERGAMON

and the input energy, based on the current scienti®cunderstanding of fragmentation, has not yet beenachieved. This has hindered the achievement of moreoptimal blasting operations.

Consequently, a blastability assessment system hasbeen developed to accommodate the di�erent degree ofin¯uence on blastability of a variety of intact rock androck mass properties, helping to put blasting oper-ations on a more logical footing. The development ofthe blastability system follows from current under-standing of the fragmentation process drawn from theliterature. The paper begins with the characterisationof blastability and its physical background with respectto energy consideration. Rock engineering systemsapproaches are then used to establish a blastability sys-tem. Appropriate sources of practical data are ®nallyintroduced for an examination of the system.

2. Blastability and its characterisation

Two di�erent rock masses, when subjected to identi-cal blast geometry and energy input from explosives,will produce quite di�erent degrees of fragmentation.This is because the rock masses have inherently di�er-ent resistance to fragmentation by blasting. That is,the two rock masses have a di�erent ease with whichthey can be fragmented by blasting. This property ishereafter referred to as the ``blastability'' of a rockmass. It appears to be a kind of intrinsic property, likethe hardness of a rock and apart from the possibilityof blast induced fragmentation from previous rounds,it is uncontrollable. As can be seen in Section 3, manyfactors a�ect the blastability of rock masses and it istherefore helpful to consider the blastability of therock mass to be a composite intrinsic property of therock mass.

2.1. The energy-block-transition model

The fragment size is a fundamental characteristic,and is mainly governed by the geomechanical natureof the host rock mass. Blasting is looked upon as atransformation from the state with an in-situ block sizedistribution (IBSD) to the state with a blasted blocksize distribution (BBSD) (e.g. from IBSD-C into eitherBBSD-1 or BBSD-2 in Fig. 1). This transforming pro-cess is implemented by inputting a certain energy, i.e.by detonating a quantity of explosive. The transform-ation result can be indicated by the block size distri-bution after blasting. In Fig. 1, two di�erent rockmasses are considered which have the same IBSD,labelled IBSD-C. BBSD-1 and BBSD-2 are the BBSDsof the ®rst and the second rock masses obtained byinputting an identical amount of explosive energy. Thetransformation areas for the two di�erent rock masses

subject to identical blast design are represented by DA1

and DA2. The second rock mass proves to be intrinsi-

cally more di�cult to fragment by blasting than the

®rst one, since the second blastpile contains more large

blocks than the ®rst although their IBSDs are identi-

cal. The area DA bounded by the IBSD and BBSD

curves and the 0 and 100% passing line, for a particu-

lar blasting operation, is considered to have the follow-

ing special signi®cance: the di�erence between DA1 and

DA2 indicates the di�erence in blastability between the

two rock masses. Let Es represent the explosive energy

input per unit rock mass that is consumed in trans-

forming the rock mass with a given IBSD into a blast-

pile with a given BBSD, in order that a working

hypothesis, EsADA, can be introduced at this

point [22, 23].

For each transformation with a certain value of DA,an e�ective size parameter Xo is introduced to re¯ect

an inverse size e�ect associated with an increase in

energy consumption, where Xo is the value of the

abscissa of the centre of gravity of the geometric shape

of DA. Such an inverse size e�ect for the dependence

of energy on an objective size can be illustrated as fol-

lows. A given value of DA can be associated with any

transformation. For example, the transformation may

be for relatively large in-situ blocks to slightly smaller

blocks in a blastpile, and this transformation would be

associated with a relatively larger Xo. Alternatively, a

transformation with the same DA could be for rela-

tively small in-situ blocks being reduced to a blastpile

resembling powdery ®nes, i.e. with a relatively smaller

Xo. But, because the latter case requires the generation

of much more fracturing and surface area, it is logical

that it would consume more energy despite the fact

that the two transformations have the same DA. Theempirical energy±size relation of other researchers

refers to an objective size parameter [24±26] that has a

similar signi®cance to this e�ective size parameter and

Fig. 1. The concept of blastability: two di�erent rock masses with

the same IBSD but with di�erent blastability are transformed to two

di�erent BBSD curves (see text for explanation).

J.-P. Latham, P. Lu / International Journal of Rock Mechanics and Mining Sciences 36 (1999) 41±5542

indicates that in general, the energy consumed in size

reduction is inversely proportional to the objective size

raised to some power. Based on the above working hy-

pothesis and the de®nition of Xo, the following re-

lationship is proposed by Lu [22, 23],

EsADA

X 1=2o

: �1�

Detailed derivations of DA and Xo are given

elsewhere [22, 23]. They yield the following results:

DA � Sai ÿ Sab �2a�

Xo0Sai � Sab

2, �2b�

where, Sai and Sab are the mean sizes of IBSD and

BBSD, respectively. They are given by the following

mathematical de®nition for the mean of a size distri-

bution:

Sa ��Su

Sl

Sf �S �dS, �3�

where, f(S) represents the distribution function of

block size, i.e. the probability density function; Sl rep-

resents the lower boundary of block size, which may

often be zero and Su is the upper boundary of block

size.

Consequently, the new relationship has been

proposed [22, 23] as follows:

Es � Sai ÿ Sab

Bi��Sai � Sab�=2�0:5�4a�

or

Bi � Sai ÿ Sab

Es��Sai � Sab�=2�0:5, �4b�

where Bi is a coe�cient, relating the speci®c energy

required to implement the transformation process.

Eqs. (4a)±(b) relate the energy input, the character-

istic sizes before and after blasting and the size distri-

butions of the in-situ and blasted blocks. It appears

that the value of Bi is an indicator of the ease with

which the process of transforming the rock mass withIBSD into the blastpile with BBSD is implemented.

The coe�cient Bi is herewith referred to as the energy-

block-transition (E-B-T) coe�cient and Eqs. (4a)±(b)

are referred to as the energy-block-transition (E-B-T)

model.

The E-B-T coe�cient Bi is a measure of the intensity

of the transformation of mean block size compared to

the objective size Xo associated with the transform-

ation process for a given input of energy. In the trans-

formation process, the in-situ rock mass with large

block sizes, characterised by the mean block size Sai, istransformed into blasted blocks with small block sizescharacterised by the mean block size Sab. The largerthe value of Bi of a rock mass, the easier it can befragmented by a given energy input for blasting.Eqs. (4a)±(b) indicate that a rock mass with a larger Bi

will be easier to break down to small blocks than arock with a lower Bi. That is, the larger the Bi, thegreater the blastability.

2.2. Preliminary examination of the energy-block-transition model

To see whether the E-B-T model proposed is animprovement on existing models requires an analysisof results from practical blasting operations. A set ofmodel scale blasts, or preferably, a series of ®eld blastswith constant and given in-situ conditions, but withdi�erences in both blasting patterns and energy input,would be ideal for examination of the applicability ofthe model.

So far, there have been three theories concerning theenergy associated with size reduction. These areRittinger's ®rst comminution theory, Kick's secondcomminution theory and Bond's third comminutiontheory. Bond's theory is a compromise betweenRittinger's and Kick's theories and is generally recog-nised to be the best model to describe blastingoperations [6]. Bond's third theory has the followingform:

Es � 10Ec

�1��Sb80

p ÿ 1��Si80

p�, �5�

where, Es is the required energy for fragmentation inkWh per ton of processing rock material; Ec is Bond'swork index; Sb80 and Si80 are the blastpile and in-situblock size. Subscripts 80 means that the block size isequivalent to the sieve opening (in microns) throughwhich 80% of the rock materials pass.

If the relationship between energy input and theblock size before and after blasting is better describedby Eq. (4a) than by Bond's third theory, the Bi in theE-B-T model should exhibit less variability than the Ec

in Bond's theory. Thus, a preliminary validation hasbeen carried out by comparing the extent to which theE-B-T coe�cient Bi and Bond's work index, Ec divergefrom a constant.

Two main sources of practical data which includeinformation about IBSD, BBSD and the energy input,were found in the literature and were used for the pre-liminary validation. This was implemented by lookingat the values of Dmax/M and sample coe�cient ofvariation s/M, where Dmax represents the maximumdi�erence between the values of Bi or Ec, s and M arethe standard deviation and the mean of Bi or Ec. The

J.-P. Latham, P. Lu / International Journal of Rock Mechanics and Mining Sciences 36 (1999) 41±55 43

examination results are brie¯y described below and thedetails can be referred to elsewhere [22, 23].

The ®rst case study cited is the work reported byWang [27], in which ®ve rounds of full scale blast trialswere carried out at the Sandside limestone quarrylocated in Cumbria, England. The information aboutIBSD, BBSD, explosive energy input and blasting pat-terns were either given or can be derived. Four out of®ve blast rounds provide a data set of full-scale blast-ing parameters with approximately the same geologicalin-situ conditions, but with di�erences in both blastingpatterns and energy input. The second case cited is thework reported by Aler et al. [28, 29], in which the as-sociated data input from production blasts carried outin two mines were provided. Two groups of data, onefrom Bench 4 in ENUSA mine and another fromBench 3 in Reocin Open Pit are used for checking thevalidity of the E-B-T model.

The E-B-T coe�cients Bi and the Bond work indicesEc were calculated and the relative dispersions wereanalysed and summarised as shown in Table 1. It isseen from Table 1 that both the coe�cient of variationand the value of Dmax/M for Bi are signi®cantly lowerthan for Ec. This indicates that Bond's work index, Ec

deviates more from a constant than the E-B-T coe�-cient Bi and suggests that the E-B-T model gives a clo-ser ®t to the blast data than the alternative Bond'smodel.

Thus, although further examinations of the applica-bility of the E-B-T model to practical blasting oper-ations are desirable, the attempted validation of themodel using the above two cases provides su�cientencouragement to examine further the E-B-T modeland ways of quantifying Bi for di�erent rock masses.

3. Factors in¯uencing blastability of rock masses

As shown above, the E-B-T coe�cient Bi, is a quan-titative measure of the blastability of a rock mass. Toapply the E-B-T model to a practical blasting oper-ation requires prior knowledge of the Bi coe�cient for

the rock mass of interest. It will be most advantageousfor the coe�cient Bi to be determined before blastingin order to help with the blast design of an excavationoperation. Without any realistic chance in the shortterm of a practical analytical solution to de®ne thevalue of Bi for a given rock mass as a function of ma-terial properties, the development of a comprehensiveassessment system for quantifying the blastability ofrock masses would appear to have great potential. Theobjective would then be to have a method for deter-mining the value of Bi from results derived from theassessment system.

In reviewing the blasting practices and literaturepublished [2, 5, 6, 9, 10, 14±17, 30±36] it is obvious thatmany factors can a�ect the blastability of rock masses.These cited factors consist of a wide, possibly compre-hensive range of intact rock properties and discontinu-ity structures, each of which in¯uences the blastingresult to a varying degree. The blastability of the rockmass is therefore considered to be a composite intrinsicproperty of the rock mass.

The factors in¯uencing blasting results fall into twogroups. The ®rst group is the intact rock properties,which includes strength, hardness, elasticity, deform-ability, density of rock, etc. They are dependent uponrock texture, internal bonds, composition and distri-bution of minerals forming the rock. The secondgroup is the discontinuity structure that consists oforientation, spacing and extent of discontinuities, andthe in-situ block sizes, created by a range of long-termgeological processes.

The problem of obtaining a satisfactory measure ofblastability from an assessment of numerous poten-tially in¯uential factors has at least three featureswhich have often been neglected in early attempts toinvestigate blastability. One is the interactions betweenfactors. Another is the degree of in¯uence (or theweighing) to be attributed to each factor or coupledfactors. A third is the need to treat subjective data, asituation often encountered in geotechnical engineeringwith systems of soils, rocks, ¯uids and discontinuities.Because of the complexity of the geotechnical system,

Table 1

Comparison between the relative dispersion of the E-B-T coe�cient, Bi and that of Bond's work index, Ec for the blast results for two case stu-

dies from the literature

Case E-B-T coe�cient Bi (m0.5/kWh/t) Bond's work index Ec (kWh/t) Blast rounds

Dmax/M (%) s/M (%) Dmax/M (%) s/M (%)

Sandside quarry* 40.38 (4.56) 16.88 (2.14) 42.73 (30.08) 16.72 (16.23) 4 (3)

ENUSA Mine 86.57 32.72 106.18 47.06 5

Reocin Mine 31.72 12.40 58.90 23.85 4

Dmax = XmaxÿXmin; and s=��P

nj ��Xj ÿ Xa�2�=N

q. *For the Sandside quarry case, ®gures in brackets are the outcome excluding the ®rst of

the four blast rounds. This data trimming may be justi®ed on grounds that there existed a signi®cant di�erence in the stemming length, decking

and distribution of explosives between the ®rst and the other three blast rounds.


it is often necessary to take advantage of all availabledata, whether it is objective observation, practical ex-perience or subjective data based on combinations ofobservation, practical experience and engineering jud-gement. The degree of in¯uence of individual factorsupon each other and upon the blastability is oftenexpressed in terms of ``strong'', ``fair'' and ``weak'',and it is important to be able to integrate such valu-able knowledge.

While uniaxial compressive strength might be an im-portant indicator of the blastability of a rock, severalothers such as sonic velocity or joint spacing might beof equal or greater importance, especially whencoupled in a certain way. It is perhaps now moreapparent, considering the three factors mentionedabove, why blastability assessment presents such achallenge.

The development of rock blasting has a relativelyshort but signi®cant history [8] and the advent of rockmass classi®cation systems [37, 38] has made signi®cantimpacts on the assessment of rock mass quality.However, a generic methodology for the appraisal ofthe blastability of a rock mass encountering a standardblasting operation remains lacking. One of the reasonshas been both the diversity of factors in¯uencing theblastability of rock and the complexity of the associ-ated representation of all the in¯uences of the variousfactors and the interactive mechanisms between them.Another has been the temptation to include controlla-ble factors relating to blast design within the scope ofthe term blastability [10, 17] and this has led to a moreconfused approach than one which retains the term forintrinsic rock mass properties.

Several questions then remain. Of the many di�erentparameters thought to be important, how can dupli-cation of similar parameters and the over-in¯uence ofminor parameters be avoided? How would all import-ant factors which cannot be easily expressed withobjective measurements be taken into account? Howcan the interactions between the individual contribu-tory factors be described and presented? It is quite dif-®cult to answer these without recourse to novelmethodologies. The new methodologies need to pro-vide a basic analytical tool and a presentational tech-nique for characterising all relevant factors andinteraction mechanisms and then to tailor the quanti-tative use of parameters to tackle the complexity ofblastability assessment. Rock engineering systemsmethodology [18] was introduced in response to theneed for an ``all-encompassing'' procedural techniqueto approach increasingly complex rock engineeringproblems, and this appears to be one promising avenuefor the development of a blastability assessment sys-tem. It is di�cult to imagine the practical data acqui-sition of su�ciently complete data set from whichconventional, e.g. multivariate statistical approaches

could provide a better alternative assessment of blast-ability.

4. Development of an assessment system of blastability

4.1. Rock engineering systems and interaction matrix

4.1.1. Rock engineering systemsThe rock engineering system (RES) aims to provide

a useful checklist for a rock engineering project. Moreimportantly, it also aims to provide a framework fromwhich the complete design procedure can be evaluated,leading a rock engineering project to an optimal result.An RES description of the overall interactive mechan-isms in rock blasting operations appears to be a prom-ising basis for an approach to blastability assessmentproblems.

The RES approach contains a very useful procedurefor devising a rock mass classi®cation scheme for anyrock engineering project. In a rock mass classi®cationscheme, a single parameter is required to comprehen-sively characterise the quality of any rock mass for agiven engineering project that is to take place withinthe rock mass. According to the RES approach, allpossible rock mass classi®cation schemes can be rep-resented by a function of the leading diagonal par-ameter values of an interaction matrix. The selectionof the parameters and the de®nition of the weightingof each parameter in a classi®cation system can bemade through the coding of the interaction matrix fol-lowing a rational procedure. This coding is crucial tothe applicability of the equation in the classi®cationscheme. The RES approach has been applied to anumber of rock engineering ®elds, for example, theassessment of stability of underground excavations [39],hazard and risk assessment of rockfall [40] and rockmass characterisation for indicating natural slopeinstability [41]. The approach forms one key stage inestablishing the blastability system.

4.1.2. The interaction matrix and its codingIn the RES approach to rock engineering, the inter-

action matrix device [18] is both the basic analyticaltool and a presentational technique for characterisingthe important parameters and the interaction mechan-isms in a rock engineering system. In the interactionmatrix for a rock engineering system (e.g. a blastabilitysystem), all factors (or parameters) in¯uencing the sys-tem are arranged along the leading diagonal of thematrix, called the diagonal terms. The in¯uence ofeach individual factor (or parameter) on any other fac-tor (or parameter) is accounted for at the correspond-ing o�-diagonal position, and these are named the o�-diagonal terms. The o�-diagonal terms, are assignedvalues which describe the degree of the in¯uence of


one factor (or parameter) on the other factor (or par-ameter). Assigning these values is called coding thematrix. A problem containing only two factors is thesimplest example of the interaction matrix, as shownin Fig. 2(a).

A general illustration of the coding of interactionmatrix is shown in Fig. 2(b). The row passing throughPi represents the in¯uence of Pi on all the other factorsin the system, while the column through Pi representsthe in¯uence of the other factors, or the rest of the sys-tem, on the Pi. Several procedures have been proposedfor numerically coding this matrix, for example, the 0±1 binary and the expert semiquantitative (ESQ)method [18] and the continuous quantitative coding(CQC) method [42]. After coding the matrix by insert-ing the appropriate values for each cell of the matrix,the sum of each row and of each column can be calcu-lated. The sum of a row is termed the ``cause'' value

and the sum of a column is the ``e�ect'' value, desig-nated as coordinates (C, E) for a particular factor. Crepresents the way in which Pi a�ects the rest of thesystem and E represents the e�ect that the rest of thesystem has on Pi. The coordinate values for each fac-tor can be plotted in cause and e�ect space, forming aso-called C±E Plot [18]. After obtaining the C±E plotfor a system, an equation de®ning a classi®cationindex that takes into account key contribution factorscan be developed. These stages are shown in Figs. 3and 4.

In principal, there is no limit to the number of fac-tors (or parameters) that may be included in an inter-action matrix, although the number of factors (orparameters) needed to solve a practical engineeringproblem are ®nite. A problem which includes n factors(or parameters) will have an interaction matrix with nrows and n columns, as shown in Fig. 2(b).

Fig. 2. Illustration of the interaction matrix in RES (from Hudson [18]) (a) Interaction matrix of two factors, (b) general illustration of the cod-

ing of interaction matrix and the set-up of the cause and e�ect coordinates.

Fig. 3. Developing a rock engineering classi®cation system by means of the interaction matrix (from Hudson [18]). (a) forming the ordered histo-

gram, (b) formulating the rock classi®cation index.


4.2. Formulating the blastability assessment

We now return to the development of a blastabilitysystem. Firstly, we select the factors in¯uencing theblastability. Identi®cation of relevant factors can beobtained from an extensive review of literature onblasting (e.g. see references listed in Section 4.1.2) com-bined with the authors' experience and judgement. Thefollowing 12 factors (see the ``factors a�ecting blast-ability'' column in Table 2) were chosen as the basicones to be considered in establishing a blastabilityclassi®cation system for a general site, i.e. these 12 fac-tors were chosen as the diagonal terms in the inter-action matrix used to establish the blastability system.The matrix might be coded by means of subjective jud-gement and experience or objective measurements, orboth. However, relating to each of these 12 factors,one (or two) measurable parameter(s) that can, tosome extent, depict the factor's in¯uence at a givensite, has been used as the diagonal term to representthis factor in the interaction matrix (see the ``depicting

parameter'' column in Table 2). The factors and theirdepicting parameters are listed below:

P1 Strength, represented by uniaxial compressionstrength (UCS) of intact rock or point-loadstrength index (PLI);

P2 Resistance to fracturing, represented by the uni-axial tensile strength (UTS);

P3 Sturdiness, represented by density of rock (r);P4 Elasticity, represented by static or dynamic mod-

ulus of rock (E);P5 Resistance of rock to dynamic loading, rep-

resented by P-wave velocity (Vp);P6 Hardness of rock, represented by Schmidt ham-

mer rebound value (SHV);P7 Deformability, represented by Poisson's ratio (m);P8 Resistance of rock to breaking, represented by

fracture toughness of rock (KIc);P9 In-situ block size of rock mass, represented by

mean in-situ block size (MIBS) or principal meanspacing (PMS);

Fig. 4. Illustration of the interaction matrix coding results. (a) Coding values, (b) the C±E plot and (c) the ordered histogram (see Section 4.2).


P10 Fragility of rock mass, represented by fractaldimension of in-situ block sizes (D);

P11 Integrity of rock mass, represented by the wavevelocity ratio, Rv (the ratio of P-wave velocity inthe ®eld to that for the laboratory-size specimen),or by RQD;

P12 Discontinuity plane's strength, represented bycohesion, C, or friction angle, f of dominant setof discontinuities.

Naturally, one can include more, such as the discon-tinuity orientation related to the face to be blasted.Bhandari [48] refers to his model experiments in whichfragmentation processes are shown in photographs tobe di�erent when dominant joint sets take the di�erentorthogonal planes with respect to the blast face. Royand Dhar [49] go further and conclude that best frag-mentation occurs when the dominant joint face strikesat between 258 and 658 to the blast face.Quanti®cation and weighting of such an orientatione�ect will require further research as the situation iscomplex and is in¯uenced by the free face and thus thedetonation sequence. Cunningham's algorithm [4, 5]for the rock factor A provides some general guidanceon likely degrees of in¯uence.

Water content in the rock mass, joint aperture andvarious other parameters could also be signi®cant vari-ables to take into account. Having chosen the various

factors to be included, it may not be possible to ®ndmeasurable parameters that fully quantify each factor.However, to simplify the system to manageable andrelatively easily obtained ®eld parameters, the set ofdepicting parameters above were chosen.

Using either the ESQ or the CQC coding method,the coding values, the C±E plot and the ordered histo-gram, all of which re¯ect the interaction intensity foreach of the factors, can be obtained (see Fig. 4, whichis the result of a case study that is described in thenext section). It is important to bear in mind that thecoding values would probably vary according to di�er-ent opinions from di�erent researchers and ideally sev-eral experts' opinions should be involved in the factorselection and coding process. The next stage after cod-ing is to calibrate the parameters with greatest inter-action intensity and contribution to the blastability ofa rock mass based on the geological and geotechnicalinformation.

Making use of the ®ndings of blasting theory andpractice, a quantitative list of classes of blastabilityconnected to individual factors and their depicting par-ameters is suggested in Table 2. This table is the basisfor both rating the in¯uence of each parameter on theblastability and obtaining the rating value used inEq. (6) below. With reference to Table 2, continuousrating charts corresponding to each single factor havebeen created to help for borderline cases and also toremove an impression that abrupt changes in ratings

Table 2

Suggested quantitative indications for the classi®cation of the blastability of a rock mass associated with individual factor [22]

Description of ease of blasting Blastability class

Pi Factors a�ecting blastability Depicting parameter

Very easy

1

Easy

2

Moderate

3

Di�cult

4

Very di�cult

5

P1 Strength uniaxial compressive strength

(UCS) (MPa)

<25 25±60 60±100 100±180 >180

point-load strength index (MPa) <1 1±2.5 2.5±4 4±9 >9

P2 Resistance to fracturing uniaxial tensile strength

(UTS) (MPa)

<1.5 1.5±3 3±6 6±12 >12

P3 Sturdiness of rock density, r (t/m3) <2.0 2.0±2.4 2.4±2.75 2.75±3.0 >3.0

P4 Elasticity of rock E(GPa) <25 25±50 50±100 100±150 >150

P5 Resistance to dynamic

loading

P-wave velocity (km/s) <1.5 1.5±2.5 2.5±3.0 3.0±4.0 4.0

P6 Hardness of rock Schmidt hardness value <15 15±30 30±40 40±50 >50

P7 Deformability Poisson's ratio >0.35 0.3±0.35 0.25±0.30 0.25±0.20 <0.20

P8 Resistance to breaking fracture toughness of rock (MPa.m1/2) <0.5 0.5±1.5 1.5±2.5 2.5±3.5 >3.5

P9 In-situ block sizes mean IBSD (m) <0.25 0.25±0.75 0.75±1.5 1.5±2.5 >2.50

mean spacing (m) <0.1 0.1±0.5 0.5±1.5 1.5±2.5 2.5.3

P10 Fragility of rock mass fractal dimension of

in-situ rock mass, D

<1.50 1.50±2.00 2.00±2.50 2.50±2.75 >2.75

P11 Integrity of rock mass ratio of P-wave in ®eld to that in lab,

Rv

<0.35 0.35±0.55 0.55±0.75 0.75±0.9 >0.90

RQD (%) <40 40±60 60±75 75±90 >90

P12 Discontinuity plane's

strength

cohesion C (MPa) <0.05 0.05±0.15 0.15±0.25 0.25±0.50 >0.50

friction angle j (8) <7.5 7.5±15 15±20 20±30 >30


occur between classes. As an example, the continuousrating chart for mean in-situ block size is illustrated inFig. 5.

It is possible to include as many factors as mightconceivably a�ect the blastability. However, only fac-tors which make major contributions to the blastabilitysystem will be of interest for practical application, asthis can probably give a relatively good approximationwhile reducing the burden of data collection. Based onthe associated C±E plot (see Fig. 9.6(b) of [18] for thesigni®cance of the C±E plot in selecting the ®nal con-tributory factors) and the ordered histogram obtained,those factors which contribute to most of the system,say larger than 70% of the a(C + E) total in theordered histogram, can be selected as the factors to beused in assessing the blastability of the rock mass.

The assessment of blastability of the rock mass canthen be made according to the following formula [22]

BD �Xnj�1

WjRj, �6�

where BD is a designation which collectively quanti®esthe resistance to fragmentation by blasting of a rockmass and is hereafter called the blastability desig-nation. Rj is the rating value of the jth factor obtainedfrom either Table 2 or preferably the correspondingcontinuous rating charts, according to values indirectlyderived or measured from site. Wj is the weightingcoe�cient determined from the jth factor according toits contribution to the system, which can be calibratedfrom the ordered histogram. It is obvious that thevalue of BD is in the range 0 to 1, and that the greaterthe BD, the more di�cult the rock is to blast.

4.3. Relationship between BD and Bi

As discussed above, BD is designed to give a com-prehensive measure of the blastability of a rock mass.The value of BD is in the range of 0 and 1, and thegreater is BD, the more di�cult the rock is to blast.

This contrasts with Bi which is lower for a rock that ismore di�cult to blast. However, both BD and Bi havethe same physical signi®cance. To progress with theapplication of the E-B-T model a relationship betweenthem is required. Unfortunately, a database of blastingoperations with parameters from Table 2 is not avail-able at present. An examination of the possible rangeof the values of both Bi and BD does provide a hint ofthe preliminary relationship.

The values of speci®c charge are usually in the range0.15±0.7 kg/m3, the ratio of Sai/Sab is usually in therange 2±10 and the range of BD is usually 0.2±0.9,thus the range of Bi is estimated to be from 5 to 60(m1/2/kWh/t). Combining these ranges with the experi-ence and results from case studies (referred to inSection 5), an empirical equation relating BD and Bi istentatively suggested [22] as follows (Fig. 6).

Bi � 10

BD: �7�

Recalling the implications of BD and Bi, a prelimi-nary classi®cation for blastability of rock massesaccording to the E-B-T coe�cient Bi or BD has there-fore been suggested, as shown in Table 3 [22].

The Kuz±Ram equation [4] has been widely used topredict block sizes of blastpiles for a given blast de-sign. One of the main challenges to improve themethod is to de®ne the rock factor, A which is oftenroughly selected by rules of thumb or by improve-ments which use empirical formulae. Based on Lilly'swork [16], Cunningham [5] proposed an algorithm forcalculating the values of A. This algorithm took fourfactors into consideration and improved the appli-cation of the Kuz±Ram equation. As demonstratedabove, BD is developed using a systems approach andit is based on a more comprehensive range of bothintact rock properties and discontinuity structures thanA in Cunningham's algorithm. The use of BD in deter-mining a value for A would appear to be an improve-ment upon Cunningham's algorithm for use with theKuz±Ram equation. A tentative empirical equation

Fig. 5. The suggested continuous rating chart for mean in-situ block

size of rock mass.

Fig. 6. Suggested empirical relationship of BD and Bi.


relating BD and A is therefore suggested as follows

A � 13� BD: �8�

The examination of Eq. (8) will be described inSection 5.

5. Blastability: a case study

The blastability assessment system developed abovehas been applied to a case study that assesses the blast-ability of the rock mass at a highway improvementcutting site in North Wales (hereafter referred to asthe G cutting site). This application served as one ofthe ®rst trials of the blastability system and it wasfound to be useful, while investigating the reasons forblasting problems encountered at the site.

5.1. Background of the case study

The main concern in the case study was to identifythe reasons for the high percentage of blasts whichproduced unsatisfactory fragmentation (i.e. excessoversize).

For the highway improvement, a new route nearly600 m long was to be created in a deep cutting to beexcavated by blasting. The road cutting was dividedinto berms, the depth of a berm was generally 4±6 m.At the time of the authors' site investigation, the cut-ting had been excavated down to the second berm andthere were one or two deeper berms to be cut. Therock types at the site were seen to include siltstones,sandstones, tu�tes, tu�s and limestones.

5.2. Site investigation and data collection

The available data from the previous geological in-vestigations, possibly restricted by the limited ex-posures, were inadequate to provide a satisfactoryexplanation for why a high percentage of blastingfailed to obtain satisfactory fragmentation. In order toprovide an up-to-date assessment of blastability ofrock materials at the site, the authors undertookfurther geological data acquisition. The investigationcarried out involved mapping discontinuities on var-ious rock cuttings, taking photos of blasting results im-mediately after blasting, performing on-site point loadtests and Schmidt Hammer tests and collecting otherassociated geological and blast design data. A sketchplan for the investigation, together with the positions

Table 3

Blastability classi®cation according to the E-B-T coe�cient Bi and BD

Description of ease of blasting Very easy Easy Moderate Di�cult Very di�cult

Blastability class 1 2 3 4 5

Bi (m0.5/kWh/t) >40 20±40 13±20 8±13 <8

BD <0.25 0.25±0.50 0.50±0.70 0.70±0.85 >0.85

Fig. 7. A sketch plan for the geological investigation at the G cutting site showing locations of scanline mapping and intact rock samples.


of the scanline mapping, the point load tests and theSchmidt Hammer tests is illustrated in Fig. 7.

5.3. Blastability assessment

With help from the resident engineers and consult-ants involved in the cutting, the interaction matrix ofthe blastability system was coded using the CQCapproach [42], and the coding results were obtained asillustrated in Fig. 4.

It is seen from Fig. 4 that the range in parameter in-teraction intensity is quite wide (refer to Fig. 9.6(b)in [18]). Thus, only those factors contributing to atotal of 72.5% of the a(C + E) in the ordered histo-gram, that is, the eight parameters, P1, P2, P3, P4, P5,P6, P9, P10 have been chosen as the main contributoryfactors of the blastability of the rock masses at thesite. The corresponding weights of the eight factorswere derived using the method illustrated in Fig. 4,and they are listed in Table 4 (column Wi). Havingcompleted the ®rst stage, which is concerned with thematrix coding and thus the parameter weighting, thesecond stage is to obtain the actual results for eachparameter (column value in Table 4) using ®eld

samples, tests and experience. Due to a lack of com-plete sets of test results, a number of empirical for-mulae based on published correlation studies [43±46]have been used to derive missing parameters. Theresults obtained from the site investigation showed thevarying degrees of both mechanical properties and dis-continuity structures from one place to another. Thisis re¯ected by the blastability assessment results, asshown in Table 4.

The data taken from the authors' site investigationand sampling based on six ®eld locations along thecutting, when subjected to the blastability analysis,yielded values of the blastability designation from0.631 to 0.725 (i.e. Bi from 15.85 to 13.75 m1/2/kWh/t),as shown in Table 4. This indicated that the rockmasses in the highway cutting area belong basically tothe border range between class 4 (di�cult blasting)and class 3 (moderate blasting), see Table 3. Applyingthe description terms to the BD results, this meansthat the rock masses are, in general, di�cult or moder-ate to blast.

The blastability of the rock mass at this site wasalso assessed at three out of the six locations utilisingonly the previous geological information that was

Table 4

Blastability assessment of rock masses at the G cutting site

Parameter Weight, Wi Blastability assessment

description unit S1 S2 S3

No. Pi value rating Wi*Ri value rating Wi*Ri value rating Wi*Ri

1 Is(50) MPa 0.1475 4.42 0.65 0.096 6.51 0.8 0.118

UCS MPa 120 0.680 0.100

2 UTS MPa 0.1344 6.82 0.670 0.090 5.53 0.580 0.078 8.14 0.700 0.094

4 E GPa 0.1273 48.80 0.395 0.050 45.13 0.380 0.048 52.39 0.410 0.052

3 r t/m3 0.1249 2.710 0.675 0.084 2.704 0.680 0.085 2.715 0.720 0.09

6 SHV 0.1225 43.6 0.710 0.087 41.2 0.660 0.081 46 0.750 0.092

5 Vp m/s 0.1208 4901 0.920 0.111 4784 0.900 0.109 4996 0.930 0.112

10 D 0.1131 1.486 0.440 0.05 1.397 0.420 0.048 1.848 0.590 0.067

9 MIBS m 0.1095 2.18 0.830 0.091 3.10 0.935 0.102 2.80 0.915 0.100

Blastability designation 0.664 0.647 0.725

No. Pi Parameter Weight, Wi Blastability assessment

S4 S5 S6

description unit value rating Wi*Ri value rating Wi*Ri value rating Wi*Ri

1 Is(50) MPa 0.1475 4.45 0.65 0.096 5.05 0.69 0.102

UCS MPa 135 0.730 0.108

2 UTS MPa 0.1344 5.563 0.590 0.079 7.67 0.710 0.095 6.31 0.680 0.091

4 E GPa 0.1273 50.07 0.400 0.051 48.47 0.400 0.050 42.9 0.330 0.042

3 r t/m3 0.1249 2.70 0.675 0.084 2.63 0.610 0.076 2.70 0.680 0.084

6 SHV 0.1225 44.85 0.725 0.089 46.07 0.740 0.091 39.7 0.550 0.067

5 Vp m/s 0.1208 4785 0.900 0.109 4908 0.920 0.111 4852 0.910 0.110

10 D 0.1131 2.113 0.690 0.078 1.499 0.450 0.051 1.194 0.370 0.042

9 MIBS m 0.1095 1.31 0.690 0.076 1.78 0.790 0.087 2.22 0.830 0.091

Blastability Designation 0.662 0.669 0.631


available. The values of BD obtained were from 0.498to 0.569, indicating that the values of BD belong toclass 2 or the border range between class 2 and class 3(see Table 3). This suggests that the new ®eld test datahas revealed that the rock mass is generally more di�-cult to blast than might have been expected from theinitial site investigation.

5.4. Estimation of BBSD based on blastabilityassessment

It is interesting to consider that the blastabilityassessment results obtained above are re¯ected in theactual blasting results which indicated by the BBSDsof the blastpiles obtained. To examine the BBSD atthe site, the following approaches will now be com-pared: (i) direct assessment of the BBSD by the photo-scanline method devised by the authors [47], (ii) esti-mation using the previously published Kuz±Ram blastdesign model [4] with no IBSD information needed,(iii) estimation using the previously published Bond±

Ram model which can take advantage of the newIBSD estimation procedure [6, 20], (iv) estimationusing the new E-B-T model and blastability assessmentand (v) an estimation of the BBSD primarily based onthe Kuz±Ram model but with a correction such thatthe rock factor in the Kuz±Ram model, A, is deter-mined by Eq. (8) (such a model is called the correctedKuz±Ram model).

A comparison of the BBSD results of two blasts,one carried out on July 31 and another on August 3,1995, which considers the di�erent estimation tech-niques mentioned above, is illustrated in Fig. 8. Theblast pattern data, the borehole parameters and theexplosive details are summarised in Table 5. FromFig. 8, the following important observations can bemade.

The BBSD directly assessed using the photo-scanlinemethod appears to lie near the average of the predic-tions from the other four techniques. The BBSD pre-dictions from the Kuz±Ram and Bond±Ram modelsform the far upper and far lower boundaries while

Fig. 8. Comparison of BBSDs from the E-B-T model with alternative prediction methods. (a) 31/07/95 blast, (b) 03/08/95 blast.

Table 5

Parameters associated with the predictions of BBSD

Blasting pattern parameters Rock mass parameters

Date of blast Date of blast

31/07/95 03/08/95 Blasting site 31/07/95 03/08/95

Q (kg) 1430 605 Is(50) (MPa) 5.05 4.45

q (kg/m3) 0.65 0.62 UCS (MPa) 111.10 97.90

Bench height (m) 7 7 UTS (MPa) 6.31 5.56

Hole depth (m) 8 8 E (GPa) 46.10 50.10

Subdrill (m) 1 1 SHV 39.70 44.85

Hole No.s 55 22 mean IBSD (m) 2.20 1.30

Hole diameter (mm) 105 105 r (t/m3) 2.70 2.70

Explosive PG800/900 PG800/900 Vi50 (m3) 6.57 1.33

Burden (m) 2.5 2.5 Vi63.2 (m3) 13.78 2.61

Spacing (m) 2.5 2.5 nv 0.938 0.554

Bottom charge (m) 1 1 Si50 (m) 2.21 1.30

Column charge (m) 3 3 Si63.2 (m) 2.83 1.63

Stemming (m) 3 3 ns 2.813 1.663


that from either the newly developed E-B-T model orthe corrected Kuz±Ram model based on the blastabil-ity assessment is approximately in the middle of therange formed by BBSDs from the Kuz±Ram and theBond±Ram models. Also, the BBSD from the E-B-Tmodel and the corrected Kuz±Ram model are close tothe BBSD assessed using the photo-scanline techniquefor the 03/08/95 blast.

5.5. Discussion of case history

It seems reasonable to assume that early blasting op-erations at the site would have begun by takingaccount of little more than geological data from the in-itial site investigation. But, it has been shown that theblastability designation based on rock mass datarevealed during excavation is greater than that likelyto be estimated from the previously available data set.Furthermore, the variability of blastability might nothave been previously recognised. Not taking accountof the variability in blastability probably contributedto unsatisfactory blasting results in various places. Apossible opportunity to optimise is indicated by thedi�erence between BD of 0.631 (site S6) and 0.725(site S3) (see Table 4) which would represent a clearincrease in speci®c charge required.

6. Concluding remarks

The E-B-T model proposed for characterising blast-ability Ð the ease with which a rock mass can be frag-mented by blasting Ð has been outlined. The E-B-Tcoe�cient Bi and E-B-T model have been proposed toaccount for the e�ects that rock masses with di�erentblastability will have.

Recognising that blastability is a composite intrinsicproperty and that conventional approaches are notwell suited to characterising the blastability, a method-ology for the assessment of blastability of rock massesusing the rock engineering systems approach has beendeveloped in this paper. The methodology has system-atically taken into account twelve factors which areview suggested would give a reasonably comprehen-sive set of factors that in¯uence the blastability of arock mass. The contribution of each of these factors tothe blastability of the rock mass is identi®ed using in-teraction matrix analysis, which is implemented by de-riving a weighting for each factor. Combining theresults from the interaction matrix analysis and theratings proposed in this research, the blastability ofthe rock mass may be represented quantitatively usingthe blastability designation, BD. A preliminary classi®-cation for blastability of rock masses according to theE-B-T coe�cient or the blastability designation hastherefore been suggested. Using the BD derived from

the assessment system, it is possible to de®ne the valueof Bi, and thereby use the E-B-T model as a blast de-sign tool.

A sample of available data sets from the literaturesuggests that the E-B-T model would generally give animprovement in describing the energy±size reduction inblasting compared with the Bond±Ram model. Thecase study presented also suggests that the proposedblastability assessment system and the associated E-B-T model represents a possible improvement on existingmodels. The calculation of the rock factor A in theKuz±Ram model based on the blastability assessmentinstead of Cunningham's A also appears to give animprovement in the accuracy of the Kuz±Ramequation when applied to the case study data.However the parameter set developed in the paper toassesses blastability has yet to include the in¯uence ofthe dominant joint set orientation with respect to thefree face.

A well-developed model or system should beexposed to a variety of case study examinations withdi�erent geological conditions in order to achieve su�-cient con®dence for its use. This could be most e�-ciently implemented by the setting up of a databasewith the full record of di�erent in-situ geological con-ditions, blast patterns, explosive energy inputs anddirectly assessed BBSD results. A series of model-scaleor full-scale trial blasts would be ideal for further vali-dation of the E-B-T model and the associated blast-ability assessment. The relationship proposed betweenthe E-B-T coe�cient and the blastability designation,Eq. (7) has a comparatively poor level of con®denceand therefore further calibration is to be rec-ommended.

The blastability assessment system presentedincludes a signi®cant amount of subjective criteriathrough the matrix coding procedure. Systemsapproaches such as the rock engineering systems andthe grey systems [42] have been exploited to reduce theojectivity. Further investigations into how to moresubjectively represent parameters of the blastabilitysystem and how to more accurately code the inter-action mechanisms in the matrix are necessary forimprovement in the blastability assessment.

In this paper the energy input for the model hasonly been related to uncontrollable factors governedby in-situ geological conditions and the term blastabil-ity has been deliberately restricted to quantify thisintrinsic resistance of the rock mass. In the companionpaper [23], it is brie¯y suggested that the controllablefactors such as burden, spacing, delays, decoupling,etc. could be introduced into the E-B-T model througha composite coe�cient fc that regulates the e�ective-ness of the input energy of explosives. The utility ofsuch an E-B-T model with or without fc remains some-what speculative.


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development of an assessment system for the blast ability of rock

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