Engineering Geology 53 (1999) 1–11

Evaluation of the quality of a granite quarry

J. Taboada a, A. Vaamonde b,*, A. Saavedra b
a Mining Department, Vigo University, c/Torrecedeira 105, 36208 Vigo, Spain
b Statistics Department, Vigo University, c/Torrecedeira 105, 36208 Vigo, Spain
Received 25 May 1998; accepted 23 October 1998

Abstract

The determination of the quality of a mass of granite with a view to its exploitation for ornamental purposes is
carried out by means of the identification of the geological, geotechnical and aesthetic factors that characterize the
granite. In order to draw up an optimal exploitation method for any given granite deposit, an assessment of the
relationship existing between these factors and the quality of the block is of the utmost importance. Using as a
starting point, data based on the observation of these factors at an extraction bank, a simple linear index was
elaborated using multivariant techniques, permitting the classification of each block in terms of quality. Subsequently,
using geostatistical techniques, the index is applied to areas of the extraction bank for which there are no a priori
data, with a view to predicting possible areas of maximum quality.
Included is a description of an application whereby the quality of a granite quarry was evaluated on the basis of
569 observations at an extraction bank. The methodology developed may be considered an objective quality evaluation
method applicable to ornamental rock quarries. © 1999 Elsevier Science B.V. All rights reserved.

Keywords: Discriminant analysis; Geoestatistics; Granite; Ornamental rocks; Quality index; Multivariate analysis

1. Introduction on the one hand for extraction planning that

permits optimum exploitation of deposits, and on
Research and exploitation activities relating to the other hand, for quality control of rock prior
ornamental granite destined for the construction to extraction.
industry have, in recent years and in various parts This lack of extraction planning and quality
of the world, become increasingly significant. control techniques is evident even in countries that
The increase in production can be explained by while utilizing and exporting the most advanced
technological advances that have permitted the extraction and transformation technologies, con-
extensive usage of modern, sophisticated tinue to apply the traditional methods of extraction
machinery and extraction equipment. Never- planning and quality control. This is in direct
theless, from a mine engineering point of view, contrast with metallic and non-metallic mineral
there still remains a need to develop technologies, industries, where there has been a profusion of
information and other technological applications
* Corresponding author. Tel.: +34 86 813713; Fax: +34 86 that guarantees optimum extraction techniques
813746; e-mail: vaamonde@uvigo.es and effective quality control (Pereira, 1988).

0013-7952/99/$ – see front matter © 1999 Elsevier Science B.V. All rights reserved.
PII: S0 0 1 3 -7 9 5 2 ( 9 8 ) 0 0 07 4 - X
2 J. Taboada et al. / Engineering Geology 53 (1999) 1–11

Compared to other materials with an industrial structures. Nevertheless, these are not so evident
origin, stone has the advantage of being a natural or easy to recognize as in other kinds of rock.
material that requires minimal industrial trans- The principal internal structures that tend to
formation other than that necessary for its final appear in a granite mass are as described in the
positioning. Consequently, given that the quality following subsections.
of the rock in the quarry itself determines the
quality of the final product, control of this aspect 3.1. Fabrics
is of the utmost importance.
These are defined by the preferred orientation
of some of the mineral components of the rock.
2. Methodology They are caused by magmatic flow and ductile
deformation processes in the rock. The magmatic
The methodological sequence used along this fabrics, which tend to be difficult to recognize
work is as follows: particularly when dealing with equigranular rocks,
$ Identification of the factors directly in relation
may be planar, linear or combined. In the granite
to the quality of a granite quarry. bed that is the subject of our study, the fabrics
$ Collection of field data from the quarry. The
were evident in the so-called rift plane, which is
samples are obtained from the accessible faces the orientation that indicates where the rock can
of the extraction bank. most easily fracture.
$ Construction of a quality index for the granite
blocks, by means of multivariate analysis
3.2. Schlieren
techniques.
$ Geostatistical characterization of the extraction
These are accumulations of biotite and other
bank, by extrapolating the values of the quality
minerals, with a limited extension and often mor-
index calculated for each support, to the
phologically planar. When more developed levels
whole quarry.
giving rise to composition bands are encountered,
reference is made to flow layers. The schlieren
structures are excellent markers of flow layers,
although they do indicate heterogeneities that are
3. Quality parameters
normally considered undesirable in a deposit of
ornamental rock.
The geological factors that condition the exploi-
tation potential of a block of granite for ornamen-
tal use are of two fundamental types, namely 3.3. Oriented enclaves
lithological and structural.
Lithological factors are the intrinsic properties These can be either microgranular, frequently
of a block that indicate its suitability as a specific ellipsoidal, or xenotith which are usually morpho-
kind of construction material. These features are logically more irregular. When the oriented
textural characteristics, composition, colour, enclaves present a systematic orientation they indi-
mechanical characteristics, alteration and cate the position of layers and flow lines. These
transformability. elements, when they appear, also account for an
Structural factors include all those elements that impairment in the quality of a rock destined for
define both the geometry of a geological body and ornamental use.
its internal structure. A granite block should not
be considered as an isotropic or homogeneous 3.4. Microfractures
mass in which the only structures present are
fractures, joints and dikes, but rather as a mass These may appear in one or various mineral
that consists of a series of very varied internal components of the rock as open or sealed fissures.
 J. Taboada et al. / Engineering Geology 53 (1999) 1–11 3

3.4.1. Fractures $ continuity, that is, the length of the fracture

Two kinds of fractures can be distinguished measured at the outcrop and which, due to its
as follows: flat geometry, is an indicator of size.
The secondary fractures of a tectonic origin limit
3.4.2. Primary the size of the natural block and thus, quarry
These are fractures that appear in relation to productivity. The structural parameters taken into
the positioning process of the irruptive body. They account are:
are associated with the flow structures and may be $ number of secondary fractures;
fractures covered by hydrothermal minerals (chlo- $ continuity or extent of secondary fractures;
rite, muscovite, quartz, pyrite, fluorite), aplite, $ spacing, that is, the perpendicular distance
pegmatite or basic rocks. A classic distinction is between two adjacent fractures from the same
that between cross joints, longitudinal joints, flat- series of discontinuities, this is directly propor-
lying joints and diagonal joints. Other less typical tional to the size of the natural block within
kinds of fracture include marginal fractures and the mass; and
flat-lying normal faults. It is normal to encounter $ inclination of the fracture with respect to the
a certain distribution of primary structures within rift plane, given that fractures parallel or per-
a granite pluton, usually to be found in greatest pendicular to the rift plane mean the extraction
abundance towards the edges of the mass and to of larger blocks than is the case when the
a lesser extent in the interior. fractures are oblique.

3.4.3. Secondary
These are fractures that develop in phases subse-
quent to positioning and consolidation of the 4. Quarry data collection
irruptive body. They may be due to tectonic
reasons or occur as a consequence of settling. The following system was used to collect field
In the granite bed that is the subject of our data. A granite extraction bank cut by means of
study, the following structural quality differentiat- diamond wire was studied. The horizontal face
ing characteristics were encountered: corresponded to the granite’s rift plane. One of
$ microgranular enclaves; the vertical faces corresponded to the hardway
$ primary fractures; plane, and the other was perpendicular to the
$ secondary fractures. horizontal face and the hardway plane. The rift
In order to distinguish between enclaves, the plane is the direction of maximum weakness in the
following structural parameters were examined: granite and is associated with the petrofabric. This
$ number of enclaves; is the face of the final block from which the slabs
$ size and shape (spherical or elliptical ). of granite are cut during the elaboration process.
This structural characteristic does not determine The hardway plane is the direction of minimum
the size or output potential of the mass, but rather weakness in the rock and constitutes the narrowest
the aesthetic value of the block, which is designated face of the final parallelopipedic block.
as of inferior quality with the corresponding reduc- In order to collect data, a 5 m×1 m grid was
tion in its market value, if it contains enclaves of traced on the three accessible faces of the extrac-
greater than a specific size. tion bank, so as to obtain a total of 569 supports
In this work the primary fractures identified or samples (see Fig. 1). Each of these samples may
were fully enclosed and mineralized diagonal joints be considered representative of the characteristics
which, as in the case of the enclaves described corresponding to a 5 m×1 m×1 m block, for
above, do not restrict the extraction process but which it is only possible to make observations with
certainly do impair both aesthetic and economic respect to one side.
value. The parameters studied are, in this case: Each support was examined with a view to
$ number of primary fractures; and establishing the presence or absence of discontinu-
4 J. Taboada et al. / Engineering Geology 53 (1999) 1–11

Fig. 1. Distribution of the supports on the extraction bank.

 J. Taboada et al. / Engineering Geology 53 (1999) 1–11 5

ities in the mass, and where present, the character- criteria traditionally used for the selection of
istics of the discontinuities (as defined above). blocks extracted from a quarry for posterior trans-
The enclaves were assessed firstly, with respect formation in granite slabs.
to the number of them appearing in the support The blocks classified as top quality will produce
and secondly, with respect to size, given that slabs that present no flaws or discontinuities that
smaller ones do not affect the ornamental quality might diminish exploitation possibilities and
of the granite whereas larger ones relegate it to a aesthetic quality. Blocks classified as of inferior
secondary quality category. quality do exhibit some discontinuity or flaw but
The primary fractures that spanned the mass may be exploited so as to obtain an acceptable
were assessed for density (the quantity that economic return. Here, the transformation equip-
appeared in each support) and for continuity or ment available is important in determining the
length, in order to determine incidence in a more minimum size of the blocks. Finally, the part of
or less extensive zone of the mass. This again, is a the bank considered to be unexploitable is that
characteristic that diminishes the quality of the which incorporates such a quantity of discontinuit-
rock. ies that it is not possible to extract even minimally
In order to determine the incidence of the sized blocks.
secondary fractures, frequently to be found in
granite masses, the following four parameters
(defined at the end of the last section) are 5. Construction of a quality index
appraised:
$ Density or number of discontinuities in the A quality index is constructed by means of a
support. linear function of independent variables that are
$ The spacing representative of the discontinuit- selected on the basis of their discriminatory capac-
ies; if >1 m (extruding from the support) the ity, that is to say, their influence on the quality of
spacing is considered valid, since this geotechni- the sample ( Taboada et al., 1997). The information
cal parameter is that which defines the possible provided by the independent variables is analysed
size of the block in the bank. as a whole in order to obtain the coefficients that
$ Continuity, where the real value in terms of form a scoring system which permits the grading
metres is used, even though it normally exceeds of granite in terms of quality. The weighting
the dimensions of the support. This is a manifes- assigned to each variable should be that which
tation of the discontinuities present in the sup- permits maximum discrimination between groups.
port, since this value indicates the extent of the To establish the weighting a calculation is made
discontinuity. of the combination of variables that maximizes
$ Inclination is measured in sexagesimal degrees the quotient between the sum of squares of the
of the dip angle of the representative discontinu- deviations (or distances) between groups, and the
ity in the support. When the rift plane is subhor- sum of the squares of the distances within groups.
izontal, as was the case in the studied area, the This is the function that causes the elements within
horizontality or verticality of a discontinuity a class to cluster and the different classes to
signals the possibility of extracting larger disassociate themselves from each other, thus guar-
blocks, more so than when a discontinuity is anteeing maximum possible discrimination. The
inclined. resulting function is the first discriminant function,
An assessment of the quantitative variables was arrived at by means of linear discriminant analysis.
carried out in the same way, for all the studied Once the discriminant function has been deter-
rock faces, on supports with the same surface area. mined, discriminant scores can be calculated, for
On the basis of the parameters analysed, the each support on the grid, by means of the linear
blocks can be classified on a scale as of top, combination coefficients. All that is required is the
inferior or reject quality. The technical criteria substitution, in the corresponding function, of the
used to define the quality scale correspond to the values of the different variables for each element.
6 J. Taboada et al. / Engineering Geology 53 (1999) 1–11

These values are used each time to calculate, using to the number of enclaves), and consequently they
Bayes’ rule, the probability of a particular element should not be discarded from the study.
belonging to any one of the classes. The coefficients of the discriminant function
The statistical programme SPSS used for this were calculated using the data from the 569
application, provides all the calculations described samples. Table 3 shows the coefficients of the
above. The programme assigns each element to calculated standard discriminant function. These
the class for which probability is highest, indicating coefficients indicate the linear combination of the
a priori and a posteriori probability values, as well eight variables represented in it, which permits on
as the second group or class to which the element the one hand, the calculation of the values of the
would be assigned as a function of the values of discriminant scores for each one of the 569
the discriminant scores. samples, and on the other hand, an analysis of the
For each one of the 569 elements in the sample, relative weight of each variable in the construction
sets of characteristics were identified that were of the discriminant function.
scored by assigning them a value which would Table 4 shows the coefficients of the non-standard
influence the final grading of the quality of the discriminant function. These coefficients permit the
granite. calculation of the values of the discriminant func-
The quality of each sample was estimated as a tion from the values of the original variables for
function of the technical criteria described above each sample of granite. In this way the value of the
and thus the clustering variable was obtained. This first discriminant function can be used as an index
clustering variable defines the quality of the gran- of granite quality, and as such it will be employed
ite, as illustrated in Table 1. Top quality granite, in subsequent geostatistical calculations.
flawless or possibly containing only very minor Table 5 shows the outcome of the classification
defects, is assigned the value of 1; inferior quality summarized in a classification matrix. It can be
granite, incorporating minor flaws whether isolated seen that the overall success rate is high (93.32%),
or combined, is assigned a value of 2; and reject which indicates a high level of efficiency for the
quality index employed. Moreover, the success rate
granite, with one serious defect or a combination
is 100% in the identification of top quality granite,
of various minor defects, is assigned a value of 3.
that is to say, not one top quality sample was
The results of the calculation of the Wilks’ l
incorrectly classified. Even for the undefined
coefficient and the corresponding univariant F
border areas between top and inferior quality, or
ratio can be seen in Table 2. The highest F values
between inferior and reject quality, the success rate
correspond to the variables with the greatest capac-
is notably high. The errors that do occur can be
ity for discriminating between classes of granite attributed in some of the cases to the diffuse nature
quality. These variables are: number of fractures; of the distinction between top and inferior, or
number of primary fractures; and continuity. The inferior and reject quality granite.
remaining variables, although having a lower F The percentage of correctly classified cases was
value, have a significance level that is practically 93.32%. The value of the index permits, for a given
zero, for which reason their capacity for differen- sample, a quasi-continuous ranking of quality level
tiation is considerable (except perhaps with respect based on the values of the original variables. Once
a value for the discriminant function has been
calculated, it directly assesses the quality of a
Table 1 sample. Given that the F function previously calcu-
Quality distribution for the sample
lated yielded values of between −1.31931 and
Quality Group Cases 10.95494, a simple linear transformation was
effected so as to simplify the interpretation of the
Top 1 355 quality index values, as follows:
Inferior 2 149
Reject 3 65 (F+1.31931)×10
Total 569 Q=10− .
1.31931+10.95494
 J. Taboada et al. / Engineering Geology 53 (1999) 1–11 7

Table 2
Lambda coefficient and F test for each variable

Variable Wilks’ l F Significance

Cont. of fractures 0.58772 198.5243 0.0000

Cont. of primary fractures 0.36227 498.1778 0.0000
Direction of fractures 0.86129 45.5766 0.0000
Spacing between fractures 0.87427 40.6992 0.0000
Number of primary fractures 0.49109 293.2742 0.0000
Number of fractures 0.35762 508.3460 0.0000
Number of enclaves 0.98879 3.2072 0.0412
Size of enclaves 0.96903 9.0431 0.0001

Thus the values for Q range from 0 (minimum

Table 3
Coefficients of the standard discriminant function quality) to 10 (maximum quality).
By analysing the values of the indices corre-
Variable F sponding to the different categories the results in
Table 6 are obtained. Using the Q values of the
Cont. of fractures 0.22274
Cont. of primary fractures 0.90639 quality index for each sample and applying the
Direction of fractures −0.67526 previous intervals, each element can be assigned
Spacing between fractures −0.45860 to a quality level which may or may not coincide
Number of primary fractures 0.08641 with that previously assigned to each sample.
Number of fractures 1.06663
Number of enclaves 0.13355
Size of enclaves 0.17047
6. Geostatistical characterization of an extraction
bank
Table 4
Coefficients of non-standard discriminant function Multivariable and simultaneous spatial predic-
Variable F tion have been applied in different fields ( Ver Hoef
and Cressie, 1993) and have lead to the study of
Cont. of fractures 0.0889838
Cont. of primary fractures 0.1897458
Direction of fractures −5.5227580 Table 6
Spacing between fractures −0.4223318 Quality index values
Number of primary fractures 0.1926246
Number of fractures 2.6604458 Quality group Quality index Q
Number of enclaves 0.5430150
Size of enclaves 0.1223964 Top >7.65
(Constant) 3.7034488 Inferior 6.35–7.65
Reject <6.35

Table 5
Classification matrix

Actual group Number of cases Predicted group

Top Inferior Reject

Top 355 355 (100%) 0 (0%) 0 (0%)

Inferior 149 25 (16.8%) 121 (81.2%) 3 (2%)
Reject 65 3 (4.6%) 7 (10.8%) 55 (84.6%)
8 J. Taboada et al. / Engineering Geology 53 (1999) 1–11

relationships between cross-variograms. However, is that given by the equation:

as the quality index of granite has been constructed

G C A BD
with quality parameters, the new Q variable can h h 3
4.05 1.5 −0.5 +0.55 h≤5.87
be interpolated using single variable techniques. c(h)= 5.87 5.87
Thus the application of multivariate analysis tech-
niques simplifies the subsequent study of the evolu- 4.6 h>5.87.
tion of the quality parameters for blocks. The second part of the geostatistical study involves
The geostatistical study is implemented in two
a spatial prediction of the quality index, based on
phases. Firstly, the relationship between the dis-
the semivariogram. To do this, 5 m×1 m×1 m
tance of the mid-points of the 5 m×1 m×1 m blocks were taken as supports and for each one a
blocks under consideration and the variability of
quality estimate ranging from 0 to 10 was made.
the indices assigned to each is determined and Indicator kriging offers many advantages in the
modeled. This relationship is represented by means handling of index variables but since it may involve
of an experimental semivariogram which is subse-
a loss of information (Solow, 1993), ordinary
quently adjusted to a theoretical model. Various kriging was used to estimate the quality index for
methods of estimation have been developed in each non-observed point, thus producing a linear
order to calculate the values of the parameters
combination of the known values that guarantees
represented in the semivariogram ( Zimmerman
and Zimmerman, 1991), but for this study the
weighted least squares method is preferred.
The graph in Fig. 2 depicts the experimental and
the theoretical semivariograms superimposed one
on the other. The experimental values are repre-
sented by points and, conforming to these, is the
theoretical model which approaches the depen-
dency structure implied by the former. The theoret-
ical model used is that corresponding to a spherical
model with a range of 5.87 and a sill value of 4.05,
somewhat less than that corresponding to the
sample variance which, represented in the graph
by a discontinuous line, is 5.4. Also evident is a
slight nugget effect with a value of 0.55.
The theoretical model to which reference is made

Fig. 2. Quality index semivariograms. Fig. 3. Estimation of the quality on the surface.
 J. Taboada et al. / Engineering Geology 53 (1999) 1–11 9

Fig. 4. Estimation of the quality on the first band. Fig. 5. Estimation of the quality on the second band.

minimum error. By this means, a quality estima- walls of the extraction bank. Fig. 6Fig. 7 illustrate
tion based on the quarry surface was arrived at the same values for the lower walls. These indicate
that could be used for the assessment of zones for the quality of the block according to its member-
which it was not possible (due to the fact that ship to one or another quality classification. All
these were covered by rubble) to collect data with these calculations take into account the limitations
which to construct the corresponding index (the imposed by the range of the semivariogram as well
area not included in the grid in Fig. 1, but in as by the different values for estimation variance
Fig. 3). obtained by means of the kriging process.
The value for the quality index was extrapolated
to the interior of the mass of rock. In order to do
this, four horizontal planes or bands, perpendicu- 7. Application to other quarries
lar to the walls of the extraction bank and intersect-
ing the sample blocks at their mid-point, were The present methodology can be easily extended
studied. Two cuts involved the upper walls and to any granite quarry or, in general, to an orna-
the other two, the lower walls. mental rock quarry. The particular lithological
Figs. 4 and 5 illustrate the estimated quality and structural factors, conditioning the exploita-
values corresponding to the cuts made in the upper tion of the quarry, have to be taken into account
10 J. Taboada et al. / Engineering Geology 53 (1999) 1–11

Fig. 6. Estimation of the quality on the third band. Fig. 7. Estimation of the quality on the fourth band.

for every different case, since they are not always (1988) shows a methodology, based on correspon-
the same. Each rocky mass has its characteristic dence analysis, specially designed for this type of
lithology and structure. For this reason, the quality data. By this procedure, each experimental support
factors conditioning the exploitation potential of is located in an arbitrary scale, defined by two
the quarry and the quality of the final product extreme poles (created by the exploitation experts,
have to be established for every different case. The assigning extreme values to the variables), by the
quality of the quarry can be evaluated by applying bias of the correspondence analysis supplementary
the present method to the characteristic parameters projection. This projection can be taken as a
of each case. quality index for the geostatistical study.
Another case to be considered is when the
observed data cannot be expressed as numerical
variables, but as a set of attributes. This could be 8. Conclusions
the case when dealing with Boolean variables such
as the presence/absence of some ornamental Statistical methods can be successfully applied
characteristics. Discriminant analysis techniques to the classification of granite production. Using
cannot be used for these observations. Pereira parameters that define quality, previously defined
 J. Taboada et al. / Engineering Geology 53 (1999) 1–11 11

and then tested on free faces of the extraction optimum yields in terms of both the quantity and
bank, and subsequently applying multivariant (dis- quality of granite.
criminant analysis) statistical techniques, it is pos-
sible to obtain a single function that is a linear
combination of the parameters in question. This References
represents all the information obtained and is an
authentic quality index for an extraction bank, Pereira, H.G., 1988. Case study on application of quantitative
serving to quantify the characteristics of a granite data analysis techniques to an uranium mineralization. In:
mass just as metal grade characterize a metallic Chung, C.F. et al. (Eds.), Quantitative Analysis of Mineral
and Energy Resources, Reidel, pp. 617–624.
deposit.
Solow, A.R., 1993. On the efficiency of the indicator approach
A geostatistical extrapolation (kriging) based on in geostatistics. Mathematical Geology 1, 53–57.
the surface quality data can be extended towards Taboada, J., Vaamonde, A., Saavedra, A., Alejano, L., 1997.
the interior of the extraction bank to the extent Application of geostatistical techniques to exploitation plan-
permitted by the semivariogram (in the case ning in slate quarries. Engineering Geology 47, 269–277.
studied, this was 6 m). The resulting information Ver Hoef, J.M., Cressie, N., 1993. Multivariate spatial predic-
tion. Mathematical Geology 25, 219–240.
permits an assessment, based on objective scientific Zimmerman, D.L., Zimmerman, M.B., 1991. A comparison of
criteria, of the quality of a granite deposit, and spatial semivariogam estimators and corresponding ordinary
therefore aids quarry planning with respect to kriging predictors. Technometrics 33, 77–91.