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Journal of Minerals & Materials Characterization & Engineering, Vol. 8, No. 9, pp 729-743, 2009
jmmce.org Printed in the USA. All rights reserved
Alternative Approaches for Determination of Bond Work Index
on Soft and Friable Partially Laterised Khondalite Rocks
of Bauxite Mine Waste Materials
Ranjita Swain and R. Bhima Rao*
Institute of Mineral s and Materials Technology
(Council of Scientific & I n d u s t r i a l Research)
Bhubaneswar 751 013
*Corresponding Author: firstname.lastname@example.org, email@example.com
PLK (Partially Laterised Khondalite) rock is a general terminology used in this paper for those
rocks which are in general associated in bauxite mining such as Partially Altered Khondalite
(PAK) rocks, Partially Kaolinised Khondalite (PKK) rocks and Lithomerge. This paper deals
with the Bond’s work index, Hardgrove index and Brittleness tests on six typical rock samples
and its correlation. As a fast method, the determination of the Bond index from the Hardgrove
index (by calculation) is almost matching with measured Bond’s work index. The Bond’s work
index of the above rock samples calculated from the Hardgrove index value has shown a
variation from 7.7 to 10.3 kWh/sh.t. A correlation is found between the friability value and work
index. The correlation coefficient of 0.93 between the friability value (S1) and Bond’s work
index, Wi = -18.193 Ln (S1) + 66.747 has been found. The brittleness test results may not be very
close to the work index values, as in brittleness tests relatively large grains are ground, whereas
the HGI values, grinding of fine –grain samples involved. Thus the grindability of PLK rocks or
bauxite can be determi ne d b y t h e simple test performance, HGI.
Keywords: Brittleness, Friability value, Hardgrove index, Bond’s work index, PLK rocks,
Bauxite mine waste.
Khondalite rocks of Easternghats containing bauxite is being mined about 6.3 million tons per
annum in the state of Orissa, India to produce around 2.1 million tons of alumina per year by
730 Ranjita Swain and R. Bhima Rao Vol.8, No.9
National Aluminium Company. While mining of this bauxite per annum, an equal amount of 6.3
million tons of Partially Laterised Khondalite (PLK) rocks is also is being generated per annum
and dumped at the mine site as waste material or sometimes used for back filling of abandoned
mines . In the earth crust of this mine, the bauxite is underlay along these PLK rocks or some
times overly. Thus selective mining is not possible and hence due to mechanized mining
methods, the generation of waste material is inevitable.
PLK rock is a general terminology used in this paper for those rocks which are in general
associated with Partially Altered Khondalite (PAK) rocks, Partially Kaolinised Khondalite
(PKK) rocks and Lithomerge. Recently it is found that after suitable beneficiation, the PLK rock
can be utilized in filler industries [2-5]. It is a fact that comminution is one of the important
processes for size reduction to meet the requirement of filler industries. The filler industries need
fine ground materials, which consumes a lot of energy during preparation.
There are only two approa ches to find out the en ergy consumption of a rock ground from infinite
size to 100 microns or even down to this. The first one, which has been widely accepted
approach, is Bond’s grindability test and the second one is Hardgrove index, which generally
used for coal. In recent, the brittleness test/friability value of bauxite, limestone, barite, marble,
copper ore, andesite and ulexite [6-9] is also suggested to find out the work index of material.
The Bond’s grindability test can be used to determine the work index of any type of ore or
material. But the process is tedious and long ti me consumption. Hardgrove index and brittleness
test can be carried out on only those ores or rocks or materials, which are soft, friable and brittle
Since the P LK rocks are bauxi tic origin and are sof t, friable and brittle easily an attempt is made
in this paper to find out the grindability of different types of rocks associated in PLK rocks by
Bond’s grindability test, Hardgrove index and brittleness test. These results are compared and
discussed in this paper.
2. MATERIALS AND METHODS
Run of mine ore sample (about 1000 kg) was collected from A-Trench mine site of NALCO,
Damanjodi. Sample was collected in a radius of five kilometer from the mine site. The six
representative samples as shown in Fig. 1 (gibbsitic rock-feldspar rich, gibbsitic rock-goethite
rich, gibbsitic rock –limonitic rich, kaolinised rock, lithomerge type rock and partially laterised
khondalite rock) were prepared separately for Brittleness tests, Hardgrove index and Bonds
grindiability studies. The experimental details are described in the following.
Vol.8, No.9 Alternative Approaches for Determination of Bond Work Index 731
Fig. 1. Six different types of rock samples associated in baux ite mine waste.
2.1 Bond’s Work Index
Representati ve samples w ere prepared sep aratel y by stage crushing to all passing a 6 mesh sieve.
The weight of 700 cc sample was placed in the mill. The grinding conditions are given below.
(Feldspar rich) rock b) Gibbsitic (Goethite rich) rock
c) Gibbsitic (Limonitic) rock d) Kaolinised rock
f) PLK rock
732 Ranjita Swain and R. Bhima Rao Vol.8, No.9
These studies were carried out in a standard ball mill 300 mm X 300 mm size. The grinding
media with steel balls weighing 20.125 Kgs has been used. The details of the number of balls
used, its sizes are given below:
No. of balls Size, mm
The materials weight of 700 cc volume sample with the balls was charged to the ball mill and
ground initially at 100 revolutions. The ground sample was screened with the test sieve and the
undersize sample was weighed and fresh unsegragated feed was added to the oversize to bring its
weight back to that of original charge. The numbers of revolution required was calculated from
the results of the previous period to produce sieve undersize equal to the 1/3.5 of the total charge
in the mill. The grinding period cycles were continued until the net grams of sieve undersize
produce per mill revolution reaches equilibrium. Then the undersize product and circulating load
was screen analyzed and the last three net grams per revolution (Gbp) is the ball mill
grindability. The test mesh used was 100 mesh (150 µm) [10-17].
The Bond Work index Wi was calculated from the following equation (Eq. 1)
Wi = 44.5/(P1)0.23 X (Gbp)0.82 [10/(P80)1/2 – 10/(F80)1/2] (Eq.1)
F80 is the size in microns at which 80 percent of the new f eed to ball mill passes
P80 is the size in micron at which 80 percent of the last cycle sieve undersize product passes
P1 is the opening in microns of the sieve size tested
2.2 Hard Grove Index
The Hard grove index experiments were carried out using ASTM D409 – type bearing mill. The
experimental process as described by Haese  was carried out. Representative sample of 50
gms. -1180 µm +600µm was prepared separately. The same was ground in Hard grove index
mill. The ground product was discharged after 60 revolutions of unit. Then the product was
screened at 75 µm. Hardgrove index of the sample has been calculated as per following formula
H = 13 + 6.93mH (Eq.2)
Vol.8, No.9 Alternative Approaches for Determination of Bond Work Index 733
Where H is the Hardgrove index and mH is the mass (in g m) of the particles smaller than 74 µm.
The mean of two to three parallel measurements are to be considered. However, the relative
deviation of which cannot exceed 3%. Bond [10, 11, 19 & 20] proposed a relationship between
the work index Wi and the Hardgrove grindability index (HGI) (Eq.3):
W B, H = 435/H 0. 91 (Eq.3)
In due course Haese modified and suggested that the Bond index can be estimated from the
Hardgrove index using the following empiric formula (Equation 4):
WB,H = 435/ H0.82 (Eq.4)
2.3 Brittleness Test
The experimental set up for the brittleness tests to find out the friability value (S1) is shown in
Fig.2. In order to carry out brittleness tests to find out the friability values of all the selected six
variety samples were crushed separately. Each sample was screened at 80 mm and 19 mm sizes.
Fig.2. Brittleness test for measuring the friability value S1
734 Ranjita Swain and R. Bhima Rao Vol.8, No.9
The selected rock sample of -80+19 mm size fraction was subjected to impact crushing for
brittleness tests. In this connection a test apparatus has been designed as shown in Fig.2. to suit
bauxite strength characteristics used in alumina production. The weight dropped is 2kgs from a
height of 75cm. In general the drop weight tests of minimum three or four parallel tests are to be
carried out and the mean value to be consid ered for deter mination of friability values . But in the
present investigation, all the rock types, subjected to brittleness tests, under the 2kg drop weight,
were produced fine powder (by single drop weight) and hence there was no scope to repeat
second drop weight test on the same sample. The friability (S1) is calculated as given below:
F = the broken weight passes 19 mm (gms)/ Sample weight X 100 (Eq.5)
Thus the friability value S1 equals the percentage of undersized material, which passes through
the 19 mm size after crushing. The energy calculation for drop weight at each fall is given below.
E = m * g* h (Eq.6)
m = mass of the weight drop on the sample
E = Energy of each fall, J
g = gravitational force, m/s2
h = height from where the falls on the sample, m
3. RESULTS AND DISCUSSION
3.1 Physicochemical Characteristics
Six chosen typical samples have posses a wide range of colours (Fig.1). The colours vary from
white, yellow, grey, brown, red and pinkish or of mixed varieties. Their brightness also varies
from sample to sample. The light brownish varieties are gibbsitic rock with feldspars and
occasionally have white clayey patches (kaolinite) or vug/cavity filled quartz (Fig. 1a). The dark
brownish varieties are also gibbsitic with goethite rich content (Fig 1b). Similarly the brown rock
associated with light to dark yellow colour limonite (Fig 1c). The white variety samples which
are soft, friable to semi-friable and clayey are mostly kaolinised or lithomerge rocks (Fig.1d and
1e). Many of the white varieties of the samples are soapy to hand. Some of the hand specimen
samples show the gneissic structure that of a fresh khondalite. The samples are partially
lateritised to fully lateritised khondalites (Fig 1f).
The physical properties and complete chemical analysis (Table 1) indicate that the physical
properties of all thes e samples are almos t similar. It is observed that the bulk density varies from
1.1 to 1.4 g/cc, true density varies fro m 2.6 to 2.8 g/cc. However, the chemical analysis of these
Vol.8, No.9 Alternative Approaches for Determination of Bond Work Index 735
six samples varies from sample to samp le. The F e2O3 varies betw een 2.5% to 4.28%, TiO2 varies
from 1.09% to 2.73%, Al2O3 varies 32.78% to 60.89% and SiO2 varies from 16.95% to 41.55%.
Thus the data indicate that all the six samples are distinct, differ in chemical composition and
exhibit closely differs in colour.The physical properties of all the samples are similar.
Table 1: Physico-chemical properties of six typical samples
3.2 Bond’s Work Index
In the grindability tests, the samples are chosen such as gibbsitic rock-feldspar rich, gibbsitic
rock-goethite rich, gibbsitic rock –limonitic rich, kaolinised rock, lithomerge type rock and
partially laterised khondalite rock the selected test sieve size was 150 µm. The 80% passing sizes
of the product and the feed of the above materials are determined and from the values obtained,
the grindability factor and the Bond’s work index are calculated. The work index value of rock
determined from the test results of Bond grindiability tests for typical PLK rock is described
The weight of PLK rock sample (700 cc) = 856gm.
B (the % undersize at 150 µm in the feed) = 28.3%
C (required product weight) = 856*0.283 = 242gm
The results of the grinding are shown in Table 2. As the last three run equilibrium is reached,
grindability factor was constant at 3.4 to 3.6 gm/rev with F80 = 1450 µm and P80 = 124 µm. From
this Bond’s work index is calculated by using Equation1. The work index values obtained for
associated PLK rocks are (a) Gibbsitic rock (Feldspar rich) 9.4 kWh/sh. ton, (b) Gibbsitic rock
(Goethite rich) 9.4 kWh/sh. ton, (c) Kaolinised rock 9.9 kWh/sh. ton, (d) Lithomerge type rock
type rock PLK
Bulk density, g/cc 1.3 1.2 1.2 1.1 1.1 1.3
True density, g/cc 2.6 2.8 2.7 2.6 2.6 2.7
Porosity,% 50 57.1 55.6 57.7 57.7 51.9
Angle of repose, º 36.6 35.8 36.2 35.7 35.4 35.9
Al2O3, % 32.78 60.89 34.65 35.37 43.64 33.94
SiO2, % 41.55 16.95 33.23 31.79 31.83 40.99
Fe2O3, % 2.746 3.63 4.80 2.536 4.28 4.18
TiO2, % 1.345 2.475 2.063 1.093 2.739 2.061
LOI, % 18.9 13.7 24.5 27.1 15.5 14.7
736 Ranjita Swain and R. Bhima Rao Vol.8, No.9
7.9 kWh/sh. ton, (e) Gibbsitic rock (Limonitic rich) 9.4 kWh/sh. ton, (f) PLK rock 7.9 kWh/sh.
ton. These values are reasonably close to 8.78 kWh/sh.t for bauxite Bond (1961).
Table 2. Bond grindability test for determination of grindability factor of natural PLK rock
Revolution R Product C Feed B C-B
100 452 213.98 238.02 2.4
55 268 248.4 48.1 0.35
51 256 84.4 171.6 3.4
47 242 76.9 165.1 3.5
51 254 72.7 181.3 3.6
3.3 Hardgrove Index
The hard grove process was developed in the US for the grindability test of coals. In the
Hardgrove index test of gibbsitic rock-feldspar rich, gibbsitic rock-goethite rich, gibbsitic rock –
limonitic rich, kaolinised rock, lithomerge type rock and partially laterised khondalite rock were
taken, the selected si eve size was 75 µm. The undersize (-75 µm) weight of the product for the
above materials are determined and from the values Hardgrove index and Bond’s work index
were calculated by using the Equation 4 and Equation 7 respectively. In this paper PLK rock
sample was taken for example:
The weight of PLK rock sample (-1.18 µm + 600 µm size) = 50 gm
mH,(the undersize at 75 µm in the product) = 17.9 gm
H, Hardgrove index = 13+ (6.93 * 17.9) = 137.25 ºH
Wi, Bond’s work index = 435 / (137.25)0.82 = 7.7 kWh/ton
The Hardgrove index of PLK rock sample was calculated as 137.25 ºH and the Bond’s work
index calculated from the Hardgrove index is 7.7 kWh/t (Table 3). Results of Hardgrove index
values obtained for gibbsitic rock (feldspar rich, goethite rich and limonite rich) are 110.02 ºH.
The lithomerge type rock, which is very soft (white colour) soils, had shown Hardgrove index
127.74 ºH. The PLK rock has shown comparatively high Hardgrove index value 137.25 ºH as it
contains some gensis structure, which has plastic structure. The kaolinised rock has shown the
lowest Hardgrove index value 96.16 ºH. This may be due to the fact that the rock contains fine
agglomerates of quartz, feldspars, altered feldspars and kaolinites. The Bond’s work index of the
six typical rock sa mples has been calculated fr om the Hardgrove index with values varying from
7.7 to 10.3 kWh/sh.t (Table 3).
Vol.8, No.9 Alternative Approaches for Determination of Bond Work Index 737
Table 3. Comparison studies of friability, Hardgrove index and Bond’s work index
Details Bond index
Wi (KW h/t) Hardgrove
index (ºH) *Calculated
Wi,h (KW h/t)
(Feldspar rich) 9.4 110.02 9.2 23.1
(Goethite rich) 9.4 110.02 9.2 23.2
9.4 110.02 9.2 23.6
rock 9.9 96.16 10.3 23.1
type rock 7.9 127.74 8.2 25.1
PLK rock 7.9 137.25 7.7 25.6
Bond’s work index calculated from Hardgrove index
3.4 Brittleness Test
It is mentioned earlier that friability value is measured from the brittleness test. Brittleness,
defined differently from author to author, is an important me chani cal property of rocks, but ther e
is no universally accepted brittleness concept or measurement method in mechanical excavation
. Many studies can be seen of the relationship between brittleness and the other performance
parameters of machines and rock properties in literatures .
The results of the friability values determined from the brittleness tests for six different type
rocks of same geological source are given in Table 3. The data indicate that these is significant
change observed in the friability values expressed in terms of percentage of -19 mm particles
produced for each rock type. The typical PLK rock and lithomerge type rock samples have
shown friability value around 25% and the rest four type rocks are shown around 23% average.
The tested PLK rock sample aggregate volume corresponds to that of a 500 gm in the fraction -
80mm+19 mm size. The friability value S1 equals the percentage of undersized material, which
passes through 19 mm size after crushing on the base mortar by one weight drop. The mean
value for a minimum of four to five tests is chosen as the rock sample S1 value. The weight
dropped is 2kgs. Therefore the energy at each fall is 2kgf x 0.75m x 9.81 m/sec2 = 14.7 J (Eq.6).
738 Ranjita Swain and R. Bhima Rao Vol.8, No.9
S1 is the broken weight passes 19mm (gm.) / sample weight (500 gm.)in percentage. The S1
value for PLK rock is found to be 25.6%. These values for all the rocks are given in Table 3.
Comparison studies of friability, Hardgrove index and Bond’s work index for six samples is
given in Table 3. The data indicate that the calculated Bond’s work index values from Hard
grove index for six types of rocks are very close to the data obtained by the Bond’s work index
of six samples. Based on these results, the relationship between Bond index, Hardgrove
grindability and fri ability values are discussed in the following.
3.5 The Relationship between Work Index (Wi) and Friability Value (S1)
Tamrock  has described the brittleness test that gives a measure for rock resistance to
crushing due to repeated weight drop impacts. In the present experiments the weight dropped
used is 2kgs. The energy at each fall is calculated as 14.7J. The friability value is the broken
weight passes 19 mm (g) per sample weight (500gm) in percentage. The values given in Table 3
indicate that the friability value is inversely proportional to the Bond’s work index value. The
data obtained from work index and friability values are shown in Fig.3.
Wi = -18.193Ln(S1) + 66.747
22.5 2323.5 2424.5 2525.5 26
Friability (S1), %
Bond work index (Wi), kWh/t
Fig.3. The relationship between Wi and S1
It is known that Bond grindiability test is used widely in assessing industrial size tumbling ball
mill and rod mill energy requirements and it gives good results . But it is a fact that it takes a
long time to obtain fairly constant value of grindiability factor. For this reason, it is important to
determine a grindiability value of materials alternatively with a simple test apparatus which gives
Vol.8, No.9 Alternative Approaches for Determination of Bond Work Index 739
quick results. The suggested brittleness test can be used for determination of work index. Thus it
cuts a long spending time determination of the work index. A correlation is found between the
friability value and work index from the straight-line as shown in Fig.3. The line shows a
standard correlation between the friability value and work index. The correlation coefficient of
0.93 between the friability value (S1) and Bond’s work index (Wi) has been found and given
below in Eq. 7 .
Wi = -18.193 Ln (S1) + 66.747 (Eq. 7)
3.6 Relationship between the Bond’s work index and Hardgrove grindiability
Both the work index (Wi) by Bond’s work index and the Hard grove index (HGI) tests are
serving for determining grindability and these two tests are widely used in many industries. It is
known that the Hardgrove method is used mostly for deter mining of grindability of coal, but also
in determining the grindability of other materials such as bauxite, limestone, talc, barite, and
marbles etc., which are brittle, soft, and soapy. Whereas the Bond’s method is used for any type
of rock hard, compact, soft, brittle etc.
Especially for these reasons manual correlation was obtained using the results of Hardgrove
method [24 & 25] and results of tests by Bond [10 & 11]. For the calculation of work index Wi
from HGI values, Bond  proposed the following formula:
Wi = 88/ HGI 0.5
In 1961 Bond specifies for Wi calculation the following modified formula:
Wi = 435/ HGI 0.91
On the basis of resear ch of grindability, McIntyre and Plitt, 1980 , recommended using of the
following formula for calculation of Wi > 8.5 value
i = 1622/ HGI 1.08
For carbonates, Hower etal., 1992 , proposed the following formula for calculation of Wi
from HGI value:
i = 14.56 – 0.10 HGI
The data shown in Table 3 indicate that there is not much difference in the measured Bond’s
work index and the calculated Bond’s work index from the Hardgrove index. The Bond’s work
740 Ranjita Swain and R. Bhima Rao Vol.8, No.9
index varies from 7.9 to 9.9 kWh/t whereas the calculated Bond’s work index from Hardgrove
index varies from 7.7 to 10.3 kWh/t. Fig. 4 shows the comparison of the measured Bond work
index estimated from the Hardgrove grindability using the relation given in Equation 4. The data
show that under the investigated conditions there is tight relationship between the Bond index
and the Hardgrove grindability.
y = 0.9982x
Me asure d Bond w ork inde x, kW h/t
Bond work index calculated from Hardgrove
Fig.4. Comparison of the measured Bond work index and the Bond work index estimated
from the Hardgrove grindability using the relation (Eq.5)
The Bond method of grindability determination is time consuming and a constant value of
material grindability is only achieved after several grinding periods, where as for determination
of the HGI, the experimental procedure takes few minutes. In contrast the brittleness test is very
rapid and friability value is obtained still in a much shorter time. However, the Wi values
obtained by calculation from HGI not always precisely correspond to the values of work index
specified by sample brittleness testing. This is associated with the fact that in brittleness tests
relatively large grains are ground, whereas the HGI values is discovered by grinding of fine –
grain samples . Brittleness test is performed on impact testing device. Hence, the brittleness
test results may not be very close to the work index values. Thus in view of the above
observations, the grindability of PLK rocks or bauxite can be determined by the simple test
Vol.8, No.9 Alternative Approaches for Determination of Bond Work Index 741
The following conclusions are drawn from the Bond’s work index, Hardgrove index and
Brittleness tests on six typical rock samples.
The work index values obtained for associated PLK rocks in the bauxite mine vary from 7.9
kWh/sh.t to 9.9 kWh/sh.t. These values are reasonably close to 8.78 kWh/sh.t for bauxite as
estimated by Bond.
As a fast method, the determination of the Bond index from the Hardgrove index (by calculation)
is almost matching with measured Bond’s work index. The Bond’s work index of the above rock
samples calculated from the Hardgrove index value has shown a variation from 7.7 to 10.3
A correlation is found between the friability value and work index. The correlation coefficient of
0.93 between the friability value (S1) and Bond’s work index, Wi = -18.193 Ln (S1) + 66.747 has
been found. However, the brittleness test results may not be very clos e to the work index values
for other types of rock samples determined by Bond.
The Wi values obtained by calculation from HGI is very close to the Bond work index values,
since the HGI values is discovered by grinding of even fine –grain samples. Thus the grindability
of PLK rocks or bauxite can be determined by the simple test performance, HGI.
The authors are thankful to Prof. B.K. Mishra, Director for his kind permission to publish this
paper. Thanks also due to Sri P. S. R. Reddy, HOD, MPD, for his constant suggestions. One of
the authors Ms. Ranjita Swain is thankful to CSIR for granting CSIR SRF.
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