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Size correction for point load testing
Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. Vol. 17, pp. 231 to 235 Pergamon Press Ltd 1980. Printed in Great Britain
Technical Note Size Correction for Point Load Testing N O R M A N BROOK*
The fundamental relationship between strain energy and strained volume in point load testing is developed to give an analytical method of 'size correction' to a chosen standard size. Possible sources of error when using this method are considered, and comparisons made with other methods of dealing with the size effect. The most convenient methods to use, for various types of rock specimens are detailed. SHAPE AND SIZE EFFECTS IN P O I N T LOAD TESTING The effects of shape for point load tests, and crossed roller tests on cores, were considered by Reichmuth 1-1i, who in order to obtain a constant tensile strength proposed the formula: P St = Ks-~ + K b P (1) where St = tensile strength, P = applied load, h = distance between loading points, K, = shape factor, Kb = brittleness factor. Values of Ks and Kb were obtained experimentally. No size effect was evident with this analysis. B r o c h & Franklin [2-1 simplified the formula to: P Ix = ~ (2) where Is = strength index, P = load, d = distance between loading points, but found that this gave considerable variation in strength values for different sizes and shapes. To overcome the problem, standard cores of 50 mm diameter were proposed as test specimens, with size correction by chart or nomogram for other core sizes. Some correction for testing cylinders axially was proposed, but other shapes required approximation to an equivalent core size. Bieniawski 1-3] confirmed the size effect for cores, and also the relationship between compressive strength, Co, and point load strength of:
This effectively removed shape effects due to variation of the ratio d/t, and reinforced Reichmuth's [11 conclusion that the min. cross sectional area through the loading points was the only factor affecting his values of shape factor, Ks. Peng [5] in a finite element analysis of Sundae's method, concluded that for a stable stress distribution d should be greater than or equal to t. This conflicts with B r o c h & Franklin's I-2] method of axial testing of cylinders. ELIMINATION O F SHAPE AND SIZE EFFECTS If standard specimens, of fixed shape and size, are used the troublesome effects of size and shape are avoided. This method is however very restrictive. The standard size of 50 mm dia cores proposed by Broch & Franklin [2-1 is not easily obtainable in bedded rocks, and may be impossible in weak rocks which fragment on coring or preparation. In previous reports [6, 71, the author has shown that if the stiffness of different sized rock specimens can be considered constant in point load testing, as the deformation is mainly very near the loading points, then considering the strain energy to be proportional to the affected volume of rock, typified by the minimum cross-sectional area A, the relationship between applied load P, and A is: P = K A °'75
(5)
with K a constant depending on the rock 'strength'. This is confirmed, using a similar approach by Buttiens [8], who derived, for cores, the expression: P dt.S - constant,
(6)
with d the core diameter. If the same analysis is applied to the uniaxial compressive strength, the stiffness is not constant, and the Co = 24 1s (3) compressive strength can be shown not to be dependent on size of specimen, provided, of course, that the Sundae (4) used the point load test to study the effect applied stress is uniform. There is little, if any, direct of specimen volume on apparent strength, using disc evidence of this in the literature, but it is generally conshaped specimens, and the formula: sidered to be true. P Figure 1 shows the relationship between applied load Strength = nd--[ (4) a n d A °'75 for Darley Dale Sandstone, using data dewith d = disc diameter, t = thickness. rived from Broch & Franklin 1-2], which using equation (2) shows a strength index variation from about * Department of Mining and Mineral Sciences, University of 2-35 MPa. Specimens with width less than depth have Leeds, Leeds LS2 9JT, U.K. been omitted from Fig. 1, as recommended by Peng 231
232
Technical Note 15 • Cores o Discs t3 Blocks
10
Load kN
/"
/
/
/
5C
Load kN
Darley Dale Sandstone
o ~
/
z
l°
360
'
Dolerlte
./
o '
,60
/
'
,~
s6o
3bo
s6o
'
'
MIn. cross -sectlanal areaO.rS,mrnI -~
MIn.cross-sectlonal areaO.rS,ram ks
Fig. 1. Load vs (area)°'Ts graph for Darley Dale Sandstone (data derived from Broeh & Franklin [2] ).
[5]. The constant slope of the graph over a very wide size range is evident, and the slope of the graph could be considered as the "strength index". Stronger rocks could simply be expected to show a greater slope, and weaker rocks a smaller slope. The slope of Fig. 1 is about 15 kN divided by 575 mm ~~, which results in an unusual mixture of units. Unfortunately all rocks do not behave exactly as in Fig. 1. Data from Reichmuth [1] and Broch & Franklin [2] were used to compile Figs 2 and 3. Although an upcurve in Fig. 2, downcurve in Fig. 3, is apparent a straight line could be used to approximate the relationship closely. Figure 4 shows the results of point load tests on local rocks, which exhibit more curvature, a straight line would be less justified, but these are fairly extreme cases. The fact that one limestone yields results with an upcurve, and another a downcurve, would seem to indicate that 0.75 is a suitable general power index to use and there would be little merit in empirically refining the value by extensive rock testing, Usually sandstones tend to give upcurves and the more crystalline rocks downcurves, but this is only a general trend. To use graphs such as Figs 1-4 to obtain a strength index in the more usual form of load/area or 'stress', a
Fig. 3. Load vs (area)°~5 graph for Dolerite (data derived from B r o c h & Franklin [2] ).
standard area must be used. To enable fragmented rocks to be tested with pieces near the standard area, a small size is required. This is proposed as 500 mm 2, as previously [6, 71 and is very near to the cross-sectional area of a 1 inch core. The strength index is then the load for a cross-sectional area of 500 mm 2, divided by this area. i.e. Tso0 =
load at 500 (mm) 2 500(mm)2
(7)
Using the slope of the load vs (area) °'75 graph to obtain this gives: T*oo-
l o a d . . , kN (500)o.7s (Area)O.75 x 500
or,
P T*oo = 211.5 A0.7-----3-... MPa
(8)
with the load P in kN, A in mm 2 and T~0o in MPa. I0
•J
w.,e S
"7/
.,>/ ./
Bedford Limestone
./ o"
/•/ o
,~o
z~o
3~o
Cross- sectionol a reo°r~,mm L~
Fig. 2. Load vs (area) 0'7~ graph for Bedford Limestone Cores (data from Reichmuth [1] ).
Io0
200
Mln.cross - sectlonal eHre~°,Ts ,mm L5
Fig. 4. Load vs (area)°'Ts graphs for White Derbyshire Limestone and Ripponden Sandstone.
Technical Note TABLE 1. VALUES OF POINT LOAD STRENGTH (Tsoo) OBTAINED BY VARIOUS METHODS, FOR PURE DERBYSHIRE LIMESTONE
Mixed sizes Standard sizes By graph By size correction Tsoo Tsoo Tsoo*
Type
Cores Blocks Discs Trimmed pieces Chisel cut pieces
6.44 ___4.7% 6.96 -+ 9.0% 6.60 + 5.8%
6.38 7.06 6.87
6.64 + 8.4% 7.18 __+8.8% 6.76 _ 3.1%
6.39 _+ 9.6%
6.89
6.76 _+ 11%
6.91 + 5.5%
6.97
6.85 _ 13.5%
233 Cores o Discs a Blocks • Trimmedpieces x Chiselcut pieces
tO
/J~,~'
•
Load kN
x
I oj,~ z
~
Derbyshire Limestone
Pure
j
x X
~
i
i
i
150
0
i
t
300
Min. cross-sectional area ° 7 5 ~rnmLs
The designation Tsoo is here used for the strength index obtained directly, or by previous methods l6, 7] and T~oo for the index obtained by equation (8), i.e. 'size corrected' values.
Comparison with other methods Figure 5 shows the results of point load testing five types of specimens of a pure limestone. The general linearity is evident over a size range of about 75-2400 mm 2. Three general ways of obtaining Tsoo are possible, standard size specimens, the use of a log-log plot [6, 7], or size correction. Table 1 shows the very close range of values obtained for the fifteen methods implied, the _ percentages being the sample standard deviations. Figure 6 and Table 2 show a comparison of the graphical and size correction methods for two limestones. Limestone 1 specimens were chisel trimmed core box fragments, trimmed to maintain width greater than depth. Limestone 2 specimens were obtained from a single small fragment, by retesting pieces, down to a cross-sectional area of 32.5 m m 2, with occasional chisel trimming to obtain reasonably regular specimens. Figure 7 and Table 3 compare methods for chisel cut specimens of siltstone from a borehole core. A further variation in technique is to use a log-log regression computation to determine the load for an area of 500 m m 2; this gave the value of Tsoo = 6.86MPa, with a correlation coefficient of 0.9915, but is merely a computational method of conTABLE 2.
POINT
LOAD TESTING FRAGMENTS
Load kN
Limestone 1 Minimum cross-sectional area mm 2
9.38 6.25 3.61 1.73
1155 600 280 96
OF
LIMESTONE
Tsoo* MPa
10.01 10.87 11.15 11.94 Average 10.99 M P a
Limestone 2 3.07 2.01 2.05 1.08 0.76 0.46
~ :
,
435 203 220 121 60 32.5
Average
6.82 7.89 7.58 6.27 7.50 7.15 7.20 M P a
Fig. 5. Load vs (area)°'75 graph for Pure Derbyshire Limestone for
various types of specimen. I0
Limestone I Core box / pieces /
5
T ~~
=11MPa
oo = 7. 2
3
Load kN
v~" f"
++v
Srne
/ +
,
O.5
.,-+/ +
o 3 i
30
i
single fragmeit I
i I i i ii
i
I.
stone 2
5o
i
ioo
()
3 0
t
500
....
i
iooo
Min. cross-sectional oroc ,rnm 2
Fig. 6. Log-log graph of load and area for two limestones, using fragments.
sidering the log-log plot, without the option of ignoring points below the general trend line, which may indicate a flawed specimen. The correspondence between the values obtained is excellent, but is undoubtedly assisted by using specimens with areas above and below the standard size of 500 mm 2. USES OF POINT LOAD TEST The principal use of the test to date has been to estimate the uniaxial compressive strength. Figure 8
Load kN
/
/7
,/ I00
*+o
+/+
Coal measures siltstone
300
•
50O
. i , t L
I000
Min. cross-sectional a r e a , mm 2 Fig. 7. Log-log graph of load and area for chisel trimmed coal measures siltstone specimens.
234
Technical Note
300
o
be the most appropriate to use. The estimate of compressive strength, Co, can be extended [10] to estimate the triaxial behaviour, but the approximate nature of the original estimation must be borne in mind. The point load index can be used directly, as a type of tensile strength measurement of rock. The numerical value of Ts00 is in fact often very close to the Brazilian type tensile strength found from 50 mm dia cores. The index has been used for rocks and rock-like material to design sand/plaster scale models of mine roadways [11, 12] for geometrical scales of ~ t h and ~oth.
Tsoo
Co MPa
• 0 V e ~•0 • o 0 v
o
o
'be
q f • o'II
;o/-"
20O
~,
o/~ o
o
v vo ~ g o
o
•
o
o v
'°oO °I.°.°°'c," 0
I0
5
,~
n
Bienlawski
o
D ' Andrea
•
Leeds University
2b
CONCLUSIONS
Broch 81 Franklin
(1) Size correction of point load tests to a chosen standard size is possible using the expression P T*o0 = 211.5 Ao.7-~,
~s
Tsoo, M P a
Fig. 8. Relationship between compressive strength Cn and point load strength Tsoo.
shows the relationship between these values, with the general trend equation being: compressive strength, Co = 12.5 Tso0
(9)
Data shown in Fig. 8 includes values from Broch & Franklin [2], Bieniawski [3] and D'Andrea et al. [9] with the point load values adjusted where necessary according to equation (8). Whilst the general trend is good, some individual estimates can be as much as 50% in error. The value of 12.5 in equation (9) was first obtained by direct testing of 25 mm dia cores, but D'Andrea et al. [9] quote a constant of 16 for 1 inch cores using equation (2). Multiplying by ~/4, to allow for the use of 'area' rather than 'd' in Tso0, gives a constant of 12.57. Using the size correction of 0.66 for 50 to 25 mm cores given by Broch & Franklin [2], and ~/4, the constant 24 of equation (3) becomes 24 x 0.66 x ~/4 = 12.44, but using equation (8) to derive a size correction factor would imply a constant of 13.40. In view of the scatter of Fig. 8, and that the 24 of equation (3) was derived from tests on 15 rocks and considered only a temporary value [2], compared to 49 rocks by D'Andrea et al. [9] and over 40 rocks by the author, to obtain 12.5. this latter figure would seem to TABLE
3.
POINT
LOAD
TESTING
OF
CHISEL
CUT
MEASURES BOREHOLE CORE
Load kN 5.89 4.13 3.80 3.35 2.60 2.18 1.83 1.18 T5oo by log-log graph Tsoo by log-log regression
Area mm 2 943 630 588 486 400 294 190 112 Average
Tsoo* MPa 7.32 6.95 6.72 6.84 6.15 6.49 7.58 7.73 6.91 MPa 6.87 MPa 6.86 MPa
COAL
but for some rocks errors may arise due to the nonlinearity of the load vs (area) T M graph. The error is not serious if the sizes are near to the standard, and should not exceed 10% even in extreme cases. (2) The method of calculation should include the load and the minimum cross-sectional area of the specimen through the loading points, irrespective of the mode of failure. This enables the most convenient shapes of specimen to be tested, from cores, split cores, discs and blocks, to chisel cut pieces. It is important, however, to maintain 'width' equal to or greater than 'depth' in all cases. Field testing need not be limited to using cores, and specimen preparation by hammer and chisel to produce approximate 'brick' proportional pieces, to be tested across the smallest dimension, is an adequate method. In the laboratory trimming of hard rocks by diamond saw is generally better, but the specimens must then be allowed to dry. (3) Where possible the specimen size should be at or near the standard, here proposed as a minimum cross section of 500 mm 2, e.g. diametral tests of 25 mm dia cores, or 25 mm discs 20 mm deep. For varied size specimens the most accurate technique is to use a loglog plot of 'load' against 'area', but size correction gives almost equally good values. (4) If the specimens are all naturally not the standard size, e.g. long runs of NQ core of diameter 47 mm approx, in isotropic rock, the size correction method is the most convenient, based on direct diametral testing of the core. Semi-circular prisms, or split cores, give results directly comparable to whole cores. (5) It is important to be able to test weak or fragmented sections of core-run, or hand specimens, on the same basis as tests on sound core, and either the log-log plot or the size correction method is convenient. (6) The compressive strength can only be obtained approximately, by the relationship Co = 12.5Ts0o. Whilst such approximations give a readily understood strength value, direct use of the point load strength is equally valid. (7) The calculation method employed can be chosen as the most convenient from a number of options, all of
Technical Note
235
TABLE 4. TYPES OF ROCK SAMPLE, TEST SPECIMENS AND CALCULATIONmental work. Many concerns generously provided rock samples for
testing, particularl.x the National Coal Board, Halifax Tool Company Limited, and local quarries, and gave encouragement by their interest in the work.
METHODSFOR POINT LOADTESTING Type of sample Intact cores of isotropic rock, perhaps including split core lengths Cores intersected by numerous bedding planes or joints
Fragmented samples or cores Block samples of isotropic rock Block samples of bedded rock Hand samples of hard isotropic rock Hand samples of weak or bedded rock
Test specimen type (width /> depth)
Calculation method
Diametral test direct on core or half core
Size correction
Direct testing of discs or parts of discs, chisel trimmed if necessary, cross drilled smaller size cores Selected or trimmed pieces (chisel cut or diamond sawn) Prepared cores or discs, of standard size if possible Prepared discs, cores or blocks
Size correction or direct
Prepared blocks or trimmed pieces (diamond sawn or chisel cut) Prepared blocks (chisel cut or diamond sawn)
Log-log plot or size correction Direct or size correction Direct, size correction or log-log plot Direct, size correction or log-log plot Direct, size correction or log-log plot
which give a consistent strength index. Table 4 summarizes most of the types of samples, specimens and test methods. Acknowledgements---The author gratefully acknowledges the help and encouragement given by his colleagues, and a number of research and undergraduate students for their careful and dependable experi-
Received 21 January 1980.
REFERENCES 1. Reichmuth D. R. Point-load testing of brittle materials to determine tensile strength and relative brittleness. Proc. 9th. Syrup. Rock Mech. Univ. of Colarado, pp. 134-159. Am. Inst. Min. Metall. Petrol. Engrs, New York (1968). 2. Broch E. & Franklin J. A. The point load test. Int. J. Rock Mech. Min. Sci. 9, 669-697 (1972). 3. Bieniawski Z. T. Estimating the strength of rock materials. Jl. S. Aft'. Inst. Min. Metall. 74, 312-320 (1974). 4. Sundae L. S. Effect of specimen volume on apparent strength of three igneous rocks. U.S. Bur. Mines R. I. 7846 (1974). 5. Peng S. S. Stress analysis of cylindrical rock discs subjected to axial double point load, Int, J. Rock Mech. Min. Sci. & Geomech. Abstr. 13, 97-101 (1976). 6. Brook N. A method of overcoming both shape and size effects in point load testing. Proc. ConJ'. Rock Engng. Univ. of Newcastle, pp. 53-70. Br. Geotechnical Soc. London (April, 1977). 7. Brook N. The use of irregular specimens for rock strength tests. Int. J. Rock Mech, Min. Sci. & Geomech. Abstr. 14, 193-201 (1977). 8. Buttiens K. Onderzoek naar correlaties tussen proeven ter bepaling van de rots-karakteristieken (Private communication). Part of "Endwerk", Univ. Leuven (1978). 9. D'Andrea D. V., Fisher R. L. & Fogelson D. E. Prediction of compressive strength of rock from other rock properties. U.S. Bur. Mines. RI 6702 (1965). 10. Brook N. Estimating the triaxial strength of rocks, Technical note. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 16, 261-264 (1979). 11. Brook N. Model studies of mine roadway deformation. Trans. Instn. Min Engrs 136, 375-384 (April, 1977). 12. Rayan A. A. "Application of rock strength tests to physical models". Ph.D. thesis. University of Leeds (1980).
Technical Note Size Correction for Point Load Testing N O R M A N BROOK*
The fundamental relationship between strain energy and strained volume in point load testing is developed to give an analytical method of 'size correction' to a chosen standard size. Possible sources of error when using this method are considered, and comparisons made with other methods of dealing with the size effect. The most convenient methods to use, for various types of rock specimens are detailed. SHAPE AND SIZE EFFECTS IN P O I N T LOAD TESTING The effects of shape for point load tests, and crossed roller tests on cores, were considered by Reichmuth 1-1i, who in order to obtain a constant tensile strength proposed the formula: P St = Ks-~ + K b P (1) where St = tensile strength, P = applied load, h = distance between loading points, K, = shape factor, Kb = brittleness factor. Values of Ks and Kb were obtained experimentally. No size effect was evident with this analysis. B r o c h & Franklin [2-1 simplified the formula to: P Ix = ~ (2) where Is = strength index, P = load, d = distance between loading points, but found that this gave considerable variation in strength values for different sizes and shapes. To overcome the problem, standard cores of 50 mm diameter were proposed as test specimens, with size correction by chart or nomogram for other core sizes. Some correction for testing cylinders axially was proposed, but other shapes required approximation to an equivalent core size. Bieniawski 1-3] confirmed the size effect for cores, and also the relationship between compressive strength, Co, and point load strength of:
This effectively removed shape effects due to variation of the ratio d/t, and reinforced Reichmuth's [11 conclusion that the min. cross sectional area through the loading points was the only factor affecting his values of shape factor, Ks. Peng [5] in a finite element analysis of Sundae's method, concluded that for a stable stress distribution d should be greater than or equal to t. This conflicts with B r o c h & Franklin's I-2] method of axial testing of cylinders. ELIMINATION O F SHAPE AND SIZE EFFECTS If standard specimens, of fixed shape and size, are used the troublesome effects of size and shape are avoided. This method is however very restrictive. The standard size of 50 mm dia cores proposed by Broch & Franklin [2-1 is not easily obtainable in bedded rocks, and may be impossible in weak rocks which fragment on coring or preparation. In previous reports [6, 71, the author has shown that if the stiffness of different sized rock specimens can be considered constant in point load testing, as the deformation is mainly very near the loading points, then considering the strain energy to be proportional to the affected volume of rock, typified by the minimum cross-sectional area A, the relationship between applied load P, and A is: P = K A °'75
(5)
with K a constant depending on the rock 'strength'. This is confirmed, using a similar approach by Buttiens [8], who derived, for cores, the expression: P dt.S - constant,
(6)
with d the core diameter. If the same analysis is applied to the uniaxial compressive strength, the stiffness is not constant, and the Co = 24 1s (3) compressive strength can be shown not to be dependent on size of specimen, provided, of course, that the Sundae (4) used the point load test to study the effect applied stress is uniform. There is little, if any, direct of specimen volume on apparent strength, using disc evidence of this in the literature, but it is generally conshaped specimens, and the formula: sidered to be true. P Figure 1 shows the relationship between applied load Strength = nd--[ (4) a n d A °'75 for Darley Dale Sandstone, using data dewith d = disc diameter, t = thickness. rived from Broch & Franklin 1-2], which using equation (2) shows a strength index variation from about * Department of Mining and Mineral Sciences, University of 2-35 MPa. Specimens with width less than depth have Leeds, Leeds LS2 9JT, U.K. been omitted from Fig. 1, as recommended by Peng 231
232
Technical Note 15 • Cores o Discs t3 Blocks
10
Load kN
/"
/
/
/
5C
Load kN
Darley Dale Sandstone
o ~
/
z
l°
360
'
Dolerlte
./
o '
,60
/
'
,~
s6o
3bo
s6o
'
'
MIn. cross -sectlanal areaO.rS,mrnI -~
MIn.cross-sectlonal areaO.rS,ram ks
Fig. 1. Load vs (area)°'Ts graph for Darley Dale Sandstone (data derived from Broeh & Franklin [2] ).
[5]. The constant slope of the graph over a very wide size range is evident, and the slope of the graph could be considered as the "strength index". Stronger rocks could simply be expected to show a greater slope, and weaker rocks a smaller slope. The slope of Fig. 1 is about 15 kN divided by 575 mm ~~, which results in an unusual mixture of units. Unfortunately all rocks do not behave exactly as in Fig. 1. Data from Reichmuth [1] and Broch & Franklin [2] were used to compile Figs 2 and 3. Although an upcurve in Fig. 2, downcurve in Fig. 3, is apparent a straight line could be used to approximate the relationship closely. Figure 4 shows the results of point load tests on local rocks, which exhibit more curvature, a straight line would be less justified, but these are fairly extreme cases. The fact that one limestone yields results with an upcurve, and another a downcurve, would seem to indicate that 0.75 is a suitable general power index to use and there would be little merit in empirically refining the value by extensive rock testing, Usually sandstones tend to give upcurves and the more crystalline rocks downcurves, but this is only a general trend. To use graphs such as Figs 1-4 to obtain a strength index in the more usual form of load/area or 'stress', a
Fig. 3. Load vs (area)°~5 graph for Dolerite (data derived from B r o c h & Franklin [2] ).
standard area must be used. To enable fragmented rocks to be tested with pieces near the standard area, a small size is required. This is proposed as 500 mm 2, as previously [6, 71 and is very near to the cross-sectional area of a 1 inch core. The strength index is then the load for a cross-sectional area of 500 mm 2, divided by this area. i.e. Tso0 =
load at 500 (mm) 2 500(mm)2
(7)
Using the slope of the load vs (area) °'75 graph to obtain this gives: T*oo-
l o a d . . , kN (500)o.7s (Area)O.75 x 500
or,
P T*oo = 211.5 A0.7-----3-... MPa
(8)
with the load P in kN, A in mm 2 and T~0o in MPa. I0
•J
w.,e S
"7/
.,>/ ./
Bedford Limestone
./ o"
/•/ o
,~o
z~o
3~o
Cross- sectionol a reo°r~,mm L~
Fig. 2. Load vs (area) 0'7~ graph for Bedford Limestone Cores (data from Reichmuth [1] ).
Io0
200
Mln.cross - sectlonal eHre~°,Ts ,mm L5
Fig. 4. Load vs (area)°'Ts graphs for White Derbyshire Limestone and Ripponden Sandstone.
Technical Note TABLE 1. VALUES OF POINT LOAD STRENGTH (Tsoo) OBTAINED BY VARIOUS METHODS, FOR PURE DERBYSHIRE LIMESTONE
Mixed sizes Standard sizes By graph By size correction Tsoo Tsoo Tsoo*
Type
Cores Blocks Discs Trimmed pieces Chisel cut pieces
6.44 ___4.7% 6.96 -+ 9.0% 6.60 + 5.8%
6.38 7.06 6.87
6.64 + 8.4% 7.18 __+8.8% 6.76 _ 3.1%
6.39 _+ 9.6%
6.89
6.76 _+ 11%
6.91 + 5.5%
6.97
6.85 _ 13.5%
233 Cores o Discs a Blocks • Trimmedpieces x Chiselcut pieces
tO
/J~,~'
•
Load kN
x
I oj,~ z
~
Derbyshire Limestone
Pure
j
x X
~
i
i
i
150
0
i
t
300
Min. cross-sectional area ° 7 5 ~rnmLs
The designation Tsoo is here used for the strength index obtained directly, or by previous methods l6, 7] and T~oo for the index obtained by equation (8), i.e. 'size corrected' values.
Comparison with other methods Figure 5 shows the results of point load testing five types of specimens of a pure limestone. The general linearity is evident over a size range of about 75-2400 mm 2. Three general ways of obtaining Tsoo are possible, standard size specimens, the use of a log-log plot [6, 7], or size correction. Table 1 shows the very close range of values obtained for the fifteen methods implied, the _ percentages being the sample standard deviations. Figure 6 and Table 2 show a comparison of the graphical and size correction methods for two limestones. Limestone 1 specimens were chisel trimmed core box fragments, trimmed to maintain width greater than depth. Limestone 2 specimens were obtained from a single small fragment, by retesting pieces, down to a cross-sectional area of 32.5 m m 2, with occasional chisel trimming to obtain reasonably regular specimens. Figure 7 and Table 3 compare methods for chisel cut specimens of siltstone from a borehole core. A further variation in technique is to use a log-log regression computation to determine the load for an area of 500 m m 2; this gave the value of Tsoo = 6.86MPa, with a correlation coefficient of 0.9915, but is merely a computational method of conTABLE 2.
POINT
LOAD TESTING FRAGMENTS
Load kN
Limestone 1 Minimum cross-sectional area mm 2
9.38 6.25 3.61 1.73
1155 600 280 96
OF
LIMESTONE
Tsoo* MPa
10.01 10.87 11.15 11.94 Average 10.99 M P a
Limestone 2 3.07 2.01 2.05 1.08 0.76 0.46
~ :
,
435 203 220 121 60 32.5
Average
6.82 7.89 7.58 6.27 7.50 7.15 7.20 M P a
Fig. 5. Load vs (area)°'75 graph for Pure Derbyshire Limestone for
various types of specimen. I0
Limestone I Core box / pieces /
5
T ~~
=11MPa
oo = 7. 2
3
Load kN
v~" f"
++v
Srne
/ +
,
O.5
.,-+/ +
o 3 i
30
i
single fragmeit I
i I i i ii
i
I.
stone 2
5o
i
ioo
()
3 0
t
500
....
i
iooo
Min. cross-sectional oroc ,rnm 2
Fig. 6. Log-log graph of load and area for two limestones, using fragments.
sidering the log-log plot, without the option of ignoring points below the general trend line, which may indicate a flawed specimen. The correspondence between the values obtained is excellent, but is undoubtedly assisted by using specimens with areas above and below the standard size of 500 mm 2. USES OF POINT LOAD TEST The principal use of the test to date has been to estimate the uniaxial compressive strength. Figure 8
Load kN
/
/7
,/ I00
*+o
+/+
Coal measures siltstone
300
•
50O
. i , t L
I000
Min. cross-sectional a r e a , mm 2 Fig. 7. Log-log graph of load and area for chisel trimmed coal measures siltstone specimens.
234
Technical Note
300
o
be the most appropriate to use. The estimate of compressive strength, Co, can be extended [10] to estimate the triaxial behaviour, but the approximate nature of the original estimation must be borne in mind. The point load index can be used directly, as a type of tensile strength measurement of rock. The numerical value of Ts00 is in fact often very close to the Brazilian type tensile strength found from 50 mm dia cores. The index has been used for rocks and rock-like material to design sand/plaster scale models of mine roadways [11, 12] for geometrical scales of ~ t h and ~oth.
Tsoo
Co MPa
• 0 V e ~•0 • o 0 v
o
o
'be
q f • o'II
;o/-"
20O
~,
o/~ o
o
v vo ~ g o
o
•
o
o v
'°oO °I.°.°°'c," 0
I0
5
,~
n
Bienlawski
o
D ' Andrea
•
Leeds University
2b
CONCLUSIONS
Broch 81 Franklin
(1) Size correction of point load tests to a chosen standard size is possible using the expression P T*o0 = 211.5 Ao.7-~,
~s
Tsoo, M P a
Fig. 8. Relationship between compressive strength Cn and point load strength Tsoo.
shows the relationship between these values, with the general trend equation being: compressive strength, Co = 12.5 Tso0
(9)
Data shown in Fig. 8 includes values from Broch & Franklin [2], Bieniawski [3] and D'Andrea et al. [9] with the point load values adjusted where necessary according to equation (8). Whilst the general trend is good, some individual estimates can be as much as 50% in error. The value of 12.5 in equation (9) was first obtained by direct testing of 25 mm dia cores, but D'Andrea et al. [9] quote a constant of 16 for 1 inch cores using equation (2). Multiplying by ~/4, to allow for the use of 'area' rather than 'd' in Tso0, gives a constant of 12.57. Using the size correction of 0.66 for 50 to 25 mm cores given by Broch & Franklin [2], and ~/4, the constant 24 of equation (3) becomes 24 x 0.66 x ~/4 = 12.44, but using equation (8) to derive a size correction factor would imply a constant of 13.40. In view of the scatter of Fig. 8, and that the 24 of equation (3) was derived from tests on 15 rocks and considered only a temporary value [2], compared to 49 rocks by D'Andrea et al. [9] and over 40 rocks by the author, to obtain 12.5. this latter figure would seem to TABLE
3.
POINT
LOAD
TESTING
OF
CHISEL
CUT
MEASURES BOREHOLE CORE
Load kN 5.89 4.13 3.80 3.35 2.60 2.18 1.83 1.18 T5oo by log-log graph Tsoo by log-log regression
Area mm 2 943 630 588 486 400 294 190 112 Average
Tsoo* MPa 7.32 6.95 6.72 6.84 6.15 6.49 7.58 7.73 6.91 MPa 6.87 MPa 6.86 MPa
COAL
but for some rocks errors may arise due to the nonlinearity of the load vs (area) T M graph. The error is not serious if the sizes are near to the standard, and should not exceed 10% even in extreme cases. (2) The method of calculation should include the load and the minimum cross-sectional area of the specimen through the loading points, irrespective of the mode of failure. This enables the most convenient shapes of specimen to be tested, from cores, split cores, discs and blocks, to chisel cut pieces. It is important, however, to maintain 'width' equal to or greater than 'depth' in all cases. Field testing need not be limited to using cores, and specimen preparation by hammer and chisel to produce approximate 'brick' proportional pieces, to be tested across the smallest dimension, is an adequate method. In the laboratory trimming of hard rocks by diamond saw is generally better, but the specimens must then be allowed to dry. (3) Where possible the specimen size should be at or near the standard, here proposed as a minimum cross section of 500 mm 2, e.g. diametral tests of 25 mm dia cores, or 25 mm discs 20 mm deep. For varied size specimens the most accurate technique is to use a loglog plot of 'load' against 'area', but size correction gives almost equally good values. (4) If the specimens are all naturally not the standard size, e.g. long runs of NQ core of diameter 47 mm approx, in isotropic rock, the size correction method is the most convenient, based on direct diametral testing of the core. Semi-circular prisms, or split cores, give results directly comparable to whole cores. (5) It is important to be able to test weak or fragmented sections of core-run, or hand specimens, on the same basis as tests on sound core, and either the log-log plot or the size correction method is convenient. (6) The compressive strength can only be obtained approximately, by the relationship Co = 12.5Ts0o. Whilst such approximations give a readily understood strength value, direct use of the point load strength is equally valid. (7) The calculation method employed can be chosen as the most convenient from a number of options, all of
Technical Note
235
TABLE 4. TYPES OF ROCK SAMPLE, TEST SPECIMENS AND CALCULATIONmental work. Many concerns generously provided rock samples for
testing, particularl.x the National Coal Board, Halifax Tool Company Limited, and local quarries, and gave encouragement by their interest in the work.
METHODSFOR POINT LOADTESTING Type of sample Intact cores of isotropic rock, perhaps including split core lengths Cores intersected by numerous bedding planes or joints
Fragmented samples or cores Block samples of isotropic rock Block samples of bedded rock Hand samples of hard isotropic rock Hand samples of weak or bedded rock
Test specimen type (width /> depth)
Calculation method
Diametral test direct on core or half core
Size correction
Direct testing of discs or parts of discs, chisel trimmed if necessary, cross drilled smaller size cores Selected or trimmed pieces (chisel cut or diamond sawn) Prepared cores or discs, of standard size if possible Prepared discs, cores or blocks
Size correction or direct
Prepared blocks or trimmed pieces (diamond sawn or chisel cut) Prepared blocks (chisel cut or diamond sawn)
Log-log plot or size correction Direct or size correction Direct, size correction or log-log plot Direct, size correction or log-log plot Direct, size correction or log-log plot
which give a consistent strength index. Table 4 summarizes most of the types of samples, specimens and test methods. Acknowledgements---The author gratefully acknowledges the help and encouragement given by his colleagues, and a number of research and undergraduate students for their careful and dependable experi-
Received 21 January 1980.
REFERENCES 1. Reichmuth D. R. Point-load testing of brittle materials to determine tensile strength and relative brittleness. Proc. 9th. Syrup. Rock Mech. Univ. of Colarado, pp. 134-159. Am. Inst. Min. Metall. Petrol. Engrs, New York (1968). 2. Broch E. & Franklin J. A. The point load test. Int. J. Rock Mech. Min. Sci. 9, 669-697 (1972). 3. Bieniawski Z. T. Estimating the strength of rock materials. Jl. S. Aft'. Inst. Min. Metall. 74, 312-320 (1974). 4. Sundae L. S. Effect of specimen volume on apparent strength of three igneous rocks. U.S. Bur. Mines R. I. 7846 (1974). 5. Peng S. S. Stress analysis of cylindrical rock discs subjected to axial double point load, Int, J. Rock Mech. Min. Sci. & Geomech. Abstr. 13, 97-101 (1976). 6. Brook N. A method of overcoming both shape and size effects in point load testing. Proc. ConJ'. Rock Engng. Univ. of Newcastle, pp. 53-70. Br. Geotechnical Soc. London (April, 1977). 7. Brook N. The use of irregular specimens for rock strength tests. Int. J. Rock Mech, Min. Sci. & Geomech. Abstr. 14, 193-201 (1977). 8. Buttiens K. Onderzoek naar correlaties tussen proeven ter bepaling van de rots-karakteristieken (Private communication). Part of "Endwerk", Univ. Leuven (1978). 9. D'Andrea D. V., Fisher R. L. & Fogelson D. E. Prediction of compressive strength of rock from other rock properties. U.S. Bur. Mines. RI 6702 (1965). 10. Brook N. Estimating the triaxial strength of rocks, Technical note. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 16, 261-264 (1979). 11. Brook N. Model studies of mine roadway deformation. Trans. Instn. Min Engrs 136, 375-384 (April, 1977). 12. Rayan A. A. "Application of rock strength tests to physical models". Ph.D. thesis. University of Leeds (1980).