Correlaciones Vp

Bull Eng Geol Environ (2008) 67:17–22
DOI 10.1007/s10064-007-0109-y
ORIGINAL PAPER
A correlation between P-wave velocity, impact strength index,
slake durability index and uniaxial compressive strength
P. K. Sharma Æ T. N. Singh
Received: 10 February 2007 / Accepted: 14 July 2007 / Published online: 5 October 2007
Ó Springer-Verlag 2007
Abstract Impact strength index, slake durability index
and uniaxial compressive strength (UCS) are important
properties of a rock mass which are used widely in geological and geotechnical engineering. In this study, the
mechanical properties of one igneous, three sedimentary
and three metamorphic rock types were determined in the
laboratory and correlated with P-wave velocity. Empirical
equations have been developed to predict the impact
strength index, slake durability index and UCS from
P-wave velocity, which may avoid the necessity for timeconsuming and tedious laboratory testing. To check the
sensitivity of the empirical relations, a t test was performed
which confirmed the validity of the proposed correlations.
resistance a la compression simple a partir de la vitesse des
ondes P, ce qui permet d’eviter de realiser des essais de
laboratoire consommateurs de temps. Afin de verifier la
sensibilite des relations empiriques etablies, Ie test t de
Student a ete mis en ceuvre et a permis de confirmer la
validite des correlations proposees.
Keywords Impact strength index P-wave velocity Slake durability index t test Uniaxial compressive strength
Seismic techniques are often employed to determine and
characterize the dynamic properties of rocks. As these
techniques are non-destructive and relatively easy to apply,
they are increasingly being used in geological and geotechnical engineering. Attempts have been made to assess
grouting, rock bolt reinforcement and blasting efficiencies
in the rock mass by the seismic velocity (Knill 1970; Price
et al. 1970; Young et al. 1985). The prediction of rock mass
deformation and stress as well as the extent of damage
zones (EDZ) developed around underground openings are
other applications of the seismic techniques (Onodera
1963; Hudson et al. 1980; Gladwin 1982). Various
researchers have found that sound velocity is closely
related to rock properties (Deere and Miller 1966;
D’Andrea et al. 1965; Saito et al. 1974; Gardner et al.
1974; Youash 1970; Lama et al. 1978; Inoue and Ohomi
1981; Gaviglio 1989).
There are a number of factors that influence the P-wave
velocity in rocks including lithology, density, shape and
size, porosity, anisotropy, pore water, confining pressure,
temperature as well as the properties of the rock as a mass,
Résumé L’indice de durete, l’indlce d’alterabilite et la
resistance a la compression simple sont des proprietes
importantes d’une roche, largement utilisees en geologie de
l’ingenieur et en geotechnique. Dans cette etude, les proprietes mecaniques d’une roche magmatique, de trois
roches sedimentaires et d’une roche metamorphique ont ete
determinees au laboratoire et correlees avec les vitesses des
ondes P. Des equations empiriques ont ete etablies pour
obtenir l’indice de durete, l’indice d’alterabilite et la
P. K. Sharma (&) T. N. Singh
Department of Earth Sciences, Indian Institute of Technology
Bombay, Powai, Mumbai 400 076, India
e-mail: [email protected]
T. N. Singh
e-mail: [email protected]
Mots clés Impact grosseur indice P-brandir velocite Slake durabilite indice t test Une-axial compressive grosseur
Introduction
123
18
P. K. Sharma, T. N. Singh
e.g. weathering and alteration zones, bedding planes and
joint properties (filling material, water, dip and strike etc.).
This paper reports an attempt to establish a correlation
between P-wave velocity and impact strength index, slake
durability index and uniaxial compressive strength (UCS),
using seven types of rock: one igneous, three sedimentary
and three metamorphic (Table 1).
Field studies
Schmidt hammer tests were performed on site prior to the
collection of the rock blocks for the laboratory testing.
During sample collection, each block was inspected for
macroscopic defects to ensure it would provide test
specimens free from fractures and joints. The Schmidt
hammer tests were performed with an N-type hammer
having impact energy of 2.207 N m. The hammer was
held vertically downwards and at right angles to the
horizontal rock faces to avoid the necessity for a correction factor to obtain a UCS value. Ten readings were
taken and the mean of the five highest values was used to
calculate the average UCS.
Laboratory studies
Ultrasonic testing of the rock specimens
The velocity of ultrasonic pulses travelling in a solid
material depends on the density and elastic properties of the
material. The quality of some materials may be related to
their elastic stiffness, such that the measurement of ultrasonic pulse velocity can be used to indicate their quality as
well as to determine elastic properties. To determine a
comparable P-wave velocity of different rocks, the blocks
were cored to provide NX (50 mm) cylinders. The
P-wave velocity was determined using a Portable Ultrasonic
Table 1 Name and geological horizon of the tested rock samples
Rock type
Rock class
Geological location
Sandstone A
Sedimentary
Lower Siwalik
Sandstone B
Sedimentary
Lower Siwalik
Sandstone C
Sedimentary
Lower Siwalik
Weathered Basalt
Igneous
Deccan Trap
Greenish Phyllite
Metamorphic
Rampur-Wantung Series
Brownish Phyllite
Metamorphic
Rampur-Wantung Series
Quartz Mica Schist
Metamorphic
Rampur-Wantung Series
Coal
Sedimentary
Lower Gondwana (Singrauli)
Shaly Rock
Sedimentary
Lower Gondwana (Jharia)
123
Nondestructive Digital Indicating Tester (PUNDIT); the
results are given in Table 2.
Impact strength test
The impact strength test was first developed by Protodyakonov, and then it was used by Evans and Pomeroy
(1966) for the classification of coal seams in the former
USSR and UK. The test was then modified by Paone et al.
(1969), Tandanand and Unger (1975), and Rabia and Brook
(1980). Tandanand and Unger (1975) obtained a simple
relation between strength coefficient and UCS. Rabia and
Brook (1980) used the modified test apparatus to determine
the rock impact hardness number and developed an
empirical equation for predicting drilling rates for both
DTH and drifter drills.
Hobbs (1964) applied this test to various rocks and
established the following equation:
qu ¼ 53 ISI 2509;
ð1Þ
2
where qu is the UCS (kgf/cm ) and ISI is the impact
strength index.
To carry out this test, fragments of rocks were impacted
20 times by a 41b (1.81 kg) plunger falling 12in.
(305 mm). The amount of fines below 1/8 in. (3.18 mm) is
considered as the strength index.
The results of impact strength test on different rocks are
illustrated in Tables 2 and 3.
Slake durability test
The slake durability of a rock is an important property and
is closely related to its mineralogical composition and
hence its resistance to degradation (weakening and disintegration) and is measured using a standard cycle of drying
and wetting.
The test was carried out following ISRM (1979). The
sample comprised of nine lumps, roughly spherical in
shape, each weighing 50 ± 10 g. These were placed in a
drum and dried in an oven at 105°C for a duration of 4–5 h
until a constant weight was obtained. For the slake durability test the drum was mounted on a trough and coupled
to the motor. The trough was then filled with water to a
level of 20 mm below the drum axis and the temperature
maintained at 25°C. After the drum had been rotated at
20 rpm for a period of 10 min, it was removed from the
trough and dried at a temperature of 105°C for 4 h. During
the test, the finer products of slaking pass through the mesh
and into the water bath. The slake durability index (Id) is
the percentage ratio of final to the initial dry weight of rock
in the drum (Singh et al. 2004).
Correlation P-wave velocity with strength
Table 2 Different properties
of rocks
19
Rock type
P-wave
velocity
(m/s)
Impact strength
index (%)
Slake durability
index (%)
Av. uniaxial
compressive
strength (MPa)
Sandstone A-1
2129.1
82.1
94.28
27
Sandstone A-2
2132.7
80.8
94.22
26
Sandstone A-3
2152.7
82.6
95.23
29
Sandstone A-4
2198.2
82.1
94.35
30
Sandstone A-5
2153.5
82.4
93.33
22
Sandstone B-1
2296.9
85.2
95.59
30
Sandstone B-2
Sandstone B-3
2378.8
2345.9
83.8
85.3
94.51
95.42
36
30
Sandstone B-4
2290.2
82.2
94.56
34
Sandstone B-5
2183.4
85.9
95.03
29
Sandstone B-6
2111.8
84.9
94.56
29
Sandstone B-7
2240.1
86.4
95.65
31
Sandstone C-1
2465.3
86.3
96.12
37
Sandstone C-2
2212.1
84.9
94.42
32
Sandstone C-3
2428.8
87.5
94.41
42
Sandstone C-4
2517.6
89.5
96.36
48
Sandstone C-5
2554.7
89.2
96.51
52
Weathered Basalt-1
2853
92.6
98.92
66
Weathered Basalt-2
2730.2
91.9
96.98
58
Weathered Basalt-3
2899.6
93.9
97.78
64
Weathered Basalt-4
3026.2
91.9
97.67
72
Greenish Phyllite-1
Greenish Phyllite-2
2007.3
1845
82.3
80.2
91.94
90.23
4.6
4.4
Greenish Phyllite-3
1903.1
81.2
90.23
4.9
Greenish Phyllite-4
1925.4
82.2
91.45
4.8
Brownish Phyllite-1
2010.9
82.2
92.88
4.9
Brownish Phyllite-2
2025.3
80.2
91.98
5
Brownish Phyllite-3
2035.5
81.6
91.98
5.2
Brownish Phyllite-4
1947
81.3
91.12
5.2
Quartz Mica Schist-1
2250.8
82.4
93.9
22.2
Quartz Mica Schist-2
2214.2
83.1
93.65
19.6
Quartz Mica Schist-3
2224.1
82.4
93.25
22.3
Quartz Mica Schist-4
2298
84.5
93.65
24.8
Coal -1
2031.3
83.6
93.51
9.5
Coal -2
2078.2
84.2
92.23
8.2
Coal -3
2012.3
83.2
91.23
8.5
Coal -4
2123
85.2
92.25
9.5
Coal -5
Shaly Rock-1
2113.6
2287.2
84.3
85.3
91.65
94.87
8.2
26
Shaly Rock-2
2100.1
82.4
93.35
22
Shaly Rock-3
2142
82.9
93.4
25
Shaly Rock-4
2159.3
81.5
93.24
24
Shaly Rock-5
2211
82.4
93.65
25
Shaly Rock-6
2280
85.3
95.44
26
Shaly Rock-7
2290.2
86.1
95.46
26
Shaly Rock-8
2274.9
84.9
95.6
28
Shaly Rock-9
2312.9
85.9
95.5
27
Shaly Rock-10
2314.2
86.5
94.36
27
123
P. K. Sharma, T. N. Singh
Table 3 Relation between P-wave velocity and UCS reported by
various researchers
Emperical relation
Coefficient of Researchers
determination
(r)
Y = axb
0.880
Mccann et al. (1990)
qu = 9.95V1.21
P
0.83
Kahraman (2001)
SV = 0.0317rc + 2.0195
0.80
Yasar and
Erdogan (2004)
Y = aebx(a = 0.78, b = 0.88)
0.533
Entwisle et al. (2005)
b
Y = ax (a = 0.78, b = 0.88)
0.531
Entwisle et al. (2005)
UCS = 0.0642VP – 117.99
0.9022
Proposed
Slake Durabi li ty Index (%)
20
y = 0.0069x + 78.577
R2 = 0.7831
101
99
97
95
93
91
89
1800
2300
2800
3300
P-wave velocity (m/s)
Fig. 2 P-wave velocity versus slake durability index
Slake durability index ðIdÞ ¼ ðC EÞ= ðA EÞ 100%
ð2Þ
ISI ¼ 0:0118 VP þ 58:105
ð3Þ
where A = Initial weight of sample + drum (kg), C =
Weight of sample + drum after second cycle of rotation
(kg), and E = Weight of empty drum.
Where VP and ISI are P-wave velocity and impact strength
index, respectively.
Similarly a linear relationship was observed between Pwave velocity and slake durability with a correlation
coefficient of 0.7831 (Fig. 2).
The equation of this relation is:
Statistical analysis
Id ¼ 0:0069 VP þ 78:577
In order to describe the relationship between P-wave
velocity and other tests, such as impact strength index,
slake durability index and UCS of the tested rocks,
regression analyses were made. The equation of the best fit
line, the 95% confidence level and the correlation coefficient (r) were determined for each test result. As can be
seen from Figs. 1, 2, 3, in each case, the best fitted relation
was found to be represented by linear regression curves.
The plot of the P-wave velocity as a function of impact
strength index is shown in Fig. 1. There is a linear relationship between P-wave velocity and impact strength
index for all the rock types. A strong correlation
(r = 0.8107) was also found between P-wave velocity and
the impact strength index for all rock types (Eq. 3).
where Id is the slake durability index.
Kahraman (2001) reported an empirical relation
between P-wave velocity and UCS with a regression
coefficient 0.83 whereas Yasar and Erdogan (2004) found a
relation with a regression coefficient of 0.80. However, in
this study a strong correlation (r = 0.9022) was found
between P-wave velocity and the UCS for all tested rocks
(Eq. 5)
ð4Þ
UCS ¼ 0:0642 VP 117:99
ð5Þ
The significance of r values can be determined by the t test,
assuming that both variables are normally distributed and
the observations are chosen randomly. The t test compares
the computed t value with the tabulated t value using the
y = 0.0118x + 58.105
94
R2 = 0.8107
92
90
88
86
84
82
80
78
1600
1800
2000
2200
2400
2600
2800
P-wave velocity (m/s)
Fig. 1 P-wave velocity versus impact strength index
123
3000
3200
Uni axial Compressi ve Strength
(MPa)
Impact Strength Index (%)
96
90
y = 0.0642x - 117.99
R2 = 0.9022
80
70
60
50
40
30
20
10
0
1800
2000
2200
2400
2600
2800
P-wave velocity (m/s)
Fig. 3 P-wave velocity versus UCS
3000
3200
21
Table 4 Student’s t test
Rock tests
t test
Calculated
value
Tabulated
value
1. P-wave velocity and impact
strength index
61.08
2.02
2. P-wave velocity and slake
durability index
60.51
2.02
3. P-wave velocity and UCS
66.23
2.02
Predicted Slake Durability
Index (%)
Correlation P-wave velocity with strength
99
97
95
93
91
89
89
91
95
93
99
97
Observed Slake Durability Index (%)
Fig. 5 Observed versus predicted slake durability index
Predicted UCS (MPa)
null hypothesis. In this test, a 95% confidence level was
chosen. If the computed t value is greater than the tabulated
t value, the null hypothesis is rejected. This means that ‘‘r’’
is significant. Using a 95% confidence level, a corresponding critical t value 2.02 is obtained from the related
tables. It can be seen from Table 4 that all the computed t
values are greater than the tabulated t vales, indicating a
real correlation of P-wave velocity with impact strength
index, slake durability index and UCS.
The empirical methods used in this study were evaluated
by comparing their results with each other. Data from each
test were used in the respective empirical equation to calculate the other properties. The predicted values of impact
strength index, slake durability index and UCS values were
then plotted against the measured values for all tested rocks
using a 1:1 slope line (Figs. 4, 5, 6). A point lying on the
1:1 slope line indicates an exact correlation. The figures
indicate that P-wave velocity is a reliable method for
estimating impact strength index, slake durability index
and UCS avoiding cumbersome and time consuming test
methods.
80
70
60
50
40
30
20
10
0
0
20
40
60
80
Observed UCS (MPa)
Fig. 6 Observed versus predicted UCS
using various standard methods in the laboratory. The
following empirical equations have been developed.
ISI ¼ 0:0118 VP þ 58:105
Id ¼ 0:0069 VP þ 78:577
ðr ¼ 0:8107Þ
ðr ¼ 0:7831Þ
Conclusions
UCS ¼ 0:0642 VP 117:99 ðr ¼ 0:9022Þ
Predicted Impact Strength
Index (%)
The P-wave velocity, impact strength index, slake durability index and UCS for seven rock types were determined
96
94
92
90
88
86
84
82
80
78
The test results were interpreted statistically and significant
linear relationships were found.
The study has shown that impact strength index, slake
durability index and UCS can be estimated by the use of Pwave velocity with the given empirical equations for similar types of rock mass. Such a correlation can provide a
good estimation of such properties as impact strength
index, slake durability index and uniaxial compressive
strength, which in many cases can avoid time-consuming
and tedious test methods.
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78
83
88
93
Observed Impact Strength Index (%)
Fig. 4 Observed versus predicted impact strength index
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