Rock properties and laboratory testing
3.3 UNIAXIAL COMPRESSIVE STRENGTH TEST
3.3.2 Test procedure
σ – φ
c=2 φ 1
c cos
sin (3.3)
where c and ϕ are the cohesion and friction angles of the rock, respectively.
3.3.2 Test procedure
The test is quite simple and the interpretation is fairly straightforward.
A cylindrical core of at least 54 mm in diameter (NX core) and length/
diameter ratio of 2.0–3.0 (ISRM suggests 2.5–3.0 and ASTM D 7012 suggests 2.0–2.5) is subjected to an axial load that is increased to failure.
The specimen is loaded axially using spherical seating, at a constant rate of strain or stress such that it fails in 5–15 minutes. Alternatively, the stress rate shall be in the range of 0.5–1.0 MPa/s. The axial loads at failure can be very large for large diameter cores in good quality intact igneous rocks.
Uniaxial compressive strength is the maximum load carried by the speci-men divided by the cross-sectional area.
The change in the specimen length is measured throughout the test, using a dial gauge or an LVDT (linear variable differential transformer). These days, it is common to use sophisticated data acquisition systems that would keep track of the load–deformation data. Figure 3.4a shows a UCS test in progress on an MTS universal testing machine with axial load capacity of 1000 kN and a data acquisition system. To prevent injury from flying rock fragments on failure, a protective shield should be placed around the test specimen as shown in the figure. The load–displacement plot generated from the MTS machine, for a rock specimen, is shown in Figure 3.4b.
From the load and displacement measured throughout the loading, the stress–strain plot can be generated. From the stress–strain plot, Young’s modulus (E) can be computed. Young’s modulus is a measure of the rock stiffness, which is required in modelling the rock and for computing defor-mations, where the rock is assumed to be an elastic continuum. You may recall Hooke’s law from the study of the strength of materials, which states
that stress is proportional to the strain in a linear elastic material. Young’s modulus is the slope of the stress–strain plot. In reality, rocks are not lin-early elastic and the stress–strain plot is not a straight line. There are a few different ways of defining Young’s modulus here. The tangent modulus (Et) is defined as the slope of a tangent to the stress–strain plot (Figure 3.5a).
(a) 400 Sample ID: DR324/05
Dia = 50.5 mm Length = 129 mm Depth = 441.0 m Failure load = 381 kN Failure strain = 0.9%
Eav = 29 GPa UCS = 190 MPa 350
300
250
Load (kN)
0 0.5 1
Displacement (mm) (b)
1.5 2
200
150
100
50
Figure 3.4 (a) UCS test on an MTS universal testing machine and (b) load–displacement plot.
The secant modulus (Es) is defined as the slope of a line joining a point on the stress–strain plot to the centre (Figure 3.5b). When the stress–strain plot is not linear, the tangent and secant moduli can vary depending on the stress level. It is common to measure the tangent and secant Young’s modulus at 50% of σc. Alternatively, an average Young’s modulus Eav can be determined as the slope of the straight line portion of the stress–strain plot (Figure 3.5c).
By measuring diametrical or circumferential strains during loading, Poisson’s ratio can be measured. Poisson’s ratio v is defined as
ν ε applied axial stress in a UCS test on a rock specimen is shown in Figure 3.6.
Here, diametrical strain is the same as the circumferential strain, defined as the ratio of the change in diameter (or circumference) to the original diame-ter (or circumference). The volumetric strain (εvol) of the specimen is given by
εvol =εa+ 2d (3.5)
Poisson’s ratio for a common engineering material varies in the range of 0–0.5. Typical values of Poisson’s ratio for common rock types are given in Table 3.3. Hawkes and Mellor (1970) discussed various aspects of the UCS laboratory test procedure in great detail. Typical values of the uniaxial compressive strength for some major rock types, as suggested by Hudson (1989), are given in Figure 3.7. As seen here, the UCS values are in the range of 0–350 MPa for most rocks. The axial strain at failure is a measure of the ductility of the intact rock. Qualitative descriptions of materials as ductile,
(a)
Figure 3.5 Young’s modulus: (a) tangent modulus, (b) secant modulus and (c) average modulus.
Diametric strain, εd +
– Axial strain, εa
Axial stress, σ
σc
Figure 3.6 Variation of axial and diametrical strains with the applied axial stress.
Table 3.3 Typical values of Poisson’s ratio for rocks
Rock type ν
Andesite 0.20–0.35
Basalt 0.10–0.35
Conglomerate 0.10–0.40
Diabase 0.10–0.28
Diorite 0.20–0.30
Dolerite 0.15–0.35
Dolomite 0.10–0.35
Gneiss 0.10–0.30
Granite 0.10–0.33
Granodiorite 0.15–0.25
Greywacke 0.08–0.23
Limestone 0.10–0.33
Marble 0.15–0.30
Marl 0.13–0.33
Norite 0.20–0.25
Quartzite 0.10–0.33
Rock salt 0.05–0.30
Sandstone 0.05–0.40
Shale 0.05–0.32
Siltstone 0.05–0.35
Tuff 0.10–0.28
Source: Gercek, H., Int. J. Rock Mech. Min. Sci., 44, 1–13, 2007.
brittle and so on based on failure strains, as suggested by Handin (1966), are given in Table 3.4.
Young’s modulus and Poisson’s ratio are the two crucial parameters in defining the rock behaviour when it is assumed to behave as a linear elastic material, obeying Hooke’s law. They are related to the bulk modulus K and shear modulus G by
K E
= −
( )
3 1 2ν
(3.6) and
G E
=2 1( +ν) (3.7)
Quartzite Basalt
Dolerite Granite Limestone Sandstone Shale
0 50 100 150
Uniaxial compressive strength, σ200 c (MPa)250 300 350 Figure 3.7 Typical values for uniaxial compressive strengths of common rock types.
(Adapted from Hudson, J.A., Rock Mechanics Principles in Engineering Practice, Butterworths, London, 1989.)
Table 3.4 Relative ductility based on axial strain at peak load
Classification Axial strain (%)
Very brittle <1
Brittle 1–5
Moderately brittlea (transitional) 2–8
Moderately ductile 5–10
Ductile > 10
Source: Handin, J., Handbook of Physical Contacts, Geological Society of America, New York, 1966.
a Note the overlap.
EXAMPLE 3.1
A 50.5-mm-diameter, 129-mm-long rock specimen is subjected to a uniaxial compression test. The load–displacement plot is shown in Figure 3.4b. Determine the uniaxial strength and Young’s modulus of the intact rock specimen.
Solution
Noting that there was no load for displacement up to 0.6 mm, the origin (i.e., the load axis) is shifted to displacement of 0.6 mm. The cross-sectional area A of the specimen is given by
25.252 2003.0 mm2
A= π × =
The failure load = 381 kN
∴ UCS = 381,000/2003 MPa = 190.2 MPa
Considering the linear segment of the load–displacement plot between displacements of 1.0 and 1.5 mm in Figure 3.4b,
E P L
A semi-quantitative classification of rocks, based on the uniaxial com-pressive strength and Young’s modulus, proposed by Hawkes and Mellor (1970), is shown in Figure 3.8. Here, the modulus ratio is the ratio of the Young’s modulus E to the uniaxial compressive strength σc. In concrete, this ratio is about 1000, which is well above the upper end of the values for rocks. The cut-off values used for the UCS in Figure 3.8 were later revised by ISRM (1978c), which are discussed later in Chapter 4 (see Table 4.1).
Typical values of modulus ratios of various rock types, suggested by Hoek and Diederichs (2006), are summarised in Table 3.5.
In clays, the ratio of undrained Young’s modulus to the undrained shear strength is expressed as a function of the overconsolidation ratio and the plasticity index, and this varies in the range of 100–1500. Note that und-rained shear strength is half of UCS. Therefore, similar modular ratios for clays are in the range of 50–750.
Generally, there is significant reduction in the uniaxial compressive strength with increasing specimen size, as evident from Figure 3.9 (Hoek and Brown, 1980). The uniaxial compressive strength of a d-diameter spec-imen σc,d and a 50-mm-diameter specimen σd,50 are related by
Table 3.5 Typical values of modulus ratios
Texture
Coarse Medium Fine Very fine
Sedimentary
schist 300–800a Slates 400–600a
Uniaxial compressive strength (MPa)30
Young’s modulus (GPa)
Very low strength LowstrengthMedium strength High
Figure 3.8 Rock classification based on UCS and Young’s modulus. (Adapted from Hawkes, I. and M. Mellor, Eng. Geol., 4, 179–285, 1970 and Deere, D.U. and R.P. Miller, Engineering classification and index properties of intact rock.
Report AFWL-TR-65-116, Air Force Weapon Laboratory (WLDC), Kirtland Airforce Base, New Mexico, 1966.)
150 200 250
50 Specimen diameter, d (mm)
UCS of d-diameter specimen/UCS of 50-mm-diameter specimen
0.70
Figure 3.9 Influence of specimen size on UCS. (After Hoek, E. and E.T. Brown, Underground Excavations in Rock, Institution of Mining and Metallurgy, London, 1980.) Table 3.5 Typical values of modulus ratios (Continued)
Texture
Coarse Medium Fine Very fine
Igneous Source: Hoek, E. and M.S. Diederichs, Int. J. Rock Mech. Min. Sci., 43, 203–215, 2006.
a Highly anisotropic rocks: the modulus ratio will be significantly different if normal strain and/or loading occurs parallel (high modulus ratio) or perpendicular (low modulus ratio) to a weakness plane. Uniaxial test loading direction should be equivalent to field application.
b Felsic granitoids: coarse-grained or altered (high modulus ratio), fine-grained (low modulus ratio).
c No data available; estimated on the basis of geological logic.
The reduction is probably due to the fact that the larger specimens include more grains, thus enabling greater tendency to fail around these grain surfaces.
Some typical values of the uniaxial compressive strength, Young’s modulus, modulus ratio and Poisson’s ratio are given in Table 3.6 (Goodman, 1980). It may be useful to cross-check your laboratory data against these values.
Table 3.6 Typical values of σc, E, modulus ratio and ν
Rock description σc
(MPa) E
(GPa) E/σc ν Fine-grained slightly porous Berea sandstone 73.8 19.3 261 0.38 Fine- to medium-grained friable Navajo sandstone 214.0 39.2 183 0.46 Calcite cemented medium-grained Tensleep
sandstone 72.4 19.1 264 0.11
Argillaceous Hackensack siltstone cemented with
hematite 122.7 26.3 214 0.22
Monticello Dam greywacke – Cretaceous sandstone 79.3 20.1 253 0.08 Very fine crystalline limestone from Solenhofen,
Bavaria 245.0 63.7 260 0.29
Slightly porous, oolitic, bioclastic limestone,
Bedford, Indiana 51.0 28.5 559 0.29
Fine-grained cemented and interlocked crystalline
Tavernalle limestone 97.9 55.8 570 0.30
Fine-grained Oneota dolomite with interlocking
granular texture 86.9 43.9 505 0.34
Very fine-grained Lockport dolomite, cemented
granular texture 90.3 51.0 565 0.34
Flaming Gorge shale, Utah 35.2 5.5 157 0.25
Micaceous shale with kaolinite clay mineral, Ohio 75.2 11.1 148 0.29 Dworshak dam granodiorite gneiss, fine-medium
grained, with foliation 162.0 53.6 331 0.34
Quartz mica schist ⊥ schistosity 55.2 20.7 375 0.31 Fine-grained brittle massive Baraboo quartzite,
Wisconsin 320.0 88.3 276 0.11
Uniform fine-grained massive Taconic white marble
with sugary texture 62.0 47.9 773 0.40
Medium-coarse grained massive Cherokee marble 66.9 55.8 834 0.25 Coarse-grained granodiorite granite, Nevada 141.1 73.8 523 0.22 Fine-medium grained dense Pikes Peak granite,
Colorado 226.0 70.5 312 0.18
Cedar City tonalite, Utah – somewhat weathered
quartz monzonite 101.5 19.2 189 0.17
Medium-grained Palisades diabase, New York 241.0 81.7 339 0.28
Fine olivine basalt, Nevada 148.0 34.9 236 0.32
John Day basalt, Arlington, Oregon 355.0 83.8 236 0.29 Nevada tuff – welded volcanic ash, with 19.8%
porosity 11.3 3.6 323 0.29
Source: Goodman, R.E., Introduction to Rock Mechanics, John Wiley & Sons, New York, 1980.