Measurement of Properties
2.4 Rupture Strength
2.4.3 Rock Strength Measurements GeneralGeneral
Intact Rock
The confined strength of fresh, intact rock is seldom of concern in practice because of the relatively low stress levels imposed.
Brittle shear failure occurs under very high applied loads and moderate to high confin-ing pressures, except for the softer rocks such as halite, foliated and schistose rocks, and lightly cemented sandstones. In softer rocks, rupture occurs in a manner similar to that in soils, and the parameters described in Section 2.4.2 hold.
Under very high confining pressures (approximately 45,000 psi or 3000 bar), some com-petent rocks behave ductilely and failure may be attributed to plastic shear (Murphy,
Compression
Examples of the occurrence of active and passive pressures encountered in practice: (a) slope; (b) retaining wall; (c) anchored bulkhead; (d) anchor block; (e) foundation.
1970). Intact specimens are tested in uniaxial compression or tension to provide data for classification and correlations. Other tests include those for flexural strength and triaxial compressive strength. Applied forces for the various tests are shown in Figure 2.37.
Rock Masses
Rock-mass strength is normally controlled either by the joints and other discontinuities or by the degree of decomposition, and the strength parameters described in Section 2.4.2 here. Strength is measured in situ by direct shear equipment or special triaxial shear equip-ment.
Uniaxial Compressive Strength Uc(ASTM D2938) Procedure
An axial compressive force is applied to an unconfined specimen (Figure 2.38) until fail-ure occurs.
Data Obtained
A stress–strain curve and the unconfined or uniaxial compressive strength (in tsf, kg/cm2, kPa) result from the test. Stress–strain curves for various rock types are given in Table 2.24.
Data Applications
Primarily used for correlations as follows:
● Material “consistency” vs. Uc— Figure 2.39.
● Schmidt hardness vs. Uc — Figure 2.40. The Schmidt hardness instrument (Figure 3.1a) is useful for field measurements of outcrops to correlate variations in Uc. Corrections are available for inclinations from the vertical.
● Hardness classification.
σd
σd
σd σd
σd
σd
σd
σd
σ3
σ3
σN σN
σ3
(f)
(e) (g) (h)
(d) (c)
(b) (a)
FIGURE 2.37
Common laboratory tests to measure strength of rock cores: (a) uniaxial compression; (b) triaxial compression;
(c) direct shear for soft specimens; (d) direct shear for joints; (e) point load; (f) direct tension; (g) splitting tension (Brazilian); and (h) four-point flexural.
Shear cracks P
P
FIGURE 2.38
Uniaxial compression test.
Unconfined compressive strength (tsf)
Unconfined compressive strength (psi) Very soft soil
6.8 680
68
0.68 6800
Minimum strength envelope
Consistency
Rock defined at 100 psi
1.0 100
10 1000 100,000
10,000 Soft soil
Firm soil
Stiff soil Hard soil
Very soft rock Soft rock
Hard rock Very hard rock Extremely hard rock
FIGURE 2.39
Relationship between “consistency” and Uc(100 psi 6.8 kg/cm2 689.5 kN/m2). (After Jennings, J. E., Proceedings of ASCE, 13th Symposium on Rock Mechanics, University of Illinois, Urbana, 1972, pp. 269–302.)
Uniaxial Tensile Strength Cable-Pull Test
Caps are attached to the ends of a cylindrical specimen with resins. The specimen is then pulled apart by cables exerting tension axially (Figure 2.37f). The method yields the low-est values for tensile strength, which generally ranges from 5 to 10% of the uniaxial com-pression strength.
Point-Load Test (Broch and Franklin, 1972) (ASTM D5731-95)
Compressive loads P are applied through hardened conical points to diametrically oppo-site sides of a core specimen of length of at least 1.4D until failure occurs. The equipment is light and portable (Figure 2.41) and is used in the field and the laboratory.
Point-load index is the strength factor obtained from the test, and is given by the empiri-cal expression (Hoek and Bray, 1977)
Is P/D2 (2.42)
where D is the diameter.
Comprehensive strength Uc of rock surface (MPa) 350
Schmidt hardness R,L hammer
±20 Rock density = 32 31 Average dispersion of
strength for most rocks
29
Correlation chart for Schmidt L. hammer, relating rock density, uniaxial compressive strength, and rebound number R (Schmidt hardness). Hammer vertical downward; dispersion limits defined for 75% confidence.
(Note: 100 MPa 14.5 103psi 1021 tsf; 1 kN/m2 6.3 pcf.) (From ISRM, Rock Characterization and Monitoring, E. T. Brown, Ed., Pergomon Press, Oxford, 1981. With permission. After Deere, D. U. and Miller, R. P., Technical Report AFWL-TR-65-116, AF Special Weapons Center, Kirtland Air Force Base, New Mexico, 1966.)
Values for Isare used to estimate Ucthrough various correlations as shown in Figure 2.42, and, for a core diameter of 50 mm,
Uc 24 Is (2.43)
Flexural Strength or Modulus of Rupture Procedure
A rock beam is supported at both ends and loaded at midpoint until failure (Figure 2.37h).
Data Obtained
The flexural strength is proportional to the tensile strength but is about three times as great (Leet, 1960).
FIGURE 2.41
Point load strength test apparatus.
Point-load strength index Is
( MP
a) Point-load strength index Is (psi)
20
500
0 10 20
Uniaxial compressive strength Uc, psi x 103
30 40 50 1000 1500 2000 2500 3000 kg/cm2 Uc
Relationship between point load strength index Isand uniaxial compressive strength Uc. (After Bieniawski, Z.
T., Proceedings 3rd International Congress for Rock Mechanics, International Society for Rock Mechanics, Vol. IIA, Denver, 1974, pp. 27–32. Reprinted with permission of National Academy Press.)
Triaxial Shear Strength Apparatus and Procedures
General description is given in Section 2.4.4 and, as applicable to rock testing, in Section 2.5.3 and in Table 2.28.
Strength Values
Studies have been made relating analysis of petrographic thin sections of sandstone to esti-mates of the triaxial compressive strength (Fahy and Guccione, 1979). Relationships have been developed for approximating peak strengths for rock masses (Hoek and Brown, 1980).
Direct Shear Strength Purpose
The purpose is to obtain measurements of the parameters φand c in situ. It is particularly useful to measure strength along joints or other weakness planes in rock masses.
In Situ Test Procedure
A diamond saw is used to trim a rock block from the mass with dimensions 0.7 to 1.0 m2 and 0.3 m in height, and a steel box is placed over the block and filled with grout (Haverland and Slebir, 1972). Vertical load is imposed by a hydraulic jack, while a shear force is imposed by another jack (Figure 2.43) until failure. All jack forces and block move-ments are measured and recorded. Deere (1976) suggests at least five tests for each geo-logic feature to be tested, each test being run at a different level of normal stress to allow the construction of Mohr’s envelope.
Laboratory Direct Shear Tests (See Section 2.4.4)
If the specimen is decomposed to the extent that it may be trimmed into the direct shear ring (Figures 2.37c and 2.51) the test is performed similar to a soil test (Section 2.4.4). If pos-sible, the shearing plane should coincide with the weakness planes of the specimen. Tests to measure the characteristics of joints in fresh to moderately weathered rock are performed by encapsulating the specimen in some strong material within the shear box as shown in Figure 2.37d (ISRM, 1981). The specimen is permitted to consolidate under a normal force and then sheared to obtain measures of peak and residual strength as described in Section 2.4.4. The normal stress is increased, consolidation permitted, and the specimen sheared again. The process is repeated until five values of shear stress vs. normal stress is obtained, from which a graph for peak and residual strength is constructed as shown in Figure 2.44.
Reaction
Thrust jack
Load jack Steel pad
Steel frame Rock
block
1 − 0.7 m FIGURE 2.43
In situ direct shear test.
Shear strength parameters φa, φb, φr, c and c are abstracted from the graph, which often is a composite of several tests, as shown in Figure 2.44 where
● φr residual friction angle.
● φa apparent friction angle below stress σa; point A is a break in the peak shear strength curve resulting from the shearing off of the major irregularities (asperi-ties) on the shear surface. Between points O and A, φa will vary slightly and is measured at the stress level of interest (φa φu j where φu is the friction angle obtained for smooth surface of rock and angle j is the inclination of surface asperities) (Figure 2.45).
● φb the apparent friction angle above stress level σa ; it is usually equal to or slightly greater than φr, and varies slightly with the stress level. It is measured at the level of interest.
● c cohesion intercept of peak shear strength which may be zero.
● c apparent cohesion at a stress level corresponding to φb. Borehole Shear Test (BST) (ASTM D4917-02)
Purpose
The borehole shear test measures peak and residual values of φ and c in situ. Initially developed at Iowa State University by R.L. Handy and N.S. Fox for the U.S. Bureau of
Shear stress τ Peak shear strength
Residual shear strength
Normal stress σn
σa graph for direct shear test on rock specimen.
Shear displacement δs
δn = δs tan j
Normal displacement δn
Average j angles for first-order
projections
FIGURE 2.45
The joint roughness angle j: (a) experiments on shearing regular projection and (b) measurements of j angles for first- and second-order projections on rough rock surface. (From Patton, F. D., Proceedings of the 1st International Congress of Rock Mechanics, Lisbon, Vol. 1, 1966, pp. 509–513. With permission.)
Mines, it was designed for near-surface or in-mine testing of coal and other fractured rocks that are difficult to core. It has been used in all soft to medium-hard rocks.
Procedure
The apparatus is shown in Figure 2.46. A shear head, consisting of opposing plates with two carbide teeth, is lowered into a 3 in. (75 mm) borehole. Normal stress is applied by pushing the shear plates into the sides of the hole using a hand-operated pump.
The pressure is then valved off so it remains constant, while the same pump is used to pull the expanded shear head a short distance upward along the hole by means of a hol-low-ram jack. Both the expansion pressure and the pulling resistance are recorded, and the test is repeated with different preselected normal stresses. Up to four tests can be con-ducted at the same depth by rotating the shear head 45° between tests. A plot of each test is made to obtain a Mohr’s envelope of shear stress vs. normal stress providing meas-urements of the angle of internal friction (φ) and cohesion (c) (Handy et al., 1976).
Comparison with data from in situ direct shear tests indicate that cohesion values from the BST are lower although the friction angles are close (R. L. Handy, personal commu-nication, 2004).
Applications
The apparatus is used in both rock (RBST) and soil (BST) in vertical, inclined, or horizon-tal boreholes. The entire apparatus, including the shear head and pulling device, is easily portable. A very significant advantage over other methods to measure shear strength is that many tests can be run in a short interval of time, as many as ten per day, and yield results on-site that can indicate if more tests are needed.
Threaded rod
Hollow jack Dial gage
Tripod Jack base plate
Hose connector
NX hole
BST body Half nut clamp
Shear hose
Shear plates Retract hose Normal hose
Rod coupling RW drill rod
RW adapter
FIGURE 2.46
Schematic of borehole shear strength tester (BST) in the borehole. (From USBM, Bureau of Mines, U.S.
Department of Interior, New Technology No. 122, 1981. With permission.)
2.4.4 Soil Strength Measurements