Measuring shear strength

The shear strength of smooth discontinuities can be evaluated using the Mohr-Coulomb failure criterion, in which the peak shear strength is given by:

Figure 5.8: Degradation test of exposed core Source: Courtesy Anglo Chile Ltda

tan

max cj n j

t = +s f (eqn 5.24)

where f_j and c_j are the friction angle and the cohesion of the discontinuity for the peak strength condition

(representing the peak value of the shear stress for a given confining pressure, which usually takes place at small displacements in the plane of the structure) and s_n is the average value of the normal effective stress acting on the plane of the structure. The criterion is illustrated in Figure 5.9.

In a residual condition, or when the peak strength has been exceeded and relevant displacements have taken place in the plane of the structure, the shear strength is given by:

tan

res cjres n jres

t = +s f (eqn 5.25)

where f_jres and c_jres are the friction angle and the cohesion for the residual condition, and s_n is the mean value of the effective normal stress acting on the plane of the structure.

It must be pointed out that in most cases c_jres is small or zero, which means that:

res ntan jres

t =s f (eqn 5.26)

ASTM Designation D4554-90 (reapproved 1995) describes the standard test method for the in situ determination of direct shear strength of rock defects and ASTM Designation D5607-95 described the standard test method for performing laboratory direct shear strength tests of rock specimens that contain defects.

ISRM (2007) described the methods suggested by the ISRM for determining direct shear strength in the laboratory and in situ.

Ideally, shear strength testing should be done by large-scale in situ testing on isolated discontinuities, but these tests are expensive and not commonly carried out. In addition to the high cost, the following factors often preclude in situ direct shear testing (Simons et al. 2001):

■ exposing the test discontinuity;

■ providing a suitable reaction for the application of the normal and shear loads;

■ ensuring that the normal stress is maintained safely as shear displacement takes place.

The alternative is to carry out laboratory direct shear tests. However, it is not possible to test representative samples of discontinuities in the laboratory and a scale effect is unavoidable. Nevertheless, the defect’s basic friction angle (f_b) can be measured on saw cut discontinuities using laboratory direct shear tests.

Sometimes the direct shear box equipment used for testing soil specimens is used for testing rock specimens containing discontinuities, but testing with these machines has the following disadvantages (Simons et al., 2001):

■ difficulty in mounting rock discontinuity specimens in the apparatus;

■ difficulty maintaining the necessary clearances between the upper and lower halves of the box during shearing;

■ the load capacity of most machines designed for testing soils is likely to be inadequate for rock testing.

The most commonly used device for direct shear testing of discontinuities is a portable direct shear box (see Figure 5.10). Although very versatile, this device has the following problems (Simons et al. 2001):

■ the normal load is applied through a hydraulic jack on the upper box and acts against a cable loop attached to the lower box. This system results in the normal load increasing in response to dilation of rough

discontinui-Figure 5.9: Mohr-Coulomb shear strength of defects from direct shear tests

Source: Hoek (2002)

Figure 5.10: Portable direct shear equipment showing the position of the specimen and the shear surface

Source: Hoek & Bray (1981)

ties during shear. Adjustment of the normal load is required throughout the test;

■ as the shear displacements increase the applied normal load moves away from the vertical and corrections for this may be required;

■ the constraints on horizontal and vertical movement during shearing are such that displacements need to be measured at a relatively large number of locations if accurate shear and normal displacements are required;

■ the shear box is somewhat insensitive and difficult to use with the relatively low applied stresses in most slope stability applications since it was designed to operate over a range of normal stresses from 0 to 154 MPa.

The direct shear testing equipment used by Hencher and Richards (1982) (see Figure 5.11) is more suitable for direct shear testing of discontinuities. The equipment is portable and can be used in the field. It is capable of testing specimens up to about 75 mm (i.e. NQ and HQ drill core).

The typical direct shear test procedure consists of using plaster to set the two halves of the specimen in a pair of steel boxes. Particular care is taken to ensure that the two pieces are in their original matched position and the discontinuity is parallel to the direction of the shear load.

A constant normal load is then applied using the cantilever, and the shear load gradually increased until sliding failure occurs. Measurement of the vertical and horizontal displacements of the upper block relative to the lower one can be made with dial gauges, but more precise and continuous measurements can be made with linear variable differential transformers (LVDTs) (Hencher &

Richards 1989).

Where the natural fractures are coated with a clay infilling or there is significant clay alteration,

consideration should be given to performing the tests saturated. This would, however, require special apparatus.

A common practice is to test each specimen three or four times at progressively higher normal loads. When the residual shear stress has been established for a normal load the specimen is reset, the normal load increased and another direct shear tests is conducted. It must be pointed out that this multi-stage testing procedure has a

cumulative damage effect on the defect surface and may not be appropriate for non-smooth defects.

The test results are usually expressed as shear

displacement–shear stress curves from which the peak and residual shear stress values are determined. Each test produces a pair of shear (t) and effective normal (s_n) values, which are plotted to define the strength of the defect, usually as a Mohr-Coulomb failure criterion.

Figure 5.12 shows a typical result of a direct shear test on a discontinuity, in this case with a 4 mm thick sandy silt infill.

It should be noted that although the Mohr-Coulomb criterion is the most commonly used in practice, it ignores the non-linearity of the shear strength failure envelope. To be valid, the shear strength parameters should be done for a range of normal stresses corresponding to the field condition. For this reason, special care must be taken when considering the ‘typical’

values reported in the geotechnical literature because, if

Figure 5.11: Direct shear equipment of the type used by Hencher and Richards (1982) for direct shear testing of defects

Source: Hoek (2002)

Figure 5.12: Results of a direct shear test on a defect (a 4 mm thick sandy silt infill). The shear displacement–shear stress curves on the upper right show an approximate peak shear stress as well as a slightly lower residual shear stress. The normal stress–shear stress curves on the upper left show the peak and residual shear strength envelopes. The shear displacement–normal

displacement on the lower right show the dilatancy caused by the roughness of the discontinuity. The normal stress–normal displacement curves on the lower left show the closure of the discontinuity and allow the computation of its normal stiffness Source: Modified from Erban & Gill (1988) by Wyllie & Norrish (1996)

these values have been determined for a range of normal stresses different from the case being studied, they might be not applicable. It must be noted that many of the

‘typical’ values mentioned in the geotechnical literature correspond to open structures or structures with soft/

weak fillings under low normal stresses. Though these

‘typical’ values may be useful in the case of rock slopes they may not be applicable to the case of underground mining, where the confining stresses are substantially larger than in open pit slopes.

When calculating the contact area of the defect an allowance must be made for the decrease in area as shear displacements take place. In inclined drill-core specimens the discontinuity surface has the shape of an ellipse, and the formula for calculating the contact area is as follows (Hencher & Richards 1989):

sin minor axes of the ellipse and d_s is the relative shear displacement.

Triaxial compression testing of drill-core containing defects can be used to determine the shear strength of veins and other defects infills using the procedure described by Goodman (1989). If the failure plane is defined by a defect (Figure 5.13a), the normal and shear stresses on the failure plane can be computed using the pole of the Mohr circle (Figure 5.13b). If this procedure is applied, the results of several tests allow the cohesion (c_j) and friction angle (Ø_j) of the defect to be determined (Figure 5.13c).