Group III: where the rock mass is affected by a number of sets of discontinuities giving rise to “small spacing” between discontinuities.
This group of rock masses can be regarded as isotropically broken media and the Hoek-Brown criterion can be applied.
“Small spacing” is a relative concept, in the sense that it depends on the foundation dimensions. Serrano and Olalla (1996) propose a parameter, the “spacing ratio of a foundation” (SR), for its quantification. SR is defined as
(4.110)
where B is the foundation width (in meters); smi is the discontinuity spacing of set i (in meters); λi is the frequency of discontinuity set i (m−1); and n is the number of discontinuity sets.
As an initial and conservative proposal, a “relatively small spacing” is suggested when SR is greater than 60. A value of 60 means that, if there are four sets of discontinuities, each of them appears at least 15 times within the foundation width. When SR>60, the mass can be regarded as an isotropically broken medium and the Hoek-Brown criterion can be applied.
For values of SR≤(0.8−4), in the case of four sets of discontinuities, the rock mass can be considered as an intact rock mass (Group I).
4.5.2 Scale effect on deformability of rock mass
The scale effect on the deformability of rock masses can be seen from the difference of rock mass modulus measured in the field and intact rock mass modulus measured in the laboratory. Heuze (1980) concluded that the rock mass modulus measured in the field ranges between 20 and 60% of the intact rock mass modulus measured in the laboratory.
One simple and apparent explanation to the reduction of rock mass modulus is that the effect of discontinuities is included in the rock masses.
4.6 DISCUSSION
The structure of jointed rock masses is highly variable; the methods used to consider the effect of discontinuities on the mechanical behavior of jointed rock masses are also variable. The selection of the methods should be based on careful studies of the in situ situation of jointed rock masses.
Laboratory and in situ tests (i.e., direct methods) can directly provide results about the mechanical properties of tested specimens. However, care need be exercised about the extent to which the measured behavior of the rock specimen reflects the actual behavior of rock masses. The extrapolation of the behavior induced by the experimental system to different circumstances can be very misleading. In addition, in situ tests are time consuming, expensive and difficult to conduct; it is extremely difficult to investigate the effects of discontinuity system on the mechanical properties of jointed rock masses through in situ tests.
Indirect methods consist of the empirical methods, the equivalent continuum approach and numerical analysis methods. It is important to note that all the indirect methods need to use some of the mechanical properties of intact rock or discontinuities obtained through laboratory or in situ tests.
Since they are simple and easy to use, and most importantly, since they originate from practical experience, the empirical methods are most widely used in design practice.
However, it is important to note their limitations as described in Sections 4.3.1 and 4.4.1.
The equivalent continuum approach usually assumes that all discontinuities are persistent and the discontinuities in one set have the same orientation. In reality, however, discontinuities are usually non-persistent and the discontinuities in one set are not in the same orientation. Kulatilake et al. (1992, 1993) and Wang (1992) considered rock masses
containing non-persistent discontinuities and derived relationships between the deformation properties and the fracture tensor parameters from the DEM analysis results of generated rock mass blocks. However, this method is also limited as described in Section 4.3.2.
The numerical methods have great potential for the complex mechanical analyses of jointed rock masses. The key problems associated with numerical methods are the representation of discontinuities and the determination of discontinuity constitutive models. The main drawback of this approach is that, due to computer limitations and difficulty in creating meshes for a heavily jointed rock mass, only rock masses with a limited number of discontinuities can be analyzed.
In summary, the limitations for each method are as follows:
1. For laboratory tests, only small specimens can be used. Since rock masses show strong scale dependent mechanical properties, the measured behavior of small rock
specimens may not reflect the actual behavior of rock masses in the field.
2. In situ tests are time consuming, expensive and difficult to conduct.
3. Empirical methods do not consider the anisotropy of rock masses caused by discontinuities and different empirical relations often give very different values.
4. The equivalent continuum approach assumes that the discontinuities are persistent and the discontinuities in one set have the same orientation. In reality, however, most of the discontinuities are non-persistent with finite size and the discontinuities in one set are not in the same orientation.
5. Numerical methods can only be used for rock masses with a limited number of discontinuities.
Because each method has its own advantages and disadvantages, it is important to select the appropriate method(s) for different purposes. Following are the principles that can be used when selecting the methods according to the nature of the problems:
1. The empirical methods can always be used in the first stage of design. For heavily jointed rock masses, the empirical methods can be used in all design stages.
2. For rock masses with persistent discontinuities which are regularly distributed, the equivalent continuum approach can be used.
3. For rock masses with a limited number of discontinuities, the numerical methods and the limit equilibrium method can be used.