Additional points 69(1) Elasticity theory has been developed assuming that the strains are in-
finitesimal. There is a theory of finite strain which can be used when
large strains are involved. This theory is used widely in structural
geology analyses, e.g. Ramsay and Huber (1983) 5. Methods of incor-
porating strains and block movements into numerical calculations
are discussed by Pan (1988) 6.
(2) Most calculations are conducted assuming that the rock is elastically
isotropic. One should always consider whether this will introduce
a significant error in the calculations, and whether this error is
important in the particular engineering context under investigation.
(3) Most calculations are also conducted assuming linear relations
between stress and strain, i.e. the Sij elastic compliances explained
in Section 5.1 are indeed constants. Often, the stress-strain relation
can be appreciably nonlinear, and certainly will be when rock failure
occurs.
(4) Remember that all energy put into an elastic material can be re-
covered. Thus, if a rock mass exhibits significant hysteresis (e.g. a
rock mass with low-modulus fractures which is being loaded and
unloaded), elasticity theory may be inappropriate.
(5) There is no time component in the theory of elasticity. If in silu
displacements are time-dependent, elasticity theory is theoretically
invalid.
(6) Other factors can affect the stresses and strains besides their relation
to each other through the theory of elasticity. For example, there can
be thermal strains and complications introduced by fluids present in
the rock mass.
Despite all these caveats, elasticity theory is useful and is used ubiquit-
ously to support rock engineering design. Our emphasis is on ensuring
that the application of elasticity theory to a particular problem is ap-
propriate, bearing in mind the assumptions that have been made, either
explicitly or implicitly. This type of check is part of the technical auditing
procedure explained in Chapter 14.
Ramsay J. G. and Huber M. I. (1983) The Techniques of Modern Structural Geology. Vol.Pan X. D. (1988) Numerical Modelling of Rock Movements Around Mine Openings. PhD1: Strain Analysis. Academic Press, London, 307pp.thesis. University of London, 375pp.