Weak rocks when subjected to moderately high confining and deviatoric stresses tend to exhibit time dependent deformation. This is most commonly characterised through phenomenological models of time-hardening strain under constant stress. An alternative description based on strength reduction with time is suggested. The implications of this approach for the design of shaft linings in evaporite rocks are discussed.
Weak rocks when subjected to moderately high confining and deviatoric stresses continue to deform after initial application or redistribution of the stresses causing deformation. This time dependent deformation or creep is most commonly characterised through laboratory maintained load tests which predict a time-hardening strain rate of the form:
Where t is time, o is deviator stress, f(0) is some function of temperature and A, B(<1) and C(3.5–4.3) are constants. This relation can be represented by rheological models of varying complexity, some of which are outlined by Jaeger and Cook (1968).
Such an approach does not explicitly consider the effect of stress redistribution. Around voids in a continuum, however, if the continuum material in its residual state is capable of mobilising shear, deformation must ultimately lead to stress redistribution. Thus equation 1 is only strictly applicable to isolated pillars.
If the effect of stress redistribution is significant, it represents a factor which has been ignored in the complex rheological models which have been developed for rock salt in particular. The most complex of these are the thermodynamic approaches of Biot (1954) and Fossum (1977). This work has often been based on developments in metallurgy where studies of micro-mechanistic phenomena (see Cittus, 1975) have been used to explain the creep of larger units. Although similar work on rock salt (see Le Compte, 1960 and Heard, 1972) has yet to yield any comparable success, probably because of the random nature of natural deposits, it does give a physical interpretation of the power law strain rate/ stress relation of equation 1.
Rock salt does, however, exhibit classical strength behaviour and behaves as a shearing, C -ø) material, when subjected to stress conditions similar to those existing in the vicinity of a void in a continuum during excavation. It is therefore sensible to suggest the existence of a zone of fractured or deformed rock capable of mobilising shear resistance under such conditions. This could be particularly important where a lining is introduced. Rheological models (see Gnirk and Johnson, 1964) suggest, ultimately,that full geostatic stresses are transferred to the lining as no other support mechanism is available. Shearing or yielding models suggest much lower stresses. Serata (1959) has suggested such a model, similar in concept to the critical state models for soil (Schofield and Wroth 1968, Atkinson and Bransby, 1979). The probability is that a true description of rock salt behaviour falls between the two extremes. To investigate this behaviour does, however, require a different approach to that used in time dependent deformation studies, involving an investigation of rock strength and involving the constant strain rate testing of rocks.
