Engineering Rock Mechanics

21 8 Rock dynamics and time-dependent aspects

-3 € t-4 )

o=o,e non-linear relaxation.

These two types of behaviour are illustrated in Fig. 13.7.
The Kelvin model consists of viscous and elastic elements in parallel.
Consequently, the strain is identical in each of the elements and the stress
developed in the material, os, is the sum of the stresses developed in the
elastic and viscous elements, oE and o,, respectively,

Again, considering a period of constant stress followed by constant strain,

de

dt

C, =EE+F-

which, on rearranging, becomes

de +c.

-jdt=J-- 1

F oo -E&

Integration and substitution of C = (l/E)log,g (because at t = 0, E = 0) yields

E = 5 (1 - e-;'] non-linear creep.

E

The strain that has accumulated at t = fl is thus

Figure 13.7 Linear creep and non-linear relaxation for the Maxwell substance.