3.6 Time-dependent deformation: Visco-elasticity

So far, we have assumed that rock strain-stress response is independent of loading rate, however, this is not true. The stiffness of rocks is not the same if loaded in a time frame of thousands of years (geological time), years (reservoir production time), or during a few minutes (drilling and laboratory time). Rocks tend to be softer and more ductile as the loading time frame increases.

Figure 3.24: Strain-rate dependent stiffness. [Put your own data]

Another manifestation of visco-elasticity is time-dependent deformation, usually known as “creep”. Whenever a change of stress is applied and set constant, deformations may continue with time. An example of this type of response is when drilling through salt rocks. Stresses intensify around the wellbore after the hole is bored. The wellbore walls will deform if left uncased and stick to the drilling string.

Figure 3.25: Time-dependent deformation: Creep.

One other manifestation of visco-elasticity is time-dependent stress change or stress relaxation. Whenever a change of strain is applied and set constant, stresses may relax with time. For example, unconsolidated sands may relax horizontal stresses with time after a tectonic strain is applied (Figure 3.27). Therefore, neglecting visco-elasticity may result in an overestimation of horizontal stresses in unconsolidated sands with a purely elastic model.

Figure 3.26: Time-dependent deformation: stress relaxation.

Figure 3.27: Impact of stress relaxation in horizontal stresses in the subsurface. (a) Decrease of $S_{Hmax}$ due to deviatoric stress relaxation caused by a paleo-tectonic strain $\varepsilon _{Hmax}$. (b)Increase of $S_{hmin}$ due to deviatoric stress relaxation caused by overburden stress.