Can Structural Optimization Explain Slow Dynamics of Rocks?
Abstract
Slow dynamics is a recovery process that describes the return to an equilibrium state after some external energy input is applied and then removed. Experimental studies on many rocks have shown that a modest acoustic energy input results in slow dynamics. The recovery process of the stiffness has consistently been found to be linear to log(time) for a wide range of geomaterials and the time constants appear to be unique to the material [TenCate JA, Shankland TJ (1996), Geophys Res Lett 23, 3019-3022]. Measurements of this nonequilibrium effect in rocks (e.g. sandstones and limestones) have been linked directly to the cement holding the individual grains together [Darling TW, TenCate JA, Brown DW, Clausen B, Vogel SC (2004), Geophys Res Lett 31, L16604], also suggesting a potential link to porosity and permeability. Noting that slow dynamics consistently returns the overall stiffness of rocks to its maximum (original) state, it is hypothesized that the original state represents the global minimum strain energy state. Consequently the slow dynamics process represents the global minimization or optimization process. Structural optimization, which has been developed for engineering design, minimises the total strain energy by rearranging the material distribution [Kim H, Querin OM, Steven GP, Xie YM (2002), Struct Multidiscip Optim 24, 441-448]. The optimization process effectively rearranges the way the material is cemented. One of the established global optimization methods is simulated annealing (SA). Derived from cooling of metal to a thermal equilibrium, SA finds an optimum solution by iteratively moving the system towards the minimum energy state with a probability of 'uphill' moves. It has been established that the global optimum can be guaranteed by applying a log(time) linear cooling schedule [Hajek B (1988, Math Ops Res, 15, 311-329]. This work presents the original study of applying SA to the maximum stiffness optimization problem. Preliminary results indicate that the maximum stiffness solutions are achieved when using log(time) linear cooling schedule. The optimization history reveals that the overall stiffness of the structure is increased linearly to log(time). The results closely resemble the slow dynamics stiffness recovery of geomaterials and support the hypothesis that the slow dynamics is an optimization process for strain energy. [Work supported by the Department of Energy through the LANL/LDRD Program].
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2009
- Bibcode:
- 2009AGUFMMR41A1853K
- Keywords:
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- 5112 PHYSICAL PROPERTIES OF ROCKS / Microstructure;
- 5120 PHYSICAL PROPERTIES OF ROCKS / Plasticity;
- diffusion;
- and creep;
- 8118 TECTONOPHYSICS / Dynamics and mechanics of faulting