Extension of the Lattice Solid Model to incorporate temperature related effects

The elastic and frictional properties of solids are temperature-dependent. Thus. heat has without doubt a major influence on the dynamics of earthquakes, particularly considering the high temperatures generated during large slip events. In order to provide a foundation for the study of these heal related effects, the Lattice Solid Model for the study of earthquake dynamics is extended to incorporate the generation and transfer of heat. The thermal and elastic properties of 2- and 3-D lattice solids in the macroscopic limit are derived. To verify the numerical implementation of heat transfer, a simulation has been performed in a simple case and the results compared to a known analytical solution for the same problem. Thermal expansion and a simple approximation of a temperature-dependent pore fluid pressure are implemented in the 2-D Lattice Solid Model. Simulations confirm that these effects influence the dynamics of the slip of a fault with fault gouge. Whereas thermal expansion has only minor influence on the dynamics of fault rupture, the influence of the increase in the pore fluid pressure generated by slip heating is more significant. The simulations show that the temperatures generated during slip events accord with those expected for real earthquakes as inferred from geologic evidence.