  Spring-block models, such as the Olami-Feder-Christensen (OFC) model, were
introduced several years ago to describe earthquake dynamics in the context of
selforganized criticality. With the aim to address the dependency of the
seismicity style on sources material properties we present an analytical
enrichment of a 2D OFC model. We concluded with an analytical expression which
introduces, through an appropriate constitutive equation, an effective
dissipation parameter a related analytically not only with the elastic
properties of the fault plane, but also with stochastic structural
heterogeneities and structural processes of the source through a gradient
coefficient. Moreover, within the proposed formulation the low b-values
experimentally observed in foreshock sequences can be modeled by a process of
material softening in the seismogenic volume. To check our analytical findings
a cellular automaton was build-up whereas simulation results have verified
models predictions for the evolution of b in macroscopic records.
