Dynamic Generalization of a Thermomechanical–Timoshenko Geomechanical Framework for Fault Instability: Critical Nucleation Length, Effective Stress, and Spatial Connectivity

The present study develops a dynamic extension of the geomechanical frameworkpreviously submitted by the author to Geosphere, in which a thick-beam Timoshenkorepresentation is coupled to Mohr–Coulomb effective stress and thermally activated ductilecreep to estimate the brittle–ductile transition (BDT) and effective seismogenic thickness. Theextension addresses a subsequent physical question: how can the computed seismogenicenvelope be related to the conditions required for unstable fault slip? We introduce a spatiallyand temporally variable critical nucleation length, Lc(x,z,t), based on rate-and-state friction,effective normal stress, shear rigidity, and critical slip distance. The formulation is written interms of Ψ = (b−a)σ′n, where σ′n = σn−Pf, so that independently inferred constraints on theproduct of frictional and effective-stress terms can be used without artificially separating porepressure from constitutive parameters. We further introduce a dimensionless connectivityratio R = Lconn/Lc, where Lconn is the spatially continuous length of a velocity-weakeningregion. The formulation is tested against Parkfield, Nankai, and Illapel. The resultingframework is not presented as a deterministic earthquake-timing predictor, but as a physicallytestable criterion for nucleation-scale instability within a thermomechanically constrainedseismogenic volume.