XFEM simulation of rupture direction on branching faults.

Abstract:

Nowadays, dynamic simulation of structures against seismic waves is increasingly used at the stage of structural design. In order to conduct reasonable simulation, we need to consider which faults rupture and how they rupture (seismic scenario). Especially for branching faults seismic scenarios are postulated by Nakata et.al. 1998, where rupture starts from the major fault segment and direct to the branches. However, in the main shock of the 2016 Kumamoto earthquake, a rupture episode of the branching fault was inconsistent with the conventional conventional model. In this study, we examined rupture patterns of the branching fault system by considering a variety of fault strengths and initial stress fields. In order to simulate the fault rupture including the blanching point, we proposed a new representation of enrich function for eXtended Finite Element Method. XFEM incorporates additional degrees of freedom to express displacement field including discontinuity, so that no mesh refining is required around discontinuity. Usually those additional degrees of freedom are allocated to each node of the element in which discontinuity such as fault is located. However, in our study they are allocated to the element itself, which results in a simpler operation of equation of motion. For simpler and more general representation of branching point, superposition of tip elements is used. Tip elements are elements in which discontinuity is partially included. For case studies, the fault trace of the 2016 Kumamoto earthquake is used but in half size for the computational cost. In order to replicate the natural heterogeneity of strength over the fault, we incorporate von Karman type autocorrelation function. And for stress field we utilize the results of Yoshida et.al. 2016 which estimated stress field around the faults of the 2016 Kumamoto earthquake. Around 100 cases are conducted and both rupture patterns are observed consistent with the conventional model and the Kumamoto earthquake type.