Analysis of main shock of thrust fault earthquake by catastrophe theory

doi:10.1007/s10483-012-1590-8

Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (7): 845-864.doi: https://doi.org/10.1007/s10483-012-1590-8

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Analysis of main shock of thrust fault earthquake by catastrophe theory

Yue PAN¹, Zhi-gang ZHAO²

1. College of Civil Engineering, Qingdao Technological University, Qingdao 266520, Shandong Province, P. R. China;
2. Key Laboratory of Mine Disaster Prevention and Control, Shandong University of Science and Technology, Qingdao 266510, Shandong Province, P. R. China

Received:2011-07-07 Revised:2012-03-29 Online:2012-07-10 Published:2012-07-10
Supported by:
Project supported by the National Natural Science Foundation of China (No. 5067059)

Abstract

Abstract: The relationship between work and energy increment of a thrust fault system with quasi-static deformation can be decomposed into two parts: volume strain energy and deviation stress energy. The relationship between work and energy increment of the deviation stress of a simplified thrust fault system is analyzed based on the catastrophe theory. The research indicates that the characteristics displayed by the fold catastrophe model can appropriately describe the condition of earthquake generation, the evolvement process of main shock of thrust fault earthquake, and some important aftershock properties. The bigger the surrounding press of surrounding rock is, the bigger the maximum principal stress is, the smaller the incidences of the potential thrust fault surface are, and the smaller the ratio between the tangential stiffness of surrounding rock and the slope is, which is at the inflexion point on the softened zone of the fault shearing strength curve. Thus, when earthquake occurrs, the larger the elastic energy releasing amount of surrounding rock is, the bigger the earthquake magnitude is, the larger the half distance of fault dislocation is, and the larger the displacement amplitude of end face of surrounding rock is. Fracturing and expanding the fault rock body and releasing the volume strain energy of surrounding rock during the earthquake can enhance the foregoing effects together.

Key words: nonlinear time-varying system, small parameter, technical stability, vector comparison principle, reduced system, linearization technique, exponential asymptotic stabili, thrust fault, earthquake, fold catastrophe model, elastic energy releasing amount, distance of fault dislocation

2010 MSC Number:

P315.3

Yue PAN;Zhi-gang ZHAO. Analysis of main shock of thrust fault earthquake by catastrophe theory. Applied Mathematics and Mechanics (English Edition), 2012, 33(7): 845-864.

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Analysis of main shock of thrust fault earthquake by catastrophe theory

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