地震不稳定性的一个简单模型
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摘要
基于断层面强度的非均匀性,将断层面的宏观破裂过程看作是断面局部微元的破裂累积过程,假设断层局部微元强度遵循Weibull概率分布,从统计力学角度推导出了宏观的断层载荷-变形的全过程本构关系。采用一维地震力学模型,以远场位移a为控制变量,用稳定性理论研究了地震不稳定性问题。研究表明,系统刚度比(围岩刚度与断层刚度之比)β是影响地震发生的重要参数,只有当β<1时才会出现地震失稳,且应力突跳发生在平衡路径曲线的位移转向点,并给出了地震过程的3个重要参数(地震后断层半错距、地震应力降和释放的弹性能)的表达式。当β≥1时,不会发生地震,仅是缓慢的断层滑动,属于无震滑动。
In terms of the heterogeneity of fault plane strength,the macro rupture process of fault plane can be treated as the rupture accumulation process of local micro elements in fault surface.Assuming the strength of fault local micro elements follows Weibull probability distribution,the macro fault constitutive relation of load-deformation complete process can be derived from statistical mechanics viewpoint.Applying one dimension earthquake mechanics model and using far filed displacement a as control variables,the problem of earthquake instability is investigated by employing stability theory in this paper.The results show that system stiffness ratio(stiffness ratio of fault to surrounding rock)β is the important parameter to affect earthquake occurrence.The earthquake instability occurs only when β<1,and the stress jump appears at the displacement turning point of equilibrium path curve.The expression of three important parameters for earthquake(fault half-dislocation after earthquake,earthquake stress drop and elastic energy release) are also given.When β≥1,earthquake does not occur and fault only slips slowly without an earthquake.
In terms of the heterogeneity of fault plane strength,the macro rupture process of fault plane can be treated as the rupture accumulation process of local micro elements in fault surface.Assuming the strength of fault local micro elements follows Weibull probability distribution,the macro fault constitutive relation of load-deformation complete process can be derived from statistical mechanics viewpoint.Applying one dimension earthquake mechanics model and using far filed displacement a as control variables,the problem of earthquake instability is investigated by employing stability theory in this paper.The results show that system stiffness ratio(stiffness ratio of fault to surrounding rock)β is the important parameter to affect earthquake occurrence.The earthquake instability occurs only when β<1,and the stress jump appears at the displacement turning point of equilibrium path curve.The expression of three important parameters for earthquake(fault half-dislocation after earthquake,earthquake stress drop and elastic energy release) are also given.When β≥1,earthquake does not occur and fault only slips slowly without an earthquake.
引文
徐曾和、徐小荷,2000,考虑围岩流变特性的地震尖点型突变模型,岩土力学,21(1),24～27。
殷有泉,2007,非线性有限元基础,北京:北京大学出版社,216～230。
殷有泉、杜静,1994,对一个地震突变模型的讨论,中国地震,10(4),363～370。
殷有泉、张宏,1984,断裂带内介质的软化特征和地震的不稳定性模型,地震学报,6(2),123～145。
殷有泉、郑顾团,1988,断层地震的尖角突变模型,地球物理学报,31(6),657～663。
Lemaitre J.,1992,ACourse on Damage Mechanics.Berlin:Spring-Verlag.
Stuart W.D.,1979a,Quasi-static earthquake mechanics.Rev.Geophys.Space Phys.,17(6),1115～1120.
Stuart W.D.,1979b,Strain softeninginstability model for the San Fernando earthquake,Science,203(4383):907～910.
Tang CA,Hudson JA,Xu XH.1993,Rock Failure Instability and Related Aspects of Earthquake Mechanisms.Beijing:China CoalIndustry Publishing House,26～32.
殷有泉,2007,非线性有限元基础,北京:北京大学出版社,216～230。
殷有泉、杜静,1994,对一个地震突变模型的讨论,中国地震,10(4),363～370。
殷有泉、张宏,1984,断裂带内介质的软化特征和地震的不稳定性模型,地震学报,6(2),123～145。
殷有泉、郑顾团,1988,断层地震的尖角突变模型,地球物理学报,31(6),657～663。
Lemaitre J.,1992,ACourse on Damage Mechanics.Berlin:Spring-Verlag.
Stuart W.D.,1979a,Quasi-static earthquake mechanics.Rev.Geophys.Space Phys.,17(6),1115～1120.
Stuart W.D.,1979b,Strain softeninginstability model for the San Fernando earthquake,Science,203(4383):907～910.
Tang CA,Hudson JA,Xu XH.1993,Rock Failure Instability and Related Aspects of Earthquake Mechanisms.Beijing:China CoalIndustry Publishing House,26～32.
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