Stability analysis of slip of a one-body spring-slider model in the presence of thermal pressurization
This study is focused on stability of slip in a one-body spring-slider system, with stiffness k of the slider, in the presence of thermal pressurizationfor two end-member models of thermal pressurization, i.e., the adiabatic-undrained- deformation (AUD) model and slip-on-a-plane (SOP) model. Analyti...
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| Format: | Article |
| Language: | English |
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Istituto Nazionale di Geofisica e Vulcanologia (INGV)
2013-08-01
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| Series: | Annals of Geophysics |
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| Online Access: | http://www.annalsofgeophysics.eu/index.php/annals/article/view/5548 |
| Summary: | This study is focused on stability of slip in a one-body spring-slider system, with stiffness k of the slider, in the presence of thermal pressurizationfor two end-member models of thermal pressurization, i.e., the adiabatic-undrained- deformation (AUD) model and slip-on-a-plane (SOP) model. Analytic studies based on the functions of frictional stress, t<sub>f</sub>, versus slip, d, of the two models show that k<sub>cr</sub>=|dt<sub>f</sub>/dd| at d=0 is the critical stiffness of the system. k<sub>cr</sub> is a finite positive value for the AUD model and infinity for the SOP model. Slip is stable when k>k<sub>cr</sub> and unstable when k<k<sub>cr</sub>. Analytic stability conditions of slip from the equations of motions of a one-body spring-slider model with the t<sub>f</sub>–d function of the ADU model are also those from |dt<sub>f</sub>/dd| at d=0. Under ADU thermal pressurization, modeled final slip and maximum velocity for k=5 to 31 MPa/m, with k<sub>cr</sub>=30 MPa/m, both decrease with increasing k. The motions become very weak when k≥k<sub>cr</sub>, thus being unable to result in unstable motions. The phase portraits of v versus d for k<30 MPa/m show the existence of a non-zero unstable fixed point. |
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| ISSN: | 1593-5213 2037-416X |