The study of 1D spring-block model of earthquake dynamics with consideration of water effects in preexisting fault deals with new forms of frictional force. An analytical study of the equation of motion enables us to establish that motion of geological fault is accelerated by water pressure. In the same setting the critical value of frictional velocity for which appears the discontinuous (first-order) transition from a stick-slip behavior to a creep motion strongly depends on water pressure. The investigation also displays the magnitude and probability of events as a function of water pressure; these two quantities decrease and increase, respectively, with the variation of water pressure. 1. Introduction Despite significant advances made in the study of geological fault structures and plate tectonics, our understanding of the physical mechanisms responsible for the initiation, propagation, and termination of earthquake rupture remains unfinished. Burridge and Knopoff [1], in 1967, introduced a one-dimensional chain block and spring-discrete model, aiming at explaining the earthquake mechanism [2]. In 1996, Vasconcelos simplified Knopoff’smodel with a single spring-block model and attempted to facilitate the understanding of earthquake using this model. The mechanism of slip instabilities in laboratory experiments has been proposed to be dependent on several factors including reduced frictional force during sliding (slip weakening) and a decrease in slip velocity [3], which is in concordance with the observation of the geologist Rick Sibson [4], who in 1981 maintained the idea affirming that water pressure in the fault was opposite to the rocks’ pressure, which intensified friction between the fault’s sides. The mathematical model which takes into consideration this idea was not yet established; however, some studies have been done in dry faults with the help of well-known mathematical models [5, 6]. Moreover, Vasconcelos [6] had investigated the phase transition in this single block model and demonstrated that it occurs (from stick-slip to creep motion) only when the characteristic velocity is equal to 0.5. This result was obtained because he considered dry fault in his study. In other cases there are several values of characteristic speed (less than 0.5) which are able to lead to the transition. The aim of this paper is to study Giovanni’s modified single block model, by considering the new shape of frictional forces (that contains water pressure), and investigate the effects of water pressure on the earthquake dynamics. The content of this paper is
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