Nature of the high-speed rupture of the two-dimensional Burridge–Knopoff model of earthquakes

Abstract

The nature of the high-speed rupture or the main shock of the Burridge-Knopoff spring-block model in two dimensions obeying the rate-and-state dependent friction law is studied by means of extensive computer simulations. It is found that the rupture propagation in larger events is highly anisotropic and irregular in shape on longer length scales, although the model is completely uniform and the rupture-propagation velocity is kept constant everywhere at the rupture front. The manner of the rupture propagation sometimes mimics the successive ruptures of neighboring "asperities" observed in real large earthquakes. Large events tend to be unilateral, with its epicenter lying at the rim of its rupture zone. The epicenter site is also located next to the rim of the rupture zone of some past event. Event-size distributions are computed and discussed in comparison with those of the corresponding one-dimensional model. The magnitude distribution exhibits a powerlaw behavior resembling the Gutenberg-Richter law for smaller magnitudes, which changes over to a more characteristic behavior for larger magnitudes. The behavior of the rupture length for larger events is discussed in terms of the strongly anisotropic rupture propagation of large events reflecting the underlying geometry.

Solution of steady state in the model polymer system with rupture and rebinding

“…The mechanism of rupture and rebinding are different in stochastic simulation and MF equations. In the stochastic simulations, a rebinding event follows a rupture event in a single simulation run, while in the MF formalism, rupture and rebinding terms occur together (equation (12). Consequently, for bonds with n near the rupture front at the steady state, q n fluctuates between 1 and 0 in the former (for each simulation run), while in MF, á ñ q n varies continuously from 1 to the steady state value.…”

“…Steady states are an integral part of the stick-slip phenomena, and we focus on those instances at low deformation forces, which do not lead to material failure; in other words, the material sticks to a rest state. Most of the stick-slip studies focus on its dynamics, for instance, in earthquake models [9][10][11][12], the transition from static to dynamic friction [5], nanomanipulation [76], biology [13,62,63], deformation experiments on biocomposites [21][22][23][24], and designing hierarchical structures [44,45]. Our generic result represents a solution of the stick state that prevents material failure.…”

“…The diversity of rupture models in addressing mechanisms between the relative motion of surfaces is abundant in literature, for instance, friction [1][2][3][4][5][6][7][8], earthquake models [9][10][11][12], cellular processes [13][14][15], including adhesion [16][17][18][19][20], biocomposites [21][22][23][24], biomimetic polymeric materials [25][26][27], to name a few. Among the earliest works, Schallamach [1][2][3] introduced one-dimensional models for rubber friction, where friction is assumed to arise from shearing and consequent thermally activated breaking and rebinding of distinct bonds between rubbing members.…”

Statistical physics of fracture and earthquakes

“…In [37], the two-dimensional Burridge-Knopoff model is simulated with a realistic rate and state friction law, in an attempt to reproduce the properties of large earthquakes. Particularly, the anisotropic characteristics of large avalanches are described.…”

“…The question here is to find the optimal time and length scale over which activity data are necessary to unambiguously determine a weak region in the system. As opposed to [37], a weak region in this model is not dynamically generated but is embedded in the relative strength of the parts of the system, effectively creating an asperity-like structure. It was found that given a rate of earthquake events, there exists an optimal scale up to which the spatial variations in the b-value and thereby the spatial variations of the stress profile can be determined within a limited error range.…”