Advances in Conception about Earthquakes - Earthquake Engineering for Structural Design - page 120

Episodical plate reorganizations are inevitable and can explain the permanent
movement of the Earth's plates (Anderson, 2001a,b, Sankaran, 2002).
4.3BLOCKMODELSANDSEISMICITY
4.3.1BifurcationTheory
Bifurcation (named also Self-organized Criticality, Wikipedia, nd) is the
phenomenon in which the system reaches the crisis at the bifurcation point (Fig.
4.10) and results in a system splitting into two possible behaviors for a small
change of one parameter. The important new possibility is that the self-organized
state can suddenly appear beyond this crisis point, far from the equilibrium in the
nonlinear range.
Fluctuations. In thermodynamics, a fluctuation is a perturbation in the
equilibrium state, which changes the bifurcation point in an accelerated behavior.
Near to equilibrium, these fluctuations have no important effects (Fig. 4.10). In
exchange, far from the equilibrium, these fluctuations produce a great changing in
system behavior, not proportional to the sizing of these fluctuations. The smallest
fluctuation can lead to a radically new behavior of the system. To predict the future
behavior, it should be necessary to measure the fluctuations with infinitely accurate
precision, which is an impossible task both in principle and in practice (Coveney,
2003). Many phenomena in nature exhibit anomalously large fluctuations,
exceeding what cannot be explained as a consequence of statistically independent
random events. Therefore, a suitable determination of the nonlinear systems is out
of the question.
Evolution in cascade (Fig. 4.12). The Complex Systems are characterized by a
cascade succession of bifurcation points. The system evolution is composed by
slow evolutions, followed by bifurcations or accelerated changing. In some cases,
jumps from a stable position to another position occur. This is a very characteristic
situation for the earthquake occurrence, when some imperceptible deformations are
accumulated for a long time in the plates due to the mantle convection and,
suddenly, a perceptible important modification of the relief or the loss of plate
equilibrium produces the earthquake.
4.3.2BlockStructureModels
As was shown in the previous sections, the Earth crust is divided into blocks
(tectonic plates), which move in different directions with different velocities. So,
these blocks are stressed, mainly along their boundary, which are represented by
the faults of the Earth crust, where they interact with the neighboring ones. The
stresses are mainly concentrated in the contact zone. It is possible to define a limit
level of pressure supported by rocks in contact (mainly given by friction under
pressure), for which a rock rupture or a slippage between the rocks occurs along a
fault plane. When the level of stress remains below this limit pressure, the blocks
are in equilibrium. When the limit level is exceeded in some part of the fault plane,
a stress-drop occurs (in accordance with the dry friction model) with important