and extremely smooth). These results lead to evidence that a nucléation phase exists and
is separable into two phases (as described in section 3.8.4), further that the nucléation
phase is severely affected by the geometric irregularity of the fault surfaces. A strong
correlation was found between the local shear strength and stress distributions on the
fault, the shear stress alo n g the fault co n c en trate s m ore at the locatio n w here the fault strength is locally h ig h er, but d esp ite that, the shear ru p tu re n u clea tes at the location w here shear stren g th is low est on the fault surface. In n u cléa tio n ph ase I, the rupture grow s at a slow, stead y sp eed , and the ru p tu re grow th rate is in d ep en d e n t o f the rupture grow th length. D uring p h ase II, the ru p tu re develops at a c celeratin g speed s, and it w as found that the ru p tu re g ro w th rate V increases with an in cre ase in the ru p tu re grow th length L, obeying a p o w e r law o f the form V/Vs = a (L/?^- )" w h ere Vs is the sh ea r w ave velocity and a and n are co n stan ts. T he critical size 2U- o f the n u cléatio n zo n e and its d uration tc depend g reatly on the su rface roughness and both U- and tc scale w ith T he resu lts indicated that the run-up di.stance and tim e are sh o rte r to attain fast speed ru pture on sm ooth fault su rfa ces than for rough surfaces. T h e slip -w ea k en in g process d uring nucléation is less stab le and m ore dynam ic on a sm o o th e r fault. F urtherm ore, O h n a k a (in press) has show n (for data from E llsw orth and B eroza, 1995) th at the n ucléation zone size scales w ith the m ag n itu d e by the fo llo w in g p ro p o rtio n al relation (F igure 3.18)
M o ttD y (3.23)
T his is p hysically re a so n a b le b ecau se D^ by definition is the slip d isp la c e m e n t required to break dow n a region o f high rupture grow th resistan ce - so m ore d isp lace m e n t is required for larger g e o m e tric a l patches.
io'
°
10 1 0 ' • • •CO
1 0'
D a t a f r o m E l l s w o r t h & B e r o z a ( 1 9 9 5 ) C r i t i c a l S i z e o f N u c l é a t i o n Z o n e 2L ^ ( m )Figure 3.18 - R e la tio n s h ip b e tw e e n critica l s iz e o f the n u c lé a tio n z o n e v e r su s the m a in sh o c k s e is m ic m o m en t (O h n a k a . in p r e ss).
It c a n b e c o n c l u d e d th a t th e s i z e - s c a l e d e p e n d e n t p a r a m e t e r D^, w h i c h is lin e a r ly
r e la te d t o is a m o s t im p o r ta n t b r e a k d o w n p a r a m e t e r s i n c e it p la y s a f u n d a m e n t a l r o le
in s c a l i n g th e o th e r b r e a k d o w n z o n e p a r a m e t e r s .
3.8.6 An advanced breakdown zone model and rupture growth resistance.
T h e e x p e r im e n t a l r e s u lt s d e s c r i b e d a b o v e c a n b e in t e g r a t e d in t o an a d v a n c e d b r e a k d o w n z o n e m o d e l . F ig u r e 3 . 1 9 . ( a ) O u o s i - s t o t i c N u c l é a t i o n t o O y n o m i c R u p t u r e M o d e l A BR EAK DO WN ZONE Z o n e o f O y n o m i c R u p t u r e P r o p c q c i i o n O v e r a l l D y n a m ic i n s l a b i h l y - ^ N u c i e o t i o n Z o n e ( i) (3)
(
2)
DISTANCE ALONG FAULT
(b)
DISTANCE ALONG FAULT O Y n .m ic I n i l . o m t y I M a r e f io c V ) ( (2) S lip O l s p l . c m . n l I 131 S lip O i s p ia c e m e n i 0< S lip D i s p la c e m e n t
Figure 3.19 A model for basic rupture nucléation, based on laboratory experiments. The hatched portion in (a) indicates the breakdown zone where slip-weakening proceeds. Point A in (a) denotes the onset of dynamic instability. is the breakdown zone size, and Tc is the breakdown time. Shown on the right hand side in (b) are the slip weakening relations, which are assumed to be constitutive relations governing the breakdown processes throughout the quasistatic nucléation to dynamically propagating rupture (Ohnaka. 1992).