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type, frictional stress was relatively unaffected by temperature - this temperature was

300°C for Westerly granite sawcuts, 600®C for Westerly granite faults, and 400®C for

San Marcos gabbro. The friction stress of seven silicate rocks were within about 10-

15%, agreed to Byerlee’s Rule, which is relatively unaffected by rock type. Stesky

(1978a) examined mechanisms of high temperature frictional sliding in faulted dry

Westerly granite (300-700^C, 250MPa, sliding rates of lO'^-lO'^cm/s) and observed

plasticity in quartz at about 500°C. Feldspars showed no plasticity until 700”C. The

micas (biotite and muscovite) were plastic at all temperatures. Similar results were

found by Tullis and Yund (1977) on dry Westerly granite deformed at 10"^s'\ At

temperatures below 500^C, the evidence (e.g., acoustic emissions indicating cracking)

strongly indicated the deform ation was brittle. However, frictional sliding at higher tem peratures was replaced by plastic flow or ductile shearing, d ue to the extensive plastic b e h a v io u r o f the q uartz and mica. A high tem perature constitutive relation will no longer be a frictional law but a How law, with strength independent o f normal stress.

a:

<

m

LT>

2 4

cr

k

cr

Ï

CO

.

'

r = 0.7 + 0.6 cr.

0

Figure 2.18 T he effect o f tem perature on the frictional strength o f dry gabbro. R ep ro d u c ed from Stesky (1978b).

Stesky ( 1978b) generalised the Byerlee equation based on results from Figure 2.18.

x = a + hOn (2.40)

w here a and h are co nstants having ap p ro x im a te values o f 0.3±0.1 and 0.6±0.1 respectively. In equation 2.40, the constant a represents the effect o f dilatancy and h is the coefficient o f frictional resistance. At pressures above 1000 M P a (less for certain rocks) or at tem peratures above 4 0 0 ‘’C, equation 2.38 does not hold. T he friction strength is less d ep e n d en t on the normal stress. U nder these extreme conditions, frictional strength will approach intact rock strength (Byerlee, 1968, Stesky, 1978b, O h n a k a, 1996), suggesting that both frictional sliding and bulk brittle failure are end m em bers o f the sam e process o f shear failure.

6-

E f t e c t i v e N o r m a l S t r e s s , K l l o b o r i

F ig u r e 2 .1 9 Friction strength o f jo in t, sa w cu t. and fa u lt su r fa c e s o f a variety o f rock typ es under d ifferen t c o n d itio n s o f tem p eratu re (to 400" C ), rate, an d a m o u n t/p ressu re o f w ater. R o ck s in clu d e sa n d sto n e , lim e sto n e , d o lo m ite , slate, m arb le, gran ite, gabbro. m o n z o n ite . d u n ite, a n d ésite, trachyte, tu ff, and serp en tin ite. R ep ro d u ced from S te sk y . 1 9 7 8 b .

Effects o f strain rate and surface ro u g h n e ss on friction have also been studied experim entally (O h n a k a, 1975). Static friction w as found to be alm ost independe nt o f loading rate. Frictional force generally increases with sliding displacem ent. This behaviour is related to the am o u n ts o f ad h e siv e and/or abrasive w ear particles. Frictional beh a v io u r o f soft rock is m ore in fluenc ed by roughne ss than that o f hard rock (in hard rock, asperity tips are crushed d u rin g n o rm al load application). Beigel et al., (1992) e xa m ine d the b e h a v io u r o f W esterly g ra n ite sheared in a rotary apparatus up to 20 M P a normal stress. T hey found m acroscopic frictional properties evolved to steady state through two distinct stages - initial slip and slip hardening. Initial stiffness was roughness dependent; sm o o th e r sam ples s u p p o rtin g equal or higher shear stresses than rough sam ples at any given displacem ent. A distin c t yield point was observed after which slip hardening ensued. R ough surfaces reached this yield point at a higher d isplace m e nt and e x hibited hig h er rates o f slip hard en in g than the smooth, and over m uch greater distances. At steady-state, friction o f the rough surfaces was greater than that o f the sm ooth.

T h e effects o f variations in sliding friction at low velocities (under constant normal stress) are show n in Figure 2.20. W ith a step increase in velocity, there is an instant increase in d y n a m ic friction (direct effect), followed by a gradual decay to a steady state value (evolving effect) w hich d ec rea ses with increasing velocity as shown in (Figure 2.20).

fast

slow slow

a-b

slip

Figure 2.20 Rate effects on friction using a single state variable constitutive law (upper diagram) direct effect (middle diagram) evolving effect (lower diagram) the combined effect. (Scholz, 1990).

The parameters a, b and dc are determined from laboratory experiments. The critical