LA ENSEÑANZA TIC Y LA MÚSICA: MÁS ALLÁ DEL AULA 38

T h e an g le o f fa ilu re m e a su re d fro m all te sts, at all c o n d itio n s, is p lo tte d a g a in st the e ffe c tiv e c o n fin in g p re ssu re in F ig u re 5.21 an d te m p e ra tu re in F ig u re 5.22. T h e d a ta is s c a tte re d an d th is is d u e to th e w id e ra n g e o f c o n d itio n s an d h u m a n e rro r in m e a su rin g the an g le (3 % , see p a g e 118). T h e to tal e x p e rim e n ta l u n c e rta in ty a p p e a rs to b e ab o u t 13% . T h is e rro r is in c lu d e d in th e c a lc u la tio n o f th e sh e a r an d n o rm al stress c o m p o n e n ts a c tin g on th e fault p la n e , a lo n g w ith erro rs in c o n fin in g p re ssu re a n d lo ad m e a su re m e n ts, an d c re a te s a ± 5 0 M P a e rro r on th e se stress co m p o n e n ts. 2 3 5 o a> o> c < 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0

Effective Confining Pressure (MPa)

F ig u re 5.21 Angle of failure as a function of the effective confining pressure.

6 0 5 0 - 2 4 0 k _3 I *5 3 0 k o U) c < 20 - 10 - 100 . 1

Tsukuba Granite (wet) Cp 480MPa, £= 10'^/sec Pp between 30-300MPa 200 3 0 0 4 0 0 Â A Temperature (C)

T h e an g le o f fa ilu re in c re a se s w ith in c re a sin g e ffe c tiv e c o n fin in g p re ssu re , e sp e c ia lly at low p re ssu re s. A b o v e 2 0 0 M P a, the an g le o f fa ilu re is not so sen sitiv e to th e e ffe c tiv e c o n fin in g p re ssu re , b u t still th e a n g le seem s to c o n tin u e in c re a se slig h tly . W ith re sp e c t to te m p e ra tu re , the an g le re m a in s re la tiv e ly c o n s ta n t w ith in the ra n g e o f sc a tte r a n d no te m p e ra tu re d e p e n d e n c y is o b se rv e d up to 480"C .

O h n a k a (1 9 9 2 , 1995) p lo tte d th e fa ilu re a n g le a g a in st te m p e ra tu re an d n o rm al stress (a c tin g on th e fa u lt p la n e ) fo r dry (in itia lly in ta c t) W esterly g ra n ite , an d fo u n d that it w as te m p e ra tu re in se n sitiv e b elo w 8 0 0 K , but in c re a se d w ith te m p e ra tu re a b o v e th is p o in t. F u rth e rm o re , th e fa ilu re a n g le w as in se n sitiv e to n o rm a l stress b elo w 1000 M P a b u t in c re a se d w ith n o rm al stress a b o v e this stress (w ith in th e p re ssu re ra n g e o f 2 0 0 M P a a n d 1100 M P a). A n g les o f fa ilu re fo r w e t tests fro m m y stu d y also sh o w a p o sitiv e re la tio n sh ip b etw e en th e fa ilu re a n g le a n d the e ffe c tiv e n o rm a l stress (F ig u re 5 .2 3 ). H o w e v er, b etw e e n 5 0 0 M P a a n d 1000 M P a, th e d a ta are q u ite sc a tte re d an d the fa ilu re an g le a p p e a rs re la tiv e ly c o n sta n t. It is o n ly b e lo w 5 0 0 M P a an d a b o v e 1000 M P a th at the p re ssu re d e p e n d e n c y is ev id e n t, w h ic h w o u ld su p p o rt O h n a k a 's (1 9 9 2 , 1995) o b se rv a tio n s fo r dry W e ste rly g ra n ite : m y d a ta are fo r w et an d dry T su k u b a g ra n ite . H o w e v er, it is to be n o te d th at as the c a lc u la tio n fo r e ffe c tiv e n o rm a l stress u ses th e fa ilu re an g le, erro rs are a c c u m u la te d an d the c o rre la tio n is e x p e c te d . H o w e v er, th e in cre ase w ith p re ssu re is su p p o rte d b y th e c o rre la tio n w ith e ffe c tiv e c o n fin in g p re ssu re (in d e p e n d e n t o f the fa ilu re angle).

2 3 (0 U_ 3 0 o 0) O) c < 0 200 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0

E ffective N orm al S tress (M P a)

5 .5 .3 T e s tin g th e d a ta to th e e ffe c tiv e s tr e s s la w

T he effective n o rm al stress is c a lc u la te d by su b tractin g p o re p ressu re fro m th e no rm al stress:

a „ '" = a „ - P p (5.3) T his is only true if the e ffe c tiv e stress law has been obeyed. O b serv atio n s b y B ra c e a n d M artin (1968) suggest th at th e effectiv e stress law is co m p ro m ised at strain rates h ig h e r th an lO 'V ^ in low p o ro sity c ry sta llin e ro ck s. S in ce T su k u b a g ran ite is a rela tiv e ly tig h t ro c k and m y tests w ere c o n d u c te d at 1 0'^ s '\ it is im p o rta n t to show th at the sam ples

w ere n o t deform ed at too h ig h a rate a n d th at p o re fluid p ressu re w as m ain tain ed in e q u ilib riu m th ro u g h o u t th e d e v e lo p in g fractu re netw ork. T he effectiv e stress law is freq u en tly ex pressed as (P aterso n , 1978):

= Gi - orPp

(5.4)

w h ere or is a constant, g e n erally treated as u n ity w hen the effe c tiv e stress law has b een strictly obeyed. T he d ep a rtu re o f or from u nity is a m easu re o f the effectiv en ess o f th e effe c tiv e stress law . F o r sim p lic ity , the w et ro o m tem p e ra tu re d a ta can be d e scrib ed by th e fo llo w in g lin ear failu re c riterio n o f th e form :

- 03 = a 4- ^ (03 - Pp) (5.5) S u b stitu tin g (5.4) into (5.5) an d rea rra n g in g gives:

Cl = a + C3( b + \ } - a b ? p (5.6) B y carry in g o ut a m ultiple lin e a r reg ressio n on th e equation:

= Co + C] O3 + CiPp (5.7)

w h ere a = co ; b = cj -1 ; a = -C2/(cj -1 ), th e resu lts o b tain ed for the w et an d dry ro o m tem p e ra tu re d a ta are show n in T able 5.1. T he values o f or are close to unity, th erefo re this study d em onstrates th at th e effectiv e stress law has not b een u n d u ly c o m p ro m ise d fo r T su k u b a granite at the e x p e rim e n tal strain rate o f 1 0 'V \

D a ta a b a M u ltip le c o r r e la tio n c o e ffic ie n t. w et data only 565.187 1.915 1.05 0.938 w et and dry d ata 6 2 2 .5 8 2 2.096 1.26 0 .9 6 0

T a b le 5.1. M ultiple linear regression fits from equation 5.7 for room tem perature T sukuba granite shear fracture data.