RS_FrictionNotes

RS_FrictionNotes - Hang on 22.3»— .EE . . ., ....

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Eng-u. as 3....» Ens—mu. .5 lingulowgqullrl =€9ir§51fi53fi5 1:&E§El§.3.unr=nnrl . . éEFnHEJEEME-riu min-Inwaprfi—Enm Fir-am naming-lyniwnssgnlal ‘ , gzkrulr-m-HEFP Ema-53.1.33!- Ania-103.5. lulu isfirflnvnlfil—Q-uwauu ._ , I gala»... §L?F&_?néfl¢aafl. 13:23.?ngagu , . EEELEYEEHEE EEEIESZEHETEF HS. :9... .35 pa. 7a r1. .335 {a «5...:- 25.55. 1.5.3.2. g: . . . 5!. figural-El. E 3.82 a! 2...! IEnSQ 5.1 .u is .r- . inns. aginrlranBrHSAFqflflu Eng... 3% as. 511... a. E... EEEEEFEE nunn-rrwguapcl.ou¢1E-lhun Jae.” _ 7 fr rmcng’r‘q _,u.fiuagfl§sfip_n sin??? irks“:qu ‘ .8 I, B-Iln... av. . . . . .....h..£;.:.i..,.££ rLEetirshrfihfi 509: .5002 LIJMAH- ::Y .q EPS KG“! 1‘? 0.L. 2000 Rain. «'1 Skin. Rah... ComIL’LuLWL Laws Mokuo-L‘ux I been”: { _ TI'MQ‘JCFIMOIHJ” SLaL‘L FH‘LI-run “ VCIoLILr -41 {telly-.3 Ffi‘dj‘iofl .. McMoFYHEpCtQJ'I I SL611. cltfutlbuq } Gmucr7"%c~l1'°“\ 0c 5: ‘- ‘ Ffi'c ‘nn MO I; ‘ “(WWW {Lift-I)? Drum-4,, “:1be L ) J I /"" =5/u(v,9 :3 / (V, 9) g ulitkngL'oh '3;wa loj-L‘M /“: é/vu le-ifx'ch/ I I0;"UQ,IJQIL? 0V1!— IcL or "I‘L'B‘i go dgnn'h cor-fka . III-Isn't. cyth" LAL-rolm? OLJnguL‘o-A: I Con5HLu‘n‘w. Law; '32? Valule J'UM’O Lula JLoI-J Ive“;qu Shaw-Mu; 439., a. Vc'otJ7 hum}; I “Mk-An) Er a oflcrwn/ who" SLR}? -— FLoLL Okay-c; IV'LmJ- :4.“ LL d141, VclociL? wealqflk) DP VgLQ‘Jl? ngmjl’L-h‘n) Cw 013$wa WQLQJN‘OIJ'. c 0'66 I I ' Load Point Velocity o 1.0 {10.0 p..q 10.0 1.0 no.0 [.1sz Ir: I I I I ) '0 0.64 [L 8.6 A “a S E o 62 .2 b .9 'a a: 8.2 O o 0.60 s. o 0 U 0.. bx“ $627150 Shear Strain EFSZC3 1?)“:{00 fl: D; , O.4mmls—>§<— 4nuan————> Load Point : Quartz 801186 2 Velocity f 6 14 14.5 15 E Load Point Displacement (mm) Roi; # Fflll‘h‘D-A Law! :_C be]; pail-Po“ rcccrv-AUL Vol“— SLt-Lt VGH‘LUL: .. r) I v 4' I? I V 8r! CLm-ocl-u-r'tcr I] I, /0 + 0' n fl PLryu'csf 111:1»: J ‘ L~Y€pcrbflm VLl-g'.’_r A“ lurchtl. } i - o ulfikn I. .' aw 1) i9: [_\./;Q (TM curl 'DQJ'U‘LLL) OH: on OM012 surch Poss-“Ht Imus fl DHch GFpLGL' } a. 1n Us EvoluL'o-A 9"ch 1 b IAKV. "' 7; $1 Dulc- L [V5]? ' /A K Q—‘KF Fug”), fat-Mob, 0" cc pacL HILL 5L“! «mu sl:J: ; 9 = 17c => dig r. o c y “9 5‘ 4. (it H‘U‘O) be.er /u-/-Io = (Ck-1?) in Va (o—L) = ("S/A...- AIHV Conn-“kw ‘1 L“ Wt a la fur Fn-LL'M 4 r?- 8 Rr sl-m: In HWL (I) coda Lt Wm“ ,3. It" To IF (a 1' B I“ Use - TE chlw‘mgr SLR“ v° T): ’ A-B : ‘C :3v VlIocl7 ij-‘jH-CMM) 0‘ {-1 L are. SMaNf ofl'wr-‘onlur ConII'th JcI-crw'neofl From EKFLrI'rwtnl-nf Mao-JuWJ-I I 30W in Hm WI-L [0”? Lo Iod- pg, L04 Mull-J up ’ija . El K V? Modmninj 40-11: //////// N S] JP“; VJ“ L? k ; f- ? ILthSLHIy _> I) -= o P Q ln 1 3- L In V. 9 u M f f (m) (T k. —. c. '_ 2-. fl, £01.? J 2') .9. ': l '- ‘LE 02‘ 0% DL V Ewan com-n3 mot Ly H-eff A5 I} 3H“ ) “(i -_. IQ (VIP - V) V. L m 6:an 1— d € ' Solvc 3 i2. 0-9 Simullrweou; Cclumhanjl wiPL ] cu c. Condra-‘AJ", 69 mm HAM Rcarrmsg (I) it but r‘n C?) L, JLLu-M'AL 9 hut-or? Farm (1) V = Va &KP[ f 7° ~blfiC/Gjec)] 0- *6/62 . / Sch/L: df‘n—J : —- V. exr[fl'/“°'b “(KEV-1) P 0 ate a " 2:? -— i " v9 072 a“: pg ----—"'—'"--—5 m , am 5 0.71 .5 4.24“ . 35 .... -- Didarich law [’5er LU. E. 5 . .13 Emu WM" 9 o 70 :3 N r n % ' Data E G” ' 8 -— Ruina Law ‘3 M“ ‘4”? Dieterich Law “0.615 15.3 m . 0-69 20.35 20.4 20.45 Dunn-men: (rum) Shear displacement (mm) “5" __ .qu Au CAL emu q, E o— ..... ..-Diezgrichllw rr€;£a' [Q U lo— 1/‘M_l E 2CD % Skew I‘lflr: ED fu- Inag f:th LE, 6 Exavf’lk or 1- flak \fwfubh. Mom‘or Gum 0.635 10.9 H Il.l Displacement (mm) D.r~ 1-9 M gr Lav: ruck Suraq‘r I low! T 09" ‘17-’60 .4 Eur jl‘ouuulch Ruujouj{ Erna; I‘Hloloe Sl'uk EVOIUL‘M Lad-J! Slip UJ'. Tn'l't EVO'UL'N‘I II EVOI-JL‘na Q V=0 EVULJLEMJ Rxflflg Law $8 = '- V9 In E (9’? * D; P; ' lg- : lxm_1/M,r W fig = 1-1;: DubacL T...“ Z a = 0.0, L I: = C2 OK 54141. CV0'9+.“.\‘ p = 10° M 0 5"“ IDDD I500 (D ’2 (Vlr_V-) th-k, ‘- / DispLI-zlmm (microns) FA clhrqu'wlv HM FD, [iv-Ma. lab-J I MOJL 51am.» JULL ryn|MLLhr "GlL‘len Jar-c Van‘AI'MA 4 «ML alwofl Fuflbh 1v- Ct:JL-/1;v;:l~, Cone bad; L, I-Lu «New wt. look aL +l‘W —¢J{Fw°QML cLanje; 23.902 MAIR ANDMARONEzFRICTIONOF FAULTGOUGEATHIGH VELOCITY iv: £1115}. Ltalrwjl 0.53 E 0.51 E 0‘55 0‘55 Pew-m - It“. ~Ehgnj LOW” ( E 0.55 3 0.54 ALTO IerAJLl—nl 9.5 IUD ID.‘ “.0 1|.5 Shear Displacemanmm) =1 1- a J' L Ln V39 ,5 I (b) /A /° "v; pa 1.0 - i 7' a \- E’ 5.5 939 2 I - E I: at t 7. DB 9.! 10.0 10.5 1'|.fl '||.6 Shear Displacemenl (mm) Mbk #MQM' 13‘}? (Jan) Coeflicienl oi Friction Coeflicient of Friction @ E95 16'; Wilo’oo Tim (4 mom?) ocpudml Hmlmj '—"—'—-—--—-—____—-—___.._.___.___.__— 0‘2er v9. ken}; $341;ch Vs. Unjl'nyca'x 49:45: Cow'le (NSC) {hunk Mari-Hind at??? (oi-ML WU)- ELLH L‘nq m Kodrhcr * Muir: I l998}ao°a I MM” JLUul-‘u Orificth SLNmA as:n;_ S l-‘Jg-L‘oicfl- flick EKfU'I'MnL’ Load point Faun surface + Typicaf oian 0.77 urer <—-10um|.udpcmmloeny ----—>-ziy .0 a... Ch I I I I Ax” 013 ’5 0.73 J E 0.72 Slide Hold ——>I;S|ide 1:, m, 0.71 - . a u 500 _ IOOO E “0 In W m Tlme (3) U a,“ "mum-m no no an m mo m 10H lhold. v“. mum 0.53 O. 77 I 7 I8 I 9 Load Point Displacement (mm) 4-— nurnh Laid polnl vole-c211 ——> Flull llll'llul —--- 0.71 21 2H 21.2 Displacement (mm) Coeificiem or Friciion [5 1s 17 I a I 9 Load Pclnl Displacement (mm) Hto-ll'hj Iaj {— Friction ( 021/6“ ) Layer thickness (mm ) Load-up iC-SHSE Partial unloadé Zero load sequence i g SHS § SHS Loading rate IO urn/s Unloading rate 300 umls Load-up iC—SHS-f Partial unloadg' Zero load sequence 5 5' SHS § SHS Dilation T l Compaction 5 10 15 2O 25 30 35 Loadpoint displacement (mm) Figure 4: Karner and Marone: submitted to .TGR 16 Aug. 2000 Frictional healingAu Zero-load SHS Conventional Partial unload SHS <—————-—> 0.07 :01chl 'Lime [005EJ m, :2.“ llJnngIofitticmtculOOSttmls I Unload rate 300 urn/5 0.05 0.04 0.03 0.02 0.01 m204-m206, m209—m211. m213. 111214 0 0 0.2 0.4 0.6 0.8 1 Normalized shear load ('t It ) hold ss.prehold Figure 5: Kamer and Marone: submitted to JGR 16 Aug. 2000 MonMj FAX-.1434“ Healing, S"Mulc-L\lunr [Flinn hr’Gm fl - inV “LOL‘M; r“(J-L's I FBLL Dal-M1; oit ire-Afr"? in.)er Junk; Os Ii-‘o'e. JuM-I/idi Phase plane plot shows variation in slip velocity, friction and state during a hold fest lines of constanl slate slope = a x 0.01 K‘I5.D,-ID Increasing um 0.65 0-“ Direct effect 0.33 io/,.,.-./J Friction Law Friclion u = 11° + a |n(VN°) + b |n(V° B/Dc) State Evolution dB/clt = 1 -V6/Dc sleady-alafe sliding friclion velocfi de endence . siope=b-a= .oo Elastic Coupling du/dt = k( VIP - V) Loadin rate effect on hea Ing Friction 0 5 10 15 2D -8 -4 -2 O 2 4 sum)= ianNu) Loading rate effect on frictional healing is due to a combination of the friction direct effect an state evolution DevaaL'on pNM ® E19915; HIM/co flak {rink Law: In cl uni; VLiocIL' ~49?» M fl 9? bare Erich-1 , iireclfiflflci /" ASSUML no a:M in I'niL'pf pn'cL'on ’LY‘LI' EPszez "ilwloo Sllda-hold-olldo simulation touhold V“: 10 urnla Numerical simulations. Effect of loading rate on healing V i 0 sh. _' Dcr-‘valw'm op loo/ml: huh“; ML. Held ands Dlaterichlaw lo Ev,“ bolt/rhk Ic‘wr' a“ 10" 1o" 10‘ 10‘ 10° 10‘ 15 Hold T'ma s I H Frlctlon Law 12 0.10 Eater-iota mm.” m: u = no + a ln(VNo) + b In(V°8/Dc) 10 State Evolution _ r b-0.00D.b-n-0.001 3 d9/dt = 1 - VBl’DE ) {J‘- 5 um.k-1x10"um" deldt = - VOID: |n( VB/Dc) Elastic COUpllng det = k( VIF - V) Norma-kn B),- l; ,J-Lu‘ IL}... {Lu U. 6L r In 10) Healing. Ap o - -v- - o m '9' 1° 1° 1°: “’3 1°. ‘° Current rate/state laws ”°”'d'me”5'°"a' “0'” “ma Vm '11 include the effect of loading 00 rate on frictional healing 6’ rtak Fn‘ck‘ow (SI—Alt; Value.) T at f 1 a?” = (£(Vlf -ij) :0 Cal- (out 1 l \/ -= (In. FLO}; Plum FIOLI) 'Hf’m' take. “'0 =V|r thing-r fuz/A‘rJ-alnv) If PL 0 A ConJL‘nL ’ ’V: 2'- — ':_ '3 I“ ,c, ‘7‘ /* .r, (C 5 ) EML do I _ V9 A-....-r‘ Coeflicient 0! Friction ‘1." “Run, «LE/k 6.1,. may Lu Can 5 we) 'Fn’l L3. (3 I?/h/O‘ “' “of”. on heal-‘6.)- cul'V‘V-J' r‘S b in? beLavn‘or 0L- An; Die. Len'cL law-J hold I .‘n cluoLk/g cruf ml” «L‘Mfi Put £31k“ 4f rc-aijerwL in these), ri-‘an5 Implias a > '3 velocin slranglhaning Dietarich law simulalion 0.73 ' Data 0.72!— . ‘ 19 a an n Hoid we I ant - ‘ 0.70 :- A I. 1.0.0101 0'69 b-O.DDII “00:05 . no“ A Dc-3.5 blaze“, gm“? load 0.68 06-3—1 ohm 34— 505 —|-E Im lies Ruina law simulalion a < b va ocity weakening 0.72 0.71 (no homo: 0-69 Ego-GOD" O 007! A l .l l- . b-omoa “’30 0.53 can” 34. 50‘ -.5E Time (s) BgA-J' £51- gr 5. radii. OE L4,; “ML; Coefficient of Friction -— Dm ------- -- Ruin: law. I slal: variable simulation I0 Huld Iim: (s) l7.5 [8 18.5 Load Point Displacement (mm) a: 0.0m L = 0. o 104 De. = lz/W‘ Figuch. Marun=.URMMS 1991 Comrarnm L mm). a 5M7“. ILL at GAJ'H-uJ‘VL para-«LL43- Simulations based nn Dam rm to slide-hold-slide 0.04 A In pmrs dltaul'Fig.3 0 1111111: — Dictarich Ruina 0.03 0.02 0.0! Static Frictional Strength and Healing Rate. Vary with Loading Rate —-0— i pm}; --° " 3 urnls -'-""‘ 10 urnfs '0' '30 umfs “+— 100 urru's 0.04 0.03 0.02 0.01 Frictional Healing. A}: 102 103 Hold Tlme (s) 10° iD' Luldlnu fill 066 q— 3 "mfg 1—1 Hml'a—b Coefficient oi Friciion O O b- 0.62 24.0 25.0 26.0 Load Polnl Dlsptacement (mm) EPSZG] iglmloo Heath-a; Pci‘c I‘J' (EXZ.?°.n) i; I g a“ aura. waiver RM Prelim-r {=52 1- 8 ‘R Phi-1 9- q x fol-3 itqu Expuémiai MQcJurimL of 51:. wk erm— on Ski-.1 Entin'... 4. Magi-5?. All Relaxation. Comparison Between Data and Predictions of Rate and State Friction Laws Constitutive Parameters from Velocity-Step Tests -—_._-——.-.. Constitutive Parameters from Hold-Slide Tests Dieterich a a: 0.008? a = 0.0075 b: 0.0062 in: 0.0101 Dcdfi um 0520.3 1:. 1o“ 10' to2 to3 10‘ 10‘ ‘HUM'J:LY DEFQJ'ICQJICLOF “(chi-M5 ‘ D‘: I Q5- ' Tim - LWVJQ titled}? Lad-4. S‘uv- C—Lgf I jam? 9. Dual-'Lf For hcgl-Nn; /Pu[¢_ EFS 363 Jepmfimu, HIID/M Distributed sheu. rapid a comminutlon \ lneipient Riedel: Riedels pervuive. curve to ‘r she-rs B shem. linking to Riedelr Shear stressJ Normal Stress Friction rate dependence Wren“? 0.003 I LII-[U mmls 0 fl i-l,“|1mt-"< 0.006 0 (mt-UJ minis A 0.00i-0.0l mm}: a March: «I: Kilgore I993 '- I c. A o . t I! l f A 0.000 Friction Velocity Dependence (a-b) p o s § 6.004 0 5 10 15 20 Shear Displacement (mm) o. - 15 MPI (b) shear displacement I 2-4 mm o 6-8 mm o 1042 mm a 14-16 turn I' 13-20 mm 0.008 P o D a .° :- a N p o 8 0.002 Friction Velocity Dependence (a—b) -D.004 0.01 0.1 l 1 0 Velocity “mp (mmls) Figure 6. (3) Friction velocity dependence (a-b) as a function of shear displacement for velocities 0.00l-I0 mm}: and 0.. = 25 MPa. Several tests are plotted for each condition. Data fi'um Mai-one and Kilgore [l9931 for velocity 0.001-D.0l mm/s and 0,. = 25 MPa are superimposed. Note the transition ii'om ve- locity strengthening to weakening with progressive slip. (b) Plot of (a-b) for the discrete displacement ranges shown as a function of upstep velocity. Lines indicate the trends at ini- tial (2-4 mm. solid line) and final (is-20 rrrn. dashed line) dis- placements. Velocity has little influence on weakening for slip > 5 mm. [—b Well-Developed Y shears /"'-' Summary of h¢J'-Ai;rioo.ml' EPYZ 6'! I9 o em.ch iM‘Wosl'I-uei-un [win dLVEIoPWb-nl' . : _._.i. Fault Zone Structure R| Riedelihelrl 7" R Riedei Shem-s r /_ ' Shem in“; ‘Hm'canLS! Moir— it Matron; I ii“)? i t’ 200 I 1.0-IO man * 1H - i .til mini-3 O (Mil-(Ll tumls 150 A 0001-001 mmls 100 D: (um) 50 0.01 0.1 1 Velocityupmp (mmls) 10 Figure 4. Critical slip displacement (0;) as a function ol'up- step velocity for a range ofexperiments at 0,, = 25 MPa. l3c is systematically larger as a function of increasing velocity. _.H- @ EPS 2C? Villa/.0 78 Rock Friction L‘ M f r... O c 3.21:0: :::::: 5;: T when “WU V = We. W 3° '70 c SD'IDLZ a ENGELDER I'IBTGI pfl-r I /_ F 15- .55 x x _H RglaL‘un LcL New .70 "5 .50 I It. I once I I I . - f 65 7 I” I VLIobL> sze.‘ .1101? I pnikon . no" no" lo" in" ID" IO" Io" ID" no" VELOCITY lemlue) Fig. 2.18 Comparison of the 11,—] and pd—u relations by assuming lhal p, after HCC‘LVj “1"” C" holding al I is equivalent lo M at a steady u - 27:. Data are from Dielerich (1913) and Soho]: and Engelder (1975): (A) p.-.“ quam. sandstone, a“ - 13.7 (3/4 2." Infill-“\(t) MP3; (B) pd—u. Westerly granite. 1.96 MPa:(C) pd—u. Westerly granite, 20 MPa. 3’- 5 pm (Dielerich. I978). Friction scales are ofl'se1 because base friction is nol reproducible. Mar 5 FLrJ-L “6L £35422”. 0 64 S ceiu a) A” : (on-b);an 0.63 —- ’- o-W Alum}; 0.62 “s a 6‘ - mm mug! 0.51 0.60 Quartz gauge. 0’ = 25 MPa Rough granite surface: 10° 10J 102 103 10“ Hold Time (s) 0.64 ........Hl (VUFI Fm“) Minn“. (Vm=l0 pmfs) 0.62 _‘ _' —°—-u. 0 0.60 Slope := —(b lnthJ b=0.004 / 0.5 B Slope = —(b-a) MID) b-a = 0.002 Quartz gauge. 0’ = '25 MP: Rough surf aces 10" 10'3 10'2 10'I 10° 10' 102 103 10“ 0.56 Origin onging Effect in Granular Quartz at 20°C: Humidity Effect R.” T‘Mrtfn In". Humidiiy = 50% 0.58 : 0.55 .9 5% .5 0.64 E 10 ' 30 h: 0.02 3 Hoid limo (I) 0 0.80 10 'I1 I! Load Polnl Displacement (mm) Humidity = 5% Coefficient of Friction Hoid1|rna (I) 1D 11 I2 Load Point Displacement (mi-n) Fry *maran‘.’ Mi I'fl'l'tl 0.020 O 5%FIH A 10%FIH I 55%FiH 0.015 10.010 <1 0.005 0.000 1000 Hold Time (seconds) 1 10 100 10000 H5153 min/h Humid: L}. 010 pm JZEHQ op {"r-‘zlflfl I Heal“) Mk 4 ring}? - rick ml; oflpvufihm are. finial-<1 Lr huh-'9‘“) 9. HI "1112. 5". RH use a. 0.!!! 0.000 PM 1.00 m 0100 I100 I000 OM Icon Shear Diupiacamoni (melons) om mmmunn um I. 0.” DJII II” IMO Icon "00 I100 “on "00 15000 Shear Dltplncemeni (n-iicronl) 0.0010 0.0005 3 5 0.0000 0.0005 0 20 40 50 80 100 YnFIH FPXL¥ Moron, NF 1'“ fH-f? 10%» ...
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This note was uploaded on 07/23/2008 for the course GEOSC 508 taught by Professor Marone during the Spring '07 term at Penn State.

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