WEEK 3 Effctiv Str and Por Watr Prur Chang 5. Effctiv tr ath undr undraind condition 5-1. Dfinition of ffctiv tr: A rvi A you mut hav larnt that th ffctiv tr, σ, in oil i dfind a σ σ u Whr σ i th total tr and u th or atr rur. Not that th or atr do not tak any har forc (in tyical ituation), o thi conct of ffctiv tr i valid only for normal tr. Thrfor ~ σ ~ σ u ~ ~ { σ x σ y σ z τ xy τ yz τ zx} { σ σ τ τ τ } t σ ~ σ σ t x y z xy yz { u u } u~ t u zx Th rooal by Karl Trzaghi that oil bhaviour i dcribd by th ffctiv tr i univrally acctd. Put in othr ord, dformation of oil klton occur hn th ffctiv tr chang. Hovr, it i oftn th total tr that chang by orking on oil, and convrly, it i th total tr that xrt rur/forc to tructur in contact ith oil. So nd to rtain th to notion (i.. total tr & ffctiv tr) at th am tim, and adot a doubl-dckd aroach. Prur from footing: Chang in total tr Prur from oil: Total tr 1
Undraind comrion v Conidr a chang in th total man ffctiv rincial tr ( ) undr undraind condition. Thi ill rult in om chang in th man ffctiv tr ( ) and or atr rur (u). Aumtion: Soil articl ar rigid. v v Th tr-train rlationhi i: u K K v K K v v nv ( K K n) / K K nk u K / n n : Poroity K : Bulk modulu of oil klton K K : Bulk modulu of atr A tyical valu for K i 22 MPa, hil K for mot oil i in ordr of 1 MPa or l. Th ratio /u i thrfor tyically l than a f rcnt. Practically it i conidrd to b zro in many ituation, maning that total tr chang undr undraind comrion ar all takn u by or atr rur chang. It alo man that th man ffctiv tr,, cannot b changd by undraind comrion. Not: Each ffctiv tr comonnt (i.. σ x, σ y, tc.) can till chang undr undraind condition. 2
5-2. Effctiv tr ath Lt u conidr ffctiv tr ath in draind and undraind condition. A an xaml, conidr a triaxial comrion tt in hich σ 1 i incrad hil σ 3 i kt contant. (i) Draind condition: Por atr rur, u, i controlld at a givn valu. If th or atr rur i kt contant, a in a tyical triaxial tt, ffctiv and total tr ath ar aralll to ach othr. Str chang ~ σ ~ σ u ~ Linar iotroic laticity Strain / K ~ ~ ~ Linar iotroic laticity laticity / K ~ ~ ~ Por atr rur, u u Effctiv tr ath Total tr ath, Str ath 3
(ii) Undraind condition: Undr undraind condition, cannot control th or atr rur chang, u, any mor. It chang ontanouly according to th imod total tr. Thi natur mak an ffctiv tr ath mor comlicatd. For imlicity, lt u aum that th bulk modulu of atr i infinit ( 2 ag arlir). Thi mak an undraind condition uivalnt to a contant-volum condition (i.. ) Ca of linar iotroic laticity: Str chang u ~ σ ~ σ u ~ u Strain / K ~ Contant volum ~ ~ Exc or atr rur, u (du to comrion) u u u u Str ath, 4
Ca of linar iotroic laticity laticity: Platicity man that volumtric train i inducd by har dformation (xlaind mor in nxt k).?? σ ~ σ ~ u ~ Str chang G? 3 / ~ ~ ~ Strain Contant volum G 3 / K K 5 Str ath, u du to latic dformation (i.. dilatancy): u u u u u du to comrion: K Th ffctiv tr ath dnd on ho much latic volumtric train i gnratd.
Ca of linar iotroic laticity laticity (continud): Dilatancy i latic volumtric training du to har dformation, and control th dirction of ffctiv tr ath. Loo and, normally conolidatd clay, tc.: Ngativ dilation (volum dcra) K > u An xtrm xaml of thi i liufaction, in hich th ffctiv tr ath rach. u u u, Dn and, ovr-conolidatd clay, tc.: Poitiv dilation (volum incra) u u u u K >, Imlication: Undr undraind condition, haring tnd to rduc th man ffctiv tr for loo, normally conolidatd oil, making it oftr and akr than undr draind condition. On th contrary, th man ffctiv tr incra undr undraind condition for dn, ovr-conolidatd oil, making it tiffr and trongr than undr draind condition. 6