15. Stress-Strain behavior of soils

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Bryce Bruce
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1 15. Strss-Strain bhavior of soils Sand bhavior Usually shard undr draind conditions (rlativly high prmability mans xcss por prssurs ar not gnratd). Paramtrs govrning sand bhaviour is: Rlativ dnsity Effctiv strss lvl Rlativ dnsity: I d = max - max - Whr max and min ar th maximum and minimum void ratios. Sand is gnrally rfrrd to as dns if I d > 0.6 and loos if I d < 0.3. min Obsrvations from th graphs blow: 1. All sampls approach th sam ultimat conditions of shar strss and void ratio, irrspctiv of th initial dnsity 2. Initially dns sampls attain highr pak angls of friction ( = tan -1 (/) ) 3. Initially dns soils xpand (dilat) whn shard, and initially loos soils comprss 4. Th loos sand comprsss until it rachs a platau in volum strain 5. Th dns sand xpands, thn th xpanding bgins to slow down bfor raching an ultimat rsistanc. 6. Th mdium dnsity sand bgins by contracting and thn starts to xpand. 7. Not: it is possibl for loos sand to xpand! Effctiv strss: Obsrvations from th graphs blow: 1. Th ultimat valus of shar strss and void ratio, dpnd on th strss lvl, but th ultimat angl of friction ( ult = tan -1 (/) ult) is indpndnt of both dnsity and strss lvl 2. Initially dns sampls attain highr pak angls of friction ( = tan -1 (/)), but th pak friction angl rducs as th strss lvl incrass. 3. Initially dns soils xpand (dilat) whn shard, and initially loos soils comprss. Incrasing strss lvl causs lss dilation (gratr comprssion). CIVL2410 Soil Mchanics

2 D 1 D 2 = tan ult 1 2 L 2 L 1 v D 1 D 2 D 1 D 2 = tan ult L 1 L 2 L 1 L 2 Dns (D) Mdium (M) = tan ult Loos (L) L M v D D M L CIVL2410 Soil Mchanics

3 Ultimat (critical) strss (sand) Whn soil is shard it will vntually attain a uniqu strss ratio (/ = tan ult ) and rach a critical void ratio which is uniquly rlatd to th normal strss. Th ultimat (ultimat) stat quation: d d = d d = d v d = 0 Soil is controlld by 3 things: 1. Shar strss 2. Void ratio 3. Effctiv strss This quation producs a critical stat lin () which can b drawn in 2D rprsntations for simplification: Straight lin = 0- ln ln = tan ult In 3D th looks lik this: CIVL2410 Soil Mchanics

4 Id = 0.5 Not: At critical stats soil bhavs as a purly frictional matrial Typical valus for th ultimat valu of fi ar: Clay- 22 dgrs Sand- 33 dgrs Gravl- 40 dgrs Strss-Dilatancy rlationship (sand) Frictional rsistanc of soil may appar to b gratr than φ ult If φ > φ ult th soil is EXPANDING If φ < φ ult th soil is COMPRESSING If φ = φ ult th soil is dforming at a constant volum Equation to rmmbr: Whr α is th rat of volumtric strain φ = φ ult + α Pak conditions (sand) pk Id = 1 Id = 0 ult CIVL2410 Soil Mchanics

5 From th graph abov it is vidnt that th pak angl cannot fall blow th ultimat angl. I(d) = 1 is a dns sand, whr as I(d) = 0 is a loos sand Th horizontal axis is th log of th ffctiv strss This graph mans that loos sands may xpand whn shard Clay bhavior Essntially idntical to th bhaviour of sands Data is usually prsntd in trms of th soils strss history (OCR) rathr than rlativ dnsity Rmmbr that: OCR = σ pc σ Th is paralll to th normal consolidation lin and lis blow it in a void ratio vs. ffctiv strss plot (shown blow) W don t know why its paralll and can t xplain why, w just know it is from obsrvation swlling lin NCL - normal consolidation lin log Normally consolidatd clays bhav similarly to loos sands Havily ovr consolidatd clays bhav similarly to dns sands As th OCR incrass (th soil gts dnsr) thr is a gradual trnd btwn th xtrms: = tan ult OCR = 1 = tan ult OCR = 8 v OCR = 8 NCL OCR = 1 CIVL2410 Soil Mchanics

6 Undraind rspons of clays In th first imag, as th shar strss initially incrass it dos not actually hit th (rmmbr its actually mant to b 3D) Volum chang dos not xist (prvntd in tsts) Thrfor th void ratio must b constant (this is vidnt in th bottom lft graph) Soil always hads towards a critical stat whn shard If th final total strsss ar known thn th xcss por prssurs can b dtrmind = tan ult OCR = 1 = tan ult OCR = 8 u +v OCR = 1 NCL -v OCR = 8 Diffrncs btwn sands and clay Undrstanding th hlps to xplain th apparnt cohsion (undraind strngth) in frictional matrials If th moistur contnt changs thn th undraind strngth will chang too This is bcaus failur will occur at a diffrnt point on th Paramtrs usd: Sands Clays Strss lvl Strss lvl Rlativ dnsity Strss history (OCR) Broad pattrns of bhaviour obsrvd for sands and clays ar vry similar CIVL2410 Soil Mchanics

ME311 Machine Design

ME311 Machine Design ME311 Machin Dsign Lctur 4: Strss Concntrations; Static Failur W Dornfld 8Sp017 Fairfild Univrsit School of Enginring Strss Concntration W saw that in a curvd bam, th strss was distortd from th uniform