Settlement of a Soil Layer. One-dimensional Consolidation and Oedometer Test. What is Consolidation?

Transcription

1 On-dimnsional Consolidation and Odomtr Tst Lctur No. 12 Octobr 24, 22 Sttlmnt of a Soil Layr Th sttlmnt is dfind as th comprssion of a soil layr du to th loading applid at or nar its top surfac. Th total sttlmnt of a soil layr consists of thr parts: Immdiat or Elastic Comprssion Comprssion du to Primary Consolidation Comprssion du to Scondary Consolidation Th immdiat or lastic comprssion can b calculatd using th lastic thory if th lastic modulus of th soil layr is known. In this topic, w will larn th consolidation thory that is usd to stimat th comprssion du to primary and scondary consolidation. 2 What is Consolidation? Th procss of consolidation is oftn confusd with th procss of compaction. Th diffrnc btwn consolidation and compaction can b apprciatd using thr-phas diagrams as shown blow: Air Compaction Rduction in th olum of th air Air Rduction in th olum of th watr Consolidation 3 What is Consolidation? (Continud..) Compaction incrass th dnsity of an unsaturatd soil by rducing th olum of air in th oids. Consolidation is a tim-rlatd procss of incrasing th dnsity of a saturatd soil by draining som of th watr out of th oids. Consolidation is gnrally rlatd to fin-graind soils such as silts and clays. Coars-graind soils (sands and grals) also undrgo consolidation but at a much fastr rat du to thir high prmability. Saturatd clays consolidat at a much slowr rat du to thir low prmability. 4

2 Th Nd for Consolidation Thory Consolidation thory is rquird for th prdiction of both th magnitud and th rat of consolidation sttlmnts to nsur th sricability of structurs foundd on a comprssibl soil layr. Diffrntial sttlmnts that can lad to structural failurs du to tilting should b aoidd. Othrwis, you ll nd xtrm masurs to sa your structur! On-dimnsional Consolidation Sinc watr can flow out of a saturatd soil sampl in any dirction, th procss of consolidation is ssntially thr-dimnsional. Howr, in most fild situations, watr will not b abl to flow out of th soil by flowing horizontally bcaus of th ast xpans of th soil in horizontal dirction. Thrfor, th dirction of flow of watr is primarily rtical or on-dimnsional. As a rsult, th soil layr undrgos ondimnsional or 1-D consolidation sttlmnt in th rtical dirction D D Consolidation Th Spring Analogy Initial Condition Tim t = Val Closd No loading on th piston Prssur gaug at zro Val Closd Loading on th piston Prssur gaug at maximum Tim t = t 1 Tim t = t final Val Opn Val Opn flows out No watr flow Prssur rading Prssur gaug drops at zro Spring taks Spring taks all som load and th load; comprsss; maximum piston sinks comprssion 7 Th Spring Analogy (Continud..) Th spring is analogous to th soil sklton. Th stiffr th spring, th lss it will comprss. Thrfor, a stiff soil will undrgo lss comprssion than a soft soil. Th stiffnss of a soil influncs th magnitud of its consolidation sttlmnt. Th al opning siz is analogous to th prmability of th soil. Th smallr th opning, th longr it will tak for th watr to flow out and dissipat its prssur. Thrfor, consolidation of a fin-graind soil taks longr to complt than that of a coarsgraind soil. Prmability of a soil influncs th rat of its consolidation. 8

3 Bath Th Odomtr Tst Soil Sampl Vrtical Load Confining Ring Th odomtr tst is usd to instigat th 1-D consolidation bhaiour of fin-graind soils. An undisturbd soil sampl 2 mm in hight and 75 mm in diamtr is confind in a stl confining ring and immrsd in a watr bath. It is subjctd to a comprssi strss by applying a rtical load, which is assumd to act uniformly or th ara of th soil sampl. Two-way drainag is prmittd through porous disks at th top and bottom as shown in th figur abo. 9 Th Odomtr Tst (Continud..) Th rtical comprssion of th soil sampl is rcordd using highly accurat dial gaugs. Initially, 1 % of th rtical load is takn by por watr bcaus, du to low prmability of th soil sampl, th por watr is unabl to flow out of th oids quickly. Thrfor, thr is ry littl comprssion of th soil sampl immdiatly aftr placing th rtical load. Th comprssion of soil is possibl only whn thr is an incras in ffcti strss which in turn rquirs that th oid ratio of th soil b rducd by th xpulsion of por watr. 1 Th Odomtr Tst (Continud..) Aftr a fw sconds, th por watr bgins to flow out of th oids. This rsults in a dcras in por watr prssur and oid ratio of th soil sampl and an incras in ffcti strss. As a rsult, th soil sampl sttls as shown in th figur. σ Strss Tim aftr application of load Sttlmnt u End of Consolidation Total Vrtical Strss σ Effcti Vrtical Strss Excss Por Prssur Tim aftr application of load Th Odomtr Tst (Continud..) Sral incrmnts of rtical strss ar applid in an odomtr tst usually by doubling th prious incrmnt. For xampl, aftr th compltion of consolidation for th first incrmnt undr a rtical strss of 5 kpa, anothr 5 kpa of rtical strss is applid so that th rtical strss during th scond incrmnt is 1 kpa. For th third incrmnt, anothr 1 kpa of rtical strss is applid so that th rtical strss during th third incrmnt is 2 kpa. For ach incrmnt, th final sttlmnt of th soil sampl as wll as th tim takn to rach th final sttlmnt is rcordd. σ = σ + u 11 12

4 Th Odomtr Tst (Continud..) Th nd points from a numbr of loading and unloading incrmnts of an odomtr tst may b plottd as a conntional strssstrain cur as shown in th figur on th right. Vrtical Strain (%) Vrtical Effcti Strss (kpa( kpa) 5 kpa Th incrmnt of rtical strain ε for ach loading incrmnt is gin by: ε = s h whr s ult is th final sttlmnt for th loading incrmnt (i.. th chang in sampl hight) and h ult Th Odomtr Tst (Continud..) Sinc th sttlmnt of th soil is only du to chang in oid ratio, th rtical strain ε can b xprssd in trms of th oid ratio of th soil sampl at diffrnt stags of th tst. 1+ o ε h h h = = h 1+ In th abo quation, is th chang in oid ratio du to th loading incrmnt and is th oid ratio of th soil sampl bfor th application of th loading incrmnt. is th initial sampl hight Th Odomtr Tst (Continud..) Sinc th oid ratio of th soil sampl at diffrnt stags of an odomtr tst can b stimatd using th quation on Pag 14, it is customary to plot th rsults in trms of rtical ffcti strss σ and oid ratio as shown in th figur on th right. σ (kpa) Th natur of th graph is not affctd by th chang in th rtical axis. 15 Th Cofficint of Volum Comprssibility Th cofficint of olum comprssibility m is 1.2 dfind as th ratio of olumtric strain or.8 chang in ffcti strss: m ε = = σ ( 1+ ) σ σ 1 2 σ (kpa) Th units for m ar th inrs of prssur, i.. m 2 /kn and its alu dpnds on th strss rang or which it is calculatd. For th scond loading incrmnt shown in th figur abo: ( ) 2 m = =.182 m /kn ( )( ) 16

5 Comprssion and Expansion Indics Th -σ cur bcoms almost linar if σ is plottd on a log scal as shown in th figur on th right. Th slop of th loading cur is calld th Comprssion Indx C c and is dimnsionlss. It is dfind as: C c 1 = log σ ( σ ) Th ngati sign is usd bcaus th oid ratio dcrass whn th ffcti strss is incrasd. 1 C C c log(σ ) Th slop of th unloading cur is calld th Expansion Indx C and is calculatd using th sam procdur. 17 Maximum Past Vrtical Effcti Strss is σ max Orconsolidation Ratio (OCR) Ic Past Ground Ll Clay Sral million yars ago Erosion Clay At prsnt Prsnt Ground Ll Prsnt Vrtical Effcti Strss is σ σ OCR = σ max OCR is dfind as th ratio of maximum past rtical ffcti strss (σ max ) or prsnt rtical ffcti strss (σ ). Th maximum past rtical ffcti strss is also calld th prconsolidation prssur (σ c ). 18 Normally Consolidatd (NC) and Orconsolidatd (OC) Soils A soil that has nr xprincd a rtical ffcti strss that was gratr than its prsnt rtical ffcti strss is calld a normally consolidatd (NC) soil. Th OCR for an NC soil is qual to 1. Most NC soils ha fairly low shar strngth. A soil that has xprincd a rtical ffcti strss that was gratr than its prsnt rtical ffcti strss is calld an orconsolidatd (OC) soil. Th OCR for an OC soil is gratr than 1. Most OC soils ha fairly high shar strngth. Th OCR cannot ha a alu lss than Prconsolidation Prssur An odomtr tst of an undisturbd Start of th tst sampl of an OC soil shows an - σ c log(σ ) cur as shown in th figur on th right. Th slop of th -log(σ ) cur is fairly flat until a rtical ffcti strss qual to th prconsolidation prssur (σ c ) is rachd. Byond this point, th slop of th - log(σ ) log(σ ) cur bcoms stpr, i.. th soil bcoms mor comprssibl. Th prconsolidation prssur is lik a yild strss for soil. σ c This fact can b apprciatd by rotating th cur by 9 in anti-clockwis dirction. Dosn t this cur rsmbl a load-xtnsion cur for a mtal rod? log(σ ) 2