9Mohr Circles & Failure Envelope The soil element does not fail if the Mohr circle is contained within the envelopeGLcYcc+Initially, Mohr circle is a point
10Mohr Circles & Failure Envelope As loading progresses, Mohr circle becomes larger…GLcYc.. and finally failure occurs when Mohr circle touches the envelope
11Orientation of Failure Plane Failure plane oriented at 45 + /2 to horizontal45 + /2YGL45 + /2c90+Ycc+
12= + Mohr circles in terms of & ’ v h v’ h’ u X X X h’ v’ h effective stressestotal stressesh’v’hvu
13Envelopes in terms of & ’ Identical specimens initially subjected to different isotropic stresses (c) and then loaded axially to failurefccufInitially…Failurec, in terms of At failure,3 = c; 1 = c+f3’ = 3 – uf ; 1’ = 1 - ufc’, ’in terms of ’
14Triaxial Test Apparatus soil sample at failurepiston (to apply deviatoric stress)failure planeO-ringporous stoneimpervious membraneperspex cellwatercell pressurepore pressure orvolume changeback pressurepedestal
15Types of Triaxial Tests deviatoric stress ()Under all-around cell pressure cShearing (loading)Is the drainage valve open?Is the drainage valve open?yesnoyesnoConsolidated sampleUnconsolidated sampleDrained loadingUndrained loading
16Types of Triaxial Tests Depending on whether drainage is allowed or not duringinitial isotropic cell pressure application, andshearing,there are three special types of triaxial tests that have practical significances. They are:Consolidated Drained (CD) testConsolidated Undrained (CU) testUnconsolidated Undrained (UU) test
17For unconsolidated undrained test, in terms of total stresses, u = 0 For normally consolidated clays, c’ = 0 & c = 0.Granular soils have no cohesion.c = 0 & c’= 0
18CD, CU and UU Triaxial Tests Consolidated Drained (CD) Testno excess pore pressure throughout the testvery slow shearing to avoid build-up of pore pressureCan be days! not desirablegives c’ and ’Use c’ and ’ for analysing fully drainedsituations (e.g., long term stability,very slow loading)
19CD, CU and UU Triaxial Tests Consolidated Undrained (CU) Testpore pressure develops during shearMeasure ’gives c’ and ’faster than CD (preferred way to find c’ and ’)
20CD, CU and UU Triaxial Tests Unconsolidated Undrained (UU) Testpore pressure develops during shear= 0; i.e., failure envelope is horizontalNot measured’ unknownanalyse in terms of gives cu and uvery quick testUse cu and u for analysing undrainedsituations (e.g., short term stability,quick loading)
211- 3 Relation at Failure Xsoil element at failureX3131
22Stress Point v h X t stress point stress point v h s (v-h)/2
23Stress Path During loading… t s Stress path is the locus of stress pointstsStress pathStress path is a convenient way to keep track of theprogress in loading with respect to failure envelope.
24Failure Envelopes t s During loading (shearing)…. failure ctan-1 (sin )stress pathc cos During loading (shearing)….
25Pore Pressure Parameters A simple way to estimate the pore pressure change in undrained loading, in terms of total stress changes ~ after Skempton (1954)Y13u = ?Skempton’s pore pressure parameters A and B
26Pore Pressure Parameters B-parameterB = f (saturation,..)For saturated soils, B 1.A-parameter at failure (Af)Af = f(OCR)For normally consolidated clays Af 1.For heavily overconsolidated clays Af is negative.