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**Shear Strength of Soils**

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**Shear failure Soils generally fail in shear**

embankment mobilised shear resistance strip footing failure surface At failure, shear stress along the failure surface reaches the shear strength.

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Shear failure failure surface The soil grains slide over each other along the failure surface. No crushing of individual grains.

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Shear failure At failure, shear stress along the failure surface () reaches the shear strength (f).

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**Mohr-Coulomb Failure Criterion**

failure envelope f friction angle cohesion c f is the maximum shear stress the soil can take without failure, under normal stress of .

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**Mohr-Coulomb Failure Criterion**

Shear strength consists of two components: cohesive and frictional. c frictional component cohesive component f f f tan c

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**c and are measures of shear strength.**

Higher the values, higher the shear strength.

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**Mohr Circles & Failure Envelope**

Y X X Y Soil elements at different locations X ~ failure Y ~ stable

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**Mohr Circles & Failure Envelope**

The soil element does not fail if the Mohr circle is contained within the envelope GL c Y c c+ Initially, Mohr circle is a point

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**Mohr Circles & Failure Envelope**

As loading progresses, Mohr circle becomes larger… GL c Y c .. and finally failure occurs when Mohr circle touches the envelope

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**Orientation of Failure Plane**

Failure plane oriented at 45 + /2 to horizontal 45 + /2 Y GL 45 + /2 c 90+ Y c c+

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**= + Mohr circles in terms of & ’ v h v’ h’ u X X X h’ v’ h**

effective stresses total stresses h’ v’ h v u

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**Envelopes in terms of & ’**

Identical specimens initially subjected to different isotropic stresses (c) and then loaded axially to failure f c c uf Initially… Failure c, in terms of At failure, 3 = c; 1 = c+f 3’ = 3 – uf ; 1’ = 1 - uf c’, ’ in terms of ’

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**Triaxial Test Apparatus**

soil sample at failure piston (to apply deviatoric stress) failure plane O-ring porous stone impervious membrane perspex cell water cell pressure pore pressure or volume change back pressure pedestal

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**Types of Triaxial Tests**

deviatoric stress () Under all-around cell pressure c Shearing (loading) Is the drainage valve open? Is the drainage valve open? yes no yes no Consolidated sample Unconsolidated sample Drained loading Undrained loading

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**Types of Triaxial Tests**

Depending on whether drainage is allowed or not during initial isotropic cell pressure application, and shearing, there are three special types of triaxial tests that have practical significances. They are: Consolidated Drained (CD) test Consolidated Undrained (CU) test Unconsolidated Undrained (UU) test

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**For 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

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**CD, CU and UU Triaxial Tests**

Consolidated Drained (CD) Test no excess pore pressure throughout the test very slow shearing to avoid build-up of pore pressure Can be days! not desirable gives c’ and ’ Use c’ and ’ for analysing fully drained situations (e.g., long term stability, very slow loading)

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**CD, CU and UU Triaxial Tests**

Consolidated Undrained (CU) Test pore pressure develops during shear Measure ’ gives c’ and ’ faster than CD (preferred way to find c’ and ’)

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**CD, CU and UU Triaxial Tests**

Unconsolidated Undrained (UU) Test pore pressure develops during shear = 0; i.e., failure envelope is horizontal Not measured ’ unknown analyse in terms of gives cu and u very quick test Use cu and u for analysing undrained situations (e.g., short term stability, quick loading)

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**1- 3 Relation at Failure**

X soil element at failure X 3 1 3 1

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**Stress Point v h X t stress point stress point v h s (v-h)/2**

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**Stress Path During loading… t s**

Stress path is the locus of stress points t s Stress path Stress path is a convenient way to keep track of the progress in loading with respect to failure envelope.

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**Failure Envelopes t s During loading (shearing)…. failure **

c tan-1 (sin ) stress path c cos During loading (shearing)….

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**Pore Pressure Parameters**

A simple way to estimate the pore pressure change in undrained loading, in terms of total stress changes ~ after Skempton (1954) Y 1 3 u = ? Skempton’s pore pressure parameters A and B

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**Pore Pressure Parameters**

B-parameter B = 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.

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Shear Strength of Soil τf = c + σ’ tan φ τf = shear strength

Shear Strength of Soil τf = c + σ’ tan φ τf = shear strength

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