UNIVERSITI MALAYSIA PERLIS

SCHOOL OF ENVIRONMENTAL ENGINEERING

Soil MechanicChapter : Shear Strengh of Soil

PREPARED BY : MISS SYAKIRAH AFIZA MOHAMMED

Introduction Safety of any geotechnical structure is

dependent on the strength of the soil.If the soil fail, a structure founded on it can

collapse.The strength of soil is therefore very

important.The word strength mean shear strengthShear strength of a soil mass is the internal

resistance per unit area that the soil mass can offer to resist failure and sliding along any plane inside it.

STRESSES

• Gravity generates stresses (force per unit area) in the ground at different points.

• Stress on a plane at a given point is viewed in terms of two components:

• Normal stress: acts normal to the plane and tends to compress soil grains towards each other (volume change)

• Shear stress: acts tangential to the plane and tends to slide grains relative to each other (distortion and ultimately sliding failure)

Shear failureSoils generally fail in shear

strip footing

embankment

At failure, shear stress along the failure surface reaches the shear strength.

failure surface mobilised shear resistance

Shear failure

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

Drain strength• Shear strength defined in terms of effective

normal stresses is referred as “drained” or “effective” strength

• To use drained or effective strength, effective normal stresses need to be known which, in turn, requires that pore water pressures are known

• Pore pressures may not be simple to determine in the field

• Typically used in analysis of stability of excavation slopes and natural slopes.

Undrained strengthIn those cases, such as at end of

construction in fine-grained soils, where determination of pore pressures are difficult “undrained” or “total” strength is used for convenience

S = cu + σ tan φu where cu = undrained cohesionφu = undrained friction angle (zero forsaturated soils), and σ = total normal stress

Shear failure• A consistent relationship exists between

the shear strength on a plane and the effective normal stress that acts on that plane

• S = c’ + σ’ tan φ’ whereS = shear strength on the planeσ’= effective normal stress on the planec’ = effective cohesion

’ = φ effective friction angle

Mohr Circles & Failure Envelope

X

Y Soil elements at

different locations

XY

X

Y

~ failure

~ stable

Mohr Circles & Failure Envelope

Y

Initially, Mohr circle is a point

c

c

c

c+

The soil element does not fail if the Mohr circle is contained within the envelope

GL

Mohr Circles & Failure Envelope

Y

c

c

c

GL

As loading progresses, Mohr circle becomes larger…

.. and finally failure occurs when Mohr circle touches the envelope

Orientation of Failure Plane

Y

c

c

c

GL

c+

90+

45 + /2

Failure plane oriented at 45 + /2 to horizontal

45 + /2

Y

Mohr circles in terms of & ’

X X X

v

h

v’

h’

u

u= +

total stresseseffective stresses

vhv’h’u

Envelopes in terms of & ’Identical specimens initially subjected to different isotropic stresses (c) and then loaded axially to failure

c

c

c

c

f

Initially… Failureuf

At failure,

3 = c; 1 = c+f

3’ = 3 – uf ; 1’ = 1 - uf

c,

c’, ’

in terms of

in terms of ’

Mohr-Coulomb Failure Criterion

Mohr-Coulomb Failure Criterion

Mohr-Coulomb Failure Criterion

tancf

c

failure envelope

cohesion

friction angle

f is the maximum shear stress the soil can take without failure, under normal stress of .

f

Mohr-Coulomb Failure Criterion

tanff c

Shear strength consists of two components: cohesive and frictional.

f

f

c

f tan

c cohesive

component

frictional component

c and are measures of shear strength.

Higher the values, higher the shear strength.

Laboratory determination ofshear strength1. SHEAR BOX TEST

2. TRIAXIAL TEST Unconfined compression test (UCT) Unconsolidated undrained test (UU) Consolidated Undrained Test (CU) Consolidated Drained Test (CD)

3. LABORATORY SHEAR VANE TEST

Shear Deformation of Soils

Interpretation of shear strengthDense sands and overconsolidation clay (OCR >2)

Loose sand and consolidated and lightly consolidated

Show peak shear stressExpand (+ve dilation)Dilation angle α > 0

No peak shear stressCompress (-ve dilation)Max shear stress α = 0

The peak effective friction angle for a dilating soil = Φ’ p = Φ’ cs + αp

Interpretation of shear strengthAll soils, critical shear strength

τcs = (σ’n)f tanΦ’cs

Dilating soils, peak shear strength.τp = (σ’n)f tan (Φ’cs + αp ) = (σ’n)f tan Φ’p

Residual shear strengthCoulomb equation for soils that exhibit

residual shear strength.τr = (σ’n)f tan Φ’r

Coulomb’s model gives no information on the shear strain required to initiate slip.

If the shear stress (τ) induces in soil is less than the peak or critical shear strength, then the soil has reserved shear strength.

Undrained and DrainedWhen a load is applied to a soil with low

permeability, the excess pore water pressure does not drain from the quickly.very little transfer of stress to the soil grain undrained condition = short-term condition.

undrained condition depend on = rate of loading, soil type, geological formation.

Drained The excess pore water pressure dissipate and

the applied stresses are transferred to the soil grain long-term condition

Granular soils have no cohesion.

c = 0 & c’= 0

For normally consolidated clays, c’ = 0 & c = 0.

For unconsolidated undrained test, in terms of total stresses, u = 0