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Chapter 9
Shear Strength of Soil
SHEAR STRENGTH
Shear strength of a soil is the capacity of the soil to resist shearing stress. It can be defined as the maximum value of shear stress that can be defined as the maximum value of shear stress that can be Mobilized within a soil mass.
Plane a a is critical plane
θ_{c} = Angle of critical plane (a – a)
σ_{1} and σ_{3} are stresses on given planes
(i)
where, β_{max }= Angle between resultant stress and normal stress on critical plane=Friction angle of soil = ∅
for clay, ∅= 0
(ii) , for sands or Φ soil.
(iii), for C Φ soil.
(iv) , for Csoil (clays).
(v)
for C∅ soil.
(vi), for Φ soil.
(vii) σ_{1}= 2C , for C– soil.
MOHR COULOMBS THEORY
where, C’ = Effective Cohesion
= Effective normal stress and ∅' = Effective friciton angle
DIRECT SHEAR TEST:
UNCONFINED COMPRESSION TEST
q_{u} = (σ_{1})_{f}
where, q_{u} = unconfined compressive strength.
Here, σ_{3}= 0
 (σ_{1})f =2C , for Csoil
 for clay’s or Csoil.
VANE SHEAR TEST:
It is suitable for sensitive clays.
Lab size  Field Size  
Height of vane (H)  20 mm  10 to 20 cm 
Dia of vane (D)  12 mm  5 to 10 cm 
Thickness of vane (t)  0.5 to 0.1 mm  2 to 3 cm 
Shear Strength:
When top and bottom of vanes both pertain in shearing.
When only bottom of vanes pertain in shearing.
where S_{f} = Sensitivity
PORE PRESSURE PARAMETER:
where,
B = Pore pressure parameter
ΔU_{c} = Change in pore pressure due to in crease in cell pressure
Δσ_{c }= Δσ_{3} = Change in cell pressure.
0 ≤ B ≤ 1
B = 0, for dry soil.
B = 1, for saturated soil.
(ii)
where A = Pore pressure parameter
where ,
ΔU_{d} = Change in pore pressure due to deviator stress.
Δσ_{d} = Change in deviator stress
(iii) ΔU=ΔU_{c} +ΔU_{d}
ΔU = change in pore pressure
(iv)
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