Shear Strength of Soils | Soil Mechanics - Civil Engineering (CE) PDF Download

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 mobilized within a soil mass.

• Plane a-a is critical plane
• θ_c = Angle of critical plane (a-a)
• σ₁ and σ₃ are stresses on given planes
  (i)  where, β_max = Angle between resultant stress and normal stress on critical plane.
  = Friction angle of soil = ∅
  θ_c = π / 4 + ∅ / 2
  ↓
  for clay ∅ = 0
  θ_c = π / 4
  (ii) 
  (iii) , for C - ∅ soil.
  
  (iv) τ = C, for C-soil (clays).
  (v)   for C-∅ soil.
  (vi) ,  for φ-soil.
  (vii)  for C-soil.

Mohr Coulomb's Theory
where, C' = Effective cohesion
 = Effective normal stress
and ∅' = Effective friction angle

Direct Shear Test

Results of Direct Shear Test

Drained conditions maintained, hence C taken as zero in results (as cohesion doesn't mobilizes in drained condition)

• σ₁ = σ₃ + σ_d
• 
• 

where, σ₃ = Cell pressure or all-round confining pressure
σ_d = Deviator stress A = Area of failure
  where, A₀ = Area of beginning
∈_v = Volumetric strain
∈_v = 0 for U - U - test
where, ΔV = Volume of water escaped out

 = Initial Volume
∈ = Axial strain

Important Points regarding Triaxial Test

• During triaxial, either pore water line is open (to get pore pressure) or Drainage line is open (to get volume change)
• UD (not possible in field)
• CD – Total = effective stress: To check long term stability of embankment which has been in existence since long ago.

1. With  more σ₁ required to canse failure hence mohr circle bigger. for normal consolidated soil, at σ₃ = 0, τ = 0
2. But for OC soil, at σ₃ = 0, τ have some value.CU – Undrained strength comes higher than in site due to isotropic confining pressure of lab and anisotripic confining in site soil.

(Direct Shear) drained condition → C can't be modified
(unconfined undrained compression test) → ∅ can't be modified

UU Test

With ↑ in σ₃, effective doesn't change hence no decrease in void ratio or increase in strength is noted, hence for all σ₃, same incremental σ₁, will come and only one Mohr's circle is obtained.

Unconfined Compression Test

• q_u = (σ₁)f where, q_u = unconfined compressive strength. Here, σ₃ = 0
• 
• 
•  for clay's or c-soil.
• For clays as sand/coarse grained soil/can't stand in equipment with no lateral pressure.
• Used to rapidly assess clay consistency in field.
• To get sensitivity values of clay.

Vane Shear Test

• It is suitable for sensitive clays.

Shear Strength

 
When top and bottom of vanes both take part in shearing.

When only bottom of vanes take part in shearing.

where s_f = Sensitivity

Pore Pressure Parameter
(i) B = ΔU_c / Δσ_c =  ΔU_c / Δσ₃
where, B = Pore pressure parameter
ΔU_c = Change in pore pressure due to increase in cell pressure
Δσ_c = Δσ₃ = Change in cell pressure.

• 0 ≤ B ≤ 1
• B = 0, for dry soil.
• B = 1, for saturated soil.

(ii)  where A = Pore pressure parameter

• ΔU_d = Change in pore pressure due to deviator stress.
  Δσ_d = Change in deviator stress
  ΔU = Change in pore pressure

(iii) ΔU = ΔU_c + ΔU_d

(iv) ΔU = B[Δσ₃ + A(Δσ₁ - Δσ₃)]