Shear Strength of Soil Part 1

By Sachin Singh|Updated : November 29th, 2021

Through Champion Study Plan for GATE Civil Engineering (CE) 2022, we are providing Shear Strength of Soil Part 1 study notes and other important materials on every topic of each subject.

These topic-wise study notes are useful for the preparation of various upcoming exams like GATE CivilIESBARCISROSSC-JEState Engineering Services examinations and other important upcoming competitive exams.

The article contains fundamental notes on the "Shear Strength of Soil"  topic of the "Geotechnical Engineering" subject.

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 mobilized within a soil mass.

image001

image002

  • Plane a-a is critical plane
  • θc = Angle of critical plane (a-a)
  • σ1 and σ3 are stresses on given planes

(i) image003 where, βmax = Angle between resultant stress and normal stress on critical plane.

= Friction angle of soil = ∅

image004

for clay ∅ = 0

image005

(ii) image006 (iii) image007, for C-∅ soil.

image008

(iv) image009 for C-soil (clays).

(v) image010 for C-∅ soil.

(vi) image011, for φ-soil.

(vii) image013 for C-soil.

image014

Mohr Coulomb's Theory

image015

where, C' = Effective cohesion

image016 = Effective normal stress

and ∅' = Effective friction angle

image017

Direct Shear Test

image015

image018

image019

Results of Direct Shear Test

image020

image021

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

  • image022
  • image023
  • image024

image025

where, σ3 = Cell pressure or all-round confining pressure

σd = Deviator stress A = Area of failure

image026 where, A0 = Area of beginning

v = Volumetric strain

image027

where, ΔV = Volume of water escaped out

image029

image030 = Initial Volume

∈ = Axial strain

Important Points regarding Triaxial Test

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

image031

  1. With image032 more σ1 required to canse failure hence mohr circle bigger. for normal consolidated soil, at σ3 = 0, τ = 0
    But for OC soil, at σ3 = 0, τ have some value.
  1. CU – Undrained strength comes higher than in site due to isotropic confining pressure of lab and anisotripic confining in site soil.

image033

image034

(Direct Shear) drained condition → C can't be modified

(unconfined undrained compression test) → ∅ can't be modified

  1. 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

  • qu = (σ1)f where, qu = unconfined compressive strength.
    Here, σ3 = 0
  • image037
  • image038
  • image039 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.

image040

image041

image042

Shear Strength

image043

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

  • image044

When only bottom of vanes take part in shearing.

  • image045

where sf = Sensitivity

Pore Pressure Parameter

(i) image046

where, B = Pore pressure parameter

ΔUc = Change in pore pressure due to increase in cell pressure

Δσc = Δσ3 = Change in cell pressure.

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

(ii) image047 where A = Pore pressure parameter

  • image048

ΔUd = Change in pore pressure due to deviator stress.

Δσd = Change in deviator stress

ΔU = Change in pore pressure

(iii) ΔU = ΔUc + ΔUd

(iv) ΔU = B[Δσ3 + A(Δσ1 - Δσ3)]

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