Shear Strength of Soils

The shear strength (or resistance) of soils is the result of two main components. Such as, frictional strength and cohesive strength. The frictional strength is similar to the classic sliding friction between solid bodies from basic statics or physics.



where,
F = force
mu = Coefficient of friction
R = reaction
A = surface area
S = Shear strength
sigma n = Normal strength

this equation is only valid when at the time of failure.

'mu' we can set off as a angle of tangent. this angle is call as "Friction angle". this is a property of the two surfaces.

Dry soil / Not saturated ( for soil without any cohesion )

Cohesive soils ( for soil with cohesion - clay type ) 

Cohesion is the molecular forces of attraction between soil particles and is analogous to that which would be exhibited between two sticky surfaces. cohesion is usually described by the variable "C"
(C- Cohesion or Coefficient of cohesion)


Note : C and phi are called as "Shear strength parameters" and it is constant for considered soil type.

Mohr - Coulomb failure line

In mixed grained soils the resistance is a combination of the separate resistance of cohesion and friction. and the Mohr-Coulomb general expression which is world wide used can give the relationship between the soil shear strength at failure and the two resisting components of friction and cohesion as follows,

S = sigma n * tan pi + C
Y = M * X + C



Variables T and N,
Change load (N) and observe the failure force (T) at failure time.

Note : Normally "S" is referred as "tau"


This graph is called as "Mohr - Coulomb failure line" or "failure envelop"

If the shear strength on any plane with a soil mass exceeds the value given in equation movement (or yield) will occur on that plane. The parameter C and Phi are called the shear strength parameters.

The significance of Mohr - Coulomb failure envelop shown in figure can be explained as follows,

- If the normal stress and shear stress on a plane in a soil mass are such they plot as A, shear failure will not occur along that plane.
- At point B, shear failure will occur along the plane
- A state of stress on a plane represented by point C, cannot exist because it plots above the failure envelop and shear failure in a soil would have occurred already.


Example: tau = 20 K pa, sigma n = 100 K pa , phi = 45 degrees , C = 0

therefore,
S = Sigma n * tan phi + C
S = 100 * 1 +
S = 100 K pa

but applied force tau = 20 K pa
Maximum allowable force is = 100 K pa
therefore no failure occurs

In general, the shear strength for different kind of soils as determined by the Mohr - Coulomb failure criteria, can be illustrated graphically as follows,

Saturated soils 

At any plane passing through a fully saturated soil, the total normal stress (sigma n) applied to the plane is in general the sum of two components: stress carried by the solid particles sigma n dash and pore water pressure i the voids "u" that is,

This implies that in terms of effective stress of the Mohr - Coulomb failure criteria should be rewritten as follows,

where,
S = shear strength of soil
C dash = soil cohesion in terms of effective stress
Phi dash = soil friction angle in terms of effective stress
sigma n dash = effective normal stress on the plane of sliding
u = pore water pressure on the plane of sliding

Drained and Undrained Shear Strength

When we consider loading of a saturated soil, additional pressure is applied to the soil. after that void ratio of the soil will decrease, because of that pore water pressure will increase therefore there is a high head development. after development of  this high head during the time it will reduce (high head to low head) this process is called as ''Dissipation" of pore water pressure.

There are 2 conditions we can observe according to this dissipation of pore water pressure.

when we consider construction of embankment very slow, dissipation will occur during loading time. therefore no significant increase in the pore water pressure. This will referred as "Drain Condition"

And when we consider a construction of an embankment very fast. there is no time to dissipation of pore water pressure. therefore pore water pressure will increase and soil will fail. This will referred as "Undrained Condition".

Sandy soil ---- permeability is high --- dissipation is very speed
Therefore there is no increase in pwp in sandy soils

Clayey soil ---- permeability is low --- dissipation is very slow
Therefore this is fail under undrain condition