## How to Calculate and Solve for Mohr – Coulomb Criterion | Rock Mechanics

The image above represents mohr – coulomb criterion.

To compute for mohr – coulomb criterion, three essential parameters are needed and these parameters are Cohesion (|τo), Co-efficient of Friction (μ) and Normal Stress (σn).

The formula for calculating the mohr – coulomb criterion:

|τ| = τo + μσn

Where;

|τ = Mohr – Coulomb Criterion
o = Cohesion
μ = Co-efficient of Friction
σn = Normal Stress

Let’s solve an example;
Find the mohr – coulomb criterion when the cohesion is 7, the co-efficient of friction is 30 and the normal stress is 28.

This implies that;

o = Cohesion = 7
μ = Co-efficient of Friction = 30
σn = Normal Stress = 28

|τ| = τo + μσn
|τ| = 7 + 30(28)
|τ| = 7 + 840
|τ| = 847

Therefore, the mohr – coulomb criterion is 847.

Calculating the Cohesion when the Mohr – Coulomb Criterion, the Co-efficient of Friction and the Normal Stress is Given.

o = |τ|  – μσn

Where;

o = Cohesion
|τ = Mohr – Coulomb Criterion
μ = Co-efficient of Friction
σn = Normal Stress

Let’s solve an example;
Find the cohesion when the mohr – coulomb criterion is 44, the co-efficient of friction is 10 and the normal stress is 4.

This implies that;

|τ = Mohr – Coulomb Criterion = 44
μ = Co-efficient of Friction = 10
σn = Normal Stress = 4

o = |τ|  – μσn
o = 44  – 10(4)
o = 44  – 40
o = 4

Therefore, the cohesion is 4.

## How to Calculate and Solve for Normal Stress | Rock Mechanics

The image above represents normal stress.

To calculate for normal stress, two essential parameters are needed and these parameters are normal force (ΔN) and area (ΔA).

The formula for calculating the normal stress:

σn = ΔN / ΔA

Where;

σn = Normal Stress
ΔN = Normal Force
ΔA = Area

Let’s solve an example;
Calculate the normal stress with a normal force of 12 and an area of 22.

This implies that;

ΔN = Normal Force = 12
ΔA = Area = 22

σn = ΔN / ΔA
σn = 12 / 22
σn = 0.54

Therefore, the normal stress is 0.54 Pa.

Calculating the Normal Force when the Normal Stress and Area is Given.

ΔN = σn x ΔA

Where;

ΔN = Normal Force
σn = Normal Stress
ΔA = Area

Let’s solve an example;
Calculate the normal force when the normal stress is 25 with an area of 10.

This implies that;

σn = Normal Stress = 25
ΔA = Area = 10

ΔN = σn x ΔA
ΔN = 25 x 10
ΔN = 250

Therefore, the normal force is 250.