Question

3. Two triaxial tests are performed on a clay. At failure, the results are:

Test 1: σ₃ = 30 kPa, P = 0.45 kN, A = 0.01 m², u = 10 kPa

Test 2: σ₃ = 60 kPa, P = 0.70 kN, A = 0.01 m², u = 20 kPa

1. Find σ₁, σ₃, σ'₁, and σ'₃ at failure for both tests.
2. Draw the effective stress Mohr's circle for both tests and draw the Mohr-Coulomb failure envelope for the clay. What are f' and c' for the clay? Write the equation for the Mohr-Coulomb failure envelope.
3. Is the clay normally consolidated or over consolidated? Why?

Answer 1

σ3	P	A	u	σd = P/A		σ1 =σ3+σd	σ1 ' = σ1-u	σ3' = σ3 - u
					σ3	σ1	σ1'	σ3'
kPa	kN	m^2	kPa	kPa	kPa	kPa	kPa	kPa
30	0.45	0.01	10	45	30	75	65	20
60	0.7	0.01	20	70	60	130	110	40

σ1 = 1.8333*σ3+ 20 as compare with

σ1 = σ3*tan(45+φ/2)^2+ 2ctan(45+φ/2)

tan(45+φ/2)^2= 1.833

φ = 17.10 degree

2ctan(45+φ/2) = 20

c = 7.38 kPa

σ1' = 2.25*σ3'+ 20 as compare with

σ1' = σ3'*tan(45+φ'/2)^2+ 2c'tan(45+φ'/2)

tan(45+φ'/2)^2= 2.25

φ' = 22.62 degree

2ctan(45+φ'/2) = 20

c' = 6.67 kPa

Soil is over consolidated because her c and phi both are not zero.

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