Mohrs Circle and NC or OC

Question 1

What is the most widely used shear strength test in soil mechanics?

Answer 1

The triaxial test.

Question 2

True or False: The triaxial test is only applicable to clays.

Answer 2

False. It is suitable for all soil types.

Question 3

What type of stress condition is applied in a triaxial test?

Answer 3

Axi-symmetric condition.

Question 4

What is the formula for axial stress in a triaxial test?

Answer 4

σ_a = σ_r + Fa/A

Question 5

Fill in the blank: The all-round pressure applied is called the ___ pressure.

Answer 5

Cell pressure (CP)

Question 6

What does CP represent in a triaxial test?

Answer 6

CP = Cell Pressure = σ_r = σ_c

Question 7

What are the two main stages of a triaxial test?

Answer 7

(1) Consolidation stage, (2) Shearing stage.

Question 8

What device measures volume change in the apparatus?

Answer 8

Drainage valve and volume measurement system (e.g., burette or gauge).

Question 9

True or False: The latex membrane used in a triaxial test is permeable to water.

Answer 9

False. It is impermeable.

Question 10

Formula: σ’_0 = σ_0 - u_0. If σ_0 = 300 kPa, u_0 = 100 kPa, what is σ’_0?

Answer 10

σ’_0 = 200 kPa

Question 11

What does “isotropic loading” mean in the context of the triaxial test?

Answer 11

Equal stress applied in all directions with no drainage.

Question 12

What does U-U stand for?

Answer 12

Unconsolidated-Undrained

Question 13

In a U-U test, is drainage allowed?

Answer 13

No, not at any stage.

Question 14

Formula: What is deviator stress in a U-U test?

Answer 14

σ_a - σ_r

Question 15

What is the corrected area formula for undrained conditions?

Answer 15

A = A_0 / (1 - ε_a)

Question 16

Fill in the blank: Axial strain ε_a = ΔH / H_0.

Answer 16

True.

Question 17

Match: < 20 kPa → __; 20–40 kPa → __; 40–75 kPa → __; 75–150 kPa → __; > 150 kPa → __

Answer 17

very soft; soft; firm; stiff; very stiff

Question 18

In U-U test Mohr’s circle, what are σ_a and σ_r?

Answer 18

Major and minor principal stresses respectively.

Question 19

What is the formula for undrained shear strength S_u?

Answer 19

S_u = (σ_a - σ_r) / 2

Question 20

True or False: Su is always a constant for a soil type.

Answer 20

False. It varies due to saturation, rate of shearing, anisotropy, etc.

Question 21

What does C-U stand for?

Answer 21

Consolidated-Undrained

Question 22

Fill in the blank: In a C-U test, drainage is allowed during ___ but closed during ___.

Answer 22

Consolidation; shearing

Question 23

What is the effect of using back pressure in a C-U test?

Answer 23

Helps maintain full saturation.

Question 24

Fill in the blank: The failure criterion is τ = c’ + σ_n’ tan φ’

Answer 24

True.

Question 25

In a C-U test, effective stress parameters obtained are:

Answer 25

c' and φ'

Question 26

What stress components define Mohr’s circle in 2D?

Answer 26

σ_x, σ_z, τ_xz

Question 27

Fill in the blank: By moment equilibrium, τ_zx = τ_xz.

Answer 27

True

Question 28

What is the sign convention for shear stresses in Mohr’s circle?

Answer 28

Clockwise shear stresses are negative.

Question 29

What is the pole in Mohr’s circle?

Answer 29

A point from which a line to any point on the circle is parallel to the plane on which the stresses act.

Question 30

True or False: The pole method helps determine stress on arbitrary planes.

Answer 30

True

Question 31

How do you find the pole if the stress and plane are known?

Answer 31

Project lines from known stress points Q and R.

Question 32

What are principal planes?

Answer 32

Planes where shear stress is zero and normal stress is either max or min.

Question 33

Fill in the blank: The directions of principal stresses are ___.

Answer 33

Orthogonal

Question 34

In triaxial tests, what are typically the principal stresses?

Answer 34

σ_1 and σ_3

Question 35

What angle does the failure plane make with the horizontal in triaxial tests?

Answer 35

θ = 45° + φ'/2

Question 36

What is the formula for normal and shear stress on plane AB?

Answer 36

σ_n' = ½(σ_1' + σ_3') + ½(σ_1' - σ_3')cos(2θ); τ = ½(σ_1' - σ_3')sin(2θ)

Question 37

What dictates the orientation of the failure plane in the shear box test?

Answer 37

Boundary conditions of the apparatus

Question 38

True or False: In the shear box, the failure plane is imposed, not freely developed.

Answer 38

True

Question 39

What is a stress path?

Answer 39

A sequence of stress states during loading, shown as Mohr’s circles or stress points.

Question 40

What does the horizontal distance between TSP and ESP represent?

Answer 40

Pore water pressure

Question 41

Fill in the blank: s' = ½(σ_1' + σ_3'), t' = ½(σ_1' - σ_3')

Answer 41

True

Question 42

True or False: t = t′ for undrained conditions.

Answer 42

True

Question 43

During undrained shearing of NC clays, what happens to effective stress?

Answer 43

It decreases as pore pressure increases.

Question 44

What is the slope of the ESP for NC clay in CU test?

Answer 44

Slope = 1

Question 45

What happens to pore water pressure during shearing of OC clay?

Answer 45

It decreases (soil dilates)

Question 46

True or False: The stress path for OC clay in CU test diverges from NC clay.

Answer 46

True