Test: Soil Mechanics- 5 - Civil Engineering (CE) MCQ

Assumptions in Terzaghi’s theory of consolidation:

1. The soil is homogeneous.

2. The soil is fully saturated.

3. The compression of the soil layer is due to the change in volume only, which, in turn, is due to the squeezing out of water from the void spaces.

4. Darcy’s law is valid.

5. Deformation of soil occurs only in the direction of the load application.

6. The coefficient of consolidation is constant during the consolidation.

C_v = (T₉₀ x d²)/ t₉₀ = 0.848 x 0.01²/ (30x60) =  4.71 x 10^-8 m²/s

In laboratory consolidation test, the soil is laterally confined and fully saturated. So there is almost no opportunity for particles to get displaced and cause initial compression. Primary consolidation is due to dissipation of pore water pressure. The time taken to dissipate excess pore pressure and transfer of stress increment in this stage is called hydrodynamic lag. After this stage is complete, the stresses are transferred to the surface of the soil particles.

It should be noted that secondary compression starts after the completion of primary consolidation.

Effect of compaction on structure

At point 1:

Flocculent structure is found on dry side of optimum and with increase in water content of soil there will be decrease in permeability of the soil due to improved orientation of the particles which results in a decrease in the size of voids.

At point 3:

At same compactive effort dispersed structure is found on wet side of optimum

Effect of shrinkage: Due to random orientation of the soil particles and stronger inter-particle bonds, shrinkage on dry of optimum side is found to be less than shrinkage on wet of optimum side.

Compactive effort: With increase in comp active effort at same water content the soil tend to become more oriented (dispersed) especially on the dry side of optimum.

Point 5:

Energy in standard proctor test

= (Wt. of hammer (kg) × free fall (m) × layer × blows per layer)/ (volume of soil mass taken)

Volume of soil mass taken = 1000 cc ≈ 1 lit.

Energy in standard proctor test = (2.6 × 0.310 × 3 × 25)/10^-3

= 60450 kg m/m³

60450 = [40/(0.3 × 0.05)] × 1.5 × n             (50% due to overlap)

n → no. of passes

∴ n = 15.11 ≈ 15

Concept:

Using the relation,

Time factor (T_V) is given by

Where t = time required to consolidate the clay layer by (U%).

d = thickness of clay layer

c_v = coefficient of consolidation

Also,

K = c_v m_v γ_w

Where,

K = permeability of soil sample

c_v = coefficient of consolidation

m_v = coefficient of volume compressibility

Calculation:

For U = 80%,
TV = T_V1 and time required will be 15 years.

Now for same U, TV = TV₂ = TV₁ but d₂ = 2d₁, k₂ = 15k₁, m_v2 = 110m_v1

 

t₂ = 0.4 years

t₂ = 4.8 months 

Consolidation settlement is given by:

Where,

C_C = Compression index

e₀ = Initial void ratio of the soil sample

H₀ = Thickness of the soil sample

σ̅₀ = Initial effective stress at the centre of the soil sample
 Increase in effective stress at the centre of the soil sample
 

Calculation:

ΔH₁ = 0.75 mm

σ̅₀ = 50 kN/m²

ΔH₂ = 1.188 mm

Immediate settlement in cohesive soil/clay is given by:

q = uniform pressure at the base of foundation

B = width of the footing

E = Modulus of Elasticity of soil

μ = poisson’s ratio

I_f = Influence factor which depend upon L/B ratio
 

Calculation:

L = 5 m

B = 3 m
L/B = 5/3 = 1.67
From the table

I_f = 0.707

Maximum permissible settlement = 4.3 mm

q = 139.82 kN/m²

Safe pressure at Base of foundation = 139.82/FOS

q_safe = 93.21 kN/m²

Safe load = 93.21 × 3 × 5 = 1398.17 kN

Safe load = 1398.17 kN