Soil Mechanics and Foundation Engineering MCQ Quiz - Objective Question with Answer for Soil Mechanics and Foundation Engineering - Download Free PDF

Concept:

Shrinkage ratio (S.R.):

It is defined as the ratio of volume change expressed as the percentage of dry volume to the corresponding change in water content above the shrinkage limit.

      ---(1)

Here,

Vo - Initial volume of saturated sample at water content w_l
Vd - Final volume of the soil sample at water content ws
Md - Mass of dry volume 'Vd' of the sample
γd, γw - The unit weight of the dry volume of soil and water respectively.
Gm - Mass-specific gravity of soil in its dry state.

Shrinkage limit:

Where, W_s = Shrinkage limit and G_s = Specific gravity of solids

Calculation:

Given, W_l = 75 %, W_s = 25 %, W_p = 45 %

Volume of soil sample(V₀) = 30 cm³, V_d = 16.6 cm³

S.R. = 1.614

Shrinkage limit:

G_s = 2.71

Explanation:

The degree of saturation (S) is the ratio of the volume of water to the volume of voids in a soil sample and mathematically, it is given as:

Volume of Voids (V_v) = Volume of Water (V_w) + Volume of air  (V_a)

Given that V_v = 10 cm³ and V_a = 3 cm³

⇒ 10 = V_w + 3

Or

∴ The volume of water in a soil sample, V_w = 7 cm³

Substituting the values of V_w and V_v in the above formula, we get

⇒ Degree of Saturation, S = 70 %

Concept:

Sensitivity(S_t):

• Sensitivity is a measure of loss in the strength of soils as a result of remolding.
• In general, it denotes the degree of disturbance of undisturbed samples of the soil upon remolding.
• Sensitivity is defined as the ratio of the unconfined compressive strength of the clay in the undisturbed state to the unconfined compressive strength of the clay in the remolded state.

• Sensitivity is generally observed in cohesive soils and these soils generally have a sensitivity value greater than 1.

The sensitivity of clay soil is as follows:

Explanation: 

The average permeability for flow perpendicular to the bedding planes is given by,

The average permeability for flow parallel to the bedding planes is given by,

∴ Average permeability for flow perpendicular to the bedding plane is harmonic mean whereas, average permeability for flow parallel to the bedding plane is the arithmetic mean.

Important PointsAs arithmetic mean is always greater than harmonic mean therefore, the average permeability for flow perpendicular to the bedding plane is always lesser than the average permeability for flow parallel to the bedding plane.

Explanation:

Particle Size classification:

This classification of soils is done on the basis of particle size composition. According to which soil may be termed as clay, silt, sand, gravel, cobbles and boulders.

I.S. Classification (Grain size distribution):

(i) Clay = d

(ii) Silt = 2μ

• Fine silt = 2μ
• Medium silt = 10μ
• Coarse silt = 20μ

(iii) Sand = 75μ

• Fine sand = 0.075 mm
• Medium sand = 0.425 mm
• Coarse sand = 2 mm

(iv) Gravel = 4.75 mm

• Fine gravel = 4.75 mm
• Coarse gravel = 20 mm

(v) Cobbles = 80 mm

(vi) Boulders = d > 300 mm

Explanation:

Porosity (η) is defined as the ratio of volume of voids to the total volume of the soil sample in a given soil mass.

The porosity of soils can vary widely.

The porosity of loose soils can be about η = 50 to 60%.

The porosity of compact soils is about η = 30 to 40%.

Concept:

Toughness Index: 

• Toughness index is defined as the ratio of plasticity index (I_P) of the soil to the flow index (I_F) of the soil.

• This gives us an idea of the shear strength of soil at its plastic limit. 
• The toughness index varies between 0 to 3. If If is more, the rate of loss of shear strength is more. Hence, the toughness index is less.
• When the toughness index is less than 1, the soil is said to be friable, which means it can be easily crushed at the plastic limit.

Explanation:

Coefficient of Earth Pressure at rest:

Where,

μ is the coefficient is the Poisson ratio.

As per IS 4651 (Part 2): 1989, Table 1

Concept:

According to Darcy’s law,

For laminar flow Vα i

V = K × i

Where,

V = velocity of water flowing in soil, K = coefficient of permeability

h_L = head difference, L = seepage length

Seepage velocity is given by,

V_S = V/n

Where,

 n = porosity of the soil

Calculation:

T = Time = 100 days

D  = distance = 100 m

h_L = head difference = 3 m

n = 15 % = 0.15

i = h_L/L = 3/100

V_S = D/T = 100/100 = 1 m/day

V = K × i

V = V_S × n

∴ V_S × n = K × i

Soil classification as per Indian standards:

∴ According to IS Classification, there are 18 groups of soils:

8 groups of coarse-grained, 9 groups of fine-grained, and 1 of peat

Explanation:

The range of optimum water content for different types of soil is as follows:

Concept:

slope =  = constant

⇒  = 

where 

w_L = LL = liquid limit

w_P = PL = plastic limit

w_s = SL = shrinkage limit

V_L = volume of soil mass at LL

V_P = volume of soil mass at PL

V_s = volume of soil mass at SL

Calculation:

Given:

SL = 20%

PL = 40%

V_P = 1.2 V_d

V_L = 1.5 V_d

⇒  = \(V_P-V_D\over {w_p - w_s}\)

Now, putting values, we get 

⇒  = 

⇒ I_P = 30%

Hence, the plasticity Index Pl of the soil is 30%.

Concept:

Over Consolidation Ratio:

Over Consolidation Ratio ( OCR ) is defined as the ratio of maximum pressure experienced in the past

( Preconsoildation pressure ) to the present overburden pressure.

OCR > 1 ⇒ It is Over consolidated soil

OCR = 1 It is Normally consolidated soil

OCR

Calculation:

OCR of clay = 4

Since the OCR of the given soil is greater than 1, it is overconsolidated clay.

A-factor:

A – factor is a function of the over-consolidation ratio in the case of overconsolidated clay.

For OC clays, A = f (OCR)

For heavily overconsolidated clay A –0.2 to –0.3

Concept:

The effective stress concept was developed by "Terzaghi". A fully saturated soil relates three types of stress:

1. Total Stress
2. Pore Pressure( Neutral Stress)
3. Effective Stress

Total Stress() on a plane within soil mass is the force per unit area of soil mass transmitted in the normal direction across a plane.

Pore pressure(u) is the pressure of the water filling the void space between solid particles.

Effective stress() is defined as equal to the total stress minus the neutral pressure.

The relation between total stress, pore pressure, and effective stress is as follows:

where = effective stress, = total stress, u= pore pressure

Explanation:

Given:

γ_w = 10 kN/m³, γsat = 20 kN/m³, γ_b = 18 kN/m3

Effective stress at a depth of 10 m below the ground level:

γ_eff = γ_b × 3 + γ_sub × 7

γeff = 18 × 3 + (20 - 10) × 7

γeff = 124 kN/m³

Concept:

Area ratio:

It can be defined as the ratio of the maximum cross-sectional area of the cutting edge to the area of the soil sample.

The area ratio can be expressed as

where

D₁ = inner diameter of cutting edge

D₂ = outer diameter of cutting edge

Note:

For stiff formation (A_r)_max = 20%

Soft sensitive clay (Ar)max = 10%

Maximum thickness of cutting edge = 

Calculation:

Given, D₂ = 70 mm 

Soil is stiff clay, So (Ar)max = 20%

D₁ = 63.9 mm

Maximum thickness of cutting edge = 

=  = 3.05 mm