Index Properties MCQ Quiz - Objective Question with Answer for Index Properties - 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.

\(S.R. = \frac{\frac{(V_o-V_d)}{V_d}\times100}{w_l -w_s} = \frac{M_d}{\rho_wV_d}=\frac{γ_d}{γ_w} = G_m\)      ---(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:

\({{\rm{W}}_{\rm{S}}} = \frac{1}{{\rm{S.R.}}} - \frac{1}{{\rm{G_s}}}\)

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

\(S.R. = \frac{\frac{(V_o-V_d)}{V_d}\times100}{w_l -w_s} \)

\(S.R. = \frac{\frac{(30-16.6)}{16.6}\times100}{75 \ -\ 25} \)

S.R. = 1.614

Shrinkage limit:

\({{\rm{W}}_{\rm{S}}} = \frac{1}{{\rm{S.R.}}} - \frac{1}{{\rm{G_s}}}\)

\({{0.25}} = \frac{1}{{\rm{1.614}}} - \frac{1}{{\rm{G_s}}}\)

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:

\(S = \frac{V_w}{V_v}\times 100\)

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

\(S = \frac{7}{10} \times 100\)

⇒ 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.

\({{\rm{S}}_{\rm{t}}}{\rm{ = }}\frac{{{{\left( {{\rm{UCS}}} \right)}_{{\rm{undisturbed}}\;{\rm{state}}}}}}{{{{\left( {{\rm{UCS}}} \right)}_{{\rm{remoulded}}\;{\rm{state}}}}}}\)

• 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:

Given Data:

Plastic Limit (P_L) = 20%

Liquid Limit (L_L) = 50%

Flow Index (I_f) = 30%

Toughness Index is given by the formula

\(I_t={{L_L-P_L} \over I_f}\)

\(I_t={{50-20} \over 30}=1\)

The correct answer is Option A.

Concepts:

The Specific Gravity of soil solids is given as:

\(G = \frac{W_s}{W_4 -W_3 + W_s}\)

Where,

Ws = Weight of soil solids in dry state

W4 = Weight of pycnometer and water filled in it completely

W3 = Weight of pycnometer plus soil solids and water filled in pycnometer

Calculation:

Given data,

Oven dry weight of soil, Ws = 1.04 N

Combined mass of bottle, soil and water, W3 = 5.38 N

Weight of pycnometer with water alone, W4 = 4.756 N

Using the above formula, the specific gravity is calculated as:

\(G = \frac{1.04}{1.04 - 5.38 + 4.756}\)

∴ Gs = 2.50

If some air is entrapped while the weight W₃ is taken, Since the air entrapped is given as 3 ml, this space, if occupied by water, would have enhanced the weight W₃ by 0.03 N.

W₃ = 5.38 + 0.03 = 5.41 N

Hence, the Correct value of G

\(G = \frac{1.04}{1.04 - 5.41 + 4.756}\) = 2.694

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.

\(\begin{array}{l} Toughess\;index = \frac{{Plasticity\;index}}{{Flow\;index}}\\ \end{array}\)

• 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.

Concept:

slope = \(dy\over dx \) = constant

⇒ \({V_L-V_P}\over {w_L - w_p} \) = \(V_P-V_D\over {w_p - w_s}\)

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

⇒ \({V_L-V_P}\over {w_L - w_p} \) = \(V_P-V_D\over {w_p - w_s}\)

Now, putting values, we get 

⇒ \({1.5 V_d - 1.2 V_d}\over I_P\) = \(1.2V_d - V_d \over {40-20}\)

⇒ I_P = 30%

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

Explanation:

(i) A quick clay is defined as a clay where the undisturbed shear strength of the soil is at least 30 times greater than the remolded (or disturbed) shear strength. 

(ii) The ratio of undisturbed to disturbed strength is termed as sensitivity.

Concept:

Core cutter test:

• This method is used to find in-situ unit weight in the case of fine-grained cohesive soils without stones.
• This method cannot be used in the case of hard and gravelly soils.

Equipment used:

1. Cylindrical core cutter, 100 mm internal diameter and 130 mm long.
2. Steel rammer of mass 9 kg and overall length 900 mm
3. Steel Dolley, 25 mm high and 100 mm diameter
4. Weighing balance of accuracy up to 1 gm

Concept:

Relative density: 

• Relative density is the measure of the compactness of cohesion-less soil.

• Relative density represents whether the soil is closest to its densest state or loosest state.

• It is defined as the ratio of the difference between the voids ratio of the soil in its loosest state and its natural state to the difference between the voids ratio in the loosest and densest state.

\({I_D} = \frac{{{e_{max}} - {e_{natural}}}}{{{e_{max}} - {e_{min}}}}\)

The relationship between the Relative Density and Void ratio of the soil sample is depicted in the graph below:

∴ Relative density varies inversely to the void ratio.

Classification of soil as per relative density as follows:

Calculation:

emax = 0.6, emin = 0.2, and natural void ratio (e) = 0.4

\({{\rm{I}}_{\rm{d}}} = \frac{{0.6 - 0.4}}{{0.6 - 0.2}} = \frac{{0.2}}{{0.4}} = 0.5\)

Expressing it in percentage = 0.5 × 100 = 50%

Concept:

From a fundamental relationship, the density of soil is given by:

\({{\rm{\gamma }}_{{\rm{bulk}}}} = \frac{{\left( {{\rm{G}} + S × e} \right) × {\gamma _w}}}{{1 + e}} = \frac{{\left( {{\rm{G}} + w × G} \right) × {\gamma _w}}}{{1 + e}} = \frac{{\left( {1 + {\rm{w}}} \right) × G × {\gamma _w}}}{{1 + e}}\)

Where

\(\gamma\) = Density of soil, \(\gamma_w\) = Density of water, G = Specific gravity of soil, S = Degree of saturation, w = Water content, and e = void ratio

For the dry density of soil: Degree of saturation (S) = 0

The dry density of soil(\(\gamma_d\)) is given by

\({{\rm{\gamma }}_{\rm{d}}} = \frac{{\left( {\rm{G}} \right) × {\gamma _w}}}{{1 + e}}\)

Calculation:

Given data

The specific gravity of solids = 3

The mass-specific gravity = 2

The dry density of soil(\(\gamma_d\)) is given by

\({{\rm{\gamma }}_{\rm{d}}} = \frac{{\left( {\rm{G}} \right) × {\gamma _w}}}{{1 + e}}\)

\({\gamma_d \over \gamma_w} = {G \over 1+e}\)

\(G_m = {G \over 1+e}\)

Where G_m = Mass specific gravity

\(2 = \frac{{\left( {\rm{3}} \right)}}{{1 + e}}\)

\({{1 + e}} = 1.5\)

e = 0.5

The void ratio is 0.5.

Concepts:

The shrinkage Limit Method is used to determine the specific gravity of solid particles. Based on Shrinkage Ratio (SR) and Shrinkage Limit (SL), the specific gravity of soil solids can be calculated using the following formula:

\(G = \frac{1}{\frac{1}{SR}-\frac{SL}{100}} \)

Important Points:

1. Oven dry method, Calcium Carbide Method, Alcohol Methods, Sand Bath Method, Torsion balance Methods are used to determine the water content of soil.

2. The other methods for determining the specific gravity of solid particles are – Core Cutter Method, Sand Replacement Method, Water displacement Method. These methods give the unit weight of soil, by dividing it with the unit weight of water, we can get specific gravity.

3. Pycnometer is used for determining the specific gravity of soil if we know the water content and also used for determining the water content if we know the specific gravity of soil. 

Explanation:

Liquid limit (WL): The water content at which soil changes its consistency from plastic to a liquid state.

Plastic limit (WP): The water content at which soil changes its consistency from brittle/crumbly to a plastic state.

Shrinkage limit (WS): A state when the decrease in moisture content leads to solid-state, no change in volume of soil mass is observed, the consistency of soil changes from semi to solid-state. The boundary water content is called shrinkage limit.

Plasticity index (IP) = WL - WP

Where, WL = Liquid limit, WP = Plastic limit, WN = Natural water content

Based on the plasticity index, the soil may be classified as followed:

Explanation:

The Activity of the soil (A)

The activity of the soil is given by the ratio of the plasticity index (Ip) and the percentage of clay fraction (C) in the soil.

It indicates water absorption capacity or indicates swelling and shrinkage characteristics.

Activity \(= \frac{{Plasticity\;Index}}{{Per\;cent\;of\;clay\;particles\;finer\;than\;2\;\mu m}}\)

Activity-based classification of clays:

Hence, The most appropriate answer is Sample A is inactive and Sample B is active.

Concept:

Specific Gravity:

Specific gravity can be defined as the ratio of the weight of a given volume of soil solids at a given temperature to the weight of the equal volume of distilled water at that temperature. It can be written as G = \(\dfrac{\gamma_s}{\gamma_w}\)

1. Density bottle method:

• The specific gravity of solid particles can be determined in a laboratory using a density bottle fitted with a stopper having a hole.
• The density bottle of 50 ml capacity is generally used [ IS:2720 (part III) 1980].

2. Pycnometer method:

• Pycnometer method is used to determine specific gravity and water content both.
• This method is suitable for cohesionless soils.
• A pycnometer is a glass jar of 1-liter capacity that is fitted at its top by a conical cap made of brass.
• It has a screw-type cover and there is a small hole at its apex of 6 mm in diameter

Explanation:

• Density bottle method can be used for every type of soil, and it is the most accurate one.
• Flask and pycnometer are used for coarse-grained soil.
• Distilled water is used in the pycnometer test and kerosene is used for the density bottle method. When kerosene is used, its specific gravity is determined accurately by a separate test.