Index Properties MCQ Quiz in मराठी - Objective Question with Answer for Index Properties - मोफत PDF डाउनलोड करा

Concept:

The formula for finding the dry unit weight of soil is given by:

\({γ _d} = \frac{γ }{{1 + w}}\)

where, 

γd = Dry unit weight of soil

γ = Total Unit weight of soil

w = Water content

Calculations:

Given Data:

\(γ\) = 5 kN/m3

w = 17 % = 0.17

So, 

\({γ _d} = \frac{5 }{{1 + 0.17}}=4.27\;kN/m^3\)

Concept:

Bulk Unit weight (γ_b): 

It is defined as the ratio of the total weight of soil to the total volume of the soil mass.

\({γ _b} = \frac{W}{V} = \frac{{{W_s} + {W_w}}}{{{V_s} + {V_w} + {V_a}}}\)

Water Content (w):​

Water content or moisture content of a soil mass is defined as the ratio of the weight of water to the weight of solids (dry weight) of the soil mass.

\({\rm{w = }}\frac{{{{\rm{W}}_{\rm{w}}}}}{{{{\rm{W}}_{\rm{s}}}}};{\rm{w}} \ge 0\)

It is denoted by the w and is commonly expressed as a percentage. The minimum value for water content is 0. There is no upper limit for water content.

Dry Unit Weight (γ­d):-​

Dry unit weight is defined as the weight of soil solids per unit volume of soil. It is denoted by the letter symbol γd it has the unit of kN/m3.

\({{\rm{γ }}_{\rm{d}}}{\rm{ = }}\frac{{{{\rm{W}}_{\rm{s}}}}}{{\rm{V}}}{\rm{ = }}\frac{{{{\rm{W}}_{\rm{d}}}}}{{\rm{V}}}\)

It is used as a measure of the denseness of soil. A high value of dry unit weight indicates that more solids are packed in a unit volume of soil hence a more compact soil.

Specific gravity of solids (G):-​

The specific gravity of solids is defined as the ratio of the unit weight of solids to the unit weight of water. It is denoted by the letter G and is a unitless quantity.

\({\rm{G = }}\frac{{{{\rm{γ }}_{\rm{s}}}}}{{{{\rm{γ }}_{\rm{w}}}}}\)

Explanation:​​

\(\begin{array}{l} {γ_d} = \frac{γ}{{1 + w}} = \frac{{20}}{{1 + 0.17}} = 17.094\; kN/{m^3}\\ {γ_d} = \frac{{{γ_w}.G}}{{1 + e}} \end{array}\)

If void ratio 'e' remains unchanged during drying,  \(γ_d\)  also remains unchanged. 

\(\begin{array}{l} {γ_d} = \frac{γ}{{1 + w}}\\ 17.094 = \frac{{19}}{{1 + w}} \end{array}\)

w = 0.11 = 11 %

Important Points

Air content:

 Air content is defined as the ratio of the volume of air to the volume of voids. It is denoted by ac.

\({{\bf{a}}_{\bf{c}}} = \frac{{{{\bf{V}}_{\bf{a}}}}}{{{{\bf{V}}_{\bf{v}}}}} = \frac{{{\bf{Volume\ of\ air}}}}{{{\bf{Volume\ of\ voids}}}}\)

Porosity:

Porosity is defined as the ratio of the volume of voids to the total volume of soil. It is denoted by n. It varies between 0 and 1.

\({\bf{n}} = \frac{{{{\bf{V}}_{\bf{v}}}}}{{\bf{V}}} = \frac{{{\bf{Volume\ of\ voids}}}}{{{\bf{Total\ volume}}}}\)

Percentage air voids:

Percentage air voids are defined as the ratio of the volume of air to the total volume of soil. It is denoted by n­­a.

\({{\bf{n}}_{\bf{a}}} = \frac{{{{\bf{V}}_{\bf{a}}}}}{{\bf{V}}} \times 100 = \frac{{{\bf{Volume\ of\ air}}}}{{{\bf{Total\ volume}}}} \times 100\)

Degree of Saturation: 

Degree of Saturation of a soil mass is defined as the ratio of the volume of water in the voids to the volume of voids. It is denoted by S.

\(S = \frac{{{V_w}}}{{{V_v}}} \times 100\;\;;0 \le S \le 100\)

• For a fully saturated soil mass Vv = Vw, hence S = 100%
• For fully dry soil mass Vw = 0, hence S = 0%

Explanation:

Methods used for finding water content:

Explanation:

Consistency Index: It is defined as a ratio of the difference between the liquid limit and the natural water content of the soil to the plasticity index.

\({I_c} = \frac{{{w_{L - W}}}}{{{I_p}}}\)

Where,

w_L = water content at liquid limit

w = Natural water content

I_p = Platicity index

Concept:

Shrinkage ratio: It is the ratio of a given volume change expressed as a percentage of dry volume to the corresponding charge in water content above the shrinkage limit expressed as a percentage of the weight of the oven dried soil.

\(\text{SR}=\frac{\frac{\left( {{\text{V}}_{1}}-{{\text{V}}_{2}} \right)}{{{\text{V}}_{\text{d}}}}\times 100}{{{\text{w}}_{1}}-{{\text{w}}_{2}}}=\frac{{{\text{V}}_{1}}-{{\text{V}}_{2}}}{{{\text{V}}_{\text{d}}}\left( {{\text{w}}_{1}}-{{\text{w}}_{2}} \right)}\times 100\)

Where,

V1 = Volume of soil mass at water content (w1)

V2 = Volume of soil mass at water content (w2)

Vd = Volume of dry soil mass

Note: Shrinkage ratio is equal to mass specific gravity of soil in its dry state.

Calculation:

WL = 42%

WP = 30%

As per given data,

(VL – Vd )/V_d= 35

(VP – Vd )/V_d= 22

Also, \(\frac{{{V_L} - {V_d}}}{{{W_L} - {W_s}}} = \frac{{{V_p} - {V_d}}}{{{W_p} - {W_s}}}\)

\(\frac{{35}}{{0.42 - {W_s}}} = \frac{{22}}{{0.3 - {W_s}}}\)

Solving we get WS = 9.69%

Shrinkage Ratio, \(SR = {{{{{V_L} - {V_d}} \over {{V_d}}} \times 100} \over {{w_L} - {w_s}}}\)

∴ \(S.R = \frac{{35}}{{42 - 9.69}} = 1.1\)

Concept:

Plasticity Index:

• Plasticity index (PI) is the range of water content over which the soil remains in the plastic state. Mathematically defined as,
• Plasticity Index = Liquid Limit - Plastic Limit.
• The plasticity of soil is its ability to undergo deformation without cracking.
• It is an important index property of fine-grained soil, especially for clayey soils.

Activity:

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

Consistency Index or Relative consistency:

• It is useful in the study of the field behavior of saturated fine-grained soil.
• It is given as subtraction of natural water content from the liquid limit to the plasticity index of the soil.

\({{\rm{I}}_{\rm{c}}} = \frac{{{{\rm{w}}_{\rm{l}}} - {{\rm{w}}_{\rm{n}}}}}{I_P}\)

IP = Plasticity Index = wl - wP

\({{\rm{I}}_{\rm{c}}} = \frac{{{{\rm{w}}_{\rm{l}}} - {{\rm{w}}_{\rm{n}}}}}{{{{\rm{w}}_{\rm{l}}} - {{\rm{w}}_{\rm{p}}}}}\)

\({{\rm{w}}_{\rm{l}}}\) = liquid limit, \({{\rm{w}}_{\rm{P}}}\) = plastic limit, \({{\rm{w}}_{\rm{n}}}\) = water content of the soil at the natural state

Calculation:

Given, W_l = 40%, W_p = 20%, Clayey silt = 70%

W_n = 30%, Clay content = 100 - silt content = 100 - 70 = 30%

a) Plasticity Index

Plasticity Index = Liquid Limit – Plastic Limit

Plasticity Index = 40 - 20 = 20%

b) Activity

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

Activity \(= \frac{{20}}{{30}}\) = 0.67

Consistency Index:

\({{\rm{I}}_{\rm{c}}} = \frac{{{{\rm{w}}_{\rm{l}}} - {{\rm{w}}_{\rm{n}}}}}{{{{\rm{w}}_{\rm{l}}} - {{\rm{w}}_{\rm{p}}}}}\)

\({{\rm{I}}_{\rm{c}}} = \frac{40 \ - \ 30}{40 \ -\ 20}\) = 0.5

Consistency Index or Relative consistency: 

It is useful in the study of the field behaviour of saturated fine-grained soil.

It is given as subtraction of natural water content from liquid limit to the plasticity index of the soil.

\({{\rm{I}}_{\rm{c}}} = \frac{{{{\rm{w}}_{\rm{l}}} - {{\rm{w}}_{\rm{n}}}}}{I_P}\)

I_P = Plasticity Index = w_l - w_P

\({{\rm{I}}_{\rm{c}}} = \frac{{{{\rm{w}}_{\rm{l}}} - {{\rm{w}}_{\rm{n}}}}}{{{{\rm{w}}_{\rm{l}}} - {{\rm{w}}_{\rm{p}}}}}\)

\({{\rm{w}}_{\rm{l}}}\) = liquid limit

\({{\rm{w}}_{\rm{P}}}\) = plastic limit

\({{\rm{w}}_{\rm{n}}}\) = water content of the soil at the natural state

Range: It can be greater than or less than 1.

For

Ic = 1, the soil is at its plastic limit

Ic = 0, the soil is at its liquid limit

Ic > 1, the soil is in semi-solid state and is stiff

Ic < 0, it indicates that the natural water content is greater than the liquid limit and hence behaves like a liquid.

Concept:

Consistency index

 \({I_C} = \frac{{{w_L} - w}}{{{w_L} - {w_P}}}\)

So, consistency index is – ve means, w > wL i.e. soil is in the liquid state and behaves like a liquid. 

\({I_C} = 0;w = {w_L}\; \Rightarrow Soil\;is\;in\;liquid\;limit.\)

\({I_C} = 1;w = {w_P}\; \Rightarrow Soil\;is\;in\;plastic\;limit.\)

\({I_C} > 1\;;\left( {{w_L} - w} \right) > \left( {{w_L} - {w_P}} \right) \Rightarrow w < {w_P}\;i.e;soil\;is\;stiff.\)

Calculation:

Given data,

Liquid limit, wL = 45%, 

Plastic limit, wp = 25%,

Shrinkage limit, ws = 15% , and

Natural moisture content, w = 30%

Consistency index

\({I_C} = \frac{{{w_L} - w}}{{{w_L} - {w_P}}}\)

\(\therefore {{\rm{I}}_{\rm{C}}} = \frac{{45 - 30}}{{45 - 25}} = \frac{{15}}{{20}}\) = 0.75

Hence, the consistency index is 75%.

Concept:

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

So, C = Percentage of clay fraction finer than 2 μ

Concepts:

The proportion of clay mineral flakes (< 0.002 mm size) in a fine soil increases its tendency to swell and shrink with changes in water content. This is called the activity of the clayey soil, and it represents the degree of plasticity related to the clay content. Mathematically, it is the ratio of Plasticity Index(IP) of soil and percentage of clay size particles 9 less than 2 micron).

\(A = \frac{IP}{\text{% of Clay size fraction}}\)

Plasticity Index, IP = Liquid Limit (LL) – Plastic Limit (PL)

Calculation:

Given: LL = 45 5; PL = 25 %; % clay size fraction = 20 %

The Activity of soil is given as:

\(A = \frac{45-25}{20}\)

∴ A = 1

Important Point:

 Based on Activity, soils can be classified as: