Worked out problem on soil mechanics

Phase diagram in soil mechanics with theory,worked problem and calculator

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Problem will be illustrated on soil mechanics.

1. 1 cum of wet soil weighs 20kN. Its dry weight is 18kN. specific gravity of soil, G_s=2.67. Determine below properties

1. Water content.
2. Void ratio.
3. Porosity
4. Degree of saturation.

Solution:

The volume and weight of the constituents are now calculated based phase diagram:

The weight of water:

\[\mathop W\nolimits_\omega = \mathop W\nolimits_{s + \omega } - \mathop W\nolimits_s = 20 - 18 = 2kN\]

The volume of solids:

\[\mathop V\nolimits_s = \frac{{\mathop W\nolimits_s }}{{\mathop G\nolimits_s \mathop { \times \gamma }\nolimits_\omega }} = \frac{{18}}{{2.67 \times 9.8}} = 0.6879{m^3}\]

The volume of water:

\[\mathop V\nolimits_\omega = \frac{{\mathop W\nolimits_\omega }}{{\mathop \gamma \nolimits_\omega }} = \frac{2}{{9.8}} = 0.2041{m^3}\]

The volume of voids:

\[\mathop V\nolimits_V = V - \mathop V\nolimits_S = 1 - 0.6879 = 0.3121{m^3}\]

1. Water content.

\[\omega = \frac{{\mathop W\nolimits_\omega }}{{\mathop W\nolimits_s }} = \frac{2}{{18}} = 0.1111 = 11.11\% \]

2. Void ratio.

\[e = \frac{{\mathop V\nolimits_\upsilon }}{{\mathop V\nolimits_s }} = \frac{{0.3121}}{{0.6879}} = 0.45\]

3. Porosity.

\[n = \frac{{\mathop V\nolimits_\upsilon }}{V} = \frac{{0.3121}}{1} = 0.3121 = 31.21\% \]

4. Degree of saturation.

\[S = \frac{{\mathop V\nolimits_\omega }}{{\mathop V\nolimits_\upsilon }} = \frac{{0.2041}}{{0.3121}} = 0.6539 = 65.4\% \]

1. cum of wet soil weighs kN.Its dry weight is kN. Specific gravity of soil, Gs= Determine below properties

1. Water content.
2. Void ratio.
3. Porosity
4. Degree of saturation.
5. Assume unit weight of water γ_w as

1. Water content: %

2. Void ratio: %

3. Porosity:

4. Degree of saturation: %

Refrence

1. Venkataramaiah, C. (2018). Geotechnical Engineering (6th ed.). New Age International Publishers Pvt Ltd.

2. Punmia, B.C( 2017)Soil mechanics and foundations(17th ed.).Laxmi publications Pvt Ltd.

3. Gopal R, Rao, A, S, R( 2016)Basic and applied Soil mechanics(3rd ed.).New Age International Publishers Pvt Ltd.

Worked out problem in Soil mechanics| Civil engineering| Geo technical engineering| Foundation engineering

Worked out problem and web Calculator in soil mechanics

Soil mechanics and Geotechnical engineering problem calculator

1. The moist unit weight of soil is 19.2kN/m³. Given that G_s=2.69 and w=9.8%. Determine below properties

1. Dry unit weight.
2. Void ratio.
3. Porosity
4. Degree of saturation.

Solution:

1. Dry unit weight.

\[\mathop \gamma \nolimits_d = \frac{\gamma }{{1 + \omega }} = \frac{{19.2}}{{1 + \frac{{9.8}}{{100}}}} = 17.5kN/{m^3}.\]

2. Void ratio.

\[\mathop \gamma \nolimits_d = \frac{{\mathop G\nolimits_s \mathop { \times \gamma }\nolimits_\omega }}{{1 + e}} \Rightarrow 17.5 = \frac{{(2.69)(9.81)}}{{1 + e}}\Rightarrow e=0.51\]

3. Porosity.

\[n = \frac{e}{{1 + e}} = \frac{{0.51}}{{1 + 0.51}} = 0.338\]

4. Degree of saturation.

\[S = \frac{{\mathop G\nolimits_s \times \omega }}{e} = \frac{{(0.098) \times (2.69)}}{{0.51}} \times 100 = 51.7\%\]

1. The moist unit weight of soil is

kN/m3. Given that Gs= and w= %, Determine below properties

1. Dry unit weight.
2. Void ratio.
3. Porosity
4. Degree of saturation.
5. Assume unit weight of water γ_w as

1. Dry unit weight:

2. Void ratio:

3. Porosity:

4. Degree of saturation:

Refrence

1. Venkataramaiah, C. (2018). Geotechnical Engineering (6th ed.). New Age International Publishers Pvt Ltd.

2. Punmia, B.C( 2017)Soil mechanics and foundations(17th ed.).Laxmi publications Pvt Ltd.

3. Gopal R, Rao, A, S, R( 2016)Basic and applied Soil mechanics(3rd ed.).New Age International Publishers Pvt Ltd.

Soil mechanics Solids-Water-Air relationships | Civil engineering| Geotechnical engineering | Foundation engineering

Definitions used in geotechnical engineering

The relative proportions of solids, water and air present in a soil influences physical properties of soil.The important definitions are illustrated below.

1. Water content (w) is defined as the ratio of weight of water to the weight of solids in a given mass of soil.it also called as moisture content.It is expressed as percentage

\[\omega = \frac{{\mathop W\nolimits_\omega }}{{\mathop W\nolimits_s }} \times 100\]

2. The void ratio (e) a mixture is the ratio of the volume of voids to volume of solids.

\[e = \frac{{{V_V}}}{{{V_S}}}\times 100\]

3. The porosity (n) a mixture is the ratio of the volume of voids to total volume.The value is expressed in percentage ranges between 0 to 100% or ( 0 to 1)

\[n = \frac{{\mathop V\nolimits_V }}{{\mathop V\nolimits_T }} \times 100\]

4. Degree of saturation (s_r) is defined as the ratio of the volume of water to volume of voids.

\[\mathop S\nolimits_r = \frac{{\mathop V\nolimits_\omega }}{{\mathop V\nolimits_v }} \times 100\]

5. Air content (a_c) is defined as the ratio of the volume of air voids to volume of voids.

\[\mathop a\nolimits_c = \frac{{\mathop V\nolimits_a }}{{\mathop V\nolimits_v }} \times 100 = 1 - S\]

6. Percentage of air voids (n_a) is defined as the ratio of the volume of air voids to total volume of soil mass.

\[\mathop n\nolimits_a = \frac{{\mathop V\nolimits_a }}{{\mathop V\nolimits_T }} \times 100\]

7. unit weight of solids (γ_s) is the ratio of the weight of solids to volume of solids.

\[\mathop \gamma \nolimits_s = \frac{{\mathop W\nolimits_S }}{{\mathop V\nolimits_S }}\]

8. Bulk unit weight (γ_t) is the ratio of the total weight of soil to total volume of soil.

\[\mathop \gamma \nolimits_t = \frac{{\mathop W }}{{\mathop V}}\]

9. Dry unit weight of solids (γ_d) is the ratio of the total weight of of fully saturated soil to total volume of soil.

\[\mathop \gamma \nolimits_{d} = \frac{{\mathop W\nolimits_{s} }}{{\mathop V }}\]

10. Saturated unit weight (γ_Sat) is the ratio of the total weight of of fully saturated soil to total volume of soil.

\[\mathop \gamma \nolimits_{sat} = \frac{{\mathop W\nolimits_{Sat} }}{{\mathop V }}\]

11. Submerged unit weight (γ^') is the ratio of submerged weight of soil to total volume. It is also equal to the saturated unit weight minus the unit weight of water.

\[\mathop \gamma \nolimits^1 = \frac{{\mathop W\nolimits_{Sub} }}{V} = \mathop \gamma \nolimits_{sat} - \mathop \gamma \nolimits_w \]

12. Specific gravity of solids (G^s) is defined as the ratio of the weight of a given volume of solids to the weight of an equivalent volume of water at 4^oC.

\[\mathop G\nolimits_S = \frac{{\mathop W\nolimits_S }}{{\mathop V\nolimits_S \times \mathop \gamma \nolimits_w }}\]

Specific gravity of solids (G^s) is defined as the ratio of unit weight of solids to unit weight of water.

\[\mathop G\nolimits_S = \frac{{\mathop \gamma \nolimits_s }}{{\mathop \gamma \nolimits_w }}\]

13. Apparent or mass specific gravity (G;^m) is defined as the ratio of the total weight of a given mass of soil to the weight of equivalent volume of water. It is also the ratio of the bulk unit weight of the soil to the unit weight of water.

\[\mathop G\nolimits_m = \frac{W}{{V \times \mathop \gamma \nolimits_w }} = \frac{\gamma }{{\mathop \gamma \nolimits_w }}\]

Refrence

1. Venkataramaiah, C. (2018). Geotechnical Engineering (6th ed.). New Age International Publishers Pvt Ltd.

2. Punmia, B.C( 2017)Soil mechanics and foundations(17th ed.).Laxmi publications Pvt Ltd.

3. Gopal R, Rao, A, S, R( 2016)Basic and applied Soil mechanics(3rd ed.).New Age International Publishers Pvt Ltd.

Geo technical engineering relations | Civil engineering| Soil mechanics| Foundation engineering

Calculator for Void ratio and Porosity relation

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Relation between void ratio and porosity

The relation between porosity and void ratio, if void ratio is unknown

\[e = \frac{n}{{1 - n}}\]

The relation between porosity and void ratio, if porosity is unknown

\[n = \frac{e}{{1 + e}}\]

The void ratio (e) a mixture is the ratio of the volume of voids to volume of solids.

\[e = \frac{{{V_V}}}{{{V_S}}}\]

The porosity (n) a mixture is the ratio of the volume of voids to total volume.The value is expressed in percentage ranges between 0 to 100% or ( 0 to 1)

\[n = \frac{{{V_V}}}{{{V_T}}}\]

Refrence

1. Venkataramaiah, C. (2018). Geotechnical Engineering (6th ed.). New Age International Publishers Pvt Ltd.

2. Punmia, B.C( 2017)Soil mechanics and foundations(17th ed.).Laxmi publications Pvt Ltd.