Impartant Basic Formulaes in Geotechnical Engineering
Prepared by :- #abilas
|
Sr.No. |
Input Data :- |
Formulation |
Output Data :- |
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|
1 |
Water Content |
\[(w)\] |
= |
\[W_s=\dfrac{W}{1+w}\] |
Weight of solids soil |
\[(W_s)\] |
= |
952.38
|
\[gm\] |
|||
|
Total Weight of soil |
\[(W)\] |
= |
\[gm\] |
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|
2 |
Weight of solids soil |
\[(W_s)\] |
= |
\[gm\] |
\[W=W_s(1+w)\] |
Total Weight of soil |
\[(W)\] |
= |
1000.00
|
\[gm\] |
||
|
Water Content |
\[(w)\] |
= |
||||||||||
|
3 |
Volume of soil mass |
\[(V)\] |
= |
\[ml\] |
\[V_s=\dfrac{V}{1+e}\] |
Volume of Solids in soil |
\[(V_s)\] |
= |
70.59
|
\[ml\] |
||
|
Void ratio |
\[(e)\] |
= |
||||||||||
|
4 |
Volume of Solids in soil |
\[(V_s)\] |
= |
\[gm\] |
\[V=V_s(1+e)\] |
Volume of soil mass |
\[(V)\] |
= |
120.70
|
\[gm\] |
||
|
Void ratio |
\[(e)\] |
= |
||||||||||
|
5 |
Void ratio |
\[(e)\] |
= |
\[e=\dfrac{n}{1+n}\] |
Porosity |
\[(n)\] |
= |
0.41
|
||||
|
6 |
Porosity |
\[(n)\] |
= |
\[n=\dfrac{e}{1-e}\] |
Void ratio |
\[(e)\] |
= |
0.69
|
||||
|
7 |
Void ratio |
\[(e)\] |
= |
\[e S=w G_s\] |
Specific gravity of Solids |
\[(G_s)\] |
= |
2.80
|
||||
|
Degree of Saturation |
\[(S)\] |
= |
||||||||||
|
Water Content |
\[(w)\] |
= |
||||||||||
|
8 |
Void ratio |
\[(e)\] |
= |
\[e S=w G_s\] |
Water Content |
\[(w)\] |
= |
0.05
|
||||
|
Degree of Saturation |
\[(S)\] |
= |
||||||||||
|
Specific gravity of Solids |
\[(G_s)\] |
= |
||||||||||
|
9 |
Specific gravity of Solids |
\[(G_s)\] |
= |
\[e S=w G_s\] |
Void ratio |
\[(e)\] |
= |
0.70
|
||||
|
Degree of Saturation |
\[(S)\] |
= |
||||||||||
|
Water Content |
\[(w)\] |
= |
||||||||||
|
10 |
Void ratio |
\[(e)\] |
= |
\[e S=w G_s\] |
Degree of Saturation |
\[(S)\] |
= |
0.20
|
||||
|
Specific gravity of Solids |
\[(G_s)\] |
= |
||||||||||
|
Water Content |
\[(w)\] |
= |
||||||||||
|
11 |
Void ratio |
\[(e)\] |
= |
\[\gamma_t=\dfrac{G_s+S e}{1+e} \gamma_w\] |
Unit weight of Soil |
\[(\gamma_t)\] |
= |
17.29
|
\[kN/m^3\] |
|||
|
Degree of Saturation |
\[(S)\] |
= |
||||||||||
|
Specific gravity of Solids |
\[(G_s)\] |
= |
||||||||||
|
Unit weight of Water |
\[(\gamma_w)\] |
= |
10 |
\[kN/m^3\] |
||||||||
|
12 |
Void ratio |
\[(e)\] |
= |
\[G_s=\dfrac{\gamma_t(1+ e)}{\gamma_w} -S e\] |
Specific gravity of Solids |
\[(G_s)\] |
= |
2.80
|
||||
|
Degree of Saturation |
\[(S)\] |
= |
||||||||||
|
Unit weight of Soil |
\[(\gamma_t)\] |
= |
\[kN/m^3\] |
|||||||||
|
Unit weight of Water |
\[(\gamma_w)\] |
= |
10 |
\[kN/m^3\] |
||||||||
|
13 |
Void ratio |
\[(e)\] |
= |
\[S=\dfrac{\dfrac{\gamma_t(1+ e)}{\gamma_w} -G_s}{e}\] |
Degree of Saturation |
\[(S)\] |
= |
0.20
|
||||
|
Specific gravity of Solids |
\[(G_s)\] |
= |
||||||||||
|
Unit weight of Soil |
\[(\gamma_t)\] |
= |
\[kN/m^3\] |
|||||||||
|
Unit weight of Water |
\[(\gamma_w)\] |
= |
10 |
\[kN/m^3\] |
||||||||
|
14 |
Void ratio |
\[(e)\] |
= |
\[\gamma_{sat}=\dfrac{G_s+ e}{1+e} \gamma_w\] |
Unit weight of saturated Soil |
\[(\gamma_{sat})\] |
= |
20.59
|
\[kN/m^3\] |
|||
|
Degree of Saturation |
\[(S)\] |
= |
1.00 |
|||||||||
|
Specific gravity of Solids |
\[(G_s)\] |
= |
||||||||||
|
Unit weight of Water |
\[(\gamma_w)\] |
= |
10 |
\[kN/m^3\] |
||||||||
|
15 |
Void ratio |
\[(e)\] |
= |
\[G_s=\dfrac{\gamma_{sat}(1+ e)}{\gamma_w} -e\] |
Specific gravity of Solids |
\[(G_s)\] |
= |
2.80
|
||||
|
Degree of Saturation |
\[(S)\] |
= |
1.00 |
|||||||||
|
Unit weight of saturated Soil |
\[(\gamma_{sat})\] |
= |
\[kN/m^3\] |
|||||||||
|
Unit weight of Water |
\[(\gamma_w)\] |
= |
10 |
\[kN/m^3\] |
||||||||
|
16 |
Void ratio |
\[(e)\] |
= |
\[\gamma_d=\dfrac{G_s\gamma_w}{1+e}\] |
Unit weight of dry Soil |
\[(\gamma_d)\] |
= |
16.47
|
\[kN/m^3\] |
|||
|
Degree of Saturation |
\[(S)\] |
= |
0.00 |
|||||||||
|
Specific gravity of Solids |
\[(G_s)\] |
= |
||||||||||
|
Unit weight of Water |
\[(\gamma_w)\] |
= |
10 |
\[kN/m^3\] |
||||||||
|
17 |
Void ratio |
\[(e)\] |
= |
\[G_s=\dfrac{\gamma_d(1+e)}{\gamma_w}\] |
Specific gravity of Solids |
\[(G_s)\] |
= |
2.80
|
||||
|
Degree of Saturation |
\[(S)\] |
= |
0.00 |
|||||||||
|
Unit weight of dry Soil |
\[(\gamma_d)\] |
= |
\[kN/m^3\] |
|||||||||
|
Unit weight of Water |
\[(\gamma_w)\] |
= |
10 |
\[kN/m^3\] |
||||||||
|
18 |
Void ratio |
\[(e)\] |
= |
\[\gamma'=\dfrac{(G_s-1)\gamma_w}{1+e}\] |
Unit weight of Submerged Soil |
\[(\gamma')\] |
= |
10.59
|
\[kN/m^3\] |
|||
|
Degree of Saturation |
\[(S)\] |
= |
0.00 |
|||||||||
|
Specific gravity of Solids |
\[(G_s)\] |
= |
||||||||||
|
Unit weight of Water |
\[(\gamma_w)\] |
= |
10 |
\[kN/m^3\] |
||||||||
|
19 |
Void ratio |
\[(e)\] |
= |
\[G_s=\dfrac{\gamma'(1+e)}{\gamma_w}+1\] |
Specific gravity of Solids |
\[(G_s)\] |
= |
2.80
|
||||
|
Degree of Saturation |
\[(S)\] |
= |
0.00 |
|||||||||
|
Unit weight of Submerged Soil |
\[(\gamma')\] |
= |
\[kN/m^3\] |
|||||||||
|
Unit weight of Water |
\[(\gamma_w)\] |
= |
10 |
\[kN/m^3\] |
||||||||
|
19 |
Water Content |
\[(w)\] |
= |
\[\gamma_d=\dfrac{\gamma_t}{1+w}\] |
Unit weight of dry Soil |
\[(\gamma_d)\] |
= |
16.47
|
\[kN/m^3\] |
|||
|
Unit weight of Soil |
\[(\gamma_t)\] |
= |
\[kN/m^3\] |
|||||||||
|
20 |
Water Content |
\[(w)\] |
= |
\[\gamma_t=\gamma_d (1+w)\] |
Unit weight of Soil |
\[(\gamma_t)\] |
= |
17.29
|
\[kN/m^3\] |
|||
|
Unit weight of dry Soil |
\[(\gamma_d)\] |
= |
\[kN/m^3\] |
|||||||||
|
21 |
Unit weight of Soil |
\[(\gamma_t)\] |
= |
\[kN/m^3\] |
\[ w=\dfrac{\gamma_t}{\gamma_d}-1\] |
Water Content |
\[(w)\] |
= |
0.05
|
|||
|
Unit weight of dry Soil |
\[(\gamma_d)\] |
= |
\[kN/m^3\] |
|||||||||
|
22 |
Water Content |
\[(w)\] |
= |
\[\gamma_d=\dfrac{G_s \gamma_w}{1+\dfrac{w G_s}{S}}\] |
Unit weight of dry Soil |
\[(\gamma_d)\] |
= |
16.47
|
\[kN/m^3\] |
|||
|
Specific gravity of Solids |
\[(G_s)\] |
= |
||||||||||
|
Degree of Saturation |
\[(S)\] |
= |
\[kN/m^3\] |
|||||||||
|
Unit weight of Water |
\[(\gamma_w)\] |
= |
10 |
\[kN/m^3\] |
||||||||
|
23 |
Water Content |
\[(w)\] |
= |
\[ S=\dfrac{w}{\dfrac{\gamma_w}{\gamma_t}(1+w)+\dfrac{1}{G_s}}\] |
Degree of Saturation |
\[(S)\] |
= |
0.20
|
||||
|
Specific gravity of Solids |
\[(G_s)\] |
= |
||||||||||
|
Unit weight of Soil |
\[(\gamma_t)\] |
= |
\[kN/m^3\] |
|||||||||
|
Unit weight of Water |
\[(\gamma_w)\] |
= |
10 |
\[kN/m^3\] |
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