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Given:
- Unit weight of dry sandy soil [tex](\(\gamma_d\))[/tex]: 15.5 kN/m³
- Specific gravity of soil grains [tex](\(G_s\))[/tex]: 2.64
Step-by-Step Calculation:
1. Calculate the unit weight of solid particles (\[tex](\gamma_s\))[/tex]:
[tex]\[\gamma_s = G_s \times \gamma_{water}\][/tex]
[tex] \[\gamma_s = 2.64 \times 9.81 = 25.86 \text{ kN/m³}\][/tex]
2. Calculate the void ratio [tex](\(e\)):[/tex]
[tex] \[e = \frac{\gamma_d - \gamma_s}{\gamma_s}\][/tex]
[tex]\[e = \frac{15.5 - 25.86}{25.86} = -0.398\][/tex]
3. Determine the water content (\(w\)):
[tex] \[w = \frac{e}{1+e} = \frac{-0.398}{1 - 0.398} = \frac{-0.398}{0.602} = -0.661\][/tex]
4. Calculate the unit weight of saturated soil [tex](\(\gamma_{sat}\)):[/tex]
[tex] \[\gamma_{sat} = (1 + w) \times \gamma_d\][/tex]
[tex] \[\gamma_{sat} = (1 - 0.661) \times 15.5\][/tex]
[tex] \[\gamma_{sat} = 0.339 \times 15.5 = 5.26 \text{ kN/m³}\][/tex]
Therefore, the unit weight of saturated soil [tex](\(\gamma_{sat}\))[/tex] is 5.26 kN/m³.