A contractor excavates 10,000 m3 soil at moist unit weight of 17.5 kN/m3 and moisture content of 10% from a borrow pit and transports it to a project site. The project has an area of 20,000 m2 to be filled with this compacted soil. If the required dry unit weight and moisture content of the compacted soil are 18.3 kN/m3 and 12.5% (assume there is no soil loss during transportation and compaction), what is the thickness of the compacted soil and how much water needs to be added?

Answer:

Part A

The thickness of the compacted soil is approximately 4.3467 × 10⁻¹ m

Part B

The weight of water to be added is approximately 19886.[tex]\overline{36}[/tex] kN, the volume of the water added is approximately 2,027.77 m³

Explanation:

The parameters of the soil are;

The volume of sol the excavator excavates, [tex]V_T[/tex] = 10,000 m³

The moist unit weight, W = 17.5 kN/m³

The moisture content = 10%

The area of the project, A = 20,000 m²

The required dry unit weight = 18.3 kN/m³

The required moisture content = 12.5%

Part A

Therefore, we have;

The moist unit weight = Unit weight = ([tex]W_s[/tex] + [tex]W_w[/tex])/[tex]V_T[/tex]

The moisture content, MC = 10% = ([tex]W_w[/tex]/[tex]W_s[/tex]) × 100

∴ [tex]W_w[/tex] = 0.1·[tex]W_s[/tex]

∴ The moist unit weight = 17.5 kN/m³ = ([tex]W_s[/tex] + 0.1·[tex]W_s[/tex])/(10,000 m³)

1.1·[tex]W_s[/tex] = 10,000 m³ × 17.5 kN/m³ = 175,000 kN

[tex]W_s[/tex] = 175,000 kN/1.1 = 159,090.[tex]\overline{09}[/tex] kN

For the required soil, we have;

The required dry unit weight = 18.3 kN/m³ = [tex]W_s[/tex]/[tex]V_T[/tex] = 159,090.[tex]\overline{09}[/tex] kN/[tex]V_T[/tex]

[tex]V_T[/tex] = 159,090.[tex]\overline{09}[/tex] kN/(18.3 kN/m³) ≈ 8,693.4923 m³

The total volume of the required soil ≈ 8,693.4923 m³

Volume [tex]V_T[/tex] = Area, A × Thickness, d

∴ d =  [tex]V_T[/tex]/A

d = 8,693.4923 m³/(20,000 m²) ≈ 4.3467 × 10⁻¹ m

The thickness of the compacted soil ≈ 4.3467 × 10⁻¹ m

Part A

The moisture content, MC = 12.5% = ([tex]W_w[/tex]/[tex]W_s[/tex]) × 100

[tex]W_w[/tex] = [tex]W_s[/tex] × MC/100 = 159,090.[tex]\overline{09}[/tex] kN × 12.5/100 = 19886.[tex]\overline{36}[/tex] kN

The weight of water to be added, [tex]W_w[/tex] = 19886.[tex]\overline{36}[/tex] kN

Where the density of water, ρ = 9.807 kN/m³

Therefore, we have;

The volume of water, V = [tex]W_w[/tex]/ρ

∴ V = 19886.[tex]\overline{36}[/tex] kN/(9.807 kN/m³) ≈ 2027.77 m³

The volume of water, V ≈ 2027.77 m³

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