# Borrow Pit Soil Calculation for Embankment

A soil in the borrow pit is at a dry density of 18 kN/ m³ with a moisture content of 12%. The soil is excavated from this pit and compacted in a embankment to a dry density of 19 kN/ m³ with a moisture content of 16%. Compute the quantity of soil to be excavated from the borrow pit and the amount of water to be added for 100 m³ of compacted soil in the embankment.

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**Soil Calculation from Borrow Pit for Embankment**

**To solve this problem, we need to calculate two things:**

The quantity of soil to be excavated from the borrow pit to achieve 100 m³ of compacted soil in the embankment.

The amount of water to be added to the soil for achieving the desired moisture content in the embankment.

**Given Data**

Moisture content of soil in the borrow pit, 𝑤1=12%

Dry density of soil in the embankment, 𝜌𝑑2=19 kN/m³

Moisture content of soil in the embankment, 𝑤2=16%

Volume of compacted soil in the embankment, 𝑉2=100 m³

**Step 1: Compute the Mass of Dry Soil in the Embankment**

Mass of dry soil in embankment=19 kN/m³×100 m³

Mass of dry soil in embankment=1900 kN

**Step 2: Compute the Volume of Soil to be Excavated from the Borrow Pit**

We need to find the volume of soil in the borrow pit that provides 1900 kN of dry soil mass.

V1=ρd1/Mass of dry soil in embankment𝑉1=1900 kN/18 kN/m³

𝑉1=105.56 m³

**Step 3: Compute the Amount of Water to be Added**

First, calculate the initial and final masses of the soil including water content.

**Initial Mass of Soil in the Borrow Pit (Including Water)**

𝜌𝑏𝑢𝑙𝑘1=𝜌𝑑1×(1+𝑤1)

𝜌𝑏𝑢𝑙𝑘1=18 kN/m³×(1+0.12)

𝜌𝑏𝑢𝑙𝑘1=18 kN/m³×1.12

𝜌𝑏𝑢𝑙𝑘1=20.16 kN/m³

Initial mass of soil (including water)=𝜌𝑏𝑢𝑙𝑘1×𝑉1

Initial mass of soil (including water)=20.16 kN/m³×105.56 m³

Initial mass of soil (including water)=2128.09 kN

**Final Mass of Soil in the Embankment (Including Water)**

𝜌𝑏𝑢𝑙𝑘2=𝜌𝑑2×(1+𝑤2)

𝜌𝑏𝑢𝑙𝑘2=19 kN/m³×(1+0.16)

𝜌𝑏𝑢𝑙𝑘2=19 kN/m³×1.16

𝜌𝑏𝑢𝑙𝑘2=22.04 kN/m³

Final mass of soil (including water)=𝜌𝑏𝑢𝑙𝑘2×𝑉2

Final mass of soil (including water)=22.04 kN/m³×100 m³

Final mass of soil (including water)=2204 kN

**Step 4: Compute the Amount of Water to be Added**

Amount of water to be added=Final mass of soil (including water)−Initial mass of soil (including water)

Amount of water to be added=2204 kN−2128.09 kN

Amount of water to be added=75.91 kN

**Summary of Results**

Volume of soil to be excavated from the borrow pit: 105.56 m³

Amount of water to be added for 100 m³ of compacted soil in the embankment: 75.91 kN or 7.74 m³ (approx)

## Soil Excavation and Water Addition Calculator

Volume of soil to be excavated from the borrow pit (V1): m³

Amount of water to be added: kN