Calculate Soil Void Ratio and Porosity

The question asks us to find the values of void ratio and porosity for a soil sample where the volume of voids is equal to the volume of solids.

Let's define the key terms involved:

• Volume of voids ($V_v$): This is the volume occupied by air and water within the soil sample.
• Volume of solids ($V_s$): This is the volume occupied by the solid particles of the soil sample.
• Total volume ($V$): This is the total volume of the soil sample, which is the sum of the volume of voids and the volume of solids. Mathematically, $V = V_v + V_s$.
• Void ratio ($e$): This is defined as the ratio of the volume of voids to the volume of solids. The formula is $e = \frac{V_v}{V_s}$.
• Porosity ($n$): This is defined as the ratio of the volume of voids to the total volume of the soil sample. The formula is $n = \frac{V_v}{V}$.

Step-by-Step Calculation

We are given the condition that the volume of voids is equal to the volume of solids:

\(V_v = V_s\)

1. Calculate the Void Ratio ($e$)

The formula for void ratio is:

\(e = \frac{V_v}{V_s}\)

Since we are given that \(V_v = V_s\), we can substitute \(V_v\) with \(V_s\) (or vice versa) in the formula:

\(e = \frac{V_s}{V_s}\)

Assuming \(V_s > 0\), this simplifies to:

\(e = 1\)

So, the void ratio is 1.00.

2. Calculate the Porosity ($n$)

The formula for porosity is:

\(n = \frac{V_v}{V}\)

We know that the total volume \(V = V_v + V_s\). We are also given that \(V_v = V_s\).

Substitute \(V_s\) with \(V_v\) in the total volume formula:

\(V = V_v + V_v\)

\(V = 2V_v\)

Now substitute \(V\) in the porosity formula:

\(n = \frac{V_v}{2V_v}\)

Assuming \(V_v > 0\), this simplifies to:

\(n = \frac{1}{2}\)

\(n = 0.50\)

So, the porosity is 0.50.

Summary of Results

Based on the condition that the volume of voids equals the volume of solids, the calculated values are:

• Void ratio ($e$) = 1.00
• Porosity ($n$) = 0.50

Therefore, the values of void ratio and porosity are 1.00 and 0.50, respectively.