______ is the ratio of the volume of voids to the total volume of the given soil.

Question

Prepp Team · Accepted Answer

Understanding Soil Phase Relationships: Porosity

Soil is a three-phase system consisting of solid particles, water, and air. Understanding the relationships between the volumes and weights of these phases is crucial in soil mechanics. Several terms are used to quantify these relationships, and one of them is the ratio of the volume of voids to the total volume of the soil sample.

Defining Key Soil Properties

Let's define the terms given in the options to identify the one that matches the description: "ratio of the volume of voids to the total volume of the given soil."

We can represent the different volumes in a soil sample as follows:

\(V_v\) = Volume of voids (sum of volume of water and volume of air)
\(V_s\) = Volume of solids
\(V_w\) = Volume of water
\(V_a\) = Volume of air
\(V\) = Total volume of the soil sample (\(V = V_v + V_s\))

Evaluating the Options:

Degree of saturation (\(S\)): This is defined as the ratio of the volume of water to the volume of voids.
Formula: \(S = \frac{V_w}{V_v}\)

This definition does not match the ratio of the volume of voids to the total volume.
Void ratio (\(e\)): This is defined as the ratio of the volume of voids to the volume of solids.
Formula: \(e = \frac{V_v}{V_s}\)

This definition does not match the ratio of the volume of voids to the total volume.
Porosity (\(n\)): This is defined as the ratio of the volume of voids to the total volume of the soil sample.
Formula: \(n = \frac{V_v}{V}\)

This definition exactly matches the description given in the question.
Air content (\(a_c\)): This is defined as the ratio of the volume of air to the volume of voids.
Formula: \(a_c = \frac{V_a}{V_v}\)

This definition does not match the ratio of the volume of voids to the total volume.

Comparing Soil Phase Definitions

Here is a summary of the definitions:

Term	Definition	Formula	Matches Question?
Degree of saturation (\(S\))	Ratio of volume of water to volume of voids	\(S = \frac{V_w}{V_v}\)	No
Void ratio (\(e\))	Ratio of volume of voids to volume of solids	\(e = \frac{V_v}{V_s}\)	No
Porosity (\(n\))	Ratio of volume of voids to total volume	\(n = \frac{V_v}{V}\)	Yes
Air content (\(a_c\))	Ratio of volume of air to volume of voids	\(a_c = \frac{V_a}{V_v}\)	No

Based on the definitions and comparison, the term that represents the ratio of the volume of voids to the total volume of the soil is Porosity.

Revision Table: Soil Phase Ratios

Ratio	Definition	Formula	Range
Porosity (\(n\))	\(V_v / V\)	\(n = \frac{V_v}{V}\)	\(0 < n < 1\) or \(0\% < n < 100\%\)
Void Ratio (\(e\))	\(V_v / V_s\)	\(e = \frac{V_v}{V_s}\)	\(e > 0\) (can be > 1)
Degree of Saturation (\(S\))	\(V_w / V_v\)	\(S = \frac{V_w}{V_v}\)	\(0 \le S \le 1\) or \(0\% \le S \le 100\%\)
Air Content (\(a_c\))	\(V_a / V_v\)	\(a_c = \frac{V_a}{V_v}\)	\(0 \le a_c \le 1\) or \(0\% \le a_c \le 100\%\)

Additional Information: Relationship Between Porosity and Void Ratio

Porosity (\(n\)) and void ratio (\(e\)) are inter-related. Since \(V = V_s + V_v\), we can derive the relationship between them:

From the definition of porosity, \(n = \frac{V_v}{V_s + V_v}\). Dividing numerator and denominator by \(V_s\), we get \(n = \frac{V_v/V_s}{V_s/V_s + V_v/V_s} = \frac{e}{1 + e}\).
From the definition of void ratio, \(e = \frac{V_v}{V_s}\). Since \(V_s = V - V_v\), we have \(e = \frac{V_v}{V - V_v}\). Dividing numerator and denominator by \(V\), we get \(e = \frac{V_v/V}{V/V - V_v/V} = \frac{n}{1 - n}\).

These formulas allow conversion between porosity and void ratio, which are both fundamental properties describing the looseness or denseness of a soil.