Understanding Soil Specific Gravity

Specific gravity ($G_s$) is a fundamental property of soil solids. It is defined as the ratio of the mass of a unit volume of soil solids at a given temperature to the mass of a unit volume of water at the standard temperature (usually $4^\circ \text{C}$). Essentially, it tells us how much denser the soil solid particles are compared to water.

Given Information

We are provided with the following measurements from a specific gravity test using a jar:

• Mass of empty jar ($M_{jar}$) = $0.8 \text{ kg}$
• Mass of jar completely filled with water ($M_{jar+w}$) = $1.5 \text{ kg}$
• Mass of oven-dried soil sample ($M_s$) = $0.1375 \text{ kg}$
• Mass of jar with soil and water added to fill it ($M_{jar+s+w}$) = $1.6 \text{ kg}$

Calculating Specific Gravity

The specific gravity ($G_s$) of soil solids is calculated using the formula:

$$G_s = \frac{\text{Mass of soil solids}}{\text{Mass of water having the same volume as soil solids}}$$

This can be written as:

$$G_s = \frac{M_s}{M_w}$$

Where $M_s$ is the mass of the dry soil sample, and $M_w$ is the mass of water that occupies the same volume as the soil solids.

Let's find the required values from the given data:

Mass of Water that Fills the Jar

The mass of water that completely fills the jar represents the mass of water occupying the entire volume of the jar. This is found by subtracting the mass of the empty jar from the mass of the jar filled with water.

Mass of water filling jar ($M_{w\_full}$) = $M_{jar+w} - M_{jar}$

$$M_{w\_full} = 1.5 \text{ kg} - 0.8 \text{ kg} = 0.7 \text{ kg}$$

Mass of Water in the Jar with Soil

When the soil sample is placed in the jar and water is added to fill it, the total mass is $M_{jar+s+w}$. To find the mass of water ($M_{w\_with\_s}$) present in the jar alongside the soil, we subtract the mass of the empty jar and the mass of the soil sample from this total mass.

Mass of water in jar with soil ($M_{w\_with\_s}$) = $M_{jar+s+w} - M_{jar} - M_s$

$$M_{w\_with\_s} = 1.6 \text{ kg} - 0.8 \text{ kg} - 0.1375 \text{ kg} = 0.8 \text{ kg} - 0.1375 \text{ kg} = 0.6625 \text{ kg}$$

Mass of Water Displaced by Soil Solids

The volume occupied by the soil solids is equal to the volume of water that is "pushed out" or displaced when the soil is added to the full jar of water. The mass of this displaced water ($M_w$) is the difference between the mass of water that can fill the jar ($M_{w\_full}$) and the mass of water that is present in the jar when the soil is also there ($M_{w\_with\_s}$).

Mass of water displaced by soil ($M_w$) = $M_{w\_full} - M_{w\_with\_s}$

$$M_w = 0.7 \text{ kg} - 0.6625 \text{ kg} = 0.0375 \text{ kg}$$

This $0.0375 \text{ kg}$ is the mass of water that occupies the same volume as the $0.1375 \text{ kg}$ of soil solids.

Calculating Specific Gravity $G_s$

Now we have the mass of the soil solids ($M_s = 0.1375 \text{ kg}$) and the mass of water occupying the same volume ($M_w = 0.0375 \text{ kg}$). We can calculate the specific gravity:

$$G_s = \frac{M_s}{M_w} = \frac{0.1375 \text{ kg}}{0.0375 \text{ kg}}$$

$$G_s = 3.666...$$

Rounding to two decimal places, the specific gravity is $3.67$.

The calculated specific gravity is $3.67$.