# Blog Archives

## Useful Soil Coefficients

Previously we discussed mechanical analysis and the method of sieve analysis. This allowed us to develop the particle size distribution curve. With this curve we can find some useful parameters. They are:

- The Uniformity Coefficient
- The Coefficient of Gradation

Both of these parameters are used in soil classification. The Uniformity Coefficient is defined as:

The Coefficient of Gradation is defined as:

where

These diameters are obtained from the particle size distribution curve by going across from the percent finer, coming to the curve, and turning 90 degrees down to the abscissa to locate the diameter as seen below.

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## Sieve Analysis

The first method of mechanical analysis is sieve analysis. It is pretty straight forward and involves straining a soil sample through a series of sieves. Generally the sieves are stacked as seen in the above diagram with a US Standard Sieve No. 4 at the top (This sieve size has a 4.75 mm opening) and a Sieve No. 200 at the bottom (with a 0.075 mm opening). The stack usually consists of 5 to 7 sieves and has a pan at the bottom. As you can see, the opening in the sieve gets smaller as you go down. Therefore larger particles will be captured while smaller particles will pass through. This allows us to measure how much soil of each size was in the original soil sample.

A few important steps:

- the soil sample needs to be oven-dried and all clumps broke.
- the weight of the empty sieves needs to be obtained.

Once this is done, the soil sample is placed into the top sieve, the lid is placed on the stack and the stack is placed in a mechanical shaker. The stack will then be shaken vigorously for approximately 5 minutes to ensure proper distribution of the particles.

The next step is to calculate what is called the *percent passing* or the *percent finer*. This is simply the percentage of the entire soil sample that passed through a particular sieve. For example, the percent passing the No. 200 sieve would be the mass of the soil in the bottom pan (since that is the soil that passed through the No. 200 sieve) divided by the total mass of the original soil sample. So in general we can write:

where

- %P is the percent passing
- i represents the ith sieve
- n represents the number of sieves
- m is the mass

Once the percent passing is determined for each sieve, a plot is made of sieve or particle size versus percent passing as seen below. The percent passing is on the ordinate and the sieve or particle size is on the abscissa. Also notice the abscissa is reverse logarithmic.

In future posts we will look more carefully at what information this distribution curve can provide, but for now we are highlighting the process. If you have any questions, please let me know in the comments.

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## Specific Gravity of Soil

The specific gravity of soil is an important weight-volume property that is helpful in classifying soils and in finding other weight-volume properties like void ratio, porosity, and unit weight. In this lab we first weighed an empty 1000 mL graduated cylinder. Then we filled it to 500 mL with distilled water and weighed it again. This allowed us to find the density or unit weight of the water. Secondly we filled another graduated cylinder with a mixture of soil and water. This mixture was heated on a stove to remove air from the mixture. Then it was filled to the 500 mL mark with additional distilled water and weighed. Finally an oven-safe container was weighed empty and then the soil/water mixture was poured into the container and dried in the oven for a 24-hour period. This enabled us to find the weight of the dry soil solids. Once this procedure was completed and the data collected, the specific gravity could be obtained via the following computations.

The specific gravity is defined as the ratio of the unit weight of the soil solids to the unit weight of water.

The unit weight of the soil solids is given by:

Where W_{s} is the weight of the soil solids and V_{s} is the volume of the soil solids. Likewise the unit weight of water is given by:

Consequently we can substitute these expressions into the first equation and obtain:

To obtain the weight of the soil we subtracted the weight of a dish container from the weight of the dish container with the oven-dried soil.

The volume of water we used was known at 500 mL.

The weight of the water corresponding to this volume was simply obtained by subtracting the weight of the flask or graduated cylinder from the weight of the flask with the volume of water.

Determining the volume of the soil was more difficult. We used the mixture that consists of the flask, soil, and water. Here the volume of the soil will be the total volume minus the volume of the water. (The volume of air is negligible)

In order to evaluate this we make the assumption that the unit weight of the water is constant.

We know all the values in this last expression except W_{w2}. This is the weight of the water in the water-soil-flask mixture. It can be found by:

This is all the information we needed. Simply substitute the solution from this last equation into the equation for the second volume of water, the solution from that into the equation for volume of soil, and all the known and determined values into the substituted equation for specific gravity to obtain the specific gravity. Here are the values and calculations we obtained in our experiment.

This was a reasonable finding since the specific gravity of soils typically falls in the range of 2.6 to 2.9.

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## Dirt or Mud – A Scientific Question?

My first soil mechanics lab was an exercise in analyzing the moisture content of a soil mixture. Soil is an aggregate consisting of what are called “phases”. The 3 phases are solids (tiny rocks and minerals), water, and air. The water and air make up what is called the void space. In evaluating moisture content (w), we are only interested in the water and solids portion. In fact, the moisture content is defined as the ratio of the weight of the water content (Ww) to the weight of the solid content (Ws). The weight of the air is considered negligible.

The procedure we followed to obtain values for these calculations was to use 3 small metal tins or canisters. First we used a digital scale to measure the weight of each canister. This weight we called W1. Next we partially filled each canister with a small sample of soil. Next we measured the canister and the soil. This weight we called W2. Finally we placed the canisters in a soil drying oven to dry out the soil and remove the water from the samples. After 24 hours we returned to the lab and used the digital scale to measure the dried soil samples in the canisters. This weight we called W3. To find the weight of the water (Ww) we used:

To find the weight of the solids (Ws) we used:

Here is a tabulation of the results we obtained:

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