Particle Size Distribution Curve

This is a really small personal project done for Department of Civil Engineering, Delhi Technological University (formerly, Delhi College of Engineering) for a course in Soil Mechanics (Course Code - CE206).

It is a simple program using Python, Pandas and Matplotlibwhich helps a user to plot a particle size distribution curve for a soil sample.

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Documentation

What is a Particle Size Distribution Curve?

A particle size distribution curve or grain size distribution curve represents the size range of soil grains in a given soil mass as percentages of the total dry weight. Engineers or lab technicians perform a sieve analysis for coarse-grain soils such as gravels and sands and hydrometer analysis for fine-grained soils like silts and clays to determine the soil sample’s grain size distribution. The results of mechanical analysis (sieve and hydrometer analyses) are generally presented by these semi-logarithmic plots known as particle-size distribution curves. The particle diameters are plotted in log scale, and the corresponding percent finer in arithmetic scale.

Sieve Analysis Results

Let’s assume we finished a sieve analysis that has the following results:

Sieve Opening (mm)	Mass Retained (g)
4.75	0
2.00	17.6
0.850	56.3
0.425	108.2
0.250	91.9
0.150	94.2
0.075	57.6
Pan	25.0

From the sieve analysis, we can determine the percent finer for each sieve, the percentage of the soil passing through the sieve, and plot the grain size distribution curve.

Calculating Percent Finer

First, we need to define a dictionary with two lists: one for the sieve opening and another for the mass retained. Then we create a pandas DataFrame from the data.

from pandas import DataFrame
data = {
        "opening": [4.75, 2.00, 0.850, 0.425, 0.250, 0.150, 0.075, 0],
        "mass_retained": [0, 17.6, 56.3, 108.2, 91.9, 94.1, 57.6, 25.0]
       }
df = DataFrame(data)

This will result into the DataFrame df as:

After this, we create a function called calculate_percent_finer that will calculate the percent finer for each sieve and create a new column in our DataFrame called percent_finer.

def calculate_percent_finer(df):
     total_mass = df.mass_retained.sum()
     arr = []
     for count, sieve in enumerate(df.opening.values):
         cumulative_mass = sum([df.mass_retained.values[i] for i in range(count + 1)])
         percent_finer = ((total_mass - cumulative_mass) / total_mass) * 100
         arr.append(percent_finer)
     return df.assign(p_finer = arr)

When this function returns and we print the new DataFrame, it will look like below:

The calculate_percent_finer function takes in the DataFrame as a single argument and returns a new DataFrame with a percent_finer column. After this, we proceed to plot the particle size distribution curve.

import matplotlib.pyplot as plt

df2 = calculate_percent_finer(df)

print (df2) 
plt.style.use("bmh")
plt.semilogx(df2.opening, df2.p_finer)
plt.gca().invert_xaxis()
plt.xlabel("Grain Size (mm) -- log scale")
plt.ylabel("Percent Passing")
plt.title("Particle Size Distribution Curve")
plt.show()

To plot the particle size distribution curve, we import matplotlib.pyplot as plt and use the semilogx() method to graph a semilog graph. The x-axis is plotted in ascending order by default. So we can use the invert_xaxis method to reverse the x-axis. Lastly, we add x-axis, y-axis and title labels to the plot and show the graph.