Sieve analysis, often called a gradation test, is a foundational laboratory method used to determine the particle size distribution of granular materials such as aggregates, soils, or powders. This procedure involves mechanically shaking a sample through a stacked series of sieves with progressively smaller openings. The analysis generates specific data points, known as the percentage passing, which are essential for quality control and material classification in various engineering and manufacturing applications. This data is used to classify the material and assess its suitability for applications like concrete production or road construction.
Gathering the Raw Data
Before calculations begin, the initial raw data must be accurately collected from the physical test. The first measurement required is the total dry mass of the sample (\(M_{total}\)), representing the entire amount of material used. The sample is dried in an oven beforehand to ensure all moisture is removed, as water content would artificially inflate the mass.
Following sieving, the mass of material retained on each individual sieve (\(M_{retained}\)) must be meticulously weighed and recorded. This mass consists of particles too large to pass through the specific sieve opening. A final check involves summing the mass retained on all sieves and the pan; this total must closely match the initial total dry mass (\(M_{total}\)). Industry standards typically require the difference between the initial and final mass to be less than 0.2 percent to validate the results.
Calculating Cumulative Mass Retained
The first step in transforming the raw data into a usable format is calculating the cumulative mass retained. This value is conceptually a running total of the material held back by the current sieve and all the coarser sieves positioned above it in the stack. By calculating this, you are tracking the total weight of particles larger than the opening size of the sieve in question.
The cumulative mass retained (\(M_{cumulative}\)) for any given sieve is found by adding the mass retained on that sieve to the cumulative mass retained on the next coarser sieve directly above it. Mathematically, this is expressed as \(M_{cumulative} = M_{current\ retained} + M_{cumulative\ above}\). For the largest sieve at the top of the stack, the cumulative mass retained is simply the mass retained on that single sieve.
This sequential addition is performed down the stack, from the largest sieve opening to the pan at the bottom. The final cumulative mass retained on the pan should ideally equal the total dry mass of the sample, providing a final verification of the measurements.
Determining Percent Passing
The ultimate objective of the analysis is to determine the percent passing, which represents the percentage of the total sample mass that is finer than the opening size of a specific sieve. This calculation is achieved through a two-step process, beginning with the cumulative percent retained.
The cumulative percent retained is calculated by dividing the cumulative mass retained (\(M_{cumulative}\)) on a given sieve by the total dry mass of the original sample (\(M_{total}\)) and multiplying by 100. This calculation, expressed as \((\frac{M_{cumulative}}{M_{total}}) \times 100\), indicates the total percentage of the sample that is coarser than the sieve opening. This percentage is the portion of the sample successfully stopped by the sieve and all those above it.
The percent passing is then calculated by subtracting the cumulative percent retained from 100 percent. The formula is \(Percent\ Passing = 100\% – Cumulative\ Percent\ Retained\). For the pan at the bottom, the percent passing is 0 percent, while for the coarsest sieve at the top, the percent passing is near 100 percent.
Visualizing the Particle Size Distribution
The calculated percent passing values are the essential data points used to create the Particle Size Distribution Curve, also known as the gradation curve. This graphical representation provides a visual summary of the material’s particle size makeup. The horizontal axis plots the sieve opening size, typically on a logarithmic scale to display the wide range of particle sizes. The vertical axis plots the calculated percent passing, usually on an arithmetic or linear scale.
The resulting curve’s shape is analyzed by engineers and material scientists to classify the material. A smooth curve spanning a wide range of sieve sizes indicates a well-graded material, meaning it contains a good mix of particle sizes. Conversely, a steep or flat curve suggests a poorly-graded material, such as one that is uniformly sized or gap-graded. The curve’s characteristics guide decisions regarding the material’s suitability for specific engineering applications, including its strength and permeability.