What is The Mathematics of Soil Expansion?
Mathematical Foundation
Laws & Principles
- Sand and Gravel Stability: Coarse materials like sand swell very little (around 15 percent). Because the particles are already large and naturally granular, they don't lock together tightly in the ground. Digging them up doesn't inject much extra air.
- The Clay Expansion Penalty: Wet, heavy clay experiences massive swelling (often exceeding 35 percent). Because clay particles are microscopic and naturally compressed into dense, water-tight sheets, tearing them apart injects huge pockets of air that refuse to compress back down naturally.
- The Blasted Rock Extremes: Solid bedrock blasted with dynamite can swell by up to 60 percent. The massive, jagged boulders stack against each other in the truck bed, leaving gigantic empty air cavities that you still must pay to have hauled away.
Step-by-Step Example Walkthrough
" An in-ground swimming pool contractor is digging a 40 foot by 20 foot rectangular pool that is 6 feet deep. The soil profile is extremely stiff, wet clay. They need to calculate how many 15-yard tandem dump trucks to hire. "
- 1. Calculate the rigid hole Bank Volume: (40 x 20 x 6) = 4,800 cubic feet.
- 2. Convert into Bank Yards: 4,800 / 27 = 177.7 Bank Cubic Yards (BCY).
- 3. Apply local Clay Swell Factor: Heavy clay expands by 35%. Multiply 177.7 * 1.35.
- 4. Calculate LCY: The 177 yard hole translates into a 240 Loose Cubic Yard (LCY) pile on the street.
- 5. Calculate Trucks: 240 yards / 15 yards per truck = 16.0 Full Trucks.