Instead of putting heavy dirt on the roof why not put 4" of foam insulation over the roof and down the sides? That should give the same effect of keeping the frost at bay.
There's a typo with the math. A cubic foot of water has 7.48 gallons and water weighs 8.33 lbs per gallon. That's 62 lbs. Soil is much heavier than water so it's got to be more than 62 lbs.Rule of thumb: 1 cu ft of water saturated soil weighs 20 lb----a 10x10 roof with 3.5 ft of wet soil on top would need to support 7000 lb (!!)