It was an extremely cold day, wasn’t it? Below zero Fahrenheit, perhaps? That was the problem. Sand won’t work when it is too cold.
In order to improve traction, the sand grains must become partially embedded into the ice, making tiny bumps in what had been a smooth surface, in effect, making “sandpaper” out of the ice. It is the pressure of the car on the sand that accomplishes this. When the tire presses a sand grain against the ice, a bit of the ice melts beneath the grain, and it sinks in. The water then refreezes around the grain.
The ice melts under this pressure because ice is the bigger-volume form of water, and when pressed upon it reverts to its smaller-volume form: liquid water. Without this pressure-melting effect, the sand could not embed itself into the ice.
The problem is that the colder the ice is, the more pressure is needed to melt it, because the water molecules in the ice crystal are more rigidly fixed in place and cannot easily be persuaded to move around loosely, as the molecules of a liquid do. Even though a car applies a lot of pressure to a grain of sand, it may not be enough to melt the ice in below-zero weather.
You might do better on foot. A rubber tire isn’t the greatest pressure applying device because of its elasticity.
The soles of your shoes are probably harder, and even though I presume that you weigh less than one-fourth as much as your car (one wheel’s worth), you may still be applying more pressure to the sand grains, more pounds per square inch of grain, than the car does, and the sand will embed itself by the melting mechanism.
