Question
Would you answer my question

Rest assured this is not a homework question. If you think the question is so Fundamental, I do not know about the Answer, therefore, I ask the question. Does digging a hole in the soil in the backyard in a state where it rains on a regular basis causes the collection of rain water and in winter snow to cause the hole to expand?

Answer
Darn, thought i answered this one - must not have hit the "enter" key!!   Sorry for the delay.

Yes and no.  A hole will not stay "open" because of the forces of gravity on the soil particles.  called erosion, the soil seeks a slope to the edges of the hole, called "angle of repose".  Add water, and the process is speeded up as soil particle friction is lessened by the presence of the water.  Like a hole dug along a shoreline, the sides will continue to cave in with the surrounding soil full of saturated water.

As to freezing, water would expand in all directions, including UP, so if the surrounding soil is ALSO wet, the whole (hole?) mass of soil would freeze and expand as one unit.  It also depends on how deep the hole is and how cold it gets.  

Called the "frost line", there is a depth at which the soil acts as an insulation, and you don't get what soil scientists call "frost heave" - the soil expansion movement caused by the mass of soil freezing and expanding.  Depths varies by area of the country.  In Southern California, it almost doesn't exist.  In Montana/North Dakota, it extends down several FEET (5 or so).

So no, the hole won't expand, IF you could keep it "open" year-round and not have the soil fill back in on itself.

All bets are off if the one side of the hole is like a stem-wall of a foundation.  Thats different (actually called "differential" settlement)

~Marc