If you dig a hole on a beach, it will probably fill with water, plugging the line and the well will overflow the casing. Making a mess around the well and percolating back into the well taking any contaminates with it.
So why not put some gravel, rip rap, or stone at the beach where the water from your line is digging a ditch or whatever the mess is? Or maybe perforated drain line? Anything to slow the flow of the water so it doesn't dig a ditch in the beach.