There is a sidewalk along the side of my house. It has settled in an
area maybe 40 feet long so that it no longer pitches away from the
house but rather towards it. I get a small amount of seepage. The
basement is finished, but in my utility room which is partially
finished, i see water trickle to a floor drain from the basement wall
during heavy rains. There is sometimes dampness in a closet down
there, but nothing major ever.

I know the obvious and proper way to fix this is to rip out the
sidewalk and repour. This would be quite expensive as there is also a
fence attached to the concrete sidewalk and the working space is
tight.

I am wondering if there is anything less drastic than replacing a 40
long sidewalk to ease the problem. i think pouring on top of the
existing concrete (to make it slope the right way) would probably just
break off (I am in a climate that freezes). I am wondering if using
caulk or something like that on the small gap between the foundation
and the sidewalk would help any.