gap between sill and foundation - help!

I inherited a house from my parents which I had been renting to a family for the past 12 years. Recently they vacated and I did an inspection. In one corner of the house, the foundation has been sinking very slowly (about 4-5 inches over 35 years). There is now a gap of about 4-6 inches between the sill and the house. Unfortunately for me, I am unemployed and I have a tenant scheduled to move in on August 1, so I have neither the time nor the money to have the foundation re-engineered- but I need to fill the gap before they move in. The gap is around 25 feet long, going around a corner. Should I fill it with cement? Should I shim it with two-by-fours and then patch it with cement? Is there a better material or a better way? Could I do it myself? If not, what kind of contractor could I call to do this work? Thanks in advance.
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And the house hasn't fallen? That's a good house. Yes, use pressure-treated lumber and possibly some hardwood shims (available at Home Depot) for the "fine tuning". It will be difficult to get cement filled in to the gap so that it would actually carry weight of the house, so just use wood and keep the pressure on each block somewhat consistent so that the house is actually resting on each block.

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Look under foundation repair and have it fixed before it is beyond repair.

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Obviously, the best advise is to fix the foundation and find the problem. You should go back and look at it with someone who has construction knowledge. This is a tiny house you describe. With a 4-6 inch gap over 25 feet, what's holding the house up? Not only has the foundation sunk, but the house would have sunk some as well. As a temporary fix so you can rent it, I would first determine how much that side has dropped. How level is the house? If possible, you would jack the house slowly and carefully to about 1/4" over level. Then fill the gap with pressure treated wood as tightly as possible and lower the jacks. If you can't or don't need to raise it, just fill it. You really need a longer term solution. However, I understand that this is a rental. In Detroit there are all kinds of homes like this that would not meet code. The inspector approves a CO (certificate of occupancy) anyway because they want the home on the tax rolls. One temporary fix after another might last a lifetime.
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