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What's the weight of your roof supported by? The photo does look a little dodgy!
Could you put some wood down and pick up the horizontal beam with telescopic supports?
I wouldn't be overly worried about clay, it just wants to expand. It's not easily washed away unless you have heavy/fast-moving water (cohesive versus non-cohesive).
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The weight of the roof is on three vertical posts like that, all with concrete footings (although on of the posts has rotted significantly due to being in contact with the wet clay) and also attached to the house on the upper side. The farthest post was encased up to the wood in the clay.
My neighbour is helping out (he's a retired building engineer) and he reckons we could straighten the beams a bit but I'm not sure on the method he's got in his head.
On a scale of 1-10 how likely is it that I get home to half my house ripped off by a subsided clay slope? We dug everything out on Friday and then it rained pretty much solidly the last two days. Plan is to get retaining wall put in before next weekend but that relies on it being at least semi dry the next few days. The area behind the house to the left is well held with some concreted in boulders, the right side is just very wet clay. There'll be a french drain between the wall and the toe of the slope, I'm thinking about adding some extra drainage into the slope along with some foliage to steady things up. Before, the slope extended around the corner pillar of the covered area. You could see it had moved already as the drain pipe was crushed against the wooden post, and none of the posts are particularly vertical.