Greetings. I am getting more experience in digging post holes in clay.
I am replacing rotten 4x4 posts, with bigger posts (most are 6x6, one was 6x12). The remainder will be 6x6. Digging a 12 inch hole is what I first tried, I don't think a 12 inch diameter hole is really enough for a 6x6. Both of those holes at one time had a sonotube in them, to try and maintain the hole. When I finally finished the holes, one hole was finished with a sonotube and one without. The remaining holes are nominally 14 inch diameter. I am packing the bottom 1 foot of the hole with 1.25 inch gravel, and packing the post in with 0.75 inch gravel.
I think every hole to be put into clay, should be approached with an open mind. I think that by and large, they are all different. And two holes adjacent to each other can be quite different.
There are a few kinds of clay. By and large, clay particles are shaped like dinner plates, and they can stack. Because of their disc like shape, they tend to have a much larger surface area per unit mass than spherical particles like sand. Some clays have undergone substantial replacement of positive ions on the surface, and this can change the properties significantly. In particular, there are clays with the surface positive ions are are replaced by sodium, which tend to have their own characteristics.
Some clays are known to swell (expand) when absorbing water. I think Montmorillinite is this biggest culprit in this regard. If the clays in your area do swell, I would say there is at least some Monmorilinite (sp?) in them.
By and large, clay soils will absorb water, and the water will take considerable time to go away. This is probably in large part due to the high surface area to volume ratio of clays, and that clays tend to be wet by water.
Concrete is something people use with posts. Concrete is a sponge (for water) which doesn't change its size.
Wood changes its size when the humidity of the wood changes.
The biggest problem for rot, is where wood is moist enough, and there is enough oxygen present. Mostly where water and air meet. A 4x4 post in wet ground doesn't fail at the bottom, there is much reduced oxygen there. It fails closer to ground level, where the oxygen is present as well as the water.
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Okay, we have a location for a (replacement) hole. We use something (I use a mattock) to strip the sod off the ground in the vicinity of the hole, to a significantly larger diameter than the hole will be. After the post is installed and packed in gravel, we want to build up "wall" of clay on the outside edge of the hole at ground level, to keep surface water from running into the hole. As this raises the level slightly, we want to add gravel as needed to keep the resulting profile flat or convex. It may be that one can put a sealing layer on top, I haven't got there yet.
With our sod striped area being bigger than our hole, we want to mark out the periphery of the hole, and start the edges with some kind of shovel. I am using a trenching shovel, it is narrow and curved. I take 8 trench shovel placements to define the "circle" of the post at ground level.
Using that trenching shovel, I try to remove the top 2-3 inches of soil around the existing hole (nominally 3.5x3.5 for a 4x4 post). Once I have a start to the overall hole, I go into hole digging mode.
If there is a pre-existing hole, that I am trying to enlarge; using an auger type hole digger can work. I have had one hole, where the pre-existing hole was on the periphery of where the new hole would be, and do I never used the auger tool there. I have had one hole, where the auger tool was basically useless. If the auger digger works, what you are trying to do is enlarge a hole, for each level you can "pilot a hole". And it isn't necessary that the pilot is in the centre, just that it is somewhere in the hole plan.
By and large, my hole digging has been with a clamshell type digger. A clamshell digger is reasonably good at shaping up a hole, where you are trying to remove a circular "shim" of material from the side.
If you are lucky enough to be digging an oval type hole (say to plant a 6x12 post), you prefer to orient your clamshell digger to work with the long axis of the hole. You want to plunge the clamshell as deep as you can. Unlike a shovel, there are no places for you to plant your feet. You have to get your bodyweight on the handles in some way. As I weigh quite a bit more than most people, I often can push down quite a ways. If the clay is "plastic", to just pull apart the two handles (to squeeze the clay a little in the hole) and you just pull up, you probably end up with some "nipple shaped thing on the bottom of the hole, and you might not have pulled up any clay.
Many plastic materials will fail in fatigue. For the last hole I dug (today), the fatigue limit of the clay was about 10. But, what I did was tilt my clamshell digger back and forth 10 or more times, to try and fracture the clay at the bottom of the clamshell. And when I lift the clamshell up, I have a bunch of clay to remove.
The clamshell squeezes along a direction. It may be that squeezing on a perpendicular direction on the same "plan" can help (with wetter clays). If the clay is too wet, the fatigue limit will be large, and you probably won't fatigue the clay in any reasonable time. As near as I can tell, at that point, you need to let the clay dry out some more.
It may be that other people have advice for digging holes in clay from the too dry side. But this advice is mostly from the wet side of clay.
Good digging!