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A building, such as a house, rests on a foundation. Beneath it is natural earth.

When it rains, the ground around the foundation becomes wet. But the ground underneath the foundation does not. There is a wet/dry boundary somewhere near the edges of the foundation.

My question is, how is this stable and safe in the long-term? Shouldn't this wet/dry boundary cause some sort of movement or instability? Shouldn't the ground start sagging?

Note, I'm not asking about sinkholes. That's a different phenomenon caused by holes developing in carbonate rocks. I'm asking about the properties of soil---soil that is permeated, or not, with water.

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Depending on the type of soil at your site, moisture content under the foundation can change depending on the change in surrounding soil.

The typical footing depth in the majority of cases will be enough to create some acceptable equilibrium below the level of the earth icing to handle moisture content changes in non expansive soils.

But for many multistory buildings to be located in soils with a high clay content, a soils engineering report is needed.

This report among other things will investigate the moisture content and advise on how to build the foundation to penetrate below certain level or in extreme cases even to drain the excess water through subterrainian canals and sump pumps.

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That water you have described where the ground is wet but the lower ground at the foundation levels were dry, is generally not going to cause significant problems because the weight of the water will cause the water to migrate further down the ground, until such that it is held up by capillary action. Given such, the addition weight of the water coming from the top typically is not an issue at all because if the ground is indeed dry below, it will just take that water further down until it leaves the site, and eventually drains somewhere (or if it is a small amount that was supported by capillary action, it will be negligible to any normal building structure). This will apply for the case you described where the foundations will still be "dry" at the bottom.

Note that for most foundations other than friction piles, you are supporting your structure through direct gravitational reaction force at either the footing or the bearing layer of your deep foundation. With that, really, anything on top of that layer has no impact on how your ground below acts unless those changes are drastic (like, say, a dam near your home failed groundwater table differentially changes by a hundred feet suddenly because that water saturated ground becomes dry now). And while yes, the additional weight of water in the soil can increase stresses on your ground, chances are it has been that way for hundreds or even thousands of years, meaning that the soil underneath it really should have already been overconsolidated with normal seasonal rainfall attributed loads at some point and will no longer experience virgin consolidation. A regular house is unlikely going to experience problems with minor fluctuations caused by secondary consolidation, which is much less than virgin consolidation. So that's why it's not really a problem unless you have a very unique case somehow for that little bit of water around the foundations.

However, when the ground is saturated, versus when it is not, then yes, that is a problem because effective stress of the soil is now lowered, which can cause bearing capacity failures because the effective shear resistance of the soil has now been lowered. That is why for some parts of the world where groundwater elevation continues to rise, building subsidence is actually a very real issue. But it only happens when the water is saturated bottom up beyond the bottom of your foundations of your house. (And what is described here inherently assume that such reduction in ground bearing capacity was not offset-ted anyway by buoyancy effects your structure experiences, which is usually insignificant for normal buildings, but it can be designed not to be - a boat made of metal is a perfect example, and for that matter, you can design a boat that sits on soil, that can theoretically float when the ground is saturated ~ like, the biblical Noah's ark that was built on land and becomes buoyant when the ground fully saturated and the groundwater table elevation exceed ground surface elevation. Now, how stable that will be is another story, because chances are, your building will get other problems like those of a boat~ sway ~ Weeeeee).

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