How does the Subgrade/base Affect Slab Design?
We go to all this effort to get the proper soil support system and what we end up with is a single input value for the slab design. The most commonly used value is the modulus of subgrade reaction, k. This value is not directly related to bearing capacity and k does not tell the designer if there is compressible or expansive soil. What it does is indicate how stiff the subbase/subgrade is over small deflections (about 0.05 inches).
Now let's look at why we need to know how flexible the subgrade is. To start with it's important to understand that a slab on ground is designed as "plain" concrete. That means that we do not count on the reinforcing steel to carry any of the load. But wait, you say, there's steel in the slab—mesh and rebars. Yes, but that steel is only there for crack control—to hold any cracks tightly together. It normally does not extend through the joints—at joints we only want to transfer shear forces, not bending moments and certainly not lateral restraint. That's what the joint is there for in the first place, to allow lateral shrinkage in the slab.
So if we aren't counting on the steel to carry any load, then the concrete has to be strong enough to carry the bending. And the support it is getting from below determines how much it will bend. As we've already discussed, concrete isn't that strong in tension, and since half of bending is tension, it's not that strong in bending. What makes it stronger in bending, though, is a thicker slab.
The weaker the subgrade, or the heavier the loads, then, the thicker the slab needs to be. Concrete strength also comes into play, but most slab concrete is around 3000 to 4000 psi, so it's not a major factor. The tensile strength of concrete is typically taken as 10 to 15% of the compressive strength, so only about 400 or 500 psi. Compare that to the tensile strength of Grade 60 rebar, which is 60,000 psi.
The thing to remember here is that a concrete slab is intended to be rigid, but we don't expect the base to be infinitely stiff. A slab will settle a little and that's OK from a design standpoint—again, as long as the settlement is uniform. The danger, though, is at the edges of the slab or at joints that are wide enough to let the slab on either side settle independently. At those free edges, the weight the slab can carry depends on the stiffness of the base and the flexural strength of the slab, which is mostly a function of slab thickness.
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