I'm looking at the usual UK/EU standards formula for the reinforcing steel area percentage, in a retaining wall. Essentially in "usual" cases it comes down to 0.13% of the cross-sectional area of Tw (wall thickness) in the upstand of the vertical wall itself, and Tb (base thickness [depth]) for the outer and inner base. If Fy is below a certain amount then the percentage changes but it's still calculated as a simple percentage.
I'm imagining trying to apply this to the retaining wall shown in the diagrams below. In this situation, the retaining wall is built onto one edge of a large and deep foundation. The foundation itself is very deep and very wide compared to the retaining wall built on it. Essentially when the foundation is considered as the base of the retaining wall, it continues on to a distance where the retaining wall is no longer affecting or affected by it.
The kind of dimensions I have in mind are - foundation/base is indefinitely wide (for these purposes), and say 900mm deep. The retaining wall upstand is say 200mm wide and 600mm high, and built at one edge of it. The foundations are deemed not to need reinforcement steel (perhaps because it's basically a large monolithic concrete block or it's on on sufficiently stable ground/rock beneath it). So the only reinforcing steel is the steel required for the retaining wall aspect.
Apparently, the inner and outer steel area is calculated as a percentage of the base's cross-section area. But I'm looking at the three diagrams below, which are roughly to scale.
- First (left) diagram - the outer steel is run down to the bottom of the foundations, so essentially the foundations act like a base that's 900mm thick and very wide.
- Second diagram - outer steel is only run down to 350mm deep; a more typical depth if it were on a slab not a foundation.
- Third diagram - the 2nd layout is re-visualised as equivalent to two parts - essentially a 400mm base with rebar along the bottom, resting on a non-reinforced 500mm slab.
What's puzzling me is why are the steel area requirements, which are based on Tb, different in these three versions? Intuitively, I expected that for any given lateral pressure, the inner/outer steel would reach a sort of limit point where there just wasn't any need to add more, because in the first two cases it's embedded with right angle bends to a point where the limiting failure mode in the base slab is pullout failure/concrete failure rather than steel elastic limitations (ie not governed by the cross section area of steel), and if the foundation itself is considered structurally adequate, then I'd have thought the second and third would be structurally equivalent and therefore need equal areas of steel too, as they are essentially the same layout.
(Alternatively, the 1st layout seems stronger than the 2nd, as there's even more grip and harder pullout, and the entire foundation slab is engaged rather than just the top half of it, so why does it seem to need more rather than less steel cross-sectional area, to achieve equal wall stability?)
But instead, the standard equation is simply 0.13% of Tb, so if the base is made thicker, which should add not remove strength, then the area of inner/outer steel required seems to have to go up, not down. That feels counter-intuitive.
So I'm left with a mess of confusion: Why does the steel area percentage differ in the three cases shown? Why does adding strength and solidity to the bottom of the base (i.e., as extra depth) cause an increase to the required steel area? Why isn't there some kind of limit based on lateral pressure rather than base dimensions beyond which more isn't needed? Why isn't a further limit reached where it doesn't matter how much deeper the base and the outer steels go, because the extra depth doesn't affect the retaining wall stability? What is the logic behind the cross section area of steel being an unqualified percentage of Tb?
What am I missing, and what should actually happen here?