I have a fairly tall bridge abutment (about 12 ft.). Vertical loads are supported by bearing piles and lateral loads from the retained soil are supported by a sheet pile wall.
However, when I consider just the cantilevered sheet pile wall for the condition where scour has occurred (i.e. maximum exposed height of sheet pile), the sheet pile alone is insufficient to carry the lateral load from retained soil - the deflection at top of abutment cap will exceed the allowable 1/2" for a PZ22 sheet pile section.
In this situation, I've been told to add tie rods to carry some of the lateral load back to a "dead man" / anchor block. Because I already have a grade beam as part of my abutment system, I'm using that as the anchor block...bad idea?
Clarifying "Grade Beam" terminology -- at the end of the bridge deck, there is a separate 20' slab of concrete called the "approach slab" spanning between the abutment and the grade beam. This helps prevent localized settlement at the beginning of bridge, which produces that "kathunk-kathunk" experience as you drive across bridges. The grade beam is just there to support the approach slab (almost like a mini bridge span).
How do I go about calculating the load in each of the tie rods?
Do I completely ignore the contribution of the sheet pile and just assume all the lateral load is transferred through the tie rods? Do I consider the contribution of both the sheet pile and tie rod using strain compatibility?
I put a sketch of the entire abutment system below - in the final configuration it's a pretty rigid system. The abutment / wing / grade beam are tied together with rebar and everything is supported on piles.
Intuitively, it seems like the center tie rods will carry more load than the exterior rods but I'm not sure how to check this mathematically... though I suspect I'm eventually going to end up with some plate approximation and a massive plug-and-chug from Roark's Formulas for Stress and Strain.