# Calculating Tie Rod Force in Bridge Abutment System

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.

• Maybe try approximating it with the multi-span beam coefficients in the AISC 14th Ed, Table 3-22c? Or do it conservatively and say that each tie rod has to take 1/2 of the total lateral load? – grfrazee Feb 5 '16 at 20:02
• Are you expecting the grade beam or abutment to deflect enough to load the tie rods? The sketch makes it look like this will be a very rigid structure. It would be very (overly) conservative to consider the design like a typical dead man anchor wall. – hazzey Feb 5 '16 at 20:39
• I don't think this can be done other than with finite element analysis. As @hazzey says, this structure seems very rigid. Since the grade beam is fixed to the abutment via the wing-walls, lateral loads may very well lead to a rigid-body motion, in which case the tie rods wouldn't do much of anything, since the abutment and the grade beam will translate equally. – Wasabi Feb 5 '16 at 23:27
• On a mostly unrelated note, I've never seen approach slabs supported by such grade beams. They've always been directly supported on (compacted) soil. As far as I can tell, the grade beam defeats the purpose of the approach slab. These slabs are meant to follow the deformations of the soil near the bridge: the soil is compacted over time and the approach slab goes down with it. But with that grade beam the stiffness of the support beneath the slab is orders of magnitude greater than that of the soil immediately before the slab. The soil will compact, the slab won't. "kathunk-kathunk" – Wasabi Feb 5 '16 at 23:38
• In the Canadian Highway Bridge Design Code, there is a surcharge that needs to be added if you are not using an approach slab. As such most highway bridges all have an approach slab to reduce the pressure from traffic on the back side of the ballast wall. With the wingwalls tied into the abutment and your grade beam, did you factor in their ability to carry earth pressure as well? Also did you analyse your sheet pile wall as being free standing? You could argue that you could treat it as being restrained at the top all ready by your concrete. – Forward Ed Jun 24 '16 at 3:52