Concrete Shear Strength in Box Culverts

[RyUIUC]

I am designing a cast-in-place concrete box culvert underneath a rail line and about 40' of fill. I have been using the 2010 Arema Manual for a guide but I am having a hard time resolving the shear check. Because of the large fill I am getting a required slab thickness over 3'!

Normally I would just run the check per ACI 318 EQ 11-3, where Vc= 2(Sqrt(f’c)*bw*d) but I happen to have come across some other references with different shear strength values and was hoping for some clarification.

For example, the AREMA 2010 Manual Volume 2, Chapter 8 EQ 2-49 states ‘For box culverts under 2 feet or more fill, Vc=2.14*sqrt(f’c)+4600(As/bd)(Vu*d/Mu)<=4*sqrt(f’c), EQ 2-47 also provides an increase for compression where Vc=2*(1+0.0005Nu/Ag)*sqrt(f’c). This may have been borrowed from the AASHTO Manual.

ACI 318 Section 11.3.2.2 is perhaps the most useful as it takes into account both the flexural and compressive effects and allows the Vu*d/Mu portion of the equation to be higher than 1.

I have also come across other DOT Manuals and the like that sometimes just specify Vc=3*sqrt(f'c).

Is there a specific approach you guys have used or observed? Is a steel reinforcing detail used for culverts under large fill depths to avoid these excessively thick slabs? Thanks for your input in advance.

 

[RyUIUC]

Another item I forgot to mention was the strength reduction factor, Phi(c) used in the AREMA Manual is still 0.85 while ACI 318 has lowered this to 0.75.