Precast Concrete Arch Design w/ Soil Interaction

[resllc05]

I am modeling a small precast concrete arch (6'-0" span by 5'-0" rise by 8'-0" length) in RISA 3D using thousands of small plates (approx. 3"x1" plates) with lateral and vertical soil springs at each node representing the restraint of the surrounding soil. I am modeling the arch in 3D rather than 2D because the arch consists of series of 6-inch deep ribs connected (cast monolithic) with a 2-inch thick membrane which cannot be modeled properly in 2D.
I am calculating the lateral and vertical soil spring stiffness using the “constant of horizontal subgrade reaction” for dense sand as described in section 7.5 (pg. 255) of “Foundation Analysis” by Ronald F. Scott. This assumes that the “coefficient of subgrade reaction” (k) increases with depth (z) and varies based on the width of the wall (B - width effect). The equation used to calculate the horizontal subgrade reaction is (k=nz/B). I am using an n-value of 127 pci (dense moist sand) and a B-value of 96 inches. Since the vertical subgrade reaction of soils is typically used for soil springs restraining movement in the (–y) direction, I am using the horizontal subgrade reaction to resist movement of the arch in the (+y) direction. I am then multiplying the calculated subgrade reaction by the tributary area of each node.
This is a very tedious and time consuming method, but I haven’t found another way to properly model the arch. Does anyone have a better way to design this arch? I am desperate for some feedback as to the method I am currently using.

 

[IDS]

Using thousands of small plates to create a 3D model of a small arch, then using springs to model the soil just doesn't make sense. The problem is that elastic springs are a very poor model of soil:

- There is no interaction between the springs
- They are linear, with no modelling of different behaviour under loading and unloading.
- There is no simple relationship between measured soil properties and spring stiffness.
- Published values for "modulus of subgrade reaction" are likely to be based on shallow foundation applications, and are likely to be way out for this purpose.

The best way to approach it is to do a 2D analysis using plane strain plate elements for the soil, with at least a mohr-coulomb model for the soil behaviour. If that is not available in your software then for an arch of this size using soil springs would be adequate providing you use conservative lower and upper bound stiffness values, and take the worst case.

For the arch, modelling with short 2D beam elements will be perfectly adequate.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/