# Assessment of Simplified Rating Factor Methodology for Shallow Cover Metal Culverts
## 10 Pavement Effect  
Both experimental results and finite element analysis have demonstrated that pavement can significantly reduce the maximum internal forces in the culvert wall resulting from live load compared to the same fill depth without pavement [8; 9; 10; 11; 12]. This is because, due to the higher shear moduli, the load-spreading effect through the pavement's thickness is much greater than the load spreading that would occur in the same thickness of soil. However, this stress-reduction from pavement was not accounted for in any current simplified spreadsheet-based load rating methodology; the pavement was only considered as an additional thickness layer of soil over the structure. However, [PERSON] [13] recently utilized the Fox two-layer elasticity solution [9] as a basis for quantifying the enhanced load spreading effect induced by pavements and thus improved the Load and Resistance Factor Rating (LRFR) methodology in both simple frame models and plane-strain FEM soil structure models. It should be recognized, though, that the configuration of typical rigid and flexible road pavement is a multi-layer system rather than merely two layers. Also, the scheme of converting a circular pressure footprint to an equivalent rectangular footprint and the parameter interpolation method introduced to represent the Fox graphical solution adds significant complexity to the calculation. As presented in [PERSON] [24], a spreadsheet-based LRFR approach was developed by coupling the existing simplified load rating methods and [PERSON]'s AAMP-0* Methodology in order to evaluate the potential benefits of pavements and then was used to analyze 17 different corrugated metal culvert configurations under 3 different truck loading cases. The results from using the AAMP-0* Methodology resulted in rating factors less than 1.0 when applied to large-span culverts buried under shallow soil cover with thin pavement, despite the fact that these culverts have been in service for decades without significant structural distress. Furthermore, some of these culverts were demonstrated to be safe through the use of advanced FEA (Finite Element Analysis) and field testing [25].  
To account for the full benefit of pavement in the load rating of shallow buried culverts, the technique developed by [PERSON] and [PERSON] [26] and later verified through numerical methods by [PERSON] et al. [11] was adopted for this study. [PERSON]'s equation demonstrated the relationship between the load-spreading effect in the pavement and the stiffness ratio of two adjacent layers:  
\[\tan\alpha_{1}=\tan\alpha_{0}\left[1+0.204\left(\frac{E_{bc}}{E_{sg}}-1\right)\right] \tag{12}\]  
where \(\alpha_{1}=\) pressure distribution angle in the base course under consideration; \(\alpha_{0}=\) reference pressure distribution angle for a uniform medium defined by \(E_{bc}=E_{sg}\); \(E_{bc}=\) elastic modulus of the base course under consideration; and \(E_{sg}=\) elastic modulus of the underlying subgrade. This equation was developed from the [PERSON] [8] basic pattern of two-layer vertical stress influence curves, which is equivalent to the Fox two-layer elasticity solution implemented by [PERSON] [13]. However, instead of requiring complex data tables for parameter interpolation to represent the Fox graphical solution, [PERSON] and [PERSON] [26] derived a simpler closed-form stress distribution angle equation for calculating the load spreading in pavement layers.