# Assessment of Simplified Rating Factor Methodology for Shallow Cover Metal Culverts
## 19 Summary and Conclusions  
The currently used simplified approaches for load rating are considered to be overly conservative for shallow buried metal culverts with cover depth less than the minimum requirement defined by AASHTO for new design and construction. The conservatism in these simplified procedures is primarily attributed to the selection of some of the parameters used in the equations for calculating the structural responses and ignoring the load-spreading effect of pavements. After clarifying and reselecting these parameters and utilizing appropriate techniques to account for the pavement effect, the responses and rating factors calculated from the presented alternative simplified approaches were found to be closer to their corresponding numerical results from 2D (plane-strain) finite element analyses. Two new equations were developed for load rating based on AASHTO LRFD 12.8.9.5 and [PERSON] (2018) to account for the combined effect of thrust and moment. Rating factors calculated from these two new equations, originally created to evaluate the development of plastic hinge, also agree well with the result predicted by 2D (plane-strain) finite element analyses. A simpler equation based on [PERSON] and [PERSON] [PERSON] (1988) and [PERSON] (1988) to calculate the maximum moment due to a live load by [PERSON]'s method was also introduced. This simpler equation can also generate accurate maximum live load effect and rating factors and, thus, is seen as another improved method for calculating live load moment. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Structural Responses** & **Original** & **Improved** & **CANDE** \\ \hline Max Factored Thrust due to Dead Load kN/m (k/ft) & 30.2 (2.07) & 30.2 (2.07) & 40.1 (2.75) \\ \hline Max Factored Thrust due to Live Load over the & & & \\ Quarter kN/m (k/ft) & NA & 72.8 (4.99) & 77.2 (5.29) \\ \hline Factored Moment at the Quarter Point due to & & & \\ Dead Load kN-m/m (k-ft/ft) & 4.09 (0.92) & 4.59 (1.03) & 1.76 (0.396) \\ \hline Factored Moment at the Quarter Point due to & & & \\ Live Load kN-m/m (k-ft/ft) & 73.9 (16.6) & 9.38 (2.11) & 6.36 (1.43) \\ \hline
**Rating Factors** & **Original** & **Improved** & **CANDE** \\ \hline ODOT RF & No Good & 1.47 & \\ \hline MDOT RF & 0.21 & 1.57 & \\ \hline AASHTO RF & NA & 1.36 & \\ \hline Duncan RF & NA & 1.23 & \\ \hline \hline \end{tabular} Note: NA indicates that the original methods do not calculate the value in this regard.  
\end{table} 
Table 7: Comparison of Responses and Rating Factors between Original Simplified Methods and Improved Methods based on Duncan and Drawsky Duncan and Drawsky (2018) and CANDE. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Structural Responses** & **Original** & **Improved** & **CANDE** \\ \hline Factored Thrust due to Live Load & & 563.47 (38.61) ODOT & & \\ over the Crown kN/m (k/ft) & 368.35 (25.24) MDOT & 260 (17.8) & 170 (11.7) \\ \hline Factored Moment due to Live Load & & & \\ kN-m/m (k-ft/ft) & NA & 7.16 (1.61) & 8.78 (1.97) \\ \hline
**Rating Factors** & **Original** & **Improved** & **CANDE** \\ \hline Castigliano MDOT RF & NA & 2.70 & & \\ Castigliano AASHTO RF & NA & 2.25 & 2.3 \\ \hline Castigliano Duncan RF & NA & 2.08 & & \\ \hline \hline \end{tabular} Note: NA indicates that the original methods do not calculate the value in this regard.  
\end{table} 
Table 8: Comparison of Responses and Rating Factors between Original Simplified Methods and Improved Methods based on Castigliano’s Equation and CANDE. However, the modified simplified approaches are only a measure of expediency. As the cover depth becomes thinner, neither the assumption that the culvert structure is under ring compression nor the method of transforming the earth weight and live load into uniform pressure over the entire span of the culvert is valid.