The Iowa Formula It's Use and Misuse when Designing Flexible Pipe

Abstract

This paper discusses the derivation and publication of the Formula (Spangler, 1941), and its later modification by Watkins (1958). In use today by many publications, the modified Iowa Formula was derived to predict ring deflection of flexible culverts, and is currently being misused as a design equation to determine wall thickness of pipe materials. The Iowa Formula demonstrates the importance of the soil on ring deflection. It overpredicts ring deflection because compression of sidefill soil is not uniaxial and elastic; but, rather, is a biaxial compression of particulate soil. The Iowa Formula for predicting ring deflection was not intended for the design of the pipe wall thickness. On the contrary, it shows that ring deflection is primarily a function of the soil embedment, not the ring stiffness of the pipe. Moreover, the properties of soil are imprecise. Published USBR values of an elastic soil modulus are based on backcalculations of the Iowa Formula from ring deflections of existing installations, all of which disregard height of soil cover. This simplification proliferates the severe conservatism of the Iowa Formula for pipe wall thickness design. Because of the importance of wall thickness in the economic design of pipeline systems, proper analysis of embedment should be optimized for structural performance and costs. The intent of this paper is to analyze the variables in the Iowa Formula based on the original intent and to give guidance to its use for pipeline design. Alternate methods of analysis are also presented, based on fundamentals of engineering mechanics and correct properties of materials.