Modulus of Soil Reaction $\left(E^{\prime }\right)$ Values for Pipeline Design

The design of buried flexible pipe involves checking for load-induced deflection, buckling strength, strain or stress under internal pressure, strain or stress from combined loading, and handling stiffness. Most of these design checks involve using the design parameter commonly referred to as the modulus of soil reaction, $E^{\prime }\text{.}$ Despite the fact that modified Spangler’s equation has been around for over several decades, few engineers in practice even know how this $E^{\prime }$ is defined let alone how to obtain a proper value for it. The most popular form for $E^{\prime }$ comes from the empirical data published by the U.S. Bureau of Reclamation and most consensus standards carry these values despite its numerous shortcomings. The irony is that the U.S. Bureau of Reclamation knew that their data were providing values of $E^{\prime }$ varying several hundred percent from a mean value, yet, never even considered other factors that would be significant in explaining their unreliable $E^{\prime }$ values. The pure simplicity of the U.S. Bureau of Reclamation values led to these being in use in the hands of the pipe supplier and never its engineering soundness. The purpose of this paper is to start from the fundamental pipe–soil interaction principles and geotechnical engineering and build the engineering know how needed to establish $E^{\prime }$ values on a project-specific basis allowing for most significant factors. A step-by-step methodology is presented.