Replacing E′ with the constrained modulus in flexible pipe design

In design of buried flexible pipe the soil stiffness has traditionally been modeled using the modulus of soil reaction, E'. This is a semi-empirical parameter required as input to the Iowa formula for predicting deflection of buried pipe. Unfortunately, E' is not a true soil parameter and efforts to develop tests to evaluate it have been largely unsuccessful. Also, the commonly used design values for E', proposed by Howard, do not reflect the change in soil stiffness that occurs with increasing depth of fill. An alternate to use of the modulus of soil:reaction is the true soil property, the constrained or one-dimensional modulus, M-s. The relationship between E' and M-s has been discussed often in the literature with several researchers concluding that the two parameters are interchangeable. Design values for M-s are derived using the hyperbolic model for Young's modulus developed by Duncan and the hyperbolic model for bulk modulus developed by Selig. The hyperbolic model is currently incorporated in the finite element buried culvert computer programs CANDE and SPIDA, and was the basis for the development of the SIDD installations for concrete pipe recently accepted by AASHTO. The model demonstrates an increase in soil stiffness with increasing depth of fill and the values for M-s of soils under low heights of fill compare well with the Howard values for E'.