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# Constrained Soil Modulus - Flexible Pipe Design

## Constrained Soil Modulus - Flexible Pipe Design

(OP)
Does anyone know if the constrained soil modulus (Ms) used to compute deflection of buried flexible pipe (Spangler's formula) is the same Ms used in settlement/consolidation analyses? The buried pipe calculation is detailed in AWWA manual, AASHTO LRFD, etc.--a screenshot of the AASHTO formulation is below. I would think that these parameters, despite having the same name, are different unless the soil is isotropic. Ms in the Spangler formula represents the constrained stiffness of the soil to sides of the buried pipe (i.e. lateral stiffness. Wouldn't most soils exhibit a different constrained stiffness under vertical loads, such as in settlement analysis? Can anyone here advise on relating these properties?

### RE: Constrained Soil Modulus - Flexible Pipe Design

Sorry, but you have been here long enough to know that double posting is frowned upon. This is especially true in the two rooms that are so similar. Most of us look at many rooms. You are welcomed to Report it and the managers will abide by your request to remove it.

### RE: Constrained Soil Modulus - Flexible Pipe Design

(OP)
Sorry about that OG. I realized this forum (mechanics) would probably be better suited for the topic. The other one has been deleted.

Any advice on the question at hand?

### RE: Constrained Soil Modulus - Flexible Pipe Design

Constrained modulus is one dimensional, by its very nature. If your soil has significant structuring there may be a difference in the vertical and horizontal stiffness (i.e. anisotropy, as you suggest).

What is the background to the above equation? Where does that 0.061 come from? Is this empirical? Is it to convert constrained modulus to some other stiffness?

### RE: Constrained Soil Modulus - Flexible Pipe Design

(OP)
LRJ - That's kind of what I was thinking. I am trying to develop general guidelines for pipe installation and so am not looking a specific soil data. Rather I'd like to provide guidance on how to approach installations depending on soil type. Would you think anisotropy is mainly a concern in silts and clays?

That equation is AASHTO's updated version of the "Modified Iowa Formula". Here's a link to a ASCE summary on that. The formula and the 0.061 is empirical. The original equation was developed mid-century through a series of deflection tests on flexible pipe by Spangler (don't have the original paper). He back calculated a soil stiffness parameter, E', from those tests based on soil type. Not much help in general since that is not a testable soil property and the original E' values based on soil type did not address confining stress or relative density. Later work established (or more like hypothesized) that constrained soil modulus, Ms, could be substituted directly for the E' parameter. And that is now the industry standard.

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