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# Re: Modulus of subgrade reaction

• To: seaoc(--nospam--at)seaoc.org
• Subject: Re: Modulus of subgrade reaction
• From: BRBATES(--nospam--at)aol.com
• Date: Thu, 12 Feb 1998 12:27:46 EST

In a message dated 98-02-12 11:11:48 EST, you write:

<< The modulus of subgrade may be calculated from Timoshenko's Theory of
Elasticity (2nd Edition) formula 212, page 370, with little mathematical
manipulations:

k= E/(m(1-v^2)(A)^.5)

Where:
m is shape factor from accompanying table
v is Poisson's ratio (v=.4 may be used)
A is the area of the foundation
E is modulus of elasticity of the soil (should be based on tests)
>>

There is a direct relationship between Es (soil elasticity modulus) and ks
(subgrade modulus), but rather than calculate ks from Es, ks can be determined
directly from plate load tests.  An earlier post listed some typical ks
values, but if a site specific ks, or series of ks values, can be determined,
this would be much more valuable.

Another concern when modeling soil behavior as a series of node springs (known
as a Winkler foundation) is that the springs are uncoupled. One easy and
fairly effective way to deal with this is to double the stiffness of the edge
springs to reflect the actual soil pressure distribution. Bowles (5th Ed.)
also describes "zoning", where the soil springs are soft near the center of
the foundation and are transitioned out to stiffer springs at the foundation
edges, but this is more work and it doesn't significantly alter the results
(versus simply doubling the edge springs).

Bruce Bates
RISA Technologies