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How to calculate the value of ks

How to calculate the value of ks

How to calculate the value of ks

(OP)
In order to do the structural analysis for square and Rectangular footings I first calculate ks using equations from reference #2. I recently came across Reference #1 which provides some extra verbage and a different equation for rectangular footings than reference #2. What is the recommended approach (Bowles or Das) to follow absent equations provided in a geotechnical report?

Reference 1: Foundation Analysis & Design 5th Ed page 502 (Joseph Bowles).
Reference 2: of Foundation Engineering 5th Ed page 277 (Braja Das).

Terzaghi proposed that ks for full-sized footings could be obtained from plate-load tests using the following equations:

For footings on clay

ks= k1 *(B1/B) (9-3 Reff #1) (6.46 Reff #2)

For footings on sand:

ks= k1 ((B+B1)/2B)2 (9-4 Reff #1) (6.48 Reff #2)

In these two equations use B1 = side dimension of the square base used in the load test to
Produce k1. In most cases B1 is 1 ft, but whatever B1 dimension was used should be input.


Extra verbiage from Reference #1:
“Also this equation deteriorates when B/B1 > 3.” (Pertaining to the two ks equations for sand or clay.)
“Equations (9-3), (9-4), and (9-5) are presented primarily for historical purposes and are not recommended by the author for general use.”

Different equation from Reference #1:

For a rectangular footing with dimensions of B X L with m = L/B,

ks= k1 (m+0.5)/1.5m (9-5 Reff #1)

ks= k(BxB) *(1+0.5(B/L))/1.5 (6.49 Reff #2)

ks is the desired value of modulus of subgrade reaction for the full-size foundation
k1is the value obtained from a plate-load test using a 1ft X 1ft or other size load plate.

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