How to calculate the value of ks

[eit09]

In order to do the structural analysis for square and Rectangular footings I first calculate k_s 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 k_s for full-sized footings could be obtained from plate-load tests using the following equations:

For footings on clay

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

For footings on sand:

k_s= 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 k_s 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,

k_s= k₁ (m+0.5)/1.5m (9-5 Reff #1)

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

k_s 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.