Getting K(Modulus of Subgrade Reaction) from CBR values(by CD225 eq2.4) for use in TR34 Calculation 2

@JLangdon (Structural),

Below find my points.

- I did not see before such a formula (E = 17.6(CBR)^0.64 ) which E is function of CBR and IMO, it is not a good idea to predict Ks values acc. to CBR.
- The soil modulus is a function of material property, density, water content etc. The following figure is copy and paste from BOWLES.


- CBR is a material property and does not change with compaction, density , water content.CBR values for common soil types according to the USCS, for example: clay around 2%, sand from 7% (poorly graded) to 10% (well graded), well graded sandy gravel 15%, clayey sand 5-20%, silty gravel 20-60%, gravel from 30-60% poorly-graded to 40-80% if well-graded.

- However, still your calculation for E = 17.9 (2.9)^0.64 = 35.38 MPa or N/mm2 seems reasonable assuming medium density clay. But the calculation of Ks is something else. For example Meyerhof suggests Ks=Es/(B(1-µ^2). Assuming B 1000 mm , µ=0.3 for unsaturated clay, Ks=35.38/(1000*(1-0.3^2)=0.038 N/mm3 = 38000 kN/m3
- The foundations are not sensitive to the Ks values. If you look to the following ref. Ks is btw 32000-80000 for normally consolidated clay . You may choose say 40000 kN/m3.

I will suggest you to look for Ks calculations;
- Bowles J.E.-Foundation Analysis and Design
- Iain Alasdair MacLeod Modern structural analysis modelling process and guidance ,

My opinion..





According to the grace of God which is given
unto me, as a wise masterbuilder, I have laid the foundation, and another buildeth thereon. . . .
I Corinthians 3:10

It appears you desire a value for the modulus of subgrade reaction (k), but are starting with a conversion from CBR to “subgrade surface modulus”, which is not the same as k, and has different units.
I believe it is acceptable to determine a k value from CBR, even though CBR is primarily a strength property.
You could use the on-line calculator at which calculates for a CBR of 2.9, k=98 pci

Refer attached.

Retrograde's linked document shows various approaches used, including the relationship in the original post.
But, this document appears to apply to only "subgrade modulus", which is a resilient modulus, not the same as modulus of subgrade reaction.

Below are some equations cited, that give results in pci:

ACPA equation: k=53.438 x CBR^0.5719
FAA equation: k=(1500 x CBR/26)^0.7788

That ACPA equation appears to be what is used by the on-line calculator I linked above.

This ASCE paper describes an updated method, I believe adopted by FAA, I could only view the first page online:

Discussion at Eng-tips: