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(OP)
Could someone please explain exactly what the modulus of subgrade reaction is and how it relates the cbr value
at the moment i cannot find any information that correlates one to the other.

any help would be much appreciated

### RE: Modulus of subgrade reaction

3
Domdem,

The modulus of sudgrade reaction is determined from a plate loading test, in which a 30 inch diameter steel plate is loading using a steel jack and beam (for reaction).  The load is applied at a predetermined rate until a pressure of 10 psi (69 kPa) is reached.  The pressure is held constant until the deflection increases not more than 0.001 inch per minute for three consecutive minutes.  The modulus of subgrade reaction (k) is calculated as:

k=p/Delta
where: p = load (10 psi)
delta is total deflection of steel plate (inches)

The following is a rough correlation between the CBR and modulus of subgrade reaction (MSR):

MSR = CBR
100 = 3
150 = 5.5
200 = 10
250 = 20
500 = 50
700 = 80

The above information was taken from "Pavement Analysis and Design" by Yang H. Huang.

### RE: Modulus of subgrade reaction

(OP)
Thank you

Can this relationship be correlated to other size plates (ie 300mm)i believe th army corps did something about it but here in the uk it is very difficult to get any information about it

best regards

### RE: Modulus of subgrade reaction

The best formula for this correlation according with my experience is:
K=-3.03E-05(CBR)^4+0.0069(CBR)^3-0.571(CBR)^24.305(CBR)

CBR    K
0       0
3      68
5     108
10     193
20     308
30     377
35     402
45     442
50     461
60     500
70     543
75     563
80     582
90     604

### RE: Modulus of subgrade reaction

how spt value correlate with modulus of sub-grade

appreciate if someone can help.

### RE: Modulus of subgrade reaction

(Sigh.)  The modulus of subgrade reaction is not a soil property.  As a result, it cannot be "determined" using a CBR test, plate load test - or any other test, for that matter.

The modulus of subgrade reaction is a calculation expedient, and nothing more.  It is the ratio of applied pressure divided by the corresponding soil or rock movement.  It is directly affected by the size of the loaded area, the soil or rock shear modulus (which is strain dependent), the direction of loading, the type of loading - and many other factors.  It is not analogous to the stiffness of a steel spring, or Young's modulus for steel.  There is no such thing as "the" modulus of subgrade reaction - and it cannot be found in some textbook or simple correlation.

If I remember the definition of CBR correctly, it is defined as:

CBR = ([Applied Pressure at 0.1 inch piston deflection]/1000 psi)*100

Assuming this equation is correct, you can directly calculate a "modulus of subgrade reaction" k-value for the test as:

k (psi) = CBR * (1000/100)/(0.1) = CBR * 100

This is markedly different than the correlations proposed by drt or drfefefe.

drt and/or drfefefe: Where do your correlations come from?

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