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# CBR and qu relationship

## CBR and qu relationship

(OP)
I am looking for correlations between CBR and unconfined compression strength. So far I found:

1. qu = 4.5xCBR (psi-Illinois DOT)
2. qu = 47xCBR (kPa-Japan)

The above equations give results with about 50% difference.

Do you have any other references? Since I am in Japan I may be ending up using equation #2. Just curious to see other correlations.

Thanks !!

### RE: CBR and qu relationship

A CBR of 100% involves an applied stress of 6.9MPa for 2.5mm penetration or 10.3MPa for 5mm penetration.
For a cohesive soil and a circular footing without embedment, Bearing Capacity theory states that applied stress = 1.3 c Nc where c is the undrained cohesion and Nc the cohesion bearing capacity factor. When friction = 0, then Nc = (2+Pi), hence applied stress = 1.3 x 5.14 x c
Thus, for 100% CBR and 2.5mm penetration, c=1.03 MPa and for 5mm penetration c=1.54MPa.
As undrained unconfined strength of a cohesive soil = 2c, hence qu=2.06 CBR/100 (MPa) = 20.6 CBR (kPa) or qu=3.08 CBR/100 MPa = 30.8 (kPa)
This assumes (at minimum) that the penetration depth doesn't incur its own bearing capacity factor, that there's no friction, and that failure occurs at the given penetration and not any earlier. At a separate thread you will see discussion that undrained strength = 17 or 23 CBR or other values. The 30.8 value is almost certainly too high in practice.

### RE: CBR and qu relationship

once you get your correlation, what will you do with the value?

f-d

ípapß gordo ainÆt no madre flaca!

### RE: CBR and qu relationship

(OP)
f-d, I have to do a soil stabilization with lime or cement for a pavement subgrade. Clients are more familiar with improved qu (unconfined compressive strength) values however, most of the contractors shown improved CBR values in their catalogs. I just wanted to look at different correlations betweeen qu and CBR to compare with what we have here.

### RE: CBR and qu relationship

Hi Okiryu,
I don't know which country you guys are from however, in Australia there is general guideline published by Austroads when it comes to stabilisation of subgrade using lime.
We do CBR test for stabilised subgrade because we use a software called CIRCLY (mechanistic-empirical pavement design software)which requires CBR. The guideline also suggest that if the stabilised subgrade has cbr of more than 15%, we still need to design for 15% max. one of the reason behind this is during construction the quality of placing and mixing is never uniform compared to laboratory test.

When carrying out stabilisation of the subbase and base layer, it is necessary to carry out Unconfined Comprehensive Strength test (qu). It will tell us whether the layer has been
- modiefed (UCS = qu < 1MPa)
- Lightly Bound (UCS = qu = 1MPa to 1.6MPa) (research is being done to to identify the exact boundary)
- Bound (UCS = qu = over 2.0 MPa)

CIRCLY uses Resilient Modulus (Mr) for the design which is simply Mr = 1200 * qu. (only for base and subbase layer)
To get the actual test result, you need to carry out repeated triaxil test.

I hope this helps.

### RE: CBR and qu relationship

In all this discussion, don't forget that CBR(in-situ) is often very different from CBR(laboratory) [due to different confinement conditions and the existence of a base at shallow depth in the laboratory mold]. It can also vary considerably due to different laboratory or on-site test arrangement. For example the use of surcharge will change the values. CBR value is also soil-dependant; i.e. two soils of different types with the same UCS will have different CBRs. IF a particular correlation is valid, its validity will be limited to either in-situ or laboratory and also to CBR results obtained with particular surcharges (or none) AND to certain soil types. So before using UCS = 17 / 20.6 (value for 2.5mm penetration according to theory) / 23 / 30.8 (value for 5mm penetration according to theory) / 31 (Illinois DOT) / 47 (Japan) / other ! it would be best to find out for which combination of conditions the particular correlation was developed.

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