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Relationship between CBR and Bearing Capacity

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Not really. A CBR is a materials characterization test. Bearing capacity is a more global response of the soil based on different parameters.
 
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Would caution using this, always consult a geotechnical engineer when not certain. Would also point out that I've seen a couple iterations of this chart and it seems to always be within the context of airfield pavements. Don't know that there's much of a relationship for other applications due to bearing capacity being more of a global response for foundations as Ron mentioned rather than the localized response that you'd be more focused on in slab on grade or pavement design.
 
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