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By Hugo Melo

The Friction Angle and Critical State Void Ratio of Sands

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The friction angle of sands is computed by Bolton as the sum of the critical state friction angle and a dilatancy term which is a function of mean effective pressure and void ratio. Critical state is reached when dilatancy vanishes, either due to volume change – in drained shear – or effective pressure change – in undrained shear. Therefore, equating Bolton’s dilatancy term to zero yields, at least theoretically, an implicit relationship between mean pressure and the critical state void ratio of sands. It is found that this relationship yields unrealistic results, mainly because Bolton’s expression if of phenomenological nature and was not intended to be used for this purpose. In this paper, a minor modification to Bolton’s dilatancy term is proposed. It is proved that the modified expression has the capacity to predict both the peak friction angle and the critical state void ratio for any void ratio and effective pressure within the range of engineering interest.