Confidence and Accuracy in Determination of the Critical State Friction Angle

Abstract

ABSTRACT The critical state friction angle, φc, is a parameter of interest in many geotechnical analyses dealing with cohesionless soils. However, despite the triaxial test being widely used to estimate this parameter, the accuracy achievable from a limited number of triaxial tests is unknown. Accuracy is of particular interest in industry, where typically only a few soil tests are possible due to budget limitations. Statistical analysis of an extensive high quality triaxial testing program from the literature is used here to obtain guidance on the number, density range, and pressure range of triaxial tests required to reach a specified level of confidence in the critical state friction angle. The adequacy of the estimating methodology is then tested against a smaller and independent set of triaxial tests on the same sand, performed in a commercial testing laboratory. The results suggest about six drained triaxial tests are needed for routine engineering where a precision of ±1.0° may suffice. However, for research or high precision work, more than twenty drained triaxial tests may be needed to determine φc to an accuracy of ±0.5° at 90% confidence. In all cases, tested samples should be uniformly distributed across the range of the soil's relative density.