Hyperspheric Integral Reliability Method for efficient reliability analysis of geotechnical ultimate limit states

This paper introduces the Hyperspheric Integral Reliability Method (HINT) for efficient reliability analysis of geotechnical ultimate limit states. The method is motivated by the mechanism of the Shear Strength Reduction Method (SSRM), which is often employed to calculate the factor of safety for geotechnical ultimate limit states. HINT exploits the observation that a factor of safety, computed by the SSRM, is not only a pointwise estimate of safety, but also a measure of distance to the failure limit along a radial direction in the space of the shear strength parameters. This observation is utilized to transform the reliability integral in the hyperspheric coordinate system and develop an efficient estimator of failure probability for geotechnical ultimate limit states. HINT was examined on several benchmarking problems, demonstrating stable and highly efficient performance on low to medium dimensional reliability problems. HINT can be also applied to general reliability problems if a radial search mechanism is implemented as in the SSRM. Given that the SSRM is already available in most commercial geotechnical software packages, HINT is perfectly suited to advance geotechnical reliability analyses and make them accessible to a wider set of use-cases.