Quantile and extreme threshold methods for geotechnical reliability-based design with inseparable parameters

This study improves the applicability of the recently developed quantile threshold method (QTM) and extreme threshold method (ETM) for reliability-based design (RBD) with inseparable parameters by introducing a vector-updating approach. First, an analytical framework is established to unify QTM and ETM within a synthesized variable space that combines load and geotechnical resistance parameters. A vector-updating technique is then proposed to approximate the design parameter thresholds of random samples. This advancement enables the effective implementation of QTM and ETM for determining design parameters that are inseparable from the performance functions in RBD. Three illustrative examples demonstrate the proposed method, showing that accurate design outcomes can be obtained within several seconds through limited vector-updating iterations (typically 3–6 cycles). The approach successfully overcomes a key limitation in previous QTM/ETM applications related to non-separable performance functions, thereby extending their applicability to design scenarios with inseparable design parameters.