f d A value of the picnotropy factor at the asymptotic state boundary surface F m Matsuoa-Nakai factor f s barotropy factor f u collapse potential factor g plastic potential G soil shear modulus G gradient of the soil shear modulus with depth G eff soil effective shear modulus G in soil initial shear modulus G L soil shear modulus at pile tip G L /2 soil shear modulus at pile mid length G m plastic potential for the Mohr-Coulomb model G mech soil mobilized shear modulus G 0 small strain soil shear modulus G 1 soil shear modulus of the shallower layer for two-layer soil G 2 soil shear modulus of the deeper layer for two-layer soil G 90 initial shear stiffness after a 90 ◦ change in the strain path direction h function for the hardening law h Heaviside function h 1 thickness of the shallower layer for two-layer soil H 2厚度的较深层的两层土壤H P硬化模量ˆ