Abstract: Hydraulic fill sand strata in coastal areas were prone to differential settlements under the self-consolidation to form undulating ground surfaces.Shallow tunnel faces were often in passive failure modes when shield tunneling in hydraulic fill sand strata.However,traditional tunnel face stability analysis models lacked a comprehensive consideration of above two factors.More accurate passive failure analysis models of tunnel face under undulating ground surfaces urgent need to be explored.The influence exerted by longitudinal slope δ₁ and transverse slope δ₂ on the ultimate support pressures and the failure zone was investigated by numerical simulations.According to the failure zone obtained from numerical simulations,a 3D passive failure model was proposed by using the spatial discretization technique,and ultimate support pressure upper-bound solutions were derived based on limit analysis methods.The results demonstrated that the influence of bidirectional slopes cannot be ignored in practical engineering,the longitudinal slope δ₁ has a more significant impact on the ultimate support pressure than the transverse slope δ₂,the effect of transverse slope δ₂ on the extent of the failure zone was more important than that of longitudinal slope δ₁.Finally,validated by comparison with numerical models and existing analytical models and with a case study.The proposed results were closer to numerical results.The results can provide theoretical guidance for shield tunneling under complex terrain conditions.