Through several centrifugal model tests and result analyses

the characteristics of bearing capacity failure envelope of pile foundations under horizontal

vertical and bending moment loads () were studied. The research results indicate that: vertical and horizontal loads affect each other. When the pile foundations are subjected to combined vertical and horizontal loads

the interaction between these loads must be considered in the design. The failure envelope curve of pile foundation is approximately elliptical

with the center not at the origin but located on the upper half of the -axis

biased towards the downward load. The failure envelope curve equation can be expressed mathematically. This curve on the load plane helps determine the safety state of the pile foundation. The spatial failure envelope surface under the combined action of horizontal load

vertical load

and bending moment load is approximately ellipsoidal

with the center not at the origin but on the upper half of the V-axis. The spatial failure envelope surface of pile foundation bearing capacity provides a basis for judging and verifying whether the pile foundation is in a safe state under horizontal load

vertical load

and bending moment load . Utilizing failure envelope surface addresses some shortcomings of traditional design methods

making it a reasonable and necessary approach in pile foundation design.