On Explicit Integration Of The Bounding-surface Plasticity Model For Saturated Sand Under Cyclic Loading

Embedded anchor structures in Marine engineering usually bear long-term lowfrequency cyclic loads caused by wind,wave and current,etc.The research on bearing capacity and dynamic response of structures under such loads is of great significance to ensure long-term safety and stability of engineering structures.At present,the cyclic loading performance of embedded structure is mainly researched by means of model test and field test,and effective numerical analysis method is not established.The bounding-surface plasticity model can be used to simulate the complex mechanical behavior of soil under cyclic load.Therefore,the bounding-surface plasticity model can be used for numerical analysis of embedded Marine structures.However,if the bounding-surface plasticity model is to be applied to a specific geotechnical engineering boundary value problem,the model must be three-dimensional and integrated numerically.Based on a bounding-surface plasticity model for saturated sand under cyclic loading,this paper is devoted to extending it from two-dimensional stress space to three-dimensional stress space and establishing a numerical integration algorithm matching the three-dimensional model.Firstly,the modified generalized Mises method is adopted to extend the boundingsurface plastic model to three-dimensional stress space.The dilatancy of sand is described by adopting non-associated flow rule and state-dependent dilatancy function.The plastic modulus formula with the concept of peak stress ratio was used to simulate the strain softening of dense sand.Secondly,this paper adopts the explicit integration algorithm of substepping with automatic error control to integrate the model,and an explicit integration procedure of the bounding-surface plasticity model is proposed.By means of user-defined material subroutine interface(UMAT)in finite element software of ABAQUS,the procedure is coded into FORTRAN format that can be applied to finite element analysis.Finally,numerical models are established to simulate triaxial tests of Toyoura sand under monotonic loading and cyclic loading,and the foundation capacity test of Leighton Buzzard sand.The results show that both at soil element level and boundary value problem level,the substepping integration algorithm has applicability and accuracy for the integration of the bounding-surface plasticity model.At the same time,it also proves the effectiveness of the modified generalized Mises method for extending the bounding-surface plasticity model into three-dimensional stress space.The stability and efficiency of the substepping integration algorithm are validated by simulating the same static triaxial test with different allowable errors and sizes of increment.