Undrained Cyclic Elastoplastic Constitutive Relation For Soft Clays And Its Application In The Deformation Analysis Of Marine Anchor Foundations

Many offshore foundations,such as deep-water suction anchors,vertically loaded anchors(VLA)and large-diameter bucket foundations,are subjected to working loads(static loads)from superstructures as well as cyclic loads from waves.Analysing the deformation process and bearing capacity of foundations under these loads is very important for evaluating the stability of offshore foundations.Therefore,A numerical analysis method was developed to describe the cyclic deformation instability process and cyclic bearing capacity of soft clay foundations in this paper.Undrained cyclic elastoplastic constitutive relation are developed for soft clays and applied to the deformation analysis of marine anchor foundations.An incremental elastoplastic bounding surface model is developed by buliding the bounding surface equation using the Mises yield criterion and describing the hardening modulus field using the methods of the hardening modulus interpolation and the mapping center movement in the deviatoric stress space.An interpolation function of the elastoplastic modulus is established based on the radial mapping rule and the mapping center moves with the variation of loading and unloading paths for the model.Because the elastoplastic modulus interpolation function and the mapping center movement rule are used in the model,the evolution of the hardening modulus field is simple and remembered parameters are less during tracing the cyclic stress path.In addition,a parameter describing the accumulation rate and the level of shear strain is used in the elastoplastic modulus interpolation function to control the accumulation of shear strain with the number of stress cycles.The model can not only describe the nonlinear and hysteretic stress-strain responses and strain accumulation of soft clays subjected to cyclic loads but also predict the stress-strain response of soil elements with different combinations of initial and cyclic stresses.The method of determining model parameters is researched and cyclic triaxial tensile tests and cyclic torsion shear tests are also performed.The cyclic triaxial tensile and torsion shear test results are predicted using determined parameters and the rationality of the model is verified by comparing predicted results with test results.The proposed cyclic elastoplastic bounding surface model was embedded in the ABAQUS software package by encoding the material subroutine UMAT.According to the model characteristics,the method of detemining elastoplastic stress states for the model was developed.Elastoplastic stress states in the end of each iteration are determined using the sub-incremental explicit Euler algorithm,and the elastoplastic matrix are updated by setting state variables associated with the elastoplastic modulus of the current stress in each iteration step.The radial fallback method is developed to modify those stress states that fall outside the bounding surface,which ensures that the stress point at any moment can only fall inside or on the bounding surface.The judgment method for stress reversal is developed based on the angle between the deviatoric stress increment vector and the exterior normal vector at the image stress point on the bounding surface.Using this method,the mapping centre is updated,and the stress states after the stress reversal can be determined.The incremental elastoplastic finite element method that calculate undrained cyclic deformation time histories of soft clays was developed by combining the user-defined material subroutine(UMAT)with the incremental solver in the main program of ABAQUS software.Two types of simple boundary value problem of cyclic triaxial and cyclic torsional shear test are predicted using the method.The method is validated by comparing the finite element predictions with the model predictions.Model tests of suction anchors were performed with a taut mooring system subjected to combined static and cyclic loads at the optimal mooring point in soft clays under 1 g condition.The tests of suction anchors subjected to static loads are performed in the stratums with uniform strength and the linear change strength along the depth.The tests of suction anchors subjected to combined static and constant amplitude cyclic loads and ones subjected to combined static and variable amplitude cyclic loads are performed in two types of stratums,respectively.The deformation process of anchors,failure modes,bearing capacity and the pore water pressure were researched for different experimental conditions.Test results show that the failure occurs due to an excessive cumulative displacement along the mooring direction when the anchors are subjected to cyclic loads.The vertical cumulative displacement is greater than horizontal cumulative displacement in two types of loading modes without additional vertical loads.The typical vertical failure and an intermediate vertical failure occur when the anchors are subjected to constant amplitude and variable amplitude cyclic loads,respectively.The typical horizontal failure occurs when an additional vertical load of 0.3kN is applied to the anchors.The movement direction angle of the anchor under cyclic loads is greater than that under static loads,and the vertical motion increases and even the failure mode changes.As can be seen from the changes of pore pressure in the bottom and lateral of the anchor,the main reason is probably that the accumulative pore pressure results that the reduction of vertical bearing capacity is more significant than the horizontal bearing capacity.The model tests of suction anchors are simulated using the proposed incremental elastoplastic finite element method,and the method are validated by comparing the predictions and model test results.The three-dimensional finite element model are established in homogeneous and layered soil seperately,and the deformation process of suction anchor are simulated under constant amplitude cyclic loads and variable amplitude cyclic loads,respectively.The feasibility of finite element method was validated by comparing the predictions and model test results.The predicted displacement-time curves along the mooring direction,the horizontal and vertical cyclic cumulative displacements at the mooring point are consistent with the test results under different loading conditions.The predictions of deformation status of anchors at failure,failure mode and the number of load cycles to failure are also consistent with the test results.The comparation results indicates that the proposed incremental elastoplastic finite element method can evaluate the deformation instability process of the suction anchor subjected to cyclic loads and also determine the cyclic bearing capacity according to the appropriate failure criterion of displacement.In addition,the cyclic instability processes of vertically loaded anchors and suction caissons are simulated using the elastoplastic finite element method to verify the general applicability of the method to different marine anchor foundations.