The bottom nodes of the soil and suction-pile skirt are fixed in a vertical direction.

Displacement in the perpendicular direction is restricted on all four sides of the underground model.

Displacement in the horizontal direction is restricted on top outer ring of the suction pile.

Figure 58.3: Boundary Conditions: Static Analysis with Nominal Geometry

Loading occurs over four steps:

 

58.5.1.2.1. Load Step 1: Gravitational Acceleration on the Soil + Initial Stress State

An initial in-situ earth pressure is generated by applying a gravitational acceleration of g = 9.81 m/s² to the soil.

The in-situ stress-state calculation leads to undesirable vertical deformations. To mitigate the problem, an initial stress state is applied, resulting in a nearly deformation-free initial state for the gravitational load step.

Typically, soil exists in an already-consolidated state. Initial displacements due to at-rest loads are therefore unnatural and should be minimized. The vertical stress state S_Z varies linearly based on the soil depth. S_Z is determined via the soil density ρ, the gravitational acceleration g, and the vertical height h of each element:

The coefficient of lateral earth pressure is defined as the ratio of horizontal- to vertical-stress components. For a horizontally-retained non-overconsolidated soil under elastic loading conditions, the coefficient is defined via Poisson’s ratio ν:

The horizontal stress components are then determined by:

The known stress state is applied as the initial state (INISTATE).

Example 58.1: Applying an Initial Stress State

/solu ! Enter the solution processor

time, 1

! Specify the data type to be set on the subsequent INISTATE,DEFINE command
INISTATE,SET,DTYP,STRE

! Define stresses to the selected elements
INISTATE, DEFINE,,,,, Cxx, Cyy, Czz, Cxy, Cyz, Cxz 

! Activate the file output of the calculated stress state at solution
inistate, write, 1, , , , , S

…

! Solve the first load step
solve

finish

Following is the resulting vertical-pressure distribution:

Figure 58.4: Vertical Stress Distribution in the Soil

The initial at-rest pressure state is correctly applied, while the soil structure retains its initial shape.

Marginal displacements (<0.5 mm Figure 6) are acceptable due to unbalanced soil pressure inside and/or outside of the soil region and contact penetrations:

Figure 58.5: Total Displacements in the Soil

 

58.5.1.2.3. Load Step 3: Interaction Forces (Upper Structure) on the Suction-Pile Top

Forces caused by interaction with the upper structure are applied to the suction-pile top. Forces/moments are distributed over the top of the pile via contact pairs (CONTA174 / TARGE170) with the pilot-node option enabled.

Upper Structure Interaction Load
	Force / Moment	Value (kN; kN.m-1)
	Fx	-5500.0
	Fy	200.0
	Fz	-13000.0
	Mx	-300.0
	My	-3500.0
	Mz	-50.0

 

58.5.1.2.4. Load Step 4: Suction Pressure and Supplementary Friction Forces

Suction pressure is applied on both the suction-pile skirt and lid. Constant pressure on the suction-pile skirt is assumed.

Suction Pressure
	Pressure Operation	Value (kPa)
	At lid	210.0
	At skirt	150.0

Assumed frictional forces are applied on the suction-pile skirt where the skirt interacts with the soil.

Frictional Forces
	Vertical Force Resultant	Value (kN)
	At outer surface	500.0
	At inner surface	500.0

A nonlinear static analysis is performed. The in-situ stress state (load step 1) is calculated in a single substep.

Load steps 2 through 4 are calculated with automatic time-stepping enabled.

Initial-stress-state results are documented in Loading. Following are the results after load step 4:

Figure 58.6: Total Displacements – Whole Model

Figure 58.7: Total Displacements – Soil

Loading on the suction pile leads to plastic strains in the soil. Plastic strains are distributed unsymmetrically due to unsymmetrical loading in load step 3 and load step 4:

Figure 58.8: Equivalent Plastic Strains – Soil

Figure 58.9: Equivalent Plastic Strains – Soil Section

Figure 58.10: Equivalent von Mises Stress – Suction Pile

Strain on the suction pile causes plastic strains at the neck of the suction-pile cap:

Figure 58.11: Equivalent Plastic Strain – Suction Pile

Boundary conditions from the prior static analysis are used.

A final load state from load step 4 in the prior static analysis is used as a reference load.

The linear buckling analysis is performed. Ten eigenmodes are calculated and expanded.

finish

/clear

/assign,rstp,buckle,rst   ! Force Eigen analysis to write to buckle.rst

/solu

antype,static,restart,last,last,perturbation
perturb,buckle,,CURRENT,ALLKEEP  ! Nonlinear buckling analysis using
                                 !   loads from prestress analysis

solve, elform             ! Generate matrices needed for perturbation analysis

bucopt,subsp,10,,,center
outres,erase
outres,all,all
mxpand,10                    		

solve

Ten eigenmodes were calculated during the buckling analysis. The resulting load factors range from 0.61086 to 1.1468.

The first buckling mode with a scaling factor of 0.135 is used to generate the structure imperfections:

Figure 58.12: Buckling Mode

Figure 58.13: Total Displacements – Buckling Mode 1

Boundary conditions from the first static analysis are used.

Loading is identical to that of the first static analysis. At the beginning of the analysis, however, the geometry is updated (UPGEOM) to account for imperfections (defined based on the buckling analysis results).

! Imperfections Resulting from Linear Buckling Analysis

esel,s,ename,,154
esel,a,ename,,170,174
esel,a,ename,,281
nsle
esln

UPGEOM,0.135,1,1,buckle,rst,

A nonlinear static analysis is performed, similar to the first, but using the updated geometry.

Following are the results after load step 4.

Figure 58.14: Total Displacements – Whole Model

Figure 58.15: Total Displacements – Soil

Figure 58.16: Equivalent Plastic Strains – Soil

Figure 58.17: Equivalent Plastic Strains – Soil Section

Compared to the static analysis results using nominal geometry, the analysis using the updated geometry with imperfections shows larger displacements and deformations on the suction-pile skirt, resulting in higher plastic strains:

Figure 58.18: Equivalent von Mises Stress – Suction Pile

The suction-pile geometry without imperfections resulted in maximum plastic strains at the neck on the suction-pile cap. After including the imperfections, the same loading results in the critical region having moved from the suction-pile neck to the skirt:

Figure 58.19: Equivalent Plastic Strain – Suction Pile

Accounting for potential structural imperfections leads to qualitatively and quantitatively different results.