Thanks Roger and Jason for your reply.
1- I’m totally agree with you @Roger.Bergua in his explanation
here’s my stiffness matrix for NREL 5 MW for layered sand soil OC3, I modeled the 6 m diameter hollow pile with 36 m length (with soil inside and outside the pile) under Moment=1.24e11 N.mm, and shear=3.91 e6 N, No vertical load. (units are N and mm)
here’s my ABAQUS model and the deflection at seabed due to (M and Q)=26.5 mm, and rotaion =0.002666 rad
I thought at the begining that my results is Ok, as the pile behave as rigid pile and the displacement and rotation are not too far from OC3 results ( displacement=22.6 mm, rotation=0.002413 rad), because it depends on the results from LPILE which based on P-Y curve that overestimate the soil resistance in sand.
My stiffness matrix is far away from the results from OC3
Regards,
Marwa
Dear @Marwa.Mohamed,
Assuming that the units in your stiffness matrix are [N, mm, rad] (the units for the angles were not stated in the previous message), you can simply compute the expected displacements as: {F} = [K]*{x}. By computing the inverse of the stiffness matrix and multiplying it by the applied force vector, you can obtain the corresponding displacements.
I believe for the NREL 5 MW, the rated thrust force is close to 0.8E6 N. According to your stiffness matrix, the expected displacements due to this horizontal force would be:
x = 1.808 mm
y = 0.002 mm
z = 0.041 mm
rx = 0.000 deg
ry = 0.006 deg
rz = 0.000 deg
Assuming the same rotor thrust force and a total weight for RNA + tower of 6.8E6 N, the expected displacements would be:
x = 1.468 mm
y = -0.012 mm
z = -4.207 mm
rx = 0.000 deg
ry = 0.005 deg
rz = 0.000 deg
Note that this weight (purely in the vertical direction) has implications in secondary directions due to the cross-coupling terms included in the stiffness matrix. For reference, the expected horizontal-rotational couplings that we show in the OC6 Phase II definition document are also aligned with the expected couplings between directions in a beam theory formulation (see the 6 by 6 submatrix of a beam element [k_e] in 4.7.6. SubDyn Theory — OpenFAST v3.5.4 documentation).
Below you can find the Matlab code that I’m using to compute these results:
K = [7.8949E5 -2.4526E2 -2.8568E4 -1.0641E6 -6.1478E9 -2.4015E7;
-4.0030E2 7.9018E5 -1.7135E3 6.1255E9 1.4480E5 3.6188E8;
-2.9542E4 -1.6805E3 1.6038E6 -4.7406E6 -1.2275E8 1.8836E4;
-1.3350E6 6.1255E9 -4.8380E6 1.1007E14 9.4926E10 1.1418E11;
-6.1478E9 -1.0737E5 -1.2271E8 9.3185E10 1.0919E14 6.1934E10;
-2.3398E7 3.6134E8 3.4426E5 1.1354E11 6.0195E10 3.4083E13];
F = [0.8E6 0 -6.8E6 0 0 0]';
x = K\F;
x(4:6) = rad2deg(x(4:6));
I hope that helps!
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Dear Roger,
Thanks for your help and these valuable comments. I’ll try to find out where is my error.
Regards,
Marwa
Dear @Jason.Jonkman
In the former reply, you mentioned that I would expect that you’d use JointType = 1 and RctTDXss = RctTDYss = RctTDZss = RctRDXss = RctRDYss = RctRDZss = 0 for JointID = 2 in SubDyn.
Does this setting indicate that the nodes at the bottom of SubDyn are not locked but free, with the purpose of receiving foundation resistance from SoilDyn? Due to this node setting, is the lower structure considered the ‘floating’ type mentioned in the SubDyn manual when analyzing the substructure modes?
Dear @RenQiang.Xi,
I agree that the use of JointType = 1 and RctTDXss = RctTDYss = RctTDZss = RctRDXss = RctRDYss = RctRDZss = 0 for JointID = 2 in SubDyn implies that the node at the bottom of the SubDyn model (JointID = 2) is “not locked but free, with the purpose of receiving foundation resistance from SoilDyn.”
However, inclusion of a base reaction joint in SubDyn (NReact > 0) tells SubDyn that the substructure is a “fixed-bottom” type, even if the reaction joint(s) is(are) free. A substructure in SubDyn in SubDyn is considered a “floating” type when the model has no reaction joints (NReact = 0).
Best regards,
@Jason.Jonkman
Thank you very much for your prompt and detailed response.
Regarding this issue, I have reviewed the SubDyn code and found that the only difference between the fixed-bottom type and floating type in SubDyn seems to lie in the GuyanLoadCorrection; there doesn’t appear to be any other differences. Is this accurate?
Additionally, for the fixed-bottom type, if SoilDyn or other similar nonlinear SSI methods are used, the soil springs (nonlinear) are not applied at the Reaction node (the nodes declared in the BASE REACTION JOINTS section). That is, for the substructure, when calculating the internal eigenmodes, these nodes involved in SSI are not subjected to external soil spring constraints. Is this correct? I am uncertain because the manual clearly mentions: “ΦL (L×L matrix) represents the internal eigenmodes, i.e., the natural modes of the system restrained at the boundary (interface and bottom nodes), and can be obtained by solving the eigenvalue problem (Eq. 4.130).”
Dear @RenQiang.Xi,
The key differences in SubDyn between “fixed” and “floating” type are well summarized in the SubDyn theory documentation: 4.2.5.6. SubDyn Theory — OpenFAST v3.5.4 documentation. Note that the Guyan load correction will always be enabled in the upcoming release of OpenFAST v4 because we never found a use case where it was important to eliminate the Guyan load correction–see the following pull request for more information: Support for large platform yaw offset in OpenFAST by luwang00 · Pull Request #2203 · OpenFAST/openfast · GitHub.
For “fixed” type systems where the reaction joint is included, but free without soil stiffness provided in SubDyn (i.e., for coupling to SoilDyn), we actually take the linear contribution of the soil stiffness from SoilDyn and use that in SubDyn to ensure that the Craig-Bampton modes are still correct and the coupled SubDyn-SoilDyn solution are numerically stable.
Best regards,
@Jason.Jonkman
Thank you very much for clarifying this issue.
This solution imply that if the stiffness matrix of the substructure is K (with interface degrees of freedom removed), and the linearized stiffness due to the soil spring is Ks, then when calculating the modes, the overall stiffness matrix used is K+Ks. The stiffness in the governing Eqs. of C-B model used to solve for the internal degrees of freedom remains K, because the constraints from the soil springs are fully reflected in the load on the right-hand side. In this case, if the stiffness matrix in the governing Eqs. of the system is K+Ks and the external loads still represent all the constraint forces from the soil springs, the linear part of the soil spring constraint forces would be redundantly calculated. Is this understanding correct?
Additionally, if Ks is not considered when calculating the internal modes (C-B modes), the system stiffness matrix remains invertible since the interface degrees of freedom have been removed. The internal modes we need can still be calculated normally. Certainly, in this case, the substructure is actually floating. From this perspective, it should be sufficient to set the nodes at the bottom of the foundation as free and apply the soil spring load there without using different stiffness matrix in the modes analysis and dynamic response analysis. This method analogizes the foundation soil to water, replacing its effects with loads. It seems physically and mathematically feasible. Of course, whether it is numerically feasible depends on factors such as stability and convergence. Do you think this method is feasible? The following paper presents a nonlinear SSI model for OpenFAST, which seems to adopt such an approach, though the author did not provide detailed technical information: Redirecting.
Best regards,
Dear @RenQiang.Xi,
When SoilDyn is coupled to SubDyn, the linear part of the soil reaction (Ks in your nomenclature) is considered on the left-hand side of the SubDyn equations of motion (and influences the Craig-Bampton modes), and the nonlinear part of the soil reaction is applied as a force on the right-hand side of the SubDyn equations of motion. In this way, the effect of the linear reaction is not double counted. We had originally tried to include the full (linear + nonlinear) soil reaction on the right-hand side as you suggest, but the coupled solution was numerically unstable.
We had some discussion with the authors of the paper you cite and their FounDyn module, hoping to get features of FounDyn merged into SoilDyn, but that merging has not yet happened as far as I know.
Best regards,
Dear @Jason.Jonkman
I understand the technical approach of SoilDyn in addressing nonlinear soil-structure interaction now.
Thank you very much for your quickly response to my questions and for your significant contributions to the OpenFAST software and its community over the years.
Best regards,
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