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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
Nonlinear Dynamic Soil-StructureInteraction in Earthquake Engineering
EDF R&D / LaMSID Supervisors: N. Greffet, G. Devésa
September 4th 2012LaMSID seminar
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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
Kashiwazaki-Kariwa Nuclear Power Station
7 units; 8 212 MWe∼ Soft soilsInstrumented from 2004
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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
Observed nonlinear behaviour
July 16th, 2007 10:13 AM
Richter Magnitude = 6.8
Depth = 17Km
Hypocenter = 23Km, Epicenter = 16Km
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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
Industrial Context
Periodic seismic risk assessments
Account for nonlinear effects in soil-structure interaction (SSI)calculations
Linear SSI analyses
Efficient BE-FE coupling in the frequency domain
Validated codes: MISS3D and Code_Aster
Goal
Enhance the existing BE-FE so that nonlinearities can beaccounted for within SSI calculations
Avoid full FEM solution (too expensive)
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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
State of the art of hybrid approachesBEM – FEM
– O. von Estorff and E. Kausel. Coupling of boundary and finite elements for soil-structureinteraction problems. Earthquake Eng. Struct. Dyn., 18, 1065–1075, 1989.
– O. von Estorff and M. Firuziaan. Coupled BEM/FEM approach for nonlinear soil/structureinteraction. Eng. Analysis Boundary Elem., 24, 715–725, 2000.
– H. Masoumi, S. François and G. Degrande. A non-linear coupled finite element-boundaryelement model for the prediction of vibrations due to vibratory and impact pile driving. Int. J. forNum. Anal. Meth. Geomech., 33(2), 245–274, 2009.
SBFEM – FEM
– C. Birk and R. Behnke. A modified scaled boundary finite element method forthree-dimensional dynamic soil-structure interaction in layered soil. Int. J. Num. Meth. in Eng.,89(3), 371–402, 2012.
– M. Cemal Genes. Dynamic analysis of large-scale SSI systems for layered unbounded mediavia a parallelized coupled finite-element/boundary-element/scaled boundary finite-elementmodel. Eng. Analysis Boundary Elem., 36, 845–857, 2012.
Infinite Elements – FEM
– J.S. Ryu, C.G. Seo and C.B. Yun. Seismic response analysis of soil–structure interactive systemusing a coupled three-dimensional FE–IE method. Nuclear Eng. Design, 240, 1949–1966,2010.
– J.S. Choi, C.B. Yun and J.M. Kim. Earthquake response analysis of the Hualien soil–structureinteraction system based on updated soil properties using forced vibration test data. EarthquakeEng. Struct. Dyn., 30(1), 1–26, 2001.
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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
State of the art of hybrid approachesBEM – FEM
– O. von Estorff and E. Kausel. Coupling of boundary and finite elements for soil-structureinteraction problems. Earthquake Eng. Struct. Dyn., 18, 1065–1075, 1989.
– O. von Estorff and M. Firuziaan. Coupled BEM/FEM approach for nonlinear soil/structureinteraction. Eng. Analysis Boundary Elem., 24, 715–725, 2000.
– H. Masoumi, S. François and G. Degrande. A non-linear coupled finite element-boundaryelement model for the prediction of vibrations due to vibratory and impact pile driving. Int. J. forNum. Anal. Meth. Geomech., 33(2), 245–274, 2009.
SBFEM – FEM
– C. Birk and R. Behnke. A modified scaled boundary finite element method forthree-dimensional dynamic soil-structure interaction in layered soil. Int. J. Num. Meth. in Eng.,89(3), 371–402, 2012.
– M. Cemal Genes. Dynamic analysis of large-scale SSI systems for layered unbounded mediavia a parallelized coupled finite-element/boundary-element/scaled boundary finite-elementmodel. Eng. Analysis Boundary Elem., 36, 845–857, 2012.
Infinite Elements – FEM
– J.S. Ryu, C.G. Seo and C.B. Yun. Seismic response analysis of soil–structure interactive systemusing a coupled three-dimensional FE–IE method. Nuclear Eng. Design, 240, 1949–1966,2010.
– J.S. Choi, C.B. Yun and J.M. Kim. Earthquake response analysis of the Hualien soil–structureinteraction system based on updated soil properties using forced vibration test data. EarthquakeEng. Struct. Dyn., 30(1), 1–26, 2001.
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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
State of the art of hybrid approachesBEM – FEM
– O. von Estorff and E. Kausel. Coupling of boundary and finite elements for soil-structureinteraction problems. Earthquake Eng. Struct. Dyn., 18, 1065–1075, 1989.
– O. von Estorff and M. Firuziaan. Coupled BEM/FEM approach for nonlinear soil/structureinteraction. Eng. Analysis Boundary Elem., 24, 715–725, 2000.
– H. Masoumi, S. François and G. Degrande. A non-linear coupled finite element-boundaryelement model for the prediction of vibrations due to vibratory and impact pile driving. Int. J. forNum. Anal. Meth. Geomech., 33(2), 245–274, 2009.
SBFEM – FEM
– C. Birk and R. Behnke. A modified scaled boundary finite element method forthree-dimensional dynamic soil-structure interaction in layered soil. Int. J. Num. Meth. in Eng.,89(3), 371–402, 2012.
– M. Cemal Genes. Dynamic analysis of large-scale SSI systems for layered unbounded mediavia a parallelized coupled finite-element/boundary-element/scaled boundary finite-elementmodel. Eng. Analysis Boundary Elem., 36, 845–857, 2012.
Infinite Elements – FEM
– J.S. Ryu, C.G. Seo and C.B. Yun. Seismic response analysis of soil–structure interactive systemusing a coupled three-dimensional FE–IE method. Nuclear Eng. Design, 240, 1949–1966,2010.
– J.S. Choi, C.B. Yun and J.M. Kim. Earthquake response analysis of the Hualien soil–structureinteraction system based on updated soil properties using forced vibration test data. EarthquakeEng. Struct. Dyn., 30(1), 1–26, 2001.
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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
Summary
1 Dynamic SSI problem
2 SSI forces evaluation in the time domain
3 Numerical validation
4 Conclusions and future work
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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
1 Dynamic SSI problemGeneral resolution strategyInteraction forces: convolution integral
2 SSI forces evaluation in the time domain
3 Numerical validation
4 Conclusions and future work
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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
SSI Problem: resolution strategy
DSSI in EE = building + soil + incident seismic field
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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
SSI Problem: resolution strategy
domain decomposition technique
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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
SSI Problem: resolution strategy
BEM - FEM coupling = MISS3D - Code_Aster coupling
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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
SSI Problem: resolution strategy
BEM - FEM coupling = MISS3D - Code_Aster coupling
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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
SSI Problem: resolution strategy
LINEAR: resolution in frequency domain
NONLINEAR: resolution in time domain
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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
Interaction forces: convolution integral
Assuming linear behaviour and FE discretization (Γ-interface):
−ω2Mu(ω) + iωCu(ω) + Ku(ω) +
[0
Zs(ω)uΓ(ω)
]=
[0
Fs(ω)
]
? ? ? ? ?
Mu(t) + Cu(t) + Ku(t) +
[0
RΓ(t)
]=
[0
Fs(t)
]where
Fs(t): seismic loading,RΓ(t): interaction forces, i.e. the convolution integral:
RΓ(t) = (Z ∗ uΓ)(t) =
∫ t
0Z(τ)uΓ(t − τ) dτ
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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
1 Dynamic SSI problem
2 SSI forces evaluation in the time domainNumerical problemsConvolution Quadrature MethodHybrid Laplace-Time domain Approach
3 Numerical validation
4 Conclusions and future work
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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
Numerical problems
Soil impedance is assumed as [COTTEREAU07]:
Z(ω) = −ω2 M + iω C + K︸ ︷︷ ︸singular part
+ Zr(ω)︸ ︷︷ ︸regular part
, Zr(ω) −−−−→ω→∞
0
MKCtime domainformulation
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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
Numerical problems
Soil impedance is assumed as [COTTEREAU07]:
Z(ω) = −ω2 M + iω C + K︸ ︷︷ ︸singular part
+ Zr(ω)︸ ︷︷ ︸regular part
, Zr(ω) −−−−→ω→∞
0
?
12π
∫ +∞
−∞Z(ω) eiωt dω
Cut-offfrequency
Z(t) = M δ(t) + C δ(t) + K δ(t) + Zr(t)
?
Singularkernel
MKCtime domainformulation
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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
Numerical problems
Soil impedance is assumed as [COTTEREAU07]:
Z(ω) = −ω2 M + iω C + K︸ ︷︷ ︸singular part
+ Zr(ω)︸ ︷︷ ︸regular part
, Zr(ω) −−−−→ω→∞
0
?
12π
∫ +∞
−∞Z(ω) eiωt dω
Cut-offfrequency
Z(t) = M δ(t) + C δ(t) + K δ(t) + Zr(t)
?
Singularkernel
(Z ∗ u)(t) = M u(t) + C u(t) + K u(t) + (Zr ∗ u)(t)
with (δ(m) ∗ f)(t) = (δ ∗ f (m))(t) = f (m)(t)
MKCtime domainformulation
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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
Numerical problems
Soil impedance is assumed as [COTTEREAU07]:
Z(ω) = −ω2 M + iω C + K︸ ︷︷ ︸singular part
+ Zr(ω)︸ ︷︷ ︸regular part
, Zr(ω) −−−−→ω→∞
0
?
12π
∫ +∞
−∞Z(ω) eiωt dω Cut-off
frequency
Z(t) = M δ(t) + C δ(t) + K δ(t) + Zr(t)
?
Singularkernel
(Z ∗ u)(t) = M u(t) + C u(t) + K u(t) + (Zr ∗ u)(t)
with (δ(m) ∗ f)(t) = (δ ∗ f (m))(t) = f (m)(t)
MKCtime domainformulation
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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
Numerical problems
Soil impedance is assumed as [COTTEREAU07]:
Z(ω) = −ω2 M + iω C + K︸ ︷︷ ︸singular part
+ Zr(ω)︸ ︷︷ ︸regular part
, Zr(ω) −−−−→ω→∞
0
?
12π
∫ +∞
−∞Z(ω) eiωt dω Cut-off
frequency
Z(t) = M δ(t) + C δ(t) + K δ(t)︸ ︷︷ ︸distributional character
+ Zr(t)
?
Singularkernel
(Z ∗ u)(t) = M u(t) + C u(t) + K u(t) + (Zr ∗ u)(t)
with (δ(m) ∗ f)(t) = (δ ∗ f (m))(t) = f (m)(t)
MKCtime domainformulation
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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
Numerical problems
Soil impedance is assumed as [COTTEREAU07]:
Z(ω) = −ω2 M + iω C + K︸ ︷︷ ︸singular part
+ Zr(ω)︸ ︷︷ ︸regular part
, Zr(ω) −−−−→ω→∞
0
?
12π
∫ +∞
−∞Z(ω) eiωt dω Cut-off
frequency
Z(t) = M δ(t) + C δ(t) + K δ(t)︸ ︷︷ ︸distributional character
+ Zr(t)
?
Singularkernel
(Z ∗ u)(t) = M u(t) + C u(t) + K u(t) + (Zr ∗ u)(t) MKCtime domainformulation
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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
Cut-off frequencyInverse Discrete Time Laplace transform (closed integration contour)
Regular soil profile (velocity increases with depth);surface foundations;gives closer results to the reference solution (linear and nonlinearanalyses);cannot be used for embedded foundations or irregular layeredsoils;whether is used or not, overall good agreement (< 15%);whether is used or not, conservative solutions are obtained.
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DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
Semi-industrial application
Goal: validation of the HLTA on a semi-industrialDynamic Soil-Structure Interaction model
SMART numerical modelModel at 1/4 scale;
Shaking table;
Large number of DoF’s(∼ 20 000);
Complex dynamics (torsionaleffects);
Known RC nonlinear model(international benchmark);
No SSI experimental solution.
[Seismic design and best-estimate Methods Assessment for Reinforced concrete buildings
subjected to Torsion and non-linear effects]46 / 61
DSSI SSI forces evaluation in the time domain Numerical validation Conclusions
Nonlinear SMART numerical model
Bending 1 Bending 2 Torsional Pumping
Eigenfrequencies [Hz] 9.0 15.9 31.6 32.3
DKT shell elements (floorsand walls):GLRC_DM [KOECHLIN07]