Introduction Nonlinear ESSI in Design Summary
Use of Nonlinear,Time Domain Analysis for
Design
Nebojša Orbovic, Boris Jeremic,José Antonio Abell Mena, Chao Luo,
Robert P. Kennedy and Andrei Blaihoanu,
SMiRT, Manchester, UK,August 2015
Jeremic et al.
Nonlinear ESSI for Design
Introduction Nonlinear ESSI in Design Summary
Outline
Introduction
Nonlinear ESSI in Design
Summary
Jeremic et al.
Nonlinear ESSI for Design
Introduction Nonlinear ESSI in Design Summary
Outline
Introduction
Nonlinear ESSI in Design
Summary
Jeremic et al.
Nonlinear ESSI for Design
Introduction Nonlinear ESSI in Design Summary
Motivation
Motivation
I Improve seismic design, safety and economy, of NuclearPower Plants (NPPs)
I Follow seismic energy within NPP ESSI system
I Accurate, high fidelity numerical modeling and simulationof Nonlinear Earthquake Soil Structure Interaction (ESSI),in time and space, for realistic analysis of NPP response
I Use realistic nonlinear ESSI for design!
Jeremic et al.
Nonlinear ESSI for Design
Introduction Nonlinear ESSI in Design Summary
Motivation
Predictive CapabilitiesI High fidelity, accurate modeling and simulation: Verification
and ValidationI Verification provides evidence that the model is solved
correctly. Mathematics issue.I Validation provides evidence that the correct model is
solved. Physics issue.I Verification and validation (V&V) require huge effort!I Verification procedures in developmentI Validation almost non-existent (new U.S. DOE project will
add significantly to ESSI validation data base)I Modeling and Parametric Uncertainties (sensitivity studies
are very important)
Jeremic et al.
Nonlinear ESSI for Design
Introduction Nonlinear ESSI in Design Summary
Motivation
UncertaintiesI Modeling Uncertainty: important features are neglected
(6D ground motions, inelasticity),unrealistic and unnecessarymodeling simplifications
I Parametric Uncertainty: spatial variability, measuring andtransformation errors
5 10 15 20 25 30 35
5000
10000
15000
20000
25000
30000
SPT N Value
You
ng’s
Mod
ulus
, E (
kPa)
E = (101.125*19.3) N 0.63
−10000 0 10000
0.00002
0.00004
0.00006
0.00008
Residual (w.r.t Mean) Young’s Modulus (kPa)
Nor
mal
ized
Fre
quen
cy
Transformation of SPT N-value: 1-D Young’s modulus, E(cf. Phoon and Kulhawy (1999B))
Jeremic et al.
Nonlinear ESSI for Design
Introduction Nonlinear ESSI in Design Summary
Motivation
Realistic, Nonlinear ESSI Modeling
I Nonlinear behaviorI Nonlinear, inelastic (saturated or dry) soil/rockI Nonlinear, inelastic (saturated or dry) contactI Nonlinear, inelastic structures, systems and componentsI Buoyant (nonlinear) forces
I Full 3D (6D) Earthquake motionsI Uncertain material and loadsI Verification and validation for accurate numerical
simulationsI Real ESSI Simulator (developed in collaboration and with
the support of NRC, CNSC, DOE)
Jeremic et al.
Nonlinear ESSI for Design
Introduction Nonlinear ESSI in Design Summary
Motivation
Realistic, nonlinear ESSI for Design
I Design standards require structure to be elastic
I Anything below foundation can be modeled as nonlinear
I Possible reduction of demand due to nonlinearities insoil/rock and contact zone
I Assesment of NPP designs using sweeps ofearthquakes/motions and realistic nonlinear ESSI analysis
Jeremic et al.
Nonlinear ESSI for Design
Introduction Nonlinear ESSI in Design Summary
Outline
Introduction
Nonlinear ESSI in Design
Summary
Jeremic et al.
Nonlinear ESSI for Design
Introduction Nonlinear ESSI in Design Summary
Results of Nonlinear Analysis
Earthquake Motions
I Earthquake record: Taiwan SMART1(45), Time:11/14/1986, Station:SMART1 E02.
0 10 20 30−1.5
−1
−0.5
0
0.5
1
1.5
t[s]
Acc
eler
atio
n [m
/s2 ]
10−2
100
102
0
0.01
0.02
0.03
0.04
f(Hz)
FF
T A
mpl
itude
10−2
10−1
100
101
0
1
2
3
4
5
T[s]
Acc
eler
atio
n [m
/s2 ]
I Horizontal #1: 100%, horizontal #2: 40%, vertical: 40%
I Full application of 3D motions, no superposition allowed(nonlinear analysis)
Jeremic et al.
Nonlinear ESSI for Design
Introduction Nonlinear ESSI in Design Summary
Results of Nonlinear Analysis
Earthquake Motion Input into FEM ModelI Domain Reduction Method (Bielak et al.)I Capable of accurately inputting all body (P, SV, SH) and
surface (Rayleigh, Love, etc.) earthquake waves into afinite element model
I Free field motions needed for input effective forcesI Radiated waves from the structures leave the systemI Inside DRM finite element layer can be fully nonlinear
(elastic-plastic)
0ub
ui
0
Pe(t) 0ue
0ue Γe
Γ+
Ω+
Γ
b
b
e
e
ΓΓ e
Local feature
Ω
Jeremic et al.
Nonlinear ESSI for Design
Introduction Nonlinear ESSI in Design Summary
Results of Nonlinear Analysis
Finite Element ModelI Soil/Rock, solids, linear elastic (can be fully elastic-plastic)I Contact (soil/rock – foundation slab) fully nonlinear,
Coulomb friction (friction coefficient µ = 0.5, taking intoaccount plastic sheets beneath foundation) and gaping
I Structure (stick model) linear elastic (can use a far moresophisticated structural model, however this is ademonstration)
I Seismic input using DRM
Jeremic et al.
Nonlinear ESSI for Design
Introduction Nonlinear ESSI in Design Summary
Results of Nonlinear Analysis
Foundation – Soil/Rock SlipI Foundation slab slips significantly during an earthquakeI Base isolation (?!) and energy dissipationI Soil on the side restricts movementsI Minimal gaping as contact sleeps before slab lifts-off
5 10 15 20 25 30Time [sec]
2.52.01.51.00.50.00.51.01.52.0
DX
[cm
]
Sliping of foundation
Jeremic et al.
Nonlinear ESSI for Design
Introduction Nonlinear ESSI in Design Summary
Results of Nonlinear Analysis
Nonlinear vs Linear Response, Top of SoilI Reduction in soil horizontal demandI Amplification of vertical due to pounding upon contactI Soil horizontal and vertical peaks at the same frequency,
hence vertical motions are from a Rayleigh surface wave
2 4 6 8 10 12 14Frequency, f [Hz]
0
1
2
3
4
5
SAX [g
]
With contactsLinear
2 4 6 8 10 12 14Frequency, f [Hz]
0
1
2
3
4
5
SAZ [g
]
With contactsLinear
horizontal verticalJeremic et al.
Nonlinear ESSI for Design
Introduction Nonlinear ESSI in Design Summary
Results of Nonlinear Analysis
Nonlinear vs Linear Response, Foundation SlabI Horizontal reduced at high frequency, due to slip,I Horizontal slightly increased at low frequency, due to slip,I Vertical reduced
2 4 6 8 10 12 14Frequency, f [Hz]
0
1
2
3
4
5
SAX [g
]
With contactsLinear
2 4 6 8 10 12 14Frequency, f [Hz]
0
1
2
3
4
5
SAZ [g
]
With contactsLinear
horizontal verticalJeremic et al.
Nonlinear ESSI for Design
Introduction Nonlinear ESSI in Design Summary
Results of Nonlinear Analysis
Nonlinear vs Linear Response, Top of Containment
I Significant reduction of horizontal motionsI Reduction of vertical motions
2 4 6 8 10 12 14Frequency, f [Hz]
0
5
10
15
20
25
30
SAX [g
]
With contactsLinear
2 4 6 8 10 12 14Frequency, f [Hz]
0
5
10
15
20
25
30
SAZ [g
]
With contactsLinear
horizontal vertical
Jeremic et al.
Nonlinear ESSI for Design
Introduction Nonlinear ESSI in Design Summary
Results of Nonlinear Analysis
Nonlinear vs Linear Response, Comments
I In general, significant reductions in motions for nonlinearresponse, both horizontally and vertically
I Larger horizontal slip, low frequency response
I Structure is still linear elastic (by modeling) and hencesatisfies standard design
Jeremic et al.
Nonlinear ESSI for Design
Introduction Nonlinear ESSI in Design Summary
Outline
Introduction
Nonlinear ESSI in Design
Summary
Jeremic et al.
Nonlinear ESSI for Design
Introduction Nonlinear ESSI in Design Summary
Concluding Remarks
I Nonlinear analysis can be used for design
I Potential for reduction of demand with realistic nonlinearanalysis
I Assesment of NPP SSI systems using fully nonlinear,realistic ESSI analysis
Jeremic et al.
Nonlinear ESSI for Design
