Post on 14-May-2018
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Motivation ESSI Simulator System Summary
Earthquake Soil Structure Interaction forNuclear Power Plants,
Modeling and Computational Issues
B. JeremicN. Tafazzoli, P. Tasiopoulou, J.A. Abell Mena, B. Kamrani,C.-G. Jeong, F. Pisanò, M. Martinelli, K. Sett, M. Taiebat
Professor, University of California, DavisFaculty Scientist, Lawrence Berkeley National Laboratory, Berkeley
CompDyn, Kos, Greece, June, 2013
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Outline
MotivationProblem – SolutionUncertainty in Modeling
ESSI Simulator SystemSystem ComponentsVerification and Validation SuiteSelect Examples: Foundation Slip and Stochastic
Summary
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Problem – Solution
Outline
MotivationProblem – SolutionUncertainty in Modeling
ESSI Simulator SystemSystem ComponentsVerification and Validation SuiteSelect Examples: Foundation Slip and Stochastic
Summary
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Problem – Solution
The Problem
I Seismic response of Nuclear Power Plants (f ≤ 50Hz!(20Hz))
I 3D, inclined seismic motions: body and surface waves
I Inelasticity (elastic, damage, plastic behavior of materials:soil, rock, concrete, steel, rubber, contact, etc.)
I Full coupling of pore fluids with soil, rock and concreteskeleton, including buoyancy effects
I Uncertainty in seismic sources, path, soil/rock andstructural response
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Problem – Solution
SolutionI Physics based modeling and simulation of seismic
behavior of soil-structure systems (NPP structures,components and systems)
I Development and use of high fidelity time domain,nonlinear numerical models, in deterministic andprobabilistic spaces, for licensing and professionalpractice (every day use)
I Accurate following of the flow of seismic energy (inputand dissipation) within soil-structure NPP system
I Directing, in space and time, with high (known)confidence, seismic energy flow in thesoil-foundation-structure system
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Problem – Solution
NPP Model(s)
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Uncertainty in Modeling
Outline
MotivationProblem – SolutionUncertainty in Modeling
ESSI Simulator SystemSystem ComponentsVerification and Validation SuiteSelect Examples: Foundation Slip and Stochastic
Summary
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Uncertainty in Modeling
Modeling Uncertainty
I Simplified (or inadequate/wrong) modeling: importantfeatures are missed (seismic ground motions, etc.)
I Introduction of uncertainty and (unknown) lack of accuracyin results due to use of un-verified simulation tools(software quality, etc.)
I Introduction of uncertainty and (unknown) lack of accuracyin results due to use of un-validated models (due to lack ofquality validation experiments)
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Uncertainty in Modeling
Complexity of and Uncertainty in Ground Motions
I 6D (3 translations, 3 rotations)
I Vertical motions usually neglected
I Rotational components usually not measured andneglected
I Lack of models for such 6D motions (from measured data))
I Sources of uncertainties in ground motions (Source, Path(Rock), Soil/Rock))
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Uncertainty in Modeling
Material Behavior Inherently Uncertain
I (a) Spatialvariability
I Point-wiseuncertainty,(b) testingerror,(c) transformationerror
(Mayne et al. (2000)
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
System Components
Outline
MotivationProblem – SolutionUncertainty in Modeling
ESSI Simulator SystemSystem ComponentsVerification and Validation SuiteSelect Examples: Foundation Slip and Stochastic
Summary
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
System Components
Desirable Modeling and Simulation CapabilitiesI Body (SH, SV, P) and Surface (Rayleigh, Love, etc) seismic
motions modeling and their input into finite element modelsI Elastic-plastic modeling of dry and saturated soil/rock
behavior beneath foundationsI Elastic-plastic modeling of soil/rock (limited data)I Soil/rock - foundation contact zone modeling (for dry and
saturated conditions)I Verification and Validation suiteI High performance, parallel simulation using dynamic
domain decomposition (Plastic Domain Decomposition) forelastic-plastic simulations
I Probabilistic elasto-plasticity and stochastic elastic-plasticfinite element methods
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
System Components
ESSI Simulator System
I The ESSI-Program is a 3D, nonlinear, time domain,parallel finite element program specifically developed forHi-Fi modeling and simulation of Earthquake Soil/RockStructure Interaction problems for NPPs onESSI-Computer.
I The ESSI-Computer is a distributed memory parallelcomputer, a cluster of clusters with multiple performanceprocessors and multiple performance networks.
I The ESSI-Notes represent a hypertext documentationsystem detailing modeling and simulation of NPP ESSIproblems.
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
System Components
ESSI Simulator ProgramI Based on a Collection of Useful Libraries (modular,
portable)
I Library centric software design
I Solids (dry, saturated), beams, shells, contacts, elastic orelastic-plastic
I Various public domain licenses (GPL, LGPL, BSD, CC)
I Verification (extensive) and Validation (not much)
I Program documentation (part of ESSI Notes)
I Target users: US-NRC staff, CNSC staff, IAEA, LBNL, INL,DOE, professional practice collaborators, expert users
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
System Components
ESSI Simulator ComputerA distributed memory parallel (DMP) computer designed forhigh performance, parallel finite element simulations
I Multiple performance CPUsand Networks
I Most cost-performanceeffective
I Source compatibility withany DMP supercomputer
I Current systems: 208CPUs,and 40CPUs (8+32) and160CPUs (8x5+2x16+24+64)...
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
System Components
ESSI Simulator Notes
I A hypertext documentation system describing in detailmodeling and simulations of NPP ESSI problems
I Theoretical and Computational Formulations (FEM, EL-PL,Static and Dynamic solution, Parallel Computing)
I Software and Hardware Platform Design (OO Design,Library centric design, API, DSL, Software Build Process,Hardware Platform)
I Verification and Validation (code V, Components V, Staticand Dynamic V, Wave Propagation V)
I Application to Practical Nuclear Power Plant EarthquakeSoil/Rock Structure Interaction Problems (ESSI with 3D,inclined, uncorrelated seismic waves, ESSI with foundationslip, Isolators)
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
System Components
ESSI: High Fidelity ModelingI Seismic energy influx, body and surface waves, 3D,
inclinedI Mechanical dissipation outside of SSI domain:
I Radiation of reflected wavesI Radiation of oscillating SSI system
I Mechanical dissipation inside SSI domain:I Plasticity of soil/rock subdomainI Viscous coupling of porous solid with pore fluid (air, water)I Plasticity and viscosity of foundation – soil/rock contactI Plasticity/damage of the structureI Viscous coupling of structure/foundation with fluids
I Numerical energy dissipation/production
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
System Components
ESSI: High Performance, Parallel Computing
I The ESSI Program can be used in both sequential andparallel modes
I For high fidelity models, parallel is really the only option
I High performance, parallel computing using PlasticDomain Decomposition Method, for elastic-plasticcomputations (dynamic computational load balancing)
I Developed for multiple/variable capability CPUs andnetworks (DMP and SMPs)
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Verification and Validation Suite
Outline
MotivationProblem – SolutionUncertainty in Modeling
ESSI Simulator SystemSystem ComponentsVerification and Validation SuiteSelect Examples: Foundation Slip and Stochastic
Summary
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Verification and Validation Suite
Verification, Validation (V&V) and PredictionI Verification: the process of determining that a model
implementation accurately represents the developer’sconceptual description and specification. Mathematicsissue. Verification provides evidence that the model issolved correctly.
I Validation: The process of determining the degree to whicha model is accurate representation of the real world fromthe perspective of the intended uses of the model. Physicsissue. Validation provides evidence that the correct modelis solved.
I Prediction: use of computational model to foretell the stateof a physical system under consideration under conditionsfor which the computational model has not been validated
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Verification and Validation Suite
Role of Verification and Validation
MathematicalModel
ComputerImplementationDiscrete Mathematics
Continuum Mathematics
Programming
Analysis
Code Verification
SimulationComputer
ValidationModel
Model Discovery
and Building
Knowledge aboutReality
Oberkampf et al. Oden et al.
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Verification and Validation Suite
V&V for ESSI Modeling and Simulations
I Code Verification
I Material modeling and simulation (elastic, elastic-plastic...)
I Finite elements (solids, structural, special...)
I Solution advancement algorithms (static, dynamic...)
I Seismic input and radiation
I Finite element model verification
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Verification and Validation Suite
Constitutive Integration Error MapsNormalized error: δr =
√(σij − σ∗ij )(σij − σ∗ij )/
√σ0
pqσ0pq
SaniSand2004, rot. kinematic hardening, bounding surface:
0 50 100 150 2000
20
40
60
80
100
p (kPa)
q (k
Pa)
0.05
0.05
0.1
0.1
0.1
0.1
0.15
0.15
0.15
0.15
0.15
0.2
0.2
0.2
0.2
0.2
0.2
0.25
0.25
0.25
0.3
0.3
0.35
0.4
(a) At θ = 0
0 0.2 0.4 0.6 0.8 10
20
40
60
80
100
θ (rad)
q (k
Pa)
0.05 0.05
0.10.1
0.150.15
0.20.2
0.25
(b) At p = 100 kPa
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Verification and Validation Suite
Material Model Validation (SanSand2004)
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Verification and Validation Suite
Verification ANDES Shell: Static
1
2
3
4
5
...
Mesh
Test 1 Test 2 Test 3 Test 4
1
2
3
4
5
6
7
8
Mesh
Test 5 Test 6 Test 7 Test 8
Material parameters chosen such that the exact solution isuz = 100.000 T = 1.0 s.Nz = 2, uz = 96.212 ; Nz = 7, uz = 100.096
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Verification and Validation Suite
Verification ANDES Shell: Dynamic
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Verification and Validation Suite
Verification for 27 Node Brick
d =PL3
3EI=
9N× 1000m3
3× 100000Pa× 112 m4
= 0.36m
errors : 0.47% 3.96% 22%
for nodal offset: 40% error: 2%
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Verification and Validation Suite
Shock Wave Propagation, Step Displacement
x
x = 0
Boundary Condition:δ (0, t) = 1 x 10-3 cm
ux = Ux = 1 x 10-3 cm
0.01 cm
4 cm ux , Ux
(10-3 cm)
t (sec)
1
Semi-finiteSoil column
No lateral flow.No lateral
displacements.0
(a) (b) (c)
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Verification and Validation Suite
Shock Wave Propagation: Porous Solid, Pore Fluid
4 6 8 10 12 14 160
0.2
0.4
0.6
0.8
1
x 10‐3 FEM Vs Analytical Solution
t [10‐6 sec]
solid
displacem
ent (cm
)
FEM (k = 10‐5 cm3s/g)
FEM (k = 10‐6 cm3s/g)
FEM (k = 10‐8 cm3s/g)
Analytical Solution (k = 10‐5 cm3s/g)
Analytical Solution (k = 10‐6 cm3s/g)
Analytical Solution (k = 10‐8 cm3s/g)
4 6 8 10 12 14 160
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6x 10
‐3 FEM Vs Analytical Solution
t [10‐6 sec]fluid displacemen
t (cm
)
FEM (k = 10‐5 cm3s/g)
FEM (k = 10‐6 cm3s/g)
FEM (k = 10‐8 cm3s/g)
Analytical Solution (k = 10‐5 cm3s/g)
Analytical Solution (k = 10‐6 cm3s/g)
Analytical Solution (k = 10‐8 cm3s/g)
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Verification and Validation Suite
Verification for Dry Contact Element:Truss Model, Normal Displacement
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Verification and Validation Suite
Solution Advancement(Newmark, Hilber-Hughes-Taylor)
I Variable integrationsteps sizes,parameters (α, β, γ)
I Compare withtheoreticalalgorithmic damping(spectral radius)and period shift
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8dt/T
0
2
4
6
8
10
12
14
ξ
Numerical damping ratio [%]
First mode
Second mode
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8dt/T
0
2
4
6
8
10
12
14
Tn−T
T
Relative Period Error
First mode
Second mode
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Verification and Validation Suite
Seismic Body and Surface Waves
I Both body (P, SV and SH) and surface (Rayleigh, Love,etc.) waves are present
I Surface waves carry most seismic energy
I Analytic (Aki and Richards, Trifunac and Lee, Hisada et al.,fk, etc.) and numerically generated, 3D, inclined (plane)body and surface waves are used in tests
I Seismic moment from a point source at 2km depth used
I Stress drop at the source: Ricker and/or Ormsby wavelets
I Seismic input into FE model using the DRM (Bielak at al.)
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Verification and Validation Suite
Plane Wave Model0m
0m
70m
240m
DRM Layer
2km10km
5km
x
y
xy
1
1
22
2km
0.2km
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Verification and Validation Suite
Seismic Source Mechanics
Stress drop, Ormsby wavelet
-0.003
-0.0025
-0.002
-0.0015
-0.001
-0.0005
0
0.0005
0.001
0 1 2 3 4 5 6 7
Dis
plac
emen
t (m
)
Time (s)
0
5e-06
1e-05
1.5e-05
2e-05
2.5e-05
3e-05
3.5e-05
4e-05
4.5e-05
0 5 10 15 20
FF
T F
unct
ion
Am
plitu
de
Frequency (Hz)
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Verification and Validation Suite
Middle (Structure Location) Plane, Top 2km
2km10km
5km
x
y
xy
1
1
22
2km
0.2km
0 0 2 4 6 8 10 12
Time (s)
0.2 m/s2
z=3000m
z=3200m
z=3400m
z=3600m
z=3800m
z=4000m
z=4200m
z=4400m
z=4600m
z=4800m
z=5000m
0 0 2 4 6 8 10 12
Time (s)
0.2 m/s2
z=3000m
z=3200m
z=3400m
z=3600m
z=3800m
z=4000m
z=4200m
z=4400m
z=4600m
z=4800m
z=5000m
horizontal accelerations vertical accelerations
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Verification and Validation Suite
Verification: Displacements, Top Middle Point
(X) (Z)
-0.0004
-0.0003
-0.0002
-0.0001
0
0.0001
0.0002
0.0003
0.0004
0 2 4 6 8 10 12
Dis
plac
emen
t (m
)
Time (s)
DRMFault Slip Model
-0.0004
-0.0003
-0.0002
-0.0001
0
0.0001
0.0002
0.0003
0.0004
0 2 4 6 8 10 12D
ispl
acem
ent (
m)
Time (s)
DRMFault Slip Model
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Verification and Validation Suite
Verification: Disp. and Acc., Out of DRM
Displacement Acceleration
-0.0004
-0.0003
-0.0002
-0.0001
0
0.0001
0.0002
0.0003
0.0004
0 2 4 6 8 10 12
Dis
plac
emen
t (m
)
Time (s)
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0 2 4 6 8 10 12A
ccel
erat
ion
(m/s
2 )Time (s)
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Select Examples: Foundation Slip and Stochastic
Outline
MotivationProblem – SolutionUncertainty in Modeling
ESSI Simulator SystemSystem ComponentsVerification and Validation SuiteSelect Examples: Foundation Slip and Stochastic
Summary
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Select Examples: Foundation Slip and Stochastic
Influence of Inelastic Foundation-Soil/Rock Contact onthe NPP Response
I Soil/rock – foundation interface slip behavior
I Changes in Earthquake Soil/Rock Structure Interaction(reduction or increase in demand)
I Dissipation of seismic energy in the slip plane
I Passive (and active) base isolation
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Select Examples: Foundation Slip and Stochastic
Example Model, ESSI with Slip
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Select Examples: Foundation Slip and Stochastic
Full 3D (wave at 45o) Ricker Wavelet
-4
-3
-2
-1
0
1
2
3
4
5
6
0 0.5 1 1.5 2 2.5 3 3.5 4
Acc
eler
atio
n (m
/s2 )
Time (s)
0
2e-05
4e-05
6e-05
8e-05
0.0001
0.00012
0.00014
0.00016
0 2 4 6 8 10
Ric
ker2
nd F
FT
Am
plitu
de
Frequency (Hz)
0m 5000m 10000m
5000m
0m
2000m
2000
m
Fault
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Select Examples: Foundation Slip and Stochastic
Acc. Response for a Full 3D (at 45◦) Ricker Wavelet
top X
-40
-20
0
20
40
0 1 2 3 4 5 6 7 8
Acc
eler
atio
n (m
/s2)
Time (s)
Slip BehaviorNo-slip Behavior
top Z
-40
-20
0
20
40
0 1 2 3 4 5 6 7 8
Acc
eler
atio
n (m
/s2)
Time (s)
Slip BehaviorNo-slip Behavior
bottom X
-40
-20
0
20
40
0 1 2 3 4 5 6 7 8
Acc
eler
atio
n (m
/s2)
Time (s)
Slip BehaviorNo-slip Behavior
bottom Z
-40
-20
0
20
40
0 1 2 3 4 5 6 7 8
Acc
eler
atio
n (m
/s2)
Time (s)
Slip BehaviorNo-slip Behavior
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Select Examples: Foundation Slip and Stochastic
FFT Response for a Full 3D (at 45◦) Ricker Wavelet
top X
0
1
2
3
4
5
6
0 5 10 15 20
FF
T A
mpl
itude
(m
s)
Frequency (Hz)
Slip BehaviorNo-slip Behavior
top Z
0
1
2
3
4
5
6
0 5 10 15 20
FF
T A
mpl
itude
(m
s)
Frequency (Hz)
Slip BehaviorNo-slip Behavior
bottom X
0
1
2
3
4
5
6
0 5 10 15 20
FF
T A
mpl
itude
(m
s)
Frequency (Hz)
Slip BehaviorNo-slip Behavior
bottom Z
0
1
2
3
4
5
6
0 5 10 15 20
FF
T A
mpl
itude
(m
s)
Frequency (Hz)
Slip BehaviorNo-slip Behavior
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Select Examples: Foundation Slip and Stochastic
SPT Based Determination of Young’s Modulus
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))Histogram of the residual (w.r.t the deterministic transformationequation) Young’s modulus, along with fitted probability densityfunction
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Select Examples: Foundation Slip and Stochastic
Uncertainty Propagation through Constitutive Eq.
I Incremental el–pl constitutive equation ∆σij = Dijkl∆εkl
Dijkl =
Del
ijkl for elastic
Delijkl −
DelijmnmmnnpqDel
pqkl
nrsDelrstumtu − ξ∗r∗
for elastic–plastic
I What if all (any) material parameters are uncertainI PEP and SEPFEM methods for spatially variable and point
uncertain material
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Select Examples: Foundation Slip and Stochastic
Eulerian–Lagrangian FPK Equation and (SEP)FEMI Advection-diffusion equation
∂P(σij , t)∂t
= − ∂
∂σab
[N(1)
ab P(σij , t)−∂
∂σcd
{N(2)
abcdP(σij , t)}]
I Complete probabilistic description of response
I Second-order exact to covariance of time (exact meanand variance)
I Any uncertain FEM problem (Mu + Cu + Ku = F) withI uncertain material parameters (stiffness matrix K),I uncertain loading (load vector F)
can be analyzed using PEP and SEPFEM to obtain PDFsof DOFs, stress, strain...
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Select Examples: Foundation Slip and Stochastic
Spectral Stochastic Elastic–Plastic FEM
I Minimizing norm of error of finite representation usingGalerkin technique (Ghanem and Spanos 2003):
N∑n=1
K epmndni +
N∑n=1
P∑j=0
dnj
M∑k=1
CijkK′epmnk = 〈Fmψi [{ξr}]〉
K epmn =
∫D
BnEepBmdV K′epmnk =
∫D
Bn√λkhkBmdV
Cijk =⟨ξk (θ)ψi [{ξr}]ψj [{ξr}]
⟩Fm =
∫DφNmdV
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Select Examples: Foundation Slip and Stochastic
Full PDFs of all DOFs (and σij , εij , etc.)
I Stochastic Elastic-PlasticFinite Element Method(SEPFEM)
I Dynamic case
I Full PDF ateach time step ∆t
−400
0
200400
0
0.02
0.04
0.06
5
10
15
20
Tim
e (s
ec)
Displacement (mm)
−200
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Select Examples: Foundation Slip and Stochastic
PDF at each ∆t (say at 6 s)
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0.0005
0.001
0.0015
0.002
0.0025
Displacement (mm)
Real Soil Data
Conservative Guess
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Select Examples: Foundation Slip and Stochastic
PDF→ CDF (Fragility) at 6 s
−1000 −500 500 1000
0.2
0.4
0.6
0.8
1
CD
F
Displacement (mm)
Real Soil DataConservative Guess
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues
Motivation ESSI Simulator System Summary
Summary
I High fidelity, extensive V & V, time domain, nonlinear,earthquake soil structure interaction (ESSI) modeling andsimulations (deterministic and probabilistic) for nuclearpower plant licensing and design
I The ESSI Simulator System (Program, Computer, Notes)
I Educational effort is essential (US-NRC, CNSC, IAEA,LBNL, INL, companies), seminars, short courses
I Funding from the US-NRC, US-DOE, US-NSF, and theCNSC is much appreciated
Jeremic et al.
Earthquake Soil Structure Interaction for Nuclear Power Plants, Modeling and Computational Issues