Before We Start Why Do You Trust a Simulation? Examples Summary

On Computational Simulations andPredictions

Boris Jeremic

Department of Civil and Environmental EngineeringUniversity of California, Davis

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Outline

Before We Start

Why Do You Trust a Simulation?Verification, ValidationPrediction

ExamplesPiles in Layered SoilsLiquefying SoilsESS Simulations

Summary

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Before We Start

Important SourcesI W. L. OBERKAMPF, T. G. TRUCANO, AND C. HIRSCH.

Verification, validation and predictive capability incomputational engineering and physics. In Proceedings ofthe Foundations for Verification and Validation on the 21stCentury Workshop, pages 1–74, Laurel, Maryland,October 22-23 2002. Johns Hopkins University / AppliedPhysics Laboratory.

I P. J. ROACHE. Verification and Validation in ComputationalScience and Engineering. Hermosa publishers, 1998.ISBN 0-913478-08-3.

I Material from Verification and Validation in ComputationalMechanics web site http://www.usacm.org/vnvcsm/at the USACM.

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Before We Start

Motivation

I How do we use experiments to develop and improvemodels?

I How much can (should) we trust model implementations(verification)?

I How much can (should) we trust numerical simulations(validation)?

I How good are our predictions?

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Before We Start

Verification, Validation 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 Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Verification, Validation

Outline

Before We Start

Why Do You Trust a Simulation?Verification, ValidationPrediction

ExamplesPiles in Layered SoilsLiquefying SoilsESS Simulations

Summary

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Verification, Validation

Importance of V & V

I V & V procedures are the primary means of assessingaccuracy in modeling and computational simulations

I V & V procedures are the tools with which we buildconfidence and credibility in modeling and computationalsimulations

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Verification, Validation

Maturity of Computational SimulationsNRC committee (1986) identified stages of maturity in CFD

I Stage 1: Developing enabling technologies (scientificpapers published)

I Stage 2: Demonstration of and Confidence in technologiesand tools (capabilities and limitations of technologyunderstood)

I Stage 3: Compilation of technologies and tools(capabilities and limitations of technology understood)

I Stage 4: Spreading of the effective use (changes theengineering process, value exceeds expectations)

I Stage 5: Mature capabilities (fully dependable, costeffective design applications)

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Verification, Validation

Role of Verification and Validation

MathematicalModel

ComputerImplementationDiscrete Mathematics

Continuum Mathematics

Programming

Analysis

Code Verification

SimulationComputer

ValidationModel

Reality Model Discovery

and Building

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Verification, Validation

Fundamentals of Verification and Validation

Real World

Benchmark PDE solutionBenchmark ODE solutionAnalytical solution

Complete System

Subsystem Cases

Benchmark Cases

Unit ProblemsHighly accurate solution

Experimental Data

Conceptual Model

Computational Model

Computational Solution

ValidationVerification

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Verification, Validation

Verification: Model is solved correctly (Mathematics)Verification: The process of determining that a modelimplementation accurately represents the developer’sconceptual description and specification.

I Identify and remove errors in computer codingI Numerical algorithm

verificationI Software quality

assurance practiceI Quantification of the

numerical errors incomputed solution

Benchmark PDE solutionBenchmark ODE solutionAnalytical solution

Highly accurate solution

Conceptual Model

Computational Model

Computational Solution

Verification

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Verification, Validation

Validation: Correct model is solved (Physics)Validation: The process of determining the degree to which amodel is accurate representation of the real world from theperspective of the intended uses of the model.

I Tactical goal:Identification and minimization ofuncertainties and errors inthe computational model

I Strategic goal:Increase confidence inthe quantitative predictivecapability ofthe computational model

Real World

Complete System

Subsystem Cases

Benchmark Cases

Unit Problems

Experimental Data

Conceptual Model

Computational Model

Computational Solution

Validation

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Verification, Validation

Validation Procedure Uncertainty

I Aleatory uncertainty→ inherent variation associated withthe physical system of the environment (variation inexternal excitation, material properties...). Also knowknown as irreducible uncertainty, variability and stochasticuncertainty.

I Epistemic uncertainty→ potential deficiency in any phaseof the modeling process that is due to lack of knowledge(poor understanding of mechanics...). Also known asreducible uncertainty, model form uncertainty andsubjective uncertainty

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Verification, Validation

Types of Physical Experiments

I Traditional ExperimentsI Improve the fundamental understanding of physics involvedI Improve the mathematical models for physical phenomenaI Assess component performance

I Validation ExperimentsI Model validation experimentsI Designed and executed to quantitatively estimate

mathematical model’s ability to simulate well definedphysical behavior

I The simulation tool (SimTool) (conceptual model,computational model, computational solution) is thecustomer

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Verification, Validation

Validation ExperimentsI A validation experiment should be jointly designed and

executed by experimentalist and computationalistI A validation Experiment should be designed to capture the

relevant physicsI A validation experiment should use any possible synergism

between experiment and computational approachesI Maintain independence between computational and

experimental resultsI Validate experiments on unit level problems, hierarchy of

experimental measurements should be made whichpresent an increasing range of computational difficulty

I Experimental uncertainty analysis should be developedand employed

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Prediction

Outline

Before We Start

Why Do You Trust a Simulation?Verification, ValidationPrediction

ExamplesPiles in Layered SoilsLiquefying SoilsESS Simulations

Summary

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Prediction

Prediction

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

I Validation does not directly make a claim about theaccuracy of a prediction

I Computational models are easily misused (unintentionallyor intentionally)

I How closely related are the conditions of the prediction andspecific cases in validation database

I How well is physics of the problem understood

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Prediction

Relation Between Validation and Prediction

Quantification of confidence in a prediction:

I How do I quantify verification and its inference value in aprediction?

I How do I quantify validation and its inference value in apredictions?

I How far are individual experiments in my validationdatabase from my physical system of interest?

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Prediction

Application Domain Complete or Partial Overlap

System Parameter

Sys

tem

com

plex

ity

DomainValidation

DomainApplication Domain

Application

System Parameter

Sys

tem

com

plex

ity

DomainValidation

I Rarely applicable to engineering systems, certainly not forbridges, buildings, port facilities, dams...

I Even if the engineering system is small, environmentalinfluences (generalized loads, conditions, wear and tare)are hard to predict

I Human factors (Mars rover example: memory overflow,operator forgot to flush the memory...)

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Prediction

Application Domain – No Overlap

System Parameter

Sys

tem

com

plex

ity

ApplicationDomain

DomainValidation

Inference

I Inference⇒ Based on physics or statistics (or both)I Validation domain is actually an aggregation of tests and

thus might not be convex (bifurcation of behavior)I Experimental facilities provide for validation domain that

are exclusively non–overlapping with the applicationdomain.

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Prediction

Importance of Models and Numerical Simulations

I Verified and Validated models can be used for assessingbehavior of

I components orI complete systems,

I with the understanding that the environmental influencescannot all be taken into the account prior to operation

I but with a good model, their influence on system behaviorcan be assessed as need be (before or after the event)

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Prediction

Prediction under Uncertainty

I Ever present uncertainty needs to be estimated forpredictions

I Identify all relevant sources of uncertainty

I Create mathematical representation of individual sources

I Propagate representation of sources through modeling andsimulation process

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Piles in Layered Soils

Outline

Before We Start

Why Do You Trust a Simulation?Verification, ValidationPrediction

ExamplesPiles in Layered SoilsLiquefying SoilsESS Simulations

Summary

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Piles in Layered Soils

Single Pile in Layered Soils: Model

����������������������������������������������������

����������������������������������������������������

1.72m

1.72m

7.86m

0.429m 2.40m

Interface

Case 3&4: SandCase 1&2: Clay

Case 1 & 2: ClayCase 3 & 4: Sand

Case 2&3: SandCase 1&4: Clay

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Piles in Layered Soils

Available Data for Prototype

I Sand:I friction angle φ of 37.1o,I Shear modulus at a depth of 13.7 m of 8960 kPa (Eo =

17400 kPa),I Poisson ratio of 0.35I Unit weight of 14.50 kN/m3.I Dilation angle 0o

I Clay (made up)I Shear strength 21.7 kPaI Young’s modulus 11000 kPaI Poisson ratio 0.45I Unit weight 13.7 kN/m3

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Piles in Layered Soils

Single Pile in Sand: M, Q, p

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Piles in Layered Soils

Single Pile in Sand with Clay Layer: M, Q, p

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Piles in Layered Soils

Single Pile in Sand: p − y Response

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Piles in Layered Soils

Single Pile in Sand with Clay Layer: p − y Response

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Piles in Layered Soils

p − y Pressure Ratio Reduction for Layered Soils

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Liquefying Soils

Outline

Before We Start

Why Do You Trust a Simulation?Verification, ValidationPrediction

ExamplesPiles in Layered SoilsLiquefying SoilsESS Simulations

Summary

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Liquefying Soils

VerificationNumber ofclosed formsolutions used(elastic, coupled,static and dynamic) 0 2 4 6 8 10 12 14 16

−0.2

0

0.2

0.4

0.6

0.8

1

time (µsec)

Sol

id D

ispl

. (x1

0−3 cm

)

@ depth of 1cm

0 2 4 6 8 10 12 14 16−0.2

0

0.2

0.4

0.6

0.8

1

time (µsec)

Flu

id D

ispl

. (x1

0−3 cm

)

Closed form, K=10−8m/s (k=10−9cm3s/gr)u elementup elementupU element

Note: All simulations withγ=0.65, K=10−8m/s,200 Elements, L=4cm(.02x.02x.02cm)

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Liquefying Soils

Material Model Validation (Dafalias-Manzari)

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Liquefying Soils

Loose Sand, Level Ground

−20

0

20

E10

τ h (kP

a)

−20

0

20

E07

τ h (kP

a)

−20

0

20

E04

τ h (kP

a)

0 50 100−20

0

20

E01

τ h (kP

a)

σ′v (kPa)

0

1E10

Ru

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1E07

Ru

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Ru

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Ru

Time (s)

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τ h (kP

a)

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τ h (kP

a)

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τ h (kP

a)

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0

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τ h (kP

a)

εh (%)

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0

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Dz

(cm

)

SoilWater

−4

0

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H

Dz

(cm

)

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0

4

E

Dz

(cm

)

0 20 40 60 80−4

0

4

B

Dz

(cm

)

Time (s)

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Liquefying Soils

Loose Sand, Sloping Ground

−25

0

25

E10

τ h (kP

a)

−25

0

25

E07

τ h (kP

a)

−25

0

25

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τ h (kP

a)

0 50 100−25

0

25

E01

τ h (kP

a)

σ′v (kPa)

0

1E10

Ru

0

1E07

Ru

0 20 40 60 800

1E04

Ru

0 20 40 60 800

1E01

Ru

Time (s)

−25

0

25

E10

τ h (kP

a)

−25

0

25

E07

τ h (kP

a)

−25

0

25

E04

τ h (kP

a)

0 10 20−25

0

25

E01

τ h (kP

a)

εh (%)

0

1.5

K

Dx

(m)

0

1.5

H

Dx

(m)

0

1.5

E

Dx

(m)

0 10 200

1.5

B

Dx

(m)

Time (s)

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

ESS Simulations

Outline

Before We Start

Why Do You Trust a Simulation?Verification, ValidationPrediction

ExamplesPiles in Layered SoilsLiquefying SoilsESS Simulations

Summary

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

ESS Simulations

Detailed 3D, FEM model

I Construction processI Two types of soil: stiff soil (UT, UCD), soft soil (Bay Mud)I Deconvolution of given surface ground motionsI Use of the DRM (Bielak et al.) for seismic inputI Soil:

I Sand (single monotonic triax test from UT...)I Clay (made up, bay mud, total stress)

I Piles→ beam-column elements in soil holesI Structural model: collaboration UCD, UCB and UWI No artificial damping (only mat. dissipation, radiation)

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

ESS Simulations

Element Size Issue

Filtering of frequencies depending on element size (want atleast 10 nodes per full wave form)

model size (el) el. size fcutoff min. G/Gmax γ

12K 1.0 m 10 Hz 1.0 <0.5 %15K 0.9 m >3 Hz 0.08 1.0 %150K 0.3 m 10 Hz 0.08 1.0 %500K 0.15 m 10 Hz 0.02 5.0 %

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

ESS Simulations

FEM Mesh (one of)

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

ESS Simulations

Simulation Results

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Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

ESS Simulations

Northridge Input Motions

0 10 20 30 40 50 60

−2

0

2

Time (s)

Acc

eler

atio

n (m

/s2 ) Acceleration Time Series − Input Motion (NORTHRIDGE EARTHQUAKE, 1994)

0 10 20 30 40 50 60−0.2

0

0.2

Time (s)

Dis

plac

emen

t (m

) Displacement Time Series − Input Motion (NORTHRIDGE EARTHQUAKE, 1994)

1 2 3 4 5 6 7 8 9 100

1

2

Period (s)Fou

rier

Am

plitu

de (

m/s

2 )

Acceleration Frequency Content − Input Motion (NORTHRIDGE EARTHQUAKE, 1994)

1 2 3 4 5 6 7 8 9 100

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0.4

Period (s)Fou

rier

Am

plitu

de (

m)

Displacement Frequency Content − Input Motion (NORTHRIDGE EARTHQUAKE, 1994)

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

ESS Simulations

Short Period E.: Left Bent, Structure and Soil, Disp.

0 10 20 30 40 50 60

−0.2

−0.1

0

0.1

0.2

0.3

Time (s)

Dis

plac

emen

t (m

)

SSS CCC SSC CCS SCS CSC SCC CSS

0 10 20 30 40 50 60

−0.2

−0.1

0

0.1

0.2

0.3

Time (s)

Dis

plac

emen

t (m

)

SSS CCC SSC CCS SCS CSC SCC CSS Freefield Input Motion

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

ESS Simulations

Short Period E.: Left Bent, Structure and Soil, Acc.

0 10 20 30 40 50 60−3

−2

−1

0

1

2

3

Time (s)

Acc

eler

atio

n (m

/s2 )

SSS CCC SSC CCS SCS CSC SCC CSS

0 10 20 30 40 50 60−3

−2

−1

0

1

2

3

Time (s)

Acc

eler

atio

n (m

/s2 )

SSS CCC SSC CCS SCS CSC SCC CSS Freefield Input Motion

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

ESS Simulations

Short Period E.: Left Bent, Structure and Soil, Acc.Sp.

0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

2

4

6

8

10

Period (s)

Fou

rier

Am

plitu

de (

m/s

2 )

SSS CCC SSC CCS SCS CSC SCC CSS

0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

1

2

3

4

5

Period (s)

Fou

rier

Am

plitu

de (

m/s

2 )

SSS CCC SSC CCS SCS CSC SCC CSS Freefield Input Motion

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

ESS Simulations

Short Period E.: Left Bent, Free Field vs Real Disp.

0 5 10 15 20 25

−0.1

−0.05

0

0.05

0.1

0.15

Time (s)

Dis

plac

emen

t (m

)

SSS CCC Freefield Input Motion

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions

Before We Start Why Do You Trust a Simulation? Examples Summary

Summary

I Importance of verification and validation for numericalprediction (simulations)

I Detailed treatment in new courses:I Spring ’08 ECI280A, Nonlinear Finite ElementsI Spring ’09 ECI280B, Nonlinear Dynamic Finite Elements

I Would you (and others) trust simulations if you followed Vand V procedures?

Jeremic Computational Geomechanics Group

On Computational Simulations and Predictions