Seismic evaluation of existing DOE facilities: a case study at Los Alamos 

National Laboratory

Andrew Whittaker, Ph.D., S.E., University at BuffaloLawrence Goen, P.E., LANL

Robert Kennedy, Ph.D., P.E., NAE, RPK Structural MechanicsBrian McDonald, Ph.D., S.E., ExponentTroy Morgan, Ph.D., P.E., Exponent

Michael Salmon, P.E., LANLLoring Wyllie, S.E., NAE, Degenkolb

Procedures for seismic evaluation

• FEMA 273/274– Early 1990s to 1997– Commercial buildings

• 1945 to 1995

– Provisions (273)– Commentary (274)– FEMA 356, ASCE 41‐06, ‐13– Performance levels

• CP, LS, IO, F

– Basic performance objectives– Deterministic basis

FEDERAL EMERGENCY MANAGEMENT AGENCY FEMA 273 / October 1997

NEHRP GUIDELINES FOR THE SEISMIC REHABILITATION OF BUILDINGS

Issued by FEMA in furtherance of the Decade for Natural Disaster Reduction

Procedures for seismic evaluation

• FEMA 273/274– Analysis methods

• Linear static • Nonlinear static

– First mode horizontal• Nonlinear dynamic

– Modeling• Linear• Nonlinear

– Acceptance criteria• Linear analysis

– m, Fμ• Nonlinear analysis

A

BC

D E

or

(a) Deformation

ab

c

QQCE

(b) Deformation ratio

A

BC

D E

,

de

c

QQCE

y

y

or h

Deformation or deformation ratio

(c) Component or element deformation limits

Nor

mal

ized

forc

e

I.O.L.S.

C.P.

P

P

P

S

S

A

BC

D E

FEMA, 1997

Procedures for seismic evaluation• FEMA P‐58

– Late 2012– Roots– Commercial buildings – Losses– Probabilistic basis

• Distributions of loss• Intensity• Scenario• Time‐based

– Analysis methods• Simplified linear • Nonlinear dynamic

– Ground motion selection and scaling• Soil‐structure‐interaction

– Modeling• Nonlinear components• Best estimates

– Fragility functions• Families of fragility functions• Damage states

– Consequence functions

0 0.5 1 1.5 2 2.5 3Earthquake intensity, e (g)

1E-006

1E-005

0.0001

0.001

0.01

Mea

n an

nual

freq

uenc

y of

exc

eeda

nce

0.21 0.54 0.87 1.2 1.53 1.86 2.19 2.52

e1 e2 e3 e4 e5 e6 e7 e8

e1

e2

e3

e4e5

e6 e7 e8

1

2

3

45678

0.1 1Period (sec)

0.001

0.01

0.1

1

10

Spe

ctra

l acc

eler

atio

n (g

)

0.02 4

LANL case study

LANL

LANL case study

LANL

LANL case study

Fluor, 1973

Existing DOE buildings• Nonlinear analysis of soil‐structure systems

– Distributions of demand at n intensities– Ground motion selection and scaling

• NIST GCR 11‐917‐15– Soil‐structure interaction analysis important

• Validated nonlinear soil models• Treatment of gapping and sliding• Size of soil domain, layering • Seismic inputs, consistent with PSHA

– Non‐ductile reinforced concrete framing • Rules for component modeling

– Cyclic backbone curves– Reliable hysteretic models

– Treatment of uncertainty and variability -3 -2 -1 0 1 2 3-600

-400-200

0200

400600

Drift Ratio (%)

Forc

e (k

ips)

Existing DOE buildings• Risk calculations

– Risk targets or performance goals• Smaller than the design basis hazard MAFE• Shaking more intense than design basis, requiring nonlinear analysis• Risk accrues at what (improper) fractions of DBE shaking?

– Known after the analysis is performed– Fragility functions for damageable components

• Safety‐critical MEP components, including HVAC• Safety‐critical structural components

– Perimeter and interior shear walls– Roof framing– Columns supporting roof and laboratory floor

• Correlated fragilities and redundancy– Understanding what is correlated– Salmon et al., Mertz

– Systems analysis

Component modeling: shear walls

• No consensus models of low aspect ratio walls• Developing an understanding of behavior

– ATC‐114 project• Data collection for walls• Datasets of Gulec (to 2009) and Luna (2010‐2015)• Cyclic tests of 240 low‐aspect‐ratio walls

– No monotonic data• Digitized reported cyclic test results

– Tabulated reported wall and material properties• Design variables

– Aspect ratio, concrete strength, web reinforcement ratio, boundary elements, axial load, OOP shear, OOP moment

Component modeling: shear walls

• Cyclic backbone– Points to define curve

• Cracking (A), yielding (B, C), post‐peak (D) 

Component modeling: shear walls

• Planar walls• Drift at cracking

– Three variables

dA

[%]

0 40 80 120f'c [MPa]

0

0.25

0.5

dA

[%]

Component modeling: shear walls

• Planar walls• Resistance at cracking

– Three variables

0 5 10 15 20 25 30 35P/Agf'c [%]

0

0.25

0.5

0.75

1

VA/V

C

ASCE 41-13 (Table 10-20)

VA/V

C

Component modeling: shear walls

• Planar walls• Resistance at cracking

– Three variables

0 5 10 15 20 25 30 35P/Agf'c [%]

0

0.25

0.5

0.75

1

VA/V

C

ASCE 41-13 (Table 10-20)

VA/V

C

Component modeling: shear walls

• Planar walls• Peak strength

– Empirical equations

ACI 318Chpt 11

ACI 318Chpt 18

Wood

Gulec

Component modeling: shear walls

• Cyclic (hysteretic) models – Based on Ibarra‐Krawinkler Pinching (IKP) model

• Trilinear pre‐peak, bilinear unloading responses• Implemented in Matlab• Calibratedmodel

LANL case study

• Planar wallFluor, 1973

LANL case study• Risk assessment of an mission‐critical building

– Mission‐critical SSCs• Integrated LANL‐led process underway

– Systems models and paths to failure– Seismic hazard calculations– Nonlinear analysis of soil‐structure models

• n intensities of ground motion• Nonlinear models for soil and components• Formal treatment of variability and uncertainty• Distributions of demand at each intensity

– Fragility calculations for damageable components• Supported by new test data as needed• Conditional probabilities of failure at each intensity

– Calculation of MAF of unacceptable performance

Hazard calculations

Systems analysis

Structural response

Component damage

Risk computation

Acknowledgments

• Dr. Greg Mertz: CJC and Associates• Dr. Said Bolourchi: Simpson, Gumpertz and Heger• Department of Energy• Eric MacFarlane: Los Alamos National Laboratory• Justin Coleman: Idaho National Laboratory• National Nuclear Security Administration• Asa Hadjian: Defense Nuclear Facilities Safety Board• National Institute of Standards and Technology

– Applied Technology Council: ATC‐114 project