seismic design basics

TRANSPORTATION RESEARCH BOARD

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Seismic Design Basics

July 16, 2020

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Learning Objectives

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1. Identify different types of seismic hazards and determine how bridge engineers minimize the potential for earthquake-induced bridge damage or collapse

2. Develop a conceptual understanding of seismic structural dynamics without complicated mathematics

3. Describe structural model types and modeling methods4. Select an appropriate model type and modeling method

to analyze the seismic response of a bridge, and develop, test, and verify computer models for seismic evaluation

Part 1: Seismic Hazards and Seismic Demands on Bridges

Tom Ostrom, ChiefCaltrans Division of Engineering Services

July 16 2020

TRB Webinar – Seismic Design BasicsSponsored by Committee AFF50

1. Seismology and Earthquakes

Tectonic Plates• Most earthquakes occur at tectonic

plate boundaries (Interplate EQ’s)

• Japan’s earthquakes occur because its on four plates including

• Some of the world’s biggest earthquakes occur between the Nazca and South American Plates (in Chile).

Faults and EarthquakesInterplate earthquakes occur at tectonic plate boundaries• Lithosphere: is the crust and

uppermost mantle made up of rigid, brittle rock that bends but does not flow. 100 km thick

• Asthenosphere: Just below the lithosphere includes the upper mantle made up of solid “plastic” rock that can flow in response to deformation. 180 km thick.

1. Seismology and Earthquakes

Faults and EarthquakesStrike-Slip Faults move laterally. If you stand on one side facing the fault and the block opposite to moves to the right, it's called a right lateral fault (like most faults in California).Normal Faults, the hanging wall moves downwards relative to the foot wall. They are caused by extensional tectonics. This kind of faulting will cause the faulted section of rock to lengthen.Thrust or Reverse Fault, the hanging wall moves upwards relative to the foot wall. Reverse faults are steeply dipping (near vertical) and thrust faults are shallowly dipping, but usually the terms thrust and reverse faults are used interchangeably.

1. Seismology and Earthquakes

Faults and EarthquakesIntraplate Faults: Occur in the interior of a tectonic plate.• Intraplate earthquakes are not well

understood; the causative fault is deeply buried, and sometimes cannot be found.

• Examples: the 1811-1812 (M8.2-7.4) Earthquakes in New Madrid, Missouri and the 1886 (M6.9-7.3) Charleston, South Carolina.

.

1. Seismology and Earthquakes

Obtaining Seismic Hazards at the Bridge Site.The Design Earthquake is the collection of seismic hazards at the bridge site used in the design of bridges. The Design Earthquake consists of the Design Spectrum and may include other seismic hazards such as liquefaction, lateral spreading, surface faulting, and tsunami. The common element for all seismic hazards is that they are derived using a Probabilistic Seismic Hazard Analysis (PSHA).

A: Ground Shaking B: Fault OffsetC: Liquefaction/Lateral SpreadingD: Tsunami

2. Seismic Hazard Fundamentals

For most states, you obtain the PGA, short period (SS), and one second period (S1) spectral accelerations from the USGS Map or Hazard Tool to create a design spectra.

Values of Fpga and Fa as a Function of Site Class and Mapped Peak Ground Acceleration or Short-Period Spectral Acceleration Coefficient.

Values of Fv as a Function of Site Class and Mapped 1 Second Period Spectral Acceleration Coefficient.

2. Seismic Hazard Fundamentals

2. Seismic Hazard Fundamentals

• Seismic design in Ca. started after the the 1933 Long Beach Earthquake

• San Francisco-Oakland Bay Bridge was designed for a lateral force of 10% of the bridge’s tributary weight

• ATC-6 adopted by AASHTO in 1983 as a guide spec. and Division 1-A in 1991

• The 1989 CT ground motions aren’t strictly comparable since it’s divided by a ‘Z’ factor

2.7g

1.5 g, 1 sec.

.75 g, 2 sec.

5% in 50 yr.s (I-15/215 IC)

2. Seismic Hazard Fundamentals

Ground Shaking Hazards Attenuation Relationships

0

1000

2000

3000

0 1 2 3 4 5 6

M6.7 San Fernando EQ and 975 Year (Caltrans) Design Spectra, SI units at

Pacoima Dam

7% in 75 Year (cm/s2) 1971 San Fernando EQ

3. Bridge Damage and Lessons Learned

210-5 Interchange

0

0.5

1

1.5

2

0 1 2 3 4 5 6

M7.1 Loma Prieta EQ and 975 Year (Caltrans) Design Spectra, both in Emeryville

975 Year (g's) 1989 Loma Prieta East Bay Bridge

0

1

2

3

0 1 2 3 4 5 6

M6.8 Northridge EQ and 975 Year (Caltrans) Spectra at Pacoima Dam

ACC (g) 1994 Northridge 14-5 Interchange

3. Bridge Damage and Lessons Learned

Before 1971 bridge columns had four main structural problems:1: Lap splice at the base of the column.2: Lack of confinement. (#4 @ 12” ties).3: No top mat in footings.4: Rebar poorly developed into the

superstructure.

1971 (M6.5) San Fernando EQFoothill Blvd UC (Rte 210)• Pre 1971 columns had #4 ties at 12

inches with 90

1994 (M6.8) Northridge, CA EQLa Cienega-Venice UC (I-10)• Pre 1971 columns had #4 ties at 12

inches • Large shear and bending moments

damaged the concrete and caused the ties to break, buckling the main reinforcement leading to collapse

• Collapse was averted by the storage buildings under the bridge

3. Bridge Damage and Lessons Learned

SFOBB East Span W2 Columns

Post 1989 Column/Bent Cap /Joint

3. Bridge Damage and Lessons Learned

1971 (M6.5) San Fernando EQThe Route 210/5 Separation and Overhead • Lap splices which pulled out of

the foundations leading to failure• Post 1971 Caltrans required

column reinforcement to be continuous through the foundations.

3. Bridge Damage and Lessons Learned

The 1971 (M6.5) San Fernando EQSan Fernando Road Overhead• Drop-in span unseated during the

earthquake. • After 1971 the earthquake

Caltrans increased minimum seat width from 12 to 18 inches.

• Caltrans began initial retrofit program to add restrainers to reduce displacements

3. Bridge Damage and Lessons Learned

3. Bridge Damage and Lessons Learned

1989 (M7.1) Loma Prieta EQThe top and bottom decks of the East Bay Bridge collapsed at Pier E-9 due to the girders sitting on 4” seats.

3. Bridge Damage and Lessons Learned

1989 (M7.1) Loma Prieta EQThe Cypress Viaduct: double-deck, cast-in-place prestressed box girder bridge built in the 1950 s in Oakland California.

The structure was designed with pin-type connections and hinges to simplify the analysis, to reduce stresses from prestress shortening, and to handle future widenings.

The upper columns had poorly reinforced pins that were damaged due to shaking causing 0.7 miles of the viaduct to fall onto the lower deck.

3. Bridge Damage and Lessons Learned

1987 M5.9 Whittier Narrows EQ Shear damage occurred to the bridge columns on the Interstate 605 and 5 Interchange. Short stiff columns failed in shear at small displacements.

1994 (M6.8) Northridge, CA EQBull Creek Canyon Bridge column damage because the plastic hinge location moved due to a stiff adjacent structure

3. Bridge Damage and Lessons Learned

1994 (M6.8) Northridge, CA EQThe 1976 Mission Gothic UC was on opposing skews and had flared columns; both of which contributed to the damage it received during the Northridge earthquake.The flare made the effective column length shorter, making it a shear critical column below the flare.After the earthquake Caltrans tested flared columns and developed an isolated flare that prevented shear damage from occurring below the flare.

3. Bridge Damage and Lessons Learned

1994 (M6.8) Northridge, CA EQGavin Canyon UC was another highly skewed bridge that became unseated during an earthquake.Bridges can have several natural modes of vibrations when they are excited by earthquakes.One of these modes is rotation about a vertical axis, causing unseating of highly skewed bridges.

3. Bridge Damage and Lessons Learned

1994 (M6.8) Northridge, CA EQThe Southbound Connector was supported on tall and short columns. The short Pier 2 couldn’t displace as much as the taller piers and collapsed resulting in the superstructure breaking on both sides of Pier 3.

After the earthquake Caltrans SDC required piers and bents to have about the same stiffness.

Bridge Damage and Lessons Learned

3. Bridge Damage and Lessons Learned

Thank You

Part 2: Structural Dynamics for Seismic Analysis

M. Lee Marsh PhD PE Technical Fellow - Earthquake Engineering WSP

16 July 2020

TRB Workshop – Seismic Design BasicsSponsored by Committee AFF50

Outline• Fundamental Observations for Basic Seismic Design• Concept of Dynamic Equilibrium & Dynamic Response –

Single-Degree-of-Freedom System• Seismic Loading• Multi-Degree-of-Freedom Systems• Estimating Inelastic Response from Elastic Response

Learning OutcomesOverall Goal: Develop a conceptual understanding of seismic

structural dynamics without complicated mathematics

Subgoals:1. Describe three key concepts used in basic seismic design2. Describe dynamic equilibrium 3. Identify the primary response “point” used for seismic design4. Identify the steps of a multi-modal demand response analysis

Outline• Fundamental Observations for Basic Seismic Design• Concept of Dynamic Equilibrium & Dynamic Response –

Single-Degree-of-Freedom System• Seismic Loading• Multi-Degree-of-Freedom Systems• Estimating Inelastic Response from Elastic Response

Three Fundamental Observations

Elastic Response is Entirely Dependent on the Local Intensity of the Ground Shaking

Three Fundamental Observations

We Can Use this Attribute to “Fuse” Our Structures and Limit the Internal Forces

Three Fundamental Observations

We Can Predict Inelastic Displacements from Elastic System Displacements Based on Empirical Studies

The Ability to Estimate Inelastic Displacements Allows Us to Use Elastic

Analysis for Our Designs

Outline• Fundamental Observations for Basic Seismic Design• Concept of Dynamic Equilibrium & Dynamic Response –

Single-Degree-of-Freedom System• Seismic Loading• Multi-Degree-of-Freedom Systems• Estimating Inelastic Response from Elastic Response

Free Vibration Response

Internal Forces / Free Vibration

Free Vibration Response – No External Loading

The Equation of Motion, fi + fs = 0, is a differential equation, but we will not focus

on its solution so much as its result.

Damping

Note: This is “Damping” Not “Dampening”, which means to make damp or wet.

The Equation of Motion now becomes:

fi + fd+ fs = 0

where fd is a damping force acting in

conjunction with the spring force, and in linear form damping

is proportional to velocity.

fi

fs

fd

Forced Vibration – Externally Applied Force

Outline• Fundamental Observations for Basic Seismic Design• Concept of Dynamic Equilibrium & Dynamic Response –

Single-Degree-of-Freedom System• Seismic Loading• Multi-Degree-of-Freedom Systems• Estimating Inelastic Response from Elastic Response

Equilibrium for Ground-Excited Structures

Earthquake Response

Define Response Spectrum

max atotal = Spectral Acceleration, SA

(each structure period has a unique SA)

General Shape of a Response Spectrum

SASA

TTs

Design Spectrum Shape

Outline• Fundamental Observations for Basic Seismic Design• Concept of Dynamic Equilibrium & Dynamic Response –

Single-Degree-of-Freedom System• Seismic Loading• Multi-Degree-of-Freedom Systems• Estimating Inelastic Response from Elastic Response

Example—Spine Model

Multiple Modes of Vibration Exist:

3 x Masses – Restraints on Masses

3 x 17 masses – 13 restraints = 38 modes

Not all modes are important. Usually only a fraction of the total number contribute to seismic response.

Example Bridge—Mode Shapes

Software provides the modal periods (or frequencies) and mode shapes.

Multimode Response Analysis

• Each mode treated as a SDOF system

Outline• Fundamental Observations for Basic Seismic Design• Concept of Dynamic Equilibrium & Dynamic Response –

Single-Degree-of-Freedom System• Seismic Loading• Multi-Degree-of-Freedom Systems• Estimating Inelastic Response from Elastic Response

Recall: Estimate Inelastic Response Using Elastic Analysis

Can use linear elastic analysis to predict nonlinear displacements!

DDuctility Demand =

D inelastic max / D yield

D yield

Elastic to Inelastic Response“Coefficient” Method

(AASHTO – LRFD and Seismic Guide Spec)

Ductility Demand

Where Ts – “corner” of design spectrum

Ampl

ifica

tion

m = 6

m = 1.2 Inelastic displacement is estimated as Rd times

the elastic displacement.

SA

TTs

Nonlinear Static “Pushover” Capacity Curve

Capacity Limit State – First Element to Reach Material Max Permissible Strain

Displacement Demand After Adjustment for Inelastic Response

Key Point:Displacement Capacity Must Exceed the Adjusted Demand

Displacement

Seismic Analysis Overview Force-Based Design – LRFD• Elastic Demand Analysis

• Response spectrum input• Use forces for design with

reduction factors to account for ductility

• Use displacements with amplification factors to account for inelastic response

• Prescriptive detailing takes care of ductility capacity

Displacement-Based Design –Seismic Guide Specifications• Elastic Demand Analysis

• Response spectrum input• Provides target demand

displacements for pushover check

• Displacements amplified for inelastic response

• Nonlinear pushover analysis• Used to directly check adequate

displacement capacity

Thank You

Part 3:Computer Modeling for

Seismic AnalysisDerek Soden, P.E., S.E.

Senior Structural EngineerFederal Highway Administration Resource Center

1

Learning Outcomes• By the end of this lesson, you should be able to:

• Describe structural model types and modeling methods• Select an appropriate model type and modeling method to

analyze the seismic response of a bridge• Develop, test, and verify computer models for seismic

evaluation

Before You Begin…• You have choices – consider:

• Model Type• Single Degree of Freedom• Spine• Finite Element

• Modeling Method• Linear• Non-Linear• Pseudo-static• Time history

3

AASHTO Analysis Requirements• LRFD:

• GS:

SM/UL

MM

No Analysis

Modeling Effort• Build your model only as complex as required to solve the

problem:

Model Types - SDOF• Advantages:

• Simple – hand calculations

• Closed form solution• Disadvantages

• Based on SDOF assumption

• Single mode only

𝑃𝑃

𝛿𝛿 = 𝑃𝑃𝐿𝐿3

3𝐸𝐸𝐸𝐸

𝑉𝑉 = 𝑃𝑃

𝑀𝑀 = 𝑃𝑃 × 𝐿𝐿

𝐿𝐿

𝐸𝐸, 𝐼𝐼

Model Types - Spine• Advantages:

• Multiple degrees of freedom• Higher-order response characteristics • Still verifiable (to a point)

• Disadvantages:• Still a simplification• Loses reliability with complex

geometry and/or behavior

7

Model Types – Finite Element• Advantages:

• Less generalization• Complex geometry and behavior• Identifies local effects

• Disadvantages:• Computation-intensive• Higher order verification• Knowledge and experience are key

Modeling Methods - Linear• Linear Analysis:

• Good for most applications• Utilizes linear approximations of

non-linear behavior• Requires less expensive

software

𝐹𝐹

𝛿𝛿𝛿𝛿𝑦𝑦 𝛿𝛿𝑢𝑢

Modeling Methods – Non-linear• Non-Linear Analysis - when a linear approximation just

won’t do:• Essential Bridges• Base isolation• Critical gaps or openings

Model Development1. Bridge Geometry2. Section Properties

• Superstructure• Substructure

3. Boundary Conditions4. Verification

Bridge Geometry• For new design

• Most recent layout• For evaluation

• As-built plans• Site visit

Section Properties - Superstructure• Spine models - Use equivalent section properties

representing entire superstructure• Consider load path and composite action (barriers, etc.)• Prestressed Concrete and Steel – Gross section properties• Reinforced Concrete – Cracked (effective) section

properties• 𝐼𝐼𝑒𝑒𝑒𝑒𝑒𝑒 = 0.50𝐼𝐼𝑔𝑔 (lightly reinforced) - 0.75𝐼𝐼𝑔𝑔 (heavily reinforced) *

• CAD Software* Ref: AASHTO

, Articles 5.6.3 and 5.6.4

Section Properties - Substructure• Use cracked (effective) section properties for concrete

substructure elements

𝐸𝐸𝐼𝐼𝑔𝑔

𝐸𝐸𝐼𝐼𝑒𝑒𝑒𝑒𝑒𝑒

(𝑀𝑀𝑦𝑦 ,𝜙𝜙𝑦𝑦)

(𝑀𝑀𝑛𝑛,𝜙𝜙𝑛𝑛) (𝑀𝑀𝑢𝑢,𝜙𝜙𝑢𝑢)

𝜙𝜙

𝜙𝜙 =𝑀𝑀𝐸𝐸𝐼𝐼

𝐼𝐼𝑒𝑒𝑒𝑒𝑒𝑒 =𝑀𝑀𝑦𝑦

𝐸𝐸𝜙𝜙𝑦𝑦

Model Generation• Superstructure

• Locate spine elements to have same neutral axis as the superstructure

• Four to five elements per span is sufficient• Pier-to-superstructure connection

• Goal is to realistically distribute superstructure mass to the substructure

• Typically comprised of hinged rigid elements

• Substructure• Discretize longer columns into at least three elements

Boundary Conditions - Piers• Foundation Modeling

• Several methods are available to model foundation boundary conditions:• Equivalent Cantilever• Equivalent Base Springs• Equivalent Soil Springs

• Choose a modeling method that is appropriate to the analysis and evaluation level of the bridge

Equivalent Cantilever• Models the foundation as a beam-column fixed at a depth 𝐷𝐷:

𝐷𝐷 = 1.85 𝐸𝐸𝐸𝐸𝑒𝑒𝑒𝑒𝑒𝑒𝑛𝑛ℎ

(sands)

𝐷𝐷 = 1.44 𝐸𝐸𝐸𝐸𝑒𝑒𝑒𝑒𝑒𝑒0.465𝑆𝑆𝑢𝑢

(clays)

Where: 𝑛𝑛ℎ = soil modulus increase with depth, from LRFD Table C10.4.6.3-2 (ksi/ft)

𝑆𝑆𝑢𝑢 = undrained shear strength of clays (ksf)

Ref: AASHTO , Article C10.7.3.13.4 after Davisson and Robinson (1965)

Equivalent Cantilever• Advantages

• Simple representation that allows some degree of cross-coupling of moment and shear

• Easily implemented in structural analysis software• Disadvantages

• Empirical – not applicable to elements in double curvature• Dependent on a generalized modulus value• Requires separate models to calculate foundation

displacement and moment• Not recommended for use beyond preliminary

evaluation

Equivalent Base Springs• Models the foundation as a set of translational and rotational

springs:

• Spring stiffnesses can be calculated using lateral analysis software (L-pile, COM624P, etc.) or generalized charts

Equivalent Base Springs• Advantages

• Better represents pile groups and footings• Accommodates generalized variation in subgrade soils

• Disadvantages• Requires more rigorous analysis• Software limits on 6x6 coupled matrix input

Equivalent Soil Springs• Models deep foundations with discrete springs• Several programs available to calculate spring

stiffnesses and/or pile displacements• L-Pile, FB-Pier, COM624P...

Equivalent Soil Springs• Advantages

• Allows the modeling of discrete soil layers• Allows the modeling of non-linear soil behavior• Integrates pile/shaft behavior into the structural model

• Disadvantages• Requires more computational power• Requires more soils data• Modeling non-linear behavior in linear analysis requires

iteration

Boundary Conditions - AbutmentsEngaging the abutments can benefit the performance of a bridge by transferring load to the approach fill, reducing demands elsewhere in the bridge

Abutment Soil Springs• Longitudinal - Resistance provided by engaging

passive pressure behind the backwall• Transverse – Resistance provided by (as appropriate):

• Passive resistance – wingwalls• Friction – bearings, sliding footings• Fusing – shear keys, bearings

Abutment Soil Springs• Non-linear behavior, typically modeled as a linear spring:

• 𝐾𝐾𝑚𝑚𝑚𝑚𝑚𝑚𝑒𝑒𝑚𝑚 is usually found through iteration

Pass

ive P

ress

ure

DisplacementGap

1

1

0.02H

𝑃𝑃𝑝𝑝 = 𝑝𝑝𝑝𝑝𝐻𝐻𝑤𝑤𝑊𝑊𝑤𝑤

Where: 𝑝𝑝𝑝𝑝 = Passive earth pressure= 2𝐻𝐻𝑤𝑤 3 𝑘𝑘𝑘𝑘𝑘𝑘

(or other refined estimate)𝐻𝐻𝑤𝑤 = Backwall height𝑊𝑊𝑤𝑤 = Backwall width

Model Verification• Now is a good time to pause and verify that the model

performs in a manner consistent with your assumptions:• Dead load

• Structure mass (including wearing surface and other superimposed dead loads)

• Load distribution• Free vibration dynamic response

• Check first mode period and displacement• Number of modes and mode shapes

• Mass participation (>90%)

Learning Outcome Review• Describe structural model types and modeling methods• Select an appropriate model type and modeling

method to analyze the seismic response of a bridge• Develop, test, and verify computer models for seismic

evaluation

Questions?

Today’s Presenters

Tom Ostrom, California DOT

Lee Marsh, WSP

Derek Soden, FHWA

Moderator: Elmer Marx, Alaska DOT&PF

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