methodology for the seismic analysis of mercado de santa … · methodology for the seismic...

Methodology for the Seismic

Analysis of Mercado de Santa

Anita

Juan M. Pestana, Sc.D., P.E.Professor, University of California, Berkeley

Contact info: [email protected]

Lima, Peru. July 6, 2016 1/48

mailto:[email protected]

Outline of Presentation

Simulation of Seismic Structural Response

• Seismic Risk:

– Design Scenarios: 2 level evaluation

– Ground Motion Intensity Measures

– Selection of “Seed” & Modified Ground Motions

• Site Response Analysis:

– Soil Behavior & Parameters. 1D vs. 2D BV problems

• Soil-Structure Interaction Analysis

– Simplified Approaches

– 2D Dynamic Analyses 2/48

Simulation of Seismic Performance

3/48

Seismic Structural Response

• Inertial vs. Kinematic Response

– Above ground: Primarily Inertial Response:

Energy input to structure. Single degree of

Freedom System: Response Spectra.

– Below ground: Primarily Kinematic Response:

controlled by ground deformation, so Soil-

Structure-Interaction is essential

• For underground structures, Soil-Foundation-

Structure is the key to correctly describe

performance.4/48



• Seismic Risk:

– Design Scenarios: 2 level verification.








Seismic Sources- Deaggregation

6/48

Seismic Hazard-

Example New Zealand

7/48

Ground Motion Intensity MeasuresSelected Ground Motion Parameters

• Amplitude Parameters

– Peak Ground Acceleration (PGA)

– Peak Ground Velocity (PGV)

– Peak Ground Displacement (PGD)

• Frequency Parameters

– Ground Motion Spectra (Fourier, Power and Structural

Response Spectra) and mean period.

• Duration (several measures, e.g. bracketed > 0.05g)

• Other: Arias Intensity, Rate of Arias intensity,

presence of velocity pulse, period of pulse.

• Time Domain Response Spectrum.8/48

Response Spectra

• Structural Response Spectra: Response of 1 DOF

system to ground motion. Therefore, it is a filter on

the ground motion. Maximum values do not occur at

the same time & does not quantify how many times

or how long the maximum value is sustained.

• Fourier vs. Response Spectra: Fourier is sometimes

reported when studying site response (in absence of

structure) because it is an accurate description of

motion.

• Please note that the Spectra is associated with a given

value of the damping ratio (typically 5% but not always) 9/48

Time Domain Response Spectra(after Perri & Pestana, 2007)

Windowing Input Motion and Evaluating Structural

Response. Window length is a function of the

Fundamental Period of Structure being evaluated

10/48

Period Dependent Duration

11/48

Ground Motion Selection

• Key is to select ground motions that are representative from

the tectonic environment (source) and scenario (e.g.,

expected EQ magnitude and distance) of interest.

• Current state of practice uses Probabilistic Hazard

Assessment and Disaggregates the contribution to select

key scenarios (e.g., low M, short distance + high M, large

distance- example, San Francisco).

• Important characteristics: amplitude, frequency content,

duration, arias intensity, directivity (for near fault events).

• Issue of How many ground motions, matched or unmatched

(to the response spectra), (1, 3, 7, 11)

12/48

Selection of Ground MotionsAdditional Resources & New Developments

• Ground Motions Prediction Equations:

– NGA: Next Generation Attenuation Relationships.

Different tectonic environments (NGA-West, NGA

East, Subduction)

• Check with Research Centers (some examples)

– PEER: Pacific Earthquake Engineering Research Center.

Large database for selection of ground motions. Reviewed.

– MCEER: Multidisciplinary Center for Earthquake Engng.

– Local Research Centers & Universities.

• Other: US. Geological Service, EERI, SCEC13/48



• Seismic Risk:

– Design Scenarios: 2 level verification.








Dynamic Numerical Simulations

• Site Response Analysis: Assessment of maximum

shear stresses and strains.

• Boundary value problems where permanent

deformation is expected or 2D cases

• Liquefaction Problems: triggering, post-liquefaction

deformation, loss of free board for dams and levees,

lateral spread, soil improvement.

• Soil Structure Interaction (deep foundations, shallow

foundation, rocking and uplift)

• Problems are becoming increasingly complex, 1D, 2D

& 3D. (Structure-structure interaction- City block)15/48

Ground surface motions are affected by local site conditions

Site effects can influence:

• Amplitude - may amplify or de-amplify motion

• Frequency content - may shift to higher or lower frequency

• Duration - may extend duration of strong shaking

Shown by:

• Measured (recorded) surface motions

• Compilations of data on local site effects

• Measured amplification functions

• Theoretical analyses

Site Response Analysis-Local Site Effects

16/48

Correlation of Shaking

Amplification with

Site Conditions

Soil Rock

• Rock outcropping motion - the motion that would occur where rock

outcrops at a free surface

• Bedrock motion - the motion that occurs at bedrock overlain by a

soil deposit. Differs from rock outcrop motion due to lack of free surface effect.

• Free surface motion - the motion that occurs at the surface of a soil

deposit.

Ground Response Analysis- Definitions

Rock outcropping motion

Bedrock motion

What is bedrock? For

earthquake engineering

purposes, it is usually

taken as material with vs

> 2,500 fps (750 m/s)

(soft rock). Sometimes,

relaxed but close.

Free surface motion

17/48

Input Ground Motion (Prescribed Motion at the Base)

•Usually, we would like to model our problem all the way down

to bedrock, and use a bedrock motion as our input motion

•In cases where bedrock is at relatively shallow depths, we can

extend our finite element mesh all the way down to bedrock

Bedrock18/48

Input Ground Motion (Prescribed Motion at the Base)

• In some cases, bedrock is so deep that it is impractical to model the

entire soil column. In such cases, we need to define an input motion at

a reasonable depth.

• That depth should be sufficient that the motion is not significantly

influenced by structures or topographic irregularities (i.e. it could be

computed from a 1-D analysis without significant error)

19/48

Ideally, the bottom layer

should not have

significant nonlinearity,

and it should be relatively

stiff and a reasonable

impedance contrast (if

applicable)

Input Ground Motion

The motion at the desired depth

can be computed from a 1-D

analysis, using PLAXIS or

other site response program

Bedrock

Base of

mesh level

Bedrock motion

Input motion

20/48

Dynamic Soil Properties

1. Density (Unit Weight) - Mass / Vol (Weight / Vol)

2. Shear Stiffness and Damping- Dependency on strain level

3. Pore pressure generation (if applicable)

Comments/ Observations:

1. Density controls inertia- typically well bounded

2. Stress-strain properties of the soil will give rise to very

different soil responses which will be reflected primarily in

shear modulus reduction and damping curves. These are a

function of stress level, density and type of material and

mode of deformation. Currently few “realistic” models

implemented in PLAXIS but situation is rapidly changing.

Propagation of Shear Waves controlled by:

21/48

Use of Realistic Shear Modulus Curves

• Example: HS Model with small strain stiffness: Two new

Parameters Goref and , small strain stiffness (related to

shear wave velocity) and a reference strain at which the shear

stiffness is approximately 70% of the original value. The

stiffness is described by this relationship:

0

0.7

1

1 0.385

G

G

22/48

0.7

Use of Realistic Shear Modulus &

Damping Relations

23/48

0.0001 0.001 0.01 0.1 1

0.793

0.742

0.696

~0.65

Single Amplitude Shear Strain, (%)

Toyoura sand

(Kokusho 1980)

Void Ratio

0.65

0.80

Void

Ratio

Model Predictions

Gb= 700, p = 100 kPa

s= 1.0,

a =1.0

0.80

0.65

Void

Ratio

0

5

10

15

20

25

0.0001 0.001 0.01 0.1 1

~20

~50

~100

~200

~300Dam

pin

g R

atio

(%

)

Single Amplitude Shear Strain, (%)

Toyoura sand

(Kokusho 1980)

Confining Pressure (kPa)20

300Increasing

Confining

Pressure

0.0

0.2

0.4

0.6

0.8

1.0

Sh

ear

Mo

du

lus

Red

uct

ion,

Gse

c/G

ref

Model Predictions

Gb= 700,

s= 1.0,

a =1.0

300

20

Confining

Pressure

(kPa)

FLAC (Version 4.00)

LEGEND

27-Aug-04 13:54

step 25165255Cons. Time 4.5365E+12

-1.328E+03 <x< 1.228E+03

-1.076E+03 <y< 1.479E+03

Grid plot

0 5E 2

Exaggerated Boundary Disp.

Magnification = 0.000E+00

Max Disp = 6.033E+01

-0.750

-0.250

0.250

0.750

1.250

(*10 3̂)

-1.000 -0.500 0.000 0.500 1.000

(*10 3̂)

JOB TITLE : San Pablo Dam, Full-20' Reservoir, Dynamic Deformation

Geomatrix Consultants, Inc. 2101 Webster Street, 12 Floor, Oa

Example of Dynamic Numerical Simulations:

San Pablo Dam (California)

Crest Settlement ~ 35 ft

WSEL +314 ft

Dow nstream Buttress (1967)

Hydraulic Fill Shell

Upstream Buttress (1979)

Foundation Alluvium

Puddle Core

Hydraulic Fill Shell

Distance (ft) (x 1000)

-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0100

140

180

220

260

300

340

Ele

va

tion

100

140

180

220

260

300

340

Courtesy of F. Makdisi

24/48


Success Dam

– 145-foot high zoned embankment dam

– Analyzed with TARA-FL, Quad4, and 3 FLAC approaches

– Recent alluvium beneath upstream and downstream shells

• Potentially liquefiable

• Modeled with FLAC – UBCSAND

Courtesy of Dr. Vlad Perlea, USACOE

25/48

Vertical

Displacement

(Contours at 5-

foot intervals)

Maximum

Shear Strain

Increment

Existing Embankment Evaluation (MCE):

Example of Dynamic Numerical

Simulations: Success Dam

Courtesy of Dr. Vlad Perlea, USACOE

26/48

FLAC (Version 5.00)

LEGEND

18-Sep-07 12:16 step 34757

Flow Time 4.0261E+00 -3.740E+02 <x< 3.740E+02

-5.435E+02 <y< 2.045E+02

User-defined GroupsLAA-C

UAMOBM

OBM-SOBM2OBM1

MPSA_ClayMPSA_Sand

SurmudRBlanket

OFillF_Course

SFillTBT

Grid plot

0 2E 2

-4.500

-3.500

-2.500

-1.500

-0.500

0.500

1.500

(*10 2̂)

-3.000 -2.000 -1.000 0.000 1.000 2.000 3.000(*10 2̂)

JOB TITLE : .

Fugro West Inc. Oakland CA


Submerged BART Tube (California)

Fully coupled dynamic analyses

Finite difference method (FLAC2D)

UBCSAND (Prof. Byrne) for liquefiable soils

Calibration through simulation of CSS tests

Alternative model in finite elements (OpenSees)

Input Motion

Stiff Clay (MPSA-C)

Hard Clay (LAA)

Stiff Clay (OBM)

Dense Sand (UAM)

-0.6

0

0.6

0 20 40 60

Courtesy of T. Travasarou27/48

Centrifuge

Model

(scale 1 : 40)

Kutter et al. (2008)

Tunnel

ρ=~ 1.1 ρw

Fill Soil Type ρ qc1N Dr % k (cm/s)

Ordinary Sand ~1.9 ρw50 40 +/- 5 0.01

Special Gravel ~2.1 ρw32 35 +/- 5 1.0

Representative Soil Properties

28/48

Simplified Analysis- “Raking” Approach

29/48


Doyle Drive Replacement (California)

30/48

Analyses of Ground Improvement and Cut and Cover Performance

Pestana, ARUP 2008

Interpretation of Results• Plots of curves:

• Plot various quantities vs. time: Time Histories

Acceleration, velocity, displacement, Shear stress, shear strain,

Effective stress, pore pressures

• Plot various quantities vs. spatial position:

Displacement : Along section, Deformed mesh

Shear stress, shear strain: Contours, Shading

Very important for proper

interpretation of results of

dynamic analysisHelps analyst

understand how

system is behaving

• Plot temporal and spatial variation together

Animation Helps identify errors in

input by providing

“reality check”

31/48

MERCADO DE SANTA ANITA

Application of Methodology to the Seismic Performance 2500 return

Period event.

32/48

Seismic Sources

• Seismic Risk arising from three potential

sources:

– Transform Faulting Seismicity

– Subduction Faulting Seismicity

– Regional Seismicity

• According to Seismic Risk Study, risk is

dominated for Subduction Faulting Seismicity

with equal contributions from events at

distances of 40 km and 130 km

33/48

Seismic Hazard- 2500 years Return Period

34/48

Seed Motions

• Selected from similar tectonic environment :

subduction zone, distance and ground conditions

Compared to Transform Fault, no database is

available. (see Carlton, Pestana and Bray, 2015).

– Maule, Chile 2010; Santiago Puente Alto station

Mw= 8.8, Rrup= 75 km, Vs= 540 m/s

– Maule, Chile 2010; Cerro Santa Lucia station

Mw= 8.8, Rrup= 75 km, Vs= 540 m/s

– South Peru, 2001; Moquegua station.

Mw= 8.4, Rrup= 71 km, Vs= 573 m/s

35/48

Spectrally Matched Ground MotionMaule, Chile 2010 Santiago Puente Alto

36/48

Ground Motion for Numerical Analyses

37/48

Short Term Response Spectrum(after Perri and Pestana, 2007)

38/48

Site Response-

Shear Wave Velocity Profile

39/48

Nonlinear Soil Properties

40/48

Example:

Dense Gravels

Deconvolution

41/48

Soil Rock

Rock outcropping motion

Bedrock motion

Free surface motion

Numerical Model of Underground

Station- Mercado Santa Anita

43/48

Close-up

Structural detail

Seismic Response of Station

44/48

-20.00

-18.00

-16.00

-14.00

-12.00

-10.00

-8.00

-6.00

-4.00

-2.00

0.00

2.00

4.00

6.00

8.00

10.00

12.00

0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00

Der

iva

[mm

]

Tiempo [s]

DERIVAS CHILE(MAULE 2500)

A-C A-B B-C

Relative Displacement

45/48

Simplified Pseudostatic

vs. Dynamic Modeling

• Analyses using the raking approach give

smaller structural demands than the Dynamic

Modeling using PLAXIS.

• Demands from PLAXIS were selected for

verification (for 475 and 2500 years).

46/48

-25

-24

-23

-22

-21

-20

-19

-18

-17

-16

-15

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

-2,200

-2,000

-1,800

-1,600

-1,400

-1,200

-1,000

-800

-600

-400

-200

0 200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

PR

OFU

ND

IDA

D (

m)

ESFUERZOS EN m·kN/ml.

LEYES DE ESFUERZOS FLECTORES EN ELA

S09.2500E:Mmax[kNm/m]

S09.2500E:Mmin [kNm/m]

S09.2500E:Mmax[kNm/m]

S09.2500E:Mmin [kNm/m]

T2.1_Rd: Mmax[kNm/m]

T2.1_Rd: Mmin[kNm/m]

Structural

Demand-

Moments in

retain wall.

TR=2500 years.

47/48

CONCLUSIONS

• Given the methodology described in here:

– Ground Motions

– Site Response

– Soil-Structure Analysis: Simplified Raking vs.

Numerical Dynamic Analysis.

• Not presented here: Evaluation for 475 years is

similar- Station performs in “elastic range”

• Evaluation for the scenario 2500 years return

period, the station does not collapse.

48/48

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