recent advances in seismic soil-structure interaction

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Soil Structure Interaction (SSI) Knowledge and Effect on theSoil Structure Interaction (SSI) Knowledge and Effect on the

Seismic Assessment of NPPs Structures and ComponentsSeismic Assessment of NPPs Structures and Components

Recent Advances in Seismic Soil-Structure

Interaction Analysis of NPPs

Mansour Tabatabaie, Ph.D., P.E.

SC Solutions

NEA/CSNI-IAGE / IAEA ISSC

SSI Workshop

Ottawa, Canada

October 6-8, 2010




SSI ANALYSIS PROCEDURE

Seismic soil-structure interaction (SSI) analysis of nuclear power plants

(NPPs) in the United States is often performed in the frequency domain

using SASSI. This enables the analyst to properly:

a) Address the effects of wave propagation in an unbounded soil

media

b) Incorporate strain-compatible soil shear moduli and damping

properties

c) Specify input motion in the free field using the deconvolution

method and/or spatially variable incoherent ground motions




SSI ANALYSIS PROCEDURE

The original code was published in 1981 and consisted of 6 program

modules. Over the past 30 years, the program SASSI has evolved. A

current version of the code incorporates many enhancements that have

culminated in 28 program modules that perform a variety of tasks.




LAYOUT OF ORIGINAL SASSI CODE




TAPE

2 SITE

CNTRL

POINT

MOTOR

HOUSE

TAPE

3

TAPE

1

TAPE

4

TAPE

9

TAPE

8

TAPE

8

TAPE

8

COMBN8 TAPE

8

TAPE

4

TAPE

4

MOTION STRESS

RANDOM

TAPE

12

TAPE

14,15

TAPE

12

CONVER

TAPE

8n

FBASE

TAPE

1

TAPE

5,10 AXSYM

TAPE

8

ANALYS

MATRIX

LOADS

TAPE

5 SOLVE

TAPE

6

TAPE

10

TAPE

7

TAPE

5 RIMP

PARTIAL LAYOUT OF MTR/SASSI PROGRAM




LARGE-SCALE SSI MODEL

Seismic response of NPPs in the United States is often required for

frequencies up to 33 Hz. In addition, NPPs founded on hard rock in the

Eastern United States are now required to be analyzed to frequencies up

to 50 Hz.

For a typical nuclear island about 100m x 100m in plan dimensions,

embedded 10m in engineered backfill (Vs = 250 m/s) and founded on

hard rock, 3-D detailed FE SSI analysis using SASSI requires:

> Max soil element size ~ 250 / 5 / 50 = 1 m

> No. of interface soil nodes ~ 100 x 100 + 4 x 100 x 10 = 14,000

> No. of virtual soil nodes ~ 100 x 100 x 10 – 14,000 = 98,600

There could another 60,000 nodes in the structure model to provide

adequate mesh refinement to extract response spectra.




CONVENTIONAL SASSI MODELING &

ANALYSIS CONSTRAINTS

Seismic SSI analysis of NPPs using SASSI has had two main constraints

in the past:

a) Because of large storage and processing requirements, SASSI has

been constrained to coarse soil and structure FE models, which has

made it difficult to address the high frequency passing requirements

for SSI analysis.

b) Because SASSI uses frequency domain procedure, it is limited to

equivalent linear systems, which makes it difficult to address local

nonlinear effects in the structure such as base sliding and/or uplift,

component isolation, etc.




HOW TO ADDRESS PROBLEM SIZE ?




LARGE CORE SOLUTION (LCS) MODEL

The LCS model takes advantage of modern computer technologies,

which now makes it possible to efficiently analyze large-scale, deeply-

embedded nuclear island models in SASSI.

Advantages of LCS:

a) Total SSI system can be analyzed in one step.

b) Provides highly efficient and accurate solution.

c) Eliminates large file storage requirements.

d) Structure model can be a duplicate copy of corresponding FE

model used for design without need for renumbering the nodes

and/or elements. This facilitates model development, translation,

calibration and maintenance for SSI analysis.




Plan View of EPRTM Nuclear island

Nuclear Island

APPLICATION OF LCS MODEL TO LARGE-SCALE

NUCLEAR ISLAND MODEL




0

10

20

30

40

50

60

70

80

15 20 25 30

Density (kN/m3)

Dep

th B

elo

w G

rou

nd

Su

rface (

m)

1u

2u

3u

4u

5u

5a

1n5a

1n2u

2n3u

3r3u

2sn4u

Extension of

generic soil

profiles

0

10

20

30

40

50

60

70

80

0 3000 6000 9000

Vp (m/s)

Dep

th B

elo

w G

rou

nd

Su

rface (

m)

1u

2u

3u

4u

5u

5a

1n5a

1n2u

2n3u

3r3u

2sn4u

Extension of

generic soil

profiles

0

10

20

30

40

50

60

70

80

0 1000 2000 3000 4000

Vs (m/s)

Dep

th B

elo

w G

rou

nd

Su

rface (

m)

1u

2u

3u

4u

5u

5a

1n5a

1n2u

2n3u

3r3u

2sn4u

Extension of

generic soil

profiles

GENERIC SOIL PROFILES & PROPERTIES




-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0 5 10 15 20 25

Time (sec)

X-A

ccele

rati

on

(g

's)

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0 5 10 15 20 25

Time (sec)

Y-A

ccele

rati

on

(g

's)

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0 5 10 15 20 25

Time (sec)

Z-A

ccele

rati

on

(g

's)

ACCELERATION TIME HISTORIES OF

REFERENCE EUR-SOFT MOTIONS




0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.1 1 10 100

Frequency (Hz)

Sp

ectr

al

Accele

rati

on

(g

's)

X-Dir.

Y-Dir.

Z-Dir.

Damping = 0.05

ACCELERATION RESPONSE SPECTRA OF

REFERENCE EUR-SOFT MOTIONS




STCICK VS DETAILED FE SASSI MODEL

EPRTM NUCLEAR ISLAND




SASSI FOUNDATION MODEL OF

EMBEDDED EPRTM NUCLEAR ISLAND

El. -0.25m Sidewalls Not Connected to Soil

Sidewalls Not Connected to Soil

SB 2/3 SB 4

RB

3 4

5 6

7

8 9

10 11

Tendon Gallery Sidewall Nos.

FB SB 1

El. -11.85m

NI Basemat

2

NAB

AB




EXCAVATED SOIL MODEL OF EMBEDDED





Case

No. Soil Case Reference EUR Outcrop Motion

Analysis

Case

1 1u Soft 1u-s

2 2u

Soft 2u-s

3 Medium 2u-m

4 3u Medium 3u-m

5 4u

Medium 4u-m

6 Hard 4u-h

7 5u Hard 5u-h

8 5a Hard 5a-h

9 1n2u Soft 1n2u-s

10 2n3u Medium 2n3u-m

11 2sn4u Medium 2sn4u-m

12 3r3u Medium 3r3u-m

13 1n5a Hard 1n5a-h

SSI ANALYSIS CASES




MAXIMUM ACCELERATION CONTOURS IN X-DIR.





MAXIMUM ACCELERATION CONTOURS IN Z-DIR.





COMPARISON OF MAXIMUM ACCELERATIONS

(SOIL ANALYSIS CASE 2SN4U-M)

Location Elev. (m) X Y Z

Center of NI Basemat -11.85 0.262 0.224 0.319

Reactor Building IS +5.15 0.379 0.320 0.374


Safeguard Building 1 +21.00 0.478 0.356 0.399

Safeguard Building 2/3 +16.30 0.400 0.433 0.413

Safeguard Building 4 +21.00 0.340 0.335 0.394

Fuel Building +4.20 0.300 0.364 0.298

Reactor Containment Bldg 58.00 0.869 0.734 0.516

Reactor Shield Bldg 61.40 0.598 0.679 0.490

Location Elev. (m) X Y Z

Center of NI Basemat -11.85 0.277 0.210 0.318


Reactor Building IS 19.50 0.421 0.391 0.366

Safeguard Building 1 29.30 0.564 0.502 0.501

Safeguard Building 2/3 12.00 0.411 0.409 0.446

Safeguard Building 4 29.30 0.580 0.621 0.556

Fuel Building 3.70 0.350 0.294 0.357

Reactor Containment Bldg 58.00 0.738 0.620 0.893

Reactor Shield Bldg 61.40 0.843 0.854 0.578

Stick

Model

Detailed

FE

Model




COMPARISON OF ACCELERATION RESPONSE SPECTRA


Top of Reactor Containment

Bldg., Eelv. +58.0 m

0.0

1.0

2.0

3.0

4.0

5.0

0.1 1 10 100

Frequency (Hz)

X-S

pe

ctr

al A

cc

ele

ra

tio

n (

g's

)

Stick ModelDetailed Model Reference Outcrop Motion

Damping = 5%

0.0

1.0

2.0

3.0

4.0

5.0

0.1 1 10 100

Frequency (Hz)

Y-S

pe

ctr

al A

cc

ele

ra

tio

n (

g's

)


Damping = 5%

0.0

1.0

2.0

3.0

4.0

5.0

0.1 1 10 100

Frequency (Hz)

Z-S

pe

ctr

al A

cc

ele

ra

tio

n (

g's

)


Damping = 5%




COMPARISON OF INTERSTORY SHEAR FORCES

& OVERTURNING MOMENTS


Shear, Vx

-20

-10

0

10

20

30

40

50

60

0 500 1,000 1,500

Vx (MN)

Ele

vati

on

(m

)

Detailed Model Stick Model

Moment about Y-axis, My

-20

-10

0

10

20

30

40

50

60

0 10,000 20,000 30,000 40,000

My (MN-m)

Ele

vati

on

(m

)


Shear, Vy

-20

-10

0

10

20

30

40

50

60

0 500 1,000 1,500

Vy (MN)

Ele

vati

on

(m

)


Moment about X-axis, Mx

-20

-10

0

10

20

30

40

50

60

0 10,000 20,000 30,000 40,000

Mx (MN-m)

Ele

va

tio

n (

m)





CONCLUSIONS

a) Stick models are capable of determining global seismic responses, but

they can lead to excessively conservative results in the vertical

direction due to the limited number of modes that can be modeled

b) Detailed FE models capture local responses, thus eliminating the need

for modeling single DOF oscillators.

c) Effects of the basemat flexibilities can be considered in the detailed FE

models.

d) Meshing can be made sufficiently small in detailed FE models to

capture the response due to high frequency input motions.




HOW TO ADDRESS LOCAL

NONLINEARITIES ?

a) Base sliding and/or uplift

b) Side soil debonding

c) Component isolation

d) Other local nonlinearities




DISTRIBUTED PARAMETER FOUNDATION (DPF) MODEL

The DPF model is a hybrid frequency/time domain procedure that allows

the structure to be partitioned from the total SSI system and analyzed in

the time domain while the foundation media is modeled using the

frequency-domain procedures.

DPF method involves four basic steps:

a) Calculating dynamic impedance at each foundation interaction node

from soil reaction forces and interaction displacements in the

frequency domain using SASSI.

b) Developing equivalent simple-damped oscillators with constant

parameters (spring, mass and dashpot) representing the dynamic

impedance functions obtained in “a”.

c) calculating foundation scattering motions at the same interaction

nodes from SASSI.

d) implementing the results as boundary conditions in the time-domain

dynamic response analysis of the structure.




DPF MODEL IN SASSI




FLOW DIAGRAM OF LINEAR SSI ALIGNMENT

SASSI Linear

Seismic SSI Model Target Linear Solution

Scattering

Motion

Dynamic

Impedance

Functions

Linearize:

KMC Model

Linear Seismic SSI

Model

Time-Domain Linear

Solution

Check

Alignment




FLOW DIAGRAM OF DPF MODEL IN SASSI

Typical In-Structure Response

Primary Containment

Reactor Building

Foundation

Diameter = 40 m

52.8 m

13.5 m

(Embedment)

Foundation Base slab

Node 18241

Node 17091

Node 17284

Node 203

Node 25

Node 16262

X

Y

Z

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.01 0.1 1 10 100

Frequency (Hz)

X-A

ccele

rati

on

(g

's)

. SASSI, One-Step

ADINA, KMC

NODE 18241

Damping = 5%

0.0

0.5

1.0

1.5

2.0

2.5

0.01 0.1 1 10 100

Frequency (Hz)

X-A

ccele

rati

on

(g

's)

. SASSI, One-Step

ADINA, KMC

NODE 17091

Damping = 5%




NEAR FIELD INELASTIC SPRINGS

FOR MODELING BASEMAT SLIDING AND/OR UPLIFT AND

SIDEWALL/SOIL DEBONDING

P

U = Ue + Up

P

Ue

P

Up

= +

U = Ue + Up

Py

Pu




FLOW DIAGRAM OF NONLINEAR SSI ALIGNMENT

Scattered

Motion

Linearized

KMC Model

Aligned Linear

Seismic Model

Time-Domain Nonlinear Seismic Model

Nonlinear Near-

Field Springs




THANK YOU

FOR YOUR ATTENTION

QUESTIONS ?

recent advances in seismic soil-structure interaction

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