Youssef Hashash Associate Professor In collaboration with Duhee Park Post-Doctoral Research Assistant University of Illinois at Urbana-Champaign PEER 2G02

Youssef HashashAssociate Professor

In collaboration with Duhee ParkPost-Doctoral Research Assistant

University of Illinois at Urbana-Champaign

PEER 2G02 First MeetingPEER 2G02 First MeetingSeptember 21, 2004

2 Hashash and Park (2004)

DEEPSOIL

1-D Site response analysis code

Nonlinear / Equivalent linear analysis

User interface


Motivation for Development

Thick soil deposits such as those encountered in the Mississippi Embayment in Mid-America

Sponsored in part by Mid-America Earthquake Center

References: Park, D. and Y. M. A. Hashash (2004). "Soil damping formulation in nonlinear time

domain site response analysis." Journal of Earthquake Engineering 8(2): 249-274. Hashash, Y. M. A., and Park, D. (2002). "Viscous damping formulation and high

frequency motion propagation in nonlinear site response analysis." Soil Dynamics and Earthquake Engineering, 22(7), pp. 611-624.

Hashash, Y. M. A., and Park, D. (2001). "Non-linear one-dimensional seismic ground motion propagation in the Mississippi embayment." Engineering Geology, 62(1-3), 185-206.

Park, D. (2003). ESTIMATION OF NON-LINEAR SEISMIC SITE EFFECTS FOR DEEP DEPOSITS OF THE MISSISSIPPI EMBAYMENT. Department of Civil and Environmental Engineering. Urbana, University of Illinois at Urbana-Champaign: 337 p.


Outline Features of DEEPSOIL

Nonlinear Numerical Model User Interface

Equivalent Linear Numerical Model User Interface

Additional Features of the User Interface


Nonlinear (NL) Features

Soil Model Viscous Damping Formulation Dynamic Integration Scheme Increased Numerical Accuracy User Interface


NL Feature – Soil Model Extended Modified Hyperbolic Model

Based on Modified Hyperbolic Model (Matasovic, 1993) Confining pressure dependent

Gsec1

Gsec2

Backbone Curve

Initial LoadingCurve

SubsequentLoading & Unloading Curves

s

r

mos

mo

mo

mo G

G

G

11

b

refr

'a

Modified Hyperbolic Model


NL Feature – Soil ModelG / Gmax

& Confinement

b

refr

'a

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.0001 0.001 0.01 0.1

G/G

max

Shear Strain,

8

7

65

43

210.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.0001 0.001 0.01 0.1

Non-Linear Pressure Dependent Model 27.6 kPa55.2 kPa110 kPa221 kPa442 kPa883 kPa1776 kPa

Laird & Stoke (Measured)Confining Pressure

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.0001 0.001 0.01 0.1

Non-Linear Pressure Dependent Model 27.6 kPa55.2 kPa110 kPa221 kPa442 kPa883 kPa1776 kPa

1=27.6 kPa 2=55.2 kPa 3=110 kPa 4=221 kPa5=442 kPa 6=883 kPa 7=1776 kPa 8=10 MPa

Damping & Confinement

0

0.02

0.04

0.06

0.08

0.1

0.12

0.0001 0.001 0.01 0.1

Dam

ping

Rat

io (

-)

Shear Strain,

7

654

32

8

1

d

c

'

0

2000

4000

6000

8000

100000.1 1

Laird & Stokoe Proposed Equation

Confi

nin

g P

ress

ure

(k

Pa)

Damping Ratio (%)at zero shear strain


NL Feature– Viscous Damping Formulation

guIMuCuKuM

Viscous damping formulation [C]

Simplified Rayleigh damping formulation

Full Rayleigh damping formulation

Conventional Selection of Frequencies/Modes (CRF)

Proposed Selection (RF)

Extended Rayleigh damping formulation (ERF)

KMC RR


Feature 2 – Viscous Damping Formulation

Target Damping Ratio

Fig 3-1 Page 68

Simplified Rayleigh damping

0

1

2

Frequency (Hz)

Eff

ecti

ve d

ampi

ng r

atio

, (

%)

fm

KMC RR


Feature 2 – Viscous Damping Formulation


Selection of frequencies/modes for Full Rayleigh damping formulation

CRF (Conventional RF) : fm = 1st mode of soil column, fn=dominant period of input motion

RF (Proposed RF) : fm and fn chosen from transfer function of soil column and frequency content of

input motion An iterative process

Full Rayleigh damping (CRF & RF)

0

1

2

Frequency (Hz)

Eff

ecti

ve d

ampi

ng r

atio

, (

%)

fn

fm

Simplified RF


NL Feature– Viscous Damping Formulation


Extended Rayleigh damping (ERF)

0

1

2

Frequency (Hz)

Eff

ecti

ve d

ampi

ng r

atio

, (

%)

fn

fm

fo

fp

Simplified RF Full RF

12 Hashash and Park

(2004)

Numerical Implementation

Multi-degree of freedomlumped parameter model

Input ground motion

Cyclic soil response model


Nonlinear (NL) Integration Scheme

Newmark Beta Method

(Average acceleration method: =1/4, =1/2 Implicit Method Unconditionally stable No numerical damping

1

221

11

5.0

1

iiiii

iiii

utututuu

ututuu

guIMuCuKuM


NL Feature – Viscous Damping Formulation

0

2

4

6

8

Fou

rier

Am

plitu

de (

g se

c)

Fou

rier

spe

ctru

m r

atio

(-) (a)

0

1

2

3

4

5

0.1110Frequency (Hz)

Eff

ectiv

e da

mpi

ng r

atio

, (

%)

Target damping ratio, = 1.8%

(b)

0

0.2

0.4

0.1 1 10

Frequency domain solution

CRF (1.1, 4 Hz= Mode: 1, 2)

Spe

ctra

l acc

eler

atio

n (g

)

Period (sec)

(c)

RF – Conventional Approach

Use first mode of soil column and a higher mode or predominant

period of ground motion


NL Feature – Viscous Damping Formulation

RF/ERF

Proposed Guideline Use iterative procedure to obtain best match with frequency domain solution Dependent on soil column Dependent on input motion

ERF: Computationally expensive

0

2

4

6

8

Four

ier A

mpl

itude

(g s

ec)

Four

ier s

pect

rum

ratio

(-) (a)

0

1

2

3

4

5

0.1110Frequency (Hz)

Eff

ectiv

e da

mpi

ng ra

tio,

(%

)

Target damping ratio, = 1.8%

(b)

0

0.2

0.4

0.1 1 10

Frequency domain solution

RF (2, 10 Hz= Mode: 2, 5)ERF (2, 10, 35, 45 Hz= Mode: 2, 5, 16, 21)

CRF (1.1, 4 Hz= Mode: 1, 2)

Spec

tral

acc

eler

atio

n (g

)

Period (sec)

(c)


NL Feature – Viscous Damping Formulation Variable [C] Matrix

Updates stiffness in the RF formulation

KMC RR

10-5

0.0001

0.001

0.01

0.1

1

1 10

Updated [C] matrixConstant [C] matrix

1000 m columnM=7, R=20km

Frequency (Hz)

Fou

rier

Am

plit

ude

(g s

ec)


NL Feature – Increased Numerical Accuracy

0

5,000

10,000

15,000

20,000

25,000

30,000

Num

ber

of I

ncre

men

tal S

olut

ion

Step

s

Fixe

d T

ime

Incr

emen

tsN

umbe

r of

Sub

step

s, N

=1

Fixe

d T

ime

Incr

emen

tsN

umbe

r of

Sub

step

s, N

=5

Flex

ible

Tim

e In

crem

ents

, Max

. Sh

ear

Stra

in In

crem

ent=

0.01

%

Flex

ible

Tim

e In

crem

ents

, Max

. Sh

ear

Stra

in In

crem

ent=

0.05

%

0.91

2

3

0.1 1

N = 1 FixedN = 5 Fixed

max = 0.01% Flexible

max

= 0.05% Flexible

Period (sec)

1000 m ColumnSpec

tral A

ccel

erat

ion

(g)

Input MotionStation JMA NS Kobe Earthquake, PGA = 0.82g

Fixed Sub-incrementation Scheme: Independent of strain levelFlexible Sub-incrementation Scheme: depends on strain level


NL User Interface – Input Soil Profile


NL User Interface – Input Soil Profile


NL User Interface – Soil Model Parameter Selection


NL User Interface – Viscous Damping Formulation

300 m ME Profile

M=8,R=32km Motion








NL User Interface – Numerical Accuracy Control


NL User Interface – Output


Equivalent linear (EQL) Features

3 Types of Complex shear modulus Frequency independent (Kramer, 1996)

Frequency dependent (Udaka, 1975)

Simplified (Kramer, 1996)

No limitation on number of layers number of materials number of motion data points

22 1221* iGG

iGG 21* 2

iGG 21*


EQL Features

(SHAKE, use with care)


Additional Features


Verification of DEEPSOILLoma Prieta Earthquake, M = 7.1, October 19, 1989-Significance of viscous damping in DEEPSOIL (Strong Motion & non-linear material)-Soil column: ~88 m


0

0.4

0.8

0 1 2 3

Treasure Island (Recorded motion)Conventional Nonlinear analysis (Simplified Rayleigh Damping)

Yerba Buena Recording (Input)

Spe

ctra

l acc

eler

atio

n (g

)

Period (sec)

0

0.2

0.4

0 1 2 3

Spe

ctra

l acc

eler

atio

n (g

)

Period (sec)

E-W

N-S

Verification of DEEPSOIL

0

0.4

0.8

0 1 2 3

Treasure Island (Recorded motion)Conventional Nonlinear analysis (Simplified Rayleigh Damping)DEEPSOIL (Full Rayleigh Damping)

Yerba Buena Recording (Input)

Spe

ctra

l acc

eler

atio

n (g

)

Period (sec)

0

0.2

0.4

0 1 2 3

Spe

ctra

l acc

eler

atio

n (g

)

Period (sec)


Nonlinear Soil Model Parameters

No Fixed Parameter Selected to match various reference

dynamic curves (G/Gmax and damping curves)


NL Soil Model Parameters – Mississippi Embayment (ME)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.0001 0.001 0.01 0.1

G/G

max

Shear Strain,

8

7

65

43

21

0

0.02

0.04

0.06

0.08

0.1

0.12

0.0001 0.001 0.01 0.1

Dam

ping

Rat

io (

-)

Shear Strain,

7

654

32

8

1

ME study

ME EPRI

1.4 0.85

s 0.8 0.9

(a)Reference strain @

’ref 0.163 0.07

’ref 0.18 0.18

b 0.63 0.4

c Varies with depth

d 0 0


NL Soil Model Parameters - EPRI

ME study

ME EPRI

1.4 0.85

s 0.8 0.9

(a)Reference

strain @ ’ref 0.163 0.07

’ref 0.18 0.18

b 0.63 0.4

c Varies with depth

d 0 0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

G/G

max

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

0.00 0.00 0.01 0.10 1.00Strain (%)

Dam

ping

(%

)

EPRI (0-20ft)

EPRI (21-50ft)

EPRI (51-120ft)

EPRI (120-250ft)

EPRI (251-500ft)

EPRI (501-600ft)

DEEPSOIL (0-20ft)

DEEPSOIL (21-50ft)

DEEPSOIL (51-120ft)

DEEPSOIL (121-250ft)




NL Soil Model Parameters-Treasure Island

0

0.2

0.4

0.6

0.8

1

1.2

G/G

ma

x

Deepsoil Young Bay

Deepsoil Old Bay Mud

Young Bay Mud

Old Bay Mud

Treasure Island

Young Bay Mud

Old Bay Mud

0.8 0.9

s 0.8 0.7

(a)Reference strain @ ’ref 0.17 0.065

’ref N/A N/A

b 0.0 0.0

c 1.5 1.5

d 0 0.00

5

10

15

20

25

30

0.0001 0.001 0.01 0.1 1 10

Strain (%)

Da

mp

ing

(%

)


NL Soil Model Parameters-Anchorage

0

0.2

0.4

0.6

0.8

1

1.2

0.0001 0.001 0.01 0.1 1 10Strain (%)

G/G

max

DEEPSOIL

Bootlegger Clay(Updike et al., 1982)

0

5

10

15

20

25

30

0.0001 0.001 0.01 0.1 1 10Strain (%)

Dam

ping

(-)

DEEPSOIL

Bootlegger Clay(Updike et al., 1982)

Bootlegger clay

0.7

s 0.7

Reference strain 0.05

’ref N/A

b 0.0

c 1.0

d 0.0


Limitations

No Pore pressure generation model Currently under development

Implementation of a NN based constitutive model


Questions?


Backup Slides

0

1

2

Full Rayleigh Damping

Simplified Rayleigh Damping

Extended Rayleigh

0 5 10 15 20 25 30 35Frequency (Hz)

Dam

ping

rat

io,

(%

)

Stiffness proportional damping

Mass proportional damping


Backup Slides

Documents

Youssef Hashash Associate Professor In collaboration with Duhee Park Post-Doctoral Research Assistant University of Illinois at Urbana-Champaign PEER 2G02