Nonlinear Dynamic SSI Analysis

concretecakeUrban and Civil

Nov 29, 2013 (3 years and 8 months ago)

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Nonlinear Dynamic SSI Analysis

of a Buried Reservoir

FWR

MWD’s Robert B. Diemer Water Treatment Plant

Finished Water Reservoir (FWR)

20 ft

720 ft

Ravine

A

A

Shear wall

Shear wall

EWWT

North

B’

B

FWR, Plot Plan & Section B
-
B’




MCE
-

M6.8 event on Wittier Fault, PGA=1.17 g


Landers, Superstition Hills, and Kobe records


Spectrally matched to design response spectrum:

Design Earthquakes

FWR, Diemer Plant

Figure
4

Design Horizontal Acceleration Histories

0
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10
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20
25
30
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Section A

FWR, Diemer Plant

East Wash Water Tank

Finished Water Reservoir

FWR
-

North Wall

Section A

FWR, Diemer Plant

East Wash Water
Tank Foundation

swale

FWR
-

North Wall

After 1971 S.F. EQ:


1.
Removal of

3 ft of earth cover

from roof


2.
Excavation behind

North Wall (up
-
slope)

And addition of a

separate retaining wall

Objectives


2D time domain, nonlinear dynamic SSI analyses with FLAC


Soil & bedrock simulated with elasto
-
plastic Mohr
-
Coulomb model


Reservoir, retaining walls, and bypass pipeline modeled with elasto
-
plastic beam elements which develop plastic hinges


Hydrostatic pressures applied to reservoir wall and bottom slab


Hydrodynamic forces of reservoir water approximated with Westergaard
added mass

1.
Investigate probable cause of horizontal cracking observed inside the
reservoir at roughly mid
-
height of the north wall

2.
Explore sensitivity

to pre
-
shaking earth pressure behind wall

3.
Evaluate seismic performance for MCE shaking

Analysis Approach

FLAC (Version 5.00)
LEGEND
29-Mar-06 15:48
step 84219
-4.341E+02 <x< 2.471E+02
4.100E+02 <y< 1.091E+03
User-defined Groups
bedrock
common_fill
Beam plot
0.450
0.550
0.650
0.750
0.850
0.950
1.050
(*10^3)
-3.500
-2.500
-1.500
-0.500
0.500
1.500
(*10^2)
JOB TITLE :
URS
Los Angeles, CA
Bedrock

Fill

FWR North Wall
-

Section A


Interface elements between soil and beam elements


Stiffness of two N
-
S shear walls simulated by rigidly
linking horizontal displacements of roof and floor slabs.

Non
-
reflective boundary

“Free
-
Field” Boundary

“Free
-
Field” Boundary

Material
Properties

Unit Weight
(pcf)

Friction Angle
(degrees)

Cohesion
(psf)

S
-
Wave
Velocity
(ft/sec)

Fill

125

30

240

920

Bedrock

135

34

6,000

2,500

North

South

Structural Properties


North Wall

Structural

Element

Section Area

(ft
2
/ft)

Moment of Inertia

*


(ft
4
/ft)

Yield Moment

(kip.ft/ft)

FWR Roof Slab

0.83

0.0241

31

FWR Floor Slab

1.04

0.0471

34

FWR Columns

**

0.22

0.0189

Elastic

FWR Wall
-

Top


-

Bottom

1.17

1.67

0.0662

0.1929

52

77

Retaining Wall
(Horizontal Leg)

1.50

2.00

0.1406

0.3333

38

67

*

Cracked section (ACI, 2005)

**

Distributed over 10
-
ft wide force trajectory for 20
-
ft column spacing

Original Structure


Fully buried


Empty reservoir


E
concrete
= 82%*E
initial


I
creep
= 22%*I
uncracked


Full reservoir (809.25 ft)


Existing Structure


Full reservoir


Excavate + retaining wall


E
concrete
= 100%*E
initial


I
eff
= 50%*I
uncracked


Empty reservoir


Ko = 0.7 produced “target”

wall deflection = 21 mm


Full reservoir

Static equilibrium

EQ shaking

Analysis Sequence with Model Calibration

Based on Measured Wall Deflections

FWR, Diemer Plant

Figure
10

815

810

805

800

795

790

785

Elevation (ft)

780

815

810

805

800

795

790

785

Elevation (ft)

780

Existing:

~21 mm

deflection

FWR, Diemer Plant

Earth
-
Pressure Distributions (Section A1)

788

790

792

794

796

798

800

802

804

806

808

810

812

F

W

R



W

a

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(

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)

814

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(

k

s

f

)

P

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)

9

786

788

790

792

794

796

798

800

802

804

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808

810

812

814

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l

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o

=

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7

0

1

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3

4

5

6

7

786

1

2

3

4

5

6

7

8

8

9

F

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R

o

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f

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R

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35

k

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/

f

t

0

Static
-
Moment Distribution (Section A1)

Original, fully buried

FWR structure

“Before Excavation


“After Excavation


(Following 1971 S.F. EQ)

FWR, Diemer Plant

41.6 kip*ft/ft

38.5 kip*ft/ft

Moment initiating concrete cracking= 18.3 kip*ft/ft

0

4

8

F

W

R



W

a

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l

0

4

8

P

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s

s

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(

k

s

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)



K

o

=

0

.

5

2

.

0

1

.

0

B

e

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E

Q

A

f

t

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E

Q

S

w

a

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)



Earth Pressure Distribution before and after EQ for Varying K
0

FWR

A

FWR

swale

Probable Cause of Horizontal Cracking

Axial
-
Force History in Swale for 0.25 PGA EQ

0

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10

15

20

25

30

T

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-
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0.0

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A

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4

8

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x

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Shaking
-
induced

Axial Force

In Swale

Swale

FWR

FWR

A

M 4.6 Whittier Narrows, 1987

0

5

10

15

20

25

30

T

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(

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-
1.2

0.0

1.2

A

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(

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60

T

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)

k

o

=

2

.

0

k

o

=

0

.

5

k

o

=

1

.

.0

Shaking
-
induced

soil force

against FWR

Input acc. history

FWR

Effect of Pre
-
EQ K
o

on Shaking
-
Induced Soil Force

FWR

A

swale

FWR North Wall
-

Post
-
shaking

permanent deformations

1.1 ft

Plastic rotation

0.025 Rads

FWR North Wall


Deflection history

0

10

20

30

T

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e



(

s

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-
1.2

0.0

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1

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o

=

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.

7

Deformed Mesh and Wall Deflection History: MCE Shaking


MCE
-

Moment & Plastic Rotation Histories at Wall and Floor

0

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30

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1.2

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1.2

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=



4

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N

.

m

/

m

Summary of Permanent Plastic Hinge Rotations for All Earthquakes

(Initial runs for determining governing EQ)

Earthquake

Plastic Rotation

(wall @ mid
-
height)

(Radian)

Plastic Rotation

(floor slab @ corner)

(Radian)

Lucerne (normal)

0.76%

0.59%

Lucerne (reversed)

0.13%

0.10%

Kobe (normal)

0.34%

0.59%

Kobe (reversed)

0

0.05%

Superstition (normal)

0.16%

0.11%

Superstition (reversed)

0.40%

0.38%

FWR, Diemer Plant

MWD’s Robert B. Diemer Water Treatment Plant

Finished Water Reservoir (FWR)

South Wall Analyses

12 caissons

(10 ft o.c.)

20 caissons

(10 ft o.c.)

Section A

Section B

Diemer FWR


South Slope

Diemer FWR


South Slope

Soil Properties

*) Shear
-
wave velocity (V
s
)

derived from downhole geophysical surveys

Diemer FWR


South Slope

Static F.S.= 1.23

Yield acceleration = 0.06g

Shaking
-
induced deformation = 5.5 ft

(MCE)


Fill

Bedrock

Topsoil (Colluvium)

Top Soil (Colluvium)

Diemer FWR


South Slope

FWR

Static F.S.= 1.34

Yield acceleration = 0.08g

Shaking
-
induced deformation = 4.8 ft


(MCE)

Bedrock

Fill

Topsoil / Slope Wash

FWR

Diemer FWR


South Slope

Wall top

~0.7ft

Reservoir

~0.3ft

Buttress

Wall

10 ft

60 ft

10 ft

FWR

South Slope

Section A

Panel top

~0.1ft

Reservoir

~0.1ft

Shear

Panels

55 ft

30 ft

10 ft

10 ft

30 ft

FWR

South Slope

Section A

Wall top

<0.1 ft

Reservoir

<0.1 ft

Diaphragm Wall

anchored into

Reservoir Floor
and/or

Shear Walls

40 ft

FWR

South Slope

Section A

FLAC (Version 5.00)
LEGEND
11-Aug-06 15:59
step 28415
5.363E+02 <x< 1.130E+03
4.206E+02 <y< 1.014E+03
User-defined Groups
bedrock1
weathered1
topsoil1
fill1
Beam plot
Pile plot
0.450
0.550
0.650
0.750
0.850
0.950
(*10^3)
0.600
0.700
0.800
0.900
1.000
1.100
(*10^3)
JOB TITLE :
URS
Los Angeles
SECTION A1
-

SOUTH

Colluvium

Fill

Weathered Bedrock

Bedrock

FWR
-

South Wall Analysis

In the ravines the reservoir is
supported by caissons to bedrock


N
-
S shear walls simulated by horizontally linking roof and floor slabs.


Soil & bedrock >>> elasto
-
plastic Mohr
-
Coulomb model


Reservoir & caissons >>> elasto
-
plastic beam elementss


Hydrostatic pressures applied to reservoir wall and bottom slab


Hydrodynamic forces approximated with Westergaard added mass

Structural Properties


South Wall

Structural

Element

Section Area

(ft
2
/ft)

Moment of Inertia

*


(ft
4
/ft)

Yield Moment

(kip.ft/ft)

FWR Roof Slab

0.83

0.0241

31

FWR Floor Slab

1.04

0.0471

34

FWR Columns

**

0.22

0.0189

Elastic

FWR Wall
-

Top


-

Bottom

1.17

1.67

0.0662

0.1929

52

77

S
-
Wall Caissons

0.5

0.0959

17

S
-
Wall Beam
***

37.3 ft
2

935 ft
4

11,150 kip.ft

*) Cracked section (ACI, 2005)

**) Distributed over 10
-
ft wide force trajectory for 20
-
ft column spacing

***) Actual wall
-
beam properties (i.e. not distributed per ft)

FLAC (Version 5.00)
LEGEND
9-May-06 21:05
step 1708901
Dynamic Time 3.0000E+01
7.622E+02 <x< 8.349E+02
7.542E+02 <y< 8.268E+02
User-defined Groups
bedrock
topsoil
fill
compact
Grid plot
0
2E 1
Displacement vectors
max vector = 5.810E+00
0
1E 1
Structural Displacement
Max Value = 9.983E-02
7.600
7.700
7.800
7.900
8.000
8.100
8.200
(*10^2)
7.700
7.800
7.900
8.000
8.100
8.200
8.300
(*10^2)
JOB TITLE :
URS
Los Angeles, CA
South Slope Displacement Vectors After Earthquake, Section A

Max displacement ~2 in

South Wall Deformations After Earthquake, Section A

Exaggerated 100 times

~ 2 in

M

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m

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.

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k

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25

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t

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(

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-
1.2

-
0.6

0.0

0.6

1.2

A

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k

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FWR

Input

South Wall
-

Model setup for “quasi
-
3D” analysis

FWR, Diemer Plant

Structure Deformations (Landers EQ, Normal Polarity)

Section A1, Exaggerated 5x

Section A2, Exaggerated 5x

South Wall, Exaggerated 2,000 x

Plastic Rotation @ Caisson Head: >5%

Plastic Rotation @ Mid of Caisson: >5%

Max. Caisson Deflection: 12.0 in

Plastic Rotation @ Caisson Head: <0.1%

Plastic Rotation @ Mid of Caisson: 0%

Max. Caisson Deflection: 0.1 in

0.06”

A1

A2

Spring1

Spring2

Spring3

Spring4

Section A1 History of Caisson Axial Force

FWR, Diemer Plant

0
5
10
15
20
25
30
T
i
m
e

(
s
e
c
o
n
d
s
)
-1.2
-0.6
0.0
0.6
1.2
A
c
c
e
l
e
r
a
t
i
o
n

(
g
)
-1.2
-0.6
0.0
0.6
1.2
0
5
10
15
20
25
30
T
i
m
e

(
s
e
c
o
n
d
s
)
-300
-200
-100
0
100
200
300
A
x
i
a
l

F
o
r
c
e

(
k
i
p
)
-300
-200
-100
0
100
200
300
L
a
n
d
e
r
s
/
L
u
c
e
r
n
e

S
t
a
t
i
o
n
,

2
7
5

d
e
g
.
Compression

Tension

Caisson is “hanging”

on the South
-
Wall beam

A1

A2

1

2

3

4

FWR, Diemer Plant

Section A2 History of Caisson Axial Force

0
5
10
15
20
25
30
T
i
m
e

(
s
e
c
o
n
d
s
)
-1.2
-0.6
0.0
0.6
1.2
A
c
c
e
l
e
r
a
t
i
o
n

(
g
)
-1.2
-0.6
0.0
0.6
1.2
0
5
10
15
20
25
30
T
i
m
e

(
s
e
c
o
n
d
s
)
0
100
200
300
400
500
600
700
800
900
A
x
i
a
l

F
o
r
c
e

(
k
i
p
)
0
100
200
300
400
500
600
700
800
900
L
a
n
d
e
r
s
/
L
u
c
e
r
n
e

S
t
a
t
i
o
n
,

2
7
5

d
e
g
.
Compression

A1

A2

1

2

3

4

FWR, Diemer Plant

History of Spring 1 Axial Force

0
5
10
15
20
25
30
T
i
m
e

(
s
e
c
o
n
d
s
)
-1.2
-0.6
0.0
0.6
1.2
A
c
c
e
l
e
r
a
t
i
o
n

(
g
)
-1.2
-0.6
0.0
0.6
1.2
0
5
10
15
20
25
30
T
i
m
e

(
s
e
c
o
n
d
s
)
0
100
200
300
400
500
600
700
800
900
A
x
i
a
l

F
o
r
c
e

(
k
i
p
)
0
100
200
300
400
500
600
700
800
900
L
a
n
d
e
r
s
/
L
u
c
e
r
n
e

S
t
a
t
i
o
n
,

2
7
5

d
e
g
.
Compression

A1

A2

1

2

3

4

FWR, Diemer Plant

0
5
10
15
20
25
30
T
i
m
e

(
s
e
c
o
n
d
s
)
-1.2
-0.6
0.0
0.6
1.2
A
c
c
e
l
e
r
a
t
i
o
n

(
g
)
-1.2
-0.6
0.0
0.6
1.2
0
5
10
15
20
25
30
T
i
m
e

(
s
e
c
o
n
d
s
)
0
100
200
300
400
500
600
700
800
900
A
x
i
a
l

F
o
r
c
e

(
k
i
p
)
0
100
200
300
400
500
600
700
800
900
L
a
n
d
e
r
s
/
L
u
c
e
r
n
e

S
t
a
t
i
o
n
,

2
7
5

d
e
g
.
Compression

A1

A2

1

2

3

4

History of Spring 2 Axial Force

FWR, Diemer Plant

0
5
10
15
20
25
30
T
i
m
e

(
s
e
c
o
n
d
s
)
-1.2
-0.6
0.0
0.6
1.2
A
c
c
e
l
e
r
a
t
i
o
n

(
g
)
-1.2
-0.6
0.0
0.6
1.2
0
5
10
15
20
25
30
T
i
m
e

(
s
e
c
o
n
d
s
)
0
100
200
300
400
500
600
700
800
900
A
x
i
a
l

F
o
r
c
e

(
k
i
p
)
0
100
200
300
400
500
600
700
800
900
L
a
n
d
e
r
s
/
L
u
c
e
r
n
e

S
t
a
t
i
o
n
,

2
7
5

d
e
g
.
Compression

A1

A2

1

2

3

4

History of Spring 2 Axial Force

Reservoir Wall Moment after Landers EQ (Section A1)

Max. = 834 kip*ft

FWR, Diemer Plant


834 kip*ft

363 kip*ft

FWR, Diemer Plant

Reservoir Wall
-
Beam Moment History

0
5
10
15
20
25
30
T
i
m
e

(
s
e
c
o
n
d
s
)
-1.2
-0.6
0.0
0.6
1.2
A
c
c
e
l
e
r
a
t
i
o
n

(
g
)
-1.2
-0.6
0.0
0.6
1.2
0
5
10
15
20
25
30
T
i
m
e

(
s
e
c
o
n
d
s
)
-10000
-8000
-6000
-4000
-2000
0
2000
4000
M
o
m
e
n
t

(
k
i
p
.
f
t
)
-10000
-8000
-6000
-4000
-2000
0
2000
4000
L
a
n
d
e
r
s
/
L
u
c
e
r
n
e

S
t
a
t
i
o
n
,

2
7
5

d
e
g
.
Note:

Moment history recorded at

wall
-
beam element to the right

of Caisson A1
-

in the axis of

the canyon

FWR, Diemer Plant

Section A1
-

Reservoir Roof Moment &Plastic Rotation

0

5

10

15

20

25

30

t

i

m

e



(

s

e

c

o

n

d

s

)

-
1.2

-
0.6

0.0

0.6

1.2

A

c

c

e

l

e

r

a

t

i

o

n



(

g

)

-
1.2

-
0.6

0.0

0.6

1.2

0

5

10

15

20

25

30

t

i

m

e



(

s

e

c

o

n

d

s

)

0.000

0.005

0.010

P

l

a

s

t

i

c



R

o

t

a

t

i

o

n



(

r

a

d

)

0.000

0.005

0.010

0

5

10

15

20

25

30

t

i

m

e



(

s

e

c

o

n

d

s

)

-
80

-
40

0

40

80

M

o

m

e

n

t



(

k

i

p

.

f

t

)

-
80

-
40

0

40

80

L

a

n

d

e

r

s

/

L

u

c

e

r

n

e



S

t

a

t

i

o

n

,



2

7

5



d

e

g



R

e

s

e

r

v

o

i

r

h

i

n

g

e



l

o

c

a

t

i

o

n

yield moment = 66 kips.
ft

yield moment =
-
66 kips.
ft

Study Conclusions



Performance Criterion: Prevention of structural collapse
which would result in uncontrolled release of water from
the reservoir


FEMA 356 allows up to 0.02 radians of plastic rotation for
“collapse prevention” level of performance of primary
structural members


Plastic rotations are less than 0.02 radians for all sections
analyzed


Finished Water Reservoir structure was concluded to be
seismically stable for MCE shaking