Transcript Nonlinear Dynamic SSI Analysis of a Buried Reservoir FWR MWD’s Robert B. Diemer Water Treatment Plant Finished Water Reservoir (FWR)

Nonlinear Dynamic SSI Analysis
of a Buried Reservoir
FWR
MWD’s Robert B. Diemer Water Treatment Plant
Finished Water Reservoir (FWR)
FWR, Plot Plan & Section B-B’
EWWT
A
North
Shear wall
Shear wall
B’
A
B
20 ft
Ravine
720 ft
Design Earthquakes
• MCE - M6.8 event on Wittier Fault, PGA=1.17 g
• Landers, Superstition Hills, and Kobe records
• Spectrally matched to design response spectrum:
Design Horizontal Acceleration Histories
1.2
1.2
Acceleration (g)
Landers / Lucerne Station, 275 Comp.
0.6
0.6
0.0
0.0
-0.6
-0.6
-1.2
-1.2
0
5
10
15
Time (seconds)
20
25
30
1.2
1.2
Acceleration (g)
Superstition Hills / Parachute Test Site Station, 225 Comp.
0.6
0.6
0.0
0.0
-0.6
-0.6
-1.2
-1.2
0
5
10
15
Time (seconds)
20
25
30
Acceleration (g)
1.2
1.2
Kobe / KGMA Station, 000 Comp.
0.6
0.6
0.0
0.0
-0.6
-0.6
-1.2
-1.2
0
FWR, Diemer Plant
5
10
15
Time (seconds)
20
25
30
Figure 4
FWR - North Wall
East Wash Water Tank
Section A
Finished Water Reservoir
FWR, Diemer Plant
FWR - North Wall
Section A
East Wash Water
Tank Foundation
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
swale
FWR, Diemer Plant
Objectives
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
•
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 elastoplastic 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
FWR North Wall - Section A
0
Fill
Bedrock
Non-reflective boundary
“Free-Field” Boundary
North
“Free-Field” Boundary
South
0
0
• 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.
0
-3.500
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
-2.500
-1.500
-0.500
0.500
0
1.500
Structural Properties – North Wall
Structural
Element
Section Area
(ft2/ft)
Moment of Inertia
(ft4/ft)
*
Yield Moment
(kip.ft/ft)
FWR Roof Slab
0.83
0.0241
31
FWR Floor Slab
1.04
0.0471
34
**
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
FWR Columns
*
**
Cracked section (ACI, 2005)
Distributed over 10-ft wide force trajectory for 20-ft column spacing
Analysis Sequence with Model Calibration
Based on Measured Wall Deflections
815
Original Structure
805
800
795
790
Elevation (ft)
810
Existing Structure
785
•Full reservoir
•Excavate + retaining wall
•Econcrete = 100%*Einitial
•Ieff = 50%*Iuncracked
•Empty reservoir
780
815
810
805
800
795
790
785
780
FWR, Diemer Plant
Elevation (ft)
Existing:
~21 mm
deflection
•Fully buried
•Empty reservoir
•Econcrete = 82%*Einitial
•Icreep = 22%*Iuncracked
•Full reservoir (809.25 ft)
Ko = 0.7 produced “target”
wall deflection = 21 mm
Full reservoir
Static equilibrium
EQ shaking
Figure 10
Earth-Pressure Distributions (Section A1)
Before Excavation
After Excavation
814
814
FW R Roof
812
FWR Wall Elevation (ft)
FWR Roof
812
810
810
808
808
806
806
804
804
Ko = 0 . 7
802
802
Total Force 35 kips/ft
800
800
798
798
796
796
794
794
792
792
790
790
FWR Bottom Slab
FWR Bottom Slab
788
788
786
0
FWR, Diemer Plant
1
2
3 4 5 6 7
P re s s u re (k s f)
8
9
0
1
2
3 4 5 6 7
Pressure (ksf)
8
9
786
Static-Moment Distribution (Section A1)
Original, fully buried
FWR structure
“Before Excavation”
41.6 kip*ft/ft
Moment initiating concrete cracking= 18.3 kip*ft/ft
“After Excavation”
(Following 1971 S.F. EQ)
38.5 kip*ft/ft
FWR, Diemer Plant
Earth Pressure Distribution before and after EQ for Varying K0
Before EQ
Swale
After EQ
Swale
FWR
swale
FWR Wall
Ko = 0 . 5
1. 0
2 .0
FWR Slab
0
FWR Slab
4
8 0
4
8
Pressure (ksf)
Pressure (ksf)
A
FWR
A xial Fo rce (kips/ft)
Probable Cause of Horizontal Cracking
Axial-Force History in Swale for 0.25 PGA EQ
8
FWR
Swale
4
Shaking-induced
Axial Force
In Swale
A c c e l. ( g )
0
0.3
M 4.6 Whittier Narrows, 1987
A
FWR
0.0
-0.3
0
5
10
15
20
T im e (s e c o n d s )
25
30
Total Force (kips/ft)
Effect of Pre-EQ Ko on Shaking-Induced Soil Force
60
FWR
ko=2.0
swale
.
30 ko =1.0
ko=0.5
Shaking-induced
soil force
against FWR
Accel. (g)
0
1.2
Input acc. history
A
0.0
-1.2
FWR
0
5
10
15
20
Time (seconds)
25
30
Deformed Mesh and Wall Deflection History: MCE Shaking
Acc. (g)
Plastic rotation
0.025 Rads
Deflec. (in.)
1.1 ft
0
-1
-2
Initial Ko=0.7
1.2
MCE - Landers
0.0
-1.2
0
10
20
30
Time (seconds)
FWR North Wall - Post-shaking
permanent deformations
FWR North Wall – Deflection history
Acc. (g)
Plastic Rotation
(% radian)
Moment (kips.ft/ft)
Moment & Plastic Rotation Histories at Wall and Floor
80
1 kip.ft/ft = 4.45 kN.m/m
Wall
40
0
Floor
-40
1.2
Reservoir
0.0
hinges
Wall
Floor
-1.2
1.2
Landers
0.0
-1.2
0
5
10
15
Time (seconds)
20
25
30
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
South Wall Analyses
MWD’s Robert B. Diemer Water Treatment Plant
Finished Water Reservoir (FWR)
12 caissons
(10 ft o.c.)
20 caissons
(10 ft o.c.)
Section A
Section B
Diemer FWR – South Slope
Diemer FWR – South Slope
Diemer FWR – South Slope
Soil Properties
*) Shear-wave velocity (Vs) derived from downhole geophysical surveys
Diemer FWR – South Slope
Static F.S.= 1.23
Yield acceleration = 0.06g
Shaking-induced deformation = 5.5 ft
FWR
(MCE)
Fill
Topsoil (Colluvium)
Bedrock
Top Soil (Colluvium)
Diemer FWR – South Slope
Static F.S.= 1.34
Yield acceleration = 0.08g
Shaking-induced deformation = 4.8 ft
(MCE)
FWR
Fill
Bedrock
Topsoil / Slope Wash
FWR
Wall top
~0.7ft
South Slope
Reservoir
~0.3ft
Section A
Buttress
Wall
60 ft
10 ft
10 ft
Panel top
~0.1ft Reservoir
FWR
South Slope
~0.1ft
Section A
Shear
Panels
55 ft
30 ft
10 ft
10 ft
30 ft
FWR
Wall top
<0.1 ft
South Slope
Section A
Diaphragm Wall
anchored into
Reservoir Floor
and/or
Shear Walls
40 ft
Reservoir
<0.1 ft
FWR - South Wall Analysis
0.8
Fill
Colluvium
Weathered Bedrock
0.7
Bedrock
SECTION A1 - SOUTH
0.6
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
0.5
0.4
Structural Properties – South Wall
Section Area
(ft2/ft)
Moment of Inertia *
(ft4/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 ft2
935 ft4
11,150 kip.ft
Structural
Element
*) 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)
0)
8.200
South Slope Displacement Vectors After Earthquake, Section A
8.100
+01
E+02
E+02
8.000
7.900
2E 1
7.800
00
7.700
2
7.600
Max displacement ~2 in
South Wall Deformations After Earthquake, Section A
Exaggerated 100 times
~ 2 in
Moment (kip .ft)
Moment and Shear Force History of Caisson During Earthquakes
100
70
40
10
-20
-50
-80
Acceleration (g)
Shear Force (kip)
0
30
20
10
0
-10
-20
-30
FWR
yield moment (39.5 kip.ft)
yield moment (-39.5 kip .ft)
5
10
15
time (seconds)
20
25
30
shear capacity (19.6 kip)
shear capacity (-19.6 kip)
0
5
10
15
time (seconds)
20
25
30
1.2
0.6
Landers/Lucerne Station, 275 Comp.
Input
0.0
-0.6
-1.2
0
5
10
15
time (seconds)
20
25
30
South Wall - Model setup for “quasi-3D” analysis
Structure Deformations (Landers EQ, Normal Polarity)
Section A1, Exaggerated 5x
Plastic Rotation @ Caisson Head: >5%
Plastic Rotation @ Mid of Caisson: >5%
Max. Caisson Deflection: 12.0 in
Section A2, Exaggerated 5x
Plastic Rotation @ Caisson Head: <0.1%
Plastic Rotation @ Mid of Caisson: 0%
Max. Caisson Deflection: 0.1 in
South Wall, Exaggerated 2,000 x
0.06”
Spring4 Spring3
FWR, Diemer Plant
Spring2
Spring1
A2
A1
Section A1 History of Caisson Axial Force
300
300
4
Compression
200
2
1
200
A2
A1
Caisson is “hanging”
on the South-Wall beam
100
0
0
Tension
Axial Force (kip)
100
3
-100
-100
-200
-200
-300
-300
0
5
10
15
Time (seconds)
20
25
30
Acceleration (g)
1.2
1.2
Landers/Lucerne Station, 275 deg.
0.6
0.6
0.0
0.0
-0.6
-0.6
-1.2
-1.2
0
FWR, Diemer Plant
5
10
15
Time (seconds)
20
25
30
Section A2 History of Caisson Axial Force
900
900
800
800
700
700
4
3
2
1
A2
600
A1
500
500
400
400
300
300
Compression
Axial Force (kip)
600
200
100
0
0
200
100
0
5
10
15
Time (seconds)
20
25
30
Acceleration (g)
1.2
1.2
Landers/Lucerne Station, 275 deg.
0.6
0.6
0.0
0.0
-0.6
-0.6
-1.2
-1.2
0
FWR, Diemer Plant
5
10
15
Time (seconds)
20
25
30
History of Spring 1 Axial Force
900
900
800
800
4
700
3
2
1
700
A1
600
600
500
500
400
400
300
300
Compression
Axial Force (kip)
A2
200
100
0
0
200
100
0
5
10
15
Time (seconds)
20
25
30
Acceleration (g)
1.2
1.2
Landers/Lucerne Station, 275 deg.
0.6
0.6
0.0
0.0
-0.6
-0.6
-1.2
-1.2
0
FWR, Diemer Plant
5
10
15
Time (seconds)
20
25
30
History of Spring 2 Axial Force
900
900
800
800
700
4
3
2
A2
600
A1
600
500
500
400
400
300
300
Compression
Axial Force (kip)
700
1
200
100
0
0
200
100
0
5
10
15
Time (seconds)
20
25
30
Acceleration (g)
1.2
1.2
Landers/Lucerne Station, 275 deg.
0.6
0.6
0.0
0.0
-0.6
-0.6
-1.2
-1.2
0
FWR, Diemer Plant
5
10
15
Time (seconds)
20
25
30
History of Spring 2 Axial Force
900
900
800
800
700
4
3
2
A2
600
A1
600
500
500
400
400
300
300
Compression
Axial Force (kip)
700
1
200
100
0
0
200
100
0
5
10
15
Time (seconds)
20
25
30
Acceleration (g)
1.2
1.2
Landers/Lucerne Station, 275 deg.
0.6
0.6
0.0
0.0
-0.6
-0.6
-1.2
-1.2
0
FWR, Diemer Plant
5
10
15
Time (seconds)
20
25
30
Reservoir Wall Moment after Landers EQ (Section A1)
363 kip*ft
834= kip*ft
Max.
834 kip*ft
FWR, Diemer Plant
Reservoir Wall-Beam Moment History
4000
4000
2000
2000
Moment (kip.ft)
0
0
-2000
-2000
-4000
-4000
-6000
-6000
Note:
Moment history recorded at
wall-beam element to the right
of Caisson A1 - in the axis of
the canyon
-8000
-8000
-10000
-10000
0
5
10
15
Time (seconds)
20
25
30
Acceleration (g)
1.2
1.2
Landers/Lucerne Station, 275 deg.
0.6
0.6
0.0
0.0
-0.6
-0.6
-1.2
-1.2
0
FWR, Diemer Plant
5
10
15
Time (seconds)
20
25
30
Section A1 - Reservoir Roof Moment &Plastic Rotation
Moment (kip.ft)
80
80
yield moment = 66 kips.ft
40
40
0
0
-40
yield moment = -66 kips.ft
-80
Plastic Rotation (rad)
0
5
10
15
time (seconds)
20
25
0.010
-40
-80
30
0.010
hingelocation
Reservoir
0.005
0.005
0.000
0
5
10
15
time (seconds)
20
25
Acceleration (g)
1.2
0.000
30
1.2
Landers/Lucerne Station, 275 deg
0.6
0.6
0.0
0.0
-0.6
-0.6
-1.2
0
FWR, Diemer Plant
5
10
15
time (seconds)
20
25
-1.2
30
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