On Seismic Earth Pressures with some … some observations on Seismic Performance of Dams ... (seismic) lateral earth pressure increment for ... Our results similarly suggest that

On Seismic Earth Pressures with some observations on

Seismic Performance of Dams

Nicholas Sitar Professor

Dept. of Civil and Environmental Engineering UC Berkeley

Presented at

Hydroelectric Generation DepartmentPublic Power Corporation

Athens, GreeceJanuary 26, 2010

N. Sitar, PPC, January 26, 20092

“Mononobe-Okabe solution”–

Assume a fully developed Coulomb wedge-

Force applied at 1/3H


What is the basis for “M-O Method”

?

Mononobe

and Matsuo, 1929


•

Two categories of walls:–

“yielding”

walls –

walls

that can move

sufficiently to develop minimum active earth pressures

–

“nonyielding”

walls –

walls

that do not satisfy the movement condition

FEMA 369

Source: Marshall Lew & SEAOSC


•

For yielding walls, the FEMA 369 commentary states that there is consensus in the geotechnical engineering practice that a simplified Mononobe-

Okabe seismic coefficient analysis reasonably represents the dynamic (seismic) lateral earth pressure increment for yielding retaining walls. The the

dynamic increment of earth pressure is based

on Seed and Whitman (1970):

ΔPAE

~ (1/2)(3/4)kh γΗ 2

•

where kh

is the “horizontal ground acceleration divided by gravitational acceleration.”

FEMA 369 cont.


•

For nonyielding

walls, the FEMA 369 commentary presents an equation developed by Wood (1973) for a rigid nonyielding

wall retaining a homogeneous

linear elastic soil and connected to a rigid base. The dynamic thrust, ∆PE

, is approximately:

ΔPE

= kh

γΗ 2

•

As for yielding walls, the point of application of the dynamic thrust is typically taken at a height of 0.6H above the base of the wall.

FEMA 369 cont.


Mononobe and Matsuo, 1929 Seed and Whitman, 1970



Delphi: polygonal wall and temple of Apollo 548 B.C., temple destroyed by quake 373 B.C., other major quakes 551, and 1870 A.D.


Kobe, 1995


Taiwan, 1999

A lot of problems with old walls onsloping ground and with sloping backfill. No problems with base-ments

and flat ground ….


Wenchuan

–

2008 –

Traditional retaining structures


U-Wall Damage During 1971 San Fernando Earthquake, Clough & Fragaszy

(1977)


Comparison of Total Horizontal Earth Pressures (T. Boardman, 2006)

0

5

10

15

20

0 500 1000 1500 2000 2500

Total Horizontal Earth Pressure (psf)

Dep

th (f

eet)

Flexible Wall Design Values

Rigid Wall Design Values

Ostadan&White (1998) ElCentro Motion

Davis (2003) G = f(z)


•

What is the magnitude of seismic earth pressures on retaining structures in native ground?

•

Do seismic earth pressures need to be applied on subterranean building walls?

•

How do we reconcile designing walls for seismic earth pressures that are stronger and larger when walls designed without consideration of seismic earth pressures have not shown any evidence of distress in recent earthquakes?

Source: WHITE PAPER ON SEISMIC INCREMENT OF ACTIVE EARTH PRESSURE Marshall Lew, Ph.D., Martin B. Hudson, Ph.D., and J. Adolfo Acosta, Ph.D.,MACTEC Engineering and Consulting, Inc., Rami Elhassan, Ph.D., S.E., Integrated Design Services, Inc., Structural Engineers

Where does all this leave us?


Example: Proposed BART Prototype


Our Approach: Use Physical Modeling to Verify Failure Mechanisms

•

Why centrifuge? –

Good scaling relationships–

Repeatability–

Reproducibility–

Cost effectiveness

•

UC Davis centrifuge: –

9.1m radius, 4,500Kg maximum payload, area of bucket 4m2


Scaling Relationships


Centrifuge Model Design

•

Assume “typical”

BART stiff and flexible concrete retaining wall structures

•

Match the stiffness of aluminum model and concrete prototype

•

Match the mass of the aluminum model and concrete prototype


Wall Instrumentation –

3 separate measurement systems

•

Array of 10 FlexiForce

pressure sensors on each wall

•

Array of 6 strain gauges on one rigid and one flexible

•

10 Instrumented “load”

bolts for direct force measurement at the wall base junction –

5 on one rigid and 5 on one flexible wall


Model Construction


Physical Model Layout


Peak Accelerations for LAA02


Ground Motion Amplification


Moments and Lateral Earth Pressures

•

Observed response:–

Moments directly measured by instrumented load bolts and strain gauges

–

Lateral earth pressures directly measured by Flexiforce

sensors and interpreted from strain

gauges responses assuming a cubic fit for moment distributions on the walls


Static Moments –

After Initial Gravity Applied

Initial - Before Shaking, LAA01

0

50

100

150

200

0 20 40 60x106Static Moment (lb-in)

Z (in

)

Meas. SG-StiffMeas. SG-FlexibleMeas. LB-StiffMeas. LB-FlexibleStatic At RestStatic Active

Initial - Before Shaking, LAA02

0

50

100

150

200

0 20 40 60x106

Static Moment (lb-in)

Z (in

)

Meas. SG-Stiff

Meas. SG-Flexible

Meas. LB-StiffMeas. LB-Flexible

Static At Rest

Static Active

φ

= 32° φ

= 35°


Static Moments –

After First Shake

φ

= 32° φ

= 35°

After Loma Prieta-2, LAA01

0

50

100

150

200

0 20 40 60x106

Static Moment (lb-in)

Z (in

)

Meas. SG-Stiff

Meas. SG-Flexible

Meas. LB-Stiff

Meas. LB-Flexible

Static At Rest

Static Active

After Loma Prieta-SC-1LAA02

0

50

100

150

200

0 20 40 60x106Static Moment (lb-in)

Z (in

)

Meas. SG-Stiff

Meas. SG-Flexible

Meas. LB-Stiff

Meas. LB-Flexible

Static At Rest

Static Active


Dynamic Moment and Earth Pressure Time History


Maximum Dynamic Earth Pressure –

without

wall inertia


0

1

2

3

4

5

6

0 20 40 60 80

Z (m

)

Pressure (KPa)

Loma Prieta-SC-2

Flexiforce-StiffFlexiforce-FlexibleSG-StiffSG-FlexibleM-O with PGAM-O with 65% PGA

0

1

2

3

4

5

6

0 10 20 30 40

Z (m

)

Pressure (KPa)

Kocaeli-YPT060-2

Maximum Dynamic Earth Pressure –

without

wall inertia


Supporting Data?

Nakamura, S. 2006. Reexamination of Mononobe-Okabe Theory of Gravity Retaining Walls Using Centrifuge Model Tests, Soils and Foundations, Vol. 46, No.2, 135-146.


Ortiz, L.A, R.F. Scott, and J. Lee (1983). Dynamic Centrifuge Testing of Cantilever Retaining Wall.Earthquake Engineering and Structural Dynamics, Vol. 11, 251-268.


-0.2

0

0.2

0.4

0.6

0.8

0.2 0.4 0.6 0.8 1

ΔK

ae

PGA

Seismic Coefficient versus PGAFlexible Wall

SG-Flexible

LB-Flexible

ΔKae at Max. Dynamic Wall Moment

y = 1.0221x - 0.4548R2 = 0.85

y = 1.0822x - 0.3853R² = 0.85

-0.2

0

0.2

0.4

0.6

0.8

0.2 0.4 0.6 0.8 1Δ

Kae

PGA

Seismic Coefficient versus PGAStiff Wall

SG-StiffLB-StiffΔKae at Max. Dynamic Wall Moment

Seismic Earth Pressure Coefficient IncrementCentrifuge Data


KitayamaKitayama

Dam, KobeDam, Kobe


Zipingpu

Dam

Photo by J. Sun


Favorable performance under seismic loadCrest Acceleration at Zipingpu Dam during Wenchuan Earthquake


Crest Settlement ~ 73 cm at center


~13 cm settlement, right abutment


Photo by K. Mosalam

Crack repair in progress, expansion seals in process of being replaced


Photo by K. Mosalam

4 unit, 760 MW powerhouse with minor damage

Wall shear cracks

Photo by K. Mosalam Photo by K. Mosalam




Spillway


Conclusions•

Earth pressure during seismic loading increases with depth similar to static and the “inverse triangle”

does not represent this condition

•

Mononobe

–

Okabe solution is strictly applicable only within the range of original model tests and cannot be simply extrapolated as has been done in the past

•

Seed & Whitman (1970) solution is similarly flawed since it relies on Mononobe-Okabe’s original work. However, their recommendation that no special provisions are needed for well designed retaining structures subject to ground motions <0.3 g are well supported by data and most recent experimental results

•

Nakamura’s (2006) experiments on gravity walls suggest no increment in lateral earth pressure in cohesionless

soil under seismic loading

•

Our results similarly suggest that lateral earth pressure increment is insignificant for a large range of ground motions. However, inertial forces on the walls have to be properly accounted for. Same conclusions

were reached by Clough and Fragaszy

(1977) who suggested that cantilever structures properly designed for inertial loading could handle seismic loads up to 0.5-0.6 g in granular backfill


What does it mean for dam design/performance?

•

The data show that maximum earth pressure and maximum moment do not occur at the same instant of time. Consequently, the actual

loads will be less than conventional computations suggest

•

Current test results are valid for medium dense dry sand –

preliminary recommendation

∆KAE

= PGAff

– 0.4

•

Dam embankments are 3-D structures and the spillway structures need be designed for kinematic response of the whole embankment

•

In absence of other data, design for full passive force may be most appropriate for structures crossing dam embankments

•

Given the dimensions of the actual structures the structural design must consider the inertial loads due to the structure response itself


Thank You!

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On Seismic Earth Pressures with some … some observations on Seismic Performance of Dams ... (seismic) lateral earth pressure increment for ... Our results similarly suggest that