FAILURE MODES - University Transportation Center

1

Embankment Embankment -- 11

SEISMIC PERFORMANCE OF SEISMIC PERFORMANCE OF EMBANKMENTSEMBANKMENTS

Richard W. Stephenson, Ph.D., P.E.Richard W. Stephenson, Ph.D., P.E.Professor of Civil, Architectural and Environmental EngineeringProfessor of Civil, Architectural and Environmental Engineering

Wanxing LiuWanxing LiuGraduate StudentGraduate Student

University of MissouriUniversity of Missouri--Rolla (UMR)Rolla (UMR)

Geotechnical and Bridge Seismic Design WorkshopGeotechnical and Bridge Seismic Design WorkshopNew Madrid Seismic Zone ExperienceNew Madrid Seismic Zone Experience

October 28October 28--29, 2004, Cape Girardeau, Missouri29, 2004, Cape Girardeau, Missouri


FAILURE MODESFAILURE MODES

•• Slope failureSlope failure–– Rotational SlideRotational Slide–– Block SlideBlock Slide

•• Lateral Spreading and Associated Lateral Spreading and Associated SettlementSettlement

2


METHODS OF ANALYSISMETHODS OF ANALYSIS•• Pseudostatic analysis,Pseudostatic analysis,•• Newmark sliding block analysis, Newmark sliding block analysis, •• MakdisiMakdisi--Seed analysis,Seed analysis,•• StressStress--deformation analysis,deformation analysis,•• Physical modeling (shaking table testing, Physical modeling (shaking table testing,

etc.).etc.).


PSEUDOSTATIC ANALYSISPSEUDOSTATIC ANALYSIS

•• A horizontal, downA horizontal, down--slope inertia force slope inertia force (M(M*a) is applied to *a) is applied to the sliding mass.the sliding mass.

•• a=a=kkhhWW•• Routine slope Routine slope

stability analyses stability analyses conductedconducted–– BishopBishop–– Method of slices,Method of slices,–– Etc.Etc.

3


•• AdvantagesAdvantages–– Relatively simpleRelatively simple–– Produces and index of Produces and index of

stability (FS)stability (FS)

•• DisadvantagesDisadvantages–– Rigid body analysisRigid body analysis–– Cannot simulate Cannot simulate

complex dynamic complex dynamic effectseffects

–– Cannot evaluate Cannot evaluate influence of porewater influence of porewater pressure builduppressure buildup

–– Cannot evaluate effect Cannot evaluate effect of degradation of of degradation of shear strength.shear strength.


Newmark Sliding Block AnalysisNewmark Sliding Block Analysis

•• First method to assess stability in terms of First method to assess stability in terms of deformations rather than factor of safety.deformations rather than factor of safety.

•• Assumes rigidAssumes rigid--plastic materialsplastic materials•• Assumes knowledge of the time history of Assumes knowledge of the time history of

the acceleration acting on the the acceleration acting on the embankment.embankment.

4


•• AdvantagesAdvantages–– Estimates Estimates

deformationsdeformations–– Relatively easy to use.Relatively easy to use.

•• DisadvantagesDisadvantages–– Potential failure mass Potential failure mass

and embankment are and embankment are assumed to be rigidassumed to be rigid

–– Lateral displacements Lateral displacements may be out of phase may be out of phase with the inertial forces with the inertial forces at different points .at different points .

–– Can significantly over Can significantly over predict deformationspredict deformations


MakdisiMakdisi--Seed AnalysisSeed Analysis

•• Based on the sliding block methodBased on the sliding block method•• Uses average accelerations and the shear Uses average accelerations and the shear

beam method.beam method.–– Plot of average maximum acceleration with Plot of average maximum acceleration with

depth of the potential failure surfacedepth of the potential failure surface–– Plot of normalized permanent displacement Plot of normalized permanent displacement

with yield acceleration.with yield acceleration.

5


Embankment Embankment --1010

6


STRESSSTRESS--DEFORMATIONDEFORMATION

•• Dynamic computer programsDynamic computer programs–– Strain potential approachStrain potential approach

•• TARATARA--33

–– Stiffness reduction approachStiffness reduction approach•• DYNAFLOWDYNAFLOW

–– Nonlinear analysis approachNonlinear analysis approach•• Finn Models (FLAC)Finn Models (FLAC)•• Hyperbolic modelHyperbolic model


Finn ModelFinn Model

τ

γ

τ

γ

7


HyperbolicHyperbolic--Martin/Byrne ModelMartin/Byrne Model


Pore Pressure CalculationPore Pressure Calculation

iiw

nk

p ε∆−=∆

ijij G εσ ∆=∆ 2

iiw

ii nkk εσ ∆+=∆ )(

31

8


EMBANKMENT MODELINGEMBANKMENT MODELING


'c 'φ

360.441794454401916SP-SM7360.321121634402120SP-SM6400.281184294502181SP580.3899353102161SM490.48561363201876ML3

110.44443932534.51947CL2190.4598482510.82023CL1

(N1)60Porosity n

Shear modulusG (kPa)

(º)(kPa)Density (Mg/m3)

SoilMaterial

Soil unit

9


Embankment modelingEmbankment modeling

•• Two cases studiedTwo cases studied–– Embankment aloneEmbankment alone–– Embankment with soil beneathEmbankment with soil beneath

•• Two source ground motionsTwo source ground motions–– motion at the ground surfacemotion at the ground surface–– motion at 40 m below the ground surface. motion at 40 m below the ground surface.


Finn Model

10


Finn Model


Hyperbolic model

11


Hyperbolic model


LIQUEFACTION EFFECT ON LIQUEFACTION EFFECT ON THE DEFORMATIONS OF THE THE DEFORMATIONS OF THE

EMBANKMENTSEMBANKMENTS

12


Two cases studied:Two cases studied:

•• Input motion without accounting for liquefaction Input motion without accounting for liquefaction of the subsoils.of the subsoils.

•• Input motion accounting for liquefaction of the Input motion accounting for liquefaction of the subsoils.subsoils.–– FreeFree--field site response analyses were performed to field site response analyses were performed to

obtain accelerationobtain acceleration--time histories at the level ground time histories at the level ground surface as input motions for the dynamic analysis of surface as input motions for the dynamic analysis of the approach embankments.the approach embankments.


Response SpectraResponse Spectra

0

0.4

0.8

1.2

1.6

2

2.4

0.01 0.1 1 10

Period (s)

Spe

ctra

l acc

eler

atio

n (g

)

M70A12N-nonliquefyM70A12N-liquefy

Normal Direction

13


0

0.4

0.8

1.2

1.6

2

0.01 0.1 1 10

Period (s)

Spe

ctra

l acc

eler

atio

n (g

) M70A12P-nonliquefyM70A12P-liquefy

Parallel direction


ResultsResults

•• Spectral accelerations for the cases Spectral accelerations for the cases accounting for liquefaction are smaller accounting for liquefaction are smaller than those without accounting for than those without accounting for liquefaction.liquefaction.

•• Predominant period shift to a shorter Predominant period shift to a shorter period in the normal direction.period in the normal direction.

14


DEFORMATIONSDEFORMATIONS

Normal direction w/o liquefaction


Normal direction with liquefaction

15


Parallel direction w/o liquefaction


Parallel direction with liquefaction

16


Displacements along Displacements along embankment profileembankment profile

Normal DirectionNormal Direction

-1

-0.5

0

0.5

1

0 20 40 60 80 100

Distance from the left (m)

Horiz

onta

l dis

plac

emen

t (m

)

NonliquefyLiquefy

-0.4

-0.2

0

0.2

0.4

0 20 40 60 80 100


Ver

tical

dis

plac

emen

t (m

)

NonliquefyLiquefy

Horizontal Vertical


CONCLUSIONSCONCLUSIONS

•• Large deformations will occur with a large Large deformations will occur with a large earthquake.earthquake.

•• Deformations mainly due to foundation Deformations mainly due to foundation soil movement.soil movement.

•• Lateral spreading may occur.Lateral spreading may occur.

17


Displacements along Displacements along embankment profileembankment profile

Parallel DirectionParallel Direction

-0.5

0

0.5

0 20 40 60 80 100


Horiz

onta

l dis

plac

emen

t (m

)

NonliquefyLiquefy

-0.2

-0.1

0

0.1

0.2

0 20 40 60 80 100


Vert

ical

dis

plac

emen

t (m

)

NonliquefyLiquefy

Horizontal Vertical


Shake Table TestingShake Table Testing

18


PurposePurpose

•• Determine the shakingDetermine the shaking--induced induced displacement and dynamic response of a displacement and dynamic response of a model of the A1466 embankment and to model of the A1466 embankment and to compare it to the numerical model. compare it to the numerical model.


--λ -1/2FrequencyλModulus

1Strainλ 1/2Timeλ 2Stiffness

λStressλ1/2Shear Wave Velocityλ3Force

λLength1Acceleration1Mass Density

Scaling LawsScaling Laws

19


CONTAINERCONTAINER


20


DeformationsDeformations

3mm

1.5m

0.5m0.5m

1mm

0.5m

0.5m3m

m

1mm

0.09

m

Documents

FAILURE MODES - University Transportation Center