SEISMIC PERFORMANCE OF EMBANKMENTS

Transcription

1 SEISMIC PERFORMANCE OF EMBANKMENTS Richard W. Stephenson, Ph.D., P.E. Professor of Civil, Architectural and Environmental Engineering Wanxing Liu Graduate Student University of Missouri-Rolla (UMR) Geotechnical and Bridge Seismic Design Workshop New Madrid Seismic Zone Experience October 28-29, 29, 24, Cape Girardeau, Missouri Embankment - 1 Slope failure Rotational Slide Block Slide FAILURE MODES Lateral Spreading and Associated Settlement Embankment - 2 1

2 METHODS OF ANALYSIS Pseudostatic analysis, Newmark sliding block analysis, Makdisi-Seed analysis, Stress-deformation analysis, Physical modeling (shaking table testing, etc.). Embankment - 3 PSEUDOSTATIC ANALYSIS A horizontal, down- slope inertia force (M*a) is applied to the sliding mass. a=k h W Routine slope stability analyses conducted Bishop Method of slices, Etc. Embankment - 4 2

3 Advantages Relatively simple Produces and index of stability (FS) Disadvantages Rigid body analysis Cannot simulate complex dynamic effects Cannot evaluate influence of porewater pressure buildup Cannot evaluate effect of degradation of shear strength. Embankment - 5 Newmark Sliding Block Analysis First method to assess stability in terms of deformations rather than factor of safety. Assumes rigid-plastic materials Assumes knowledge of the time history of the acceleration acting on the embankment. Embankment - 6 3

4 Advantages Estimates deformations Relatively easy to use. Disadvantages Potential failure mass and embankment are assumed to be rigid Lateral displacements may be out of phase with the inertial forces at different points. Can significantly over predict deformations Embankment - 7 Makdisi-Seed Analysis Based on the sliding block method Uses average accelerations and the shear beam method. Plot of average maximum acceleration with depth of the potential failure surface Plot of normalized permanent displacement with yield acceleration. Embankment - 8 4

5 Embankment - 9 Embankment -1 5

6 STRESS-DEFORMATION Dynamic computer programs Strain potential approach TARA-3 Stiffness reduction approach DYNAFLOW Nonlinear analysis approach Finn Models (FLAC) Hyperbolic model Embankment -11 Finn Model τ γ Embankment -12 6

7 Hyperbolic-Martin/Byrne Model Embankment -13 Pore Pressure Calculation p = kw n ε ii σ ij = 2G ε ij 1 3 k n w σii = ( k + ) ε ii Embankment -14 7

8 EMBANKMENT MODELING Embankment -15 Soil unit Soil Material c' φ' CL CL ML SM SP SP-SM SP-SM Density (Mg/m 3 ) (kpa) (º) Shear modulus G (kpa) Porosity n (N 1 ) Embankment -16 8

9 Embankment modeling Two cases studied Embankment alone Embankment with soil beneath Two source ground motions motion at the ground surface motion at 4 m below the ground surface. Embankment -17 Finn Model Embankment -18 9

10 Finn Model Embankment -19 Hyperbolic model Embankment -2 1

11 Hyperbolic model Embankment -21 LIQUEFACTION EFFECT ON THE DEFORMATIONS OF THE EMBANKMENTS Embankment

12 Two cases studied: Input motion without accounting for liquefaction of the subsoils. Input motion accounting for liquefaction of the subsoils. Free-field site response analyses were performed to obtain acceleration-time time histories at the level ground surface as input motions for the dynamic analysis of the approach embankments. Embankment -23 Response Spectra Spectral acceleration (g) M7A12N-nonliquefy M7A12N-liquefy Period (s) Normal Direction Embankment

13 Spectral acceleration (g) M7A12P-nonliquefy M7A12P-liquefy Period (s) Parallel direction Embankment -25 Results Spectral accelerations for the cases accounting for liquefaction are smaller than those without accounting for liquefaction. Predominant period shift to a shorter period in the normal direction. Embankment

14 DEFORMATIONS Normal direction w/o liquefaction Embankment -27 Normal direction with liquefaction Embankment

15 Parallel direction w/o liquefaction Embankment -29 Parallel direction with liquefaction Embankment -3 15

16 Displacements along embankment profile Normal Direction Horizontal displacement (m) 1.5 Nonliquefy -.5 Liquefy Distance from the left (m) Vertical displacement (m).4 Nonliquefy.2 Liquefy Distance from the left (m) Horizontal Vertical Embankment -31 CONCLUSIONS Large deformations will occur with a large earthquake. Deformations mainly due to foundation soil movement. Lateral spreading may occur. Embankment

17 Displacements along embankment profile Parallel Direction Horizontal displacement (m) Nonliquefy Liquefy Distance from the left (m) Vertical displacement (m).2 Nonliquefy.1 Liquefy Distance from the left (m) Horizontal Vertical Embankment -33 Shake Table Testing Embankment

18 Purpose Determine the shaking-induced induced displacement and dynamic response of a model of the A1466 embankment and to compare it to the numerical model. Embankment -35 Scaling Laws Mass Density 1 Acceleration 1 Length λ Force λ 3 Shear Wave Velocity λ 1/2 Stress λ Stiffness λ 2 Time λ 1/2 Strain 1 Modulus λ Frequency λ -1/2 - - Embankment

19 CONTAINER Embankment -37 Embankment

20 Deformations 3mm 1mm.9m 3mm.5m 1mm.5m.5m 1.5m.5m Embankment -39 2