Effective-stress Based Dynamic Analysis and Centrifuge Simulation of Earth Dam Yii-Wen Pan 1 Hui-Jung Wang 1 C.W.W. Ng 2 1 National Chiao-Tung University 2 Hong Kong University of Science and Technology

Contents Introduction Constitutive Model of Compacted Soil Numerical Analysis and Centrifuge Tests Comparison of Calculated and Experimental Results Application Conclusions

Objectives Effective-stress modeling for earth dam Verification by centrifuge models Purposes of dynamic analysis for earth dam to evaluate dam response under earthquake Stress / Acceleration Liquefaction Potential Permanent deformation/settlement Types of analysis Total stress analysis Effective stress analysis Introduction Dynamic Stress Analysis for Earth Dam

Effective Stress Constitutive Models for Soil under Cyclic Loading  v = f( , , No of cycles,…) e.g., ： Martin-Finn (1975) dilatancy = f( stress state, state parameters,…) e.g., Li et al. (2000) Ueng and Lee (1990)   u = f(damage parameters)  u = f(k) or  v = f (k) e.g., Finn et al.(1981) endochronic model Park(2000) disturbed state concept Elasto-plastic model e.g., Manzari ＆ Dafalias (1997), Prevost （ 1985 ） Pastor et al, (1990), Iai et al. (2000)

Effective-stress Based Dynamic Analysis FEM & FDM incorporating effective stress model appropriate for cyclic loading e.g., Zienkiewicz, et al. (1981, 1984) Beaty and Byrne (1999) Dakoulas and Eltaher (1998) Ming and Li (2003) among others Application on dynamic response of earth dam Simulation of failure case e.g., Lower San Fernando Dam – built by hydraulic fill

Typical Behavior of heavily compacted fill  =10 -3 %  =10 -2 %  =10 -1 % ~1%

A Constitutive Model of Compacted Soil Stress-strain relation 1.Incrementally linear 2.Stress-level dependent 3.Modulus degradation - disturbed state concept 4.Irrecoverable dilatancy  Assumption Saturated Soil

DSC ( Disturbed State Concept) Desai and co-workers (1991) 1.Disturbance due to external loading 2.RI (Related Intact)  FA (fully adjusted ) Follows a specific rule 3.Separate Constitutive laws for RI ＆ FA

Constitutive Relations Seed-Idriss formula (1970) As D d   RI State : FA State : As D d   Along the failure line  =M Li and Dafalias (2000)

Intermediate state For an arbitrary disturbed state (i.e., for 1>D d   Accounting for stress history

Modeling Pore Water Pressure Build-up : slope of phase transformation line C &  : material parameters : shear strain increment : plastic volumetric strain Irrecoverable Dilatancy Pore Water Pressure Build-up

1.Progressive yielding Stress history 4. Pore pressure build-up Summary of Model

Model Behavior Stress Path Stress-Strain Pore Water Pressure Build-up

Calibration of Parameters Type of parameters Elastic Constants Modulus Related Dilatancy Critical States Parameters K max, G max β, λ,  C, ω M, ψ μ Calibration by optimization (through GA, Nonlinear) Objective function Parameters

Centrifuge Testing Purposes Observation of the dynamic response of model earth dam subjected to dynamic loadings Verification of Numerical Model Centrifuge tests Carried out in Hong Kong University of Science and Technology Capacity : 400 g-tons Arm radius : about 4.2m Maximum centrifuge acceleration : 70g Shaker: max. shaking acceleration 40g

Model Embankment Dam Detail of the model embankment dam in rectangular rigid container 712mm x 432mm x 440mm symmetrical slopes (slope ratio 1:2) height and base width : 190 mm and 660 mm Leighton-Buzzard sand with D r =90% Carboxy methylcellulose (CMC) as the substituted pore fluid (Dewoolkar et al 1999) to take time conflict of dynamic and diffusion problems into account CMC is a water-soluble cellulose ether odorless, harmless, use in food & pharmacy

Installed miniature sensors: accelometers, pore pressure transducers, LVDTs, Laser sensors Model Embankment Dam

Triaxial Tests Purpose: Calibration of parameters for the material as same as the model embankment dam (D r =90%) Types of Test Cyclic triaxial tests Stress controlled cyclic triaxial tests  c =0.3 、 0.5 、 1kg/cm 2 Monotonic CU tests  c = 0.3 、 0.5 、 1 kg/cm 2

Dam Construction Modeling Static Stress Analysis Modeling Seepage Analysis (obtain steady state phreatic surface) Stress Analysis after Steady State Seepage (static equilibrium after steady state seepage) Dynamic Analysis (in time domain) Effective Stress Based Numerical Analysis

Pore Water Pressure

Acceleration

Settlement

Application in Li-Yu-Tan Dam Li-Yu-Tan Dam A well instrumented earth dam. Data was successfully recorded in Chi-Chi earthquake Input motion in numerical simulation Using the recorded bedrock acceleration in Chi-Chi earthquake Comparison of the numerical results and the recorded data in Chi-Chi earthquake

Mesh Vertical Stress Horizontal Stress Vertical Deformation Horizontal Deformation Results of Static Analysis

Pore Water Pressure Steady-state Flow Vertical Stress Horizontal Stress Vertical Deformation Horizontal Deformation

Results of Dynamic Analysis Pore Water Pressure Vertical Stress Horizontal Stress Vertical Deformation Horizontal Deformation

Acceleration history in bedrock & Crest m /sec 2 sec

Comparison of Numerical Results and Recorded Data Maximum settlement Recorded settlement < 10 cm Calculated settlement ~10cm Horizontal deformation Downstream slope moves toward downstream, and vice versa Agree with the trend of instrumented data Amplification of acceleration About 3 times at crest Close to the recorded data

Conclusions Heavily compacted fill in an earth dam behaves like a very dense soil. An effective stress based constitutive model for compacted fill was proposed. This model takes into account Progressive degradation Stress-level dependency Effects of stress history & Stress history Pore water pressure build-up

Conclusions (con ’ d) A numerical model for an effective stress based analysis was developed for dynamic analysis of earth dam verified by the results of centrifuge tests Effective stress analysis for a well instrumented earth dam using the Chi-Chi earthquake data numerical and instrumented results were consistent

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