Site Response Using Effective Stress Analysis

Transcription

1 Site Response Using Effective Stress Analysis Faiz Makdisi, Zhi-Liang Wang, C.Y. Chang and J. Egan Geomatrix Consultants, Inc. Oakland, California 1 TRB 85 th Annual Meeting, January 22-26, 26, 2006, Washington, D.C.

2 Introduction Non linear vs. Equivalent Linear Analyses Effective Stress Model Description Simulation of recorded Ground Motions at a Liquefaction Site Example Site Response Analyses Observations and Conclusions 2

3 Nonlinear and Equivalent Linear Analysis Deep Stiff Soil Site Mw 6 ½ earthquake, PGA=0.2 g Mw 7 ½ earthquake, PGA=0.5g Average of 25 input time histories Total Stress Analysis Compared results of SHAKE, Rascal, SUMDES and DMOD-2 3

4 Comparison with Equivalent Linear Analysis Total Stress Analysis 2 Spectral Pseudo-Acceleration (g) Mw 6.5, Med. Deep Profile ft Input PGA=0.2g Average Ground Surface Response SHAKE RASCAL SUMDES D-MOD Period (sec)

5 Comparison with Equivalent Linear Analysis Total Stress Analysis 3 Spectral Pseudo-Acceleration (g) Mw 7.5, Med. Deep Profile ft Input PGA=0.5g Average Ground Surface Response SHAKE RASCAL SUMDES D-MOD Period (sec)

6 Linear Vs. Nonlinear Response (Total Analysis) PEER Program (Stewart and Kwok, 2005) Non Linear Total Stress Analyses - CYCLIC 1D (Yang and Elgamal,, 2004) - DEEPSOIL (Hashash( and Park, 2002) - D-MOD_2 (Matasovic( Matasovic,, 2004) - SUMDES (Wang, 2005) - TESS (Pyke( Pyke,, 2000) 6

7 Effective Stress Site Response Analyses SUMDES (Li, Wang & Shen,, 1992) one-dimensional wave propagation with bounding surface plasticity constitutive model FLAC (Itasca, 2005) Two-dimensional finite difference code incorporated with bounding surface plasticity model of Wang,

8 Nonlinear Analysis Bounding Surface Hypo-plasticity Model (Wang et al, 1990) J Line of Phase Transformation R-R p =0 Failure Surface R-R f =0 Loading dσ ij Maximum Pre-stress Surface R-R m =0 Unloading dσ ij p 8

9 Bounding Surface Hypo-plasticity Model Simulations (Wang et al 2000) (a) (a) q (kpa) 1000 q (kpa) 2000 q (KPa) Dashed lines: Test Results from Verdugo & Ishihara (1996) Solid lines: Model Simulations Axial Strain, ε a 1000 Axial Strain (%) 4000 Dashed lines: Test Results from Verdugo & Ishihara (1996) Solid lines: Model Simulations Axial Strain, ε a (b) (b) q (kpa) 1000 q (kpa) p (kpa) P (KPa) Consolidated Undrained Triaxial Tests on Sand p(kpa)

10 Simulation of Cyclic Triaxial Tests on Sands Test Results Model Prediction 10

11 Sample Model parameters used in non linear response analysis φ G o * h r R p /R f b k r d κ * h r is variable to fit G/G max used in equivalent linear analysis 11

12 Dynamic Properties Used in Analyses Normalized Shear Modulus, G/Gmax Damping Ratio (%) Upper Bound Sand Curve (Seed & Idriss, 1970) Non-linear Model at Typical Depths (p= 8 to 39 ksf) Lower Bound (Seed & Idriss, 1970) p=8ksf ksf Effective Shear Strain Amplitude (%) 12

13 Cyclic Strength From Field Liquefaction Data (from Seed et al, 1985) (Wang and Makdisi, 1998) 13

14 Bounding Surface Hypo-plasticity Model Simulations Sandy Fill, p = 2 ksf Shear Stress (ksf) Stress ratio 0.2 Phase Transformation Line Failure Line Shear Stress (ksf) Sandy, p = 2 ksf stress ratio = Effective Confining Pressure (ksf) Shear Strain Cyclic Tri-axial Tests on Sand 14

15 Dynamic Response of 100-foot Embankment (QUAD4M, FLUSH, and FLAC comparisons) 5 4 Mid Slope Spectral Acceleration (g) 3 2 At Middle of Slope QUAD4M, after 5 Iteration FLUSH, after 5 Iterations FLAC, QUAD4M Propertie and To=0.25 Second Period (sec) 15

16 Dynamic Response of 100-foot Embankment (QUAD4M, FLUSH, and FLAC comparisons) 5 4 Crest Spectral Acceleration (g) 3 2 At Crest QUAD4M, after 5 Iterations FLUSH, after 5 Iterations FLAC, QUAD4M Properties and To=0.25 Seconds Period (sec)

17 Port Island Downhole Array Site Port Island Downhole Blowcount V s,, m/s V p, m/s Fill Gravel Alluvial Deposits Diluvial Sandy Gravelly Deposits Sand with Gravel Clay Sand Sand with Gravel Sand Depth (m) Depth (m) Depth (m) Diluvial Clayey Deposits Clay Location of Downhole Instruments (at depths of 0, 16, 23, 32, and 83 m) 17 (After Iwasaki and Tai, 1996)

18 Model Simulation of Masado Fill at Port Island 1.0 Cyclic Stress Ratio Reclaimed Soils at Port Island Average of Test Results (after Nagase etal., 1995; Yasuda. 1990) Model Simualtion at 12m Depth Model Simulation at 4m Depth Number of Cycles to 5% D.A. Axial Strain

19 Recorded Motions at 83m During 1995 Hyogoken- Nanbu Kobe Earthquake (after CEORKA) Acceleration (g) 0.2 N00E Component Acceleration (g) N90E Component 19 Acceleration (g) Vertical Component Time (second)

20 Acceleration, g Comparison of computed and recorded motions (N00E component) Recorded at Ground Surface Computed Using SUMDES (3D) Acceleration, g Acceleration, g at Depth 16m at Depth 32m Time, seconds

21 Comparison of computed and recorded motions (N90E component) Acceleration, g Acceleration, g Acceleration, g Recorded at Ground Surface Computed Using SUMDES (3D) at Depth 16m at Depth 32m Time, seconds

22 Comparison of computed and recorded motions (VERT component) 22 Acceleration, g Acceleration, g Acceleration, g Recorded at Ground Surface Computed Using SUMDES(3D) at Depth 16m at Depth 32m Time, seconds

23 Comparison of recorded spectra (N00E) Spectral Acceleration (g) Recorded at Ground Surface Computed using SUMDES (3D) Spectral Acceleration (g) at Depth 16m Period (second) Period (second) 2.0 at Depth 32m Corrected Motion Recorded at 83m Depth Spectral Acceleration (g) Spectral Acceleration (g) Period (second) Period (second)

24 Comparison of recorded spectra (N90E) Spectral Acceleration (g) Recorded at Ground Surface Computed Using SUMDES (3D) Spectral Acceleration (g) Recorded at Depth 16m Period (second) Period (second) 2.0 Recorded at Depth 32m Corrected as Input Motion Spectral Acceleration (g) Spectral Acceleration (g) Period (second) Period (second)

25 Comparison of recorded spectra (VERT) Spectral Acceleration (g) Recorded at Ground Surface Spectral Acceleration (g) Corrected Record at Depth 16m Computed Using SUMDES (3D) Period (second) Period (second) 2.0 Recorded at Depth 32m Recorded at Depth 83m Spectral Acceleration (g) Spectral Acceleration (g) Period (second) Period (second)

26 Excess Pore Pressure Distribution with Depth Depth below Surface (meter) Peak Pore Water Pressure Ratio Base Motion Used: Three Components Component N00E only Component N90E only Pore Water Pressure Ratio 26

27 Time Histories of Mean Effective Stress at Various Depths 300 at 32m Effective Mean Pressure p', kpa at 16m at 12m at 6m Times, Second

28 Example of Site Response Analysis Used Port Island Soil Profile and properties Five recordings from 5 Earthquakes Magnitude Range: M w =6 ½ - 7 Recordings within km from source Records scaled to PGA of 0.6 to 0.7g 28

29 Example Site Response Equivalent Linear Analysis SHAKE Erzincan, Erzincan 1992 Amagasaki, Kobe 1995 El Centro ICC, Superstition Hills 1987 Duzce, Duzce 1999 Holtville PO, Imperial Valley 1979 Average Spectral Acceleration (g) Period (sec)

30 2.5 2 Example Site Response Non Linear Effective Stress Analysis SUMDES Erzincan, Erzincan 1992 Amagasaki, Kobe 1995 El Centro ICC, Superstition Hills 1987 Duzce, Duzce 1999 Holtville PO, Imperial Valley 1979 Average Spectral Acceleration (g) Period (sec)

31 Nonlinear Effective vs. Equivalent Linear Analyses Average of SHAKE Results Average of SUMDES Results Spectral Acceleration (g) Period (sec)

32 Observations on Results of Site response Surface response spectral amplitudes from effective stress analyses are lower than routinely used total analyses Induced stresses are limited by low shear strength, build up of excess pore pressure and softening 32

33 Summary and Conclusions Effective stress analyses are available for site response Results of analyses provided reasonable comparisons with recorded ground motions Refinements of these analyses will continue with further validation using earthquake recordings at instrumented sites Analyses may be useful for estimating site response for soft and liquefiable sites but should be calibrated with analyses at recorded sites 33

34 Summary and Conclusions (Cont d.) Their development and their predominant use is for estimating permanent deformations At present their application for site response in practice is still rather limited Ongoing research programs should help transfer the technology to practicing engineers 34