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らむとどろき
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3 (a) (b) 1) ) LIQCAOka 199Oka 1999 ),3) )

4 1) a) b) i) 1) 1 FEM Zhang ) 1 1)

5 FEM ii) () 1 Dr=9% Dr=35% Tatsuoka 19Fukushima and Tatsuoka19 5),) Dr=35% Dr=35% Dr=3%1kPa 1kPa

6 1 ρ (t/m 3 ) k (m/s) e V s (m/s) R L λ κ.9.. OCR G /σ' m M f M m B B γ p r..3.1 γ e r..5.3 D n.. 5. Dr=35% -1 Creager Dr=9% Dr=35%(a) (b)(c)(d) 3% 1kPa

7 .3. 5 Shear strain Shear stress (kpa) Shear stress (kpa) step 15 (a) Shear strain (b) Shear stress (kpa) Effective mean stress (kpa) (c) (d) 3 Dr=35% step.5. Model Experiment 1.. Toyoura Dr=3%.3.5 Shear stress ratio.3. G/G Damping factor.1 Toyoura Dr=3% DA=7.5% Number of cycles (a) Shear strain amplitude (b) Toyoura Dr=3% R= shear stress (kpa) shear stress (kpa) Toyoura Dr=3% R= x shear strain effective mean stress (kpa) (c) (d) Dr=35%.3 Dr=35% (a)(b)

8 .1 1 Shear strain Shear stress (kpa) x1 3 1 step (a) Shear strain (b)..5 Shear stress (kpa) 5-5 Volumetric strain x1 3 Effective mean stress (kpa) (c) (d) 5 step (c)(d) 1 Tatsuoka 19 5) (c) 5 (a) (b)(c)(d) 1.35g/cm 3 1kPa (d) 1.1 () 1GPa 7.5t/m 3 5.mm 1.5mm mm

9 iii) FEM 1 1 1cm5cm 1 (a)(b) 5mm.5mm

10 (a) (b) 1 (a) (b) 7 1 (a)(b) mm 5Gal 5Hz.15 Newmark =.35=. Rayleigh 1.9 3%

11 c) d) 1 i) Dr=35% 9 W-1 W3- W-1 W1- W Dr=35% 1 Dr=35% 1 ii) 1 Dr=35% Dr=35%

12 W-1 W1- E.P.W.P (kpa) E.P.W.P (kpa) E.P.W.P (kpa) 1 1 Time (s) Time (s) (a) W-1 (b) W1- Time (s) W- E.P.W.P (kpa) 1 1 Time (s) (a) W- (b) W3-1 W (a) (b) 13 (c) 9 DY-NL(d) 13 1/ 1/

13 Y-Acceleration (m/s/s) - - Input motion Y-Acceleration (m/s/s) Top of pile- X-Displacmement (m) Time (s) (a) Top of sheet pile Time (s) (b) X-Displacmement (m) x1-3 Top of pile- Time (s) Time (s) (c) (d) 11 1 iii) No.1No.3 No. No. No.1No.3 No.No. Dr=35%.5m1.m Dr=35% 11 1 e) 3 i)

1. 1. No. 1. 1. No.5 1. 1. No. 1. 1. 1. Height (m) 1.. Height (m) 1.. Height (m) 1......... -.5.. -.5.. -.5. Moment (knm) Moment (knm) Moment (knm) (a) (b) (c) 1. 1. No.1 1. 1. No. 1. 1. No.3 1.

14 1. 1. No No No Height (m) 1.. Height (m) 1.. Height (m) Moment (knm) Moment (knm) Moment (knm) (a) (b) (c) No No No Height (m) 1.. Height (m) 1.. Height (m) Moment (knm) Moment (knm) Moment (knm) (d) (e) (f) (a) 9 DY-NL (b)

15 X-Displacmement (m) Top of sheet pile 3 X-Displacmement (m) x1-3 3 Top of pile- Time (s) Time (s) (a) (b) 1 3 (a) (b) 3 15 H=1.m 3 (a) (b) 3 1 H=1.m %

16 m 1 Dr=35% 1.m Dr=35% 1.m ii) No No No Height (m) 1.. Height (m) 1.. Height (m) Moment (knm) Moment (knm) Moment (knm) (a) (b) (c)

17 ) Hashiguchi, 199: Hashiguchi and Chen, 199 7),) Masing Sekiguchi and Ohta (1977) 9) Hashiguchi and Tsutsumi, 1 1) 1)1 1 i) 3 Layers 1-3 Layer Dr=5%9 Layers 1 & 3 Layer 1 (dry) P-1 P- Layer (saturated) Total mesh number: 1 Mesh size: 11m P-3 Sine wave: 5Hz, 5Gal Layer 3 (saturated) Input (sine wave) 1 Shear stress ratio Toyoura Dr = 5 % DA =7.5 % Model Experiment Number of cycle

18 3 1. ν ( G). ρ 3. γ. p i 5. φ ( m). u 7. c. µ 9. φ ( m ) 1. b r 11. φ ( m ) 1. σ d b d b s F 15. β ν =.33 ρ =.5 γ =.1 Layer Layers 1 & 3 F = f u = φ = c = 1 φ d = 33 µ =. ν =.33 ρ =.5 γ =.1 F = 1 f u = φ = 1 c = φ d = µ = f = p (1+ )φ - 3 -

19 Shear stress (kpa) P-1 P- P Effective mean stress (kpa) Shear stress (kpa) P-1 P- P Shear strain

20 1) 1/1/ ) (e) 1).3.. ) Oka, F., Yashima, A., Shibata, T., Kato, M. and Uzuoka, R.: FEM-FDM coupled liquefaction analysis of a porous soil using an elasto-plastic model, Applied Scientific Research, Vol.5, pp.9-5, ) Oka, F., Yashima, A., Tateishi, A., Taguchi, Y. and Yamashita, S.: A cyclic elasto-plastic constitutive model for sand considering a plastic-strain dependence of the shear modulus, Geotechnique, pp.1-, ) Zhang, F., Kimura, M., Nakai, T. and Hoshikawa, T.: Mechanical behavior of pile foundations subjected to cyclic lateral loading up to the ultimate state, Soils and Foundations, Vol., No.5, pp.1-17,. 5) Tatsuoka, F., Muramatsu, M. and Sasaki, T.: Cyclic undrained stress-strain - 3 -

21 behavior of dense sands by tosional simple shear test, Soils and Foundations, Vol., No., pp.55-7, 19. ) Fukushima, S. and Tatsuoka, F.: Strength and deformation characteristics of saturated sand at extremely low pressures, Soils and Foundations, Vol., No., pp.3-, 19. 7) Hashiguchi, K.: Subloading surface model in unconventional plasticity, Int. J. Solids Struct., 5(), , 199. ) Hashiguchi, K. and Chen, Z. P.: Elastoplastic constitutive equation of soils with the subloading surface and the rotational hardening, Int. J. Numer. Anal. Meth. Geomech.,, 199-7, ) Sekiguchi, O. and Ohta, H.: Induced anisotropy and time dependency in clays, Constitutive Equations of Soils (Proc. 9th Int. Conf. Soil Mech. Found. Eng., Spec. Session 9), Tokyo, JSSMFE, pp. 9-3, ) Hashiguchi, K. and Tsutsumi, S.: Elastoplastic constitutive equation with tangential stress rate effect. Int. J. Plasticity, Vol. 17(1), pp , 1. (f) Prediction of Earth Pressures on a Pile Group Due to Liquefaction-induced Ground Flow Sixth World Congress on Computational Mechanics (WCCM VI) in conjunction with the Second Asian-Pacific Congress on Computational Mechanics (APCOM') (g) ) 3)

22 (3) (a) - (b) 1 1 E - 3 -

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-37- ) ) ) ) ) ) (a) (b) -36- -37- (a) ) ) (b) ) -3 3 LIQCA ) ) a) Oka 999 3 LIQCA -38- u-p formulationoka 994 Newmark 3 FEM -39- b) (i) 3 FEM Zhang 9 3 (ii) () Tatsuoka 98Dr=9% 89% RL=.6DA=7.5% 998 999 Dr=5%