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1 ) ) ) ) ) ) (a) (b) -36-
2 -37-
3 (a) ) ) (b) ) -3 3 LIQCA ) ) a) Oka LIQCA -38-
4 u-p formulationoka 994 Newmark 3 FEM -39-
5 b) (i) 3 FEM Zhang 9 3 (ii) () Tatsuoka 98Dr=9% 89% RL=.6DA=7.5% Dr=5% 49% RL=.3DA=7.5% Iwasaki and Tatsuoka977 Pradhan 989 Pradhan 989 CD Fukushima and Tatsuoka984 CD -3-
6 ρ (t/m 3 ).9.9. k (m/s) e V s (m/s) R L λ κ... OCR..5.5 G /σ' m M f M m B B γ p r -.3. γ e r D n Model Experiment..8 Toyoura Dr=5%.3.5 Shear stress ratio.3... Toyoura Dr=5% DA=7.5% Number of cycles 3(a) Dr=5% G/G Shear strain amplitude (b) Dr=5% Damping factor Toyoura Dr=5% R=.3 shear stress (kpa) - - shear stress (kpa) - - Toyoura Dr=5% R=.3-5x shear strain effective mean stress (kpa) 4(a) 4(b) Dr=5% Dr=5% - -3-
7 - Dr=5% 3 4 Dr=9% Dr=5% CD Dr=5% () GPa 7.85t/m 3 5mm mm 6mm (iii) FEM -3-
8 (a) (b) 5 6 Acceleration (Gal) Time (s) 6 (a) (b) ss / σ 5 ij ij m 35mm 3 cm 4cm 35mm 6.5 Newmark =.35=.6 Rayleigh.6 3%
9 c) (i) Dr=5% 7 8 P P4 4 7 P P P4 P P3 P4 P Dr=5% Dr=5%.5. (ii) (iii) 6 No.No.3 No.4No.6 No.No.3 No.4No.6-34-
10 Dr=5% Dr=9% -.m....8 P E.P.W.P.R P E.P.W.P.R Time (s) (a) P Time (s) (b) P.. P3.. P4 E.P.W.P.R E.P.W.P.R Time (s) Time (s) (a) P3 (b) P X-displacement (m) Top of sheet pile Experiment Computed Z-displacement (m) Top of sheet pile Time (s) Time (s) (a) (b) -35-
11 Dr=9% No.4 (X=-.5, Y=.) Experiment Computed No.5 (X=., Y=.) Experiment Computed No.6 (X=.5, Y=.) Experiment Computed Depth (m) Depth (m) Depth (m) Moment (Nm) Moment (Nm) Moment (Nm) (a) (b) (c) No. (X=-.5, Y=-.5) Experiment Computed No. (X=., Y=-.5) Experiment Computed No.3 (X=.5, Y=-.5) Expetiment Computed Depth (m) Depth (m) Depth (m) Moment (Nm) Moment (Nm) Moment (Nm) (d) (e) (f) -36-
12 ) 96 Mroz, 966, 967; Iwan, 967; Krieg, 975; Dafalias and Popov, 975; Hashiguchi, 985 a; Mroz et al., 98; Dafalias and Popov, 977; Mroz et al., 979; Hashiguchi, 985 b; Hashiguchi and Ueno, 977; Dafalias and Herrmann, 98; Hashiguchi, 986, 989 Masing (Hashiguchi and Yoshimaru, 995) (Hashiguchi et al., 989; Topolnicki, 99) 993 Sekiguchi and Ohta (977) Hashiguchi (977, 979b) ( 996; Hashiguchi and Chen, 998) Hashiguchi et. al., 998; Hashiguchi, ; Hashiguchi and Okayasu, (Hashiguchi and Tsutsumi, ; Tsutsumi et. al., ) (Hashiguchi and -37-
13 Tsutsumi, in press), ; Tsutsumi and Hashiguchi, submitted ( 996; Hashiguchi and Chen, 998) ( 996; Hashiguchi and Chen, 998) Dr=5% 4 3 µ = µ c = c 3 σ =9.8 I F = ν =.33 ρ =.5 φ = 4 u = c = µ =. φ d = 33 γ =.8-38-
14 p p (A) (B) p p (C) (D) in the (p, ) plane (%) (%) (A) (B) (%) (%) (C) (D) 3 in the (, ) plane -39-
15 A ( )B ( )C ) D ( ) p, 3, A p,, A B A A C, D p,, ) Dr=5% ) (e) ) 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.66-68, 999. ) 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.9-45,
16 3) :, 35, pp ) :, 36, pp ),,, : 3,, Vol., No., pp.-4,. 6)..3. 7) ) 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.4, No.5, pp.-7,. 9) Tatsuoka, F., Muramatsu, M. and Sasaki, T.: Cyclic undrained stress-strain behavior of dense sands by tosional simple shear test, Soils and Foundations, Vol., No., pp.55-7, 98. ) 33 pp ) 55 III-A ) 56 III-A4. 3) Iwasaki, T. and Tatsuoka, F.: Effects of grain size and grading on dynamic shear moduli of sands, Soils and Foundations, Vol.7, No.3, pp.9-35, ) Pradhan, T.B.S., Tatsuoka, F. and Sato, Y.: Experimental stress-dilatancy relations of sand subjected to cyclic loading, Soils and Foundations, Vol.9, No., pp.45-64, ) Fukushima, S. and Tatsuoka, F.: Strength and deformation characteristics of saturated sand at extremely low pressures, Soils and Foundations, Vol.4, No.4, pp.3-48, ) Dafalias, Y. F. and Popov, E. P. (975): A model of nonlinearly hardening materials for complex loading. Acta Mech., 3, ) Dafalias Y. F. and Popov, E. P. (977): Cyclic loading for materials with a vanishing elastic domain. Nucl. Eng. Design, 4, ) Dafalias, Y. F. and Herrmann, L. R. (98): A bounding surface soil plasticity model. Proc. Int. Symp. Soils under Cyclic Trans. Load. (Pande, G. N. and Zienkiewicz, O. C. eds.). Swansea, Balkema Publ. (Rotterdam). pp ) Hashiguchi, K. and Ueno, M. (977): Elastoplastic constitutive laws of granular materials. Constitutive Equations of Soils (Proc. 9th Int. Conf. Soil Mech. Found. Eng, Spec. Ses.9), Tokyo, JSSMFE, pp
17 ) Hashiguchi, K. (977): An expression of anisotropy in a plastic constitutive equation of soils. idem, ) Hashiguchi, K. (979 a): Constitutive equations of granular media. Proc. 3rd Int. Conf. Numer. Meth. Geomech., pp ) Hashiguchi, K. (979 b): Constitutive equations of granular media with an anisotropic hardening. Proc. 3rd Int. Conf. Numer Meth. Geomech., pp ) Hashiguchi, K. (986): Elastoplastic constitutive model with a subloading surface. Proc. Int. Conf. Comput. Mech. (Atluri, S. N. and Yagawa, G. eds.). Tokyo, Springer-Verlag (Berlin), pp. V ) Hashiguchi, K., Ueno, M. and Imamura, T. (989): Prediction of deformation behavior of sands by the subloading surface model. Proc. Int. Workshop on Constitutive Equations for Granular Noncohesive soils, pp ) Hashiguchi, K. (989): Theoretical assessments on basic structures of constitutive models (Panel Report). ibid., pp ) Hashiguchi, K. (989): Subloading surface model in unconventional plasticity, Int. J. Solids Struct., 5(8), ) Hashiguchi, K. (994): On the loading criterion, Int. J. Plasticity, (8), ) Hashiguchi, K. (995): On the linear relations of V-lnp and lnv-lnp for isotropic consolidation of soils, Int. J. Numer. Anal. Meth. Geomech., 9, ) Hashiguchi, K. and Yoshimaru, T. (995): A generalized formulation of the concept of nonhardening region. Int. J. Plasticity, Vol., ) (996) No. 547/ ) Hashiguchi, K. and Chen, Z. P. (998): Elastoplastic constitutive equation of soils with the subloading surface and the rotational hardening, Int. J. Numer. Anal. Meth. Geomech.,, ) Hashiguchi, K., Wu, X., Okayasu, T. and Tsutsumi, S. (998): Time-dependent elastoplastic constitutive model, Metals & Materials, 4, ) Hashiguchi, K. (): Time-dependent Elastoplastic Constitutive Equation, Archives Mechanics, 5, ) Hashiguchi, K. and Okayasu, T. (): Time-dependent elastoplastic constitutive equation Based on subloading surface model and its application to soils, Soils & Foundations, 4(3), ) Hashiguchi, K. and Tsutsumi, S. (): Elastoplastic constitutive equation with tangential stress rate effect. Int. J. Plasticity, Vol.7, pp ) Hashiguchi, K. and Tsutsumi, S. (in press): Shear band formation analysis in soils by the subloading surface model with tangential stress rate effect. Int. J. Plasticity. 37) Hill, R. (958): A general theory of uniqueness and stability in elasto-plastic -33-
18 solids, J. Mech. Phys. Solids, 6, ) Hill, R. (967): On the classical constitutive relations for elastic/plastic solids, Recent Progress in Appl. Mech. (The Folke Odqvist Volume), John Wiley & Sons, ) Iwan, W. D. (967): On a class of models for the yielding behavior of continuous and composite systems. J Appl. Mech., ASME, 34, ) Krieg, R. D. (975): A practical two surface plasticity theory. J Appt. Mech., ASME, 4, ) Mroz, Z. (966): On forms of constitutive laws for elastic-plastic solids. Archiwum Mechaniki Stosowanej, 8, ) Mroz, Z. (967): On the description of anisotropic workhardening. J Mech. Phys. Solids, 5, ) Mroz, Z., Norris, V. A. and Zienkiewicz, O. C. (979): Application of an anisotropic hardening model in the analysis of elasto-plastic deformation of soils. Geotechnique, 9, ) Mroz,. Z., Norris, V. A. and Zienkiewicz, O. C. (98): An anisotropic, critical state model for soils subject to cyclic loading. Geotechnique, ) Sekiguchi, O. and Ohta, H. (977): Induced anisotropy and time dependency in clays, Constitutive Equations of Soils (Proc. 9th Int. Conf. Soil Mech. Found. Eng., Spec. Session 9), Tokyo, JSSMFE, ) (993) 6. () Vol. 4No ) Topolnicki, M. (99): An elasto-plastic subloading surface model for clay with isotropic and kinematic mixed hardening parameters, Soils and Foundations, 3(), ) Tsutsumi, S., Hashiguchi, K., Okayasu, Y., Saitoh, K. and Sugimoto, M. (): Mechanical response of subloading surface model with tangential plasticity. J. Appl. Mech., JSCE, Vol.4, pp ) Tsutsumi, S. and Hashiguchi, K. (submitted): On the description of general non-proportional loading behaviour of soils. Geotechnique
19 ) 3) (a) (b)
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