Geomechanics and Engineering

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Settlement analysis of viscoelastic foundation under vertical line load using a fractional Kelvin-Voigt model

  • Zhu, Hong-Hu (School of Earth Sciences and Engineering, Nanjing University) ;
  • Liu, Lin-Chao (School of Civil Engineering, Xinyang Normal University) ;
  • Pei, Hua-Fu (Department of Civil and Structural Engineering, The Hong Kong Polytechnic University) ;
  • Shi, Bin (School of Earth Sciences and Engineering, Nanjing University)
  • Received : 2011.01.23
  • Accepted : 2012.03.05
  • Published : 2012.03.25
⟨ Previous Next ⟩

Abstract

Soil foundations exhibit significant creeping deformation, which may result in excessive settlement and failure of superstructures. Based on the theory of viscoelasticity and fractional calculus, a fractional Kelvin-Voigt model is proposed to account for the time-dependent behavior of soil foundation under vertical line load. Analytical solution of settlements in the foundation was derived using Laplace transforms. The influence of the model parameters on the time-dependent settlement is studied through a parametric study. Results indicate that the settlement-time relationship can be accurately captured by varying values of the fractional order of differential operator and the coefficient of viscosity. In comparison with the classical Kelvin-Voigt model, the fractional model can provide a more accurate prediction of long-term settlements of soil foundation. The determination of influential distance also affects the calculation of settlements.

Keywords

References

  1. Atanackovic, T. M. and Stankovic B. (2004), "Stability of an elastic rod on a fractional derivative type of foundation", J. Sound Vib., 277(1-2), 149-161. https://doi.org/10.1016/j.jsv.2003.08.050
  2. Bagley, R. L. and Torvik, P. J. (1983), "Fractional calculus-a different approach to the analysis of viscoelastically damped structures", Am. Inst. Aeronaut. Astronaut. J., 21(5), 741-748. https://doi.org/10.2514/3.8142
  3. Bagley, R. L. and Torvik, P. J. (1986), "On the fractional calculus model of viscoelastic behavior", J. Rheol., 30(1), 133-155. https://doi.org/10.1122/1.549887
  4. Bjerrum, L. (1967), "Engineering geology of Norwegian normally-consolidated marine clays as related to settlement of buildings", Geotechnique, 17(2), 81-118.
  5. Christie, I. F. (1964), "A re-appraisal of Merchant's contribution to the theory of consolidation", Geotechnique, 14(4), 309-320. https://doi.org/10.1680/geot.1964.14.4.309
  6. Dikmen, U. (2005), "Modeling of seismic wave attenuation in soil structures using fractional derivative scheme", J. Balkan Geophys. Soc., 8(4), 175-188.
  7. Gemant, A. (1936), "A method of analyzing experimental results obtained from elasto-viscous bodies", J. Appl. Phys., 7, 311-317.
  8. Justo, J. L. and Durand, P. (2000), "Settlement-time behaviour of granular embankments", Int. J. Numer. Anal. Meth. Geomech., 24(3), 281-303. https://doi.org/10.1002/(SICI)1096-9853(200003)24:3<281::AID-NAG66>3.0.CO;2-S
  9. Kaliakin, V. N. and Dafalias, Y. F. (1990), "Theoretical aspects of the elastoplastic-viscoplastic bounding surface model for cohesive soils", Soil Found., 30(3), 11-24. https://doi.org/10.3208/sandf1972.30.3_11
  10. Li, G. G., Zhu, Z. Y. and Cheng, C. J. (2001), "Dynamical stability of viscoelastic column with fractional derivative constitutive relation", Appl. Math. Mech. -Engl. Ed., 22(3), 294-303.
  11. Liu, L. C., Yan, Q. F. and Sun, H. Z. (2006), "Study on model of rheological property of soft clay", Rock Soil Mech., 27(S1), 214-217. (in Chinese)
  12. Miller, K. S. and Ross, B. (1993), An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York .
  13. Padovan, J. (1987), "Computational algorithms for FE formulations involving fractional operators", Comput. Mech., 2(4), 271-287. https://doi.org/10.1007/BF00296422
  14. Paola, M. Di., Marino, F. and Zingales M. (2009), "A generalized model of elastic foundation based on long-range interactions: Integral and fractional model", Int. J. Solids Struct., 46(17), 3124-3137. https://doi.org/10.1016/j.ijsolstr.2009.03.024
  15. Rossikhin, Y. A. and Shitikova M. V. (2010), "Application of fractional calculus for dynamic problems of solid mechanics: novel trends and recent results", Appl. Mech. Rev., 63(1), 010801, 1-52. https://doi.org/10.1115/1.4000563
  16. Timoshenko, S. P. and Goodier, J. N. (1970), Theory of Elasticity, McGraw-Hill, New York.
  17. Welch, S. W. J., Rorrer, R. A. L. and Ronald, G. D. Jr. (1999), "Application of time-based fractional calculus methods to viscoelastic creep and stress relaxation of materials", Mech. Time-Depend. Mater., 3(3), 279-303. https://doi.org/10.1023/A:1009834317545
  18. Yin, J. H. and Graham, J. (1994), "Equivalent times and one-dimensional elastic viscoplastic modelling of time-dependent stress-strain behaviour of clays", Can. Geotech. J., 31(1), 42-52. https://doi.org/10.1139/t94-005
  19. Zhang, W. and Shimizu, N. (1998), "Numerical algorithm for dynamic problems involving fractional operators", J. Soc. Mech. Eng. Int. J. Ser. C., 41(3), 364-370.
  20. Zhu, H. H., Liu, L. C. and Ye, X. W. (2011), "Response of a loaded rectangular plate on fractional derivative viscoelastic foundation", J. Basic Sci. Eng., 19(2), 271-278. (in Chinese)

Cited by

  1. Fractional modeling of Pasternak-type viscoelastic foundation vol.21, pp.1, 2017, https://doi.org/10.1007/s11043-016-9321-0
  2. A new analytical model to determine dynamic displacement of foundations adjacent to slope vol.6, pp.6, 2014, https://doi.org/10.12989/gae.2014.6.6.561
  3. Theoretical investigation of interaction between a rectangular plate and fractional viscoelastic foundation vol.6, pp.4, 2014, https://doi.org/10.1016/j.jrmge.2014.04.007
  4. Assessing composition and structure of soft biphasic media from Kelvin–Voigt fractional derivative model parameters vol.28, pp.3, 2017, https://doi.org/10.1088/1361-6501/aa5531
  5. Blind Source Separation Model of Earth-Rock Junctions in Dike Engineering Based on Distributed Optical Fiber Sensing Technology vol.2015, 2015, https://doi.org/10.1155/2015/281538
  6. Prediction of one-dimensional compression behavior of Nansha clay using fractional derivatives vol.35, pp.5, 2017, https://doi.org/10.1080/1064119X.2016.1217958
  7. Short note: Method of Dimensionality Reduction for compressible viscoelastic media. I. Frictionless normal contact of a Kelvin-Voigt solid vol.98, pp.2, 2018, https://doi.org/10.1002/zamm.201700128
  8. Limit analysis of supporting pressure in tunnels with regard to surface settlement vol.22, pp.1, 2015, https://doi.org/10.1007/s11771-015-2522-x
  9. A non-linear thermo-viscoelastic rheological model based on fractional derivatives for high temperature creep in concrete vol.55, 2018, https://doi.org/10.1016/j.apm.2017.11.028
  10. Bending of a rectangular plate resting on a fractionalized Zener foundation vol.52, pp.6, 2014, https://doi.org/10.12989/sem.2014.52.6.1069
  11. A long term evaluation of circular mat foundations on clay deposits using fractional derivatives vol.94, 2018, https://doi.org/10.1016/j.compgeo.2017.08.018
  12. Time-Dependent Settlement of Pile Foundations Using Five-Parameter Viscoelastic Soil Models vol.18, pp.5, 2018, https://doi.org/10.1061/(ASCE)GM.1943-5622.0001122
  13. The fractional derivative Kelvin–Voigt model of viscoelasticity with and without volumetric relaxation vol.991, pp.1742-6596, 2018, https://doi.org/10.1088/1742-6596/991/1/012069
  14. Fractional calculus-based compression modeling of soft clay vol.2, pp.10, 2012, https://doi.org/10.3208/jgssp.chn-54
  15. Material property analytical relations for the case of an AFM probe tapping a viscoelastic surface containing multiple characteristic times vol.8, pp.None, 2012, https://doi.org/10.3762/bjnano.8.223
  16. Dynamic Mechanical Properties of Soil Based on Fractional-Order Differential Theory vol.55, pp.6, 2019, https://doi.org/10.1007/s11204-019-09550-5
  17. Determination of Viscoelastic Properties of Soil and Prediction of Static and Dynamic Response vol.19, pp.7, 2012, https://doi.org/10.1061/(asce)gm.1943-5622.0001456
  18. Long-Term Deformation Analysis for a Vertical Concentrated Force Acting in the Interior of Fractional Derivative Viscoelastic Soils vol.20, pp.5, 2012, https://doi.org/10.1061/(asce)gm.1943-5622.0001649
  19. On the transient response of plates on fractionally damped viscoelastic foundation vol.39, pp.4, 2012, https://doi.org/10.1007/s40314-020-01285-6
  20. Theoretical and Numerical Analysis of Soil-Pipe Pile Horizontal Vibration Based on the Fractional Derivative Viscoelastic Model vol.2021, pp.None, 2012, https://doi.org/10.1155/2021/4767892
  21. An existence result for the fractional Kelvin-Voigt’s model on time-dependent cracked domains vol.21, pp.4, 2012, https://doi.org/10.1007/s00028-021-00713-2