Volume 6 Issue 4
Oct.  2013
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Article Navigation >  Water Science and Engineering  > 2013  >  6(4): 446-455
De-shun YIN, Yan-qing LI, Hao WU, Xiao-meng DUAN. 2013: Fractional description of mechanical property evolution of soft soils during creep. Water Science and Engineering, 6(4): 446-455. doi: 10.3882/j.issn.1674-2370.2013.04.008
Citation: De-shun YIN, Yan-qing LI, Hao WU, Xiao-meng DUAN. 2013: Fractional description of mechanical property evolution of soft soils during creep. Water Science and Engineering, 6(4): 446-455. doi: 10.3882/j.issn.1674-2370.2013.04.008
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Fractional description of mechanical property evolution of soft soils during creep

doi: 10.3882/j.issn.1674-2370.2013.04.008

  • College of Mechanics and Materials, Hohai University, Nanjing 210098, P. R. China

Funds:  This work was supported by the Natural Science Foundation of Jiangsu Province of China (Grant No. BK2012810) and the Fundamental Research Funds for the Central Universities (Grant No. 2009B15114).
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  • Corresponding author: De-shun YIN
  • Received Date: 2012-12-19
  • Rev Recd Date: 2013-06-02
    Abstract
  • The motion of pore water directly influences mechanical properties of soils, which are variable during creep. Accurate description of the evolution of mechanical properties of soils can help to reveal the internal behavior of pore water. Based on the idea of using the fractional order to reflect mechanical properties of soils, a fractional creep model is proposed by introducing a variable-order fractional operator, and realized on a series of creep responses in soft soils. A comparative analysis illustrates that the evolution of mechanical properties, shown through the simulated results, exactly corresponds to the motion of pore water and the solid skeleton. This demonstrates that the proposed variable-order fractional model can be employed to characterize the evolution of mechanical properties of and the pore water motion in soft soils during creep. It is observed that the fractional order from the proposed model is related to the dissipation rate of pore water pressure.   

     

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  • Bagley, R. L., and Torvik, P. J. 1983. Theoretical basis for the application of fractional calculus to viscoelasticity. Journal of Rheology, 27(3), 201-210. [doi: 10.1122/1.549724]
    Bagley, R. L., and Torvik, P. J. 1985. Fractional calculus in the transient analysis of viscoelastically damped structures. AIAA Journal, 23(6), 918-925. [doi: 10.2514/3.9007]
    Bagley, R. L., and Torvik, P. J. 1986. On the fractional calculus model of viscoelastic behavior. Journal of Rheology, 30(1), 133-155. [doi: 10.1122/1.549887]
    Coimbra, C. F. M. 2003. Mechanics with variable-order differential operators. Annalen der Physilk, 12(11-12), 692-703. [doi: 10.1002/andp.200310032]
    Cooper, G. R. J., and Cowan, D. R. 2004. Filtering using variable order vertical derivatives. Computers & Geosciences, 30(5), 455-459. [doi: 10.1016/j.cageo.2004.03.001]
    Eldred, L. B., Baker, W. P., and Palazotto, A. N. 1996. Numerical application of fractional derivative model constitutive relations for viscoelastic materials. Computers & Structures, 60(6), 875-882. [doi:10.1016/ 0045-7949(95)00447-5]
    Enelund, M., Mfhler, L., Runesson, K., and Josefson, B. L. 1999. Formulation and integration of the standard linear viscoelastic solid with fractional order rate laws. International Journal of Solids and Structures, 36 (16), 2417-2442. [doi: 10.1016/S0020-7683(98)00111-5]
    Enelund, M., and Olsson, P. 1999. Damping described by fading memory–analysis and application to fractional derivative models. International Journal of Solids and Structures, 36(7), 939-970. [doi: 10.1016/S0020-7683(97)00339-9]
    Ferry, J. D. 1980. Viscoelastic Properties of Polymers. New York: John Wiley & Sons.
    Gaul, L., Klein, P., and Kemple, S. 1991. Damping description involving fractional operators. Mechanical Systems and Signal Processing, 5(2), 81-88. [doi: 10.1016/0888-3270(91)90016-X]
    Ingman, D., and Suzdalnitsky, J. 2004. Control of damping oscillations by fractional differential operator with time-dependent order. Computer Methods in Applied Mechanics Engineering, 193(52), 5585-5595. [doi: 10.1016/j.cma.2004.06.029]
    Ingman, D., and Suzdalnitsky, J. 2005. Application of differential operator with servo-order function in model of viscoelastic deformation process. Journal of Engineering Mechanics, 131(7), 763-767. [doi: 10.1016/(ASCE)0733-9399(2005)131:7(763) ]
    Koeller, R. C. 1984. Applications of fractional calculus to the theory of viscoelasticity. American Society of Mechanical Engineers, 51(2), 299-307. [doi: 10.1115/1.3167616]
    Lazopoulos, K. A. 2006. Non-local continuum mechanics and fractional calculus. Mechanics Research Communications, 33(6), 753-757. [doi: 10.1016/j.mechrescom.2006.05.001]
    Libertiaux, V., and Pascon, F. 2010. Differential versus integral formulation of fractional hyperviscoelastic constitutive laws for brain tissue modelling. Journal of Computational and Applied Mathematics, 234(7), 2029-2035. [doi: 10.1016/j.cam.2009.08.060]
    Liu, H. L., Hu, S. X., and Ali, H. 2008. Test study on creep characteristics of soft clayey soils under consolidation by vacuum-surcharge combined preloading method. Rock and Soil Mechanics, 29(1), 6-12. (in Chinese)
    Lorenzo, C. F., and Hartley, T. T. 1998. Initialization, Conceptualization, and Application in the Generalized Fractional Calculus. Cleveland: Lewis Research Center, National Aeronautics and Space Administration.
    Lorenzo, C. F., and Hartley, T. T. 2002. Variable order and distributed order fractional operators. Nonlinear Dynamics, 29(1-4), 57-98. [doi: 10.1032/A:1016586905654]
    Luo, Y. 2010. Study on Creep Characteristics of Loess. M. E. Dissertation. Yanglin: Northwest A & F University. (in Chinese)
    Padovan, J. 1987. Computational algorithms for FE formulations involving fractional operators. Computational Mechanics, 2(4), 271-287. [doi: 10.1007/BF00296422]
    Ramirez, L. E. S., and Coimbra, C. F. M. 2007. A variable order constitutive relation for viscoelasticity. Annalen der Physilk, 16(7-8), 543-552. [doi: 10.1002/andp.200710246]
    Schapery, R. A. 1975. A theory of crack initiation and growth in viscoelastic media. International Journal of Fracture, 11(1), 141-159.
    Shah, S. H. A. M., and Qi, H. T. 2010. Starting solutions for a viscoelastic fluid with fractional burgers’ model in an annular pipe. Non-linear Analysis: Real World Applications, 11(1), 547-554. [doi:10.1016/ j.nonrwa.2009.01.12]
    Sheng, H., Sun, H. G., Chen, Y. Q., and Qiu, T. S. 2011. Synthesis of multifractional Gaussian noises based on variable-order fractional operators. Signal Processing, 91(7), 1645-1650. [doi:10.1016/j.sigpro.2011. 01.010]
    Soon, C. M. 2005. Dynamics with Variable Order Operators. M. E. Dissertation. Hawaii: University of Hawaii.
    Soon, C. M., Coimbra, C. F. M., and Kobayashi, M. H. 2005. The variable viscoelasticity oscillator. Annalen der Physilk, 14(6), 378-389. [doi: 10.1002/andp.200410140]
    Sun, H. G., Chen, W., and Chen, Y. Q. 2009. Variable-order fractional differential operators in anomalous diffusion modeling. Physica A: Statistical Mechanics and Its Applications, 388(21), 4586-4592. [doi: 10.1016/j.physa.2009.07.024]
    Tseng, C. C. 2006. Design of variable and adaptive fractional order FIR differentiators. Signal Processing, 86(10), 2554-2566. [doi: 10.1016/j.sigpro.2006.02.004]
    Umarov, S., and Steinberg, S. 2009. Variable order differential equations with piecewise constant order-function and diffusion with changing modesZeitschrift Fur Analysis Und Ihre Anwendungen, 29(4), 431-450..
    Yin, D. S., Wu, H., Cheng, C., and Chen, Y. Q. 2013. Fractional order constitutive model of geomaterials under the condition of triaxial test. International Journal for Numerical and Analytical Methods in Geomechanics,37(8), 961-972.
    Zhou, Q. J., and Chen, X. P. 2006. Experimental study on creep characteristics of soft soils. Chinese Journal of Geotechnical Engineering, 28(5), 626-632. (in Chinese)
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