One-dimensional rheological consolidation analysis of saturated clay using fractional order Kelvin’s model

LIU Zhong-yu1 YANG Qiang1

(1.School of Civil Engineering, Zhengzhou University, Zhengzhou, Henan Province, China 450001)

【Abstract】The Kelvin model is modified by the spring-pot element based on the Caputo fractional derivative to describe the one-dimensional rheological constitutive relation of saturated clay. The rheological consolidation equation is derived with the assumptions proposed in Terzaghi’s one-dimensional consolidation theory of saturated soil. The numerical analysis is performed by using the Laplace transform and its numerical inversion based on Fourier series expansions. To verify this method, the numerical solutions by the present method for the cases of the integer order derivative are compared with their analytical solutions. The applicability of the modified Kelvin model is verified by the simulation results of one-dimensional rheological consolidation test in the literature. The influences of the fractional order and the coefficient of viscosity of spring-pot component on the rheological consolidation process of soil are investigated. The calculated results show that the dissipation rate of pore water pressure is greater than that based on Terzaghi’s one-dimensional consolidation theory in a long period of consolidation and then less than the latter in the final stage of consolidation. Furthermore, the settlement rate of foundation is always less than that based on Terzaghi’s theory in the process. Overall, the settlement of ground lags the dissipation of pore water pressure. This phenomenon is obvious and it takes more time to achieve the final settlement with the decrease in the fractional order or the increase in the coefficient viscosity.

【Keywords】 rheological consolidation; fractional order derivative; Kelvin model; Laplace transform; pore water pressure; degree of consolidation;

【DOI】

【Funds】 National Natural Science Foundation of China (51578511)

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This Article

ISSN:1000-7598

CN:42-1199/O3

Vol 38, No. 12, Pages 3680-3687+3697

December 2017

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Article Outline

Abstract

  • 1 Introduction
  • 2 Kelvin model based on Caputo fractional derivative
  • 3 Rheological consolidation equation based on modified Kelvin model and its solution
  • 4 Laplace transform and its numerical inversion
  • 5 Test verification of rheological consolidation model
  • 6 Parameter analysis
  • 7 Conclusions
  • References