Investigation Progresses and Applications of Fractional Derivative Model in Geotechnical Engineering

Jinxing Lai,Sheng Mao,Haobo Fan,Jianxun Chen,Zhinan Hu,Junling Qiu,Qian Zhang

doi:10.1155/2016/9183296

Abstract

Over the past couple of decades, as a new mathematical tool for addressing a number of tough problems, fractional calculus has been gaining a continually increasing interest in diverse scientific fields, including geotechnical engineering due primarily to geotechnical rheology phenomenon. Unlike the classical constitutive models in which simulation analysis gradually fails to meet the reasonable accuracy of requirement, the fractional derivative models have shown the merits of hereditary phenomena with long memory. Additionally, it is traced that the fractional derivative model is one of the most effective and accurate approaches to describe the rheology phenomenon. In relation to this, an overview aimed first at model structure and parameter determination in combination with application cases based on fractional calculus was provided. Furthermore, this review paper shed light on the practical application aspects of deformation analysis of circular tunnel, rheological settlement of subgrade, and relevant loess researches subjected to the achievements acquired in geotechnical engineering. Finally, concluding remarks and important future investigation directions were pointed out.

Highlights

In practical engineering, massive unstable failure is closely related to the rheological characteristic of rock and soil
The classical constitutive model for rock and soil can be classified into three distinct approaches, namely, empirical and semiempirical models, rheology theory based models, and visco-elastic-plastic component models
We began with an introduction to relevant concepts and developments of fractional calculus, providing an up-to-date review of key constitutive models which had been widely applied in the field of geotechnical engineering

Summary

Introduction

Massive unstable failure is closely related to the rheological characteristic of rock and soil. Fractional derivative model is applied to describe the nonlinear viscoelastic property, deformation property, shear contraction and dilatation, and damage growth during accelerated stage of creep in geotechnical engineering [9, 22, 23]. We began with an introduction to relevant concepts and developments of fractional calculus, providing an up-to-date review of key constitutive models which had been widely applied in the field of geotechnical engineering. Following this we comprehensively reviewed the state of the art subjected to practical applications of fractional derivative model, including three major aspects of deformation analysis of circular tunnel, rheological settlement of the subgrade, and relevant loess researches

Model Structure Research

Determination of Model Parameters

Engineering Application

Summary and Perspectives