Investigation Progresses and Applications of Fractional Derivative Model in Geotechnical Engineering

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.

Field Experiment on Soaking Characteristics of Collapsible Loess

“…Meanwhile, the water intake point of west-route of the South-to-North Water Transfer Project is only dozens of kilometers away from Xinzhuangling tunnel, which will be unified with current irrigation system. On this occasion, the large increase of water will cause huge hidden danger for the safety of existential tunnels [37][38][39][40][41]. Therefore, performing the large-scale field soaking experiment near Xinzhuangling tunnel has great engineering significance.…”

A Bayesian Network Model on the Public Bicycle Choice Behavior of Residents: A Case Study of Xi’an

“…Therefore, the 10-fold cross-validation will be conducted 10 times to validate the model. In summary, the process of travel mode selection model based on the Bayesian network combining mutual information and expert knowledge is presented in Figure 2 [42][43][44][45][46].…”

Investigation into the Application of Construction and Demolition Waste in Urban Roads

“…As shown in Figure 1, the recycling rate in China was merely 9.5% in 2012, which was lower than the recycling rate of most EU countries [2]. e recycling and reuse of waste materials, such as C&D waste, waste plastics and rubber, tailing, and ladle furnace slag, has been carefully studied in the last few decades in a number of countries around the world, and techniques have been proposed for how to successfully use these materials in pavements or subgrades [10][11][12][13][14][15][16][17][18][19]. Research on recycled aggregates of C&D waste has mainly re ected its basic performance in road base or subbase applications.…”