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.

Compared with electrical strain gauges, fiber Bragg grating (FBG) sensing technology is a relatively novel method for tunnel structural health monitoring, which has a number of advantages including high accuracy, multiplexing, electromagnetic interference resistance, and good repeatability. In order to study the internal force of the tunnel liner and detect the potential safety hazards, series of strain monitoring tests of a loess tunnel, taking into account the complex stress and strain variation of the loess during tunnelling, were performed by employing the tandem linear FBG sensor arrays controlled by the wavelength division multiplexing (WDM) technology. The concrete strain has obvious linear characteristics over time in the early stage and then gradually tends to a stable value. Moreover, after the necessary temperature compensation, loess tunnel structure safety was assessed through the analysis of real-time strain and internal force of the liner concrete, and the FBG monitoring data and safety assessment results indicate that the safety factors of various liner sections all meet the code requirements, which verify the safety and stability of the tunnel liner structure. The FBG sensors-based in situ monitoring technology can be well applied in the loess tunnel structure safety assessment.

It is well known that the tunnel structure will lose its function under the long-term repeated function of the vibration effect. A prime example is the Xi’an cross tunnel structure (CTS) of Metro Line 2 and the Yongningmen tunnel, where the vibration response of the tunnel vehicle load and metro train load to the structure of shield tunnel was analyzed by applying the three-dimensional (3D) dynamic finite element model. The effect of the train running was simulated by applying the time-history curves of vibration force of the track induced by wheel axles, using the fitted formulas for vehicle and train vibration load. The characteristics and the spreading rules of vibration response of metro tunnel structure were researched from the perspectives of acceleration, velocity, displacement, and stress. It was found that vehicle load only affects the metro tunnel within 14 m from the centre, and the influence decreases gradually from vault to spandrel, haunch, and springing. The high-speed driving effect of the train can be divided into the close period, the rising period, the stable period, the declining period, and the leaving period. The stress at haunch should be carefully considered. The research results presented for this case study provide theoretical support for the safety of vibration response of Metro Line 2 structure.

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