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A finite element approach is extended to study the ground vibrations induced by metro trains and their propagation properties. Two dynamic interaction models are established: the two-dimensional train-track interaction model, which provides the excitation loads of moving trains onto the tunnel structure, and the three-dimensional track-tunnel-ground interaction model, by which the propagation properties of ground accelerations and velocities are analyzed. The results show that there exists a vibration amplifying area in certain distance away from the tunnel center, and the dominant frequencies of the ground vibration concentrate in a certain range. Buildings located in that area with their natural frequencies falling in the specific frequency range will be sensitive to the ground vibrations induced by metro trains.

Presented herein is a computationally efficient 2D theoretical model for simulating the steady response of a floating slab track-tunnel-soil system. The track-tunnel coupled system is simplified as a beam-spring system and embedded in soil layers. The tunnel is modeled by a Timoshenko beam with its interaction with the soil layers accounted for by two transfer matrices, with each derived for the soil layer above and beneath the tunnel. The approach as proposed herein has been referred to as the Timoshenko beam-transfer matrix method (TTMM), that allows one to analyze the response of the coupled system, including the tunnel motion and soil stresses. The results obtained were compared with those furnished by the pipe-in-pipe (PIP) approach, and were found to be consistent for exciting frequencies smaller than the tunnel second-mode cut-on frequency. The origin of discrepancies was investigated by the dispersion characteristic analysis, which is attributed to the absence of several in-plane modes when the tunnel is simplified as a Timoshenko beam.

A layered rock mass is a special type of geological body. The existence of a bedding surface may lead to a poor cutting effect (over/under-excavation of the surrounding rock), falling of blocks, or collapse, thereby affecting most constructions in areas with such rocks. Given the lack of a proper quantitative analysis method for surrounding rock damages, the construction process of layered surrounding rock tunnels becomes difficult. To address these problems, three types of cut blasting models with single, double, and four holes are studied in this paper. With this, the LS-DYNA program is used to analyze the behaviors of stress wave propagation, crack propagation, and fracture modes, as well as fracture mechanisms of mudstone, sandstone, and layered rock. Using the image processing technology and fractal theory, the fractal dimension change trend and progressive damage evolution behavior of the three types of rocks under different cut blasting conditions are determined. Also determined is the corresponding relationship between the fractal dimension and the rock damage degree. The results indicate that crack initiation, propagation, bifurcation, and fractal dimension evolution are more closely related to the phenomenon where the compression wave is ahead of the tension wave, and the$\setminus$incompatible deformation of the bedding under single-hole blasting. Under double-hole and four-hole blasting, the phenomena, such as spalling, bedding crack penetration, and fracture connection between the explosive holes are caused mainly by the effects of stress concentration, reflected tension waves, and stress wave superposition. Moreover, under different blasting conditions, the rocks exhibit a similar progressive damage process, i.e. a rapid increase at first, then a slow rise, and finally a stabilization phase. The dynamic damage degree of the rock exhibits a linear increasing trend under different blasting holes. The study results provide a useful reference for blasting scheme design and optimization of underground engineering projects.