Nonstationary vibration responses of a three-dimensional tunnel-soil system excited by moving stochastic loads

Abstract This study investigates the nonstationary vibration problem of a three-dimensional tunnel-soil system under moving stochastic loads. A semi-analytical model combing an integral-transform method (ITM) with the pseudo-excitation method (PEM) is proposed to calculate the stochastic responses of the tunnel-soil system. Due to the load movement and randomness, the dynamic responses of the tunnel and soil remain nonstationary at a fixed location. With the aid of the PEM, the nonstationary random vibration problem can be transformed into a moving pseudo harmonic load analysis. To verify the accuracy and efficiency of the proposed method, it is compared with the Monte Carlo simulation. The nonstationary power spectral density (PSD) function and its spatial distribution of the dynamic responses of soil are then systematically analyzed. High frequency stochastic loads play an important role in shaping the PSD response. The stochastic load can cause a more apparent oscillation of wave propagation around the tunnel. Finally, a parametric study is conducted on the effects of the load velocity, soil and tunnel lining parameters on the nonstationary stochastic responses. The maximum RMS of radial stress and pore-water pressure are shown to increase, whereas the radial displacement is demonstrated to decrease with an increase in soil stiffness.