Non-linear Dynamic Analysis Of Subway

In this paper the development and condition are reviewed systemetically for the study on analysis of seismic responses of subway and the related aspacts in the past few decades. And some problems existed are pointed out. Some works on dynamic constitutive model of soil, non-linear dynamic finite element algorithm, boundary condition and wave input method are also done in this paper. The following questions are studied.1. Considered the main performance soil body distorts under the earthquake function for the elastoplasticity, D-P elastoplasticity model, which needs relatively few experimental parameters, and been used relative frequently in engineerings, is adopted for the constitutive model of soil around the tunnel, in this paper. However, the D-P model is generally used as a ideal elastoplasticity model in the engineering calculation. It is feasible for static problems. However, researches indicated that soil body appears hardening phenomenon under cyclic load. Therefore this paper improves the ideal model to be the hardening D-P elastoplasticity construction model which is in consideration of function of hardening, and infers the stress-strain relationship matrix which unified with the finite element mothed. Numerical example is also given to prove that the hardening D-P elastoplasticity construction model is more suitable for dynamic calculation compared to the ideal D-P constitutive model.2. On the numerical integration method, the explicit step-by-step integration form is adopted, beacause it spents less machine-hour. Calculation example given in this paper shows that the non-linear step-by-step integration form quoted by reference [34], when applied in the two-dimensional finite element computation, easily causes drift instability, and does not unify the increment finite element equation easily. Therefore, this paper infers another kind of non-linear explicit step-by-step integration form unifying the centered difference and the unilateral difference, to solve the above problem.3. In view of that the shear wave velocity of the lining of tunnel concrete is greater than that of the soil body around the lining, and the lining of tunnel as the main object of study, is often divided relative thin, the maxmum time step ?t in the tunnel region is smaller than that in the soil body region by the stability criterion c s?t / ? x< 1, when the explicit numerical integration algorithm is applied. A varying time-step explicit numerical integration algorithm[59] is quoted and applied in the two dimensional finite element computation in this paper. Calculation example shows that it saves machine-hour greatly.4. Multi-transmitting formula(MTF) is used to simulate artificial boundary condition, and wave separation technical is applied to solve wave input problem.5. Two-dimensional finite element program is compiled using fortran 90, to calculate the dynamic responses of 7381 tunnel engineering.