Influence mechanism of permeability coefficient in homogeneously saturated strata on responses of deep tunnels under incidence of SV waves

For the seismic analysis of underground structures in saturated sites, the coupling effects of pore water and soil skeleton are determined by the permeability coefficient of strata, which is one of the key parameters in the interaction analysis between saturated strata and structures. However, the current researches are usually based on the assumption that the permeability coefficient is zero or infinite, ignoring the permeability of the actual formation, and its influence mechanism is still unclear. Based on the Biot poroelasticity theory, firstly the u-w format model is established for homogeneously saturated strata with different permeability coefficients. According to the distribution ranges of the permeability coefficients corresponding to different types of saturated strata, the analytical expressions for wave velocity of P₁, P₂ and S waves are derived when the permeability coefficient is finite, zero and infinite respectively, and the influences of variation of the permeability coefficient on the free-field wave velocity is analyzed. In addition, a dynamic analysis model is established for different types of saturated strata and deep tunnels, and the proposed model is verified by providing comparisons with the known solutions of typical examples. Furthermore, the response mechanisms of the tunnel structures and surrounding pore water pressures in four typical saturated strata, including sandstone, pebble soil, sandy soil and silt soil, are investigated under the scenarios of variable permeability coefficients and two extreme values (i.e., zero and infinite). The results show that the propagation velocities of three kinds of waves (P₁, P₂ and S waves) in different strata all increase with the permeability coefficient k. When k is less than 10^-4 m/s, the wave velocity reaches the minimum and is consistent with that of the extreme value k=0. When k is greater than 10² m/s, the wave velocity reaches the maximum and is consistent with that of the extreme value k=∞. More specifically, for the saturated sandstone, the amplitudes of tunnel response and pore water pressure of strata gradually increase with the permeability coefficient and tend to the extreme case with the assumption of k=∞. While for the pebble soil and the sandy soil, the amplitudes of tunnel response and pore water pressure of strata gradually increase with the decrease of the permeability coefficient and tend to the extreme case with the assumption of k=0. What's more, for the saturated strata with permeability coefficient in the range of 10^-4 m/s~10² m/s, the dynamic responses of tunnel structures and strata are quite different from those with permeability coefficient of two extreme values, which indicates the assumption that the permeability coefficient is zero or infinite cannot be used in the computational model for this situation. Therefore, the permeability coefficient of saturated strata has a significant influence on the dynamic responses of the tunnel structures and surrounding strata, and should be considered in the seismic design of practical projects.