Seismic response study of free-field earthquakes in unsaturated soils with P-wave incidence under thermal effects

Based on the theory of wave propagation in single-phase thermoelastic media and unsaturated porous thermoelastic media, a free-field model of unsaturated soil under plane P-wave incidence is established, and the Helmholtz vector decomposition principle is adopted to analyze the wave field in the free-field of unsaturated soil under the action of thermal effect, and analytical solutions for the seismic response of the free-field of unsaturated soil under the action of thermal effect with plane P-wave incidence are obtained. The influence of thermal physical parameters such as thermal conductivity, medium temperature, and thermal expansion coefficient on the seismic response of an unsaturated soil-free field is analyzed through numerical calculations. The results show that: the displacement magnification factors of the ground obtained under the two theoretical models considering thermal effect and not considering thermal effect have apparent differences; the horizontal displacement magnification factor gradually increases with the increase of thermal conductivity, but the vertical displacement magnification factor is almost unchanged; the horizontal displacement magnification factor gradually increases with the increase of the coefficient of thermal expansion, while the vertical displacement magnification factor decreases gradually; With the increase of medium temperature, the horizontal displacement magnification factor decreases, and the vertical displacement magnification factor gradually increases; in addition, with the increase of saturation degree, the horizontal displacement magnification factor gradually decreases, and the vertical displacement magnification factor gradually increases, which indicates that the existence of gas phase in the soil has a significant influence on the surface displacement magnification factor.