Seismic energy distribution characteristics of soil-tunnel systems and a tunnel lining energy distribution coefficient (TLC)-based evaluation method

The seismic response of underground tunnels is strongly influenced by soil properties, wave-propagation characteristics and soil-structure interaction. However, conventional response measures such as acceleration, spectral characteristics and strain cannot directly quantify the relative energy participation of the tunnel lining within the local soil-tunnel interaction system. This study combines shaking table tests and three-dimensional dynamic numerical modeling to propose and illustrate a tunnel lining energy distribution coefficient (TLC). Free-field and soil-tunnel tests were first conducted to examine how the tunnel affects surface acceleration, spectral characteristics and circumferential lining strain. The TLC was then formulated from lining strain energy and the dynamic energy of adjacent soil, and its evolution was analyzed under different ground motions and lining regions using a full-scale numerical model. The tests show that the tunnel reduces the acceleration amplification factor at the central ground surface by approximately 2.58%-37.82% and shifts the dominant frequency to a lower range. Lining strain is strongly non-uniform around the circumference, with concentrations near slab-wall joints and corners. The numerical results further indicate that TLC captures temporal changes in the relative energy contribution of the lining within the prescribed local lining-soil region. The full-duration energy-weighted TLC consistently follows the regional ranking of sidewall > roof > invert under all three numerical input motions. TLC therefore provides a complementary energy-based measure for comparing the relative participation of different lining regions when interpreted together with conventional response indices.