The coupled thermo‑hydro‑mechanical (THM) response in saturated porous media is critical for energy piles and related geotechnical applications. Existing analytical solutions mainly rely on integral transforms (Laplace, Hankel, or Fourier)(Ai & Wang, 2018; Gao et al., 2017; Zhu et al., 2021), which introduce numerical inversion errors, require oversimplified boundary thermal loads (typically constant or sinusoidal), and assume homogeneous media(Niu et al., 2020) – thus completely ignoring soil layering. These drawbacks severely restrict their use in real‑world problems.

This study proposes an eigenfunction expansion method for multilayered saturated strata. By constructing orthogonal eigenfunctions that satisfy interface continuity, the coupled PDEs are reduced to ODEs in time and solved exactly without any approximation. A key advantage is that the method accepts arbitrary functional forms for boundary thermal fluxes/temperatures and initial temperature/pore‑pressure distributions, enabling direct input of measured or extreme climate data (heatwaves, cold spells, wildfire heating). This flexibility supports quantitative evaluation of temperature‑driven geohazards, including thaw‑induced landslides, thermal subsidence, frost heave, and slope failures under rapid thermal fluctuations. The framework fills a long‑standing gap in layered‑media THM analysis and provides a practical tool for hazard warning under changing climates.

References
Ai, Z. Y., & Wang, L. J. (2018). Precise Solution to 3D Coupled Thermohydromechanical Problems of Layered Transversely Isotropic Saturated Porous Media. International Journal of Geomechanics, 18(1), Article 04017121.
Gao, J. J., Deng, J. G., Lan, K., Song, Z. C., Feng, Y. T., & Chang, L. (2017). A porothermoelastic solution for the inclined borehole in a transversely isotropic medium subjected to thermal osmosis and thermal filtration effects. Geothermics, 67, 114-134.  
Niu, J. J., Wang, X. K., Gong, S. L., & Ling, D. S. (2020). Exact Solutions for Investigating Thermal Response of Saturated Soil Induced by Temperature Change. International Journal of Geomechanics, 20(10), Article 04020177.  
Zhu, B., Ye, Z. G., Wang, L. J., Xu, W. J., Kong, D. Q., Nagel, T., Kolditz, O., & Chen, Y. M. (2021). Theoretical Investigation into Thermo-Osmosis and Thermofiltration Effects on Hydromechanical Behavior of Saturated Soils. Journal of Engineering Mechanics, 147(4), Article 04021005.

THM,analytical solution,layered,geohazard assessment