Transient Responses of 1D Unsaturated Soil Columns Based on the Biot-Type Wave Equations

Liu Yanshan; Ji Zijie; Zhao Yun

doi:10.21656/1000-0887.460155

Volume 47 Issue 7

Jul. 2026

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Liu Yanshan, Ji Zijie, Zhao Yun. Transient Responses of 1D Unsaturated Soil Columns Based on the Biot-Type Wave Equations[J]. Applied Mathematics and Mechanics, 2026, 47(7): 886-894. doi: 10.21656/1000-0887.460155

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Transient Responses of 1D Unsaturated Soil Columns Based on the Biot-Type Wave Equations

doi: 10.21656/1000-0887.460155

Liu Yanshan^1
,,
Ji Zijie²,
Zhao Yun^{2
,
,}

1.
Urban & Rural Construction and Designing Institute of Henan Province Co., Ltd., Zhengzhou 451452, P.R. China
2.
College of Civil Engineering and Architecture, Henan University of Technology, Zhengzhou 450001, P.R. China

Received Date: 2025-08-28
Rev Recd Date: 2026-06-23
Publish Date: 2026-07-01

Abstract

Abstract

Based on the Biot-type wave equations for unsaturated soils, the transient responses of 1D unsaturated soil columns subjected to dynamic loading were investigated, to analyze wave propagation characteristics in unsaturated soils and derive analytical solutions to provide a theoretical basis for relevant engineering problems. The effects of saturation on both the permeability coefficient and the dynamic shear modulus were incorporated into the governing equations. With the separation of variables method plus the state space method, a systematic analytical solution of the transient response was obtained. The validity of the solution was verified through comparison with the finite element results from COMSOL's PDE module. The results indicate that, only 1 compression wave occurs in unsaturated soil due to its relatively low permeability. As the intrinsic permeability increases, the peak transient pore water pressure response will gradually decreases. Furthermore, an increase in the saturation leads to a significant rise in the amplitude of the pore water pressure response. Both the saturation and the permeability considerably influence the wave-induced responses in unsaturated soils. The proposed analytical method effectively predicts transient response characteristics and provides a theoretical support for analyzing the dynamic behaviors of unsaturated soils.
- transient response,
- unsaturated soil,
- analytical solution,
- state-space method

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References(20)

References

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