基于Biot形式波动方程的一维非饱和土柱瞬态响应研究

刘砚山; 吉姿洁; 赵云

doi:10.21656/1000-0887.460155

基于Biot形式波动方程的一维非饱和土柱瞬态响应研究

doi: 10.21656/1000-0887.460155

1. 河南省城乡建筑设计院有限公司，郑州 451452;
2. 河南工业大学土木工程学院，郑州 450001

基金项目:

国家自然科学基金（52578399）；河南省科技攻关计划（252102320021）；河南工业大学拓新团队培育项目（2024TXTD15）；河南省高等学校重点科研项目（26B410001）

详细信息

作者简介:
c刘砚山(1989—)，男，高级工程师（E-mail: yanshan_8903@163.com);赵云（1989—），男，博士（通信作者. E-mail: zhaoyun1106@163.com）.

通讯作者:
赵云（1989—），男，博士（通信作者. E-mail: zhaoyun1106@163.com）.

中图分类号: TU435
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- 文章访问数: 6
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- 被引次数: 0
出版历程
- 收稿日期: 2025-08-28
- 修回日期: 2026-06-23
- 网络出版日期: 2026-07-23

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

Liu Yanshan¹,
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

Funds:

The National Science Foundation of China(52578399)

摘要

摘要: 基于Biot形式的非饱和土波动方程，本文研究了一维非饱和土柱在动力荷载作用下的瞬态响应问题.目的在于分析非饱和土中的波动特性，并推导该问题的解析解，为相关工程问题提供理论依据.在方法上，考虑饱和度对渗透系数和动剪切模量的影响，采用分离变量法和状态空间法相结合的方式系统求解了一维非饱和土柱在动载下的瞬态响应问题解析解，并通过与Comsol PDE模块的有限元数值结果对比，验证了解答的正确性.结果显示：在非饱和土中，由于渗透系数较低，仅能观测到一种压缩波；随着固有渗透系数的增大，孔隙水压力的瞬态响应峰值逐渐减小；同时，饱和度增加会导致孔隙水压力响应幅值明显上升.结论认为，饱和度与渗透系数对非饱和土中的波动响应具有显著影响，解析解能够有效预测瞬态响应特征，并为非饱和土动力学行为分析提供理论支持.
- 瞬态响应 /
- 非饱和土 /
- 解析解 /
- 状态空间法
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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参考文献(20)

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基于Biot形式波动方程的一维非饱和土柱瞬态响应研究

doi: 10.21656/1000-0887.460155

作者简介:
c刘砚山(1989—)，男，高级工程师（E-mail: yanshan_8903@163.com);赵云（1989—），男，博士（通信作者. E-mail: zhaoyun1106@163.com）.

通讯作者:
赵云（1989—），男，博士（通信作者. E-mail: zhaoyun1106@163.com）.

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

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目录

留言板

基于Biot形式波动方程的一维非饱和土柱瞬态响应研究

doi: 10.21656/1000-0887.460155

作者简介: c刘砚山(1989—)，男，高级工程师（E-mail: yanshan_8903@163.com);赵云（1989—），男，博士（通信作者. E-mail: zhaoyun1106@163.com）.

通讯作者: 赵云（1989—），男，博士（通信作者. E-mail: zhaoyun1106@163.com）.

计量

出版历程

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

计量

出版历程

目录

作者简介:
c刘砚山(1989—)，男，高级工程师（E-mail: yanshan_8903@163.com);赵云（1989—），男，博士（通信作者. E-mail: zhaoyun1106@163.com）.

通讯作者:
赵云（1989—），男，博士（通信作者. E-mail: zhaoyun1106@163.com）.