基于非局部Biot理论的平面波作用下饱和地基动力响应

doi:10.16183/j.cnki.jsjtu.2020.149

上海交通大学学报 ›› 2021, Vol. 55 ›› Issue (6): 663-671.doi: 10.16183/j.cnki.jsjtu.2020.149

所属专题：《上海交通大学学报》2021年“土木建筑工程”专题；《上海交通大学学报》2021年12期专题汇总专辑

基于非局部Biot理论的平面波作用下饱和地基动力响应

王宁¹^,², 丁海滨¹^,²(), 童立红¹^,², 蒋亚龙¹^,²

1.华东交通大学江西省岩土工程基础设施安全与控制重点实验室,南昌 330013
2.江西省地下空间技术开发工程中心,南昌 330013

收稿日期:2020-05-22 出版日期:2021-06-28 发布日期:2021-06-30
通讯作者: 丁海滨 E-mail:hbding@ecjtu.edu.cn
作者简介:王宁(1983-),男,山东省东营市人,讲师,主要从事基础动力学与土动力学及动力检测技术应用等研究
基金资助:
研究生创新基金(YC2019-B105);国家自然科学基金地区基金(51868021);国家自然科学基金青年基金(11702095);国家杰出青年基金(51725802);高铁联合基金(U1934208);江西省自然科学基金(20192BAB216031);江西省教育厅自然科学基金(GJJ190300)

Dynamic Responses of Saturated Soil Foundation Subjected to Plane Wave Based on Nonlocal-Biot Theory

WANG Ning¹^,², DING Haibin¹^,²(), TONG Lihong¹^,², JIANG Yalong¹^,²

1. Jiangxi Key Laboratory of Infrastructure Safety Control in Geotechnical Engineering, East China Jiaotong University, Nanchang 330013, China
2. Engineering Research and Development Centre for Underground Technology of Jiangxi Province, Nanchang 330013, China

Received:2020-05-22 Online:2021-06-28 Published:2021-06-30
Contact: DING Haibin E-mail:hbding@ecjtu.edu.cn

摘要/Abstract

摘要：

为探究孔隙尺寸效应对饱和土地基动力响应的影响,基于非局部-Biot理论,构建了P波及SV波作用下饱和土地基表面动力响应的计算模型.采用波函数展开法,求解了地表位移及应力的解析解.分析了孔隙尺寸(以非局部参数描述)、入射波频率及入射角对地表位移及应力响应的影响.结果表明:低频下,非局部Biot理论计算结果与经典Biot理论计算结果基本一致;高频时,地表位移及应力随非局部参数变化较为明显,即高频率下,孔隙尺寸效应对地表响应影响不可忽略.入射波频率对地表响应的影响与孔隙尺寸有关,孔隙越大,频率影响越为显著.相同幅值的P波及SV波作用下,SV波引起的地表动力响应大于P波,且SV波在入射角为45° 时发生全反射.研究成果可为半空间饱和土中波动问题的研究提供借鉴.

关键词: 饱和土, 非局部-Biot理论, 孔隙尺寸, 孔隙动应力, 非局部参数

Abstract:

To investigate the influence of pore size effect on dynamic response of saturated soil foundation, a model for predicting the dynamic response of the ground surface of the saturated soil foundation under incident P wave and SV wave is proposed based on the nonlocal-Biot theory. The analytical solution is obtained using the wave function expansion method. The influence of pore size described by nonlocal parameter, input frequency, and the incident angle on the dynamic response of displacement and stress is discussed in detail. The results show that at low frequencies, the calculation results of the nonlocal-Biot theory are basically the same as those of the classical Biot theory. At high frequencies, the surface displacement and stress change significantly with nonlocal parameters, that is, at high frequencies, the effect of pore size on the surface response cannot be ignored. The influence of incident wave frequency on the ground-surface response is related to pore size, that is, the larger the pore size, the more significant the frequency effect. The influence of SV wave on the dynamic response of ground surface is larger than that of P wave. Besides, the total reflection phenomenon is observed at an incident angle of 45° for the incident of SV wave. The results obtained in this work can provide reference for studying the problem of wave propagation in half-space saturated soil foundation.

Key words: saturated soil, nonlocal-Biot theory, pore size, pore dynamic stress, nonlocal parameter

中图分类号:

TU312

王宁, 丁海滨, 童立红, 蒋亚龙. 基于非局部Biot理论的平面波作用下饱和地基动力响应[J]. 上海交通大学学报, 2021, 55(6): 663-671.

WANG Ning, DING Haibin, TONG Lihong, JIANG Yalong. Dynamic Responses of Saturated Soil Foundation Subjected to Plane Wave Based on Nonlocal-Biot Theory[J]. Journal of Shanghai Jiao Tong University, 2021, 55(6): 663-671.

图/表 10

图1

表1

系数矩阵表达式

系数	P波	SV波
G₁_i	$k αi 2$ ( $k αi 2$ τ²-1)(λ_c+μ+ξ_iαM+μcos2θ_αi)	[-1+τ²(k²- $ν αi 2$ )][k²(λ_c+αMξ_i)- $ν αi 2$ (λ_c+2μ+αMξ_i)]
G₁₃	μ $k b 2$ ( $k b 2$ τ²-1)sin 2θ_β	-2jkμν_β[-1+τ²(k²- $ν b 2$ )]
G₂_i	-μ $k αi 2$ ( $k αi 2$ τ²-1)sin 2θ_α₁	2jkμν_αi[-1+τ²(k²- $ν αi 2$ )]
G₂₃	μ $k β 2$ ( $k β 2$ τ²-1)cos 2θ_β	μ(k²-k⁴τ²+ $ν b 2$ +τ² $ν b 4$ )
G₃_i	$k αi 2$ M(ξ_i+α)	M(k²- $ν α 1 2$ )(α+ξ₁)

表1

图2

表2

图3

图4

图5

图6

图7

图8

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参数	数值	参数	数值
土颗粒密度ρ_s/(kg·m^-3)	2650	渗透系数k/(m^-2)	1.0×10^-8
流体密度ρ_f/(kg·m^-3)	1000	黏滞系数η/(Pa·簚s)	1.0×10^-3
孔隙比n₀	0.30	Biot 参数α	0.9982
泊松比ν	0.30	Biot 参数M/MPa	5859.2
土颗粒模量K_g/GPa	36.0	弯曲因子ξ	1
流体体积模量K_f/GPa	2.0	孔隙半径a/μm	23
拉梅常数λ/MPa	49.7

基于非局部Biot理论的平面波作用下饱和地基动力响应

Dynamic Responses of Saturated Soil Foundation Subjected to Plane Wave Based on Nonlocal-Biot Theory

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