饱和地基中骨架非流动黏性对体波传播特性的影响分析

兰州理工大学学报 ›› 2023, Vol. 49 ›› Issue (3): 140-146.

饱和地基中骨架非流动黏性对体波传播特性的影响分析

任圆圆^*

陕西交通职业技术学院公路与铁道工程学院, 陕西西安 710018

收稿日期:2022-04-28 出版日期:2023-06-28 发布日期:2023-07-07
通讯作者: 任圆圆(1986-),女,陕西宝鸡人,讲师. Email:450179069@qq.com
基金资助:
国家自然科学基金(51978320,11962016)

Effect of skeletal flow-independent viscosity on the propagation characteristics of body waves in saturated foundations

REN Yuan-yuan

College of Highway and Railway Engineering, Shaanxi College of Communications Technology, Xi’an 710018, China

Received:2022-04-28 Online:2023-06-28 Published:2023-07-07

摘要/Abstract

摘要： 基于饱和多孔介质的研究成果,考虑天然土体中骨架的非流动黏性和孔隙流体的流动黏性的影响,研究了黏弹性饱和地基中体波的传播特性.利用Biot波动理论,引入Kelvin-Voigt线性黏弹性模型,建立了饱和土体的黏弹性动力耦合模型.通过引入位移势函数,根据Helmholtz势函数分解定理推导给出了黏弹性饱和地基中体波的特征方程.利用数值算例,结合参数分析讨论了各类体波的波速和衰减系数随土体非流动黏性松弛时间、频率和渗透系数等物理力学参数的变化规律.结果表明:土体非流动黏性松弛时间的增大将引起P₁波、P₂波和S波的波速和衰减系数的增大;频率和渗透系数的不同区间对P₁波、P₂波和S波的波速和衰减系数的影响不同.

关键词: 黏弹性, 饱和地基, 体波, 波速, 衰减系数

Abstract: Based on the research results of saturated porous medium, considering the influences of flow-independent viscosity of natural soil, the propagation behaviors of body waves in viscoelastic saturated foundation were studied in the present work. The viscoelastic dynamic coupling model of saturated soil were established by employing Biot model and Kelvin-Voigt linear viscoelastic model. The characteristic equations of body waves in viscoelastic saturated foundation were theoretically derived by Helmholtz potential function decomposition theorem with introducing displacement potential function. The variations law of the wave velocity and attenuation coefficient of body waves with physical parameters such as flow-independent viscosity relaxation time of soil, frequency and permeability were analyzed using a numerical example. The results show that the wave velocity and attenuation coefficient of P₁, P₂ and S waves increase with the extension of relaxation time of soil causes . Frequency and permeability in different ranges have different effects on the wave velocity and attenuation coefficient of P₁, P₂ and S waves.

Key words: viscoelasticity, saturated ground, body wave, wave velocity, attenuation coefficient

中图分类号:

TU435

任圆圆. 饱和地基中骨架非流动黏性对体波传播特性的影响分析[J]. 兰州理工大学学报, 2023, 49(3): 140-146.

REN Yuan-yuan. Effect of skeletal flow-independent viscosity on the propagation characteristics of body waves in saturated foundations[J]. Journal of Lanzhou University of Technology, 2023, 49(3): 140-146.

参考文献

[1] SHIOTANI T,MOMOKI S,CHAI H,et al.Elastic wave validation of large concrete structures repaired by means of cement grouting[J].Construction and Building Materials,2009,23(7):2647-2652.
[2] GUDRA T,STAWISKI B.Non-destructive strength characterization of concrete using surface waves[J].Ndt & E International,2000,33(1):1-6.
[3] POPOVICS J S,ZHU J.Crack depth measurement in concrete using surface wave transmission[J].American Institute of Physics,2003,657(1):1125-1131.
[4] BIOT M A.Theory of Propagation of elastic waves in a fluid-saturated porous solid.I.Low-frequency range[J].The Journal of the Acoustical Society of America,1956,28(2):168-178.
[5] BIOT M A.Theory of propagation of elastic waves in a fluid-saturated porous solid.II.Higher frequency range[J].The Journal of the Acoustical Society of America,1956,28(2):179-191.
[6] PLONA T J.Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies[J].Applied Physics Letters,1980,36(4):259-261.
[7] BERRYMAN J G.Confirmation of Biot’s theory[J].Appl Phys Lett,1980,37(4):382-385.
[8] LU J F,HANYGA A,JENG D S.A linear dynamic model for a saturated porous medium[J].Transport in Porous Media,2006,68(3):321-340.
[9] KIM S H,KIM K J,BLOUIN S E.Analysis of wave propagation in saturated porous media.I.Theoretical solution[J].Computer Methods in Applied Mechanics and Engineering,2002,191(37):4061-4073.
[10] SHARMA M D.Wave propagation in a dissipative poroelastic medium[J].IMA Journal of Applied Mathematics,2013,78(1):59-69.
[11] ZHOU F,LAI Y,SONG R.Propagation of plane wave in non-homogeneously saturated soils[J].Science China Technological Sciences,2013,56(2):430-440.
[12] 周凤玺,柳鸿博,蔡袁强.饱和多孔热弹性介质中Rayleigh波传播特性分析[J].岩土力学,2020,41(1):315-324.
[13] 周凤玺,赵王刚,曹永春.气饱和与水饱和多孔介质的弹性波场数值模拟[J].固体力学学报,2015,36(S1):152-159.
[14] 柳鸿博,周凤玺,张瑞玲,等.饱和多孔介质中热弹耦合对体波传播特性的影响分析[J].岩石力学与工程学报,2020,39(S1):2693-2702.
[15] 柳鸿博,周凤玺,郝磊超.平面S波在饱和多孔热弹性介质边界的反射问题研究[J].地震工程学报,2021,43(1):105-112.
[16] ZHOU F,MA Q.Propagation of Rayleigh waves in fluid-saturated non-homogeneous soils with the graded solid skeleton distribution[J].International Journal for Numerical and Analytical Methods in Geomechanics,2016,40(11):1513-1530.
[17] SILLS G C,WHEELER S J,THOMAS S D,et al.Behaviour of offshore soils containing gas bubbles[J].Géotechnique,1991,41(2):227-241.
[18] CHENG Z,LEONG E C.Finite element simulations of wave propagation in soils using a Viscoelastic model[J].Soil Dynamics and Earthquake Engineering,2016,88: 207-214.
[19] BISHOP A W,BLIGHT G.Some aspects of effective stress in saturated and partly saturated soils[J].Géotechnique,1963,13(3):177-197.
[20] 杨峻,吴世明,蔡袁强.饱和土中弹性波的传播特性[J].振动工程学报,1996,9(2):128-137.