Analysis of P-wave propagation in filled joints based on the <italic style="font-style: italic">g-λ</italic> model

CHAI Shaobo; WEN Chengwu; SONG Lang; XU Yinglong

doi:10.16152/j.cnki.xdxbzr.2025-03-013

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Analysis of P-wave propagation in filled joints based on the g-λ model

更新时间：2025-06-26

- Analysis of P-wave propagation in filled joints based on the g-λ model
- Journal of Northwest University (Natural Science Edition) Vol. 55, Issue 3, Pages: 658-667(2025)
- 作者机构：
  
  1.长安大学　建筑工程学院，陕西　西安　 710064
  2.西安交通大学　城市学院，陕西　西安　 710018
- 作者简介：
- 基金信息：
- DOI：10.16152/j.cnki.xdxbzr.2025-03-013
  CLC： TH212;TH213.3
- Received：13 May 2025，
  
  Published：25 June 2025
- 稿件说明：
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CHAI Shaobo, WEN Chengwu, SONG Lang, et al. Analysis of P-wave propagation in filled joints based on the g-λ model[J]. Journal of northwest university (natural science edition), 2025, 55(3): 658-667.
DOI：

CHAI Shaobo, WEN Chengwu, SONG Lang, et al. Analysis of P-wave propagation in filled joints based on the g-λ model[J]. Journal of northwest university (natural science edition), 2025, 55(3): 658-667. DOI： 10.16152/j.cnki.xdxbzr.2025-03-013.

摘要

作为岩体软弱结构面，节理中的应力波传播规律对岩体动力稳定性分析至关重要。特别地，充填节理因其厚度及充填材料特性，使得应力波传播规律变得复杂。现有关于充填节理中的波传播理论分析研究较少，且很少考虑接触界面的非线性变形特征。为此，采用

g-λ

模型来描述充填节理接触面法向变形行为，考虑节理充填层的影响，利用改进的时域递归法建立了应力波在充填节理中的传播方程，并对P波的透反射系数进行参数化分析。通过理论分析，认为

是关于节理黏聚力和内摩擦角的参数，随着λ的增大，节理刚度非线性增加的速度会增加；应力波的透反射系数对入射角的变化较为敏感，P波的反射系数会随着入射角度的增加先减小后增大，P波的透射系数变化较为平缓，而入射角继续增大时，P波的透射系数会陡降；整体来看，节理的初始法向刚度的变化对P波的透反射系数影响较大，而切向刚度的变化对S波的透反射系数影响较大。研究结果对应力波在含充填节理岩体中的传播规律提供了一定的理论依据。

Abstract

The propagation law of stress waves in joints

as weak structural planes in rock masses

plays a pivotal role in assessing the dynamic stability of rock mass. In particular

the wave propagation characteristics become complicated in filled joints due to their thickness and the properties of the filling materials. Current theoretical investigations on wave propagation in filled rock joints remain scarce

with insufficient consideration of nonlinear deformation characteristics at contact interfa

ces. Therefore

this paper adopts the

g-λ

model to characterize nonlinear normal deformation behavior at filled joint interfaces. Taking into account the influence of the filling layer

the propagation equation of stress waves in filled joints is established by the improved time-domain recursive analysis method. Moreover

a parametric analysis is conducted on the transmission and reflection coefficients of P waves. Through theoretical analysis

it is found that the parameter

is related to the cohesion and internal friction angle of the joints

with increasing

amplifying nonlinear stiffness enhancement rates. The transmission and reflection coefficients of stress waves are quite sensitive to changes in the incident angle. As the incident angle increases

the reflection coefficient of P waves first decreases and then increases. The transmission coefficient of P waves remains relatively stable as the incident angle increases

but drops sharply when the incident angle continues to increase. Overall

changes in the initial normal stiffness of the joint have a significant impact on the transmission and reflection coefficients of P waves

while changes in the tangential of the joint have dominant influence on the transmission and reflection coefficients of S waves. The results provide a theoretical basis for the propagation law of stress waves in the rock masses with filled joints.

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references

夏才初 , 孙宗颀 . 工程岩体节理力学 [M ] . 上海 : 同济大学出版社 , 2002 .

SCHOENBERG M . Elastic wave behavior across linear slip interfaces [J ] . The Journal of the Acoustical Society of America , 1980 , 68 ( 5 ): 1516 - 1521 .

PYRAK N , LAURA J , LARRY R , et al . Transmission of seismic waves across single natural fractures [J ] . Journal of Geophysical Research: Solid Earth , 1990 , 95 ( B6 ): 8617 - 8638 .

LI J C , MA G W . Analysis of blast wave interaction with a rock joint [J ] . Rock Mechanics and Rock Engineering , 2010 , 43 ( 6 ): 777 - 787 .

LI J C , LI H B , MA G W , et al . A time-domain recursive method to analyse transient wave propagation across rock joints [J ] . Geophysical Journal International , 2012 , 188 ( 2 ): 631 - 644 .

贾帅龙 , 王志亮 , 熊峰 , 等 . 充填节理岩体中应力波传播特性研究 [J ] . 合肥工业大学学报(自然科学版) , 2021 , 44 ( 8 ): 1073 - 1081 .

JIA S L , WANG Z L , XIONG F , et al . Study on propagation characteristics of stress wave in rockmass with filled joint [J ] . Journal of Hefei University of Technology (Natural Science Edition) , 2021 , 44 ( 8 ): 1073 - 1081 .

柴少波 , 李建春 , 李海波 . 柱面波在节理岩体中的传播特性 [J ] . 岩石力学与工程学报 , 2014 , 33 ( 3 ): 523 - 530 .

CHAI S B , LI J C , LI H B . Propagation characteristics of cylindrical wave in joint rock mass [J ] . Chinese Journal of Rock Mechanics and Engineering , 2014 , 33 ( 3 ): 523 - 530 .

LIU T T , DING L , ZHENG Y , et al . Calculating the attenuation of stress waves passing through an in situ stressed joint using a double nonlinear model [J ] . Waves in Random and Complex Media , 2024 , 34 ( 6 ): 5056 - 5076 .

BANDIS S C , LUMSDEN A C , BARTON N R . Fundamentals of rock joint deformation [J ] . International Journal of Rock Mechanics & Mining Sciences and Geomechanics Abstracts , 1983 , 20 ( 6 ): 249 - 268 .

俞缙 , 宋博学 , 钱七虎 . 节理岩体双重非线性弹性介质中的纵波传播特性 [J ] . 岩石力学与工程学报 , 2011 , 30 ( 12 ): 2463 - 2473 .

YU J , SONG B X , QIAN Q H . Propagation of pwaves in dual nonlinear elastic mediumfor jointed rock mass [J ] . Chinese Journal of Rock Mechanics and Engineering , 2011 , 30 ( 12 ): 2463 - 2473 .

周建民 , 许宏发 , 杨红禹 . 岩体节理法向变形的数学模型分析 [J ] . 岩石力学与工程学报 , 2000 ( S1 ): 853 - 855 .

ZHOU J M , XU H F , YANG H Y . Power function model of normal deformation for rock joints [J ] . Chinese Journal of Rock Mechanics and Engineering , 2000 , 19 ( S1 ): 853 - 855 .

费鸿禄 , 包士杰 , 杨智广 . 应力波斜入射对岩体节理端部的影响 [J ] . 岩土力学 , 2018 , 39 ( 7 ): 2327 - 2335 .

FEI H L , BAO S J , YANG Z G . Influence of oblique incidence of stress wave on rock joint ends [J ] . Rock and Soil Mechanics , 2018 , 39 ( 7 ): 2327 - 2335 .

柴少波 , 周涛 , 田威 , 等 . 考虑岩体应力的结构面中应力波传播特性分析 [J ] . 岩土力学 , 2022 , 43 ( S1 ): 184 - 192 .

CHAI S B , ZHOU T , TIAN W , et al . Analysis of stress wave propagation through a rock structural plane considering rock mass stresses [J ] . Rock and Soil Mechanics , 2022 , 43 ( S1 ): 184 - 192 .

RONG G , HUANG K , ZHOU C B , et al . A new constitutive law for the nonlinear normal deformation of rock joints under normal load [J ] . Science China Technological Sciences , 2012 , 55 ( 2 ): 555 - 567 .

FAN Z F , ZHANG J C , XU H , et al . Transmission and application of a P-wave across joints based on a modified g-λ model [J ] . International Journal of Rock Mechanics and Mining Sciences , 2022 , 150 : 104991 .

刘婷婷 , 李新平 , 郑允 , 等 . 基于三单元模型分析P波在充填结构面处的传播规律 [J ] . 岩石力学与工程学报 , 2017 , 36 ( S1 ): 3247 - 3257 .

LIU T T , LI X P , ZHENG Y , et al . P-wave propagation across a filling structure with three element model [J ] . Chinese Journal of Rock Mechanics and Engineering , 2017 , 36 ( S1 ): 3247 - 3257 .

JIA C J , CHEN F L , ZHOU S J , et al . Effect of joint density on mechanical behavior of rock mass: Insight from 3D printing tests and DEM simulation [J ] . Engineering Fracture Mechanics , 2025 , 315 : 110846 .

闫亚涛 , 李建春 . 节理粗糙度及吻合状态对岩体动态压缩特性影响的试验研究 [J ] . 岩石力学与工程学报 , 2021 , 40 ( 6 ): 1132 - 1144 .

YAN Y T , LI J C . Experimental study on the influence of joint roughness and matching state on dynamic compression characteristics of rock masses [J ] . Chinese Journal of Rock Mechanics and Engineering , 2021 , 40 ( 6 ): 1132 - 1144 .

陈昕 , 李建春 , 任奋华 , 等 . JMC对应力波透射系数和节理比刚度影响的实验研究 [J ] . 岩石力学与工程学报 , 2016 , 35 ( 5 ): 957 - 963 .

CHEN X , LI J C , REN F H , et al . Experimental research of JMC effect on stress wave propagation and joint specific stiffness [J ] . Chinese Journal of Rock Mechanics and Engineering , 2016 , 35 ( 5 ): 957 - 963 .

CHAI L Z , CHAI S B , LI P , et al . Analysis of P-wave propagation in filled jointed rock mass with viscoelastic properties [J ] . Geomechanics and Geophysics for Geo-Energy and Geo-Resources , 2023 , 9 ( 1 ): 102 .

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Analysis of P-wave propagation in filled joints based on the g-λ model

DOI：10.16152/j.cnki.xdxbzr.2025-03-013

摘要

Abstract

关键词

Keywords

references