(1. School of Civil Engineering，Qinghai University，Xining，Qinghai 810016，China；2. Institute of Geotechnical Engineering，Xi'an University of Technology，Xi'an，Shaanxi 710048，China)
Abstract：Based on the propagation theory of elastic waves in frozen saturated porous and single-phase elastic media，the energy transfer problem of plane-S-wave incidence at the interface between elastic and saturated frozen soil media is studied. According to the boundary conditions at the interface and using the Helmholtz vector decomposition，the theoretical expressions for the transmission and reflection amplitude ratio and energy rates are derived. The energy rate of S-wave incidence at the interface between elastic and saturated frozen soil media is investigated numerically in relation to the incident angle，incident frequency，cementation parameters，porosity，saturation and contact parameters. The results show that the energy rate of the transmitted P1，P2，P3，S1 and S2 waves increased with the incident angle increased，and the reflected P waves disappear and the transmitted P1 and S1 waves show a significant pulse under the critical angle. The energy interaction rate between transmitted waves only decreased with saturation increased and increases with the remaining parameters. The energy rate of the transmitted S1 wave accounts for more than 90% of the total energy rates of the transmitted and reflected waves，and the energy rate of transmitted S1 waves will be increased with the various parameters increased. In addition，the incident frequency，cementation parameters，porosity and contact parameters have a significant effect on the energy ratios coefficient.
引用本文:
蒋汇鹏1，马 强1，2，邵生俊2，邵 帅2. 平面S波在弹性介质与饱和冻土介质分界面上的能量传输特性[J]. 岩石力学与工程学报, 2023, 42(4): 976-992.
JIANG Huipeng1，MA Qiang1，2，SHAO Shengjun2，SHAO Shuai2. Characteristic of energy transmission of plane-S-wave at interface between elastic medium and saturated frozen soil medium. , 2023, 42(4): 976-992.
[1] SANTOS J E，RAVAZZOLI C L，CARCIONE J M. A model for wave propagation in a composite solid matrix saturated by a single-phase fluid[J]. Journal of the Acoustical Society of America，2004，20(6)：2 749–2 760.
[2] BIOT M A. Theory of propagation of elastic waves in a fluid-saturated porous solid. I：low-frequency range；II：higher frequency range[J]. The Journal of the Acoustical Society of America，2005，28(2)：168–191.
[3] LECLAIRE P，COHEN‐TÉNOUDJI F，AGUIRRE‐PUENTE J，et al. Extension of Biot’s theory of wave propagation to frozen porous media[J]. The Journal of the Acoustical Society of America，1994，96(6)：3 753–3 768.
[4] LECLAIRE P，COHEN‐TÉNOUDJI F，AGUIRRE‐PUENTE J，et al. Observation of two longitudinal and two transverse waves in a frozen porous medium[J]. The Journal of the Acoustical Society of America，1998，97(4)：2 052–2 055.
[5] CARCIONE J M，GUREVICH B，CAVALLINI F. A generalized Biot-Gassmann model for the acoustic properties of shaley sandstones1[J]. Geophysical Prospecting，2000，48(3)：539–557.
[6] CARCIONE J M，SANTO J E，RAVAZZOLI C L，et al. Wave simulation in partially frozen porous media with fractal freezing conditions[J]. Journal of Applied Physics，2003，94(12)：7 839–7 847.
[7] CARCIONE J M，SERIANI G. Wave simulation in frozen porous media[J]. Journal of Computational Physics，2001，170(2)：676–695.
[8] 周凤玺，赖远明. 饱和冻土中弹性波的传播特性[J]. 岩土力学，2011，32(9)：2 669–2 674.(ZHOU Fengxi，LAI Yuanming. Propagation characteristics of elastic waves in saturated frozen soil[J]. Rock and Soil Mechanics，2011，32(9)：2 669–2 674.(in Chinese))
[9] 仇浩淼，夏唐代，郑晴晴，等. 饱和冻土中弹性体波传播特性影响参数研究[J]. 岩土力学，2018，39(11)：4 053–4 062.(QIU Haomiao，XIA Tangdai，ZHENG Qingqing，et al. Parametric studies of body waves propagation in saturated frozen soil[J]. Rock and Soil Mechanics，2018，39(11)：4 053–4 062.(in Chinese))
[10] 仇浩淼. 含孔隙固体多孔介质中弹性波的传播特性研究[博士学位论文][D]. 杭州：浙江大学，2019.(QIU Haomiao. Research on propagation characteristics of elastic waves in Biot-type three-phase medium[Ph. D. Thesis][D]. Hangzhou：Zhejiang University，2019.(in Chinese))
[11] CAO L，ZHOU B，LI Q，et al. Vertically dynamic response of an end-bearing pile embedded in a frozen saturated porous medium under impact loading[J]. Shock and Vibration，2019，2019：1–18.
[12] 周 斌. 冻土地区地基表面地震动及瑞利波传播特性研究[硕士学位论文][D]. 舟山：浙江海洋大学，2020.(ZHOU Bin. Study on ground motion and Rayleigh wave propagation characteristics in frozen soil area[M. S. Thesis][D]. Zhoushan：Zhejiang Ocean University，2020.(in Chinese))
[13] 赵成刚，高福平，崔 杰. 波在饱和多孔介质与弹性固体介质交界面上的界面效应[J]. 地震工程与工程振动，1999，19(1)：1–6. (ZHAO Chenggang，GAO Fuping，CUI Jie. Interfacial effects of waves at the interface of saturated porous media and elastic solid media[J]. Earthquake Engineering and Engineering Vibration，1999，19(1)：1–6.(in Chinese))
[14] 李伟华. 饱和度对波在土层交界面的反射、透射系数的影响[J]. 地震工程学报，2002，24(4)：303–309.(LI Weihua. Influence of saturation on reflection and transmission coefficients of waves at the interface of soil layers[J]. Chinese Journal of Earthquake Engineering，2002，24(4)：303–309.(in Chinese))
[15] 叶陈江，史焱永，蔡袁强. S波由饱和土入射于弹性土时在界面上的反射与透射[J]. 振动与冲击，2005，24(2)：41–45.(YE Chenjiang，SHI Yanyong，CAI Yuanqiang. Reflection and transmission of s-waves at the interface when incident from saturated soil to elastic soil[J]. Vibration and Shock，2005，24(2)：41–45.(in Chinese))
[16] 徐 平，夏唐代. 弹性波在准饱和土和弹性土界面的反射与透射[J]. 力学与实践，2006，28(6)：58–63.(XU Ping，XIA Tangdai. Reflection and transmission of elastic wave at the interface of nearly saturated soil and elastic soil[J]. Mechanics and Practice，2006，28(6)：58–63.(in Chinese))
[17] 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.(ZHOU Fengxi，LIU Hongbo，CAI Yuanqiang. Analysis of propagation characteristics of Rayleigh waves in saturated porothermoelastic media[J]. Rock and Soil Mechanics，2020，41(1)：315–324.(in Chinese))
[18] LO W C，SPOSITO G，MAJER E L，et al. Wave propagation through elastic porous media containing two immiscible fluids[J]. Water Resources Research，2005，41(2)：1–20.(in Chinese)
[19] TOMAR S K，ASHISH A. Reflection and transmission of elastic waves at an elastic/porous solid saturated by two immiscible fluids[J]. International Journal of Solids and Structures，2006，43(7)：1 991–2 013.
[20] 陈炜昀，夏唐代，陈 伟，等. 平面P波在弹性介质和非饱和多孔弹性介质分界面上的传播[J]. 应用数学和力学，2012，33(7)：781–795.(CHEN Weiyun，XIA Tangdai，CHEN Wei，et al. Propagation of plane P waves at the interface between an elastic solid and an unsaturated poroelastic medium[J]. Applied Mathematics and Mechanics，2012，33(7)：781–795.(in Chinese))
[21] LIU H B，DAI G L，ZHOU F X，et al. Propagation behavior of homogeneous plane-P1-wave at the interface between a thermoelastic solid medium and an unsaturated porothermoelastic medium[J]. The European Physical Journal Plus，2021，136：1 163.
[22] LIU H B，JIANG M，ZHOU F X，et al. Attenuation characteristics of thermoelastic waves in unsaturated soil[J]. Arabian Journal of Geosciences，2021，14(18)：1–11.
[23] LIU H B，DAI G L，ZHOU F X，et al. A mixture theory analysis for reflection phenomenon of homogeneous plane-P1-wave at the boundary of unsaturated porothermoelastic media[J]. Geophsical Journal International，2022，228(2)：1 237–1 259.
[24] CHEN W Y，CHEN G X，XIA T D，et al. Energy flux characteristics of seismic waves at the interface between soil layers with different saturations[J]. China Science Technological Sciences，2014，57(10)：2 062–2 069.
[25] KUMAR R，MIGLANI A，KUMAR S. Reflection and transmission of plane waves between two different fluid saturated porous half spaces[J]. Bulletin of the Polish Academy of Sciences-Technical Science，2011，59(2)：227–234.
[26] QIU H M，XIA T D，YU B Q，et al. Modeling of wave reflection in gas hydrate-bearing sediments[J]. Wave Motion，2019，85：67–83.
[27] KUMAR M，SINGH A，KUMARI M，BARAK M S. Reflection and refraction of elastic waves at the interface of an elastic solid and partially saturated soils[J]. Acta Mechanica，2021，232(1)：33–55.
[28] DVORKIN J，HELGERUD M B，WAITE W F，et al. Introduction to physical properties and elasticity models，in：natural gas hydrate[M]. Netherlands：Springer，2000：245–260.
[29] ACHENBACH J D. Wave propagation in elastic solids[M]. Amsterdam：North-Holland，1973，165–201.
[30] LUO J，STEVENS R. Porosity-dependence of elastic moduli and hardness of 3Y-TZP ceramics[J]. Ceramics International，1999，25(3)：281–286.
[31] 刘志军. 双相多孔介质中波传播特性及相关问题研究[博士学位论文][D]. 杭州：浙江大学，2015.(LIU Zhijun. Research on wave propagation characteri-stics and related problems in two-phase porous medium[Ph. D. Thesis][D]. Hangzhou：Zhejiang University，2015.(in Chinese))
2023, Vol. 42 
