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| Plane shear-wave propagation across the interface between saturated frozen soil and saturated soil |
| MA Qiang1, 2, ZHANG Jialun1, ZHOU Fengxi3*, XU Anhua4, CAO Yapeng5, 6 |
(1. School of Civil Engineering and Water Resources, Qinghai University, Xining, Qinghai 810016, China; 2. Qinghai Provincial Key Laboratory of Energy-saving Building Materials and Engineering Safety, Qinghai University, Xining, Qinghai 810016, China;
3. School of Civil and Hydraulic Engineering, Lanzhou University of Technology, Lanzhou, Gansu 730050, China; 4. Qinghai Vocational and Technical University, Xining, Qinghai 810003, China; 5. State Key Laboratory of Cryospheric Science and Frozen Soil Engineering, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou, Gansu 730000, China; 6. Navier Laboratory, École Nationale des Ponts et Chaussées, Marne-la-Vallée Cedex 77455, France) |
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Abstract To elucidate the mechanisms of wave transmission and reflection and the associated energy-partitioning characteristics at the interface between saturated frozen soil and saturated unfrozen soil under plane shear-wave incidence, an interfacial wave-propagation model is developed within a Biot-type poroelastic framework. The continuity conditions for interfacial stresses and displacements are derived, and a plane-wave potential method is used to determine the amplitude ratios and energy-flux coefficients of all transmitted and reflected modes. A deterministic sensitivity analysis is then conducted to investigate the effects of key parameters, including the angle and frequency of incidence, porosity, Poissons ratio and temperature. The computational implementation is validated by comparing a limiting case with published results and by verifying energy conservation. The results show that the angle of incidence governs the transmission and reflection responses. Pronounced peaks or discontinuities in the amplitude ratios and energy-flux coefficients generally occur near the critical angles, indicating the high sensitivity of interfacial mode conversion and energy redistribution. The incident frequency primarily modulates the magnitude of energy partitioning, while the critical angles remain largely unchanged. Furthermore, variations in porosity, Poissons ratio and temperature substantially affect slow-wave-related modes, demonstrating that the slow-wave channel is the principal carrier of parameter sensitivity. Parameters associated with the frozen medium exert a particularly strong influence on energy redistribution. These findings provide a theoretical basis for assessing the dynamic response of layered interfaces and identifying freeze-thaw states in cold-region engineering.
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[1] LI S Y,LAI Y M,ZHANG M Y,et al. Study on long-term stability of Qinghai–Tibet railway embankment[J]. Cold Regions Science and Technology,2009,57(2/3):139–147.
[2] OBU J,WESTERMANN S,BARTSCH A,et al. Northern Hemisphere permafrost map based on TTOP modelling for 2000–2016 at 1 km² scale[J]. Earth-Science Reviews,2019,193:299–316.
[3] LECLAIRE P,COHEN-TÉNOUDJI F,AGUIRRE-PUENTE J. 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] 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.
[5] LECLAIRE P,COHEN-TÉNOUDJI F,AGUIRRE-PUENTE J. Observation of two longitudinal and two transverse waves in a frozen porous medium[J]. The Journal of the Acoustical Society of America,1995,97(4):2 052–2 055.
[6] CARCIONE J M,TINIVELLA U. Bottom-simulating reflectors: seismic velocities and AVO effects[J]. Geophysics,2000,65(1): 54–67.
[7] TINIVELLA U,CARCIONE J M. Estimation of gas-hydrate concentration and free-gas saturation from log and seismic data[J]. The Leading Edge,2001,20(2):200–203.
[8] CARCIONE J M,SERIANI G. Wave simulation in frozen porous media[J]. Journal of Computational Physics,2001,170(2):676–695.
[9] CARCIONE J M,SANTOS 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.
[10] LEE M W,WAITE W F. Estimating pore-space gas hydrate saturations from well log acoustic data[J]. Geochemistry,Geophysics,Geosystems,2008,9(7):2008GC002081.
[11] WAITE W F,SANTAMARINA J C,CORTES D D,et al. Physical properties of hydrate-bearing sediments[J]. Reviews of Geophysics,2009,47(4):2008RG000279.
[12] HELGERUD M B,DVORKIN J,NUR A,et al. Elastic-wave velocity in marine sediments with gas hydrates: effective medium modeling[J]. Geophysical Research Letters,1999,26(13):2 021–2 024.
[13] LEE M W,COLLETT T S. Elastic properties of gas hydrate-bearing sediments[J]. Geophysics,2001,66(3):763–771.
[14] LEE M W. Velocities and attenuations of gas hydrate-bearing sediments:scientific investigations report 2007-5264[R]. Reston,VA:U.S. Geological Survey,2007.
[15] GUERIN G,GOLDBERG D. Sonic waveform attenuation in gas hydrate-bearing sediments from the Mallik 2L-38 research well,Mackenzie Delta,Canada[J]. Journal of Geophysical Research:Solid Earth,2002,107(B5):EPM 1-1–EPM 1-11.
[16] GUERIN G,GOLDBERG D. Modeling of acoustic wave dissipation in gas hydrate-bearing sediments[J]. Geochemistry,Geophysics,Geosystems,2005,6(7):2005GC000918.
[17] PRIEST J A,BEST A I,CLAYTON C R I. Attenuation of seismic waves in methane gas hydrate-bearing sand[J]. Geophysical Journal International,2006,164(1):149–159.
[18] PRIEST J A,BEST A I,CLAYTON C R I. A laboratory investigation into the seismic velocities of methane gas hydrate-bearing sand[J]. Journal of Geophysical Research:Solid Earth,2005,110(4):1–13.
[19] BEST A I,PRIEST J A,CLAYTON C R I,et al. The effect of methane hydrate morphology and water saturation on seismic wave attenuation in sand under shallow sub-seafloor conditions[J]. Earth and Planetary Science Letters,2013,368:78–87.
[20] ZHAN L S,MATSUSHIMA J. Frequency-dependent P-wave attenuation in hydrate-bearing sediments: a rock physics study at Nankai Trough,Japan[J]. Geophysical Journal International,2018,214(3):1 961–1 985.
[21] MATSUSHIMA J,SUZUKI M,KATO Y,et al. Ultrasonic measurements of attenuation and velocity of compressional and shear waves in partially frozen unconsolidated sediment and synthetic porous rock[J]. Geophysics,2016,81(2):D141–D153.
[22] 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.
[23] YANG J. Influence of water saturation on horizontal and vertical motion at a porous soil interface induced by incident P wave[J]. Soil Dynamics and Earthquake Engineering,2000,19(8):575–581.
[24] GREGOR D,MOCZO P,KRISTEK J,et al. Seismic waves in medium with poroelastic/elastic interfaces:a two-dimensional P–SV finite-difference modelling[J]. Geophysical Journal International,2021,228(1):551–588.
[25] KUMAR R,KUMAR S,MIGLANI A. Reflection and transmission of plane waves between two different fluid-saturated porous half-spaces[J]. Journal of Applied Mechanics and Technical Physics,2011,52(5):773–782.
[26] QI Q M,CAO J X,WANG X J,et al. Influence of interface condition on reflection of elastic waves in fluid-saturated porous media[J]. Geophysics,2021,86(4):MR223–MR233.
[27] KANG Y G,WEI P J,LI Y Q,et al. Modeling elastic wave propagation through a partially saturated poroviscoelastic interlayer by fractional order derivatives[J]. Applied Mathematical Modelling,2021,100:612–631.
[28] LIU G H,LI X Y. Theoretical solutions of transmission and reflection of seismic waves propagation in three-phase unsaturated soil-seawater interface and research implications[J]. Ocean Engineering,2025,336: 121816.
[29] TOMAR S K,ARORA 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(7/8): 1 991–2 013.
[30] SHARMA M D,KUMAR M. Reflection of attenuated waves at the surface of a porous solid saturated with two immiscible viscous fluids[J]. Geophysical Journal International,2011,184(1):371–384.
[31] MA Q,JIANG H P,ZHOU F X. Reflection and transmission of plane harmonic P wave at planar interface between elastic medium and frozen poroelastic medium[J]. Geophysical Journal International,2023,234(2):948–971.
[32] JIANG H P,MA Q,ZHANG W Y. Study on transmission and reflection characteristics of plane S1 wave at the interface between saturated frozen soil and elastic solid bedrock[J]. Geophysics,2023,88(6):T305–T320.
[33] MA Q,JIAO H,WAN X S. Seismic ground motion study of layered site of saturated frozen soil under P-wave incidence[J]. Cold Regions Science and Technology,2025,231:104426.
[34] ZHANG M,XU Z D,CUI K M,et al. Tunable periodic surface wave barriers via water level variation[J]. International Journal of Mechanical Sciences,2025,307:110873.
[35] ZHANG M,MA Q,ZHOU F X. Analysis of the vibration isolation performance of layered periodic wave impeding blocks in unsaturated soil[J]. Journal of Engineering Mechanics,2025,151(6):04025020.
[36] MA Q,ZHANG M,ZHOU F X,et al. Analytical analysis of the scattering problem of plane SV waves caused by a circular arc canyon in an unsaturated half-space[J]. International Journal of Geomechanics,2025,25(5):04025058.
[37] 孙 静,公茂盛,熊宏强,等. 冻融循环对粉砂土动力特性影响的试验研究[J]. 岩土力学,2020,41(3):747–754.(SUN Jing,GONG Maosheng,XIONG Hongqiang,et al. Experimental study of the effect of freeze-thaw cycles on dynamic characteristics of silty sand[J]. Rock and Soil Mechanics,2020,41(3):747–754.(in Chinese))
[38] 张 泽,马 巍,ROMAN L,等. 基于冻融次数-物理时间比拟理论的冻土长期强度预测方法[J]. 岩土力学,2021,42(1):86–92.(ZHANG Ze,MA Wei,ROMAN Lidia,et al. Freeze-thaw cycles-physical time analogy theory-based method for predicting long-term shear strength of frozen soil[J]. Rock and Soil Mechanics,2021,42(1):86–92.(in Chinese))
[39] 张 锋,唐康为,尹思琪,等. 冻融粉质黏土的剪切波速与动态回弹模量及其转换关系[J]. 岩土力学,2023,44(增1):221–233. (ZHANG Feng,TANG Kangwei,YIN Siqi,et al. Shear wave velocity and dynamic resilient modulus of frozen and thawed silty clay and their conversion relationship[J]. Rock and Soil Mechanics,2023,44(Supp.1):221–233.(in Chinese))
[40] 李 斌,朱志武,李 涛. 冻融循环冻土的冲击动态力学性能[J].爆炸与冲击,2022,42(9):164–178.(LI Bin,ZHU Zhiwu,LI Tao. Impact dynamic mechanical properties of frozen soil with freeze-thaw cycles[J]. Explosion and Shock Waves,2022,42(9):164–178.(in Chinese))
[41] XU J R,LI L,JIAO H Y,et al. Propagation characteristics of thermo-elastic waves in saturated frozen soil[J]. Computers and Geotechnics,2025,186:107410.
[42] BONETTI S,BOTTI M,MAZZIERI I,et al. Numerical modeling of wave propagation phenomena in thermo-poroelastic media via discontinuous Galerkin methods[J]. Journal of Computational Physics,2023,489:112275.
[43] BA J,FANG Z J,FU L Y,et al. Acoustic wave propagation in a porous medium saturated with a Kelvin–Voigt non-Newtonian fluid[J]. Geophysical Journal International,2023,235(3):2 056–2 077.
[44] SOLTANI K,SEYEDPOUR S M,RICKEN T,et al. Transient high-frequency spherical wave propagation in porous medium using fractional calculus technique[J]. Acta Mechanica,2024,235(4):1 845–1 863.
[45] 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 characteristics and relevant problems in two-phase porous media[Ph. D. Thesis][D]. Hangzhou:Zhejiang University,2015.(in Chinese))
[46] 蒋汇鹏,马 强,邵生俊,等. 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 Huipeng,MA qiang,SHAO Shengjun,et al. Characteristic of energy transmission of plane-S-wave at interface between elastic medium and saturated frozen soil medium[J]. Chinese Journal of Rock Mechanics and Engineering,2023,42(4):976–992.(in Chinese))
[47] HOU X M,GAO Y C,LIU X J,et al. Experimental study on the pore structure and permeability characteristics of clay soil under freezing–thawing cycles[J]. Scientific Reports,2025,15:31216.
[48] KAPLAR C W. Laboratory determination of dynamic moduli of frozen soils and of ice[R]. [S. l.]:Cold Regions Research & Engineering Laboratory,1969.
[49] SHAN W,WU J X,GUO Y. Establishment and experimental validation of a temperature-unfrozen water content model for frozen soil[J]. Water,2025,17(6):846. |
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