多相介质弹性参数的研究及波速计算
摘要
本文对多相介质的等效体积模量及弹性波传播速度进行了深入的研究，并在以下几方面取的了新的进展：(1) 采用新的、简单的分析方法，对Biot理论中一些物理含义理解起来不直观的弹性参数，用物理含义明确直观的基本参数表示出来。(2) 利用修正项代替修正系数，重新修正Brandt球粒模型弹性理论，导出了修正项的具体表达式。在工程中的绝大多数情况下，该结果与Biot-Geertsma理论的结果在形式及数值上几乎完全一致，从而使这两个不直接相关的经典理论较好的统一起来。(3) 在土动力学中常用的不排水条件下，分别证明了Carroll的应力-应变关系中不排水体积模量、Kuster散射波理论的体积模量与Biot-Geertsma理论是完全一致的。(4) 论证了了土动力学中串联与并联的力学模式是不排水条件下应力-应变关系的两个特例，从应力-应变关系上统一了串联与并联的力学模式，不排水条件下，应力-应变关系有一新的重要的结论是：骨架的体积应变等于总的体积应变。为实际工作中选择模式提供了理论依据。(5) 重新分析了孔隙相互孤立型土体力学模型，使该模型的应力-应变关系更加合理。(6) 提出了含水土体骨架波速的概念，用其代替干土体波速的概念，能更好地反映工程土体的性状。(7) 提出了由实测饱和土体波速计算骨架弹性参数及骨架波速的方法。认为潜水面下纵波速度能反映更多的信息，并且，横波速度与骨架的横波速度也可以由孔隙率及结构因子引起差异。(8) 根据Kuster散射波理论，计算了饱和度大于85％的准饱和土体的弹性波速，其结果与试验非常吻合；但是，通常所用的等效孔隙流体压缩系数的方法所计算的结果与实验结果差别很大，对此，笔者给予了一定的解释。(9) 通过试验运用了骨架波速和黄土加固凝聚力的概念，将饱和度的增加引起土体密度的增加对波速的影响与水破坏加固凝聚力对波速的影响区分开来；在相同的压力和饱和度(近似)条件下，采用动力作用前后分别测试弹性波速的方法，将动力荷载对加固凝聚力的破坏作用与土样自身的颗粒组分对波速的影响因素区分开来。初步研究了水及动力作用对黄土加固凝聚力的破坏及黄土波速的变化规律。
Based on quasi-static hypothesis, some parameters of Boit-Gertsma's elastic theory which could not be directly perceived through the senses, was showed by explicit physical parameters. In spite of modifying coefficient, a modifying term is used to modify Brandt's theory of sphere grain model ; this term's expression has been acquired , and the result is identical to Biot-Geertsma's theory in form and quantity, in which the two classics theories is in perfect harmony .It is also confirmed that the constitutive relation of Carroll and N.Katsube theory, and the bulk modulu of Kuster scattered waves are identical to Biot theory. Serial and parallel stress-strain relations in saturated soils have been theoretically deduced from un-drained stress-strain relations with a new condition of frame volume deformation equaling to total volume deformation, which were suggested for the first time in this thesis and proved a theoretical method to choose suitable mechanical models. The mechanipal model for saturated soils with isolated holes has been discussed in a new more reasonable way and the stress-strain relations and bulk moduli for this kinds of soils have been supposed. A new concept, the skeleton elastic wave velocity (SEWV), was introduced to replace the velocities of dry soil, which could reflect the engineering characteristic of soil more accurately .New methods to calculate SEWV from measured velocities in saturated soil were suggested. The longitudinal wave velocity in saturated soil could not only be useful , but reflect more information as well. The shear wave velocity may be different from the shear SEWV ,the difference is proved to be caused by porosity and structure factor. The fact that wave velocity in quasi-saturated soil is equal to that of fully saturated soil could not be calculated by effective fluid compressibility or explained by unwell-distributed saturation .We account for this in a new reasonable way which was based on Kuster scattering effect analysis. Based on the concepts of elastic wave velocity of skeleton and reinforced cohesion, the effect on the velocity by soil density with different saturation was distinguished from that by weakened reinforced cohesion; On the condition of same confined press and saturation, the elastic wave velocity was measured before and after soil samples were dynamically loaded, so that the elastic wave velocity changed by dynamic load was distinguished from that by soil.nature characteristic. Some regular patterns of reinforced cohesion and velocity in loess under different saturation and dynamic load have been discussed in a preliminary way. Some results of this research was applied in practical work and certain effect has bas been acquired.
Based on quasi-static hypothesis, some parameters of Boit-Gertsma's elastic theory which could not be directly perceived through the senses, was showed by explicit physical parameters. In spite of modifying coefficient, a modifying term is used to modify Brandt's theory of sphere grain model ; this term's expression has been acquired , and the result is identical to Biot-Geertsma's theory in form and quantity, in which the two classics theories is in perfect harmony .It is also confirmed that the constitutive relation of Carroll and N.Katsube theory, and the bulk modulu of Kuster scattered waves are identical to Biot theory. Serial and parallel stress-strain relations in saturated soils have been theoretically deduced from un-drained stress-strain relations with a new condition of frame volume deformation equaling to total volume deformation, which were suggested for the first time in this thesis and proved a theoretical method to choose suitable mechanical models. The mechanipal model for saturated soils with isolated holes has been discussed in a new more reasonable way and the stress-strain relations and bulk moduli for this kinds of soils have been supposed. A new concept, the skeleton elastic wave velocity (SEWV), was introduced to replace the velocities of dry soil, which could reflect the engineering characteristic of soil more accurately .New methods to calculate SEWV from measured velocities in saturated soil were suggested. The longitudinal wave velocity in saturated soil could not only be useful , but reflect more information as well. The shear wave velocity may be different from the shear SEWV ,the difference is proved to be caused by porosity and structure factor. The fact that wave velocity in quasi-saturated soil is equal to that of fully saturated soil could not be calculated by effective fluid compressibility or explained by unwell-distributed saturation .We account for this in a new reasonable way which was based on Kuster scattering effect analysis. Based on the concepts of elastic wave velocity of skeleton and reinforced cohesion, the effect on the velocity by soil density with different saturation was distinguished from that by weakened reinforced cohesion; On the condition of same confined press and saturation, the elastic wave velocity was measured before and after soil samples were dynamically loaded, so that the elastic wave velocity changed by dynamic load was distinguished from that by soil.nature characteristic. Some regular patterns of reinforced cohesion and velocity in loess under different saturation and dynamic load have been discussed in a preliminary way. Some results of this research was applied in practical work and certain effect has bas been acquired.
引文
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Ament W. S., 1953, Sound Propagation in gross mixtures: Journal of the acoustical society of America, Vol. 25, No. 4, P. 638-641.
Bagi K., 1999, Microstructural stress tensor of granular assemblies with volume forces:Transaction of the ASME Journal of applied mechanics, Vol. 66, P. 934-936
Biot M. A., 1956a,Theory of propagation of elastic waves in a fluid-saturated porous solid.Ⅰ. Low-frequency range: The Journal of the acoustical society of America. Vol. 28,168-178.
Biot M.A.,1956b,Theory of propagation of elastic waves in a fluid-saturate soils.Ⅱ. Higher-frequency range: The Journal of the acoustical of America. Vol. 28. P. 179-191
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Blot M. A., 1962, The mechanics of deformation and acoustic in porous media: Journal of applied physics, Vol. 33, No. 4, P. 1482-1498.
Blot M. A., 1962, Generalized theory of acoustic propagation in porous dissipative media: The Journal of the acoustical society of America. Vol.34, P. 1254-1264.
Bishop A. W, Blight G. E, 1962, Some aspects of effective stress in saturated and partly saturated soils. Geotechnique, Vo1.13, No. 3, P. 177-196.
Brandt H., Habra Land Calif, 1955, A study of the speed of sound in porous granular media: Journal of applied mechanics, Vol. 22, P. 479-486.
Brandt H.,1960, Factors affecting compressional wave velocity in unconsolidated marine sand sediments: The Journal of the acoustical society of America. Vol. 32, No. 2 P. 171-179.
Carroll M.M., 1980, Mechanical response, of fluid-saturated porous materials: IUTAM (International Union of Theoretical and Applied Mechanics)Proceedings of 15th International. congress of theoretical and applied mechanics, Eds by F.P.J. Rimrott, and B. Tabarrok, North-Holland, New York P. 251-262.
Christoffersen J.,Mehrabadi M.M., and S. Nemat-nasser, 1981, Amicromechanical description of granular material behavior: Transaction of the ASME Journal of applied mechanics, Vol. 48, P. 339-344
Digby P. J., 1981, The effective elastic Moduli of porous granular rocks: Transaction of the ASME Journal of applied mechanics, Vol.48, P. 803-808.
Digby P. J., and Walton K., 1989, Wave propagation through elastically-anisotropic fluid-saturated porous rocks: Transaction of the ASME Journal of applied mechanics, Vol. 56,P. 744-750.
Domenico S. N., 1977, Elastic properties of unconsolidated porous sand reservoirs:Geophysics, Vol. 42, No. 7, P. 1339-1368.
Duffy J. and Mindlin R. D., 1957, Stress-Strain relations and vibrations of a granular medium: Transaction of the ASME Journal of applied mechanics, Vol. 24, P. 585-593.
Dunn M. L., Ledbetter H.,1995, Elastic moduli of composites reinforced by multiphase particles: Journal of applied mechanics, Vol.62. P. 1023-1028.
Elliot, S. E., and Wiley, B. F., 1975, Compressional velocities of partially saturated,unconsolidated sands: Geophysics, Vol. 40, P. 949-954.
Geertsma J, and Smit, D. C.1961, Some aspects of elastic wave propagation in fluid-saturated porous solids: Geophysics, Vol. 26, P. 168-181.
Horne M.R.,1965,The behaviour of an assembly of rotund, rigid,cohesionless particles.Ⅰ: Proceedings of the royal society, Series A, Vol.206, No.1404, P. 62-78
Horne M.R.,1965,The behaviour of an assembly of rotund, rigid,cohesionless particles.Ⅱ: Proceedings of the royal society, Series A, Vol. 206, No. 1404, P. 79-97
Iwan W.D., 1967, On a class of models for the yielding behavior of continuous and composite systems: Transactions of the ASME Series E Journal of applied mechanics, Vol. 34,No. 3, P. 612-617
James G. Berryman, 1981, Elastic wave propagation in fluid-satruated porous media Ⅱ: The Journal of Acoustical Society of America, Vol.70, No. 6, P. 1752-11756.
James W. Spencer, Jr. Michael E. Cares, and Don D. Thompson, 1994, Frame modull of unconsolidated sands and sand-stones: Geophysics, Vol. 59, No. 9, P.1352-1361.
Johnson D. L., Schwartz L. M.,. Elata D, Berryman J. G., etc, 1998, Linear and no-linear elasticity of granular media: stress-induced anisotropy of a random sphere pack:Transaction of the ASME Journal of applied mechanics, Vol. 65, P. 380-388.
Katsube N.,1985,The constitutive theory for fluid-filled porous materials:Transaction of the ASME Journal of applied mechanics, Vol.52, P. 185-189.
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