برآورد تخمینی خاک غیر اشباع با استفاده از معادلات بروتزرت Porosity estimation of unsaturated soil using Brutsaert equation

1. Introduction The elastic wave velocity has been used to investigate subsurface structures and obtain the design parameters when applying the theory of wave propagation in a medium. Among the various design parameters, porosity is essential for assessing the stability of soil under static and dynamic loadings, including compression, consolidation, earthquakes and liquefaction [39,9]. Porosity can be obtained through a laboratory testing of an extracted sample. However, obtaining reliable porosity data is difficult because the extraction procedure is limited to special soil types, and extracting and moving the soil causes disturbances that hinder the reliability [38]. To overcome the above mentioned disadvantages, the seismic wave velocity has been used to obtain the porosity as an in-situ method. Wood [36] expressed porosity in terms of compressional wave velocity using compressibility, a reciprocal of the elastic modulus, as an intermediary. Gassmann, whose work was translated by Berryman [8], proposed a relationship between porosity and elastic wave velocity for a low frequency range in an isotropic porous medium. Applying [10] theory of linear poroelasticity, Foti et al. [16] suggested a method for estimating the porosity under the assumptions that pore water is an undrained condition and the number of soil particles is infinite. Lee and Yoon [20] recently summarized techniques for evaluating the porosity using a variety of assumptions, and assessed the sensitivities of every parameter to compare the resolutions of these techniques. A study was also conducted to investigate the characteristics of porosity in unsaturated soils using elastic waves. Lu and Sabatier [25] monitored the elastic wave velocity according to changes in the water potential, moisture content, and soil temperature during a two-year period. Shin et al. [30] used the elastic wave velocity to estimate the effects of soil structure, moisture content, and strength on plant growth in unsaturated soil. Although these previous researches include no direct description of the change in porosity, the alternation of porosity can be indirectly estimated through the measured total potential, effective stress, and moisture content. Gao et al. [17] showed the possibility of estimating the porosity in unsaturated soil using matric suction deduced through the measured elastic wave velocity, and Whalley et al. [35] demonstrated the elastic wave velocity as a function of porosity using Bishop’s equation. Changes in elastic wave velocity in shallow surface soil have recently been addressed to determine seasonal and weather effects [24], and the results of this study show that the elevation of the elastic wave velocity is caused by increased rigidity and decreased porosity of the surface soil. Previous studies have shown that the porosity has a significant influence on the elastic wave velocity under unsaturated soil conditions; however, there has been a lack of methodological content to directly obtain the porosity. Therefore, in the present study, we propose a practical method for estimating the porosity of unsaturated soil using the seismic velocity.