Applicability of BRUTSAERT’s model in soil moisture detection

The acoustic detection technology has shown its advantage in the field of soil moisture detection. The recent soil moisture detection methods mainly rely on the acoustic-based strategy, which explores the influence of the unsaturated soil moisture content on the pressure wave velocity (PWV) and the attenuation coefficient and analyzes the impact of soil moisture content on the acoustic parameters. It focuses on modeling the soil moisture content and the acoustic parameters. However, the agricultural soil holds the complicated components and has many types. Moreover, it exists the unmatched spatial-temporal distribution, causing that the structural and initial saturation of the soil is undetermined. Hence, these existing methods have challenges, giving rise to the unreliable results. The BRUTSAERT’s model is such a theoretical model that demonstrates the propagation of elastic waves in the unsaturated soil. It mainly focuses on the relationship between PWV and the soil saturation. In BRUTSAERT’s model, different soil textures result in difference of both PWV and soil saturation. Yet, it avoids the negative impact of soil structural and initial saturation on the model. Inspired by this, this study theoretically analyzed: 1) the application condition with inertia viscosity coefficient of soil was less than 1, and the sound wave frequency≤708 Hz was suitable for any soil texture, which can be viewed as a superior; 2) the propagation of the sound waves in soil should be approximate to a plane, and this resulted in a lower boundary. The minimum frequencies of sound waves were 796, 380, 266, 199, and 160 Hz when the distances between the sound wave transmitter and the acoustic adapter were 0.1, 0.2, 0.3, 0.4, and 0.5 m. Besides, the relationships between PWV and the soil moisture, with different conditions were discussed. BRUTSAERT indicated that the speed of sound wave propagation in soil relied on tree aspects: the total density of the measured soil, soil stress, and the soil particle gap parameter. This stduy proved that the three aspects were related to the saturation degree of the liquid. Based on this, the BRUTSAERT model was simplified. In addition, BRUTSAERT might hold the so called “writing errors” caused by bulk modulus of fluid mixture. Nevertheless, this study explored the impact of the vanilla BRUTSAERT with the fixed soil Poisson's ratio on the prediction results. In the vanilla BRUTSAERT’s model, no matter how the soil texture or saturation changed, the Poisson's ratio was always a fixed value with 0.2. Obviously, the vanilla BRUTSAERT model did not consider the impact of using the fixed Poisson's ratio on the predicted results. Based on this, the study reported results related to Poisson’s ratio, and the concluded results show that there is a significant difference of Poisson's ratio between the dry soil and the saturated soil were summarizes and concludes. We found that it is questionable to use a fixed and saturation independence-Poisson's ratio for unsaturated porous aggregates such as soil and sand.