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Open AccessArticle

A New Method to Determine the Spatial Sensitivity of Time Domain Reflectometry Probes Based on Three-Dimensional Weighting Theory

1
College of Civil Engineering, Taiyuan University of Technology, Taiyuan 030024, China
2
Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China
3
College of Economic and Management, Shanghai University of Electric Power, Shanghai 200090, China
*
Author to whom correspondence should be addressed.
Water 2020, 12(2), 545; https://doi.org/10.3390/w12020545
Received: 11 December 2019 / Revised: 6 February 2020 / Accepted: 12 February 2020 / Published: 15 February 2020
(This article belongs to the Section Hydraulics and Hydrodynamics)
The time domain reflectometry (TDR) method has been widely used to measure soil water content for agriculture and engineering applications. Quick design and optimization of the probe is crucial to achieving practical utilization. Generally, the two-dimensional weighting theory, calculation of the spatial sensitivity of TDR probes in the plane transverse to the direction of electromagnetic wave propagation, and relevant numerical simulation techniques can be used to solve any issues. However, it is difficult to tackle specific problems such as complex probe shape, end effect, and so forth. In order to solve these issues, a method including a three-dimensional weighting theory and the relevant numerical simulation technique was proposed and verified to confirm the feasibility of this method by means of comparing the existing experimental results and the computational values. First, a shaft probe was used to determine the impact of the shaft on the effective dielectric constant of the probe. Then, three-rod probes were calibrated by a sample with a special shape and water-level variations around the probe using the proposed method to determine the values of the apparent dielectric constant. Besides, model boundary size and end effect were also considered in the computation of dielectric constants. Results showed that compared with the experimental and computational data, the newly proposed method calculated the measurement sensitivity of the shaft probes well. In addition, it was observed that experiment dielectric constant values were slightly different from computational ones, not only using a vertical probe but also horizonal probe. Moreover, it was also found that there was a slight influence of sample shape and end effect on the apparent dielectric constant, but model boundary size has a certain impact on the values. Overall, the new method can provide benefits in the design and optimization of the probe. View Full-Text
Keywords: time domain reflectometry; numerical simulation; spatial sensitivity; three-dimensional weighting theory time domain reflectometry; numerical simulation; spatial sensitivity; three-dimensional weighting theory
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MDPI and ACS Style

Qin, P.-J.; Liu, Z.-R.; Lai, X.-L.; Wang, Y.-B.; Song, Z.-W.; Miao, C.-X. A New Method to Determine the Spatial Sensitivity of Time Domain Reflectometry Probes Based on Three-Dimensional Weighting Theory. Water 2020, 12, 545.

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