Development of soil type-independent calibration relationships for water content and dry density measurements using time-domain reflectometry

Zhiyong Zhou¹Lin Li¹Wentao Yu²Ruisong Zhang³Hui Tang³Qingyi Mu^4*

• ¹Shandong Electric Power Engineering Consulting Institute Corp Ltd, Shandong, China
• ²State Grid Corporation of China, Extra High Voltage Construction Branch, Beijing, China
• ³China JIKAN Research Institute of Engineering Investigations and Design, Xi'an, China
• ⁴Chang'an university, Xi'an, China

Soil water content and dry density are critical parameters for assessing loess collapsibility and other geotechnical applications. However, existing time-domain reflectometry (TDR) calibration methods are often constrained by soil-specific limitations. This study aimed to develop soil type-independent calibration relationships for TDR measurements of soil water content and dry density. Laboratory experiments were conducted on four distinct soil types to calibrate and validate existing TDR models. The results indicated that current models exhibited suboptimal performance, necessitating parameter calibration for specific soil types.To enhance the accuracy and applicability of TDR measurements, the Multi Expression Programming (MEP) algorithm was employed to develop a soil type-independent calibration relationship for dry density. The MEP model demonstrated robust performance in both training and validation phases, achieving a slope of 0.925 and an R² value of 0.88 for the training dataset，with most validation data points falling within a ±10% relative error range.Additionally, a soil type-independent calibration relationship for water content was established based on the dry density model, achieving high accuracy with most predicted values exhibiting absolute errors within ±0.04. The developed calibration relationships were further validated using 64 datasets from the literature, covering various soil types, and through two field in-situ tests. The validation results demonstrated that the developed model could accurately determine dry density with relative errors less than ±10% for most test points. Water content measurements also showed strong agreement with laboratory oven-drying results, with absolute errors within ±0.02 for the majority of test points. This work provides a reference for applying TDR to rapid in-situ measurement of soil water content and dry density, which is of significant importance for evaluating loess collapsibility and other geotechnical applications.