Application of mathematical function to estimate the compaction characteristics of unsaturated soils

Abstract

The study aims to propose a mathematical approach to determine the optimum moisture content (WOP) and the corresponding maximum dry unit weight (γdmax) of unsaturated fine-grained clay soils with accuracy. Laboratory tests such as grain size distribution, Atterberg limits, specific gravity, Proctor compaction test, and soil suction measurement are conducted to assess soil properties. The WOP and γdmax are determined using the mathematical approach based on differential function (∂) and the graphical method. The differences in optimum moisture content values between the mathematical approach and the graphical method (∆WOP) values are 0.43 %, 0.36 %, 0.42 %, 0.24 %, respectively for soils PES, BFS, WIS, BES, and induced differences in total suction of 179.17 kPa, 144.00 kPa, 175.00 kPa, 96.00 kPa, respectively for soils PES, BFS, WIS, BES. Moreover, the differences in matric suction are 148.27 kPa, 116.13 kPa, 144.83 kPa, 80.00 kPa, respectively for soils PES, BFS, WIS, BES. ∆WOP and ∆γdmax values are smaller than 0.5 % and marginal in the context of saturated soil mechanics. However, the total suction and matric suction values induced by ∆WOP values are significant for unsaturated soils. An accurate estimation of γdmax and WOP can be performed on unsaturated compacted soils using the mathematical approach.