A numerical–statistical hybrid modelling scheme for evaluation of draught requirements of a subsoiler cutting a sandy loam soil, as affected by moisture content, bulk density and depth

The development of simple regression relationships, based on finite element (FEM) analyses of cutting a sandy loam soil by medium–deep subsoiler will provide confidential and quick tools to predict the subsoiler draught requirement for any combination of moisture content (w), wet bulk density (ρw) and tillage depth (d). Large number of FEM analyses were performed to assess the effect of w, d and ρw on subsoiler draught. This draught was calculated from the output of 126 FEM modelling analyses. The model variations were selected based on the interaction among the studied variables, namely, six moisture contents ranging from 0.03 to 0.22 m3 m−3, five wet bulk densities ranging from 1.3 to 2.0 Mg/m3 and six tillage depths ranging from 0.10 to 0.37 m. The interaction among these three variables was also taken into consideration, and a multiple linear regression analysis was performed aiming at establishing a mathematical relationship for simulating the draught variation as a function of these variables. Further relationship was developed for relating the variation in draught with w, d and dry bulk density (ρd). M showed that subsoiler draught increased with d, ρw and ρd, whereas it decreased with w. The decrease in draught with w did not extend beyond a w of 0.17 m3 m−3, since the draught calculated for 0.22 m3 m−3 w was very close to that calculated for a w of 0.17 m3 m−3. Regression equations developed to relate the subsoiler draught with w, d, ρw and ρd were of quite simple forms, and had high determination coefficients (R2) close to 0.95. These equations indicated that the horizontal force varied linearly with w and non-linearly with d, ρw and ρd. This non-linear variation of draught was found to be a quadratic function of d and ρw, and a cubic function of ρd. A comparison of the calculated and measured draught for cutting a similar sandy loam soil with a similarly designed subsoiler, showed a good approximation. The small divergence between the calculated and measured draught was attributed to the difference in soil texture and subsoiler chisel length. Thus, the regression equation developed proved to be a capable tool of predicting the draught requirements of the selected tillage tool design, when cutting sandy loam soils under any combination of w, d and ρw.