In this paper, a probabilistic approach is proposed for quantifying thevariability of the tillage forces for the shank of a chisel plough with narrowtines and to estimate the failure probability. An existing three-dimensionalanalytical model of tool forces from McKyes was used to model the interactionbetween the tillage tools and the soil. The variability of tillage forces wasmodeled, taking into account the variability of soil engineering properties,tool design parameters and operational conditions. The variability of the soilengineering properties was modeled by means of experimental observations. Thedispersion effect of each tillage system parameter on the tillage forces wasdetermined by a sensitivity analysis. The results show that the variability ofthe horizontal and vertical forces follows a lognormal distribution (μ=0.872,ξ=0.449; μ=0.004, ξ=0.447) and the relationship between these forces is positiveand quasi-linear (ρ(PH,Pv)=0.93).This lognormal variability was integrated intothe estimation of the failure probability for the shank by using Monte Carlosimulation (MCS) and the first-order reliability method (FORM). The resultsobtained by these two methods, with the assumption of non-correlation betweenthe horizontal and vertical forces, were almost identical. However, the FORMmethod was faster and simpler, compared to the MCS technique. Furthermore, thecorrelation between the horizontal and vertical forces has no significant effecton the failure probability, regardless of the correlation strength. Therefore,it is concluded that the FORM method can be used to estimate the failureprobability without considering the correlation between horizontal and verticalfo
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