Soil Failure Models for Vertically Operating and Horizontally Operating Strength Sensors

Soil strength, or mechanical resistance of a soil to failure, has been widely used to estimate the degree of soilcompaction. Conventional measurements with cone penetrometers are laborious; therefore, an on-the-go soil strength profilesensor that collects data dense enough to show the spatial within-field variability in soil strength would be a desirablealternative. Because soil failure involves complex interactions among many variables, determining design parameters of asoil strength sensor and interpreting test results could be improved with a theoretical understanding of the soil failure process.Mathematical models to estimate the force required to penetrate (cut and displace) soil with a prismatic cutter travelinghorizontally and with a cone penetrometer traveling vertically were developed based on the passive earth pressure theory andthe concept of a variable failure boundary. Both models were expressed as additive forms of density, cohesion, and adhesioncomponents of the soil, with each effect multiplied by a corresponding dimensionless number. Charts of dimensionlessnumbers were developed to investigate the behavior of each strength component at various values of soil internal frictionangle, soil-metal friction angle, and tool cutting angle. The models were used in simulation to optimize design parametersof the sensor, including component dimensions and the location and spacing of sensing elements. Based on this optimization,a prismatic sensing tip with a 3.61 cm2 base area and a 60 cutting angle was selected, and the corresponding simulatedmaximum force and strength measurements were 2.2 kN and 6.0 MPa when operating at speeds up to 5 m s-1. Model validationshowed that the extension of the failure boundary was significantly correlated with soil properties such as bulk density, watercontent, and internal friction angle. The variable failure boundary model developed in this study more consistently andaccurately represented field data than did three previously developed modeling approaches.