Novel Pseudo-dynamic Closed-Form Solution for Individual Nail Force in Nailed Vertical Cut

A vertical cut reinforced with inclined nails subjected to sinusoidal seismic loading at the base was analyzed using the modified pseudo-dynamic approach within a limit equilibrium framework. Novel calculus-based closed-form solutions were formulated to estimate individual nail force demands. This study enables the use of spreadsheet programs instead of costly commercial software either based upon rigorous method of slices or finite element method to estimate complex dynamic response for nail forces and locus of maximum tension. The maximum nail force demands at various levels and locus of maximum tension are critical inputs in nailed cut design. Effects of geometrical, loading and material parameters were investigated. The height of cut to S wave wavelength ratio proved to be a vital parameter as it predicted a worst-case design scenario at a value of 0.25. The maximum nail force demands exhibited a nonlinearly increasing trend with respect to the depth of nails. Higher nail force requirements at all levels and larger active zone were predicted for more horizontal base acceleration amplitudes and smaller angle of friction. More nail inclination requires more nail length in the passive zone but lesser nail length in the active zone.