Evaluating the N gamma coefficient for rough strip footing located adjacent to the slope using the stress characteristics method

The method of characteristics was used to estimate the coefficients N gamma for shallow strip footings located adjacent to the slopes. The soil-footing interface roughness (delta) was considered from perfectly smooth to fully rough state by 1/3 increments in each step. The effect of roughness factor (delta/phi) on the magnitude of N gamma has been evaluated for different friction angles (phi) and slope inclinations (beta degrees). The arrays of the slip lines have been extracted and the geometric properties of plastic and non-plastic regions have been presented in tabular form. The results of the present research for both smooth and rough footings rested on the horizontal ground and adjacent to the slope showed a favorable consistency with findings reported in the literature by adopting various solution approaches. It was found that the N gamma coefficient increases and diminishes dramatically by increasing phi and beta degrees, respectively. More than almost 95% of the N gamma magnitude in full roughness state is provided by mobilizing about 60% of the footing's roughness. The sizes of the plastic region as well as the elastic wedge beneath the rough footing extend with increasing both phi and delta/phi. An increase in beta degrees leads to increasing and decreasing the plastic domains on the downslope zone and the horizontal ground part behind the crest, respectively. The dimensions of the non-plastic curved wedge slowly reduce and the intersection point of two plastic regions gradually tends toward the left edge of the footing. For beta = 20 degrees and beyond, the maximum depth of the right plastic region from the right edge shifts toward the sloping ground face.