Intro Doc
$\underline{Manual}$ $\\$ This is an open source python program to analyze the stability of a circular arc slope using Fellenius and Bishop simplified methods. $\\$ there are two options in this program: first, you can choose a specific point and one circular arc surface (want_Evaluate_Only_One_Surface = True) to analyze the slope. In this case you need to determine:$\\$ $\bullet$Horzontal distance of point A from crown (negetive value)$\\$ $\bullet$Horzontal distance of point B from crown (positive value) $\\$ $\bullet$Slip radious$\\$ Second, you can use multi surface (want_Evaluate_Only_One_Surface = False) and get the smallest safety factor for the slope. in this case you need to define:$\\$ $\bullet$number of circles$\\$ $\bullet$radious_increment $\\$ $\bullet$number_of_increments$\\$ $\underline{Bishop\space Simplified\space Method}$ $\\$ Bishop Simplified method only considers horizontal interslice forces and neglects shear forces between slices. Equations for calculating the factor of safety is: \begin{equation}\label{eq1} F=\frac{\sum[ ( c^\prime \Delta x + ( W - u \Delta x ) tan \phi^\prime ) \frac{1}{M_\alpha}]}{\sum (W sin \alpha)} \end{equation} Where: \begin{equation}\label{eq2} M_\alpha=cos \alpha + \frac{sin \alpha tan \phi^\prime}{F} \end{equation} In which $W$ is the weight of each slice, $c^\prime$ is the effective cohesion, $\Delta x$ is width of each slice, $u$ is the pore pressure, and $\alpha$ is the angle of inclination. $\\$ $\underline{Fellenius\space Method}$ $\\$ Fellenius method is one of the first methods of slices and it does not calculate the factor of safety iteratively. Fellenius method assumes that resultant interslice forces are parallel to the base of the slice. This method does not consider interslice forces in its calculations. The equation for factor of safety based on this method is: \begin{equation}\label{eq3} F = \frac {\sum (c^\prime l + N^\prime tan \phi^\prime)}{\sum W sin \alpha} \end{equation} Where: \begin{equation}\label{eq4} N^\prime = W cos \alpha - u l \end{equation}