# slope safety factor

The stability (safety factor) of a undrained cut or built slope.

Controller: **CodeCogs**

doubleslope_safety_factor( | double | radius | |

double | a | ||

double | b | ||

double | H | ||

double | slope | ||

double | soil_density | ||

double | soil_c | ) |

Computes the safety factor of a relatively short cut or built slope, where undrained conditions exist along a potential circular failure plane. The mode of failure is shown in the figure below, and is described by the selection of

*a*,*b*and the radius*r*that intersect the slope and describe the slip plane. The factor of safety is calculated by taking moments about the center of the slip circle (O): where the*resistance*moment is caused by the shear resitance of the soil along the length of the potential failure plane and the*activation*moment is caused by the weight of the soil above the presumed slip plane.Private Section

## Example

#include <stdio.h> #include <codecogs/engineering/geotechnics/slope_safety_factor.h> int main() { double soil_c=45; double soil_density=1900; double H=9; // height of bank double slope=90; double a=6; // horizontal distance to toe of slope // Find the vertical position of the circle that gives the lowest factor of safety for (double b=10; b < 40; b += 1) { double R=sqrt(b*b+a*a); // assume minimum radius to toe of slope double F=Engineering::Soil::slope_safety_factor(R, a, b, H, slope, soil_density, soil_c); printf("\n b=%lf Radius=%lf F=%lf",b,R,F); } return 0; }

**Output:**TODO: Need to compute

### Parameters

radius The radius r of the slip circle. Note the radius must be sufficient to reach below the toe of the slope and beyond the top of the slope. [m] a The horizontal offset from the toe of the slope to the center of the slip cicle. [m] b The vertical offset from the toe of the slope to the cetner of the slip circle. [m] H The height of the slope. [m] slope The angle of the slope. [degrees] soil_density The average density of the soil within the slope. [kg/m3] soil_c The natural cohesion (base shear strength) of the soil, . [N/m^2]

##### Source Code

Source code is available when you buy a Commercial licence.

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