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slope safety factor

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



Slope Safety Factor

doublesoil_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


#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;
TODO: Need to compute


radiusThe 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]
aThe horizontal offset from the toe of the slope to the center of the slip cicle. [m]
bThe vertical offset from the toe of the slope to the cetner of the slip circle. [m]
HThe height of the slope. [m]
slopeThe angle of the slope. [degrees]
soil_densityThe average density \inline  \gamma of the soil within the slope. [kg/m3]
soil_cThe natural cohesion (base shear strength) of the soil, \inline  c_u. [N/m^2]
Source Code

Source code is available when you buy a Commercial licence.

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Last Modified: 11 May 13 @ 00:37     Page Rendered: 2022-03-14 17:35:42