CodeCogs

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

Interface

#include <codecogs/engineering/geotechnics/slope_safety_factor.h>

using namespace Engineering::Geotechnics;

double slope_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,\e 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):

$F=\frac{M_{resistance}}{M_{activation}}$

(1)

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.

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Example 1

#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]

The horizontal offset from the toe of the slope to the center of the slip cicle. [m]

The vertical offset from the toe of the slope to the cetner of the slip circle. [m]

The height of the slope. [m]

slope

The angle of the slope. [degrees]

soil_density

The average density $\gamma$ of the soil within the slope. [kg/m3]

soil_c

The natural cohesion (base shear strength) of the soil, $c_u$ . [N/m^2]

Interactive Calculator

radius

slope

soil_density

soil_c

Result –