Handbook of Civil Engineering Calculations

The action line of C is parallel to the x axis. Determine the distance a by taking moments
about O. Thus M = aC = acLc.

a = (Y\ (28)

\ LC I

Or a = (154.6/131.0)78.8 = 93.0 ft (28.35 m). Draw the action line of C.

7. Locate the action line of R
   For this purpose, consider the resultant force dR acting on an elemental area. Its action
   line is inclined at an angle with the radius at that point, and therefore the perpendicular
   distance r' from O to this action line is

r' = rsin</> (29)

Thus, r' is a constant for the arc AC. It follows that regardless of the position ofdR along
this arc, its action line is tangent to a circle centered at O and having a radius r'; this is
called the circle, or friction circle. It is plausible to conclude that the action line of the
total resultant is also tangent to this circle.
Draw a line tangent to the (/> circle and passing through the point of intersection of
the action lines of W and C. This is the action line of R. (The moment of H about O is
counterclockwise, since its frictional component opposes clockwise rotation of the soil
mass.)

8. Using a suitable scale, determine the magnitude of C
   Draw the triangle of forces; obtain the magnitude of C by scaling. Thus, C = 67,000 Ib
   (298,016N).


9. Calculate the maximum potential cohesion
   Apply Eq. 27, equating c to the unit cohesive capacity of the soil. Thus, Cmax = 550(131)
   = 72,000 Ib (320,256 N). This result indicates a relatively low factor of safety. Other arcs
   of failure should be investigated in the same manner.

ANALYSIS OF FOOTING STABILITY

BY TERZAGHI'S FORMULA

A wall footing carrying a load of 58 kips/lin ft (846.4 kN/m) rests on the surface of a soil
having these properties: w = 105 lb/ft^3 (16.49 kN/m^3 ); c = 1200 lb/ft^2 (57.46 kPa); 4> =
15°. Applying Terzaghi's formula, determine the minimum width of footing required to
ensure stability, and compute the soil pressure associated with this width.

Calculation Procedure:

1. Equate the total active and passive pressures and state the
   equation defining conditions at impending failure
   While several methods of analyzing the soil conditions under a footing have been formu-
   lated, the one proposed by Terzaghi is gaining wide acceptance.
   The soil underlying a footing tends to rupture along a curved surface, but the Terzaghi
   method postulates that this surface may be approximated by straight-line segments with-