- Compute the length of arc AD
Scale the radius of the arc and the central angle AOD, and compute the length of the arc
AD. Thus, radius = 82.7 ft (25.2 m); arc AD = 120 ft (36.6 m). - Determine the distance horizontally from O to the applied load
Scale the horizontal distance from O to the applied load. This distance is 52.6 ft (16.0 m). - Divide the soil mass into vertical strips
Starting at the toe, divide the soil mass above AC into vertical strips of 12-ft (3.7-m)
width, and number the strips. For simplicity, consider that D lies on the boundary line be-
tween strips 9 and 10, although this is not strictly true. - Determine the volume and weight of soil in each strip
By scaling the dimensions or using a planimeter, determine the volume of soil in each
strip; then compute the weight of soil. For instance, for strip 5: volume of soil A = 252 ft^3
(7.13 m^3 ); volume of soil B = 278 ft^3 (7.87 m^3 ); weight of soil = 252(110) + 278(122) =
61,600 Ib (273,996.8 N). Record the results in Table 1. - Draw a vector below each strip
This vector represents the weight of the soil in the strip. (Theoretically, this vector should
lie on the vertical line through the center of gravity of the soil, but such refinement is not
warranted in this analysis. For the interior strips, place each vector on the vertical center-
line.) - Resolve the soil weights vectorially into components normal
and tangential to the circular arc - Scale the normal and tangential vectors; record the results in
Table 1 - Total the normal forces acting on soils A and B; total the
tangential forces
Failure of the embankment along arc AC would be characterized by the clockwise rota-
tion of the soil prism above this arc about an axis through O, this rotation being induced
TABLEI. Stability Analysis of Slope
Tangential
Normal component, component, kips
Strip Weight, kips (KN) kips (KN) (KN)
1 10.3 (45.81) 8.9 (39.59) -5.2 (-23.13)
2 28.1(124.99) 26.0 (115.65) -10.7 (-47.59)
3 41.9(186.37) 40.6 (180.59) -10.4 (-46.26)
4 53.0(235.74) 52.7 (234.41) -5.5 (-24.46)
5 61.6(274.00) 61.5 (273.55) 2.6 (11.56)
6 67.7(301.13) 66.5 (295.79) 12.8 (56.93)
7 71.0(315.81) 67.0 (298.02) 23.4 (104.08)
8 67.1 (298.46) 58.8 (261.54) 32.4 (144.12)
9 54.8(243.75) 43.0 (191.26) 34.0 (151.23)
10 38.3(170.36) 24.9 (110.76) 29.1 (129.44)
11 14.3 (63.61) 7.0 (31.14) 12.5 (55.60)
Total, 1 to 9 425.0 (1890.40)
Total, 10 and 11 31.9 (141.89)
Grand total 456.9(2032.29) 115.0(511.52)