- Considering BC as the true plane of failure, develop equations
for x*, u, and P
Thus,
jc
2
= BE(BD) (17)-^
P = V 2 WU
2
Sm(P-S) (19)- Evaluate P, using the foregoing equations
Thus, <£ = 34°; 8 = 20°; 0 = 9°; p = 82°; LABD = 64°; LBAE = 54°; LAEB = 62°; LBAD
= 91°; ^4£>£ = 25°; AB = 20 esc 82° = 20.2 ft (6.16 m). In triangle ABD: BD = AB sin
91°/sin 25° = 47.8 ft (14.57 m). In triangle ABE: BE = AB sin 54°/sin 62° = 18.5 ft (5.64
m); AE = AB sin 64°/sin 62° = 20.6 ft (6.28 m); x^2 = 18.5(47.8); x = 29.7 ft (9.05 m); u =
20.6(47.8)7(29.7 + 47.8) = 12.7 ft (3.87 m); P = y 2 (100)(12.7)^2 sin 62°; P = 7120 Ib/ft
(103,909 N/m) of wall.
5. Alternatively, determine u graphically
Do this by drawing Fig. 9a to a suitable scale.
Many situations do not lend themselves to analysis by Rebhann's theorem. For in-
stance, the backfill may be nonhomogeneous, the earth surface may not be a plane, a sur-
charge may be applied over part of the surface, etc. In these situations, graphical analysis
gives the simplest solution. Select a trial wedge, compute its weight and the surcharge it
carries, and find P by constructing the force polygon as shown in Fig. 9b. After several
trial wedges have been investigated, the maximum value of P will become apparent.
If the backfill is cohesive, the active pressure on the retaining wall is reduced. Howev-
er, in view of the difficulty of appraising the cohesive capacity of a disturbed soil, most
designers prefer to disregard cohesion.
EARTHTHRUSTONTIMBERED
TRENCH CALCULATED BY GENERAL
WEDGE THEORY
A timbered trench of 12-ft (3.7-m) depth retains a cohesionless soil having a horizontal
surface. The soil weighs 100 Ib/ft^3 (15.71 kN/m^3 ), its angle of internal friction is 26°30',
and the angle of friction between the soil and timber is 12°. Applying Terzaghi's general
wedge theory, compute the total thrust of the soil on a 1-ft (30.5-cm) length of trench. As-
sume that the resultant acts at middepth.
Calculation Procedure:- Start the graphical construction
Refer to Fig. 10. The soil behind a timbered trench and that behind a cantilever retaining
wall tend to fail by dissimilar modes, for in the former case the soil is restrained against
horizontal movement at the surface by bracing across the trench. Consequently, the soil
behind a trench tends to fail along a curved surface that passes through the base and is
vertical at its intersection with the ground surface. At impending failure, the resultant