Sample Problems Problem 5.1 A gravity retaining wall is supporting a cohesionless soil. The active lateral force per linear foot of the retaining wall is most nearly (A) 5,000 lb/ft (B) 6,000 lb/ft (C) 7,200 lb/ft (D) 8,500 lb/ft Solution Compute the lateral force per linear foot with sloping backfill and inclined wall. Use Equation No. 51, page 93. Press ENTER. S? 110 R/S Density of backfill (lb/ft 3 ) H? 20 R/S Height of wall (ft) A? 30 R/S Angle of internal friction of backfill B? 85 R/S Angle of inclined wall from horizontal C? 20 R/S Angle of friction between the soil and wall face I? 10 R/S Angle of sloping backfill from horizontal 8,486.0369 -- Active lateral force per linear foot of the wall (lb/ft) 117
The answer is (D). Problem 5.2 A ten-foot-high retaining wall is supporting a sand backfill. The elevation of the sand backfill equals the top elevation of the retaining wall. The angle of internal friction and dry density of the backfill are 31 and 110 lb/ft 3, respectively. The active lateral force per linear foot of the retaining wall is most nearly (A) 1,700 lb/ft (B) 1,800 lb/ft (C) 2,200 lb/ft (D) 3,500 lb/ft Solution The procedure for calculating the active lateral force per linear foot is as follows: Step 1. Calculate the Rankine active earth pressure coefficient. Use Equation No. 47, page 89. Press ENTER. A? 31 R/S Angle of internal friction of backfill K = 0.3201 -- Rankine active earth pressure coefficient Step 2. Compute the active lateral force per linear foot of the retaining wall. Use Equation No. 50, page 92. Press ENTER. S? 110 R/S Density of backfill (lb/ft 3 ) H? 10 R/S Height of the wall (ft) K? = 0.3201 R/S Rankine active earth pressure coefficient 1,760.5436 -- Total active lateral force per unit length of the wall (lb/ft) The answer is (A). Problem 5.3 A retaining wall is supporting an 8-foot-high clayey sand backfill. The angle of internal friction of the backfill is 20, the density is 100 lb/ft 3, and the cohesion is 500 lb/ft 2. The active earth pressure per unit length of wall is most nearly (A) 250 lb/ft 2 (C) 400 lb/ft 2 (B) 300 lb/ft 2 (D) 700 lb/ft 2 118
Solution Calculate the active earth pressure per unit length of the wall. Use Equation No. 49, page 91. Press ENTER. S? 100 R/S Density of clayey sand backfill (lb/ft 3 ) H? 8 R/S Height of backfill (ft) K? * K? 0.4903 R/S Rankine active earth pressure coefficient C? 100 R/S Cohesion of clayey sand backfill (lb/ft 2 ) 252.1910 -- Active earth pressure per unit length of the wall (lb/ft 2 ) * Keys for calculating Rankine active earth pressure coefficient using RPN: 45 ENTER 20 ENTER 2 TAN (HP 35s) 45 ENTER 20 ENTER 2 TAN (HP 33s) The answer is (A). Problem 5.4 The retaining wall shown is supporting a sandy soil with an active equivalent fluid pressure of 38 lb/ft 3 and 31 lb/ft 3 above the water table and below the water table, respectively. The total active lateral force at the retaining wall is most nearly (A) 5,200 lb/ft (B) 6,000 lb/ft (C) 6,200 lb/ft (D) 7,000 lb/ft 119
Solution Compute the lateral force with given equivalent fluid pressures. Use Equation No. 46 (P), page 87. Press ENTER. Q? 200 R/S Surcharge load (lb/ft 2 ) X? 6 R/S Distance from top of backfill to water table (ft) A? 38 R/S Equivalent fluid pressure above water table (lb/ft 3 ) Z? 5 R/S Distance from water table to bottom of the wall (ft) B? 31 R/S Equivalent fluid pressure below water table (lb/ft 3 ) W? 62.4 R/S Unit weight of water (lb/ft 3 ) 5,191.5000 -- Total active lateral force per unit length of the wall (lb/ft) The answer is (A). Problem 5.5 The retaining wall shown can yield sufficiently to develop an active state. The overturning moment per unit length of wall at point A is most nearly (A) 16,000 ft-lb (B) 22,000 ft-lb (C) 25,000 ft-lb (D) 27,000 ft-lb 120
Solution The calculation involves the following steps. Step 1. Calculate the Rankine active force per unit length of the wall. Use Equation No. 52 (P), page 94. Press ENTER. Q? 0 R/S Surcharge load (lb/ft 2 ) X? 8 R/S Distance from top of backfill to water table (ft) A? 30 R/S Angle of internal friction of moist soil D? 110 R/S Density of moist soil (lb/ft 3 ) C? 0 R/S Cohesion of moist soil (lb/ft 2 ) B? 33 R/S Angle of internal friction of saturated soil E? 0 R/S Cohesion of saturated soil (lb/ft 2 ) Z? 7 R/S Distance from water table to bottom of retaining wall (ft) S? 120 R/S Density of saturated soil (lb/ft 3 ) W? 62.4 R/S Unit weight of water (lb/ft 3 ) 4,934.1298 -- Rankine active force per unit length of the wall (lb/ft) Step 2. Compute the location of resultant line of action from the bottom of the wall. Use Equation No. 52 (Y), page 94. Press ENTER. Press R/S every time you are prompted. You ll get Y = 4.5066 (ft). 121
Step 3. Calculate the overturning moment at point A. Use Equation No. 52 (O), page 94. Press ENTER. Press R/S every time you are prompted. You ll get O = 22,236.0498 (ft-lb). The answer is (B). 122