Question

b) In a construction site of a congested city, a vertical cut slope will be constructed to maximize the land area. Hence, a 5.0 m height of concrete cantilever wall was selected. If the unit weight of the concrete wall is 24 kN/m and the cross-sectional view of the wall is shown as in Figure Q2(b); (i) Draw the lateral earth pressure diagram using Rankine-Bell theory for active and passive state. Determine the lateral thrust (P) and its line of action (ñ) for active and passive state. (iii) Calculate the factor of safety (FOS) against overturning of the concrete cantilever wall. (CO2-P03) (C3-C4) (15 marks) 0.5 m y = 18.0 kN/m c* = 0 kN/m * = 32 5.0 m 1.5 m y = 20.5 kN/m c=10 kN/m 0 = 250 y = 20.5 kN/m c=10 kN/m 0 = 250 0.5 m Base = 2.Om Figure Q2(b)

Answer 1

According to Rancino to Ranokino - bell theory Active cooth pressure; Pa= kaovac Vka passive earth pressure ; pp kooli ac VK Ak z=0) Pa 0.307 X18XO - 2ox v0.307 = 0 Ak z = 3.5m 2x0XV0:307 = 19.34 kwho? ou 0.307x18x3.5

AE z = 5 m. Pa = 0.3405 * (18x3.5+ 20.5x1,5) 2x10 80.405 = 25.24kwim? passive earth presswee; Ak Z= 3:5 Pp=kportacVip 2,46x dxz tacte Ak z= 5 m; Pp = 2.46x 20.5x1.5 + 2x10 x V 2.46 107.01 knim? Resultank passive thrust; Ix 107.01 X 1.5 80.25kN lm Co.sm) achs at height of his above iks Gase

H= EPH P; xH slino Thaust point de application < P; Py=- = 1 x 19.349x3.5x) 1.5 +3.5 3 90.02 = 2.66 = 33.845 knim 1.572 21.75 2 p = 19.34X1,5X1 H = 113.98 67.28 2 = 0.75 = 29.01 kwim = 1.697 1.5 3 3 Po = I x (25.24-19.340x 2 1.51 2.212 = 0.5 4.425 EP; A = 113.98 *P;= 67.28 Resulkank active chaust 67.28 kNlm above its wall at 1. 69 m achs the on base.

= factor of safety Resisting moment Overturning momont р you 0.5 80.25 x 67. 28 x 1.69 0.3528 -

A 3.5 m 19:34 B P2 1.5 m ON с 25.2 107.01 Active earth pressure coefficiank; ka In sind It sind 人。 of internal friction Angle Kair I sin 32 = 0.307 Itsin 3 2 kar lasin 25 0.405 I + sin 23 Rassive earth pressure coefficient; kpa I+ sin Ø la sind kp= 1 tsin 25 = 2.46 1-sin25