backfill surface and develops hydrostatic pressure behind the retaining wall, while the unit weight of the backfill equals its saturated unit weight ysat = 19.0 kN/m³. Herein, the unit weight of the retaining wall is ye = 24.0 kN/m³, the unit weight of water is yw = 9.8 kN/m³, and the friction angle of the backfill is = 35°. According to Rankine's active earth pressure, answer the following questions. Note that the uplift force under the base of the retaining wall above the original ground can be neglected. Table 4.2 Bearing Capacity Factors B= T if T≤BI√2, B' = B/√2 if T>B/√2, B" =√2B' $' No N₁ Ny $' N N₁ Ny 0 5.14 1.00 0.00 16 11.63 4.34 3.06 B" 1 5.38 1.09 0.07 17 12.34 4.77 3.53 CN 1+0.23 2 5.63 1.20 0.15 18 13.10 5.26 4.07 L FS= 3 5.90 1.31 0.24 19 13.93 5.80 4.68 4 6.19 1.43 0.34 20 14.83 6.40 5.39 2+ H H 5 6.49 1.57 0.45 21 15.82 7.07 6.20 6 6.81 1.72 0.57 22 16.88 7.82 7.13 1 m 1 m Surcharge q = 10 kN/m² 7 7.16 1.88 0.71 23 18.05 8.66 8.20 1 Yav= +₂H₂++H] 8 7.53 2.06 0.86 24 19.32 9.60 9.44 Cav= = — — [c₁₁ + c₁₂H₂+---+ CH] H 9 7.92 2.25 1.03 25 20.72 10.66 10.88 ☑ 10 8.35 2.47 1.22 26 22.25 11.85 12.54 (A)(s²) M. (C₁+C₂)(s²) M = max max Groundwater table rose to 11 8.80 2.71 1.44 27 23.94 13.20 14.47 8 8 12 9.28 2.97 1.69 28 25.80 14.72 16.72 the backfill surface 13 9.81 3.26 1.97 29 27.86 16.44 19.34 Yw 9.8 kN/m³ 14 10.37 3.59 2.29 30 30.14 18.40 22.40 15 10.98 3.94 2.65 31 32.67 20.63 25.99 (continued) K. 1-sino K≈0.95-sin &' K Rankine's active earth pressure 4 m Retaining wall: Cohesionless backfill Ya 15.5 kN/m³ Ye=24 kN/m³ Ysat 19.0 kN/m³ =35° Clogged drain holes Table 4.2 Bearing Capacity Factors (Continued) o(overconsoldate) K o(normally consolidated) √OCR Coulomb's active earth pressure Pa(max) Active force $' No Na Ny $' No N₁ Ny 32 35.49 23.18 30.22 42 93.71 85.38 155.55 C G 33 38.64 26.09 35.19 43 105.11 99.02 186.54 Wall movement away from soil Collector pipe 34 42.16 29.44 41.06 44 118.37 115.31 224.64 P. B-8 35 46.12 33.30 48.03 45 133.88 134.88 271.76 σ' Original ground Groundwater table dropped 36 50.59 37.75 56.31 46 152.10 158.51 330.35 H 2 m far below the base of the wall 37 55.63 42.92 66.19 47 173.64 187.21 403.67 c'=0 w R ✓ 38 61.35 48.93 78.03 48 199.26 222.31 496.01 39 67.87 55.96 92.25 49 Figure 2 40 75.31 64.20 109.41 50 50 229.93 265.51 613.16 H/3 (b) 266.89 319.07 762.89 Pa 41 83.86 73.90 130.22 (a) (2.1) Calculate the resisting moment per unit length of the wall around point O, considering its top width of 1 m and base width of 2 m. (5%) (2.2) Calculate the total resultant force per unit length of the wall and the corresponding overturning moment per unit length of the wall about point O during the dry season. (2.3) Calculate the total resultant force per unit length of the wall and the corresponding overturning moment per unit length of the wall about point O during the rainy season. (2.4) Determine the safety factors against overturning for dry and rainy seasons. (2.5) Discuss the importance of drainage systems in retaining walls from the viewpoint of their stability. Equations and Tables: Bearing capacity equation: q=c'NFFF+q'NFFF+0.5BN FFF Shape factors by De Beer Depth factors by Hansen (1970) (1970) F₁ = 1+ (B) N LN Inclination factors by Meyerhof (1963) and Hanna and Meyerhof (1981) F = F = (1-B Fd=1+0.4(- D B F=1+()tan o' L Fad=1+2 tan o'(1-sin ')2. F₁ =1 D В F= (1-5 B 90° 0.25 H 0.25 H * 0.5 H HAD 0.75 H 4c 二[10] (a) σ =0.657HK (b) the larger of σ =yH|1- YH 0.25 H and σ =0.37H (c) σ = 0.2yH to 0.4yH F1-0.4( K = cosa cosa-cos² a-cos² cosa + √cos o a-cos² Q' K = sin² (B+) sin ẞsin(-8) 1+. sin(+6) sin('-a) sin(B-) sin(a + B)