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Unformatted text preview: 1. For the retaining wall shown in Figure 1, determine the at-rest lateral earth force per unit meter length of the wall. Also, find the location of the resultant for the following cases: a) H 1 = 2.5 m, H 2 = 2.5 m, q = 0, γ sat = 19 kN/m 3 . The backfill is granular material with c ′ = 0, and φ ′ = 30°. b) H 1 = 6 m, H 2 = 0 m, q = 0, γ = 18 kN/m 3 . The backfill is over-consolidated clay with a plasticity index of 26 and over consolidation ratio of 2. c) Redo case b assuming that the surcharge q = 40 kN/m 2 . This problem can be approached by making one of two assumptions. The first is that it can be assumed that there is a complete and fully saturated capillary rise from the top of the water table up and into the ‘unsaturated’ granular soil, all the way to the ground surface. The saturated unit weight can then be used for this region (labelled as ‘1’ in the diagram above). This will provide more conservative values which will result in a more robust design. The second option will be presented below, however the procedure for both cases is the same for determining the static loads. The only difference between both assumptions is that the forces and stresses will not be the same. In order to estimate the dry unit weight of the soil above the water table, it will be assumed that the void ratio below the water table is the same as the void ratio above it. It can also be assumed that G s ≅ 2.65 , a common and average value for granular material. w s e Se G γ γ ⋅ + + = 1 γ sat = 19 kN/m 3 , and solving for e , e = 0.76. Assignment 3 Solutions CIVE 416 - Geotechnical Engineering 1 of 14 Winter, 2008 w s dry e G γ γ ⋅ + = 1 ∴ γ dry 14.8 kN/m ≅ 3 . The at-rest coefficient of lateral pressure is 2 1 ) 30 sin( 1 ) sin( 1 = ° − = − = φ K The stress distribution along the wall can now be computed: At z = 0 m, p z=0 = 0 kPa. At z = 2.5 m, p z=2 = (0.5)(2.5)(14.8) = 18.4 kPa. At z = 5.0 m, p z=4 = p z=2 + (0.5)(2.5)( γ ’ ) = p z=2 + (0.5)(2.5)(19 – 9.81) = 29.9 kPa. The hydrostatic pressure is: h p = (2.5)(9.81) = 24.5 kPa. By adding the hydrostatic pressure distribution to the corresponding stress block (i.e. where the water table is), the final stress distribution can be obtained as shown in the figure above. The resultants for each stress block can now be determined: ) 5 . 2 )( 4 . 18 ( 2 1 1 = R = 23.1 kN/m....
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This note was uploaded on 04/19/2011 for the course CIVE 416 taught by Professor Meguid during the Winter '10 term at McGill.
- Winter '10
- Geotechnical Engineering