1 Retaining Wall
Retaining Walls What are retaining walls Retaining walls are soil-structure systems intended to support earth backfills. Type of retaining walls Gravity retaining wall gravity walls rely on their own weight to provide static equilibrium. typically made of plain (unreinforced) concrete or stone blocks. Cantilever retaining walls cantilever walls derive a portion of their stabilizing forces and moments from the backfill soil above the heel. require the use of steel reinforcement to resist the large moments and shear stresses.
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Retaining Walls 5 MSE walls Mechanically Stabilized Earth (MSE) walls derive their stability from the internal stresses developing at the interface between the soil and the reinforcement elements. MSE walls are constructed by compacting the soil in layers separated by reinforcement strips or sheets. Reinforcement strips are attached to facing units, and extend far enough into the backfill to ensure adequate pullout resistance. Soil-Nailed walls
Retaining Walls Reinforced Earth Walls Geotextile-Reinforced Walls Cantilever Sheet Piles 6
Reinforced Earth Walls 7
Cantilever Sheet Piles 8
Cantilever Retaining Walls Basic Principles Cantilever walls are made of reinforced concrete, & come in different geometries. Rely on their self-weight to resist sliding & overturning, but derive part of their stability from the weight of the backfill above the heel of the wall. 9
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Cantilever Retaining Walls Typical Dimensions of retaining walls 11
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Cantilever Retaining Walls Basic Design Principles In addition to the external stability, cantilever walls must also satisfy internal structural. The wall section should be able to withstand the shear stresses and bending moments resulting from the lateral earth pressure as well as the difference in pressure between the top and bottom faces of the base. 14
Cantilever Retaining Walls 15 External stability In analyzing or designing for external stability, all the forces acting on the structure are considered. These forces include lateral earth pressures, the self-weight of the structure, & the reaction from the foundation soil. The stability of the wall is then evaluated by considering the relevant forces for each potential failure mechanism. The wall has to be stable against: Sliding Overturning Bearing capacity FS BC q q all max 1
Cantilever Retaining Walls Design Example Given data As shown in the figure f ' 5 f c y MPa 40MPa q 150 kn / m all Design the retaining wall 16
Design Example Step 1: Check for overturning Calculate the weight per unit width (W i ) W (per meter) 1 3.5 0.5 0.7 8.3kN W 3.5 50.5 58.75kN W 3 3.5 0.51.4 16.45kN W 4 (17.5 19 0.)1.4 11.7kN 17 Moment arm (x i ) x1 0.35m x 0.95m x3 1.9m x 4 1.9m
Design Example 18 Calculate the active earth pressure & the water pressure 1 sin 35 K a 0.7 1 sin 35 ' 17.5 0.71 11.5kPa h1 ' (17.5 (19 9.8).5) 0.71 17.75kPa h u 9.8.5 4.5kPa W 4 (17.5 19 0.)1.4 11.7kN The active forces P 1 to P 4 per unit width P1 0.511.5.5 14.4kN P 17.75.5 44.38kN P3 0.5 (17.75 11.5).5 7.79kN P4 0.5 4.5.5 30.63kN Moment arm (y i ) y1.5.5 / 3 3.33m y3.5 / 3 0.83m y.5 / 1.5m y 4 0.83m
Design Example Calculate the active earth pressure & the water pressure M Wx R i i FS overturning M P y O i i 8.3 0.35 58.75 0.95 16.451.9 11.7 1.9 14.4 3.33 44.381.5 7.79 0.83 30.63 0.83 304.1. 1.5 135.3 OK 19 Step : Check for bearing capacity The eccentricity on the wall base e 0.5 B ( M M ) / W R 0.5(.6) (304.1 135.3) /196.1 e 0.4 m B / 6 0.43 OK O The maximum & minimum soil pressures at the toe & heel of the base are F M x 196.1 196.10.4 6 qmax qtoe y 148.5 kn / m A Ix.6.6 196.1 196.1 0.4 6 qmin q heel.3 kn / m.6.6
Design Example FS BC qall 150 1.01 1 q 148.5 max OK 0 Step 3: Check for shear strength at critical section The ultimate shear on the base at a distance d from the face of the wall is d 0.5.075 0.0 0.405m qmax 148.5 kn / m Effective depth of base At the TOE Pressure at distance d from the face of the wall (148.5.3).95 q d.3 131.3 kn / m.6 V 1.6 qb(0.7 d ) u V 148.5 131.3 1.6 10.7 0.405 66 c 0.17 fc ' b d 0 kn 0.17 0.85 30 10.405 93 kn V u OK
Design Example At the HEEL Pressure at distance d from the face of the wall (148.5.3) 0.995 q d.3 58. kn / m.6 qmin.3 kn / m 1 V 1.6 qb(1.4 d ) u V 58..3 1.6 11.4 0.405 50 kn c 0.17 fc ' b d 0 0.17 0.85 30 10.405 93 kn V u OK Step 3: Flexural reinforcement At the HEEL Case I 1.4 1.4 M u 1.6M heel 1.6.3 81.3 6 M 44.8 kn. m u
Design Example 3 0.85 f ' c.6110 M u 1 1 f y bd f c ' 3 0.855.6110 (44.8) 1 1 0.0007 min 0.0018 40 1(0.405) 5 As Case II 0.0018(100)(40.5) 7.3cm Use 1mm @ 15cm M 1.6M 1.6 16.45 11.7 0.7 144.6 kn u heel W3 + W4 3 0.855.6110 (144.6) 1 1 0.004 40 1(0.405) 5 As 0.004(100)(40.5) 9.7cm Use 14mm @ 15cm
Design Example At the TOE 0.7 0.7 M u 1.6M toe 1.6109.1 148.5 109.1 3 M 53.1 kn. m u 3 3 0.855.6110 (53.1) 1 1 0.0009 min 0.0018 40 1(0.405) 5 As 0.0018(100)(40.5) 7.3cm Use 1mm @ 15cm At the STEM M 14.4.83 44.38 0.75 7.79 0.33 30.63 0.33 M stem stem M 1.6M 1.6 86.7 138.7 kn. m u 86.7 kn. m stem 3 0.855.6110 (148.7) 1 1 0.003 40 1(0.405) 5
Design Example 4 As 0.003(100)(40.5) 9.3cm Use 14mm @ 15cm Step 4: Shrinkage reinforcement As 0.0018(100)(40.5) 7.3cm Use 1mm @ 15cm
Design Example 5 1mm @ 15cm Flexural reinforcement Shrinkage reinforcement 1mm @ 15cm 1mm @ 15cm 1mm @ 15cm 14mm @ 15cm 1mm @ 15cm 14mm @ 15cm