Page 1 NPTEL - ADVANCED FOUNDATION ENGINEERING-1 Module 7 (Lecture 27) RETAINING WALLS Topics 1.1 RETAINING WALLS WITH METALLIC STRIP REINFORCEMENT ? Calculation of Active Horizontal and vertical Pressure ? Tie Force ? Factor of Safety Against Tie Failure ? Total Length of Tie 1.2 STEP-BY-STEP DESIGN PROCEDURE (METALLIC STRIP REINFORCEMENT ? Internal Stability ? External Stability ? Internal Stability Check ? Tie thickness ? Tie length ? External Stability Check ? Check for overturning ? Check for sliding ? Check for bearing capacity Page 2 NPTEL - ADVANCED FOUNDATION ENGINEERING-1 Module 7 (Lecture 27) RETAINING WALLS Topics 1.1 RETAINING WALLS WITH METALLIC STRIP REINFORCEMENT ? Calculation of Active Horizontal and vertical Pressure ? Tie Force ? Factor of Safety Against Tie Failure ? Total Length of Tie 1.2 STEP-BY-STEP DESIGN PROCEDURE (METALLIC STRIP REINFORCEMENT ? Internal Stability ? External Stability ? Internal Stability Check ? Tie thickness ? Tie length ? External Stability Check ? Check for overturning ? Check for sliding ? Check for bearing capacity NPTEL - ADVANCED FOUNDATION ENGINEERING-1 RETAINING WALLS WITH METALLIC STRIP REINFORCEMENT Reinforced earth walls are flexible walls. Their main components are 1. Backfill, which is granular soil 2. Reinforcing strips, which are thin, wide strips placed at regular intervals 3. A cover on the front face, which is referred to as the skin Figure 25 is a diagram of a reinforced earth wall. Note that, at any depth, the reinforcing stripes or ties are placed with a horizontal spacing of ???? ???? center-to-center; the vertical spacing of the strips or ties is ???? ???? center-to-center. The skin can be constructed with sections of relatively flexible thin material. Lee et al. (1973) showed that, with a conservative design, a 0.2-in.thick ( Ëœ 5 mm) galvanized steel skin would be enough to hold a wall about 45-50 ft (14-15 m) high. In most cases, precast concrete slabs can be used as skin. The slabs are grooved to fit into each other so that soil cannot flow out between the joints. When metal skins are used, they are bolted together, and reinforcing strips are placed between the skins. Figure 7.25 Reinforced earth retaining wall Calculation of Active Horizontal and vertical Pressure Figure 26a shows a retaining wall with a granular backfill having a unit weight of ???? 1 and a friction angle of ???? 1 . Below the base of the retaining wall, the in situ soil has been excavated and reccopacted, with granular soil used as backfill. Below the backfill, the in situ soil has a unit weight of ???? 2 and a friction angle of ???? 2 , and cohesion of ???? 2 . A surcharge having an intensity of q per unit area lies atop the retaining wall. The wall has reinforcement ties at depths ???? = 0, ???? ???? , â€¦ . . , ???????? ???? . The height of the wall is ???????? ???? = ???? . Page 3 NPTEL - ADVANCED FOUNDATION ENGINEERING-1 Module 7 (Lecture 27) RETAINING WALLS Topics 1.1 RETAINING WALLS WITH METALLIC STRIP REINFORCEMENT ? Calculation of Active Horizontal and vertical Pressure ? Tie Force ? Factor of Safety Against Tie Failure ? Total Length of Tie 1.2 STEP-BY-STEP DESIGN PROCEDURE (METALLIC STRIP REINFORCEMENT ? Internal Stability ? External Stability ? Internal Stability Check ? Tie thickness ? Tie length ? External Stability Check ? Check for overturning ? Check for sliding ? Check for bearing capacity NPTEL - ADVANCED FOUNDATION ENGINEERING-1 RETAINING WALLS WITH METALLIC STRIP REINFORCEMENT Reinforced earth walls are flexible walls. Their main components are 1. Backfill, which is granular soil 2. Reinforcing strips, which are thin, wide strips placed at regular intervals 3. A cover on the front face, which is referred to as the skin Figure 25 is a diagram of a reinforced earth wall. Note that, at any depth, the reinforcing stripes or ties are placed with a horizontal spacing of ???? ???? center-to-center; the vertical spacing of the strips or ties is ???? ???? center-to-center. The skin can be constructed with sections of relatively flexible thin material. Lee et al. (1973) showed that, with a conservative design, a 0.2-in.thick ( Ëœ 5 mm) galvanized steel skin would be enough to hold a wall about 45-50 ft (14-15 m) high. In most cases, precast concrete slabs can be used as skin. The slabs are grooved to fit into each other so that soil cannot flow out between the joints. When metal skins are used, they are bolted together, and reinforcing strips are placed between the skins. Figure 7.25 Reinforced earth retaining wall Calculation of Active Horizontal and vertical Pressure Figure 26a shows a retaining wall with a granular backfill having a unit weight of ???? 1 and a friction angle of ???? 1 . Below the base of the retaining wall, the in situ soil has been excavated and reccopacted, with granular soil used as backfill. Below the backfill, the in situ soil has a unit weight of ???? 2 and a friction angle of ???? 2 , and cohesion of ???? 2 . A surcharge having an intensity of q per unit area lies atop the retaining wall. The wall has reinforcement ties at depths ???? = 0, ???? ???? , â€¦ . . , ???????? ???? . The height of the wall is ???????? ???? = ???? . NPTEL - ADVANCED FOUNDATION ENGINEERING-1 Figure 7.26 Analysis of a reinforced earth retaining wall According to the Rankine active pressure theory ???? ???? = ???? ???? ???? ???? - 2 ???? ? ???? ???? Where ???? ???? = Rankine active pressure at any depth ???? For dry granular soils with no surcharge at the top, ???? = 0, ???? ???? = ???? 1 ???? , and ???? ???? = tan 2 (45 - ???? 1 /2). Thus ???? ???? (1) = ???? 1 ???? ???? ???? [7.30] When a surcharge is added at the top, as shown in figure 29, ???? ???? = ???? ???? (1) ? = ???? 1 ???? Due to soil only + ???? ???? (2) ? Due to the surcharge [7.31] The magnitude of ???? ???? (2) can be calculated by using the 2:1 method of stress distribution described in equation (14 chapter 4) and figure 6 (from chapter 4). It is shown in figure 27a. According to Laba and Kennedy (1986), Page 4 NPTEL - ADVANCED FOUNDATION ENGINEERING-1 Module 7 (Lecture 27) RETAINING WALLS Topics 1.1 RETAINING WALLS WITH METALLIC STRIP REINFORCEMENT ? Calculation of Active Horizontal and vertical Pressure ? Tie Force ? Factor of Safety Against Tie Failure ? Total Length of Tie 1.2 STEP-BY-STEP DESIGN PROCEDURE (METALLIC STRIP REINFORCEMENT ? Internal Stability ? External Stability ? Internal Stability Check ? Tie thickness ? Tie length ? External Stability Check ? Check for overturning ? Check for sliding ? Check for bearing capacity NPTEL - ADVANCED FOUNDATION ENGINEERING-1 RETAINING WALLS WITH METALLIC STRIP REINFORCEMENT Reinforced earth walls are flexible walls. Their main components are 1. Backfill, which is granular soil 2. Reinforcing strips, which are thin, wide strips placed at regular intervals 3. A cover on the front face, which is referred to as the skin Figure 25 is a diagram of a reinforced earth wall. Note that, at any depth, the reinforcing stripes or ties are placed with a horizontal spacing of ???? ???? center-to-center; the vertical spacing of the strips or ties is ???? ???? center-to-center. The skin can be constructed with sections of relatively flexible thin material. Lee et al. (1973) showed that, with a conservative design, a 0.2-in.thick ( Ëœ 5 mm) galvanized steel skin would be enough to hold a wall about 45-50 ft (14-15 m) high. In most cases, precast concrete slabs can be used as skin. The slabs are grooved to fit into each other so that soil cannot flow out between the joints. When metal skins are used, they are bolted together, and reinforcing strips are placed between the skins. Figure 7.25 Reinforced earth retaining wall Calculation of Active Horizontal and vertical Pressure Figure 26a shows a retaining wall with a granular backfill having a unit weight of ???? 1 and a friction angle of ???? 1 . Below the base of the retaining wall, the in situ soil has been excavated and reccopacted, with granular soil used as backfill. Below the backfill, the in situ soil has a unit weight of ???? 2 and a friction angle of ???? 2 , and cohesion of ???? 2 . A surcharge having an intensity of q per unit area lies atop the retaining wall. The wall has reinforcement ties at depths ???? = 0, ???? ???? , â€¦ . . , ???????? ???? . The height of the wall is ???????? ???? = ???? . NPTEL - ADVANCED FOUNDATION ENGINEERING-1 Figure 7.26 Analysis of a reinforced earth retaining wall According to the Rankine active pressure theory ???? ???? = ???? ???? ???? ???? - 2 ???? ? ???? ???? Where ???? ???? = Rankine active pressure at any depth ???? For dry granular soils with no surcharge at the top, ???? = 0, ???? ???? = ???? 1 ???? , and ???? ???? = tan 2 (45 - ???? 1 /2). Thus ???? ???? (1) = ???? 1 ???? ???? ???? [7.30] When a surcharge is added at the top, as shown in figure 29, ???? ???? = ???? ???? (1) ? = ???? 1 ???? Due to soil only + ???? ???? (2) ? Due to the surcharge [7.31] The magnitude of ???? ???? (2) can be calculated by using the 2:1 method of stress distribution described in equation (14 chapter 4) and figure 6 (from chapter 4). It is shown in figure 27a. According to Laba and Kennedy (1986), NPTEL - ADVANCED FOUNDATION ENGINEERING-1 Figure 7.27 (a) notation for the relationship of ???? ???? (2) - equations (32 and 33); (b) notation for the relationship of ???? ???? (2) - equations (35 and 36); ???? ???? (2) = ???????? ' ???? ' + ???? (for ???? = 2 ???? ' ) [7.32] And ???? ???? (2) = ???????? ' ???? ' + ???? 2 + ???? ' (for ???? > 2 ???? ' ) [7.33] Also, when a surcharge is added at the top, the lateral pressure at any depth is ???? ???? = ???? ???? (1) ? = ???? ???? ???? 1 ???? Due to soil only + ???? ???? (2) ? Due to the surcharge [7.34] According to Laba and Kennedy (1986), ???? ???? (2) may be expressed (figure 30b) as ???? ???? (2) = ???? ? 2 ???? ???? ( ???? - sin ???? cos2 ???? ) ? ? (in radius) [7.35] Where ???? = 1.4 - 0.4 ???? ' 0.14 ???? = 1 [7.36] The net active (lateral) pressure distribution on the retaining wall calculated by using equations. (34, 35 and 36) is shown in figure 29b. Tie Force Refer again to figure 29. The tie force per unit length of the wall developed at any depth z is Page 5 NPTEL - ADVANCED FOUNDATION ENGINEERING-1 Module 7 (Lecture 27) RETAINING WALLS Topics 1.1 RETAINING WALLS WITH METALLIC STRIP REINFORCEMENT ? Calculation of Active Horizontal and vertical Pressure ? Tie Force ? Factor of Safety Against Tie Failure ? Total Length of Tie 1.2 STEP-BY-STEP DESIGN PROCEDURE (METALLIC STRIP REINFORCEMENT ? Internal Stability ? External Stability ? Internal Stability Check ? Tie thickness ? Tie length ? External Stability Check ? Check for overturning ? Check for sliding ? Check for bearing capacity NPTEL - ADVANCED FOUNDATION ENGINEERING-1 RETAINING WALLS WITH METALLIC STRIP REINFORCEMENT Reinforced earth walls are flexible walls. Their main components are 1. Backfill, which is granular soil 2. Reinforcing strips, which are thin, wide strips placed at regular intervals 3. A cover on the front face, which is referred to as the skin Figure 25 is a diagram of a reinforced earth wall. Note that, at any depth, the reinforcing stripes or ties are placed with a horizontal spacing of ???? ???? center-to-center; the vertical spacing of the strips or ties is ???? ???? center-to-center. The skin can be constructed with sections of relatively flexible thin material. Lee et al. (1973) showed that, with a conservative design, a 0.2-in.thick ( Ëœ 5 mm) galvanized steel skin would be enough to hold a wall about 45-50 ft (14-15 m) high. In most cases, precast concrete slabs can be used as skin. The slabs are grooved to fit into each other so that soil cannot flow out between the joints. When metal skins are used, they are bolted together, and reinforcing strips are placed between the skins. Figure 7.25 Reinforced earth retaining wall Calculation of Active Horizontal and vertical Pressure Figure 26a shows a retaining wall with a granular backfill having a unit weight of ???? 1 and a friction angle of ???? 1 . Below the base of the retaining wall, the in situ soil has been excavated and reccopacted, with granular soil used as backfill. Below the backfill, the in situ soil has a unit weight of ???? 2 and a friction angle of ???? 2 , and cohesion of ???? 2 . A surcharge having an intensity of q per unit area lies atop the retaining wall. The wall has reinforcement ties at depths ???? = 0, ???? ???? , â€¦ . . , ???????? ???? . The height of the wall is ???????? ???? = ???? . NPTEL - ADVANCED FOUNDATION ENGINEERING-1 Figure 7.26 Analysis of a reinforced earth retaining wall According to the Rankine active pressure theory ???? ???? = ???? ???? ???? ???? - 2 ???? ? ???? ???? Where ???? ???? = Rankine active pressure at any depth ???? For dry granular soils with no surcharge at the top, ???? = 0, ???? ???? = ???? 1 ???? , and ???? ???? = tan 2 (45 - ???? 1 /2). Thus ???? ???? (1) = ???? 1 ???? ???? ???? [7.30] When a surcharge is added at the top, as shown in figure 29, ???? ???? = ???? ???? (1) ? = ???? 1 ???? Due to soil only + ???? ???? (2) ? Due to the surcharge [7.31] The magnitude of ???? ???? (2) can be calculated by using the 2:1 method of stress distribution described in equation (14 chapter 4) and figure 6 (from chapter 4). It is shown in figure 27a. According to Laba and Kennedy (1986), NPTEL - ADVANCED FOUNDATION ENGINEERING-1 Figure 7.27 (a) notation for the relationship of ???? ???? (2) - equations (32 and 33); (b) notation for the relationship of ???? ???? (2) - equations (35 and 36); ???? ???? (2) = ???????? ' ???? ' + ???? (for ???? = 2 ???? ' ) [7.32] And ???? ???? (2) = ???????? ' ???? ' + ???? 2 + ???? ' (for ???? > 2 ???? ' ) [7.33] Also, when a surcharge is added at the top, the lateral pressure at any depth is ???? ???? = ???? ???? (1) ? = ???? ???? ???? 1 ???? Due to soil only + ???? ???? (2) ? Due to the surcharge [7.34] According to Laba and Kennedy (1986), ???? ???? (2) may be expressed (figure 30b) as ???? ???? (2) = ???? ? 2 ???? ???? ( ???? - sin ???? cos2 ???? ) ? ? (in radius) [7.35] Where ???? = 1.4 - 0.4 ???? ' 0.14 ???? = 1 [7.36] The net active (lateral) pressure distribution on the retaining wall calculated by using equations. (34, 35 and 36) is shown in figure 29b. Tie Force Refer again to figure 29. The tie force per unit length of the wall developed at any depth z is NPTEL - ADVANCED FOUNDATION ENGINEERING-1 ???? = active earth pressure at depth ???? × area of the wall to be supported by the tie = ( ???? ???? )( ???? ???? ???? ???? ) [7.37] Factor of Safety Against Tie Failure The reinforcement ties at each level and thus the walls cold fail by either (a0 tie breaking or (b) tie pullout. The factor of safety against tie breaking may be determined as ???????? ( ???? ) = yield or breaking strength of each tie maximum tie force in any tie = ???????? ???? ???? ???? ???? ???? ???? ???? ???? [7.38] Where ???? = width of each tie ???? = thickness of each tie ???? ???? = yield or breaking strength of the tie material A factor of safety of about 2.5-3 is generally recommended for ties at all levels. Reinforcing ties at any depth, z, will fail by pullout if the frictional resistance developed along their surfaces is less than the force to which the ties are being subjected. The effective length of the ties along which the frictional resistance is developed may be conservatively taken as the length that extends beyond the limits of the Rankine active failure zone, which is the zone ???????????? in figure 29. Line ???????? in figure 29 makes an angle of 45 + ???? 1 /2 with the horizontal. Now, the maximum friction force ???? ???? that can be realized for a tie at depth z is ???? ???? = 2 ???? ???? ???? ???? ???? tan ???? ???? [7.39] Where ???? ???? = effective length ???? ???? = effective vertical pressure at a depth ???? ???? ???? = soil - tie friction angle Thus the factor of safety against tie pullout at any depth z is ???????? ( ???? ) = ???? ???? ???? [7.40] Where ???????? ( ???? ) = factor of safety against tie pulloutRead More

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