Seismic Design of Geosynthetic-Reinforced Soil Bridge Abutments with Modular Block Facing (2012) / Chapter Skim
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CHAPTER 1 LITERATURE REVIEW INTRODUCTION Few methods for the seismic design of geosynthetic-reinforced soil (GRS) bridge abutments exist in the literature.
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6 Figure 1.1: Forces and Geometry used in Pseudo-Static Seismic Analysis of Segmental Retaining Walls (Bathurst and Cai, 1995) The positive sign convention for the horizontal seismic coefficient, +kh, is to be consistent with active earth pressure conditions in which the horizontal inertial forces are assumed to act outward.
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7 Where: φ = Peak soil friction angle ψ = Total wall inclination (positive in a clockwise direction from the vertical) δ = Mobilized interface friction angle assumed to act at the back of the wall β = Backslope angle (from horizontal)
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8 Where: KA = Static active earth pressure coefficient ΔKdyn = Incremental dynamic active earth pressure coefficient Distribution of Dynamic Lateral Earth Pressures and Point of Application The position of the dynamic earth force, PAE, acting against gravity retaining walls is variable and depends on the magnitude of ground acceleration. The application point of the incremental dynamic earth force increment, ΔPdyn, is located at ηH above the toe of the wall where η is assumed to be 0.6 for segmental retaining wall structures (Seed and Whitman, 1970)
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9 Using the decomposed equations for the total dynamic earth force proposed by Seed and Whitman (1970) , it has been recommended by The Reinforced Earth Company (1995)
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10 The interface friction angle, δ, is assumed to be equal to 3/2φ for internal stability analysis (facing column-reinforced soil interface) and equal to φ for external stability analysis (reinforced soil-retained soil interface)
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11 sliding, bearing and overturning; Second, verification of the stability of the overall reinforced earth abutment. Sill Stability The Reinforced Earth Company (1995)
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12 Force Transmitted From Backfill. Stability checks of the sill also include the static and dynamic pressure exerted directly behind the seat and its backwall from the backfill overlying the reinforced earth mass.
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13 External Stability of the Reinforced Earth Mass Potential external failure modes of the reinforced mass include translational sliding along the base, overturning about the toe of the reinforced mass and bearing capacity of the foundation as shown in Figure 1.4. It is assumed that the foundation provides a competent base such that excessive settlement and bearing capacity failure is not of concern.
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14 the effective weight of the overlying fill, Pi2, is also assumed to act at the center of gravity of its weight. The total weight of the overlying fill, W2, is defined as the weight of the overlying fill that extends 0.5H in from the face of the wall.
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15 External Stability Static Seismic F.S. with respect to base sliding 1.5 1.1 F.S.
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16 βtan 2 12 H LL a w − += (26) L = Minimum width of the gravity mass Lw = Width of the facing column λ = An empirical constant used to artificially reduce the internal force of the gravity mass used under the assumption that the inertial forces in the gravity mass and the retained soil will not peak simultaneously during an earthquake.
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17 Overturning. The dynamic force moment arm, Ydyn, normalized with respect to wall height, H, is given by m as shown in equation 27: ( )
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18 The dynamic factor of safety against overturning about the toe of the free body comprising of the reinforced soil mass and the facing column given by Bathurst and Cai (1995)
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19 Figure 1.8: Minimum Static Factor of Safety Against Overturning Required to give a Factor of Safety of 1.5 Against Dynamic Overturning for a Range of Seismic Coefficients, kh and kv, Backslope Angle, β, and Length to Height Ratio, L/H (Bathurst and Cai, 1995) Internal Stability Seismic loading increases the magnitude of the horizontal force carried by the geosynthetic reinforcement as well as the percentage of total lateral force to be carried by the reinforcing elements in the upper portions of the wall.
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20 reinforced mass itself and the concentrated load transmitted by the sill are calculated. The load, Pi, is distributed among the reinforcement layers in proportion to their resistant area and added to the tensile load calculated in the static case.
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21 Figure 1.10: Calculating Internal Dynamic Force, Pi, in Different Cases (The Reinforced Earth Company, 1995) The applied load from the sill consists of the dead load, Qd, 50% of the live load, 0.5Qll, and the weight of the sill, Ws, which includes the backwall and soil above the heel.
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22 Over-Stressing of Reinforcement. For the geometry shown in Figure 1.11, the dynamic factor of safety against over-stressing, FSos, of a reinforcement layer at depth z below the crest of the wall is given by: ( )
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23 sufficiently accurate for designs within this range. Figure 1.12: Influence of Seismic Coefficients, kh and kv, and Normalized Depth Below Crest of Wall, z/H, on Dynamic Reinforcement Force Amplification Factor, rF (Bathurst and Cai, 1995)
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24 Figure 1.13: Influence of Seismic Coefficients, kh and kv, and Soil Friction Angle,φ , on Ratio of Minimum Reinforcement Lengths, statdyn LL / , to Capture the Inertial Failure Wedge in PseudoStatic Coulomb Wedge Analyses (Bathurst and Cai, 1995) Internal Sliding.
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25 The dynamic factor of safety against internal sliding along a horizontal surface at depth z below the crest of the wall is: ( )
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27 Figure 1.16: Influence of Seismic Coefficients, kh and kv, and Normalized Depth Below Crest of Wall, z/H, on the Ratio of Dynamic to Static Interface Shear Factor of Safety (Bathurst and Cai, 1995) Connections.
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28 Toppling. Internal moments that cause a net outward moment at the toe of a facing unit provide a possible failure mechanism and must be evaluated.
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29 Figure 1.17: Influence of Seismic Coefficients, kh and kv, and Normalized Depth Below Crest of Wall, z/H, on the Ratio of Dynamic to Static Local Toppling Factor of Safety (Bathurst and Cai, 1995) PSEUDO-DYNAMIC METHOD Steedman and Zeng (1990)
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30 Considering a typical fixed base cantilever wall as shown in Figure 1.18, when the base is subjected to a harmonic horizontal seismic acceleration, ah ( = khg) , and harmonic vertical seismic acceleration, av ( = kvg)
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31 Figure 1.18: Model Retaining Wall Considered for Computation of Pseudo-Dynamic Active Earth Pressure (Choudhury et al.
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32 The total (static +seismic) earth pressure on the wall is computed as: ( )
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33 embankments during earthquakes. Cai and Bathurst (1996)
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34 λ = An empirical constant used to artificially reduce the internal force of the gravity mass used under the assumption that the inertial forces in the gravity mass and the retained soil will not peak simultaneously during an earthquake. A value of λ = 0.6 has been used for design purposes.
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35 Where: =dsφ Soil-geosynthetic interface friction angle The second component is the shear resistance of the geosynthetic-block interface at the same depth given by: ( ) uvwuu kWaV λtan1−+= (50)
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36 Figure 1.20: Free Body Diagram of Sliding Mass along a Soil-Geosynthetic Interface and through the Facing Column at Depth z below Crest of Wall (Cai and Bathurst, 1996) Block Interface Shear between Facing Column Units Sliding at the block-block or block-geosynthetic interface may occur when shear capacities of these interfaces are exceeded.
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37 Figure 1.21: Calculation of Dynamic Interface Shear Force Acting at a Reinforcement Elevation. Fdyn, Dynamic Force in Reinforcement Layer; Sdyn, Dynamic Interface Shear Force; N, Total Number of Reinforcement Layers; M, Total Number of Facing Units (Cai and Bathurst, 1996)
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38 amax = Ag aT = Ng BN = bN WBT φ tantan == history that are above and below the critical acceleration until the relative velocity between the sliding mass and sliding base become zero. Consider the rigid block shown in Figure 1.22.
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39 Figure 1.23: Acceleration and Velocity Profiles of Block and Plane Subjected to a Rectangular Pulse Excitation Suppose that a plane is subjected to a rectangular earthquake impulse of magnitude Ag and the maximum acceleration transmitted to the block through friction forces is aT = Ng. The acceleration and the resulting velocity profiles of block and plane are shown in Figure 1.23.
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40 For evaluation of retaining wall displacements according to Newmark's sliding block theory, additional vertical and horizontal earth pressure forces should be considered as shown in Figure 1.24: Figure 1.24: Idealization of the Retaining Wall Problem by Richards-Elms (1979)
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