Seismic Design of Geosynthetic-Reinforced Soil Bridge Abutments with Modular Block Facing (2012) / Chapter Skim
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CHAPTER 2 ASD SEISMIC DESIGN OF GEOSYNTHETIC-REINFORCED SOIL (GRS) BRIDGE ABUTMENTS INTRODUCTION Allowable Stress Design (ASD)
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43 fact, results in a slightly more conservative value of PAE than values calculated assuming that the vertical component of seismic earth force acts upward (kv < 0)
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44 Total abutment height, H = 3.6 m Load bearing wall height, H1 = 3.2 m Back wall height, H2 = 0.4 m The bridge vertical dead load, Qd, is taken as one-half of the weight of the simply supported bridge. The live load, Ql, and the traffic surcharge load, q, are taken as zero since there will be no live load and traffic load applied to the bridge during the shake table test.
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45 0 10 20 30 40 50 60 70 80 90 100 0.01 0.1 1 10 100 Grain Size, D (mm) Pe rc en t Fi ne r Sample 1 Sample 2 Sieve No.
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46 Foundation Soil Friction angle of the foundation soil: °= 44fsφ Unit weight of the foundation soil: 52.21=fsγ kN/m 3 Allowable bearing capacity of the foundation soil: qaf = 300 kPa ESTABLISH DESIGN REQUIREMENTS External Stability Design Requirements Factor of safety against sliding: FSsliding ≥ 1.1 Factor of safety against overturning: FSoverturning ≥ 1.5 Eccentricity of GRS abutment: e ≤ L/6 Average sill pressure, psill ≤ allowable bearing pressure of the reinforced fill, qallow, as determined in Section 2.5 Average contact pressure at the foundation level, pcontact ≤ allowable bearing pressure of the foundation soil, qaf Internal Stability Requirements Factor of safety against geosynthetic pullout: FSpullout ≥ 1.1 Factor of safety against geosynthetic breakage: FSbreakage ≥ 1.1 DETERMINE ALLOWABLE BEARING PRESSURE OF REINFORCED FILL Determine the allowable bearing pressure of the reinforced fill below the sill, qallow, with the following conditions: -Design friction angle of the reinforced fill, °= 44rfφ -Reinforcement spacing, 2.0=s m (uniform spacing with no truncation) -Isolated sill -Sill width, 75.0=B m
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47 (1) From Table 3-1 NCHRP 556 (See Appendix A)
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48 H2 = 0.4 m t = 0.2 m b = 0.2 m Center of gravity of sill (with reference to pt.
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49 Inertial force of dead load, Fd AQF dd ×= ( ) 17.3320084.165 =×= .Fd kN/m Qd = 82.92 kN/m is the dead load reaction supported by the abutment, and is equal to one-half of the bridge weight.
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51 The bridge live load, Ql, and its inertial component, Fl, are not included in sliding analysis as their inclusion would tend to increase the factor of safety against sliding. Check Factor of Safety Against Sill Overturning Sum of resisting moments about point A: (See Figure 2.3)
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52 Eccentricity at base of sill, e' sld OR WQQ MMB e AA ++ − −=′ ∑ ∑ 5.02 Sum of resisting moments about point A: (See Figure 2.3)
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53 Figure 2.4: Static and Dynamic Forces Acting on Soil Mass From before: Qd = 82.92 kN/m, Fd = 33.17 kN/m, Ws = 4.48 kN/m With reference to Figure 2.4, the inertial force of sill, Pis2, is: msis AWP ×=2 12.125.048.42 =×=isP kN/m Weight of overlying fill, W2 ( ) rfvkHBdLW γ×±××−−= 1)
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54 Specifications (2007)
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55 The calculated weight of the reinforced fill, W, includes the weight of the facing blocks which are assumed to here have the same unit weight as the reinforced fill. With reference to Figure 2.5, the effective weight of reinforced soil, Weff, is: ( )
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56 °= ± = ± = −− 14 01 25.0 tan 1 tan 11 v h k k θ °== 44reφδ (soil-to-soil) Check Factor of Safety Against Abutment Sliding aeiirisd fssd PPPPPF WWWQ ×+++++ ×+++ = 5.0 )
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57 ∑ →≥== OK5.178.110.231/33.410FS goverturnin The bridge live load, Ql, and its inertial component, Fl, are usually not included in overturning analysis as their inclusion would have little or no effect on the factor of safety against overturning. (In the current analysis Ql = Fl = 0 kN/m)
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58 e = 0.17 m ≤ L / 6 = 0.47 m →OK The influence length, D1 at foundation level: (See Figure 2.7)
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59 STATIC INTERNAL STABILITY AT EACH REINFORCEMENT LEVEL The first phase in evaluating internal stability of the GRS abutment is the calculation of tensile forces resulting from static forces alone. The second phase, (Section 2.9 below)
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60 Pullout resistance, Pr RcCLFPr ev ×××××= )
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62 Table 2.1: Static Internal Stability No.
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63 The ultimate tensile strength of the geotextile used in the GRS abutment tested is: Tult = 70 kN/m (GEOTEX 4x4 fabric) The reduction factor for tensile strength of fabric: RF = 1.331 The allowable tensile strength of the geotextile is calculated as: 59.52331.1/70/ === RFTT ultal kN/m The maximum tensile force in the reinforcement at depth z is calculated as: Figure 2.8: Assumed Active Zone for Calculating Dynamic Forces in the Reinforcement Layers
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64 ∑ = = ×= ni i e e imd i i L L PT 1 Where: = ie L Length of embedment in resistant zone behind the dynamic failure surface at depth z as shown in Figure 2.8 TTotal = Static + Dynamic tensile forces in the reinforcement at depth z Ttotal = Tmax + Tmd Define the factor of safety against geosynthetic breakage as: FSbreakage = Tal / Ttotal Define the factor of safety against geosynthetic pullout as: FSpullout = Pr / Ttotal FSbreakage and FSpullout are calculated for all geosynthetic layers as shown in Table 2.2 The factors of safety obtained in Table 2.2 are above the 1.1 limit at every reinforcement level, thus no further reinforcement is required.
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65 Table 2.2: Overall (Static + Dynamic) Internal Stability No.
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