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CHAPTER 7 PARAMETRIC ANALYSIS INTRODUCTION The analytical study was conducted by using a finite element code, Abaqus (2002). The capability of Abaqus for analyzing the performance of segmental facing GRS bridge abutments, subjected to seismic loading, was first evaluated. The evaluation included comparing the analytical results with measured data of a near full-scale shake table experiment of a GRS abutment with a bridge. The analyses of this experiment are presented next. Abaqus was then used to perform a parametric study of full-scale bridges with actual earthquake loadings. The findings of a parametric study and findings of performance analysis, all obtained by using the analytical model, are presented in this chapter. After the finite element code, Abaqus, was satisfactorily verified, a parametric study was conducted to investigate performance characteristics of GRS bridge abutments subjected to earthquake loading. The performance characteristics, as affected by soil placement condition, bridge height, bridge span, geosynthetic reinforcement stiffness, and geosynthetic reinforcement spacing were investigated. When analyzing the results, the maximum and permanent lateral deformations of abutment wall, the maximum and permanent lateral deformations of the sill, the maximum and permanent lateral deformations of bridge, and the maximum acceleration of abutment wall and the bridge were emphasized. VERIFICATION OF THE FINITE ELEMENT COMPUTER PROGRAM ABAQUS® The capability of Abaqus for analyzing the seismic performance of segmental facing GRS bridge abutments was critically evaluated. The evaluation was done by comparing the analytical results with measured data of the near full-scale seismic GRS bridge abutment experiment conducted as part of this study (referred to as the NCHRP seismic GRS abutment experiment). Chapter 5 included a complete description of the NCHRP seismic GRS abutment experiment, and Chapter 6 included a complete presentation of test results.
198 FINITE ELEMENT SIMULATION OF THE NCHRP SEISMIC GRS TEST ABUTMENT EXPERIMENT Figure 7.1 shows the configuration of the NCHRP seismic GRS abutment experiment. The GRS abutment model was constructed on the shake table platform as shown in the figure. The bridge consisted of two girders and a set of concrete slabs and steel plates that provided the dead load; the total dead load was 445 kN acting on a 6.7 m simply supported bridge. Two elastomeric pads were used to support the girders on the GRS abutment side, and two rollers (slide bearings) were used on the other side. Figure 7.1 Configuration of the Full-Scale Shake Table Test of a GRS Abutment-Bridge System
199 The far right side of Figure 7.1 shows the backwall which makes up the fourth face of the abutment model. The wall was rigidly connected to the shake table and was made adequately stiff to limit wall displacements to an acceptable level. A 5-cm thick Styrofoam layer was fastened to the wall. This Styrofoam layer was in direct contact with the GRS abutment and is used to alleviate compressive waves reflected by the rigid backwall. The backfill soil is classified as a poorly graded gravel with sand and clay (ILDOT CA-6), and satisfies the grain size distribution requirements suggested in the NCHRP Report 556 for GRS bridge abutments. The results of conventional triaxial compression tests conducted on reconstituted backfill soil samples (with the same dry unit weight and moisture content as the backfill soil) indicated that the soil has an internal friction angle °= 44Ï (Figure 7.2). Several triaxial cyclic tests were performed on the backfill soil at various confining pressures. Figure 7.3 shows a triaxial cyclic test result with a confining pressure of 70 kPa. It is noteworthy that the backfill requirements for GRS abutments should âpreferablyâ be higher than those of the FHWA MSE wall minimum backfill requirements for bridge sites having higher seismic conditions. The parametric analysis described below suggests that backfills with °= 34Ï perform well for various bridge lengths and abutment heights. An additional shake table test with backfill having °= 34Ï and with realistic earthquake motion will provide information needed for further verification of the parametric analysis. The NCHRP seismic GRS abutment experiment utilized a woven polypropylene geotextile (GEOTEX 4Ã4). Figure 7.4 shows the results of a uniaxial tension test conducted on the geotextile. The behavior of the geotextile is nearly linear with an estimated stiffness of Et=700 kN/m, where E is the elastic modulus and t is the thickness of the geotextile.
200 Figure 7.2 Shear Strength Parameters of Backfill Soil 0.00 0.25 0.50 0.75 (E-2) Axial Strain 0 100 200 300 400 500 D ev ia to ric S tre ss , k P a Ï3=70 kPa Laboratory Test FEM Figure 7.3 Cyclic Triaxial Test Results and Simulation
201 A three-dimensional finite element analysis of the NCHRP seismic GRS abutment experiment was carried out using Abaqus. Figure 7.5 shows the three-dimensional finite element model used in the analysis. The model includes only one half of the geometry because of symmetry. The backfill soil was simulated using a simple cyclic model with isotropic/kinematic hardening. The basic concept of this pressure-independent model is that the yield surface shifts in stress space so that straining in one direction reduces the yield stress in the opposite direction, thus simulating the Bauschinger effect and anisotropy induced by work hardening. The combined isotropic/kinematic hardening model is also capable of describing other phenomenaâsuch as ratchetting, relaxation of the mean stress, and cyclic hardeningâthat are typical of materials subjected to cyclic loading. The model performance is compared to the triaxial cyclic test results with reasonable agreement as shown in Figure 7.3. Figure 7.4 Uniaxial Tension Test Results on GEOTEX 4Ã4
202 Figure 7.5 Finite Element Model of the Shake Table Test Three-dimensional eight-node continuum elements were used to model the soil and the modular block facing, four-node membrane elements were used for the geosynthetic reinforcement, and two-node beam elements were used for the bridge girders. The complicated structure of the elestomeric pads was carefully modeled using eight-node continuum elements for the polymeric material, and four-node shell elements for the steel plate inclusions. Interface elements were used between the modular blocks and reinforcement, between soil and reinforcement, and between blocks and backfill soil. The interface element used in the analysis is a penalty-type element that allows sliding with friction and separation between different parts involved in the model. The penalty formulations also allow different parts to be back in contact after separation. For simplicity, a friction coefficient of 0.5 was assumed between all surfaces. As was described in Chapters 5 and 6, the NCHRP seismic GRS abutment experiment consisted of five shaking tests (stages) each lasting 20 seconds. In Test 1 the model was subjected to a sinusoidal motion in the longitudinal direction with an acceleration amplitude of approximately 0.17 g at 1.5-Hz frequency. In Test 2 the amplitude was nearly doubled to 0.35 g and the frequency was increased to 3 Hz (doubled). Subsequent Tests were all performed at a 3-Hz frequency with increasing acceleration amplitudes (up to 1 g). Tests 1 and 2 are particularly interesting--even though the input acceleration amplitude in Test 2 was double that of Test 1, the
203 model had a much more favorable response (i.e., less vibration) in Test 2 than Test 1 (see Figures 7.6-7.10). This is mainly attributed to the difference in input frequency. A successful finite element simulation must be capable of simulating this frequency-dependent behavior. The simulation results of Tests 1 and 2 are presented next. In the simulation only the rigid base of the finite element model (Figure 7.5) is subjected to a sinusoidal acceleration with a prescribed frequency and magnitude that matches the measured experimental base acceleration. Figure 7.6 presents a comparison between the measured and calculated lateral displacement of the bridge deck and the sill for both Test 1 and Test 2. Reasonable agreement between the measured and calculated values is noted in the figure. Most notable is the capability of the finite element simulation of capturing the essence of the two tests- -The displacements of the bridge and the sill are very significant in Test 1 while the applied base acceleration is small (0.17 g), whereas the displacements of the bridge and the sill are very small even though the base acceleration was doubled (0.35 g).
204 0 10 20 30 40 50 60 -0.40 -0.20 0.00 0.20 0.40 Ba se A cc el er at io n, g 0 10 20 30 40 50 60 -10 -5 0 5 10 Br id ge x -D is pl ac em en t, cm Measured FEM 0 10 20 30 40 50 60 Time, second -10 -5 0 5 10 Si ll x- D is pl ac em en t, cm Measured FEM Test 2 Test 1 1.5 Hz 3 Hz Test 1 Test 1 Test 2 Test 2 Figure 7.6 Measured and Calculated Bridge and Sill Responses in Tests 1 and 2
205 -0.40 -0.20 0.00 0.20 0.40 Measured FEM -0.40 -0.20 0.00 0.20 0.40 -0.40 -0.20 0.00 0.20 0.40 -0.40 -0.20 0.00 0.20 0.40 -0.40 -0.20 0.00 0.20 0.40 -0.40 -0.20 0.00 0.20 0.40 -0.40 -0.20 0.00 0.20 0.40 -0.40 -0.20 0.00 0.20 0.40 -0.40 -0.20 0.00 0.20 0.40 -0.40 -0.20 0.00 0.20 0.40 -0.40 -0.20 0.00 0.20 0.40 -0.40 -0.20 0.00 0.20 0.40 0 5 10 15 20 25 Time, s -0.40 -0.20 0.00 0.20 0.40 A cc el er at io n, g TEST 1 A 11 A 13 A 10 A 9 A 8 A 7 A 6 A 5 A 4 A 3 A 2 A 1 A 12 Figure 7.7 Measured and Calculated Acceleration History of GRS Wall Facing (Test 1)
206 -6 -4 -2 0 2 Measured FEM -6 -4 -2 0 2 -6 -4 -2 0 2 -6 -4 -2 0 2 -6 -4 -2 0 2 -6 -4 -2 0 2 -6 -4 -2 0 2 -6 -4 -2 0 2 -6 -4 -2 0 2 -6 -4 -2 0 2 -6 -4 -2 0 2 -6 -4 -2 0 2 0 5 10 15 20 25 Time, s -6 -4 -2 0 2 R el at iv e La te ra l D is pl ac em en t, cm LVDT 11 LVDT 10 LVDT 12 LVDT 13 LVDT 9 LVDT 8 LVDT 7 LVDT 6 LVDT 5 LVDT 4 LVDT 3 LVDT 2 LVDT 1 x-Displacement (-) TEST 1 Figure 7.8 Measured and Calculated Displacement History of GRS Wall Facing (Test 1)
207 -0.40 -0.20 0.00 0.20 0.40 Measured FEM -0.40 -0.20 0.00 0.20 0.40 -0.40 -0.20 0.00 0.20 0.40 -0.40 -0.20 0.00 0.20 0.40 -0.40 -0.20 0.00 0.20 0.40 -0.40 -0.20 0.00 0.20 0.40 -0.40 -0.20 0.00 0.20 0.40 -0.40 -0.20 0.00 0.20 0.40 -0.40 -0.20 0.00 0.20 0.40 -0.40 -0.20 0.00 0.20 0.40 -0.40 -0.20 0.00 0.20 0.40 -0.40 -0.20 0.00 0.20 0.40 0 5 10 15 20 25 Time, s -0.40 -0.20 0.00 0.20 0.40 A cc el er at io n, g TEST 2 A 11 A 13 A 10 A 9 A 8 A 7 A 6 A 5 A 4 A 3 A 2 A 1 A 12 Figure 7.9 Measured and Calculated Acceleration History of GRS Wall Facing (Test 2)
208 -6 -4 -2 0 2 Measured FEM -6 -4 -2 0 2 -6 -4 -2 0 2 -6 -4 -2 0 2 -6 -4 -2 0 2 -6 -4 -2 0 2 -6 -4 -2 0 2 -6 -4 -2 0 2 -6 -4 -2 0 2 -6 -4 -2 0 2 -6 -4 -2 0 2 -6 -4 -2 0 2 0 5 10 15 20 25 Time, s -6 -4 -2 0 2 R el at iv e La te ra l D is pl ac em en t, cm LVDT 11 LVDT 10 LVDT 12 LVDT 13 LVDT 9 LVDT 8 LVDT 7 LVDT 6 LVDT 5 LVDT 4 LVDT 3 LVDT 2 LVDT 1 x-Displacement (-) TEST 2 Figure 7.10 Measured and Calculated Displacement History of GRS Wall Facing (Test 2)
209 Figure 7.7 shows a comparison between measured and calculated lateral accelerations at several points located on the modular concrete block facing for Test 1. Figure 7.8 shows a comparison between measured and calculated lateral relative displacements (relative to the shake table) at several points located on the modular concrete block facing for Test 1. Good agreement between measured and calculated values is noted in both figures for Test 1. Figure 7.9 shows a comparison between measured and calculated lateral accelerations at several points located on the modular concrete block facing for Test 2. Figure 7.10 shows a comparison between measured and calculated lateral relative displacements (relative to the shake table) at several points located on the modular concrete block facing for Test 2. Again, good agreement between measured and calculated values is noted in both figures for Test 2. PARAMETRIC ANALYSIS Base Case Geometry, Material Properties, and Loading After the finite element code, Abaqus, was satisfactorily verified, a parametric study was conducted to investigate seismic performance characteristics of GRS bridge abutments. The performance characteristics as affected by soil placement condition, bridge height (clearance), bridge span, reinforcement stiffness, reinforcement spacing, and earthquake history were investigated. The present parametric analysis included three backfill soil types (Ï'=34°, 37°, and 40°), two earthquake motions (Kobe and Northridge), two bridge heights (3.4 m and 4.9 m), two bridge spans (12.2 m and 21.3 m), two geosynthetic stiffness (350 kN/m and 700 kN/m), and two geosynthetic spacing (20 cm and 40 cm). In total there were 96 combinations in this parametric study. When analyzing the results, the following parameters were emphasized: the maximum and permanent lateral deformations of the GRS abutment wall, the maximum and permanent lateral deformations of the sill, the maximum and permanent lateral deformations of the bridge, and the maximum acceleration of the GRS abutment wall and the bridge.
210 The âBase Caseâ geometry used in the parametric analysis is shown schematically in Figure 7.11. The dimensions and parameters of the base case, listed below, are kept constant for all cases of the parametric study unless otherwise stated. Figure 7.11 Finite Element Model of the "Base Case" for Parametric Analysis Base Case Dimensions (see Figure 7.11): ⢠Model length: 2 m (transverse direction) ⢠Girder: Type II Beam ⢠Bridge height (clearance): H1=3.4 m ⢠Total GRS abutment Height: 4.5 m ⢠Concrete block dimensions: 20 cm wide (toe to heel), 20 cm high, 40 cm long ⢠Sill width: 0.75 m ⢠Sill clearance: 30 cm ⢠Elastomeric pad dimensions: 30 cm wide Ã46 cm long à 10 cm thick ⢠Expansion joint (Gap between bridge edge and back wall): 7.5 cm ⢠Geosynthetic spacing: 20 cm ⢠Geosynthetic length: 3 m (= height of the lower GRS wall (H))
211 Base Case Parameters: ⢠Geosynthetic stiffness: 700 kN/m ⢠Soil internal friction angle: 34º Base Case Loading: ⢠gravity load for all model parts including the bridge ⢠Seismic loading using Kobe 1995 earthquake horizontal acceleration history applied at the base of the model. Geometrical Variations from Base Case In the parametric analysis the length of the geosynthetic reinforcement is always assumed to be equal to the height H of the lower GRS wall (Table 7.1). Two types of beams are used: Type II beam and Type III beam. The former is used when the bridge span is 12.2 m, and the latter is used when the bridge span is 21.3 m. The dimensions of the elastomeric pad change with the bridge span as shown in the same table. In all analysis cases the length of the finite element mesh behind each abutment is taken as 5 times the total height of the GRS abutment. This is deemed necessary to reduce the boundary effects on the finite element model of the GRS abutment-bridge system. Table 7.1: Geometrical Variations Case Geosynthetic Length Beam Type (see figure below Elastomeric Pad Dimensions Bridge Clearance Bridge Span width length thickness H1=3.4 m L=12.2 m 3 m II 30 cm 45 cm 10 cm H1=3.4 m L=21.3 m 3 m III 30 cm 56 cm 10 cm H1=4.9 m L=12.2 m 4.5 m II 30 cm 45 cm 10 cm H1=4.9 m L=21.3 m 4.5 m III 30 cm 56 cm 10 cm
212 Description of Parameters Analyzed Earthquake Histories Two earthquake histories are considered in the present parametric analysis: Kobe 1995 (6.9 Magnitude) and Northridge 1994 (6.7 Magnitude). In all analysis only the horizontal component of the earthquake is applied in the longitudinal direction of the bridge. The near field horizontal acceleration history of Kobe 1995 earthquake (Takarazuka Station) is used for the base case analysis and several other cases of this parametric study (Source: CUE, Conference on the Usage of Earthquake). The peak ground acceleration of this earthquake is 0.694g. The bracketed duration of the earthquake is 10.88 seconds at acceleration level of 0.05 g. Figure 7.12a shows the acceleration, velocity, and displacement histories of the earthquake. The acceleration history in Figure 7.12a is applied to the base of the FE model without scaling. Figure 7.12b shows the acceleration, velocity, and displacement spectra of the earthquake (5% damping). Another earthquake, the Northridge 1994 earthquake, is used in the analysis of several cases. The near field horizontal acceleration (75 Sylmar-Converter Station East) used herein has a peak ground acceleration of 0.828g (Source: DWP, Los Angeles Department of Water and Power). Its bracketed duration is 17.06 seconds at acceleration level of 0.05g. Northridge 1994 acceleration, velocity, and displacement histories are shown in Figure 7.13a. Figure 7.13b shows the acceleration, velocity, and displacement spectra of Northridge earthquake (5% 1 ft = 30.48 cm 1 inch=2.54 cm
213 damping). No scaling was applied to the acceleration history used in the FE analysis. The Northridge earthquake has a significantly greater peak ground acceleration than the Kobe earthquake. Its duration is substantially longer than that of Kobe earthquake. 0 5 10 15 20 -1 0 1 Ac ce le ra tio n, g 0 5 10 15 20 -100 0 100 Ve lo ci ty , c m /s 0 5 10 15 20 Time, s -20 -10 0 10 20 D is pl ac em en t, cm Kobe, 1995, Horizontal (Max PGA), Strike Slip, Near Field<20 km Figure 7.12(a) Acceleration, Velocity, and Displacement History of Kobe 1995 Earthquake 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 SA (g ) 0 1 2 3 4 5 6 7 8 9 10 0 100 200 300 SV (c m /s ) 0 1 2 3 4 5 6 7 8 9 10 Frequency, Hz 0 10 20 30 40 50 SD (c m ) Kobe, 1995, Horizontal (Max PGA), Strike Slip, Near Field<20 km Figure 7.12(b) Response Spectra of Kobe 1995 Earthquake
214 0 5 10 15 20 -1 0 1 Ac ce le ra tio n, g 0 5 10 15 20 -200 -100 0 100 Ve lo ci ty , c m /s 0 5 10 15 20 Time, s -40 -30 -20 -10 0 10 20 30 40 D is pl ac em en t, cm Northridge, 1994, Horizontal (Max PGA), Reverse Normal, Near Field<20 km Figure 7.13(a) Acceleration, Velocity, and Displacement History of Northridge 1994 Earthquake 0 1 2 3 4 5 6 7 8 9 10 0 1 2 SA (g ) 0 1 2 3 4 5 6 7 8 9 10 0 100 200 300 SV (c m /s ) 0 1 2 3 4 5 6 7 8 9 10 Frequency, Hz 0 20 40 60 80 100 SD (c m ) Northridge, 1994, Horizontal (Max PGA), Reverse Normal, Near Field<20 km Figure 7.13(b) Acceleration, Velocity, and Displacement History of Northridge 1994 Earthquake
215 Backfill Soil Type Three backfill soils with internal friction angles of 34º, 37º, and 40º and relative compactions of RC = 90%, 95%, and 100% (ASTM D698), respectively, are used in the analysis to investigate the effects of backfill soil type on the seismic performance of the GRS abutment. The soil parameters used in the analysis were deduced from triaxial tests results conducted on numerous backfill materials (Duncan et al., 1980). Figure 7.14 shows the stress-strain behavior and the volumetric strain-axial strain behavior of the three soils. Table 7.2 shows the material parameters of the cyclic model with isotropic/kinematic hardening that were used to generate the curves in Figure 7.14. 0.00 0.02 0.04 0.06 0.08 0.10 Axial Strain 0 100 200 300 400 500 D ev ia to ric S tre ss , k P a 0.00 0.02 0.04 0.06 0.08 0.10 Axial Strain 0.0000 0.0025 0.0050 0.0075 0.0100 V ol um et ric S tra in ï¦=40ø, RC=100% ï¦=37ø, RC=95% ï¦=34ø, RC=90% ï¦=40ø, RC=100% ï¦=37ø, RC=95% ï¦=34ø, RC=90% ï³3=70 kPa ï³3=70 kPa Figure 7.14 Assumed Behavior of Backfill Soils Used in the Parametric Analysis The study by Duncan et al (1980) presented estimates of stress-strain-strength parameters and volumetric strain-axial strain parameters for various soil types and degrees of compaction. These estimates were made using the compilations of data taken from 135 different soil parameters. Using these data, conservative parameter values have been interpreted for the soils
216 under various types and degrees of compaction. The values of stress-strain-strength parameters and volumetric strain-axial strain parameters of 16 materials averaged from the aforementioned 135 materials were presented in the study. These parameters are called conservative in the sense that they are typical of the lower values of strength and modulus, and the higher values of unit weight for each soil type. Table 7.2: Model Parameters for Backfill Soils Used in the Parametric Study Backfill soil E (kPa) Ï Yield stress at zero plastic strain (kPa) Kinematic hardening parameter C1 Kinematic hardening parameter γ1 Ï'=34° 10342 0.3 103 3000 200 Ï'=37° 16464 0.3 148 4000 200 Ï'=40° 31026 0.3 186 5000 200 Bridge Clearance (Height) Use two heights: H1=3.4 m and H1=4.9 m. Bridge Span Use two spans: L=12.2 m and L=21.3 m. Geosynthetic Spacing Use S=20 cm and S= 40 cm. Geosynthetic stiffness Use EA=350 kN/m and EA=700 kN/m. RESULTS The results of the parametric study are presented in Figures 7.15-7.26. As indicated above, two earthquake histories are used in the present parametric analysis: Kobe 1995 and Northridge 1994. In all analysis, only the horizontal component of the earthquake is applied in the longitudinal direction of the bridge. With this condition applied, the parametric analysis results described below show that the GRS abutment is highly resistant to such destructive earthquakes. Nonetheless, future FE analysis and shake table testing should consider applying three
217 dimensional earthquake histories (two horizontal components and one vertical) on three- dimensional bridge models. Effects of Bridge Span For Kobe earthquake and H1=3.4 m Figure 7.15 presents the results of the parametric analysis for a GRS abutment with different backfill soils (internal friction angle: 34º, 37º, 40º) with L=12 m and subjected to Kobe earthquake. In general, the performance of the GRS abutment is very favorable for the three backfill soil types. From Figure 7.15a, the maximum permanent displacement of approximately 8 cm occurred at the top of the lower GRS wall with backfill soil having an internal friction angle of 34º. The maximum acceleration of the facing also occurred at the top of the GRS wall. The acceleration for the backfill soil having an internal friction angle of 34º is approximately 1.1 g. The maximum acceleration increased with increasing the internal friction angle as shown in Figure 7.15b. This may seem counterintuitive. However, when the stiffness of any part of the model is changed, especially the backfill soil that possesses the largest mass in the model, the natural frequency of the entire model will change. This change in model natural frequency will change the model dynamic response based on the acceleration spectra of Kobe earthquake shown in Figure 7.12b. Note that the backfill soil with a higher internal friction angle has a greater initial elastic modulus (i.e., greater initial stiffness). Figure 7.15c presents the maximum and the permanent displacements of the sill. These displacements are greatly affected by the mass of the bridge and the characteristics of the elastomeric pad used in the analysis. The permanent displacements of the sill are very small as shown in the figure. Figure 7.15d presents the clearance (the distance between the edge of the sill and the back of the facing block) at maximum displacement of the facing and the sill. The figure indicates that the clearance remained nearly unchanged even at maximum ground shaking. Figure 7.15e shows the bridge maximum and permanent displacements. These displacements are also greatly affected by the mass of the bridge and the characteristics of the elastomeric pads
218 used in the analysis. The permanent displacements of the bridge are very small as shown in the figure. Figure 7.15f presents the maximum acceleration of the bridge deck. The maximum acceleration of the bride deck (approximately 1.1 g) seems to be independent of the backfill soil type. This can be attributed to the use of the elastomeric pads. To illustrate the effects of a longer bridge span, the above analysis was repeated using a longer bridge with L=21.3 m. A longer bridge requires the use of a heavier girder (Type III Beam- Table 7.1) and a stiffer elastomeric pad (Table 7.1). Figure 7.16a indicates that the facing of the GRS wall suffered slightly smaller maximum and permanent displacements than those in Figure 7.15a for a short span bridge with L=12.2 m. The same observation is noted in Figures 7.16c and 7.16e for the sill and bridge, respectively. As indicated earlier, when the stiffness and/or mass of any part of the model is changed, the natural frequency of the entire model will slightly change, therefore, the model dynamic response will change based on the acceleration spectra of the earthquake used in the analysis.
219 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 Fa ci ng D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 Fa ci ng A cc el er at io n, in ch /s 2 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 S ill D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg -10 0 10 20 30 S ill D is p. R el at iv e to F ac in g, in ch 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 B rid ge D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 B rid ge A cc el er at io n, in ch /s 2 Facing-max Facing Sill initial clearance clearance at max displacements Ground-max Facing-permanent Sill-max Sill-permanent Bridge-max Bridge-permanent Facing-max Bridge-max Ground-max Ground-max Ground-max Ground-max Facing-initial Sill-initial Bridge-initial 1 inch=2.54 cm 386 inch/s 2=1 g 1 inch=2.54 cm 1 inch=2.54 cm 1 inch=2.54 cm 386 inch/s 2=1 g (a) (b) (c) (d) (e) (f) Figure 7.15 Parametric Analysis: Kobe Earthquake, H1=3.4 m, L=12.2 m, 700 kN/m Reinforcement with 20-cm Spacing
220 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 Fa ci ng D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 Fa ci ng A cc el er at io n, in ch /s 2 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 S ill D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg -10 0 10 20 30 S ill D is p. R el at iv e to F ac in g, in ch 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 B rid ge D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 B rid ge A cc el er at io n, in ch /s 2 Facing-max Facing Sill initial clearance clearance at max displacements Ground-max Bridge-initial Sill-max Sill-permanent Bridge-max Bridge-permanent Facing-max Bridge-max Ground-max Ground-max Ground-max Ground-max Facing-initial Facing-permanent Sill-initial 1 inch=2.54 cm 1 inch=2.54 cm 1 inch=2.54 cm 1 inch=2.54 cm 386 inch/s 2=1 g 386 inch/s 2=1 g (a) (b) (c) (d) (e) (f) Figure 7.16 Parametric Analysis: Kobe Earthquake, H1=3.4 m, L=21.3 m, 700 kN/m Reinforcement with 20-cm Spacing
221 For Kobe earthquake and H1=4.9 m For a larger bridge clearance (H1=4.9 m) and a bridge with a short span (L=12.2 m), Figure 7.17a indicates that the facing of the GRS wall has suffered very substantial permanent lateral displacement of approximately 15 cm for the less compacted backfill. Better compacted backfill soils showed slight improvement in term of lateral displacements. Figure 7.17b shows that the GRS facing has suffered high accelerations exceeding 1.3 g. The bridge, on the other hand, has suffered relatively smaller accelerations likely because of the use of seismic isolators (elastomeric pads). In contrast, Figure 7.18a shows that for a larger bridge clearance (H1=4.9 m) and a bridge with a longer span (L=21.3 m) the permanent lateral displacements are much smaller than those for a bridge with a shorter span. Accelerations of the facing and the bridge were nearly the same as those of a bridge with a shorter span (Figures 7.18b and 7.18f).
222 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 Fa ci ng D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 Fa ci ng A cc el er at io n, in ch /s 2 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 S ill D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg -10 0 10 20 30 S ill D is p. R el at iv e to F ac in g, in ch 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 B rid ge D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 B rid ge A cc el er at io n, in ch /s 2 Facing-max Facing Sill initial clearance clearance at max displacements Ground-max Facing-permanent Sill-max Sill-permanent Bridge-max Bridge-permanent Facing-max Bridge-max Ground-max Ground-max Ground-max Ground-max Facing-initial Sill-initial Bridge-initial 1 inch=2.54 cm 1 inch=2.54 cm 1 inch=2.54 cm 1 inch=2.54 cm 386 inch/s 2=1 g 386 inch/s 2=1 g (a) (b) (c) (d) (e) (f) Figure 7.17 Parametric Analysis: Kobe Earthquake, H1=4.9 m, L=12.2 m, 700 kN/m Reinforcement with 20-cm Spacing
223 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 Fa ci ng D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 Fa ci ng A cc el er at io n, in ch /s 2 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 Si ll D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg -10 0 10 20 30 Si ll D is p. R el at iv e to F ac in g, in ch 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 Br id ge D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 Br id ge A cc el er at io n, in ch /s 2 Facing-max g g p Facing Sill initial clearance clearance at max displacements Ground-max Facing-permanent Sill-max Sill-permanent Bridge-max Bridge-permanent Facing-max Bridge-max Ground-max Ground-max Ground-max Ground-max Facing-initial Sill-initial Bridge-initial 1 inch=2.54 cm 1 inch=2.54 cm 1 inch=2.54 cm 1 inch=2.54 cm 386 inch/s 2=1 g 386 inch/s 2=1 g (a) (b) (c) (d) (e) (f) Figure 7.18 Parametric Analysis: Kobe Earthquake, H1=4.9 m, L=21.3 m, 700 kN/m Reinforcement with 20-cm Spacing
224 For Northridge earthquake and H1=3.4 m The Northridge earthquake is substantially larger than Kobe earthquake in terms of peak ground acceleration and duration. When subjected to Northridge earthquake, the GRS abutment with a short-span bridge (12.2 m) and low bridge clearance (3.4 m) sustained significant permanent lateral displacements up to 15 cm. The displacements decreased with increasing the backfill strength and stiffness as shown in Figure 7.19a. The same observation applies to the displacement of the sill and the bridge as shown in Figures 7.19c and 7.19e, respectively. The GRS wall and the bridge both suffered significant accelerations as shown in Figures 7.19b and 7.19f, respectively. The effect of increasing the length of the bridge span seems to have a little effect on lateral displacements in this case. This can be seen in Figures 7.20a, 7.20c, and 7.20e. The accelerations of the GRS wall in Figure 7.20b are also nearly the same for the shorter span bridge (Figure 7.19b). The bridge accelerations shown in Figure 7.20f, however, are substantially smaller than those for the short-span bridge (Figure 7.19f).
225 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 Fa ci ng D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 Fa ci ng A cc el er at io n, in ch /s 2 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 S ill D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg -10 0 10 20 30 S ill D is p. R el at iv e to F ac in g, in ch 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 B rid ge D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 B rid ge A cc el er at io n, in ch /s 2 Facing-max Facing Sill initial clearance clearance at max displacements Ground-max Facing-permanent Sill-max Sill-permanent Bridge-max Bridge-permanent Facing-max Bridge-max Ground-max Ground-max Ground-max Ground-max Facing-initial Sill-initial Bridge-initial 1 inch=2.54 cm 1 inch=2.54 cm 1 inch=2.54 cm 1 inch=2.54 cm 386 inch/s 2=1 g 386 inch/s 2=1 g (a) (b) (c) (d) (e) (f) Figure 7.19 Parametric Analysis: Northridge Earthquake, H1=3.4 m, L=12.2 m, 700 kN/m Reinforcement with 20-cm Spacing
226 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 Fa ci ng D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 Fa ci ng A cc el er at io n, in ch /s 2 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 S ill D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg -10 0 10 20 30 S ill D is p. R el at iv e to F ac in g, in ch 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 B rid ge D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 B rid ge A cc el er at io n, in ch /s 2 Facing-max Facing Sill initial clearance clearance at max displacements Ground-max Facing-permanent Sill-max Sill-permanent Bridge-max Bridge-permanent Facing-max Bridge-max Ground-max Ground-max Ground-max Ground-max Facing-initial Sill-initial Bridge-initial 1 inch=2.54 cm 1 inch=2.54 cm 1 inch=2.54 cm 1 inch=2.54 cm 386 inch/s 2=1 g 386 inch/s 2=1 g (a) (b) (c) (d) (e) (f) Figure 7.20 Parametric Analysis: Northridge Earthquake, H1=3.4 m, L=21.3 m, 700 kN/m Reinforcement with 20-cm Spacing
227 For Northridge earthquake and H1=4.9 m When subjected to Northridge earthquake, the GRS abutment with a short-span bridge (12.2 m) and high bridge clearance (4.9 m) suffered significant permanent lateral displacements approaching 20 cm. The permanent displacements decreased slightly with increasing the backfill strength and stiffness as shown in Figure 7.21a. The same observation applies to the displacement of the sill and the bridge as shown in Figures 7.21c and 7.21e, respectively. The GRS wall and the bridge both suffered significant accelerations as shown in Figures 7.21b and 7.21f, respectively. Increasing the length of the bridge span to 21.3 m caused less permanent lateral displacements as shown in Figures 7.22a, 7.22c, and 7.22e. The accelerations of the GRS wall in Figure 7.22b are nearly the same for the shorter span bridge (Figure 7.21b).
228 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 Fa ci ng D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 Fa ci ng A cc el er at io n, in ch /s 2 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 S ill D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg -10 0 10 20 30 S ill D is p. R el at iv e to F ac in g, in ch 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 B rid ge D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 B rid ge A cc el er at io n, in ch /s 2 Facing-max Facing Sill initial clearance clearance at max displacements Ground-max Facing-permanent Sill-max Sill-permanent Bridge-max Bridge-permanent Facing-max Bridge-max Ground-max Ground-max Ground-max Ground-max Facing-initial Sill-initial Bridge-initial 1 inch=2.54 cm 1 inch=2.54 cm 1 inch=2.54 cm 1 inch=2.54 cm 386 inch/s 2=1 g 386 inch/s 2=1 g (a) (b) (c) (d) (e) (f) Figure 7.21 Parametric Analysis: Northridge Earthquake, H1=4.9 m, L=12.2 m, 700 kN/m Reinforcement with 20-cm Spacing
229 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 Fa ci ng D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 Fa ci ng A cc el er at io n, in ch /s 2 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 S ill D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg -10 0 10 20 30 S ill D is p. R el at iv e to F ac in g, in ch 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 B rid ge D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 B rid ge A cc el er at io n, in ch /s 2 Facing-max Facing Sill initial clearance clearance at max displacements Ground-max Facing-permanent Sill-max Sill-permanent Bridge-max Bridge-permanent Facing-max Bridge-max Ground-max Ground-max Ground-max Ground-max Facing-initial Sill-initial Bridge-initial 1 inch=2.54 cm 1 inch=2.54 cm 1 inch=2.54 cm 1 inch=2.54 cm 386 inch/s 2=1 g 386 inch/s 2=1 g (a) (b) (c) (d) (e) (f) Figure 7.22 Parametric Analysis: Northridge Earthquake, H1=4.9 m, L=21.3 m, 700 kN/m Reinforcement with 20-cm Spacing
230 Effects of Bridge Clearance For Kobe earthquake and L=12.2 m For short span bridges (L=12.2 m) subjected to Kobe earthquake, increasing the bridge clearance causes greater permanent lateral displacement of the GRS wall as evident from Figures 7.15a and 7.17a. Also, the calculated acceleration of the GRS wall is substantially greater for a bridge with a higher clearance (Figure 7.17b) than a bridge with a lower clearance (Figure 7.15b). For Kobe earthquake and L=21.3 m For long span bridges (L=21.3 m) subjected to Kobe earthquake, increasing the bridge clearance causes slightly greater permanent lateral displacement of the GRS wall as shown in Figures 7.16a and 7.18a. The calculated acceleration of the GRS wall is substantially greater for a bridge with a higher clearance (Figure 7.18b) than a bridge with a lower clearance (Figure 7.16b). For Northridge earthquake and L=12.2 m As shown in Figures 7.19a and 7.21a, increasing the bridge clearance causes greater permanent lateral displacement of the GRS wall for the case of short span bridges (L=12.2 m) subjected to Northridge earthquake,. The calculated acceleration of the GRS wall for a bridge with a higher clearance (Figure 7.21b) is nearly the same as the calculated accelerations for a bridge with a lower clearance (Figure 7.19b). For Northridge earthquake and L=21.3 m For long span bridges (L=21.3 m) subjected to Northridge earthquake, increasing the bridge clearance causes slightly greater permanent lateral displacement of the GRS wall as shown in Figures 7.20a and 7.22a. The calculated acceleration of the GRS wall is nearly the same for a bridge with a higher clearance (Figure 7.22b) and a bridge with a lower clearance (Figure 7.20b). Effects of Earthquake History For H1=3.4 m and L=12.2 m
231 Although Kobe earthquake and Northridge earthquake have nearly the same magnitudes (6.9 and 6.7, respectively), they differ in their peak ground accelerations (0.694g and 0.828g, respectively) and in their durations (10.88 s and 17.06 s, respectively). Their effects on the GRS abutment-bridge system are very different. For a low clearance bridge with a short span, the permanent lateral displacement of the GRS wall caused by Kobe earthquake is approximately 8 cm (Figure 7.15a) for a backfill with an internal friction angle of 34º. In contrast, the Northridge earthquake caused a permanent lateral displacement of 15 cm approximately (Figure 7.19a). On the other hand, both earthquakes caused about the same acceleration of the GRS wall as shown in Figures 7.15b and 7.19b. For H1=3.4 m and L=21.3 m For a low clearance bridge with a long span, the permanent lateral displacement of the GRS wall caused by Kobe earthquake is approximately 0.5 cm (Figure 7.16a) for a backfill with an internal friction angle of 34º. The Northridge earthquake caused a permanent lateral displacement of 15 cm (Figure 7.20a). Both earthquakes caused about the same acceleration, on average, of the GRS wall as shown in Figures 7.16b and 7.20b, even though the acceleration trends are different. For H1=4.9 m and L=12.2 m For this case, the permanent lateral displacement of the GRS wall caused by Kobe earthquake is approximately 13 cm (Figure 7.17a) for a backfill with an internal friction angle of 34º. The Northridge earthquake caused a permanent lateral displacement of 23 cm (Figure 7.21a). The GRS wall acceleration caused by the Northridge earthquake are surprisingly smaller than those caused by Kobe earthquake as shown in Figures 7.21b and 7.17b, respectively. For H1=4.9 m and L=21.3 m Again, Northridge earthquake caused much more permanent lateral displacements of the GRS wall than Kobe earthquake as shown in Figures 7.22a and 7.18a, respectively. The accelerations of the GRS wall were comparable for both earthquakes (Figures 7.18b and 7.22b).
232 Effects of Geosynthetic Stiffness For H1=3.4 m and L=12.2 m (Kobe and Northridge) The effect of reducing the geosynthetic stiffness on the seismic behavior of the GRS abutment-bridge system is very small. For a bridge clearance of 3.4 m and a bridge span of 12.2 m, reducing the geosynthetic stiffness from 700 kN/m (base case) to 350 kN/m caused very little effect on the system during the application of Kobe earthquake as shown in Figures 7.15 and 7.23. For the same configuration with Northridge earthquake application Figures 7.19 and 7.24 show very little change in system performance due to Geosynthetic stiffness reduction. In fact all the other system configuration combinations with H1=3.4 m, 4.9 m and L=12.2 m, 21.3 m showed similar response indicating that the geosynthetic stiffness has a minimal effect on the dynamic response of the system. The dynamic response of the GRS abutment-bridge system is dominated by the backfill soil characteristics including initial soil stiffness and its hysteretic energy-absorbing cyclic behavior.
233 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 Fa ci ng D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 Fa ci ng A cc el er at io n, in ch /s 2 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 S ill D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg -10 0 10 20 30 S ill D is p. R el at iv e to F ac in g, in ch 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 B rid ge D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 B rid ge A cc el er at io n, in ch /s 2 Facing-max Facing Sill initial clearance clearance at max displacements Ground-max Facing-permanent Sill-max Sill-permanent Bridge-max Bridge-permanent Facing-max Bridge-max Ground-max Ground-max Ground-max Ground-max Facing-initial Sill-initial Bridge-initial 1 inch=2.54 cm 1 inch=2.54 cm 1 inch=2.54 cm 1 inch=2.54 cm 386 inch/s 2=1 g 386 inch/s 2=1 g (a) (b) (c) (d) (e) (f) Figure 7.23 Parametric Analysis: Kobe Earthquake, H1=3.4 m, L=12.2 m, 350 kN/m Reinforcement with 20-cm Spacing
234 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 Fa ci ng D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 Fa ci ng A cc el er at io n, in ch /s 2 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 S ill D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg -10 0 10 20 30 S ill D is p. R el at iv e to F ac in g, in ch 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 B rid ge D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 B rid ge A cc el er at io n, in ch /s 2 Facing-max Facing Sill initial clearance clearance at max displacements Ground-max Facing-permanent Sill-max Sill-permanent Bridge-max Bridge-permanent Facing-max Bridge-max Ground-max Ground-max Ground-max Ground-max Facing-initial Sill-initial Bridge-initial 1 inch=2.54 cm 1 inch=2.54 cm 1 inch=2.54 cm 1 inch=2.54 cm 386 inch/s 2=1 g 386 inch/s 2=1 g (a) (b) (c) (d) (e) (f) Figure 7.24 Parametric Analysis: Northridge Earthquake, H1=3.4 m, L=12.2 m, 350 kN/m Reinforcement with 20-cm Spacing Effects of Geosynthetic Spacing For H1=3.4 m and L=12.2 m (Kobe and Northridge) (a) (c)
235 The effect of increasing geosynthetic spacing on the seismic behavior of the GRS abutment- bridge system is also very small. For a bridge clearance of 3.4 m and a bridge span of 12.2 m, increasing the geosynthetic spacing from 20 cm (base case) to 40 cm caused very little effect on the system during the application of Kobe earthquake as shown in Figures 7.15 and 7.25. For the same configuration with Northridge earthquake application Figures 7.19 and 7.26 show very little change in system performance due to Geosynthetic spacing increase. All the other system configuration combinations with H1=3.4 m, 4.9 m and L=12.2 m, 21.3 m showed similar response indicating that increasing geosynthetic spacing from 20 cm to 40 cm has a minimal effect on the dynamic response of the system. As indicated earlier, the dynamic response of the GRS abutment-bridge system is dominated by the backfill soil characteristics including initial soil stiffness and its hysteretic energy-absorbing cyclic behavior. Using smaller geosynthetic spacing would cause the backfill soil to be better compacted under the same compaction effort (because of the smaller lift thickness). This effect was not accounted for in this parametric analysis Previous study has revealed that reinforcement spacing has significant effect on compaction- induced stresses in the fill. The increase in lateral stresses due to fill compaction at close reinforcement spacing will increase soil stiffness and perhaps its cyclic energy absorption behavior, which were not accounted for in this parametric study. The effects of reinforcement spacing on seismic resistance of GRS abutment should be further investigated.
236 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 Fa ci ng D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 Fa ci ng A cc el er at io n, in ch /s 2 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 S ill D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg -10 0 10 20 30 S ill D is p. R el at iv e to F ac in g, in ch 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 B rid ge D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 B rid ge A cc el er at io n, in ch /s 2 Facing-max Facing Sill initial clearance clearance at max displacements Ground-max Facing-permanent Sill-max Sill-permanent Bridge-max Bridge-permanent Facing-max Bridge-max Ground-max Ground-max Ground-max Ground-max Facing-initial Sill-initial Bridge-initial 1 inch=2.54 cm 1 inch=2.54 cm 1 inch=2.54 cm 1 inch=2.54 cm 386 inch/s 2=1 g 386 inch/s 2=1 g (a) (b) (c) (d) (e) (f) Figure 7.25 Parametric Analysis: Kobe Earthquake, H1=3.4 m, L=12.2 m, 700 kN/m Reinforcement with 40-cm Spacing
237 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 Fa ci ng D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 Fa ci ng A cc el er at io n, in ch /s 2 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 S ill D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg -10 0 10 20 30 S ill D is p. R el at iv e to F ac in g, in ch 34 37 40 Soil's Friction Angle, deg -2 2 6 10 14 18 22 B rid ge D is pl ac em en t, in ch 34 37 40 Soil's Friction Angle, deg 0 100 200 300 400 500 600 B rid ge A cc el er at io n, in ch /s 2 Facing-max Facing Sill initial clearance clearance at max displacements Ground-max Facing-permanent Sill-max Sill-permanent Bridge-max Bridge-permanent Facing-max Bridge-max Ground-max Ground-max Ground-max Ground-max Facing-initial Sill-initial Bridge-initial 1 inch=2.54 cm 1 inch=2.54 cm 1 inch=2.54 cm 1 inch=2.54 cm 386 inch/s 2=1 g 386 inch/s 2=1 g (a) (b) (c) (d) (e) (f) Figure 7.26 Parametric Analysis: Northridge Earthquake, H1=3.4 m, L=12.2 m, 700 kN/m Reinforcement with 40-cm Spacing
