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41 Contact Pressures on the Rigid Foundation measured contact pressure although the calculated pressures are somewhat higher than the measured average values at Figure 2-27 shows the measured contact pressures under higher applied pressures. different applied pressures at three selected points on the rigid floor of the Mirafi test section. The three points are located along the centerline of the abutment and are 0.25 m, Summary of Measured Results of the NCHRP 1.72 m, and 3.13 m from the wall face. The largest contact Test Abutments pressure occurred at 0.25 m from the wall face, which is roughly underneath the front of the sill. As expected, the A summary of the measured performance and observed contact pressure reduced with increasing distance from behavior of the two full-scale test abutments is presented in the wall face. At an average applied pressure of 200 kPa, the Table 2-3. contact pressures at the three points were 77 kPa, 40 kPa, and 12 kPa. FINDINGS FROM THE ANALYTICAL STUDY The NHI manual (Elias et al., 2001) recommends a method based on the 2:1 distribution with a cutoff at wall The analytical study was conducted by using a finite ele- face to calculate vertical stress in a soil mass because of a ment code, DYNA3D (Hallquist and Whirley, 1989), and its concentrated vertical load applied on a footing for external PC version, LS-DYNA. The use of DYNA3D requires a and internal stability assessment. The contact pressure on the workstation (such as CRAY, VAX/VMS, SUN, SILICON rigid foundation as calculated by the method is uniform at GRAPHICS, or IBM RS/6000), while LS-DYNA requires any given depth. The calculated contact pressures at the base only a personal computer. The two computer codes give were 23 kPa, 46 kPa, 69 kPa, and 92 kPa at applied pressures essentially the same results although LS-DYNA offers more of 100 kPa, 200 kPa, 300 kPa, and 400 kPa, respectively. The user-friendly interfaces and greater flexibility in preparing corresponding measured average contact pressures are 24 the input file. The analytical model is briefly described in kPa, 45 kPa, 59 kPa, and 77 kPa. A comparison of these con- Appendix B. tact pressures suggests that (1) the actual contact pressure is The capability of DYNA3D/LS-DYNA for analyzing the higher near the wall face and decreases nearly linearly with performance of segmental facing GRS bridge abutments was the distance from the wall face, and (2) the computation evaluated. The evaluation included comparing the analytical method in the NHI manual yields roughly the "average" results with measured data of five full-scale experiments, 160 140 120 Contact Pressure (kPa) 100 100 kPa-Measured 200 kPa-Measured 80 300 kPa-Measured 400 kPa-Measured 60 40 20 0 0 0.5 1 1.5 2 2.5 3 3.5 Distance from Abutment Wall Face (m) Figure 2-27. Measured contact pressure distribution on rigid foundation.

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42 TABLE 2-3 Summary of measured performance and observed behavior of the NCHRP test abutments Amoco Test Section Mirafi Test Section Reinforcement Amoco 2044,Tult = 70 kN/m Mirafi 500x, Tult = 21 kN/m Upon termination of loading: Average Applied Pressure 814 kPa 414 kPa Sill Settlement (front) 175 mm (6.9 in.) 189 mm (7.4 in.) Sill Settlement (back) 152 mm (6.0 in.) 160 mm (6.3 in.) Max. lateral movement in abutment wall 82 mm @ 4.5 m from base 115 mm @ 4.5 m from base Max. lateral movement in wing wall 33 mm @ 3.8 m from base 86 mm @ 3.8 m from base At 200 kPa (limiting bearing capacity, per NHI manual) Applied Pressure (average) 207 kPa 214 kPa Sill Settlement (front) 45 mm (1.8 in.) 81 mm (3.2 in.) Sill Settlement (back) 35 mm (1.4 in.) 64 mm (2.5 in.) Max. lateral movement in abutment wall 24 mm @ 4.5 m from base 36 mm @ 4.5 m from base Max. lateral movement in wing wall 18 mm @ 3.8 m from base 30 mm @ 3.8 m from base Observed Behavior: The sills in both tests tilted toward the abutment wall face (i.e. the front of the sill settled more than the back; Left and right sides of the sill settled evenly. The abutment wall leaned forward with the maximum movement occurring near the top of the wall. The top three courses of facing blocks were pushed outward at higher loads. The wing wall also leaned forward with the maximum movement occurring at approximately 1/6H from the top of the wall. In both tests, tension cracks occurred parallel to the wall face and were located at end of the reinforcement. Tension cracks initiated around 150200 kPa average applied pressure. Most strain gauges were damaged by moisture due to the long delay of actual loading experiments; maximum strain at 200 kPa was about 2.0% The measured contact pressure on the rigid foundation was larger in front and decreased linearly toward the back. The computation procedure in the NHI Manual yielded about the average value of the contact pressures at a given applied load. including (1) the spread footing experiments by Briaud and Parametric Study Gibbens (1994), (2) the spread footing experiments on rein- forced sands by Adams and Collin (1997), (3) the FHWA Base Case Geometry, Material Properties, Turner-Fairbank GRS bridge pier by Adams (1997), (4) the and Loading "Garden" experimental embankment in France (Gotteland et After the finite element code, DYNA3D, was satisfacto- al., 1997), and (5) the two full-scale GRS bridge abutment rily verified, a parametric study was conducted to investi- loading experiments conducted as part of this study (referred gate performance characteristics of GRS bridge abutments to as the NCHRP GRS abutment experiment). Very good and the approach fill. The performance characteristics, as agreements between the analytical results and the measured affected by soil placement condition, reinforcement stiff- data (including measured performance and failure loads) ness/strength, reinforcement spacing (varying from 20 to were obtained. 60 cm), reinforcement truncation, footing (sill) width, and The analyses of the five full-scale experiments are pre- the clearance between the front edge of the footing and the sented in Appendix C, available as NCHRP Web-Only Doc- back face of the wall facing were investigated. When analyz- ument 81. The findings of a parametric study and findings ing the results, the settlement of footing, rotation of the foot- of performance analysis, all obtained by using the analyti- ing, lateral deformation of abutment wall, maximum shear cal model, are presented in this chapter. The findings of stress levels in the GRS soil mass, ultimate load carrying performance analysis were used as the basis for the allow- capacity of the abutment, and potential failure mechanisms able sill pressures in the recommended design procedure. were emphasized.

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43 The analytical results obtained from the parametric study Base Case Loading: served as the basis for establishing preliminary design guide- lines of GRS abutments. The maximum tolerable settlement Uniformly distributed vertical load was applied to the and horizontal movement of bridges, as suggested by Moul- 80-cm-wide loading pad and increased monotonically ton et al. (1985) and by others (as summarized in NCHRP until failure or until 1000 kPa was reached, whichever Report 343), may be used as the performance limits when occurred first. establishing the design guidelines. The "Base Case" geometry used in the parametric analy- sis is shown schematically in Figures 2-28 and 2-29. The Effects of Geosynthetic Spacing dimensions and parameters of the base case, listed below, were kept constant for all cases of the parametric study To investigate the effect of vertical spacing between unless otherwise stated. geosynthetic layers on the GRS bridge abutment, three dif- Base Case Dimensions (see Figure 2-28): ferent spacings were used: 20 cm (Base Case), 40 cm, and 60 cm. Four parameters were thought important in describing Segmental wall height: 4.6 m the performance of a GRS abutment when subjected to Total GRS abutment height: 7.1 m superstructure loads. These parameters, termed herein "per- Concrete block dimensions: 28 cm wide (toe to heel), formance parameters," are the vertical displacement at the 20 cm high, 50 cm long abutment seat (where the girder load is applied), the hori- Sill width: 1.5 m zontal displacement at the abutment seat, the maximum dis- Sill clearance: 15 cm placement of the segmental facing, and sill distortion. Loading pad width: 80 cm Figure 2-31 shows the effects of increasing spacing on the Geosynthetic spacing: 20 cm selected performance parameters. Figure 2-31a shows that Geosynthetic length: 5 m the vertical displacement at the abutment seat increases with spacing increase. The increase in displacement becomes Base Case Parameters: more significant as the applied pressure increases. At 200 kPa of applied pressure (moderate pressure), there is a 24 Geosynthetic stiffness: 530 kN/m percent increase in vertical displacement at 40 cm spacing as Soil internal friction angle: 34 deg (See Figure 2-30) compared with the base case with 20 cm spacing. An increase Figure 2-28. Configuration of the base case for the parametric analysis.

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44 Figure 2-29. Three-dimensional representation of the base case. Figure 2-30. Stress-strain-volume change characteristics of soils used in the parametric analysis.

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45 Figure 2-31. Effects of geosynthetic spacing. of 50 percent in vertical displacement was observed at 60 cm which were intolerable. The tolerability of the movement spacing as compared with the base case. Similar trends with was judged qualitatively by the agency responsible for each similar increases were noted for the horizontal displacement bridge in accordance with the following criterion: "Move- at abutment seat (Figure 2-31b) and for the maximum lateral ment is not tolerable if damage requires costly maintenance displacement of the segmental facing (Figure 2-31c). The and/or repairs and a more expensive construction to avoid distortion of the sill, as shown in Figure 2-31d, ranged from this would have been preferable." +0.1 degree at 20 cm spacing to +0.41 degree at 60 cm spac- ing (positive distortion = forward tilt). At an applied pressure of 200 kPa, the vertical and hor- Effects of Backfill Soil Type izontal displacements of the abutment seat for the base case were 4.7 cm and 2.1 cm, respectively (Figure 2-31). Three backfill soils with internal friction angles of = 34, Judging from the criteria that the vertical movement 37, and 40 and relative compactions (RC) of 95 percent, should not exceed 100 mm and the horizontal movement 100 percent, and 105 percent, respectively, are used in the should not exceed 50 mm (Wahls, 1990), the values of ver- analysis to investigate the effects of backfill soil type on the tical and horizontal movements associated with the base performance of the GRS abutment. The soil parameters used case at 200 kPa pressure were deemed acceptable. This in the analysis were deduced from triaxial test results con- suggests that the displacements of the abutment are ducted on numerous backfill materials (Duncan et al., 1980). unlikely to cause any damage to the bridge superstructures. Figure 2-30 shows the stress-strain behavior and the volumet- Judging from the same criteria, the vertical and horizontal ric strain-axial strain behavior of the three soils. The study by displacements of the abutment seat for the base case at 400 Duncan et al. (1980) presented estimates of stress-strain- kPa are unacceptable (barely acceptable): the vertical dis- strength parameters and volumetric strain-axial strain parame- placement is 10.3 cm, and the horizontal displacement is ters for various soil types and degrees of compaction. These 4.6 cm (Figure 2-31). estimates were made using the compilations of data taken from The maximum displacement criterion suggested by Wahls 135 different soil parameters. Using these data, conservative (1990) was based on a comprehensive study of bridge move- parameter values have been interpreted for the soils under var- ments reported by Moulton et al. (1985). In the study, mea- ious types and degrees of compaction. The values of stress- sured movements were evaluated for 439 abutments of which strain-strength parameters and volumetric strain-axial strain most were perched abutments. The study included assess- parameters of 16 materials averaged from the aforementioned ment of which movements were regarded as tolerable and 135 materials were presented in the study. These parameters

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46 are called conservative in that they are typical of the lower val- The horizontal displacement at the abutment seat (Figure ues of strength and modulus and the higher values of unit 2-33b) and the maximum lateral displacement of the seg- weight for each soil type. mental wall (Figure 2-33c) closely follow the trend of the Figure 2-32 shows the effects of backfill soil type, as sig- vertical displacement at the abutment seat. The distortion of nified by , on the performance parameters for geosynthetic sill changed from +0.23 at = 34 to +0.035 at = 40 as spacings of 20 cm. More favorable response is attained when shown in Figure 2-33d. The response of the base case ( = 34, using soil types that have higher stiffness and strength and s = 20 cm, Figure 2-32) is very similar to the case of = 37 lower deformations. At 200 kPa of applied pressure, the ver- and s = 40 cm, indicating that a better soil compaction may tical displacement at the abutment seat decreased 23 percent substitute for closer spacing (to a certain extent). when increased from 34 (base case) to 37 as indicated in Figure 2-32a. The vertical displacement decreased 35 per- cent when was increased from 34 to 40. The effect of Effects of Geosynthetic Stiffness increasing on the horizontal displacement of the abutment seat was similar in trend but with smaller magnitudes as The effects of geosynthetic stiffness (E * t) on the perfor- shown in Figure 2-32b. As shown in Figure 2-32c, at 200 kPa mance of the GRS abutment is shown in Figure 2-34 for of applied pressure, the maximum lateral displacement of the geosynthetic spacings of 20 cm, and in Figure 2-35 for s = 40 segmental facing decreased roughly linearly with increasing cm. The stiffness of the base case was assumed to be 530 , with a total reduction of 45 percent at = 40 as compared kN/m. A lower stiffness of 53 kN/m and a higher stiffness of with the base case. The distortion of sill changed from +0.1 5300 kN/m were used to investigate the effects of geosyn- at = 34 to +0.04 at = 40 as shown in Figure 2-32d. thetic stiffness on performance parameters. Figure 2-33 shows the effects of backfill soil type on the Figure 2-34a shows that the vertical displacement of the performance parameters for geosynthetic spacing s = 40 cm. abutment seat of the base case is 4.7 cm for an applied pres- As shown in Figure 2-33a, for = 34, s = 40 cm, and at an sure of 200 kPa. This displacement is reduced 43 percent applied pressure of 200 kPa, the vertical displacement of the when the geosynthetic stiffness is increased to 5300 kN/m. abutment seat is 5.8 cm, which is 24 percent greater than that On the other hand, a drastic increase of 252 percent in dis- corresponding to the base case ( = 34, s = 20 cm, Figure placement is noted when the geosynthetic stiffness is reduced 2-32a). For = 37 and s = 40 cm, the vertical displacement to 53 kN/m. The same trend is noted for the horizontal dis- at the abutment seat is 9 percent smaller than the base case. placement of the abutment seat (Figure 2-34b) and for the For = 40 and s = 40 cm, the vertical displacement at the maximum lateral displacement of the segmental wall (Figure abutment seat is 28 percent smaller than that of the base case. 2-34c). The distortion of the sill for the base case is +0.1 Figure 2-32. Effects of backfill internal friction angle for s = 20 cm.

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47 Figure 2-33. Effects of backfill internal friction angle for s = 40 cm. Figure 2-34. Effects of geosynthetic stiffness for s = 20 cm.

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48 Figure 2-35. Effects of geosynthetic stiffness for s = 40 cm. (forward tilt) as shown in Figure 2-34d. This distortion increase of 11 percent in displacement is noted when the becomes -0.1 (backward tilt) when the stiffness is increased clearance is increased to 30 cm. The same trend and magni- to 5300 kN/m. The distortion corresponding to a geosyn- tude is noted for the horizontal displacement of the abutment thetic stiffness of 53 kN/m is +1.67. seat (Figure 2-36b). For the maximum lateral displacement Figure 2-35a indicates that at an applied pressure of 200 of the segmental wall (Figure 2-36c), the trend was similar kPa, s = 40 cm, and E * t = 530 kN/m, there is a 24 percent but with smaller magnitudes. The distortion of the sill for the increase in vertical displacement of the abutment seat as com- base case is +0.1 (forward tilt) as shown in Figure 2-36d. pared with the base case (Figure 2-34a). For E * t = 5300 kN/m This distortion becomes -0.1 (backward tilt) when the and s = 40 cm, there is a 34 percent reduction in the magnitude clearance is reduced to 0 cm. The distortion corresponding to of the vertical displacement at the abutment seat as compared a clearance of 30 cm is +0.22. with the base case (Figure 2-34a). Similar trends, but with Figure 2-37a indicates that at an applied pressure of 200 greater changes, are noted in Figure 2-35b for the horizontal kPa, s = 40 cm and a clear distance of 0 cm, there is a 4 per- displacement of the abutment seat and in Figure 2-35c for the cent increase in vertical displacement of the abutment seat as maximum lateral displacement of the segmental wall. The dis- compared with the base case (Figure 2-36a). For a clear dis- tortion of the sill ranged from +1.8 at E * t = 53 kN/m to tance of 30 cm and s = 40 cm, there is a 37 percent increase 0.05 at E * t = 5300 kN/m as shown in Figure 2-35d. in the magnitude of the vertical displacement at the abutment seat as compared with the base case (Figure 2-36a). Similar trends with comparable magnitudes are noted in Figure Effects of Sill Clear Distance 2-37b for the horizontal displacement of the abutment seat and in Figure 2-37c for the maximum lateral displacement of Sill clear distances of 0 cm, 15 cm (base case), and 30 cm the segmental wall. The distortion of the sill ranged from were used to investigate the effects of clearance on the GRS 0.02 at a clear distance of 0 cm to +0.33 at a clear distance abutment. The effects of sill clear distance on the perfor- of 30 cm as shown in Figure 2-37d. mance of the GRS abutment is shown in Figure 2-36 for Figures 2-36 and 2-37 show that the performance of the geosynthetic spacing s = 20 cm and in Figure 2-37 for GRS abutment caused by decreasing sill clear distance is s = 40 cm. counter-intuitive. Decreasing clear distance indicates that the Figure 2-36a shows that the vertical displacement of the applied pressure is closer to the segmental facing, thus, abutment seat of the base case is 4.7 cm for an applied pres- greater displacements of the segmental facing, and therefore sure of 200 kPa. This displacement is reduced 20 percent greater displacements at the abutment seat are expected. This when the clearance is reduced to 0 cm. On the other hand, an discrepancy may be attributed to the fact that when the clear

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49 Figure 2-36. Effects of sill clear distance for s = 20 cm. Figure 2-37. Effects of sill clear distance for s = 40 cm.

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50 distance is small, there will be more contribution, in terms of placement of the abutment seat is 5.8 cm, which is 24 percent stiffness, from the segmental facing. Nevertheless, this greater than that corresponding to the base case (sill width = counter-intuitive response can be ascertained via large-scale 150 cm, s = 20 cm, Figure 2-38a). For a sill width of 100 cm testing of a GRS bridge abutment with small and large sill and s = 40 cm, the vertical displacement at the abutment seat clearances. is 67 percent greater than the base case. The horizontal displacement at the abutment seat (Figure 2-39b) and the maximum lateral displacement of the segmental wall (Figure Effects of Sill Width 2-39c) follow the same trend of the vertical displacement at the abutment seat. The distortion of sill changed from +0.4 To investigate the effect of sill width on the GRS bridge at sill width of 150 cm to +0.28 at sill width of 100 cm, as abutment, two sill widths were used: 150 cm (Base Case), shown in Figure 2-39d. Figures 2-38 and 2-39 show that the and 100 cm. The effects of sill width on the performance of performance parameters increased at a higher rate under the GRS abutment is shown in Figure 2-38 for s = 20 cm and higher applied loads. in Figure 2-39 for s = 40 cm. At 300 kN/m of applied load (corresponding to 200 kPa of applied pressure for the 150-cm-wide sill, and 300 kPa for Effects of Reinforcement Truncation the 100-cm-wide sill), the vertical displacement at the abut- ment seat increased 21 percent when the width decreased To study the effects of truncated reinforcement on the per- from 150 cm (base case) to 100 cm, as indicated in Figure formance of the GRS abutment, the GRS abutment was mod- 2-38a. The effect of decreasing sill width on the horizontal ified so that the reinforcement length is truncated at the base. displacement of the abutment seat was similar in trend and The truncated base was assumed to be H/4 and increases magnitude as shown in Figure 2-38b. As shown in Figure upward at 45 angle (H is the height of the segmental wall). 2-38c, at 300 kN/m of applied load, the maximum lateral dis- Figure 2-40 shows the effect of truncated reinforcement on placement of the segmental facing increased roughly 11 per- the performance parameters for s = 40 cm. The figure com- cent when sill width decreased to 100 cm. The distortion of pares the truncated and non-truncated reinforcement cases sill changed from +0.1 at sill width of 150 cm to +0.18 at and indicates that the effect of truncated reinforcement is sill width of 100 cm as shown in Figure 2-38d. insignificant in terms of displacements. Figure 2-40d shows As shown in Figure 2-39a, for a sill width of 150 cm, s = that there is a small decrease in sill distortion in the case of 40 cm, and an applied load of 300 kN/m, the vertical dis- truncated reinforcement. Figure 2-38. Effects of sill width for s = 20 cm.

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51 Figure 2-39. Effects of sill width for s = 40 cm. Predicting Failure Loads load but suffered very significant displacements and dis- tresses without sudden failure. It is suitable to think about In the parametric study, none of the GRS bridge abutments shear strain in the soil mass as a measure of distress in a GRS failed "catastrophically" as in the Garden experiment and the abutment. Thus, a simple failure criterion based on the max- Garden test analysis described in Appendix C (NCHRP Web- imum shear strain is proposed herein in order to estimate the Only Document 81). All abutments withstood the 1000 kPa allowable bearing pressure of a spread footing. Figure 2-40. Effects of reinforcement truncation for s = 40 cm.

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Figure 2-72. Relationship between applied pressure and sill lateral movement: integrated sill, s = 0.2 m, and rigid foundation. 85

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86 Figure 2-73. Relationship between applied pressure and sill lateral movement: integrated sill, s = 0.4 m, and rigid foundation.

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Figure 2-74. Relationship between applied pressure and sill lateral movement: isolated sill, s = 0.2 m, and rigid foundation. 87

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88 Figure 2-75. Relationship between applied pressure and sill lateral movement: isolated sill, s = 0.4 m, and rigid foundation.

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Rotation of Sill (), Positive for Counter-Clockwise Rotation Figure 2-76. Relationship between applied pressure and rotation of sill: integrated sill, s = 0.2 m, and rigid foundation. 89

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90 Rotation of Sill (), Positive for Counter-Clockwise Rotation Figure 2-77. Relationship between applied pressure and rotation of sill: integrated sill, s = 0.4 m, and rigid foundation.

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Rotation of Sill (), Positive for Counter-Clockwise Rotation Figure 2-78. Relationship between applied pressure and rotation of sill: isolated sill, s = 0.2 m, and rigid foundation. 91

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92 Applied Pressure (kPa) 0 100 200 300 400 500 600 700 800 900 1000 -5 Rotation of Sill (), Positive for Counter-Clockwise Rotation -4 = 34 (Sill Width = 0.8 m) (facing failure @ 906 kPa) -3 = 37 (Sill Width = 0.8 m) = 40 (Sill Width = 0.8 m) = 34 (Sill Width = 1.5 m) -2 (facing failure @ 600 kPa) = 37 (Sill Width = 1.5 m) (facing failure @ 717 kPa) -1 = 40 (Sill Width = 1.5 m) (facing failure @ 817 kPa) = 34 (Sill Width = 2.5 m) (facing failure @ 500 kPa) 0 = 37 (Sill Width = 2.5 m) (facing failure @ 583 kPa) = 40 (Sill Width = 2.5 m) 1 (facing failure @ 700 kPa) denotes facing failure 2 3 Figure 2-79. Relationship between applied pressure and rotation of sill: isolated sill, s = 0.4 m, and rigid foundation.

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93 The reinforcement spacing and sill width affects the lat- ical shear strain distribution reached the back edge of the sill eral movement of the sill significantly. With an isolated (i.e., heel of the sill). The 1 percent H criterion came from the sill, the lateral movement of the sill is nearly indepen- existing maximum settlement criteria for bridge abutments dent of soil friction angle for a small sill width (0.8 m). proposed by Bozozuk (1978), Walkinshaw (1978), Grover The effect became slightly more pronounced when sill (1978), and Wahls (1990). The existing settlement criteria width became larger. for ride quality and structural distress range from 51 mm to A major difference between the integrated sill and iso- 102 mm based on experience with real bridges. Given that lated sill is in the rotation of the sill. The integrated sills the finite element analysis results should be regarded as all experienced counter-clockwise tilting (positive val- short-term response, and the long-term settlement is likely to ues of rotation in the figures), while the isolated sills be of about the same magnitude as the short-term settlement generally experienced clockwise rotation (negative val- (see "Assessment of the NCHRP Test Abutments" in Chap- ues of rotation in the figures), except for sill width = ter 3), 1 percent H or 47 mm short-term settlement as obtained 2.5 m, where the rotations were clockwise. from the analysis was adopted as a criterion for evaluating With a rigid foundation, the abutments tended to have the allowable bearing pressures. significantly smaller sill settlements, smaller maximum The critical shear strain concept has been used in the Cam lateral wall displacements, smaller sill lateral move- clay model, a widely used soil model developed at Cam- ments, and smaller sill rotations (except for isolated bridge University in the United Kingdom, for assessing fail- sills) than the abutments situated over a medium sand ure of a soil mass. The critical shear strain for the three soils foundation. used in the analysis was 3.2 percent, as determined from the triaxial test results. A more detailed explanation of the criti- cal shear strain distribution criterion is in the parametric Allowable Bearing Pressures study in this chapter. Tables 2-7 and 2-8 show the values of the bearing pres- The allowable bearing pressures of GRS abutments were sures corresponding to the 1 percent H settlement criterion evaluated using the results of the 36 analyses that were and the critical shear strain distribution criterion for all 36 done with a medium sand foundation, because they offered analyses with a medium sand foundation. The critical shear more conservative allowable bearing pressures than those strain distribution criterion generally yields a somewhat with a rigid foundation. Two performance criteria were exam- higher allowable bearing pressure for reinforcement spacing ined. One criterion involved a limiting sill settlement, where of 0.2 m than that with the 1 percent H settlement criterion. the allowable bearing pressure corresponded to a sill settlement This observation, however, is less consistent for reinforce- of 1 percent of the lower wall height (i.e., 1 percent H). The ment spacing of 0.4 m. The values of bearing pressures other criterion involved distribution of the critical shear strain presented in Tables 2-7 and 2-8 were used as the basis for the in the reinforced soil mass, where the allowable bearing pres- recommended allowable bearing pressures in the recom- sures corresponded to a condition in which a triangular crit- mended design method (Chapter 3).

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94 TABLE 2-7 Allowable bearing pressures based on the 1%H settlement criterion Sill Sill Width Reinforcement Applied Pressure at Type (m) Spacing (degrees) Settlement = 1%H (m) (kPa) 34 259 0.2 37 315 40 354 0.8 34 231 0.4 37 284 40 324 34 162 0.2 37 192 40 221 Integrated 1.5 34 145 0.4 37 175 40 202 34 132 0.2 37 154 40 175 2.5 34 121 0.4 37 143 40 162 34 207 0.2 37 242 40 268 0.8 34 166 0.4 37 201 40 225 34 132 0.2 37 157 Isolated 40 180 1.5 34 109 0.4 37 132 40 150 34 110 0.2 37 131 40 148 2.5 34 91 0.4 37 115 40 132

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95 TABLE 2-8 Allowable bearing pressures based on the critical shear strain distribution criterion Allowable Bearing Sill Reinforcement Type Sill Width Spacing (degrees) Pressure (critical = 3.2%) (m) (m) (kPa) 34 281 0.2 37 375 40 500 0.8 34 156 0.4 37 281 40 406 34 167 0.2 37 217 40 283 Integrated 1.5 34 117 0.4 37 167 40 233 34 150 0.2 37 200 40 267 2.5 34 100 0.4 37 150 40 217 34 188 0.2 37 250 40 313 0.8 34 125 0.4 37 156 40 219 34 150 0.2 37 200 Isolated 40 250 1.5 34 83 0.4 37 133 40 167 34 133 0.2 37 167 40 233 2.5 34 67 0.4 37 117 40 150