Design Guide for Bridges for Service Life (2013)

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559 This appendix summarizes the work for addressing the effect of skew on lateral move- ment of the bridge at the abutment. B.1 bAckground A skewed bridge is a bridge with the longitudinal axis at an angle other than 90° with the piers and abutments. The skew angle (q) is shown in Figure B.1. With skewed inte- gral abutment bridges, the soil passive pressure developed in response to thermal elon- gation has a component in the transverse direction, as illustrated in Figure B.1. Within certain limits of the skew angle, soil friction on the abutment will resist the transverse component of passive pressure. However, if the soil friction is insufficient, then, de- pending on the transverse stiffness of the abutment, either significant transverse forces or significant transverse movements could be generated. Figure B.2 shows a two-span bridge with a skew angle of 45° (Nicholson et al. 1997). This bridge was constructed in 1969 with semi-integral abutments. The semi- integral construction included an integral end diaphragm that was designed to move with the superstructure, which slides longitudinally and is guided transversely by rela- tively stiff abutments. Figure B.3 shows cracking in the abutment wall near an acute corner of the super- structure, presumably caused by transverse forces related to soil pressures. Figure B.4 shows distress in an asphalt overlay at the skewed end of an approach slab as a result of transverse movement (Tabatabai et al. 2005). Figure B.5 shows a closer view of the barrier wall joint from Figure B.4 at the end of the approach slab. The expansion joint in the barrier wall was made perpendicular to the longitudinal direction and could not accommodate the transverse movement. B DiSpLACEMENT OF SKEWED BRiDGE

560 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE Figure B.1. Components of abutment soil passive pressure response to thermal elongation in skewed integral abutment bridges. Figure B.2. Two-span semi-integral abutment bridge with an overall length of 89 m (259 ft), width of 11.6 m (38 ft), and a skew angle of 45°. Source: Nicholson et al. 1997.

561 Appendix B. DiSpLACEMENT OF SKEWED BRiDGE Figure B.3. Cracking in the abutment wall near an acute corner of the superstructure for the bridge shown in Figure B.2. Source: Nicholson et al. 1997. Figure B.4. Asphalt overlay distress (west end). Source: Tabatabai et al. 2005.

562 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE Because of potential problems and uncertainty related to the response of skewed integral abutments, many state departments of transportation limit the skew angle. A typical limit for maximum skew angle for integral abutment bridges used by many states is 30°. However, maximum skew angle limits in various states range from 0° to no limit (Chandra 1995). In response to the potential problems of skewed inte- gral abutments, studies on jointless and integral abutment bridges were conducted by FHWA (Oesterle and Lotfi 2005) to 1. Develop a relationship between skew angle and abutment soil friction for limiting skew. 2. Develop a relationship for the magnitude of forces required to restrain transverse movement in integral abutment bridges with large skew angles. 3. Develop a relationship between skew angle and expected transverse movement for a typical integral stub abutment with no special design features to restrain this movement. 4. Compare analytical results with field data for a skewed bridge that was monitored as part of the experimental portion of this project. 5. Perform a sensitivity study to demonstrate the relationship between transverse movement and longitudinal expansion for various skew angles and ratios of bridge length to width. This work was accomplished by developing equilibrium and compatibility equa- tions for end abutment forces and, for the case of a typical stub abutment, solving these relationships for various skew angles and bridge length-to-width ratios. Figure B.5. Barrier distress at west abutment. Source: Tabatabai et al. 2005.

563 Appendix B. DiSpLACEMENT OF SKEWED BRiDGE B.2 AnALySeS For trAnSverSe reSPonSe to thermAL exPAnSion B.2.1 Skew Angle Limit for Limiting transverse Effects Figure B.6 shows the passive soil pressure response (Pp) due to thermal expansion and soil–abutment interface friction (Faf), assuming no rotation in the plane of the bridge superstructure. Equation B.1 shows Faf for rotational equilibrium: ( ) ( )θ = θF L P Lcos sinaf p (B.1) and Equation B.2 shows Faf from interface behavior: = δF P tanaf p (B.2) where tan δ is the friction coefficient for the interface of formed concrete and soil. Equation B.3 is obtained by substituting Equation B.1 into Equation B.2: δ δ = θ θ = θ θ tan sin cos tan or = (B.3) Therefore, the bridge superstructure can be held in rotational equilibrium until the skew angle exceeds the angle of interface friction. Integral abutments are typically backfilled with granular material. NCHRP Report 343 lists a friction angle of 22° to 26° for formed concrete against clean gravel, gravel sand mixtures, and well-graded rock fill (Arsoy et al. 2002). Based on these data, the angle of q = 20° represents a reasonably conservative skew angle limit below which special considerations for trans- verse forces or transverse movement are not needed. Figure B.6. Soil pressure load (Pp ) and soil–abutment interface friction (Faf ).

564 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE With larger skew angles, the integral abutment either can be designed to resist the transverse force generated by the soil passive pressure in an attempt to guide the abutment movement to be predominantly longitudinal, or it can be detailed to accom- modate the transverse movement. B.2.2 forces Required to Resist transverse movement Adding lateral resistance of the abutment (Fa) to wall–soil interface friction (Faf) in Figure B.6, rotational equilibrium is found by Equation B.4: ( )( ) ( )+ θ = θF F L P Lcos sina af p (B.4) Equation B.5 is obtained by substituting from Equation B.2 into Equation B.4: ( )= θ − δF P tan tana p (B.5) Fa is the summation of abutment lateral resistance from pile and passive pressure on the substructure surface perpendicular to the abutment. Figure B.7 shows the relationship between Fa and Pp, assuming the interface fric- tion angle (δ) to be 20º. As shown in Figure B.7, the force required to resist transverse movement is a significant portion of the soil passive pressure (Pp). Pp is not necessarily full passive pressure, but can be determined for the end movement by using relation- ships calculated by Clough and Duncan (1991; also Barker et al. 1991) shown in Figure B.6. The end movement to consider in calculating passive pressure is the end movement normal to the abutment (Dln). Figure B.7. Relationship between force required for abutment lateral resistance (Fa ) and passive pressure response (Pp ) to restrain lateral movement.

565 Appendix B. DiSpLACEMENT OF SKEWED BRiDGE For relatively short bridges or bridges in locations with small effective temperature ranges, it may be feasible to design the abutment substructure to resist Fa . However, it should be understood that for whatever means used to develop Fa (battered pile and/ or lateral passive soil resistance), lateral movements are required to develop the resis- tance. Therefore, details anticipating some transverse movement should be used. The expected movements are a function of the relative stiffnesses of response for Pp and Fa. Adding battered piles to an integral abutment for lateral loading will also increase the stiffness in the longitudinal direction, which induces more demand on the super- structure and connections between the girders and abutments. As illustrated in Figure B.8, this end movement is given by Equation B.6: l l cosn θ∆ = ∆ (B.6) where Dl is the maximum expected end movement for thermal reexpansion from the starting point of full contraction for the full range of effective bridge temperatures, as discussed in Section 8.6.2.3.1. From Figure B.8, it can be seen that Dln is reduced with respect to Dl as the skew angle (θ) increases. This relationship helps offset the increase in Fa /Pp with increasing θ. However, Fa will still be a sizable portion of Pp. Figure B.8. Relationship between end normal movement (Dln) and end thermal expansion (Dl).

566 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE B.3 exPected trAnSverSe movement with tyPicAL integrAL Abutment B.3.1 method of Analyses To investigate the relationship between skew angle and expected transverse movement for a typical integral stub abutment, a set of relationships was derived based on equi- librium and the compatibility of end abutment forces in the plane of the bridge super- structure. For this analysis, the superstructure is assumed to act as a rigid body with rotation b about the center of the deck (for a longitudinally symmetrical bridge). The rotation occurs to accommodate the thermal end movement (Dl). Forces considered in response to this movement include soil pressure on the abutment and wingwalls, wall–soil interface friction on the abutment, and pile forces normal to and in line with the abutment and wingwalls. Details of the forces, stiffness, and equations of compat- ibility and equilibrium are provided in the final report on FHWA’s analytical work on jointless bridges (Oesterle 2005). A spreadsheet program was used for solving the rotational equilibrium in the plane of the deck. For a given end thermal movement (Dl), the equilibrium position can be found using an iterative analysis by progressively increasing the rotation angle (b) until the sum of the in-plane moments is zero. B.3.2 Results of Analyses for instrumented Bridge As part of the experimental program for studying jointless bridges (Tabatabai et al. 2005), a heavily skewed bridge in Tennessee was instrumented and monitored for 1 year. This bridge carries U.S. Interstate 40 over Ramp 2B in Knox County, Tennessee. It has a three-span steel-plate girder superstructure with an overall length of 415.92 ft and integral abutments. This structure is sharply skewed, with a skew angle of 59.09º. The three span lengths are 139.83, 208, and 68.08 ft. The bridge was instrumented to monitor the longitudinal and transverse movements of the east abutment and obtain an indication of restraint to the longitudinal expansion. The east abutment was analyzed using the spreadsheet program developed to solve for rotational equilibrium (Oesterle 2005; Oesterle and Lotfi 2005). On the basis of the experimental data, an end movement of Dl = 0.781 in. was used in the analysis. A measured superstructure rotation angle of b = 0.000224 radians corresponded with Dl = 0.781 in. Using the spreadsheet to determine rotational equilibrium, an angle of b = 0.000226 radians was calculated. The calculated value indicated very good agree- ment with the measured data.

567 Appendix B. DiSpLACEMENT OF SKEWED BRiDGE B.3.3 Sensitivity Analyses for the Effects of Skew Angle on transverse movement and Longitudinal Restraint To demonstrate the effects of skew angle on expected transverse movement and lon- gitudinal restraint forces, further analyses were carried out using the spreadsheet pro- gram. Variables included skew angle and the length-to-width ratio for the bridge. The abutment for the instrumented bridge is a relatively typical type of stub abutment used in Tennessee and was used as the baseline abutment for the analyses (Oesterle 2005; Oesterle and Lotfi 2005). The instrumented bridge is relatively wide compared with the length. The ratio of length to width (L/W) for this bridge is 3.15. To demonstrate the sensitivity to the bridge L/W ratio, the analyses were repeated for abutments reduced to 2/3W and 1/3W. The length of the wingwalls at each skew angle was kept constant. Results of these analyses for the ratio of transverse movement to longitudinal movement (Dt1/Dl) are shown in Figure B.9 for Dl = 1 in. The transverse movement (Dt1) is the transverse movement of the acute corner of the bridge deck. This is the corner that experiences the greatest transverse movement because of the skew angle. The results in Figure B.9 demonstrate the increase in the transverse movement with increasing skew angle. The data in Figure B.9 also demonstrate the increase in transverse movement with decreasing L/W. The change in L/W was accomplished Figure B.9. Relationship between transverse movement at the acute corner (Dt1) and thermal expansion (Dl) for an expansion of 1 in. with constant length bridge (L = 415.92 ft) and varying L/W.

568 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE in the analyses by decreasing the width and keeping the length constant. The length of the wingwall at each skew angle was constant; therefore, the results in Figure B.9 demonstrate the effects of increasing the ratio of the length of the wingwalls to the length of the abutment wall. The data in Figure B.9 show that increasing the wingwall length relative to the abutment wall length (which includes increasing the number of wingwall piles relative to the number of abutment wall piles) can significantly decrease the transverse movement. However, the wingwalls and abutment must be designed to transmit the wingwall forces into the superstructure. Figure B.10 shows the resulting total longitudinal restraint force for these analyses and demonstrates the decrease in longitudinal restraint with increasing skew angle. For the full-width bridge with L/W = 3.15, the longitudinal restraint at a skew angle of q = 60° is approximately 60% of the longitudinal restraint at q = 25°. For the larger L/W = 9.45, the ratio of longitudinal restraint at q = 60° is approximately 70% of the restraint at q = 25°. This change demonstrates the increase in restraint resulting from the increase in resistance to lateral moment because of the larger ratio of wingwall length to abutment length. Figure B.10. Relationship between resultant longitudinal restraint force and skew angle for thermal expansion (Dl) of 1 in. with constant length bridge (L = 415.92 ft) and varying L/W.

569 Appendix B. DiSpLACEMENT OF SKEWED BRiDGE B.3.4 Design Recommendations Because the baseline abutment used in these analyses is a relatively typical stub abut- ment (but also relatively deep, with an abutment height of 13.0 ft and with strong axis pile bending for movement normal to the abutment versus weak axis bending for movement parallel to the abutment), the data in Figure B.9 represent a reasonably large estimate for the transverse movement of skewed abutments. Although there is significant uncertainty for actual soil and pile stiffness, the maximum expected end movement (Dl) discussed in Section 8.6.2.3.1 includes a multiplier to account for un- certainty. Therefore, it is suggested that the data in Figure B.9 can be used by designers to determine an approximate estimate for expected transverse movement in skewed integral abutments resulting from the restraint of longitudinal thermal expansion. In addition, the relationships between longitudinal restraint force and skew angle shown in Figure B.10 can be used to estimate the relative decrease in restraint forces in a skewed bridge. The transverse movements can be used to estimate the transverse forces on the wingwall resulting from passive soil load and pile and to estimate longitudinal and transverse movements for the abutment pile for biaxial bending considerations. All the other components of movement and forces can be determined from Dt1 and Dl by using equations presented in the full analytical report (Oesterle 2005).