EFFECTIVENESS OF ROCKING SEISMIC ISOLATION ON BRIDGES

Transcription

1 4th International Conference on Earthquake Engineering Taipei, Taiwan October 12-13, 26 Paper No. 86 EFFECTIVENESS OF ROCKING SEISMIC ISOLATION ON BRIDGES Kazuhiko Kawashima 1 and Takanori Nagai 2 ABSTRACT This paper presents an analysis on the effectiveness of rocking seismic isolation of bridges supported by spread foundations. Separations of the footing from and contacts of the footing with the underlying ground which could occur during an extreme ground motion result in mitigation of bridge response. The separations and contacts of the footing must have occurred in past earthquakes although their effect was not rigorously included in seismic design. The effect of rocking seismic isolation is presented for a 1 m tall standard bridge supported by spread foundations under three directional excitation. It is shown that the effect of rocking seismic isolation is significant in reducing the plastic deformation of the columns at the plastic hinge regions although this increases the deck and columns response displacement. Keywords: Rocking isolation, Seismic isolation, Bridge INTRODUCTION Direct or spread foundations are widely used to support bridges where the soil condition is stable. They are designed so that the seismic performance for sliding, settlement and overturning can be assured. Since overturning is generally critical in spread foundations, it is important to clarify the safety for overturning. Rocking response of spread foundations provides a unique structural response. Although spread foundations have been conservatively designed so that uplift from the underlying ground be minimum for preventing overturning, it is often observed from the post-earthquake investigation that cracks along footings occurred on the ground surface. This obviously shows that rocking response occurred in the spread foundations during past earthquakes. Positive use of the rocking response of spread foundations results in the isolation effect on the bridges response. The rocking response of spread foundations increases as the size of footings decreases however it could result in overturning of bridges under an extreme ground motion. Consequently careful evaluation on the size of spread foundation is required. Rocking response of structures has been investigated by many researchers. Housner studied rocking response of a rigid block on a rigid base (Housner 1963). Inelastic rocking response of large rigid foundations was investigated by Kawashima et al., and it was found that the rigid foundations do not overturn even if they are subjected to ground motions with peak accelerations much larger than the static accelerations in the conventional static analysis (Kawashima et al. 1989, 1991, 1994). This fact was taken into account in the seismic design of Honshu-Shikoku Bridges, including the world longest Akashi Straight Bridge and Kurushima Straight Bridge. Ciampoli et al. presented an importance of rocking response and bridge response (Ciampoli et al., 1995). Priestley et al. presented a contribution of rocking response of a footing to a total deck displacement (Priestley et al. 1996). Mergos and 1 Professor, Tokyo Institute of Technology, Tokyo, Japan, kawasima@cv.titech.ac.jp 2 Graduate Student, Tokyo Institute of Technology, Tokyo, Japan, nagai@cv.titech.ac.jp

2 Kawashima analyzed the rocking isolation of a typical spread foundation under three directional excitation (Mergos and Kawashima, 26), and Sakellaraki and Kawashima showed the effectiveness of rocking isolation based on a shake table experiment (Sakellaraki and Kawashima 26). This paper shows the rocking isolation effect of spread foundations on the seismic response of bridges, and clarifies the effect of bilateral excitation on the rocking isolation of a spread foundation. An experimental verification is also presented. ROCKING OF SPREAD FOUNDATIONS AND IDEALIZATION In the static seismic design, a spread foundation is sized so that the seismic performance can be assured I terms of the bearing capacity of ground, sliding and overturning of foundation as V S B < S Ba a A FL M B = ; S S = < SSa ; e = < ea (1) σ F V La in which, S B and S S, S Ba and S Sa : safety factors for bearing capacity and sliding, respectively, and their allowable safety factors; σ a : capacity of the vertical stress at the bottom of the footing for the static load; F L and F La : demand and capacity of sliding force, respectively; e and e a : eccentricity resulting from the lateral force and its allowable value, respectively; M B and V : moment resulted from the lateral force and the vertical force resulted from the dead weight of the deck, the column, the footing and the overburden soil, respectively; and A : base area of the footing. It is noted that e a is generally one third of the width of the foundation. (c) Figure 1. Uplift of spread foundation from the underlying ground; static equilibrium, uplift at left edge, and (c) equilibrium after uplift However, as the rocking response increases, the footing starts to uplift and separate from the underlying ground at an edge as shown in Fig. 1. The static settlement of a spread foundation, v FS, with a width l resulted from a static dead load of the deck, the column and the footing, V, may be written as v FS V = (2) k l sv When the foundation uplifts with an angle θ F from the resting position, the edge of the foundation starts to separate from the underlying ground as the upward displacement of the footing at the edge, l θ FS / 2, increases larger than the initial settlement v FS. Rotational spring stiffness of the foundation, K ~ Fθ, may then be written as < = l / 2 2 l θ / 2 ( ) ~ l k F sv x x dx vfs K 2 Fθ (3) l / 2 2 l θ FS X ksv ( x) x dx vfs 2

3 (c) Figure 2. Idealization of spread foundation; without separation, with separation of the footing from underlying ground, and (c) idealization of restoring force of underlying ground in which X represents the distance from the center of the footing to a point where the footing uplifts to the original level of the ground. To represent the soil-foundation interaction for rocking response, an analytical model as shown in Fig. 2 is conventionally used. The rotational spring stiffness, K Fθ, idealizes the soil-foundation interaction for rocking response. Assuming that the subgrade reaction of soils per unit area, k sv, is linear at the entire response displacement range, the rotational stiffness of the foundation K Fθ may be obtained as l / 2 2 K F θ = l / 2 ksv ( x) x dx (4) in which x is the distance from the center of the footing. Because the idealization by Fig. 2 with a linear rotational stiffness K Fθ only represents the linear response of a spread foundation, an analytical model as shown in Fig. 2 is used here to take account of uplift and separation of a spread foundation from the underlying ground. It is assumed in the model that the i-th soil spring has nonlinear restoring force with a stiffness of k SVi for compression and for separation as shown in Fig. 2(c). Consequently, the restoring force of the i-th spring is written as fvi ksvi ( vfi = vfsi ) vfi < vfsi vfi vfsi (5) in which k SVi : stiffness of i-th soil spring, vfsi : initial settlement of the footing due to the dead weight, and vfi : relative displacement at i-th soil spring between the footing and the ground which is defined as v v v Fi = Fi Gi (6) where v Fi and v Gi are vertical response displacement of the footing and the ground, respectively, at i-th soil spring. Although it is not shown in this paper, the underlying ground may yield due to rocking of a spread foundation when the underlying soil does not have sufficient strength. The saturation of the restoring force of the underlying ground can be incorporated in the idealization by Fig. 2 (Kawashima et al 1991, Mergos and Kawashima 26). It is known that sliding and uplift of a rocking body develops a complex interaction between sliding, rocking and jumping (Ishiyama 1982), however the sliding is restrained in the following analysis because the sliding is not critical in the spread foundations embedded in the ground.

4 TARGET BRIDGE A bridge which is analyzed here is presented in Fig. 3. It is a 2m long five span continuous bridge supported by two abutments and four reinforced concrete columns. The abutments and columns rest on six spread foundations. The superstructure is supported by five fixed steel bearings. Spread foundations are embedded in sandy soils resting on gravels with N-value of the standard penetration test over 5. Since the fundamental natural period of the ground is less than.2 s, this site is regarded as a stiff site (ground group I) according to the Japanese highway bridge design code (Japan Road Association 22). Since the bridge and the soil condition are almost uniform along the bridge axis, a structural system consisting of a column, a foundation and a tributary deck is analyzed here. The seismic response in the longitudinal, transverse and vertical directions is analyzed. A spread foundation determined from the static seismic design assuming.2g lateral acceleration is 2 m thick, 6.5 m long in the longitudinal direction and 7 m wide in the transverse direction. Overturning is the critical requirement for sizing the foundation. A A foundation, a column and a part of the deck are idealized by a three-dimensional discrete analytical model as shown in Fig. 4. The footing was idealized by a rigid grid consisting of beam elements. Four sides of the footing in the longitudinal and transverse directions are referred hereinafter A- and s and C- and D-sides, respectively (refer to Fig. 4). The soil-foundation interaction is idealized by nonlinear soil springs as shown in Fig. 2(c). The soil spring stiffness is determined from the subgrade reaction of soils based on the design practice (Japan Road Association 22). The column at the plastic hinge is idealized by the fiber elements, and linear beam elements with the cracked stiffness elsewhere. Flexure strength and ductility capacity of the column are determined based on the empirical stress and strain relation of confined concrete (Hoshikuma et al 1997, Sakai et al. 2) and reinforcing bars (Menegotto et al. 1973). The foundation and the deck aree assumed rigid and their (c) (d) Figure 3. Bridge analyzed; side, front, (c) side and (d) soil profile C A B D Figure 4. Idealization of a spread foundation-underlying ground-a column-a deck system

5 masses are lumped at their gravity centers. The evaluation of overburden soil is important in the analysis. It is assumed here that the weight of the overburden soil is included in the evaluation of the static settlement v FS in terms of V in Eqs. 1 and 2, but it is disregarded in the evaluation of the inertia force. Three-dimensional bridge response under bilateral and vertical excitation is computed. NS, EW and vertical components of the ground accelerations measured at Kobe Observatory of Japan Meteorological Agency (JMA Kobe record) during the 1995 Kobe, Japan earthquake are imposed to the bridge in the longitudinal, transverse and vertical directions, respectively. Response under unilateral and vertical excitation is also computed for clarifying the effect of unilateral excitation. NS and UD components are imposed to the model in the longitudinal and vertical directions, respectively, in this evaluation. Rayleigh damping is assumed to represent the energy dissipation (Clough and Penzien 1993). Damping ratio is assumed.5 for the first and second modes. Acceleration (m/s 2 ) 2-2 Displacement (m) Figure 5. Deck response in the longitudinal direction under unilateral excitation when uplift of the footing is not taken into account; acceleration, and displacement..15 Displacement (m) Restoring Force (kn) Time (s) Figure 6. Response of the footing at A and B sides under unilateral excitation when uplift of the footing is not taken into account; vertical displacement of the footing, and reaction restoring force of the soil spring

6 SEISMIC RESPONSE UNDER UNILATERAL EXCITATION For clarifying the effect of bilateral excitation, response of the bridge under unilateral excitation is first evaluated. Fig. 5 shows the deck accelerations and displacements when the bridge is subjected to NS and US components in the longitudinal and vertical directions, respectively. Only the longitudinal responses are shown here. The soil-foundation interaction is idealized by a linear rotational soil spring (refer to Fig. 2) without taking uplift and separation of the footing from the underlying ground into account. The peak deck acceleration and displacement are 13.1 m/s 2 and.219 m, respectively. Fig. 6 shows the relative vertical displacement of the footing vfi and restoring force of a soil spring f Vi at A- and s in the longitudinal direction. The peak vertical displacement of the footing resulted from rocking response is 15.2 mm and 22.9 mm at the A-and s, respectively. The peak compression and tension of a soil spring is 93 kn and 472 kn, respectively, at. They result in compression and tension stress of 2.54 MPa and 1.33MPa, respectively, in the underlying ground. As a consequence, the column shows the moment vs. curvature hysteresis at the plastic hinge in the longitudinal direction as shown in Fig. 7. The column undergoes significant plastic range with the peak curvature of 9.4x1-3 /m. On the other hand, Fig. 8 shows the deck accelerations and displacements of the bridge computed by taking uplift and separation of the footing from the underlying ground into account. The bridge is subjected to NS and US components of JMA Kobe ground motion in the longitudinal and vertical 1 4 Moment (knm) 5-5 Moment (knm) Curvature (1/m) Curvature (1/m) Figure 7. Moment vs. curvature hysteresis of the column at the plastic hinge under unilateral excitation; uplift of the footing is not taken into account and uplift of the footing is taken into account Acceleration (m/s 2 ) Displacement (m) Figure 8. Column response at the top in the longitudinal direction under unilateral excitation when uplift of the footing is taken into account; acceleration, and displacement

7 .15 Displacement (m) Restoring force (kn) Time (s) Figure 9. Response of the footing at A and B sides under unilateral excitation when uplift of the footing is taken into account; vertical displacement of the footing, and reaction restoring force of the soil spring directions, respectively. The peak deck acceleration and displacement in the longitudinal direction are 6.69 m/s 2 and.253 m, respectively, which are 49% smaller and 16% larger, respectively, than the peak acceleration and displacement computed by disregarding the uplift and separation of the footing from the underlying grounds. It is obvious that the significant decrease of the peak deck acceleration results from the rocking isolation. It should be assured that the slight increase of the deck displacement does not result in any problem for the seismic performance of the bridge. Fig. 9 shows the vertical relative displacement of the footing vfi and the restoring force of a soil spring f Vi at A- and s in the longitudinal direction. The footing rocked and uplifted 11 mm and 56 mm at A- and s, respectively, from an initial settlement due to dead weight v FS (refer to Eq. 2) of 2.48 mm. It is important to note that the spread foundation which is designed in accordance with the static design assuming.2 g lateral acceleration by Eq. 1 uplift mm. This means that the rocking isolation must have occurred in past significant earthquakes although this effect was not considered in design. The peak compression of a soil spring is 725 kn at, which corresponds to compression stress of 2.4 MPa. No tension stress is induced in the soil springs. The compression stress of 2.4 MPa is 8 % of that developed in the underlying ground by disregarding the uplift and separation of the footing from the underlying ground. Fig. 7 shows the moment vs. curvature hysteresis of the column at the plastic hinge in the longitudinal direction. Plastic deformation of the column is limited and the peak curvature is 7.63x1-4 /m. This is only 8% of the curvature developed by disregarding the uplift and separation of the footing from the underlying ground. The rocking isolation effect is thus significant for mitigating the damage of column at the plastic hinge. SEISMIC RESPONSE UNDER BILATERAL EXCITATION Fig. 1 shows the deck responses under bilateral and vertical excitation evaluated by taking uplift and separation of the footing from the underlying ground into account. The peak deck acceleration and displacement are 7.16 m/s 2 and.263, respectively, in the longitudinal direction and 7.5 m/s 2 and.194 m, respectively, in the transverse direction. Because the peak deck acceleration and displacement in the longitudinal direction are 6.69 m/s 2 and.253 m, respectively, under unilateral and

8 Acceleration (m/s 2 ) Acceleration (m/s 2 ) Displacement (m) Displacement (m) (d) (e) Figure 1. Deck responses under bilateral excitation when uplift of the footing is taken into account; longitudinal acceleration, transverse acceleration, (c) longitudinal displacement, and (d) transverse displacement Displacement (m) Restoring force (kn) (c) Figure 11. Response of the footing at A and s under bilateral excitation when uplift of the footing is taken into account; vertical displacement of the footing, and reaction restoring force of the soil spring vertical excitation, the peak deck acceleration and displacement increase by 7% and 4%, respectively, under bilateral and vertical excitation. Fig. 11 shows the relative vertical displacement of the footing vfi and restoring force of a soil spring f Vi at A- and s in the longitudinal direction and C- and D-sides in the transverse direction. The peak relative uplift vfi is 127 mm and 79 mm at A- and s, respectively. Because vfi at A- and s under unilateral and vertical excitation is 11 mm and 56 mm, respectively, vfi under bilateral and vertical excitation is 15% and 41% larger. The peak compression is larger at the corners.

9 5 5 Moment (knm) Moment (knm) Curvature (1/m) Curvature (1/m) Figure 12. Moment vs. curvature hysteresis of the column at the plastic hinge under bilateral excitation when uplift of the footing is taken into account; longitudinal direction and transverse direction For example, it is 647 KN and 117kN at the AC and BC corners, respectively, which results in stress of 1.8 MPa MN/m 2 and 6.23 MPa, respectively. Consequently, the compression stress induced in the underlying soil at the corners under bilateral excitation is nearly times larger than that under unilateral excitation. Protection of soils at the corners is needed depending on the bearing capacity of the ground. Fig. 12 shows the moment vs. curvature hysteresis of the column at the plastic hinge in the longitudinal and transverse directions. The peak curvature is 8.24x1-4 /m and 2.x1-4 /m in the longitudinal and transverse directions, respectively. Since the strength of column is much lager in the transverse direction than the longitudinal direction, the curvature of the column developed in the transverse direction is limited. Because the peak curvature in the longitudinal direction is 7.63x1-4 /m under unilateral and vertical excitation, it increases by 7% under bilateral and vertical excitation. CONCLUSIONS Effectiveness of the rocking isolation of spread foundations on the seismic performance of bridges was studied based on the nonlinear analysis for a 1 m tall standard bridge. Based on the results presented herein, the following conclusions may be deduced on the effect of rocking isolation: 1) As separation of the footing from the underlying ground due to seismic rocking response increases, the plastic deformation of the column at the plastic hinge significantly decreases as a result of the softening of moment vs. rotation hysteresis of the footing. As a consequence, the inelastic rocking of the footing results in an isolation effect on the response of the bridge. However because the isolation effect results in an increase of response displacement of the bridge, the size of footing has to be properly selected in design. 2) A spread foundation which is designed in accordance with the conventional static seismic design using the lateral static acceleration of.2g and working stress design approach rocks separating from the underlying ground when the bridge is subjected to the JMA Kobe near-field ground motion. The uplift at edge of the footing is in the range of 8-13 mm for the 1 m tall standard bridge under JMA Kobe ground motion recorded during the 1995 Kobe earthquake. This means that the rocking isolation must have happened similarly in past significant earthquakes although it was not detected in the postearthquake inspection. Positive use of the rocking isolation brings benefit in seismic design of bridges. 3) Uplift and separation of the footing from the underlying ground can be realistically analyzed using nonlinear soil spring idealization as shown in Fig. 2.

10 4) Bilateral excitation results in an increase of bridge response acceleration and displacement compared to the unilateral excitation. In particular, stress induced in the underlying ground at the corners significantly increases. Consequently underlying ground at the corners needs to be protected, if necessary, for use of the rocking isolation. REFERENCES Ciampoli, M. and Pinto, P. E. (1995). Effects of Soil-Structure Interaction on Inelastic Seismic Response of Bridge Piers, Journal of Structural Engineering, ASCE, 121 (5), Clough R.W. and Penzien J. (1993). Dynamics of Structures, 2nd edn, McGraw Hill, New York. Hoshikuma, J. Kawashima, K. Nagaya, K. and A. W. Taylor (1997). Stress-Strain Model for Confined Reinforced Concrete in Bridge Piers, Journal of Structural Engineering, ASCE, 123(5), Housner, G. W. (1963). The Behaviour of Inverted Pendulum Structures during Earthquakes, Bulletin Seismological Society of America, 53, Ishiyama, Y. (1982). Motion of Rigid Bodies and Criteria for Overturning by Earthquake Excitations, Earthquake Engineering and Structural Dynamics, 1, Japan Road Association (22). Design Specifications of Highway Bridges, Maruzen, Tokyo. Kawashima, K. and Unjoh, S. (1989). Rocking Response of a Rigid Foundation subjected to Seismic Excitation, Civil Engineering Journal, 32 (1), 6-66 (in Japanese). Kawashima, K. and Unjoh, S (1991). Overturning of Rigid Foundation Resting on Ground with Insufficient Yield Strength, Civil Engineering Journal, 33(3), (in Japanese). Kawashima, K., Unjoh, S. and Mukai, H. (1994). Inelastic Rocking of Direct Foundation during an Earthquake, Civil Engineering Journal, 36(7), 5-55 (in Japanese). Kawashima, K. and Hosoiri, K. (23). Rocking Response of Bridge Columns on Direct Foundations, Proc. fib-symposium, Concrete Structures in Seismic Region, 118 (CD-ROM), Athens, Greece. Menegotto, M.and Pinto, P.E. (1973). Method of Analysis for Cyclically Loaded R.C. Plane Frames including Changes in Geometry and Non-Elastic Behavior of Elements under Combined Normal Force and Bending, Proc. of IABSE Symposium on Resistance and Ultimate Deformability of Structures Acted on by Well Defined Repeated Loads; Mergos, P. E. and Kawashima, K., (26), Rocking Response Isolation of a Typical Pier on Spread Foundation, Journal of Earthquake Engineering, 9(2), Priestley, N. M. J., Seible, F. and Calvi, G. M. (1996). Seismic Design and Retrofit of Bridges, John Wiley & Sons, New York. Sakai, J. and Kawashima, K. (26). Unloading and Reloading Stress-Strain Model for Concrete Confined, Journal of Structural Engineering, ASCE, 132(1), Sakellaraki, D. and Kawashima, K. (26). Effectiveness of Seismic Rocking Isolation of Bridges based on Shake Table Test, First European Conference on Earthquake Engineering and Seismology, Paper No. 364, Geneva, Switzerland