implications of spatial variation of ground motion - Semantic Scholar

ACI International - Special Publication SP-187 K. Krishnan Editor, 299-327 1999.

Implications of Spatial Variation of Ground Motion on the Collapse of Sr14/I5 Southbound Separation and Overhead Bridge in the Northridge Earthquake

by George Mylonakis 1 , Vassil Simeonov 2 , Andrei M. Reinhorn2, and Ian G. Buckle 3

Synopsis: Linear and non-linear analytical studies were conducted for evaluating the performance of the southbound separation and overhead bridge at the SR14/I5 interchange during the Northridge earthquake of January 17, 1994. The analyses are focused on potential implications of the spatial variability of ground motion on the collapse of the structure. The influences of vertical ground motion, soil-structure interaction, non-linear contact effects at the expansion joints and abutments, are also examined. The parameter studies help to determine some of the causes of collapse and offer insight in the complex seismic behavior of long multi-span concrete bridges.

1

City University of New York State University of New York at Buffalo 3 University of Auckland, New Zealand 2

George Mylonakis, Vassil Simeonov, Andrei M. Reinhorn, Ian G. Buckle Implications of Spatial Variation of Ground Motion on the Collapse of SR14/I5 Southbound Separation and Overhead Bridge in the Northridge Earthquake

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George Mylonakis is Assistant Professor of Civil Engineering at the City College of the City University of New York. He graduated from the National Technical University of Athens, Greece, and received his Doctorate from the State University of New York at Buffalo. His research is focused on the areas of earthquake engineering, foundation engineering, and soil-structure interaction. Vassil Simeonov is Graduate Research Assistant in the Department of Civil Engineering, SUNY at Buffalo. His research work has been focused on the areas of computational structural dynamics, dynamic analysis of bridges under non-uniform seismic excitation, soil-structure interaction. Andrei M. Reinhorn is Professor and Chairman of the Department of Civil Engineering, SUNY at Buffalo. Member ACI Committees on seismic loadings and use of computers. Published more than 100 papers in journals and books in the areas of theoretical and experimental research of RC structures, vibration reduction systems, seismic retrofit, base isolation, earthquake engineering. Ian G. Buckle is Vice-Chancellor of the University of Auckland, New Zealand, and Research Professor in the Department of Civil Engineering, SUNY at Buffalo. A recognized authority in earthquake engineering, Dr. Buckle has served as Deputy Director of the National Center of Earthquake Engineering Research, and published in the areas of bridge engineering and seismic isolation.

INTRODUCTION

The SR14/I5 interchange is located approximately 40 km (25 mi) to the northwest of downtown Los Angeles. The southbound separation and overhead bridge of the interchange was severely damaged during the 1971 San Fernando and 1994 Northridge 4 earthquakes. At the time of the former event the bridge was under construction. It suffered loss of two spans and was reconstructed after the earthquake. In the latter event, the bridge was sited right above the ruptured zone, about 10 km (6 mi) from the epicenter. With peak ground acceleration and velocity exceeding 0.5 g and 50 cm/s (20 in/sec), respectively, throughout the near-field region, two piers of the bridge failed and three spans supported by those piers collapsed. Two basic failure mechanisms have been speculated (Buckle, ed. 1994): according to the first scenario, failure was initiated by the seat loss in the expansion joint H2 (Fig. 1) connecting the first two segments of the bridge; in the second scenario, collapse started with the failure of the shortest pier (P2), which was later found completely crushed under the deck. Given the length of the bridge, 480 m (1575 ft), and the different soil conditions at the locations of the various supports, spatial effects in ground motion were possibly implicated in the collapse. 4

Details of the engineering aspects of the Northridge earthquake are given, in alphabetical order, by: Buckle ed. (1994), Caltrans (1994), EERI (1995), Gazetas (1996), Goltz (1994), Moehle ed. (1994), Priestley et al (1994), Yegian et al (1995).


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With the actual failure mechanism of SR14/I5 separation and overhead still being unclear, the present paper aims at determining the influence of spatial variation of ground motion on the seismic performance of the structure. Extensive analytical studies were conducted using several models of the prototype. Based on the analysis results, the influence of the spatial effects and the modeling issues are evaluated. Finally, an attempt is made to identify the beginning of the progressive failure of the bridge.

DESCRIPTION OF THE BRIDGE SYSTEM

Superstructure

The SR14/I5 southbound separation and overhead is a 10-span cast-in-place concrete box girder bridge with seat type abutments and single column piers founded on single drilled shafts (Fig. 1). The bridge is 480 m (1575 ft) long and 16 m (53 ft) wide, with the deck skewed at an angle of 3.53o and slightly curved to a radius of about 670 m (2200 ft). It is constructed in 5 segments, with 4 intermediate and 2 abutment expansion joints. Spans 1, 2, 3, 5, 6, 9 and 10 are prestressed by post-tensioning whereas the remainder of the spans (4, 7, 8) are constructed of non-prestressed reinforced concrete. The deck is supported by 9 centrally positioned reinforced concrete columns and 2 seat-type abutments. The free height of the piers varies between, approximately, 10 m (33 ft) at Pier 2 to 38 m (125 ft) at Pier 7. The cross sectional dimensions of the columns are: 1.2 x 3.6 m (4 x 12 ft) for Piers 2 to 5 and Pier 10; 1.5 x 3.6 m (5 x 12 ft) for Pier 6; and 1.8 x 3.6 m (6 x 12 ft) for Piers 7 to 9. Each expansion joint is equipped with transverse shear keys, 5 vertical restrainers, 6 elastomeric pads and longitudinal restrainers --- 28 in expansion joints H2 and H5; 32 in expansion joints H3 and H4. The longitudinal restrainers are Caltrans type 1, 19 mm (¾ in) diameter galvanized steel wire ropes. Each restrainer has 6 strands with 19 wires per strand. No restrainers are provided in the abutment expansion joints. The support ledge dimension at each joint is 0.36 m (14 in).

Soil and Foundation Properties

Information on the near-surface geology was obtained from the 1976 “as built” plans as well as from more recent borehole data (Cole and Vickery, 1994). The soil profile consists of a stiff 10 m (33 ft) thick surface layer of silts and sands characterized by maximum (low-strain) shear wave velocity Vs of about 300 m/s (1000 ft/sec), followed by a second layer of soft rock with Vs equal to about 700


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m/s (2300 ft/sec). The second layer outcrops at the locations of the abutments and Piers 4, 5, and 10. No borehole information is available for depths greater than 30 m (100 ft). There is evidence (Horton and Barstow, 1995), however, that the two layers overlay a rock formation, which is located approximately 30 m (100 ft) from the surface. The single drilled shafts supporting the superstructure penetrate the soil to depths ranging from about 11 m (36 ft) at Piers 8 and 9 to 17 m (56 ft) at Pier 4. The cross-sectional area of these shafts is slightly larger than that of the piers to ensure proper transfer of loads to the bearing soil and structural yielding above grade.

GROUND MOTION

Unfortunately, no accelerograms were recorded near the bridge during the main event. The motions used in this study were calculated analytically by Horton and Barstow (1995). Their method is based on a frequency domain back analysis of actual strong motion recordings from the earthquake to infer the slip velocity distribution on a deterministic fault model. The fault model was used to generate a “low-frequency” 0.1 - 3 Hz Fourier band of the three-dimensional motion at a reference location, which was taken to be Abutment 11 (Fig. 1). The bandwidth was then extended to 20 Hz by scaling the spectra of aftershocks recorded at the site by temporary arrays 5 . Spatial variability was introduced in the motions based on the following procedure: (i) the high frequency bandwidth (3 - 20 Hz) was randomized to account for the incoherence effects at the various supports; (ii) a simplified wave propagation model was utilized to account for the time lag in ground motion based on an assumed (apparent) wave velocity of 2000 m/s (6500 ft/sec) along the bridge axis; (iii) the reference motion of Abutment 11 was deconvoluted to generate the motion at the “base-rock” level, which was considered to be located at a depth of 30 m (100 ft); (iv) the rock motion was amplified to obtain the free-field surface motions at the bridge supports. The resulting set of 11 x 3 x 3 = 99 acceleration, velocity and displacement time histories define the ground excitation in our analyses. A typical record is shown in Fig. 2 along with the corresponding response spectra. The peak values of this record, 0.57 g, 87 m/s (285 ft/sec), and 43 cm (17 in), for ground acceleration, velocity, and displacement, respectively, are consistent with those observed in the near-field region (Naeim and Anderson, 1996). The maximum relative displacement between the two abutments (Fig. 3) along the longitudinal axis of the bridge (N-S) is about 10 cm (3.9 in). A summary of ground motion characteristics is given in Table 1. More details can be found in Horton and Barstow (1995).

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Aftershock information was obtained at the site by several agencies during the week following the earthquake for the purpose of quantifying spatial effects (Buckle ed., 1994).


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It is worth mentioning that another seismological study (Hutching and Jarpe, 1996) produced signals with somewhat different characteristics than those of Horton and Barstow (1995), especially regarding the differential displacements along the bridge. Since the above work came to the attention of the authors when this paper was essentially completed, no results based on that study were included herein.

SPATIAL EFFECTS IN GROUND MOTION

Part I: Spectral Evaluation

The response of a bridge to spatially varying ground motion depends on the structural behavior as well as on the complexities of ground motion input. In the case of complicated multi-degree-of-freedom structures as the bridge studied here, the influence of the spatially-varying ground motion on the overall response is difficult to quantify. Systematic studies of the input records are, therefore, necessary before the results obtained from a detailed structural model can be firmly evaluated. To this end, a simple model was employed for this preliminary task: a single-degree-of-freedom (SDOF) rigid bridge deck supported by a number of linear elastic elements (i.e., piers and abutments), excited in the longitudinal direction by ground motions, which are different at each support. With these assumptions, the absolute displacement of the deck, ut(t), can be written as (Clough and Penzien, 1993; Mylonakis and Nikolaou, 1993): n

u t (t ) = ∑ i =1

ki u g ,i (t ) + u d (t ) K

(1)

The first term in the right-hand side of Eq. 1 is the so-called pseudostatic response, which corresponds to the response of the deck if the mass and damping of the structure are set equal to zero, whereas the second term, ud(t), is the additional dynamic response of the system 6 ; ki is the stiffness and ug,i(t) - the ground displacement time history at support i; K denotes the total stiffness of the n

elements supporting the structure (i.e., K = ∑ k i ). i =1

The dynamic response, ud(t), is calculated from the dynamic equilibrium of the structure (Clough and Penzien, 1993): 6

It is worth mentioning that, in the case of uniform ground excitation, the decomposition of response into a “pseudostatic” and a “dynamic” component is equivalent to the traditional partition into a “rigid-body” displacement and a “relative” deformation with respect to the base of the structure.


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n

u d (t ) + 2ζω0 u d (t ) + ω02 u d (t ) = − ∑ i =1

ki u g ,i (t ) K

(2)

where ωo and ξ denote the natural frequency and damping of the structure, respectively. The ratio ki / K lies between 0 and 1 and can be interpreted as a weighting factor (Loh et al, 1982; Mylonakis and Nikolaou, 1993). This factor may be used to define a “weighted average” of the spectral values at the various supports: n

Save (T, ζ ) = ∑ i =1

ki Si (T, ζ ) K

(3)

where Si(T, ξ) represents any desired spectral value at support i. In the particular case of supports with equal stiffnesses, the “effective” input motion at the right hand side of Eq. 2 becomes equal to the average of the individual acceleration records and the excitation becomes independent of the characteristics of the structure. In any case, the response is obtained by considering only three parameters: (i) structural period; (ii) damping ratio; (iii) stiffness distribution among the supports. This makes the above formulation an attractive model for preliminary evaluation of spatial effects. Results from analyses, based on the approach discussed so far, are shown in Fig. 4 and 5. In Fig. 4a, the absolute longitudinal acceleration of the deck is plotted as a function of the structural period. Also plotted in the graph are the weighted average and the envelope of spectral accelerations obtained from the individual records. The comparison reveals that the spectral acceleration due to spatially varying motion is always smaller than the corresponding average of the individual spectra. This can be explained by recalling that time-domain summation of the support motions (Eq. 1 and 2) tends to cancel out components of opposite signs 7 . In contrast, spectral averaging involves only positive numbers (Eq. 3) and, therefore, yields larger response values. This phenomenon becomes more pronounced in the high frequency range (T < 0.1 sec) where the motion is essentially random. In contrast, oscillators with low natural frequencies (T > 0.8 sec) are less sensitive to spatial effects because the time lag in ground motion between the two abutments, dt = 0.121 sec, cannot separate adequately wavelengths with frequencies smaller than about 1 Hz (Horton and Barstow 1995). In the intermediate frequency range (0.1 < T < 0.4 sec), spatial variability in ground motion leads to significantly reduced deck acceleration (of the order of 50% of the weighted spectral average). This frequency window coincides with the frequency range between the first and the third resonance of the soil profiles under the bridge supports (Horton and Barstow, 1995). Therefore, significant 7

This is equivalent to destructive interference of the seismic waves at the “rigid” deck.


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amplitude and phase changes are developed for periods between 0.1 sec and 0.4 sec among the various records; the corresponding waves interfere destructively when reaching the deck and reduce its response. The peak relative displacements between the top and bottom of Pier 2 are plotted in Fig. 5a versus the average and envelope of the individual displacement spectra; the corresponding ratios are plotted in Fig. 5b. The relative displacement, Dj(t), between the top and the base of an arbitrary pier j is calculated by subtracting the ground displacement ug,j(t) from the absolute displacement ut(t):

D j ( t ) = u t ( t ) − u g , j (t )

(4)

Many interesting features are worthy of note in this figure: First, the peak relative displacements of a pier, j , under spatially variable excitation may exceed the envelope of the individual spectral values --- as opposed to the absolute accelerations of the deck, which are always reduced by spatial effects. Clearly, this is due to the presence of the pseudostatic component in Eq. 1. The magnitude of the pseudostatic displacement can be calculated directly from Eq. 1 and 4. For Pier 2 we obtain: n

max D 2 (T → 0) = max ∑ i =1

ki u g ,i (t ) − u g , 2 (t ) ≈ 28mm K

(5)

In the zero frequency limit, the demand in relative displacement is exactly equal to the above pseudostatic component (Fig. 5). This corresponds to an “infinite” increase in drift demand compared to the uniform excitation (recall that for any earthquake record SD(T→0) →0). This is, however, rather misleading since the actual displacement demand at any pier remains finite and equal to the maximum difference of weighted (pseudostatic) displacement of the deck and the displacement at the base of the pier (Eq. 5). Second, in the period range 0.1 < T < 0.4 sec, the increase in drift demand may reach 20% compared to the spectral average (Fig. 5). Third, at large periods (T > 1 sec), the deck structure tends to remain immovable in space. Therefore, the maximum drift at each support becomes equal to the corresponding peak ground displacement, regardless of the spatial effects in the excitation. Part II: Non-Linear Dynamic Analyses

Bridge modeling--To calculate the dynamic response of the bridge, a detailed model of the prototype was generated using the computer platform IDARC-BRIDGE (Reichman and Reinhorn, 1995). The program is capable of analyzing the nonlinear dynamic response of three-dimensional structural configurations by incorporating element models specifically developed to represent the behavior of typical bridge components, such as inelastic concrete


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columns, gap elements, foundation elements, isolators, etc. A brief description of the SR14/I5 bridge model in IDARC-BRIDGE is given in the sequel. More details can be found in a report by the authors (Simeonov et al, 1997). The bridge deck was modeled as a series of three-dimensional elastic beam elements with nodal locations at the end, middle and quarter points of each span, with the exception of Span 2, where 8 nodes were considered. The flexural characteristics of the deck were calculated using beam theory, whereas its torsional stiffness was evaluated based on the theory of thin-walled hollow sections (Hambly, 1976). The small skew of box girder and curvature of the bridge were neglected in the analyses reported herein. The piers were modeled as inelastic beam-column elements. The envelope of hysteretic response at each end of this element type is defined by the monotonic moment-curvature relation for the respective end section. A fiber-element analysis approach utilizing very fine discretization of the cross section was employed to obtain the cracking, yielding and ultimate moments for the most probable magnitude of axial load and the respective curvatures. Straining the extreme fiber in compression to 0.005 was the criterion to indicate that the ultimate curvature and bending moment, which can be sustained by the section, are reached. The tangent stiffness of the element is derived (and updated at each analysis step) from the instantaneous rigidity of its two end sections and a spread plasticity formulation to account for the damage along the member. Strength deterioration and stiffness degradation on unloading and reloading, phenomena inherent to the behavior of reinforced concrete under cyclic loading, are adequately simulated by the hysteretic model. In the current version of the program, multiaxial inelastic effects are calculated by superimposing two uniaxial spread plasticity models of the type developed in IDARC-2D (Valles et al, 1996). The ultimate shear capacity of the bridge columns was assessed by adding the contributions of three shear-resisting mechanisms: (i) shear carried by concrete (aggregate interlock, compression zone shear transfer, etc.); (ii) shear carried by the steel truss; and (iii) shear carried by axial compression provided by gravity and seismic loads, primarily as an increase in the compression-zone shear transfer (Buckle and Friedland, 1995). The ultimate deformation capacity of the piers in Tables 4 and 5 was determined by superimposing the flexural and shear deformation in the ultimate state. See Simeonov et al (1997) for detailed account of column properties, procedures for their derivation and analysis assumptions. Rigid blocks were defined at the pier tops to properly represent their real heights and to account for the vertical distance between the soffit of the deck and its geometric centerline. An attempt was made to consider accurately the geometry of the regions of varying transverse cross-sectional dimension (flares) in the upper part of the piers by defining additional nodes in those regions, typically ending 4.27 m (14 ft) below the soffit of the deck. Depending on the height of each pier, intermediate nodes were specified at half, third or quarter points between the flare ends and the ground. Masses were lumped at all nodal locations taking into account the self weight of the superstructure and piers. Rotational masses and inertial effects due to live loads were neglected.


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The intermediate and abutment expansion joints were modeled through a series of uniaxial “joint-gap” elements, which simulate: (i) the elastic stiffening and subsequent increase of load transfer when collision of adjacent bridge segments occurs (gap closed), and (ii) the elastic-perfectly plastic behavior of the restrainers (gap open). Three such elements were considered at each joint, two at the ends of the deck and one at the center. The flexibility of the bearings and the restraining effect of the shear keys in the transverse direction were also incorporated in the analyses. More modeling details are given in Simeonov et al (1997). Foundation modeling--The flexibility of the single drilled shafts was calculated using the Beam-on-Dynamic-Winkler-Foundation (BDWF) model developed by Mylonakis (1995). The method yields a set of frequency-dependent linear foundation springs and dashpots representing the stiffness, radiation damping and hysteretic energy dissipation of and into the soil. The “cross-terms” between the swaying and rocking vibrations, frequently ignored in approximate methods of analysis, are included in the model. To be compatible with the time-domain framework of the computational platform IDARC-BRIDGE, frequency-independent values were assigned to the foundation impedances corresponding to a frequency of 2.5 Hz (T = 0.4 sec) where the predominant components of the earthquake motion appear. The validity of the approximation stems from the fact that, in low-frequencies, the stiffness and damping coefficients of single pile shafts are essentially frequency-independent (Gazetas and Dobry, 1984). Parametric analyses in the frequency range between 0 and 10 Hz showed variation of stiffness and damping of about 5% or less. The “low-frequency” zone can be approximated by fu = Vs / 20 d, with Vs being the shear wave velocity of the soil and d - an “equivalent” shaft diameter (Gazetas and Dobry, 1984; Mylonakis, 1995). Using Vs = 250 m/s (820 ft/sec), a lower bound of the shear wave velocity accounting for inelastic soil response, and d = 2.5 m (8.2 ft), we obtain fu = 250 / 50 = 5 Hz, which justifies the validity of our approximation for all modes up to 5 Hz. To account in an approximate way for the inelastic behavior of soil around the shafts due to the response of the superstructure, the following procedure was adopted: First, the shear modulus of the near-surface soil was considered equal to approximately ½ of the low-strain value Go(z) (Cole and Vickery, 1984) and increasing linearly to 2/3 Go(z) at a depth of 8 m (26 ft), which corresponds roughly to 2-3 shaft “diameters” below grade. Since the shafts are relatively short [i.e., the length does not exceed the corresponding “active length” (Gazetas and Dobry, 1984)], the soil shear modulus was kept equal to 2/3 Go(z) between the depth of 8 m (26 ft) and the bottom of the shafts. Second, the radiation damping was reduced to ½ of the value calculated for layered soil. This is to account for soil inhomogeneity with horizontal distance from the shafts due to inelastic soil response, randomness of soil properties, installation effects, and other parameters that tend to reduce the radiation of waves away from the foundation.


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It is fair to mention that placing the foundation springs at surface level will not account for potential inelastic response of the reinforced-concrete shaft below grade. Nevertheless, the resulting reduction in foundation stiffness will be compensated, in a somewhat approximate manner, by the generous reduction of the “effective” soil modulus in our analysis. The interaction effects between abutment and soil were represented by independent soil springs, one for each global direction, which account for the stiffness of the backfill and underlying soil. In the absence of reliable research data, the compressional stiffness of the backfill was taken equal to 115000 kN/m per linear meter (200 kips/in per linear foot) of wall, whereas its tensile stiffness was considered zero (Buckle et al, 1986). The contribution of the wing walls to the longitudinal stiffness was neglected. The transversal stiffness of the abutment was modeled by a linear spring, assuming that soil resistance is mobilized by the wing walls only. To account for the flexibility of these walls, the inelastic behavior and the negligible tensile resistance of soil, the number of “effective” walls was reduced from 2 to 1, and the effective stiffness was further decreased by one-third (Buckle et al, 1986). The values of the foundation springs and dashpots are given in Simeonov et al (1997). To further investigate the effects of soil-structure interaction, which is desirable since many of the aforementioned assumptions regarding the compliance of soil entail a degree of uncertainty, two alternative models were developed: (i) a “fixed base” model, in which the bridge columns are fully fixed at ground level (Case 6 in Table 3); (ii) a model where the presence of the abutment was excluded (Case 5 in Table 3). Damping of the soil-structure system--The damping characteristics of the system were represented by a damping matrix having dimensions equal to the total number (i.e., free and restrained) of degrees of freedom of the structure. To derive the matrix, two independent types of damping were considered: (i) distinct sources of damping (the concentrated SSI dashpots at the pier bases); (ii) distributed “inherent” damping in the system. The latter was calculated, considering damping of the Rayleigh type (Clough and Penzien, 1993), by specifying damping ratios in two natural modes of the structure in its initial state. The final damping matrix [C] = [C(t)] is written as:

[C(t )] = α[M ] + β[K(t )] + [CSSI ]

(6)

where α and β are parameters, [M] is the mass matrix of the structure, [K(t)] the stiffness matrix of the structure and [CSSI] stands for concentrated damping due to soil-structure interaction. The time variable, t, appears explicitly in Eq. 6 to denote that stiffness and damping matrices vary during the nonlinear analyses. In the present study, α and β were calculated by assuming 5% equivalent viscous damping for the first and tenth mode of the bridge. Modal characteristics--The first 10 natural periods of the bridge in its elastic state are shown in Table 2. They have been calculated assuming that the


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expansion joints are open with longitudinal constraint provided only by the bearings. The periods of the lowest four modes are 2.58, 1.84, 1.57, and 1.31 sec with the first mode being transversal and the second longitudinal. To get an idea about the importance of soil-structure interaction, the first 10 natural periods of the system are compared with the corresponding values calculated by considering the piers to be completely fixed at ground level (Table 2). The order of the modes is different in the two cases, and the differences in periods appear to be significant. Case studies--Table 3 summarizes the types of dynamic analysis performed in this study. The most complete model of bridge was analyzed in cases 1 through 3 with the three-dimensional seismic excitation being: spatially varying (Case 1); uniform at all supports, based on the “reference” motion at Abutment 11 (Case 2); spatially varying without the vertical component (Case 3). Cases 4 through 6 were selected for investigating the sensitivity of the response of the bridge to excluding from the analysis the influence of certain components or effects such as, longitudinal restrainers (Case 4), abutment stiffness (Case 5), and soil-structure interaction (Case 6). Cases 7 and 8 consider the stress-strain characteristics of bridge material to be linearly elastic. Case 7 includes non-linear pounding and tie effects in the expansion joints, while in Case 8 no kinematic restrictions are imposed in the joints (apart from the transverse constraint due to the shear keys.). In all cases, the models of the SR14/I5 bridge were subjected to uniform or spatial excitation, represented by the motions generated by Horton and Barstow (1995). Parametric results--Time histories of the longitudinal and transversal relative displacements between the top and base (grade level) of Piers 2, 4, 6, 8, and 10 from the most complete analysis case (Case 1) are plotted in Fig. 6. The different response patterns obtained atop the various piers elucidate the complicated dynamic behavior of long multi-span bridge structures. The peak values of relative displacements obtained in all analysis cases are listed in Tables 4 and 5, for the longitudinal and transverse direction, respectively. The corresponding maximum separations in the expansion joints are listed in Table 6. The effects of the spatial variation of the seismic ground motion can be examined by comparing the results of Case 1, which incorporates spatial effects, and Case 2, where uniform ground excitation is applied (Table 4). The differences in the response of the structure between the two cases are minor and no clear trends are apparent. Considering the spatial variation in the ground motion, in some elements the seismic demand increases, whereas in others it decreases or remains the same. In the short Piers 2 and 3, the demand in longitudinal relative displacement increases by approximately 15% [9.9 vs. 8.6 cm (3.9 vs. 3.4 in) in Pier 2] compared to the uniform excitation of Case 2 (Fig. 7). In general, the differences in demand between Cases 1 and 2 do not exceed 20%. The effect of the vertical components of the ground vibration is even smaller as obtained by comparing Cases 1 and 3 in Tables 4, 5, and 6. Although the spread plasticity models used in the analyses (Valles et al, 1996) do not incorporate explicitly the effect of axial load variation with time, the vertical acceleration


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(0.14 g --- see Table 1) is not very large and, therefore, its influence on the inelastic behavior of the structure is expected to be limited. The importance of including the restrainers in the computational models is quantified by comparing Case 4 and Case 1. The presence of the restrainers in Case 1 tends to “even out” the displacements in the expansion joints as compared to Case 4. However, the forces along the piers (not shown here) have the tendency to increase in the restrained portions of the structure. The differences may account for up to 5% in pier drifts and up to 25% in joint movements, as shown in Tables 4, 5 and 6. The effect of soil-structure-interaction (SSI) is studied by comparing the results of Case 1 to Case 6, where the response is calculated assuming the piers to be perfectly fixed at ground level. In the longitudinal direction, SSI seems to be significant only for the stiff first segment of the bridge. Neglecting SSI leads to smaller longitudinal displacement at Pier 2 [6.6 vs. 9.9 cm (2.6 vs. 3.9 in)], as compared to the “complete” analysis of Case 1. The corresponding bending moment at the top of Pier 2 increases from 32800 kNm (24190 k-ft) to 33900 kNm (25000 k-ft), near the ultimate value of about 34500 kNm (24450 k-ft). As expected, the effect of SSI on the longitudinal response of the long piers is small. The response of all segments in the transverse direction is coupled. The displacement response of all piers is invariably smaller due to the stiffening resulting from neglecting SSI. The average reduction in pier displacement is approximately ½, which is consistent with the ratio of spectral values in the transverse direction, 300 mm / 520 mm = 0.58 (12 in / 21 in), calculated using the fundamental periods of Table 2 and Fig. 2b. The influence of modeling the bridge using elastic beam-column elements can be quantified by comparing Cases 7 and 2. The elastic model underestimates the deformations by about 10% in the short piers and up to 45% in the long piers (Table 5). The movement in the expansion joints is either underestimated or overestimated; variation of the order of 10% is customary. The differences between the two analysis cases are more noticeable in the transverse direction (20-45%), where the inelastic behavior is more pronounced (Table 5). The crudest, yet most common, way of modeling bridges in engineering analysis is to use elastic beam-column elements for the entire structure with the neighboring segments of the bridge deck transversely connected but longitudinally disconnected in the expansion joints (Case 8). The model grossly overestimates both the expansion joint movements (Table 6) and the piers drift demands in the longitudinal direction (Table 5). An attempt was made to developed a model capable of predicting the initiation of collapse of the bridge. For this purpose, the inelastic deformation capacity of the piers was determined using a non-linear monotonic push-over analysis. By comparing these capacities to the seismic demands of Case 1 (see Tables 4 and 5), it can be concluded that all piers deform below their ultimate limits in the longitudinal direction. In the transverse direction, the seismic demand of the piers seem to exceed the deformation capacity of Piers 3, 4, and 5. The discrepancy between the calculated seismic demand and the observed failure in the actual


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event may be attributed to inaccuracies in the artificial earthquake records compared to the (unknown) ground motion at the site, as well as to inaccuracies in the computational model. However, careful inspection of the response time histories (Fig. 6) shows that strong vibrations develop in the longitudinal direction before the corresponding peaks in the transverse direction (i.e., at t = 3 sec vs. 5 sec in the longitudinal and transverse directions, respectively). It seems, therefore, that the collapse in the longitudinal direction may have preceded the maximum response in the transverse direction and thus may have “prevented” the out-of-plane collapse of the bridge. To further investigate this possibility, an alternative modeling approach was adopted in Case 5 - the abutment expansion joints were assumed to allow longitudinal movement beyond the available gap of 2.5 cm (1 in). Such modeling would have been valid if: (i) sliding had occurred at the base of the abutment, or (ii) if the sacrificial unit atop the abutment backwall yielded due to the pounding between the abutment and the deck. In such case, the deformation demand at Pier 2 (Table 4, Fig. 8) closely approaches the available deformation capacity of the column first (i.e., before the other piers), thereby possibly initiating failure and collapse of the entire first bridge segment. Since the present analytical model does not include a progressive collapse capability, the response time histories calculated after the hypothesized failure of Pier 2 are not relevant and must be ignored (Case 5). It is clear that, even for this model, the relative movement in the joint gaps did not exceed the available seat length, therefore initiation of collapse due to unseating of the deck, which has been speculated as a potential collapse mechanism (Buckle ed., 1994), seems unlikely. Failure analysis can be extended further by varying parametrically the free height of each pier. For example, the free height of Pier 2, which, based on the “as-built” plans, was considered to be equal to 10 m (33 ft) from grade level to deck, seems to be overestimated (Priestley et al, 1994). Additional factors to be considered are the initial distress of Pier 2, which was not retrofitted after the 1971 San Fernando earthquake that caused other portions of the bridge to collapse, and better estimation of the non-linear interaction between the abutments and the soil.

CONCLUSIONS

1. Simplified spectral analyses can provide useful information for the effects of spatial variability of ground motion on the response of bridge structures and for the effects of different modeling approximations. 2. Based on results from spectral evaluations, the following conclusions may be deduced: (a) The maximum acceleration developed at the bridge deck, considered to be rigid in the longitudinal direction with the gaps at the joints closed, under spatially varying seismic excitation is always smaller than the “weighted average” of the spectral values (SA) of the individual motions at the pier bases; it is therefore smaller than the maximum, but can be larger than the minimum.


(b) The maximum drifts developed at the bridge piers under spatially varying seismic excitation may be larger than the average of the spectral values (SD) of the individual motions at the piers. The drift is non-zero even for very small structural periods because of the presence of the pseudostatic component. This effect may be detrimental for stiff non-ductile bridge systems. (c) For long-period bridges, inertial forces dominate the response and the deck tends to remain immovable in space. Consequently, the maximum drift at each support would be equal to the corresponding peak ground displacement, regardless of spatial variation. 3. Results from analyses of the SR14/I5 southbound bridge for non-uniform seismic excitation did not exhibit clear trends of increase or decrease in seismic demand. The spatial variability of ground motion appears to have lesser impact on the structural response than other modeling factors (ex., soil-structure interaction). This is probably due to the minor spatial variability of the ground motions used in the analyses, which may or may not represent accurately the actual motions. Stronger differential excitations may have more significant influence on the seismic demand. 4. The vertical component of the ground motion does not seem to incur additional damage on the system. This may be attributed to the small maginitude of the vertical motion. It seems, however, that vertical gound excitation may be more important in tall buildings with heavily-loaded columns than in extended structures such as the bridge studied herein. 5. Variations in bridge modeling seems to influence the displacement demand by about 10-20%. Modeling of abutments, however, may alter the longitudinal response by more than 100%. In any case, the influence on force demands would be smaller if inelastic behavior is triggered during the response.

ACKNOWLEDGEMENT

Financial support for this study was provided by the National Center for Earthquake Engineering Resereach (NCEER), Task No. 106-E-2.6.2 and the Federal Highway Administration (FHWA), Contract No. DTFH61-92-C-00106. Their support is gratefully acknowledged.

REFERENCES

1. Buckle, I.G., editor, (1994), “The Northridge, California Earthquake of January 17, 1994: Performance of Highway Bridges”, Report NCEER-94-0008, National Center for Earthquake Engineering Research, Buffalo, New York.


14


2. Buckle, I.G., Mayes, R.L. and Button, M.R., (1986), “Seismic Design and Retrofit Manual for Highway Bridges”, Report No. FHWA-IP-87-6, Federal Highway Administration, Washington DC. 3. Buckle, I.G. and Friedland, I.M., (1995), “Seismic Retrofitting Manual for Highway Bridges”, Report No. FHWA-RD-94-052, Federal Highway Administration, Washington DC. 4. Caltrans, (1994), “The Northridge Earthquake: Post-earthquake Investigation Report”, California Department of Transportation. 5. Clough, R.W. and Penzien, J., “Dynamics of Structures”, Mc-Graw Hill, New York, 1993. 6. Chopra, A.K., “Dynamic of Structures”, Prentice Hall, 1995. 7. Cole, K.A. and Vickery, D.K., (1994), “Shear Wave Velocity Measurements”, Memorandum to State of CA Dept. of Transporation, File No: Route 14/5 Separation and Overhead, Bridge No. 53-2795F. 8. EERI, (1995), “Northridge Earthquake Reconnaissance Report,” Vol. 1, Earthquake Spectra Supplement to Volume 11. 9. Fenves, G.L, Fillipou, F.C., and Sze, D., (1992), “Response of the Durbampton Bridge in the Loma Prieta Earthquake”, Report No. UCB/EERC-92/02, University of California at Berkeley. 10. Gazetas, G., “Soil Dynamic and Earthquake Engineering. Case Studies: Kalamata 1986, Northridge 1994, Kobe 1995, Egion 1994”, Symeon Publ., 1996 (in Greek). 11. Gazetas, G. and Dobry, R., (1984), “Horizontal Response of Piles in Layered Soil”, Journal of Geotech Engng, ASCE, Vol 110, No. 6, 937-956. 12. Goltz, J., editor, (1994), “The Northridge, California Earthquake of January 17, 1994: General Reconnaissance Report”, Report NCEER-94-0005, National Center for Earthquake Engineering Research, Buffalo, New York. 13. Horton, S.P., and Barstow, N., (1996), “Simulation of Ground Motion at I5 / Route 14 Interchange Due to the 1994 Northridge, California Earthquake”, Report NCEER-96-xxxx (in press), National Center for Earthquake Engineering Research, Buffalo, New York. 14. Hambly, E.C., “Bridge Deck Behavior”, 2nd ed., Van Nostrand Reinhold, NY, 1991. 15. Hutchings, L., and Jarpe, J., (1996), “Ground Motion Variability at the Highway 14 and I-5 Interchange in the Northern San Fernando Valley”, BSSA, Vol 86, No 1B, pp 289-299. 16. Imbsen, R.A. and Penzien, J., (1986), “Evaluation of Energy Absorption Characteristics of Highway Bridges under Seismic Conditions. Volume I”, Report No. UCB/EERC-84/17, University of California at Berkeley. 17. Loh, C., Penzien, J., and Tsai, Y.B., (1982), “Engineering Analysis of SMART 1 Array Accelerograms”, Earthq. Engng. Struct. Dyn. 10, 575-591. 18. McGuire, J., Cofer, W.F., Marsh, M.L., and McLean, D.I., (1993), “Analytical Modeling of Spread Footing Foundation for Seismic Analysis of Bridges”, Transportation Research Record, 1447 pp 80-92.


15


19. Moehle, J., editor, (1994), “Preliminary Report on the Seismological and Engineering Aspects of the January 17, 1994 Northridge Earthquake”, Report No. UCB/EERC-94/01, University of California at Berkeley. 20. Maragakis, E.A., Thornton, G., Saiidi, M., and Siddharthan, R., (1989), “A Simple Non-Linear Model for the Investigation of the Effects of the Gap Closure at the Abutment Joints of Short Bridges”, Earthq. Engng. Struct. Dyn. 18, 1163-1178. 21. Mylonakis, G., and Nikolaou, A., (1993), “Variability of Strong Earthquake Motion and its Effects on the Response of Large Structures”, Diploma Thesis, National Technical University of Athens, Greece. 22. Mylonakis, G., (1995), “Contributions to Static and Dynamic Analysis of Piles and Pile-Supported Bridge Piers”, Ph.D. Thesis, State University of New York at Buffalo. 23. Mylonakis, G., Nikolaou, A., and Gazetas, G., (1996), “Soil-Pile-Bridge Seismic Interaction. Kinematic and Inertial Effects. Part I: Soft Soil”, Earthquake Engineering and Structural Dynamics, Vol. 26, No. 3, pp. 337-359. 24. Naeim, F. and Anderson, J.C., (1996), “Design Classification of Horizontal and Vertical Ground Motion (1933-1994)”, Report to U.S. Geological Survey. 25. Priestley, M.J.N., Seible, F., and Uang, C.M., (1994), “The Northridge Earthquake of January 17, 1994: Damage Analysis of Selected Freeway Bridges”, University of California, San Diego, Report No SSRP 94/06. 26. Reichman Y., and Reinhorn A.M., (1995), “Extending the Seismic Life Span of Bridges. Analytical Evaluation of Retrofit Measures”, Structural Engineering Review, No 3, pp 207-218. 27. Reinhorn, A.M, Reichman, Y., Simeonov, V., and Mylonakis, G., (1997), “IDARC-BRIDGE: A Computational Platform for Seismic Damage Assessment of Bridge Structures”, Report NCEER-97-xxxx (under review), National Center for Earthquake Engineering Research, Buffalo, New York. 28. Tseng, W.S. and Penzien, J., (1975), “Seismic Analysis of Long Multiple-Span Highway Bridges”, Earthq. Engng. Struct. Dyn. 4, 1-25. 29. Tseng, W.S. and Penzien, J., (1975), “Seismic Response of Long Multiple-Span Highway Bridges”, Earthq. Engng. Struct. Dyn. 4, 25-48. 30. Simeonov, V., Mylonakis, G., and Reinhorn, A.M., (1997), “Implications of Spatial Variation in Ground motion on the Performance of SR14/I5 Interchange during the Northridge Earthquake”, Report NCEER-97-xxxx (under review), National Center for Earthquake Engineering Research, Buffalo, New York. 31. Shinozuka, M., and Deodatis, G., (1991), “Stochastic Wave Models for Stationary and Homogeneous Seismic Ground Motion”, Structural Safety, Vol. 10, No. 4, pp. 191-204. 32. Wilson, J.C., and Jennings, P.C., (1986), “Spatial Variation of Ground Motion Determined from Accelerograms Recorded on a Highway Bridge”, Bulletin Seism. Soc. Am. 75, 1515-1533. 33. Yegian, M.K. et al, (1995), “The Northridge Earthquake of 1994: Ground Motion and Geotechnical Aspects”, Proc. 3rd Inst. Conf. on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, Vol. III, 1383 – 1389.


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34. Valles, R.E, Reinhorn, A.M., Kunnath, S.K., Li, C., and Madan, A., (1996), “IDARC2D Version 4.0: A Computer Program for the Inelastic Damage Analysis of Buildings”, Technical Report NCEER-96-0010, National Center for Earthquake Engineering Research, Buffalo, New York.


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Table 1—Summary of Ground Motion Characteristics Component Maximum Average of Maxima Value Peak Ground Acceleration (m/s2) Longitudinal 5.70 (A1) 4.66 Transverse 5.47 (A1) 4.84 Vertical 1.63 (P3) 1.37 Peak Ground Velocity (m/s) Longitudinal 0.83 (A1) 0.82 Transverse 0.87 (A11) 0.83 Vertical 0.19 (P8) 0.17 Peak Rel. Ground Displacement (m) Longitudinal 0.100 (A1-A11) Transverse 0.080 (A1-A11) Vertical 0.017 (A1-A11)

Table 2--Elastic Modal Characteristics of the SR14/I5 Bridge Mode Period / Description Period / Description (with SSI) (no SSI) 1 2.58 Transverse 1.51 Transverse 2 1.84 Long. (Seg. 3) 1.45 Long. (Seg. 3) 3 1.57 Transverse II 1.08 Long. (Seg. 3, 4, 5) 4 1.31 Long. (Seg. 3, 4, 5) 0.97 Transverse II 5 1.20 Long. (Seg. 1) 0.89 Long. (Seg. 3, 4, 5) II 6 1.05 Transverse III 0.67 Vert. (Seg. 1) 7 1.02 Long. (Seg. 3, 4, 5) II 0.66 Transverse III 8 0.91 Transverse IV 0.61 Long. (Seg. 1, 2) 9 0.78 Long. (Seg. 2) 0.61 Long. (Seg. 1, 2, 3) 10 0.69 Vert. (Seg. 1) 0.57 Vert. (Seg. 3)


18


Case

1

Table 3--Case Studies Structural Modeling Approximations Full modeling

Ground Excitation Spatially varying

2

Full modeling

Uniform

3

Full modeling

No vertical component

4

No longitudinal restrainers

Spatially varying

5

No longitudinal abutment stiffness No SSI

Spatially varying

Elastic structure (with non-linear gap elements) Elastic structure (without gap elements)

Uniform

6 7 8

Spatially varying

Uniform

Table 4:Relative Longitudinal Displacement between Pier Top and Bottom Analysis P2 P3 P4 P5 P6 P7 P8 P9 P10 Case [m] [m] [m] [m] [m] [m] [m] [m] [m] Case 1 0.099 0.095 0.115 0.115 0.107 0.100 0.087 0.089 0.084 Case 2 0.086 0.088 0.110 0.110 0.097 0.093 0.083 0.082 0.100 Case 3 0.099 0.095 0.116 0.116 0.108 0.100 0.087 0.088 0.083 Case 4 0.104 0.100 0.117 0.117 0.112 0.103 0.078 0.078 0.081 Case 5 0.165 0.170 0.229 0.225 0.245 0.258 0.242 0.249 0.280 Case 6 0.066 0.056 0.110 0.111 0.134 0.119 0.112 0.109 0.106 Case 7 0.079 0.081 0.104 0.105 0.097 0.096 0.087 0.086 0.096 Case 8 0.185 0.192 0.123 0.125 0.665 0.306 0.277 0.288 0.296 Capacity 0.171 0.178 0.476 0.509 1.070 2.140 1.250 1.350 0.410


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Table 5--Relative Transverse Displacement between Pier Top and Bottom Analysis P2 P3 P4 P5 P6 P7 P8 P9 P10 Case [m] [m] [m] [m] [m] [m] [m] [m] [m] Case 1 0.086 0.235 0.366 0.274 0.400 0.631 0.433 0.397 0.196 Case 2 0.084 0.223 0.377 0.274 0.398 0.632 0.401 0.357 0.162 Case 3 0.086 0.235 0.366 0.274 0.400 0.631 0.434 0.398 0.197 Case 4 0.085 0.230 0.368 0.281 0.408 0.670 0.494 0.403 0.190 Case 5 0.073 0.209 0.376 0.353 0.392 0.674 0.441 0.313 0.149 Case 6 0.039 0.061 0.094 0.101 0.237 0.362 0.263 0.179 0.069 Case 7 0.092 0.185 0.261 0.203 0.274 0.527 0.341 0.271 0.129 Case 8 0.088 0.185 0.280 0.241 0.332 0.674 0.485 0.334 0.143 Capacity 0.183 0.175 0.238 0.246 0.755 1.820 1.210 1.110 0.225

Table 6--Relative Opening of the Expansion Joints Analysis A1 P4 P5 P7 P9 A11 Case [m] [m] [m] [m] [m] [m] Case 1 0.170 0.031 0.032 0.048 0.050 0.095 Case 2 0.154 0.036 0.032 0.057 0.042 0.131 Case 3 0.170 0.031 0.032 0.047 0.052 0.094 Case 4 0.177 0.031 0.049 0.062 0.048 0.091 Case 5 0.252 0.068 0.066 0.064 0.046 0.292 Case 6 0.060 0.066 0.055 0.054 0.066 0.108 Case 7 0.146 0.040 0.032 0.052 0.051 0.127 Case 8 0.315 0.328 0.781 0.751 0.165 0.339 Capacity 0.360 0.360 0.360 0.360 0.360 0.360


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Fig. 1--SR14/I5 Southbound Separation and Overhead Bridge


(a)

(b)

0.6

0.6

acceleration : g

0.0 -0.3

-0.3 0.50

-0.6

250

500

0

0

-250

-500

-500 0

2

4

6

8

500

displacement : mm

1000 displacement velocity

velocity : m / s

500

displacement : mm

0.0

-1000 10

1000 displacement velocity

250 0

0

-250

-500

-500 0

2

4

time : s 1000

0

0 2

period : s

3

4

PSA : g

500 1

SD : mm

PSA : g

-1000 10

1000 5 % damping

spectral acceleration spectral displacement

1

8

3

5 % damping

0

6

time : s

3

2

500

velocity : m / s

-0.6

0.3

spectral acceleration spectral displacement

2

500 1

0

0 0

1

2

3

4

period : s

Fig. 2--Reference Motions at Abutment 11 and Corresponding 5% Damped Response Spectra: (a) Longitudinal (N-S) Direction, (b) Transverse (E-W) Direction

SD : mm

acceleration : g

0.44

0.3


relative displacement : m

0.10

longitudinal 0.05

vertical 0.00

-0.05 transverse

-0.10 0

2

4

6

8

10

time : s

Fig. 3--Differential Displacements between Abutments A1 and A11


23

deck absolute acceleration : g


3 spatially varying motion weighted average of individual spectra envelope of individual spectra 2

1

(a)

0 0.0

0.5

1.0

1.5

2.0

base shear ratio

1.0

PSAspv / PSAave PSAspv / PSAenv 0.5

(b) 0.0 0.0

0.5

1.0

1.5

2.0

period : s

Fig. 4--(a) Absolute Longitudinal Acceleration Spectra (ζ = 5%), (b) Ratios between Spectral Values Expressing the Differences in Base Shear


24

deck - pier base relative displacement : mm


500 spatially varying motion weighted average of individual spectra envelope of individual spectra

400 300

200

100

28

(a)

0 0.0

0.5

1.0

1.5

2.0

2.0 SDspv / SDave SDspv / SDenv

drift ratio

1.5

1.0

0.5

(b) 0.0 0.0

0.5

1.0

1.5

2.0

period : s

Fig. 5--(a) Longitudinal Deck-Pier-Base Relative Displacement Spectra at Pier 2 (ζ = 5%), (b) Ratios between Spectral Values Expressing the Differences in Drift Demand


25

displacement : m

displacement : m

displacement : m

displacement : m displacement : m


0.2

PIER 2, Long

0.6

0.1

0.3

0.0

0.0

-0.1

-0.3

-0.2

-0.6

0.2

PIER 4, Long

0.6

0.1

0.3

0.0

0.0

-0.1

-0.3

-0.2

-0.6

0.2

PIER 6, Long

0.3

0.0

0.0

-0.1

-0.3

-0.2

-0.6 PIER 8, Long

0.3

0.0

0.0

-0.1

-0.3

-0.2

-0.6 PIER 10, Long

PIER 8, Trans

0.6

0.1

0.3

0.0

0.0

-0.1

-0.3

-0.2

PIER 6, Trans

0.6

0.1

0.2

PIER 4, Trans

0.6

0.1

0.2

PIER 2, Trans

PIER 10, Trans

-0.6 0

2

4

6

time : s

8

10

0

2

4

6

8

10

time : s

Fig. 6--Time Histories of Relative Displacements between Pier Top and Base for Selected Bridge Piers Using Differential Ground Excitation (Case 1)


26

displacement : m

displacement : m

displacement : m



0.2

PIER 2, Long

0.6

0.1

0.3

0.0

0.0

-0.1

-0.3

-0.2

-0.6

0.2

PIER 4, Long

0.6

0.1

0.3

0.0

0.0

-0.1

-0.3

-0.2

-0.6

0.2

PIER 6, Long

0.3

0.0

0.0

-0.1

-0.3

-0.2

-0.6 PIER 8, Long

0.3

0.0

0.0

-0.1

-0.3

-0.2

-0.6 PIER 10, Long

PIER 8, Trans

0.6

0.1

0.3

0.0

0.0

-0.1

-0.3

-0.2

PIER 6, Trans

0.6

0.1

0.2

PIER 4, Trans

0.6

0.1

0.2

PIER 2, Trans

PIER 10, Trans

-0.6 0

2

4

6

time : s

8

10

0

2

4

6

8

10

time : s

Fig. 7--Time Histories of Relative Displacements between Pier Top and Base for Selected Bridge Piers Using the Motions at Abutment 11 as Uniform Ground Excitation (Case 2)


27

displacement : m

displacement : m

displacement : m



0.30

PIER 2, Long

0.6

0.15

0.3

0.00

0.0

-0.15

-0.3

-0.30

-0.6

0.30

PIER 4, Long

0.6

0.15

0.3

0.00

0.0

-0.15

-0.3

-0.30

-0.6

0.30

PIER 6, Long

0.3

0.00

0.0

-0.15

-0.3

-0.30

-0.6 PIER 8, Long

0.3

0.00

0.0

-0.15

-0.3

-0.30

-0.6 PIER 10, Long

PIER 8, Trans

0.6

0.15

0.3

0.00

0.0

-0.15

-0.3

-0.30

PIER 6, Trans

0.6

0.15

0.30

PIER 4, Trans

0.6

0.15

0.30

PIER 2, Trans

PIER 10, Trans

-0.6 0

2

4

6

time : s

8

10

0

2

4

6

8

10

time : s

Fig. 8--Time Histories of Relative Displacements between Pier Top and Base for Selected Bridge Piers Using Differential Ground Excitation and without the Longitudinal Stiffness of the Abutments (Case 5)


28


Keywords: Northridge earthquake, SR14/I5 intersection, spatial variation, multiple-support excitation, bridge, pier, abutment, modeling, soil-structure interaction, expansion joint.


29


List of Illustrations Fig. 1--SR14/I5 Southbound Separation and Overhead Bridge Fig. 2--Reference Motions at Abutment 11 and Corresponding 5% Damped Response Spectra: (a) Longitudinal (N-S) Direction, (b) Transverse (E-W) Direction Fig. 3--Differential Displacements between Abutments A1 and A11 Fig. 4--(a) Absolute Longitudinal Acceleration Spectra (ζ = 5%), (b) Ratios between Spectral Values Expressing the Differences in Base Shear Fig. 5--(a) Longitudinal Deck-Pier-Base Relative Displacement Spectra at Pier 2 (ζ = 5%), (b) Ratios between Spectral Values Expressing the Differences in Drift Demand Fig. 6--Time Histories of Relative Displacements between Pier Top and Base for Selected Bridge Piers Using Differential Ground Excitation (Case 1) Fig. 7--Time Histories of Relative Displacements between Pier Top and Base for Selected Bridge Piers Using the Motions at Abutment 11 as Uniform Ground Excitation (Case 2) Fig. 8--Time Histories of Relative Displacements between Pier Top and Base for Selected Bridge Piers Using Differential Ground Excitation and without the Longitudinal Stiffness of the Abutments (Case 5)


30