Computational studies on the seismic response of the State Route 99 bridge in Seattle with SMA/ECC plastic hinges

Abstract

This paper reports a computational study on the seismic response of a three-span highway bridge system incorporating conventional and novel substructure details for improved seismic performance. The bridge has three continuous spans supported by two single-column piers and integral abutments founded on drilled shafts. It will be the first full-scale highway bridge to use superelastic shape memory alloy bars (SMA) and engineered cementitious composite (ECC) to mitigate column plastic hinge damage and minimize residual displacements after a strong earthquake. A three-dimensional computational model capturing the nonlinear constitutive response of the novel materials and the effects of dynamic soil-structure interaction was developed to assess the seismic response of the bridge in finite-element software OpenSees. Two versions of the same bridge were analyzed and compared, one with conventional cast-in-place reinforced concrete columns, and the other with top plastic hinges incorporating Nickel-Titanium (NiTi) SMA reinforcing bars and ECC. The novel SMA/ECC plastic hinges were found to substantially reduce damage and post-earthquake residual displacements in the bridge substructure, but led to larger maximum drifts relative to the bridge with conventional reinforced concrete plastic hinges. The analysis results suggested that the novel plastic hinges could lead to improved post-earthquake serviceability of bridges after intense earthquakes.

Keywords

seismic design / analytical simulation / near-fault earthquakes / shape memory alloy / engineered cementitious composite / self-centering

Introduction

The primary performance objective of ordinary reinforced concrete (RC) bridges complying with modern seismic design guidelines is to prevent collapse under strong earthquakes. Since designing bridges to remain elastic is impractical and cost-prohibitive, bridge substructures are typically detailed to dissipate energy through repeated yielding and plastic deformations in the steel reinforcement which generally lead to permanent tilting of the bridge columns after the earthquake. The large strains experienced in the plastic hinge regions of the column cause extensive concrete cracking and spalling, both of which require extensive repairs to be made after the earthquake. The extent of damage and large permanent drifts seen after past strong earthquakes show that although the design objective of preventing collapse can be met, bridges are likely to be rendered inoperative for safety and damage assessment, repair, or demolition after a strong earthquake. After the 1995 Kobe, Japan earthquake, for example, about 100 bridge columns had to be demolished and rebuilt because the permanent drift exceeded 1.75% and it was not feasible to return the superstructures to their original upright position [¹]. A new paradigm is emerging among bridge owners, who desire bridges that are able to remain in service after extreme events, preventing disruption to traffic and minimizing economic losses [²–⁴].

To maintain functionality after a strong earthquake, a bridge system must be capable of accommodating the earthquake demands while experiencing minimal damage in the plastic hinges and re-centering after the earthquake. Previous research has shown that superelastic shape memory alloy (SMA) bars combined with engineered cementitious composite (ECC) substantially reduce permanent drifts and the extent of apparent damage. ECC is a high-performance fiber-reinforced cementitious material that exhibits high tensile strength and strain-hardening. Polyvinil Alcohol (PVA) fibers in combination with special admixtures allow ECC to develop multiple fine cracks when subjected to tensile loading, thus providing ECC with a self-confining mechanism that prevents spalling even under high compressive strains [⁵–⁷]. On the other hand, superelastic SMAs are materials that have the unique ability to return to their initial shape with essentially zero permanent strain when the applied stress is removed. This property is due to the flag-shaped stress-strain hysteresis of superelastic SMAs, which provides an effective source of re-centering to structural elements subjected to earthquakes [⁸].

Wang [⁹] and Saiidi and Wang [¹⁰] were the first researchers to utilize SMA bars as longitudinal reinforcement in RC bridge column plastic hinges. Through shake-table studies on bridge column models they demonstrated that SMA and ECC substantially reduced permanent drifts and plastic hinge damage, respectively. The work by Saiidi et al. [¹¹] showed that a high ductility and damage-tolerant material such as ECC had to be used along with SMA because conventional confined concrete cannot accommodate the high strain capacity of SMA. Other researchers have arrived at similar conclusions regarding the superior performance of ECC and SMA for bridge column plastic hinges in high seismic areas through a variety of experimental programs [²–⁴,⁶,⁷]. Note that there are many types of SMA alloys. Nickel-Titanium (NiTi) SMA has received increased attention because of its capacity to recover large strains, high energy dissipation, excellent low- and high-cycle fatigue properties, and corrosion resistance [⁸]. Although this study focuses only on NiTi SMA, recent publications have reported the potential of other emerging alloys for seismic bridge applications [¹²,¹³].

The potential adoption of SMA and ECC in the bridge design practice requires that the structural performance of these novel materials and details be predictable and well understood, while being demonstrated through extensive testing and analysis. Previous large-scale experimental seismic studies on bridge systems [²,⁶,⁷,¹⁴] have shown the effectiveness of NiTi SMA and ECC as part of an actual bridge structure, while providing insight that goes beyond the observations that can be drawn from work at the structural component level. However, the development of proper computational analysis tools is also crucial to perform parametric studies and assess the response of structural details and systems under conditions beyond those that can be tested in the laboratory. These tools, along with field experience and documented performance under actual earthquakes over time, are needed to develop sound and reliable design provisions that generate confidence among bridge owners and designers and that lead to safe and cost-effective bridges that protect the safety and welfare of the public.

A few authors have conducted computational studies contributing to understanding the seismic behavior of bridge columns and systems with SMA and ECC. Cruz Noguez [²] evaluated the seismic performance of a 4-span bridge system incorporating SMA/ECC and built-in rubber pad plastic hinges as well as post-tensioned piers. Varela and Saiidi [³] and Varela [⁴] performed analytical modeling to study the seismic response of novel deconstructible bridge columns for seismic resiliency. Tazarv and Saiidi [¹⁵] investigated the performance of bridge columns with SMA instead of conventional reinforcing steel to mitigate residual displacements. Billah and Alam developed fragility-based seismic vulnerability assessments for a SMA-RC bridge pier [¹⁶,¹⁷] and performance-based damage states for SMA-RC bridge piers [¹⁸]. Shrestha and Hao [¹⁹] presented numerical investigations on the performance of SMA-RC bridge bents to monotonic and seismic loadings.

These studies have been limited to individual substructure systems or relatively simple bridges neglecting the effects of soil-structure interaction. Depending on the characteristics of a given bridge system, the peculiarities of the ground motion, and those of the soil in which the bridge is founded, soil-structure interaction may play a key role on the seismic performance of the structure that must be accounted for during analysis and design. The stiffness, strength, and damping characteristics of the foundation soil at bents and abutments may significantly alter the frequency and amplitude properties of the input ground motion relative to those of the same motion measured on rock and the nonlinear lateral stiffness of the soil affects the maximum displacements and internal forces experienced by a bridge structure. A proper analytical model that provides a realistic view of the seismic response of a bridge must explicitly incorporate the effect of nonlinear soil-structure interaction if these are expected to be dominant.

SMA and ECC are being used, for the first time in an actual highway bridge, by the Washington State Department of Transportation (WashDOT) in the construction of the state route (SR) 99 off-ramp bridge in Seattle, Washington that is part of the Alaskan Way Viaduct replacement program. The construction of this novel bridge is a demonstration project funded by the United States Federal Highway Administration (FHWA) aimed at showcasing the improved performance and post-earthquake serviceability provided by SMA and ECC. Because of the soil conditions and column detailing, the columns in each pier are pinned at the base and have a moment connection at the top incorporating SMA bars and ECC designed for plastic hinging. Given the unique aspects of these columns, an experimental and analytical study was conducted by Nakashoji and Saiidi in 2014 [²⁰] to assess their seismic performance and provide design recommendations to be used by WashDOT. The study by Nakashoji and Saiidi [²⁰], however, focused on the behavior at the component level and did not comprise an analytical investigation of the SR99 bridge at the system level.

The present study was aimed to analytically investigate the seismic response of computational three-span bridge models with conventional and novel materials with the purpose of understanding how the individual bridge components interact within a bridge system. The main objective was to assess the effect of utilizing novel materials to reduce damage and residual displacements in the column plastic hinges under strong earthquakes and compare it to the damage and residual displacements of bridges with conventional concrete columns.

Bridge description

The SR-99 Alaskan Way Viaduct south access connection bridge is a three-span continuous box-girder structure with two single-column piers founded on oversized drilled shafts and integral abutments at the ends, as shown in Fig. 1. The superstructure consists of two 6 ft. (1.83 m) deep precast spliced girders with trapezoidal tub girder section U72PTG6, spaced 15.25 ft (4.65 m) on center with an 8 in (20.32 cm) thick cast-in-place concrete slab. The overall bridge width is 30.5 ft (9.30 m) and the bridge has two AASHTO design lanes 12 ft (3.66 m) wide each. The piers are constructed from 6 ft (1.83 m) deep by 7 ft (2.13 m) wide integral cap beams supported by single 5 ft by 5 ft (1.52 m by 1.52 m) square CIP columns. The height of piers 2 and 3, measured from the top of the drilled shaft to the soffit of the box girder is 16.98 ft (5.18 m) and 19.25 ft (5.87 m), respectively. The column cross section is square with longitudinal reinforcement placed in a circular pattern enclosed by hoops, forming a circular core, as shown in Fig. 2. Additional longitudinal and transverse reinforcement is provided for anarchitectural finish at the corners.

The columns have a moment connection at the top designed for plastic hinging consisting of 30-#10 (30-Ø32mm) SMA bars, for a longitudinal reinforcement ratio of 1.04% relative to the gross square column section. The SMA bars are connected to 30-#10 Gr. 60 (420 MPa yield strength) mild steel reinforcing bars using up-set headed couplers. The couplers are stronger than the bars and they force failure in the bars rather than the coupler. The SMA bars are used only at the top plastic hinges because preliminary analysis by the bridge designers indicated that top plastic hinges would develop prior to the bottom plastic hinges while the foundation soil provided minimal rotational restraint. The length of the SMA bars is 4 ft (1.22 m), measured from the column-girder interface to the bottom of the couplers. ECC is used over the upper 5 ft (100% of the column side dimension) of the column clear height. The transverse reinforcement consists of #8 (Ø25mm) butt-welded hoops spaced at 4 in (0.102 m) for a transverse reinforcement ratio of 1.43%. Each column is supported by a single 8 ft (2.44 m) diameter CIP drilled shaft. The abutments are supported by two identical 6.5 ft (1.98 m) diameter drilled shafts, spaced 20 ft (6.10 m) on centers. Based on the subsurface information encountered in the geotechnical studies for the site, the elevated structure and approaches are underlain by approximately 100 ft (30 m) of fill deposits, estuarine-alluvial transitional deposits and beach deposits. Hence, the bridge will be founded on site class F soil per the AASHTO LRFD Bridge Design Specifications [²¹]. Site class F is defined as one in which there are peats or highly organic clays, very high plasticity clays, and very thick soft/medium clays, requiring a site-specific evaluation.

Computational study

Model description

Two models of the SR99 bridge were developed and analyzed in finite element software OpenSees [²²], which offers a wide selection of nonlinear models for materials and elements. One bridge model incorporated conventional CIP concrete columns with mild steel longitudinal reinforcement (referred to as RC hereafter) and the other used SMA bars in the plastic hinge region and ECC over the upper 5 ft of the column clear height (referred to as SMA/ECC). Although the SR99 bridge has integral abutments, seat-type abutments were assumed throughout this study to maximize the displacement demands on the columns. A global view of the analytical model is shown in Fig. 3, where it is seen that the global X-axis was oriented along the longitudinal direction of the bridge, the global Y-axis was along the transverse direction, and the Z-axis was vertical. The bridge superstructure was modelled as a 3-dimensional spine with four elastic frame elements for the outer spans and six elements for the inner span. The superstructure was connected to the columns at each pier through an assemblage of rigid link elements representing the rigid end offsets of the column within the superstructure. Since OpenSees does not have the option to create a fiber section comprised of a circular mesh placed inside a square, the fiber sections for the columns were created in sectional analysis software XTRACT [²³] and then imported into OpenSees. Figure 4 shows the discretization of the fiber sections utilized.

Material properties

Based on the studies by Varela and Saiidi [³,¹²–¹⁴] and Tazarv and Saiidi [¹⁵], the ‘Concrete02’ uniaxial material model was used for confined and unconfined ECC. The ‘ReinforcingSteel’ uniaxial material model was used to represent the behavior of mild steel reinforcement in the plastic hinges of the SR99-RC columns and the inelastic portions of the SR99-SMA columns below the top plastic hinges. This model was selected because it can adequately capture the cyclic strength and stiffness degradation of steel reinforcement due to cyclic loading. The ‘SelfCentering’ material model was used to simulate the flag-shaped stress-strain hysteresis response of NiTi SMA, after the findings of Varela and Saiidi [³,¹²–¹⁴] and Tazarv and Saiidi [¹⁵,²⁴]. A summary of the nonlinear parameters for all material models are listed in Table 1. The reader is referred to the OpenSees online documentation for further information on nonlinear material model formulation and limitations [²²].

Modeling of abutment backfill

The lateral passive stiffness and force capacity provided by the soil in abutment backfills and within foundations can have a significant influence in the static and dynamic response of a bridge. This lateral force-displacement relationship has been found to be adequately captured by bi-linear or other higher-order nonlinear models [²⁵,²⁶]. The full passive resistance in soils behind abutment backwalls is usually mobilized due to the large longitudinal superstructure displacements associated with strong earthquake ground motions. Therefore, abutments may resist a significant portion of the seismic forces in the longitudinal direction of a bridge and their influence must be accounted for to properly simulate the seismic response of bridge systems. The earth passive force was calculated as:

(1)P_p=p_p{h}_w{w}_w,

where P_p= 5.45 ksf (261 kPa) is the passive lateral earth pressure behind the abutment backwall, h_p= 6 ft (1.83 m) and w_w= 21.25 ft (6.48 m) are the height and width of the backwall, respectively. The passive lateral earth pressure was calculated as \frac{{5h}_w}{5.5} (ksf), per recommendations in the California Department of Transportation (Caltrans) Seismic Design Criteria [²⁷]. The total passive force provided by the abutment backfill was estimated at 695.5 kips (3094 kN). The initial stiffness of the abutment backfill was calculated as:

(2)K_{eff}={\displaystyle \frac{P_p}{(F_w{H}_w+D_g)}},

where F_w is a factor that ranges from 0.01 to 0.05 for dense sand to compacted clays, and in this case was assumed to be 0.02 [²¹]. D_g is the width of the gap between the backwall and the superstructure, which was taken as 2 in (5.08 cm). The initial stiffness was estimated at 202 kips/in (35,375 kN/m). The passive resistance of the abutment backfill backwall resistance was modeled through an elasto-plastic spring based on the initial stiffness and yield force computed from the passive soil force. Abutment backfills can only engage in compression. Hence, during an earthquake only one abutment provides resistance, while the other engages when the seismic motion direction is reversed. Since the abutments were modelled with springs than resist both tension and compression, one-half of the soil stiffness was assigned to the spring in each abutment, thereby simulating the equivalent net effect of the passive soil resistance behind the backwalls. Wingwall effects were neglected for simplicity and because their influence relative to the other resisting elements was minimal.

Modeling of soil springs and soil-pile interaction

Just like abutment backfills, the soil surrounding foundation elements plays an important role in the seismic response of bridge systems. The soil in contact with the drilled shafts was modelled by 40 uniaxial compression-only zero-length springs and “PySimple1” elements spaced at 2.5 ft (0.76 m) along the length of the shafts. To calculate the soil spring properties, a separate p-y nonlinear lateral load analysis was performed in OpenSees, considering the nonlinear lateral moment-displacement behavior of the drilled shafts embedded in the soil.

Bond-slip model

Slippage of reinforcing bars relative to the surrounding concrete when stressed under tensile forces is known as bond-slip effect or strain penetration and it affects the local and global response of RC members. The cumulative strain difference between the bar and concrete causes a slip at the loaded end of an anchored bar. Consequently, a crack forms at the predominant crack location, which coincides with the transverse cross-section of maximum flexure usually located at the end of a structural member. An end rotation occurs because of the crack, which adds to the flexural rotation and displacement of the member. Studies have indicated that bond-slip rotation at the column-footing interface can account for as much as 15% to 20% of the lateral displacement of a bridge column [²⁸]. Thus, it is critical to account for bond-slip when developing analytical models of RC structures.

The mild steel bars were modeled in the zero-length section using the Bond_SP01 material from the OpenSees library [²²]. The bond slip effect was not included in the SR99-SMA/ECC model because the SMA bars are smooth and the headed couplers act as mechanical anchors at a shallow depth within the cap beam. Neglecting bond slip for SMA-reinforced plastic hinges with mechanical connections to mild steel bars has been found to be appropriate based on previous experimental and analytical studies [³,⁴,¹²–¹⁵,²⁴]. Note that slippage effects within the mechanical connections were neglected as they are often negligible relative to the other sources of displacement in the column.

Selection of input ground motions

WashDOT provided three representative unscaled ground motions that were selected based on the soil conditions and tectonic environment of the site. The motions were the Tabas station record from the 1978 Tabas, Iran earthquake, the TCU052 station record from the 1999 Chi Chi Taiwan, China, earthquake, and the Pacoima Dam downstream station record from the 1994 Northridge, California earthquake. These motions were referred to as the ‘design’ suite of ground motions.

Previous earthquakes such as Landers and Erzincan in 1992, Northridge, California in 1994, Kobe, Japan in 1995, and Chi Chi, Taiwan China in 1999 have demonstrated that near-fault ground motions can cause severe damage and permanent displacement in concrete bridges. Near-fault ground motions differ from ordinary ground motions in that they contain a sudden, high ground velocity pulse and lead to permanent ground displacements. The fault-normal component of the Rinaldi Receiving Station 228 record from the 1994 Northridge, California earthquake and the Takatori station record from the 1995 Kobe, Japan earthquake, which are near-fault ground motions, were added to the suite of analysis motions to subject the bridge to large displacement demands and maximize the possibility of large permanent displacements. These motions were referred to as the ‘strong’ ground motions. Figure 5 shows a comparison among the response spectra of the ground motions selected and the target site-specific design response spectra. The properties of each ground motion are listed in Table 2.

Calculated seismic response

Two series of analyses were conducted. First, displacement-controlled cyclic load analyses of individual columns were carried out to assess the overall response of each pier and fine-tune the configuration of nonlinear elements and sections prior to dynamic analysis, which is comparatively more time-consuming, thereby hindering refinement. These were followed by response history analyses of the SR99-RC and SR99-SMA/ECC bridge models.

Cyclic load analysis of single columns

Two individual columns were first analyzed under cyclic loading, each one incorporating either conventional RC or SMA/ECC plastic hinges. The objective was to investigate the influence of novel materials in the lateral response of the columns without the effect of other bridge components, thus, the base of the column in both cases was restrained using a fixed support. The columns were modeled as cantilevered members. The height of the column was taken as the vertical distance from the centroid of the box girder to the top of the drilled shaft. An assemblage of five displacement-based distributed plasticity elements each with five Gauss-Lobatto integration points and nonlinear fiber sections was used to represent each column. Cyclic load analysis was conducted by first applying the full tributary axial load for each column, which was estimated at 1556 kips (6921 kN), and then the target lateral displacement for each cycle was incremented by ±1 in (0.0254 m) until failure. Failure was assumed to occur when there was a significant drop in the calculated moment capacity due to rupture of any of the longitudinal bars.

Transverse drift ratios were calculated by dividing the measured transverse displacement at the top of the column by the column height. Residual displacements from quasi-static cyclic analysis provide a general indication of the ability of a column to recenter following inelastic deformations. The residual displacement was taken as that in which the column crossed the zero-force axis. For comparison purposes, the residual displacement measured on the unloading path from the peak displacement was defined as the quasi-static residual displacement for each displacement cycle.

The moment-drift hysteresis curves of the two columns are shown in Fig. 6(a) and the stress-strain hysteresis behavior at a control point in one of the reinforcing fibers is shown in Fig. 6(b). Because the area enclosed by the mild steel hysteresis is larger than that of SMA, as seen in Fig. 6(b), the RC column dissipated more energy relative to the SMA/ECC column, as seen in Fig. 6(a). However, it is seen that the SMA/ECC column was more flexible due to the lower elastic moduli of SMA and ECC relative to steel and concrete, respectively. As intended, the SMA/ECC column had lower residual displacements due to the superelastic effect of SMA, and the unloading path from the point of maximum displacement essentially returned to the origin.

Abutment effects

The seismic response of a bridge can be very sensitive to boundary conditions particularly in short bridges. In the transverse direction of a bridge, abutment shear keys are typically used to provide rigidity under service loads and small to moderate earthquake motions, but shear keys are designed to fail under strong earthquakes to avoid overloading the abutments, which are capacity-protected components. There are many ways to incorporate shear key effects in computational bridge models. Two extreme cases for the role of shear keys were considered in this study. In case 1, vertical roller supports were assumed allowing free transverse displacement of the bridge at the abutments. This would represent the case of a bridge under strong ground motions following failure of the shear keys. In case 2, it was assumed that the abutment shear keys were intact and acted as horizontal roller supports restraining superstructure displacements along the transverse direction of the bridge.

Eigenvalue analyses were performed to obtain the dynamic properties (natural frequencies and mode shapes) of the bridge models. Since the bridge transverse displacements are expected to exceed longitudinal displacements, only the mode shapes and periods in the transverse direction were determined. Modal analyses revealed that for case 1, the bridge superstructure responded primarily with displacement along the transverse direction with no interaction with the abutments, which exercised the bents in flexure. For case 2, the abutments were fully restrained and attracted part of the lateral forces, which decreased the displacement demands at the bents.

The periods in the transverse direction for the first four modes were calculated as listed in Table 3. The periods of pinned condition are smaller than those of the free condition because the pinned boundary conditions increased the stiffness of the structure. The first mode had a period of 1.21 s and 0.96 s for the free and restrained conditions, respectively, which led to a 26% period increase because of shear key effects. Assuming the response of the structure was entirely dominated by the fundamental mode in the transverse direction, shear key effects would not lead to any difference in the acceleration spectral ordinate for force-based design of the structure as the spectral ordinate for both periods would be the same as seen in Fig. 5. However, shear key effects led to changes in stiffness as stated before and these were found to lead to significant differences during dynamic analyses.

The peak and residual drifts for the two abutment boundary conditions are presented in Table 4. Except for the Kobe motion, the residual displacements were generally negligible when the ends were pinned. The peak and residual drifts for the free condition were all larger than the pinned condition as expected, which validates the premise of neglecting shear key effects to maximize maximum and residual drift demands in the columns.

An eigenvalue analysis of the two versions of the SR-99 bridge was also conducted. The periods of SR99-RC were 1.197 s and 0.757 s in the transverse and longitudinal directions, respectively. The periods of SR99-SMA/ECC were 1.208 s and 0.765 s in the transverse and longitudinal directions, respectively, and were expectedly longer because of the lower stiffness and lower energy dissipation of SMA/ECC columns. This indicates that the softer SMA material changed the dynamic properties of the bridge only slightly.

Transverse seismic response under design earthquakes

One of the primary indicators of the response to earthquake excitation during an analysis of any structural system is the moment-drift relationship. Figure 7 shows the moment versus drift hysteresis curves of pier 3 for the different ground motions. The hysteresis plots were stable with minimal capacity degradation. From the displacement results, it is seen that there was essentially no re-centering in the RC bridge, while there was significant recentering in the SMA bridge.

The maximum and residual drifts in each bent are listed in Table 4 for the two shear key assumptions. It is seen that among the design earthquakes, the Chi Chi record is the most demanding since it caused the largest column maximum drifts and permanent deformations in the three bridge models, varying from 5.45% in the SMA model to 4.88% in the RC model. In contrast, the Tabas earthquake led to the smallest displacements, varying from 4.89% in the SMA model to 4.25% in the RC model. Note that seismic response parameters such as maximum and permanent drifts are a function of both the input ground motion and the dynamic characteristics of the structural system. The results for the strong earthquakes show that the RC column exhibited a maximum drift of 6.51% for Kobe; For the same excitation, among the columns with innovative details, the SMA column had a maximum drift of 7.53%. The largest residual drift was in the RC bridge (0.49%) for the design earthquake. For the stronger excitation, among the columns with innovative details, the RC column had a maximum residual drift of 1.92% and the SMA column had a maximum of 0.32%. The use of SMA/ECC instead of RC reduced the residual displacement by 83% for Rinaldi and by 91% for Kobe, but increased the maximum displacement by 5% and 16% for the Rinaldi and Kobe records, respectively. The maximum drifts in SR99-SMA/ECC exceeded those of SR99-RC because of the lower elastic modulus of the SMA bars and to a lesser extent, of the ECC. The increase in maximum drift as a result of replacing steel and concrete by SMA and ECC, respectively, ranged from 5% to 17%, with an average of 12%. Despite the lower energy dissipation and hysteretic damping capability of SMA, the increase in the maximum drift was relatively small.

Figure 8 shows the stress-strain relationships at control reinforcement tensile steel and SMA fibers. The corresponding maximum stresses and strains are listed in Table 5. It is seen that the Chi Chi record was the most demanding of all three design records since it caused the largest strain in the three models, varying from 0.033 in the SMA model to 0.022 in the RC model. In contrast, the Tabas earthquake led to the smallest strain, varying from 0.013 in the SMA model to 0.009 in the RC model. The results for the stronger earthquake show that the RC column exhibited a maximum strain of 0.047 for Kobe. For the same level of excitation, among the columns with innovative details, the SMA column had a maximum strain of 0.055 and the RC column had a strain of 0.047. For the columns with innovative materials, the SMA column had the larger strain demand and the RC column had the smallest.

Transverse seismic response under extreme earthquakes

The peak ground acceleration of the five records used in the analysis presented thus far ranged from 0.325g to 0.825g leading to maximum drift ratios that were moderate except for the response to the Kobe record. To determine the effectiveness of SMA/ECC in reducing residual displacements when the bridge models are subjected to extreme earthquakes, the amplitude of each motion was scaled to produce a peak drift of 10%. This analysis was representative of the dynamic response for earthquake events much more intense than the design earthquake.

Table 6 shows the peak drifts and the resulting residual drifts for extreme earthquakes. In general, the scale factor to achieve a maximum drift ratio of 10% for SR99-RC was higher than SR99-SMA/ECC due to the higher stiffness of the RC columns. SR99-SMA/ECC had lower residual drifts for all the ground motions. The seismic bridge design code in Japan places a limit of 1% on the calculated residual displacement [¹]. For SR99-RC, two out of the five ground motions produced a residual drift greater than 1%, whereas for SR99-SMA/ECC the residual drift was always less than 1%. The use of SMA/ECC reduced the residual displacement of the bridge relative to its RC version from 65% to 94%, and 77% on average.

Figure 9 shows the base shear versus drift hysteresis curves for selected excitations, the hysteresis plots were stable and there was effective recentering mechanism in the SMA bridge compared to the RC bridge.

Figure 10 shows the stress-strain relationships of extreme tensile bars. The corresponding maximum stresses and strains when ground motions produce 10% drift are listed in Table 7. It is seen that the SMA columns had the largest strain demands. In the three design records, the extreme tensile strain of the SMA was approximately 0.08, which is near failure [²⁴].

Longitudinal seismic response

The seismic response of the bridges under the longitudinal ground motion alone was investigated under the three design earthquakes and the two “strong” earthquakes. The abutment-superstructure connections along the transverse direction were assumed to be rollers, representing seat-type abutments.

Figure 11 shows the moment versus drift hysteresis curves. It is noted that the hysteresis plots were stable. For the design-level earthquakes (Figs. 11(a)‒11(c)), residual displacements were small in both bridge models and no beneficial effect was observed in using SMA/ECC. However, SMA/ECC again was seen to be effective in reducing residual displacements under strong earthquake records (Figs. 11 (d) and 11(e)).

Figure 12 presents the drifts in the longitudinal direction. Overall, it is seen that the two versions of the bridge had similar dynamic characteristics and moved in-phase in all analyses, with no significant residual drifts when subjected to the design ground motions. For the strong ground motions however, SMA and ECC reduced the permanent drifts significantly. Similar to what was generally seen in the transverse direction, SR99-SMA/ECC had larger relative drifts than SR99-RC due to the lower modulus of elasticity of the constituent materials within the plastic hinge and the lower hysteretic damping provided by SMA.

The corresponding maximum column drifts and residual drifts are listed in Table 8. It is seen that the Chi Chi record was the most demanding of all three design records since it caused the largest maximum and permanent drifts in both models. The results for the strong earthquakes show that the Rinaldi motion led to a maximum drift of 6.22% for the RC model. For the same motion, the SMA model experienced a maximum drift of 6.64%. The data in the table shows that the largest design-level residual drift in the RC bridge was 0.35%. For the strong excitations, SR99-RC had a residual drift of 1.65% while SR99-SMA/ECC had a residual drift of 0.40% for the same motion, which implies a 75% reduction. The maximum drift for SR99-SMA/ECC was 7% to 20% higher than that of SR99-RC with an average of 14% for all earthquakes.

Conclusions

This study was aimed at assessing through computational seismic studies, the performance of variations of the novel low-damage columns for the SR-99 highway bridge that is part of the Alaskan way viaduct replacement program currently being built in Seattle, Washington. Computational models of single columns and entire bridge systems were analyzed under cyclic loading and horizontal ordinary and near-fault earthquake motions. Two versions of the bridge models were analyzed, one with conventional reinforced concrete columns and the other with SMA/ECC plastic hinges. The findings of the study led to the following conclusions:

1) Cyclic loading analysis of individual cantilever column models show their hysteretic moment-behavior is dominated by the flag-shaped stress-strain hysteresis of SMA. As a result, the column with SMA/ECC plastic hinges returned to its original undeformed position and experienced minimal permanent drifts.

2) Columns with SMA/ECC plastic hinges exhibit lower energy dissipation relative to conventional steel-reinforced columns because of the flag shaped stress-strain hysteresis of SMA, which encloses a smaller area than that of mild steel. However, the lower hysteretic damping in SMA/ECC columns does not lead to a substantial increase in maximum drifts relative to steel-reinforced RC columns under earthquake motions, with differences of less than 15%.

3) Response history analyses showed that the benefits of using SMA/ECC plastic hinges in recentering bridge columns within an actual bridge system are not realized under design-level earthquakes causing maximum drift demands of up to 5.45%. However, under strong and extreme earthquakes with maximum drift demands exceeding 10%, SMA/ECC plastic hinges reduced the residual displacements substantially with an average of 77% relative to those in columns with conventional steel-RC plastic hinges. These findings demonstrate that the full potential of novel materials may be better utilized for critical and essential bridge structures in areas of high seismic hazard, where improved performance under extreme events will greatly offset increased construction costs. In addition, novel materials for critical and essential bridges can provide all the structural benefits of nonlinear behavior, cyclic softening under large drifts, energy dissipation, and ductility all with minimal damage and permanent drifts.

4) Taking 1% residual drift as the functionality limit for most bridges subjected to earthquakes, the limit was violated in several cases for the RC version of the models-99 bridge. However, when SMA/ECC plastic hinges were used the residual drift was always below 1%. Therefore, the proposed design incorporating SMA and ECC was found to be effective in keeping bridges functional after strong and extreme earthquakes.

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