10NCEE Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska SOIL-STRUCTURE INTERACTION ANALYSIS OF THE MANHATTAN BRIDGE FOUNDATIONS L. H. Mejia 1, R. Arulnathan 2, S. Murugaiah 3 and T. Thomann 4 ABSTRACT The seismic evaluation of long-span bridges typically requires consideration of dynamic soilstructure interaction (SSI) effects on the seismic response of such bridges. Dynamic SSI effects depend primarily on the bridge structural system and its dynamic characteristics, the configuration of the bridge foundations, and the stratigraphy and properties of the supporting soils and rock. This paper illustrates the formulation of the substructuring method of SSI analysis for the seismic evaluation of the Manhattan Bridge in New York City. The paper presents the approach used to formulate the SSI models for the tower caissons and for the anchorage foundations. It discusses the options considered for model selection and presents typical results for the dynamic impedances of the bridge foundations and for the effects of kinematic interaction. Also, it discusses possible pitfalls that may be encountered in the formulation of substructure SSI models and that can lead to improper simulation of SSI effects. 1 Vice President, URS, 1333 Broadway, Suite 800, Oakland, CA 94612 2 Senior Project Manager, URS, 1333 Broadway, Suite 800, Oakland, CA 94612 3 Senior Geotechnical Engineer, URS, 1333 Broadway, Suite 800, Oakland, CA 94612 4 Vice President, URS Corporation, 1255 Broad Street, Suite 201, Clifton, NJ 07013 Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.
Soil-Structure Interaction Analysis of the Manhattan Bridge Foundations L.H. Mejia 1, R. Arulnathan 2, S. Murugaiah 3, and T. Thomann 4 ABSTRACT The seismic evaluation of long-span bridges typically requires consideration of dynamic soilstructure interaction (SSI) effects on the seismic response of such bridges. Dynamic SSI effects depend primarily on the bridge structural system and its dynamic characteristics, the configuration of the bridge foundations, and the stratigraphy and properties of the supporting soils and rock. This paper illustrates the formulation of the substructuring method of SSI analysis for the seismic evaluation of the Manhattan Bridge in New York City. The paper presents the approach used to formulate the SSI models for the tower caissons and for the anchorage foundations. It discusses the options considered for model selection and presents typical results for the dynamic impedances of the bridge foundations and for the effects of kinematic interaction. Also, it discusses possible pitfalls that may be encountered in the formulation of substructure SSI models and that can lead to improper simulation of SSI effects. Introduction The seismic evaluation of major long-span bridges typically requires consideration of dynamic soil-structure interaction (SSI) effects on the seismic response of such bridges. Dynamic SSI effects depend primarily on the bridge structural system and its dynamic characteristics; the configuration of the bridge foundations including aspects such as foundation type(s), plan dimensions and embedment, and stiffness; and the stratigraphy and material properties of the supporting soils and rock. Long-span bridges are often supported on massive foundations for which kinematic and inertial interaction effects are likely to be significant under earthquake shaking. Inertial interaction effects can be very significant because such bridges typically have a large superstructure supported on a few isolated foundations that, consequently, transmit large inertial loads to the supporting ground under earthquake shaking. Kinematic interaction effects can be significant because such bridge foundations are typically stiff, massive, and deeply embedded. The substructuring method offers a convenient and effective approach to consider dynamic SSI effects in the seismic analysis of bridges and other massive structures. In this method, the structure-foundation-soil system is partitioned into two or more parts at one or more appropriate interfaces, requiring a corresponding partitioning of the system equations of motion. Such partitioning allows efficient modeling of each part of the system and rigorous SSI analysis of the complete system by appropriate combination of the forces, reactions, and displacements, at the interfaces between the system parts. For long-span bridges, it is typically advantageous to partition the soil-structure system at the interface between the superstructure (consisting of the bridge deck and the above-ground supporting elements), and the substructure (consisting of the bridge foundations and the supporting soils and rock). Multiple options are often available for the choice of interface(s), which makes the method easily adaptable to structures of varied configurations. This paper illustrates the formulation of the substructuring method of SSI analysis and the selection of the interface between substructure parts for the seismic evaluation of the Manhattan Bridge in New York City.
The paper presents the approach used to formulate the SSI models for the tower caissons and for the anchorage foundations. It discusses the options considered for model selection and presents typical results for the dynamic impedances of the bridge foundations and for the effects of kinematic interaction. Also, it discusses possible pitfalls that may be encountered in the formulation of substructure SSI models and that can lead to improper simulation of SSI effects. Bridge Description The bridge is a vital transportation link spanning over the East River between lower Manhattan and Brooklyn. At full capacity, the bridge carries 500,000 subway passengers and 110,000 vehicles per day. It is a 6,900-foot-long suspension bridge with a main span length of 1,470 feet and two side spans 725 feet long each (Fig. 1). The suspension cables for the main and side spans are supported on two 320-foot-tall steel towers and are fastened at two anchorages at the ends of the side spans. Atop the towers, four cables rest on ornamental saddles and each cable supports a stiffening truss. In cross-section, the bridge has two decks. The upper deck is at the level of the top truss chords and consists of two roadways, each placed between one pair of inner and outer trusses and carrying two lanes of traffic. The lower deck is at the level of the lower truss chords and has a three-lane roadway between the two inner trusses, two transit tracks under each upper roadway, and two walkways cantilevered beyond the outer trusses. In total, the bridge carries seven vehicular lanes, four transit tracks, and two pedestrian walkways. Figure 1: Longitudinal Section of the Manhattan Bridge. The Substructuring Method For many applications, the substructuring method makes use of compatibility of forces and displacements at foundation level to divide a complete system into two major parts: soil and structure [1]. To establish the impedance and scattering properties at the soil-structure interface, the soil is analyzed first as a half-space. In a subsequent analysis, those properties are used as boundary conditions in the dynamic analysis of the structure with a loading that depends on the free-field motions. The SSI analysis of structures founded at the surface using the substructuring method is relatively simple. However, for structures that are embedded, the analysis is quite complex mainly due to the difficulty associated with specifying the distribution of free-field forces on the embedded part of the structure. The free-field motions vary considerably with depth particularly in softer materials. The substructuring method may be formulated using any one of three approaches: rigid boundary, flexible boundary, and flexible volume methods. The flexible boundary and volume
methods are commonly used for SSI analysis of embedded structures because, as the terminology suggests, these methods consider the flexibility of the embedded part of the structure. Figure 2. Schematic Illustration of Partitioning of Soil-Structure System. In the flexible boundary method, the partitioning is specified at the interface between soil and structure. In the flexible volume method, the partitioning is specified at all nodes of the structure that are buried, thereby greatly simplifying the scattering and the impedance problems (Fig.2). This form of partitioning allows for interaction at all nodes of the embedded part of the structure. The flexible volume method eliminates the scattering problem and simplifies the impedance problem because of the regular boundary at the surface, but increases the analysis time because of the increased number of interaction nodes. SSI Analysis of Bridge Foundations During an earthquake, the ground motions transmit energy through the foundations to the bridge superstructure. In turn, the bridge responds dynamically and transmits forces back to the soil through the foundations. The foundations interact with the surrounding soils and the motions at the top of the foundation can be significantly different from the free-field motion. Analysis formulation To model SSI effects in the seismic evaluation of the overall bridge, SSI analyses were performed to calculate the foundation impedances and motions at the main bridge supports: the tower caissons, the anchorage mat foundations, and the approach piers. The SSI analyses of tower caissons and anchorage foundations are presented in this paper. The partitioning and the corresponding interface between the superstructure and the substructure were selected based on discussions between the superstructure and the substructure analysis teams. The interface for the tower caissons was selected at the top of the caissons as shown in Fig. 3. The interface for the anchorage mat foundations was selected at the bottom of the mat. Therefore, massless mat models were used for the substructure SSI analysis. The analysis consisted of the following steps: Select material properties for soil and structure. Develop three-dimensional finite element models of the substructures for analysis with the computer program SASSI [3]. From SASSI analyses, develop the foundation stiffness coefficients (also referred to as impedance functions) at the interfaces for use in the superstructure analysis. Develop the input rock outcrop ground motions for analysis of the bridge.
Perform a site response analysis to compute the free-field surface motions using the computer program SHAKE [4]. Using SASSI, perform SSI analyses to calculate the motions at the interfaces (e.g., top of caissons, bottom of mats) for input into the superstructure analysis. Figure 3. Partitioning of Superstructure and Substructure for the Tower Caissons. The seismic performance of the bridge was analyzed for two ground motion levels corresponding to 500- and 2500-year return periods. The rock outcrop acceleration time histories were developed for those two return periods. The computer program SHAKE was used to perform one-dimensional site response analyses using the rock outcrop motions as input. The site response analyses were used to estimate strain-compatible soil properties, and to calculate the within motions from the outcrop motions. The within motions were subsequently used in the SSI analyses of the foundations using SASSI. Tower Caissons Modeling Substructure The Manhattan and Brooklyn towers are each supported by a single 78-by-144-feet concrete caisson. The bottoms of the caissons are at approximately elevation -92 feet (mean sea level datum). Whereas the Manhattan tower caisson is founded on dense silty sands, the Brooklyn tower caisson is founded on glacial till (Fig. 4). The caissons, foundation soils, and water in the caisson voids were included in the finite element model for both towers (Fig. 5). Because of geometrical symmetry about the XZ and YZ planes passing through the geometrical center of the caissons (Fig. 5), only one-quarter of the caissons was discretized in the finite element mesh. The caissons were modeled using three-dimensional solid elements. Weightless rigid link beams were used at the top of the caissons to ensure rigidity on the plane at the top of the caisson, which is required for an adequate interface with the superstructure. The maximum element size and the thickness of the soil layers were taken as less than or equal to λ s /5, where λ s is the minimum wavelength of the transmitted waves. The effects of water outside the caisson were assumed to be minor because the added mass of water is small relative to the mass of the caisson in the frequency range of interest. However, when necessary, those
effects may be readily represented by added masses on the outside the caissons. Manhattan Tower Caisson Brooklyn Tower Caisson Figure 4. Foundation and Soil Details for the Manhattan and Brooklyn Tower Caissons. rigid link beam (1) (2) Figure 5. Isotropic View of the Finite Element Models for the (1) Manhattan and (2) Brooklyn Tower Caissons. Material Properties The concrete properties were estimated using a compressive strength of 3000 psi [5]. Three sets of soil properties, namely, lower, best-estimate, and upper bound, were developed to account for uncertainty in the shear wave velocities of the soils. The upper and lower bound estimates were used for sensitivity analysis to assess the impact of soil properties (shear wave velocity, Poisson s ratio and unit weight) on the calculated impedance functions and acceleration time
histories. The available caisson drawings indicate that the bottom part of the caissons contain a large volume of timber framing surrounded by concrete and the upper part of the caisson is composed primarily of limestone and granite masonry (i.e. large limestone and granite blocks joined by mortar). The combined material will have a lower equivalent modulus for the bottom part and significantly higher equivalent modulus for the upper part than that of concrete. The properties for the combined materials were estimated using the estimated volumes of materials and the properties of limestone, granite, mortar, and timber. Sensitivity analyses were performed on the Manhattan tower caisson model to assess the impact of the combined structural properties on the impedance functions. Two sets of dynamic impedance functions were developed: one set using concrete properties for the caisson and the second set using combined material properties. Impedance Functions The dynamic impedance functions were developed at the geometric center of the top of the caissons. These impedance functions are represented by frequency-dependent stiffness and damping coefficients, k(f) and c(f), for each mode of vibration, where f is the frequency in Hz (i.e., horizontal translation in the X and Y directions, vertical translation, and rocking about the X and Y axes). The vertical and horizontal translational and the rocking stiffness and damping coefficients are estimated for both 2500 year and 500 year events. The translation impedance in the transverse axis and rocking impedance around the longitudinal axis for the 2500 year event for the Manhattan tower caisson are shown on Fig.6 as an example of the computed impedance functions. The calculated stiffness values were reasonably consistent with those estimated using formulas proposed by Gazetas [2] for arbitrarily shaped embedded footings. The results from the sensitivity analyses indicated that the variations in the soil properties and the use of the combined material property for the caissons did not have a significant impact on the calculated impedance functions. Figure 6. Computed Translation and Rocking Impedance Functions for the Manhattan Tower Caisson.
Computed Time Histories The SSI time history analyses were performed using horizontal and vertical acceleration time histories for both return periods. The computed acceleration time histories at various elevations and the corresponding spectra for 5% damping are shown in Fig.7 for the 2500-year return period for the Manhattan Tower caisson. The structural motions at the mudline are significantly smaller than the free-field motions. Similar results were calculated for the Brooklyn Tower caisson. Figure 7. Computed Time Histories in the Transverse Axis for Manhattan Tower Caissons. Anchorage Foundations Modeling The Manhattan and Brooklyn anchorages are each founded on a 182-by-137-feet mat foundation. The mats are embedded 25 feet below the ground surface. Whereas the Manhattan anchorage mat is supported by 4,042, 12-inch-diameter, 25-foot-long timber piles driven into silty sand, the Brooklyn anchorage mat is supported by 1,086, 12-inch-diameter, 25-foot-long timber piles driven into glacial till (Fig. 8). The mat and supporting soils were modeled in the finite element mesh for both anchorages (Fig. 9). It was not practical to model individual timber piles in the finite element mesh. Therefore, a parametric study was performed to determine the most efficient way to model the piles so their contributions to the foundation impedances were represented appropriately in the SSI analysis. Based on the parametric evaluations, the piles were represented by surrogate piles, with equivalent bending and shear characteristics, at the nodes of the mat model.
Manhattan Tower Caisson Brooklyn Tower Caisson Figure 8. Profiles of the Manhattan and Brooklyn Anchorage Foundations. Figure 9. Isotropic Views of the Finite Element Models for the (1) Manhattan and (2) Brooklyn Anchorage Foundations. One-half of the mat foundation was represented in the mesh, taking advantage of geometrical symmetry about the YZ plane. The mat and soil with piles were modeled using 3D solid elements and beam elements. Weightless rigid link beams were used to ensure rigidity of the bottom of the mat foundation for adequate interface with the superstructure. Material Properties The mat was modeled as a weightless rigid block. Three sets of soil properties, namely, lower, best-estimate, and upper bound, were used to account for uncertainty in the shear wave velocity of the soil. The upper and lower bound properties were used for sensitivity analysis to assess the impact of soil properties on the calculated impedance functions and acceleration time histories. Impedance Functions (1) (2) The dynamic impedance functions were calculated at the geometric center of the bottom of the mat foundation in the same format as those shown in Figure 6. They are not presented herein due to space constraints.
Computed Time Histories The acceleration time histories were computed at the geometric center of the bottom of the mat. The computed time histories at various elevations and the corresponding spectra for 5% damping are shown in Fig.10 for the 2500-year return period for the Manhattan anchorage foundation. The motions at the bottom of the mat and in free-field at the same elevation are similar because of the relatively shallow embedment of the foundation and the massless characteristic of the model. Analogous results were calculated for the Brooklyn anchorage foundation. Figure 10. Computed Time Histories at Various Elevations and Corresponding Spectra for 5% Damping. Discussion Proper analysis of SSI effects was a key necessary element of the seismic evaluation analysis of the Manhattan Bridge because of its importance as a vital transportation link between lower Manhattan and Brooklyn. Although the direct approach to SSI analysis was considered, the substructuring approach was selected as more practical for such a large structure. In this approach, the SSI analysis is broken down into analyses of simpler sub-systems. The solutions to the subsystems are superimposed to obtain the overall dynamic response of the bridge system. The computer program SASSI was used to perform the SSI analysis in the frequency domain. The selection of an appropriate interface between superstructure and substructure and the corresponding partitioning of the bridge structure are key steps in the overall analysis of the bridge. The main objectives of the SSI analysis of the substructures were to compute the impedance functions and acceleration time histories at the interfaces for use in the superstructure analysis. The computed impedance functions and acceleration time histories were then input into the dynamic analysis of the superstructure.
The substructuring method can lend itself to improper SSI analysis if the interface and corresponding partitioning are not properly established between the teams that perform the superstructure and substructure SSI analyses. Thus, the interface for the analysis of the tower caissons was selected at the top of caissons and weightless rigid link beams were needed at the top of the caisson to ensure the rigidity of the top of the caisson consistent with the assumptions of the superstructure analysis. Similarly, the interfaces for the analysis of the anchorage mat foundations were selected at the bottom of the mats and weightless rigid link beams were needed at the bottom of each mat to ensure rigidity consistent with the assumptions of the superstructure analysis. Conclusions Seismic SSI analyses of the tower caissons and anchorage foundations were performed as part of the seismic performance evaluation of the Manhattan Bridge. The results from the impedance analysis showed that variations in soil properties within the range of expected uncertainty do not have a significant impact on the calculated impedance functions. The computed motions at the mudline for the tower caissons are significantly lower than the free-field motions at the same elevation because of the large mass and embedment of the caissons. However, the motions calculated at the bottom of the anchorage mats are similar to the free-field motions at the same elevation reflecting the different choice of interface between the substructure and superstructure at those locations. Kinematic interaction effects are significant for the tower caissons because they are massive, stiff, and deeply embedded relative to the anchorage foundations. A rigid interface between the substructure and superstructure analyses was essential for proper SSI simulation. Acknowledgments The authors thank the New York Department of Transportation for permission to publish this paper. They also wish to acknowledge and thank the large team of professionals from Weidlinger Associates, the New York Department of Transportation, and URS who contributed to the work presented herein and to the seismic evaluation of the Manhattan Bridge. References 1. Chopra, A.K and Gutierrez, J.A. Earthquake analysis of multistory buildings including foundation interaction, EERC Report 75/22, University of California, Berkeley. 1973. 2. Gazetas, G. Formulas and Charts for Impedances of Surface and Embedded Foundations, Journal of Geotechnical Engineering, Vol. 117, No. 9, September 1991. 3. Ostadan, F. SASSI2000: A Computer Program for A System for Structural Analysis of Soil Structure Interaction, Revision 2. 2006. 4. Schnabel, P.B., Lysmer, J. and Seed, H.B. SHAKE: A computer program for earthquake response analysis of horizontally layered sites, Report No. UC/EERC-72/12, Earthquake Engineering Research Center, University of California, Berkeley, December. 1972. 5. Weidlinger Associates. The Manhattan Bridge: Seismic Evaluation and Retrofit Recommendations, Final Report, Volume III, October, 2003.