Abstract
Soil-structure interaction (SSI) in pile-supported bridges coupled with non-linear behavior of the structural bridge elements is a complex problem. A sub-structuring technique that accounted for the kinematic and inertial SSI effects and non-linear finite element method (FEM) numerical model in the software SAP2000 were employed to investigate the response of a typical 4-span continuous bridge in two orthogonal directions founded in five soil profiles belonging to AASHTO site classes C and D. The FEM analysis results were disaggregated to delineate the effect of SSI and pier column inelasticity (PCI) on three output quantities, i.e., bridge deck acceleration (A), bridge displacement (δ), and pier column shear force (V). Sensitivity analysis, conducted using Morris method, ascertained the influence of SSI and PCI on the output quantities. It was revealed that all three response quantities were more sensitive to PCI in both orthogonal directions in all soil profiles compared to SSI. However, sensitivity of the response quantities to SSI was significant in the transverse bridge direction in all but one soil profile, which was explained through a lumped parameter model. Contrary to the current AASHTO code requirement, the inclusion of SSI for the design of pile-supported bridges in all seismic design categories (SDCs) is recommended for the bridge typology studied herein.
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References
Chaudhary MT, Piracha A (2021) Natural disasters—origins, impacts, management. Encyclopedia 1(4):1101–1131
United Nations Office for Disaster Risk Reduction (2022). Global Assessment Report on Disaster Risk Reduction 2022: Our World at Risk: Transforming Governance for a Resilient Future. Geneva, 256 pp. Available at: https://www.undrr.org/gar2022-our-world-risk (accessed 23 Dec. 2022).
United Nations Department of Humanitarian Affairs (1994), Yokohama Strategy and Plan of Action for a Safer World: Guidelines for Natural Disaster Prevention, Preparedness and Mitigation, World Conference on Natural Disaster Reduction, Yokohama. 19 pp. Available at: https://www.preventionweb.net/files/8241_doc6841contenido1.pdf (accessed 23 Dec. 2022).
Hyogo framework for action 2005–2015: building the resilience of nations and communities to disasters. Geneva: United Nations Office for Disaster Risk Reduction; 2007. Available from: http://www.unisdr.org/files/1037_hyogoframeworkforactionenglish.pdf [accessed 23 Dec. 2022].
Sendai framework for disaster risk reduction 2015–2030. In: UN world conference on disaster risk reduction, 2015 March 14–18, Sendai, Japan. Geneva: United Nations Office for Disaster Risk Reduction; 2015. Available from: http://www.wcdrr.org/uploads/Sendai_Framework_for_Disaster_Risk_Reduction_2015-2030.pdf [accessed 23 Dec. 2022].
Richart FE, Hall JR Jr, Woods RD (1970) Vibrations of Soils and Foundations. Prentice-Hall
Kausel E (1976) Soil–structure interaction. Soil Dynamics for Earthquake Design, International Centre for Computer-aided Design (ICCAD), Santa Margherita, Italy
Wolf J (1985) Dynamic soil structure interaction, 1st edn. Prentice Hall Inc, Englewood Cliffs, NJ
Prevost JH, Scanlan RH (1983) Dynamic soil-structure interaction: centrifugal modeling. Int J Soil Dyn Earthq Eng 2(4):212–221
Dobry R, Gazetas G (1986) Dynamic response of arbitrarily shaped foundations experimental verification. J Geotech Eng Div—ASCE 112(2):109–135
Todorovska MI (2002) Full-scale experimental studies of soil-structure interaction. ISET J Earthq Technol 39(3):139–165
Zhang X, Wegner JL, Haddow JB (1999) Three-dimensional dynamic soil–structure interaction analysis in the time domain. Earthquake Eng Struct Dynam 28(12):1501–1524
Von Estorff O, Firuziaan M (2000) Coupled BEM/FEM approach for nonlinear soil/structure interaction. Eng Anal Boundary Elem 24(10):715–725
Bull, J. W (Ed.) (2002). Soil-Structure interaction: Numerical analysis and modelling. CRC Press, 742 pp.
Pitilakis D, Dietz M, Wood DM, Clouteau D, Modaressi A (2008) Numerical simulation of dynamic soil–structure interaction in shaking table testing. Soil Dyn Earthq Eng 28(6):453–467
Stewart JP, Fenves GL, Seed RB (1999) Seismic soil–structure interaction in buildings, II: empirical findings. J Geotech Geoenviron Eng 125(1):38–48
Chaudhary MTA, Abe M, Fujino Y (2001) Identification of soil–structure interaction effect in base-isolated bridges from earthquake records. Soil Dyn Earthq Eng 21(8):713–725
Star LM, Tileylioglu S, Givens MJ, Mylonakis G, Stewart JP (2019) Evaluation of soil-structure interaction effects from system identification of structures subject to forced vibration tests. Soil Dyn Earthq Eng 116:747–760
Kausel E (2010) Early history of soil–structure interaction. Soil Dyn Earthq Eng 30(9):822–832
Lou M, Wang H, Chen X, Zhai Y (2011) Structure–soil–structure interaction: Literature review. Soil Dyn Earthq Eng 31(12):1724–1731
Anand, V., & Kumar, S. S. (2018). Seismic soil-structure interaction: a state-of-the-art review. In Structures. Elsevier, pp 317–326
Dutta SC, Roy R (2002) A critical review on idealization and modeling for interaction among soil–foundation–structure system. Comput Struct 80:1579–1594
Veletsos AS, Verbic B. (1973) Dynamics of elastic and yielding structure-foundation systems. In: Proceedings of the Fifth World Conference Earthquake Engineering. Rome, Italy, pp 2610–2613.
Bielak J (1978) Dynamic response of non-linear building-foundation systems. Earthquake Eng Struct Dynam 6:17–30
Avilés J, Pérez -Rocha LE. (2003) Soil-structure interaction in yielding systems. Earthq Eng Struct Dyn 32:1749–1771
Sextos AG, Kappos AJ, Pitilakis KD (2003) Inelastic dynamic analysis of RC bridges accounting for spatial variability of ground motion, site effects and soil–structure interaction phenomena Part 2: parametric study. Earthq Eng Struct Dyn 32(4):629–652
Mylonakis G, Syngros C, Gazetas G, Tazoh T (2006) The role of soil in the collapse of 18 piers of Hanshin Expressway in the Kobe earthquake. Earthquake Eng Struct Dynam 35(5):547–575
Zheng Y, Chen B, Chen W (2015) Elasto-plastic seismic response of RC continuous bridge with foundation-pier dynamic interaction. Adv Struct Eng 18(6):817–836
Hassani N, Bararnia M, Amiri GG (2018) Effect of soil-structure interaction on inelastic displacement ratios of degrading structures. Soil Dynamics Earthquake Eng 104:75–87
Faraonis P, Sextos A, Papadimitriou C, Chatzi E, Panetsos P (2019) Implications of subsoil-foundation modelling on the dynamic characteristics of a monitored bridge. Struct Infrastruct Eng 15(2):180–192
Anand V, Satish Kumar SR (2021) Evaluation of seismic response of inelastic structures considering soil-structure interaction. Innov Infrastruct Solut 6:83. https://doi.org/10.1007/s41062-020-00423-7
Gomez HC, Ulusoy HS, Feng MQ (2013) Variation of modal parameters of a highway bridge extracted from six earthquake records. Earthq Eng Struct Dynam 42(4):565–579
Fraino, M., Ventura, C.E., Liam Finn, W.D., & Taiebat, M. (2012, September). Seismic soil-structure interaction effects in instrumented bridges. In: Proceedings of the 15th World Conference on Earthquake Engineering (pp 1–10). Portuguese Association for Earthquake Engineering.
Chaudhary MTA (2020) Sensitivity of modal parameters of multi-span bridges to SSI and pier column inelasticity and its implications for FEM model updating. Latin Am J Solids Struct. https://doi.org/10.1590/1679-78255895
Mylonakis G, Gazetas G (2000) Seismic soil-structure interaction: beneficial or detrimental? J Earthq Eng 4(3):277–301
Pecker A, Chatzigogos CT (2010) Non Linear Soil Structure Interaction Impact on the Seismic Response of Structures. In: Garevski M, Ansal A (eds) Earthquake Engineering in Europe Geotechnical Geological and Earthquake Engineering. Springer, Dordrecht
Kwag S, Ju B, Jung W (2018) Beneficial and detrimental effects of soil-structure interaction on probabilistic seismic hazard and risk of nuclear power plant. Adv Civ Eng. https://doi.org/10.1155/2018/2698319
El-Naggar MHE (2012) Bridging the Gap Between Structural and Geotechnical Engineers in SSI for Performance-Based Design. In: Sakr M, Ansal A (eds) Special Topics in Earthquake Geotechnical Engineering. Geotechnical, Geological and Earthquake Engineering, Springer, Dordrecht
Ouanani M, Tiliouine B (2015) Effects of foundation soil stiffness on the 3-D modal characteristics and seismic response of a highway bridge. KSCE J Civ Eng 19(4):1009–1023
Lizundia, B. (2020). A practical guide to soil-structure interaction, Structures Magazine, December, pp 8–12, ASCE, Structural Engineering Institute.
Zadeh, K. A. (2020). Investigation of effects of soil-structure interaction on the seismic response of RC bridges using a performance-based design approach, Doctoral dissertation, Dept. of Civil Engineering, Univ. of British Columbia. https://open.library.ubc.ca/media/stream/pdf/24/1.0394827/4
AASHTO (2020) AASHTO LRFD Bridge Design Specifications, 9th edn. American Association of State Highway and Transportation Officials, Washington, DC
Zangeneh A, Svedholm C, Andersson A, Pacoste C, Karoumi R (2018) Identification of soil-structure interaction effect in a portal frame railway bridge through full-scale dynamic testing. Eng Struct 159:299–309
Gara F, Regni M, Roia D, Carbonari S, Dezi F (2019) Evidence of coupled soil-structure interaction and site response in continuous viaducts from ambient vibration tests. Soil Dyn Earthq Eng 120:408–422
Taciroglu, E., Shamsabadi, A., Abazarsa, F., Nigbor, R. L., & Ghahari, S. F. (2014). Comparative Study of Model Predictions and Data from the Caltrans-CGS Bridge Instrumentation Program: A Case study on the Eureka-Samoa Channel Bridge. Technical Report 2014–01, University of California, Los Angeles, CA, pp. 164. Available at: https://dot.ca.gov/-/media/dot-media/programs/research-innovation-system-information/documents/final-reports/ca14-2418-finalreport-a11y.pdf
Reynders E, Teughels A, De Roeck G (2010) Finite element model updating and structural damage identification using OMAX data. Mech Syst Signal Process 24(5):1306–1323
De Carlo, G., Dolce, M., & Liberatore, D. (2000, January). Influence of soil-structure interaction on the seismic response of bridge piers. In: Proceedings of the 12th World Conference on Earthquake Engineering, Upper Hut, New Zealand: New Zealand Society for Earthquake Engineering (pp 1–8).
Anastasopoulos I, Sakellariadis L, Agalianos A (2015) Seismic analysis of motorway bridges accounting for key structural components and nonlinear soil–structure interaction. Soil Dyn Earthq Eng 78:127–141
Ni P (2013) Effects of soil-structure interaction on direct displacement-based assessment procedure of multi-span reinforced concrete bridges. Eur J Environ Civ Eng 17(7):507–531
Chaudhary MTA (2016) Effect of soil-foundation-structure interaction and pier column non-linearity on seismic response of bridges supported on shallow foundations. Aust J Struct Eng 17(1):67–86
Billah AM, Alam MS (2021) Seismic fragility assessment of multi-span concrete highway bridges in British Columbia considering soil–structure interaction. Can J Civ Eng 48(1):39–51
Capatti MC, Tropeano G, Morici M, Carbonari S, Dezi F, Leoni G, Silvestri F (2017) Implications of non-synchronous excitation induced by nonlinear site amplification and of soil-structure interaction on the seismic response of multi-span bridges founded on piles. Bull Earthq Eng 15(11):4963–4995
Feng ZR, Su L, Wan HP, Luo Y, Ling XZ, Wang XH (2019) Three-dimensional finite element modelling for seismic response analysis of pile-supported bridges. Struct Infrastruct Eng 15(12):1583–1596
Ramadan OM, Mehanny SS, Kotb AAM (2020) Assessment of seismic vulnerability of continuous bridges considering soil-structure interaction and wave passage effects. Eng Struct 206:110161
CSI (2022) SAP2000 – Linear and nonlinear static and dynamic analysis and design of three-dimensional structures: Basic Analysis Reference Manual. Computers and Structures Inc, Berkeley, California
Morris MD (1991) Factorial sampling plans for preliminary computational experiments. Technometrics 33(2):161–174
CEN (European Committee for Standardization) (2004) Eurocode 8: Design of structures for earthquake resistance, Part 5: Foundations, Retaining Structures, Geotechnical Aspects. EN 1998–5:2004. Brussels, Belgium.
PEER (2021). PEER NGA-West2, PEER ground motion database, Pacific Center for Earthquake Engineering Research, Berkeley, CA. online: https://ngawest2.berkeley.edu/
Choi E, DesRoches R, Nielson B (2004) Seismic fragility of typical bridges in moderate seismic zones. Eng Struct 26(2):187–199
Whittaker, A. , Atkinson, G. , Baker, J. , Bray, J. , Grant, D. , Hamburger, R. , Haselton, C. and Somerville, P. (2011), Selecting and Scaling Earthquake Ground Motions for Performing Response-History Analyses, Grant/Contract Reports (NISTGCR), National Institute of Standards and Technology, Gaithersburg, MD, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=915482 (Accessed August 23, 2022)
Douglas J, Gehl P, Bonilla LF, Scotti O, Régnier J, Duval AM, Bertrand E (2009) Making the most of available site information for empirical ground-motion prediction. Bull Seismol Soc Am 99(3):1502–1520
Toro GR (1995) Probabilistic Models of Site Velocity Profiles for Generic and Site-Specific Ground-Motion Amplification Studies. Brookhaven National Laboratory, Upton, New York
Chaudhary MTA (2021) Influence of site conditions on seismic design parameters for foundations as determined via nonlinear site response analysis. Front Struct Civ Eng 15(1):275–303
Güllü A, Hasanoğlu S, Yüksel E (2022) A Practical Methodology to Estimate Site Fundamental Periods Based on the KiK-net Borehole Velocity Profiles and Its Application to Istanbul. Bull Seismol Soc Am 112(5):2606–2620
Civiltech Software (2018). ALLPILE, Software for design of piles and pile groups, Seattle, WA, USA. https://civiltech.com/allpile/
Reese, L.C., Cooley, L.A. and Radhakrishnan, N. (1984). Laterally loaded piles and computer program COM624G. University of Texas, Austin, Technical Report K-84–2, Prepared for US Army Corps of Engineers, US Army Engineer Waterways Experiment Station, Vicksburg, Mississippi. https://apps.dtic.mil/sti/pdfs/ADA144641.pdf
Brown DA, Morrison C, Reese LC (1988) Lateral load behavior of pile group in sand. J Geotech Eng 114(11):1261–1276
NIST, (2012). Soil-Structure Interaction for Building Structures, NIST GCR 12–917–21, prepared by the Applied Technology Council and the Consortium of Universities for Research in Earthquake Engineering for the National Institute of Standards and Technology, Gaithersburg, Maryland. https://www.nehrp.gov/pdf/nistgcr12-917-21.pdf.
Lysmer J, Kuhlemeyer RL (1969) Finite dynamic model for infinite media. J Eng Mech ASCE 95:759–877
Hadjian AH, Luco JE, Tsai NC (1974) Soil-structure interaction: continuum or finite element? Nucl Eng Des 31(2):151–167
Lu J, Elgamal A, Yan L, Law K, Conte J (2011) Large-scale numerical modeling in geotechnical earthquake engineering. Int J Geomech 11:490–503. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000042
Mackie K, Lu J, Elgamal A (2012) Performance-based earthquake assessment of bridge systems including ground-foundation interaction. Soil Dyn Earthq Eng 42:184–196
Rahmani A, Taiebat M, Finn WDL (2014) Nonlinear dynamic analysis of meloland road overpass using three-dimensional continuum modeling approach. Soil Dyn Earthq Eng 57:121–132
Elgamal A, Arulmoli AK (2017) Seismic performance of a pile-supported wharf: three dimensional finite element simulation. Soil Dyn Earthq Eng 95:167–179
Forcellini D (2020) A resilience-based methodology to assess soil structure interaction on a benchmark bridge. Infrastructures 5:90. https://doi.org/10.3390/infrastructures5110090
Ali, W. (2018). Soil-structure interaction modelling on the seismic performance of a continuous span bridge – a cost-benefit analysis, MS Thesis, University of Surrey.
Riaz MR, Motoyama H, Hori M (2021) Review of soil-structure interaction based on continuum mechanics theory and use of high performance computing. Geosciences 11(2):72
Kausel E, Roesset JM (1974) Soil-structure interaction problems for nuclear containment structures. Electronic Power and Civil Engineer Conf Paper Power Div Specially Conf. Boulder, Colorado, pp 469–498
FEMA (2020) A Practical Guide to Soil-Structure Interaction, FEMA P-2091. Prepared by Applied Technology Council, Redwood, California
Carbonari, S., Morici, M., Dezi, F., Leoni, G., Nuti, C., Silvestri, F., Tropeano, G. and Vanzi, I., 2012. Seismic response of viaducts accounting for soil-structure interaction. In: 15th World Conference on Earthquake Engineering.
Dhar S, Ozcebe AG, Dasgupta K, Petrini L, Paolucci R (2019) Different approaches for numerical modeling of seismic soil-structure interaction: impacts on the seismic response of a simplified reinforced concrete integral bridge. Earthq Struct 17(4):373–385
Asli SJ, Saffari H, Zahedi MJ, Saadatinezhad M (2019) Comparing the performance of substructure and direct methods to estimate the effect of SSI on seismic response of mid-rise structures. Int J Geotech Eng 15(1):81–94. https://doi.org/10.1080/19386362.2019.1597560
Dezi F, Carbonari S, Leoni G (2009) A model for the 3D kinematic interaction analysis of pile groups in layered soils. Earthq Eng Struct Dyn 38(11):1281–1305
Sextos AG, Pitilakis KD, Kappos AJ (2003) Inelastic dynamic analysis of RC bridges accounting for spatial variability of ground motion, site effects and soil–structure interaction phenomena Part 1: methodology and analytical tools. Earthq Eng Struct Dyn 32(4):607–627
Fan K, Gazetas G, Kaynia A, Kausel E, Ahmad S (1991) Kinematic seismic response of single piles and pile groups. J Geotech Eng, ASCE 117(12):1860–1879
Avilés J, Pérez-Rocha LE (1998) Effects of foundation embedment during building-soil interaction. Earthq Eng Struct Dynam 27:1523–1540
Dom´ınguez J, (1993) Boundary Elements in Dynamics, Computational Mechanics Publication: Southampton and Elsevier. Applied Science, New York
Di Laora R, de Sanctis L (2013) Piles-induced filtering effect on the foundation input motion. Soil Dyn Earthq Eng 46:52–63
Sen R, Davies TG, Banerjee PK (1985) Dynamic analysis of piles and pile groups embedded in homogeneous soils. Earthquake Eng Struct Dynam 13(1):53–65
Sen R, Kausel E, Banerjee PK (1985) Dynamic analysis of piles and pile groups embedded in non-homogeneous soils. Int J Numer Anal Meth Geomech 9(6):507–524
Dobry R, Gazetas G (1988) Simple method for dynamic stiffness and damping of floating pile groups. Geotechnique 38(4):557–574
Kaynia AM, Kausel E (1991) Dynamics of piles and pile groups in layered soil media. Soil Dyn Earthq Eng 10(8):386–401
Makris N, Gazetas G (1992) Dynamic pile-soil-pile interaction Part II: Lateral and seismic response. Earthq Eng Struct Dyn 21(2):145–162
Konagai K, Yin Y, Murono Y (2003) Single beam analogy for describing soil-pile group interaction. Soil Dyn Earthq Eng 23(3):213–221. https://doi.org/10.1016/S0267-7261(02)00212-9
Konagai, K. (2018). TLEM v1.3 – Thin layer element method for dynamic pile-group interaction analysis, User’s Manual, University of Tokyo. Available at: http://konalab.main.jp/home-e/software/TLEM/TLEM1_3-2018.pdf.
Aviram A, Mackie KR, Stojadinović B (2008) Guidelines for nonlinear analysis of bridge structures in California. PEER report 2008–03. University of California, Berkeley.
Kappos A (2014) Seismic Analysis of Concrete Bridges: Numerical Modeling. In: Beer M, Kougioumtzoglou I, Patelli E, Au IK (eds) Encyclopedia of Earthquake Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36197-5_127-1
Thorenfeldt, E. (1987). Mechanical properties of high-strength concrete and applications in design. In: Symposium Proceedings, Utilization of High-Strength Concrete, Stavanger, Norway, pp 149–159.
Carvalho G, Bento R, Bhatt C (2013) Nonlinear static and dynamic analyses of reinforced concrete buildings-comparison of different modelling approaches. Earthq Struct 4(5):451–470
Rahai AR, Fallah Nafari S (2013) A comparison between lumped and distributed plasticity approaches in the pushover analysis results of a pc frame bridge. Int J Civ Eng 11(4):217–225
Banda SC, Kumar GR (2022) A comparative study of different numerical element and material models to study the nonlinear responses of RC bridge pier. Asian J Civ Eng 23(8):1305–1320
Borgonovo E, Plischke E (2016) Sensitivity analysis: A review of recent advances. Eur J Oper Res 248(3):869–887
Iooss B, Saltelli A (2017) Introduction to Sensitivity Analysis. In: Ghanem R, Higdon D, Owhadi H (eds) Handbook of Uncertainty Quantification. Springer, Cham, pp 1103–1122. https://doi.org/10.1007/978-3-319-12385-1_31
Razavi S, Jakeman A, Saltelli A, Prieur C, Iooss B, Borgonovo E, Maier HR (2021) The future of sensitivity analysis: An essential discipline for systems modeling and policy support. Environ Model Softw 137:104954
Saltelli A, Ratto M, Tarantola S, Campolongo F (2006) Sensitivity analysis practices: Strategies for model-based inference. Reliab Eng Syst Saf 91(10–11):1109–1125
Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S (2008) Global sensitivity analysis: The primer. John Wiley & Sons
Iooss B, Lemaître P (2015) A Review on Global Sensitivity Analysis Methods. In: Dellino G, Meloni C (eds) Uncertainty Management in Simulation-Optimization of Complex Systems. Operations Research/Computer Science Interfaces Series, Springer, Boston, MA, pp 101–122. https://doi.org/10.1007/978-1-4899-7547-8_5
Qian G, Mahdi A (2020) Sensitivity analysis methods in the biomedical sciences. Math Biosci 323:108306
Asheghi R, Hosseini SA, Saneie M, Shahri AA (2020) Updating the neural network sediment load models using different sensitivity analysis methods: a regional application. J Hydroinf 22(3):562–577
Pang Z, O’Neill Z, Li Y, Niu F (2020) The role of sensitivity analysis in the building performance analysis: a critical review. Energy and Buildings 209:109659
Yang S, Tian W, Cubi E, Meng Q, Liu Y, Wei L (2016) Comparison of sensitivity analysis methods in building energy assessment. Procedia Engineering 146:174–181
Herman JD, Kollat JB, Reed PM, Wagener T (2013) Method of Morris effectively reduces the computational demands of global sensitivity analysis for distributed watershed models. Hydrol Earth Syst Sci 17(7):2893–2903
Paul, M., Charan, V., Soni, V., & Ghosh, I. (2018). Calibration methodology of microsimulation model for unsignalized intersection under heterogeneous traffic conditions. Urbanization challenges in emerging economies: Energy and water infrastructure; transportation infrastructure; and planning and financing, 618–627.
Mahmoudi E, Hölter R, Georgieva R, König M, Schanz T (2019) On the global sensitivity analysis methods in geotechnical engineering: a comparative study on a rock salt energy storage. Int J Civ Eng 17(1):131–143
Ho VL, Khatir S, Roeck GD, Bui-Tien T, Abdel Wahab M (2020) Finite element model updating of a cable-stayed bridge using metaheuristic algorithms combined with Morris method for sensitivity analysis. Smart Struct Syst 26(4):451–468
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This study was supported by Kuwait University, Research Grant No. EV01/16.
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Chaudhary, M.T.A. Sensitivity of seismic response of pile-supported, multi-span viaduct bridges to interaction between soil-foundation and structural parameters. Innov. Infrastruct. Solut. 8, 180 (2023). https://doi.org/10.1007/s41062-023-01145-2
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DOI: https://doi.org/10.1007/s41062-023-01145-2