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A probabilistic investigation on the dynamic behaviour of pile foundations in homogeneous soils

  • S.I. : Soil-Structure Interaction Effects on the Dynamics of Structures
  • Published:
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A Correction to this article was published on 09 December 2021

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Abstract

Soil-structure interaction is a complex problem to address in structural design due to difficulties related to the modelling of the soil-foundation behaviour, which is frequency-dependent and affected by uncertainties. The substructure method is an efficient approach to include the soil-foundation behaviour in the superstructure response, since it allows addressing separately the soil-foundation and the superstructure analysis exploiting different tools and expertise. A deterministic approach is usually adopted for the soil-foundation system analysis selecting properties of foundation and soil based on an engineering judgment, despite uncertainties due to the intrinsic variability of soil parameters are largely recognised by both scholars and practitioners, as well as confirmed by experimental campaigns and laboratory tests. This paper presents a probabilistic perspective of the dynamic behaviour of pile foundations in homogeneous soils, focusing on the effects of the uncertainties in: (i) the frequency-dependent impedance functions; and (ii) the kinematic response factors necessary to derive the foundation input motion from the free-field motion. Single piles and square pile groups are considered. Uncertainties are described through the probabilistic distributions of parameters governing the soil-foundation dynamic response, while the samples are generated using the quasi-random sampling technique. Probabilistic analyses are performed utilizing an efficient numerical model that has been developed, and the variability of the output quantities is presented and discussed. The latter reveals to be strongly affected by frequency. In addition, sensitivity analyses are performed to investigate the influence of each variable uncertainty on the system response. The response quantities are highly sensitive to the shear wave velocity while the soil density and the pile elastic modulus may have a significant role, depending on the foundation layout.

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Data availability

Data are available upon reasonable request from the corresponding author.

Code availability

Codes are developed by the authors in Matlab environment (MATLAB 2020b).

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References

  • Álamo GM, Martínez-Castro AE, Padrón LA, Aznárez JJ, Gallego R, Maeso O (2016) Efficient numerical model for the computation of impedance functions of inclined pile groups in layered soils. Eng Struct 126:379–390

    Article  Google Scholar 

  • Aviles J, Pιrez-Rocha LE (2003) Soil–structure interaction in yielding systems. Earthq Eng Struct Dyn 32(11):1749–1771

    Article  Google Scholar 

  • Bartlett FM, MacGregor JG (1996) Statistical analysis of the compressive strength of concrete in structures. ACI Mater J 93(2):158–168

    Google Scholar 

  • Capatti MC, Carbonari S, Dezi F, Gara F, Leoni G (2017) Validation of a 3D model for dynamic soil-structure-interaction of pile foundations by means of in situ tests. In: Atti del XVII Convegno ANIDIS L'ingegneria Sismica in Italia: Pistoia, pp 68–77

  • Carbonari S, Dezi F, Leoni G (2011a) Linear soil–structure interaction of coupled wall–frame structures on pile foundations. Soil Dyn Earthq Eng 31(9):1296–1309

    Article  Google Scholar 

  • Carbonari S, Dezi F, Leoni G (2011b) Seismic soil-structure interaction in multi-span bridges: application to a railway bridge. Earthq Eng Struct Dyn 40(11):1219–1239

    Article  Google Scholar 

  • Carbonari S, Morici M, Dezi F, Leoni G (2016) Analytical evaluation of impedances and kinematic response of inclined piles. Eng Struct 117:384–396

    Article  Google Scholar 

  • Carbonari S, Morici M, Dezi F, Gara F, Leoni G (2017) Soil-structure interaction effects in single bridge piers founded on inclined pile groups. Soil Dyn Earthq Eng 92:52–67

    Article  Google Scholar 

  • CNR. Guide for the probabilistic assessment of the seismic safety of existing buildings. Report CNR-DT 212/2013, CNR – Advisory Committee on Technical Recommendations for Construction, Rome; 2014.

  • Cottereau R, Clouteau D, Soize C (2007) Construction of a probabilistic model for impedance matrices. Comput Methods Appl Mech Eng 196(17–20):2252–2268

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Dezi F, Carbonari S, Morici M (2015) A numerical model for the dynamic analysis of inclined pile groups. Earthq Eng Struct Dyn 45(1):45–68

    Article  Google Scholar 

  • Dezi F, Roia D, Capatti MC, Carbonari S, Gara F, Leoni G, Morici M (2019) Evaluation of dynamic soil-pile interaction based on both full scale in situ tests and numerical simulations. In: 7th International conference on earthquake geotechnical engineering (ICEGE), CRC Press

  • Dobry R, Gazetas G (1988) Simple method for dynamic stiffness and damping of floating pile groups. Geotechnique 38(4):557–574

    Article  Google Scholar 

  • Dobry R, Vicente E, O’Rourke MJ, Roesset JM (1982) Horizontal stiffness and damping of single piles. J Geotech Eng Div ASCE 108(GT3):439–459

    Article  Google Scholar 

  • El-Marsafawi (1993) Dynamic analysis of single piles and pile groups. Doctoral dissertation, University of Western Ontario

  • EN1992–1–1:2004 Eurocode 2: Design of concrete structures - Part 1–1: General rules and rules for buildings.

  • Fan K, Gazetas G, Kaynia A, Kausel E, Ahmad S (1991) Kinematic seismic response of single piles and pile groups. J Geotech Eng 117(12):1860–1879

    Article  Google Scholar 

  • Gazetas G, Dobry R (1984a) Horizontal response of piles in layered soil. J Geotech Eng 110(1):20–34

    Article  Google Scholar 

  • Gazetas G, Dobry R (1984b) Simple radiation damping model for piles and footings. J Eng Mech ASCE 110(6):937–956

    Article  Google Scholar 

  • Griffiths SC, Cox BR, Rathje EM, Teague DP (2016) Surface-wave dispersion approach for evaluating statistical models that account for shear-wave velocity uncertainty. J Geotech Geoenviron Eng 142(11):04016061

    Article  Google Scholar 

  • Jin S, Lutes LD, Sarkani S (2000) Response variability for a structure with soil–structure interactions and uncertain soil properties. Probab Eng Mech 15(2):175–183

    Article  Google Scholar 

  • Jones AL, Kramer SL, Arduino P. Estimation of uncertainty in geotechnical properties for performance-based earthquake engineering. Technical Report 2002/16, Pacific Earthquake Engineering Research Center, PEER, Univ. of California at Berkeley, Berkeley, Calif., 2002.

  • Kaynia AM (1982) Dynamic stiffness and seismic response of pile groups (Doctoral dissertation, Massachusetts Institute of technology)

  • Lou M, Wang H, Chen X, Zhai Y (2011) Structure–soil–structure interaction: Literature review. Soil Dyn Earthq Eng 31(12):1724–1731

    Article  Google Scholar 

  • Lutes LD, Sarkani S, Jin S (2000) Response variability of an SSI system with uncertain structural and soil properties. Eng Struct 22(6):605–620

    Article  Google Scholar 

  • Makris N, Gazetas G (1992) Dynamic pile–soil–pile interaction Part II lateral and seismic response. Earthq Eng Struct Dyn 21(2):145–162

    Article  Google Scholar 

  • Makris N, Gazetas G (1993) Displacement phase differences in a harmonically oscillating pile. Geotechnique 43(1):135–150

    Article  Google Scholar 

  • MATLAB 2020b, The MathWorks, Inc., Natick, Massachusetts, United States.

  • Mayne PW, Coop MR, Springman S, Huang AB, Zornberg J (2009) State-of-the-Art Paper (SOA-1): GeoMaterial behavior and testing. Proc Int Conf Soil Mech Geotech Eng 4:2777–2872

    Google Scholar 

  • Minnucci L, Dezi F, Carbonari S, Morici M, Gara F, Leoni G. Effects of uncertainties of soil and pile mechanical properties on the dynamic stiffness of single piles in homogenous deposits. In 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN) 2018.

  • Moghaddasi M, Cubrinovski M, Chase JG, Pampanin S, Carr A (2011) Probabilistic evaluation of soil-foundation-structure interaction effects on seismic structural response. Earthq Eng Struct Dyn 40(2):135–154

    Article  Google Scholar 

  • Moon SW, Ku T (2016) Empirical estimation of soil unit weight and undrained shear strength from shear wave velocity measurements. In: Proceedings of 5th international conference on geotechnical and geophysical site characterization (ISC’5), vol 2. Australian Geomechanics Society pp 1247–1252

  • Mylonakis G, Gazetas G (1998) Vertical vibration and additional distress of grouped piles in layered soil. Soils Found 38(1):1–14

    Article  Google Scholar 

  • Mylonakis G, Gazetas G (2000) Seismic soil-structure interaction: beneficial or detrimental? J Earthq Eng 4(3):277–301

    Google Scholar 

  • Mylonakis G, Nikolaou A, Gazetas G (1997) Soil–pile–bridge seismic interaction: kinematic and inertial effects Part I: soft soil. Earthq Eng Struct Dyn 26(3):337–359

    Article  Google Scholar 

  • Nielson, BG. Analytical fragility curves for highway bridges in moderate seismic zones. Georgia Institute of Technology; 2005.

  • Padrón LA, Aznárez JJ, Maeso O (2007) BEM–FEM coupling model for the dynamic analysis of piles and pile groups. Eng Anal Bound Elem 31(6):473–484

    Article  Google Scholar 

  • Phoon KK, Kulhawy FH (1999) Evaluation of geotechnical property variability. Can Geotech J 36(4):625–639

    Article  Google Scholar 

  • Phoon K, Nadim F, Uzielli M, Lacasse S (2006) Soil variability analysis for geotechnical practice. In: Characterisation and engineering properties of natural soils. Taylor Francis

  • Rubinstein RY, Kroese DP. Simulation and the Monte Carlo method. Vol. 10, John Wiley & Sons, 2016.

  • Saltelli A, Tarantola S, Campolongo F, Ratto M (2004) Sensitivity analysis in practice: a guide to assessing scientific models. England, Chichester

    Google Scholar 

  • Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola, S (2008) Global sensitivity analysis: the primer. Wiley

  • Saltelli A, Annoni P, Azzini I, Campolongo F, Ratto M, Tarantola S (2010) Variance based sensitivity analysis of model output Design and estimator for the total sensitivity index. Comput Phys Commun 181(2):259–270

    Article  Google Scholar 

  • Sextos AG, Pitilakis KD, Kappos AJ (2003a) 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

    Article  Google Scholar 

  • Sextos AG, Pitilakis KD, Kappos AJ (2003b) 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

    Article  Google Scholar 

  • Sobol’ IM, Turchaninov VI, Levitan YL, Shukhman BV (1992) Quasirandom sequence generators. Institute of Applied Mathematics, Russian Academy of Sciences, Moscow

  • Soize C (2000) A nonparametric model of random uncertainties for reduced matrix models in structural dynamics. Prob Engrg Mech 15:277–294

    Article  Google Scholar 

  • Soize C (2001) Maximum entropy approach for modeling random uncertainties in transient elastodynamics. J Acoust Soc Am 109(5):1979–1996

    Article  Google Scholar 

  • Stefanidou SP, Kappos AJ (2017) Methodology for the development of bridge-specific fragility curves. Earthq Eng Struct Dyn 46(1):73–93

    Article  Google Scholar 

  • Stefanidou SP, Sextos AG, Kotsoglou AN, Lesgidis N, Kappos AJ (2017) Soil-structure interaction effects in analysis of seismic fragility of bridges using an intensity-based ground motion selection procedure. Eng Struct 151:366–380

    Article  Google Scholar 

  • Stewart JP, Fenves GL, Seed RB (1999a) Seismic soil–structure-interaction in buildings I: analytical methods. ASCE J Geotech Geoenviron Eng 125(1):26–37

    Article  Google Scholar 

  • Stewart JP, Fenves GL, Seed RB (1999b) Seismic soil–structure-interaction in buildings II: empirical findings. ASCE J Geotech Geoenviron Eng 125(1):38–48

    Article  Google Scholar 

  • Wolf JP (1985) Dynamic soil–structure interaction. Prentice-Hall, New Jersey

    Google Scholar 

Download references

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Authors and Affiliations

  1. Università Politecnica delle Marche, DICEA Via Brecce Bianche, 60131, Ancona, Italy

    Lucia Minnucci, Sandro Carbonari & Fabrizio Gara

  2. University of Camerino, SAAD Viale Della Rimembranza, 63100, Ascoli Piceno, Italy

    Michele Morici & Graziano Leoni

  3. University of San Marino, DESD Via Consiglio dei Sessanta, 99 47891, Dogana, San Marino

    Francesca Dezi

Authors
  1. Lucia Minnucci
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  2. Michele Morici
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  3. Sandro Carbonari
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  4. Francesca Dezi
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  5. Fabrizio Gara
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  6. Graziano Leoni
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Correspondence to Sandro Carbonari.

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Minnucci, L., Morici, M., Carbonari, S. et al. A probabilistic investigation on the dynamic behaviour of pile foundations in homogeneous soils. Bull Earthquake Eng 20, 3329–3357 (2022). https://doi.org/10.1007/s10518-021-01272-0

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