Abstract
This article proposes an optimization framework, based on genetic algorithms (GA), to calibrate the constitutive law of von Wolffersdorff. This constitutive law, known as Sand Hypoplasticity (SH), allows for robust and accurate modelling of the soil behaviour but requires a complex calibration involving eight parameters. The proposed optimization can automatically fit these parameters from the results of an oedometric and a triaxial drained compression test, by combining the GA with a numerical solver that integrates the SH in the test conditions. By repeating the same calibration several times, the stochastic nature of the optimizer enables the uncertainty quantification of the calibration parameters and allows studying their relative importance on the model prediction. After validating the numerical solver on the ExCalibre-Laboratory software from the SoilModels’ website, the GA calibration is tested on a synthetic dataset to analyse the convergence and the statistics of the results. In particular, a correlation analysis reveals that two couples of the eight model parameters are strongly correlated. Finally, the calibration procedure is tested on the results from von Wolffersdorff, 1996, and Herle and Gudehus, 1999, on the Hochstetten sand. The model parameters identified by the GA optimization improves the matching with the experimental data and hence lead to a better calibration.
Similar content being viewed by others
Notes
References
Bauer E (1996) Calibration of a comprehensive hypoplastic model for granular materials. Soils Found 36(1):13–26
Calista M, Pasculli A, Sciarra N (2015) Reconstruction of the geotechnical model considering random parameters distributions. Eng Geol Soc Territ 2:1347–1351. https://doi.org/10.1007/978-3-319-09057-3_237
Dafalias Y (1986) Bounding surface plasticity. I: mathematical foundation and hypoplasticity. J Eng Mech ASCE 112:966–987
Desrues J, Viggiani G (2004) Strain localization in sand: an overview of the experimental results obtained in grenoble using stereophotogrammetry. Int J Numer Anal Methods Geomech 28(4):279–321. https://doi.org/10.1002/nag.338
Duriez T, Brunton SL, Noack BR (2017) Machine learning control—taming nonlinear dynamics and turbulence. Springer, Berlin. https://doi.org/10.1007/978-3-319-40624-4
Fuentes W, Triantafyllidis T (2015) ISA model: a constitutive model for soils with yield surface in the intergranular strain space. Int J Numer Anal Methods Geomech 39(11):1235–1254. https://doi.org/10.1002/nag.2370
Fuentes W, Wichtmann T, Gil M, Lascarro C (2020) ISA-hypoplasticity accounting for cyclic mobility effects for liquefaction analysis. Acta Geotech 15(6):1513–1531. https://doi.org/10.1007/s11440-019-00846-2
Gambirasio L, Chiantoni G, Rizzi E (2014) On the consequences of the adoption of the Zaremba–Jaumann objective stress rate in FEM codes. Arch Comput Methods Eng 23(1):39–67
Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Choice Rev Online 27(02):270936. https://doi.org/10.5860/choice.27-0936
Gudehus G (1996) A comprehensive constitutive equation for granular materials. Soils Found 36(1):1–12
Gudehus G, Amorosi A, Gens A, Herle I, Kolymbas D, Mašín D, Muir Wood D, Nova R, Niemunis A, Pastor M, Tamagnini C, Viggiani G (2008) The soilmodels.info project. Int J Numer Anal Methods Geomech 32:1571–1572
Haupt RL, Haupt SE (2003) Practical genetic algorithms. Wiley, London. https://doi.org/10.1002/0471671746
Herle I, Gudehus G (1999) Determination of parameters of a hypoplastic constitutive model from properties of grain assemblies. Mech Cohesive-Frict Mater 4(5):461–486
Holland JH (1992) Adaptation in natural and artificial systems. The MIT Press, Cambridge. https://doi.org/10.7551/mitpress/1090.001.0001
Imposimato S, Nova R (1998) An investigation on the uniqueness of the incremental response of elastoplastic models for virgin sand. Mech Cohes-Frict Mater 3:65–87
Jekel CF, Venter G, Venter MP, Stander N, Haftka RT (2018) Similarity measures for identifying material parameters from hysteresis loops using inverse analysis. Int J Mater Form 12(3):355–378. https://doi.org/10.1007/s12289-018-1421-8
Jin Y, Yin Z, Zhou W, Liu X (2020) Intelligent model selection with updating parameters during staged excavation using optimization method. Acta Geotech 15(9):2473–2491. https://doi.org/10.1007/s11440-020-00936-6
Kadlíček T, Janda T, Šejnoha M (2016) Calibration of hypoplastic models for soils. Appl Mech Mater 821:503–511
Kadlíček T, Janda T, Šejnoha M (2019) Automatic online calibration software excalibre. In: 24th international conference engineering mechanics, Svratka, pp 353–356
Kolymbas D (2000) Introduction to hypoplasticity. In: Advances in geotechnical engineering and tunnelling. A. A. Balkema, Rotterdam
Kolymbas D, Bauer E (1993) Soft oedometer—a new testing device and its application for the calibration of hypoplastic constitutive laws. Geotech Test J 16(2):263–270
Kolymbas D, Wu W (1990) Recent results of triaxial tests with granular materials. Powder Technol 60:99–119
Lee C (2018) A review of applications of genetic algorithms in operations management. Eng Appl Artif Intell 76:1–12. https://doi.org/10.1016/j.engappai.2018.08.011
Mašín D (2005) A hypoplastic constitutive model for clays. Int J Numer Anal Methods Geomech 29(4):311–336
Mašín D (2013) Clay hypoplasticity with explicitly defined asymptotic states. Acta Geotech 8(5):481–496
Mašín D (2014) Clay hypoplasticity model including stiffness anisotropy. Géotechnique 64(3):232–238
Mašín D (2015) The influence of experimental and sampling uncertainties on the probability of unsatisfactory performance in geotechnical applications. Géotechnique 65:897–910
Mašín D (2018) Modelling of soil behaviour with hypoplasticity: another approach to soil constitutive modelling. Springer, Cham
Matsuoka H, Nakai T (1974) Stress-deformation and strength characteristics of soil under three different principal stresses. In: Japanese society of civil engineers, vol 232, pp 59–70
Michalewicz Z (1996) Genetic algorithms + data structures = evolution programs. Springer, Berlin. https://doi.org/10.1007/978-3-662-03315-9
Mirjalili S, Dong JS, Sadiq AS, Faris H (2019) Genetic algorithm: theory, literature review, and application in image reconstruction. In: Nature-inspired optimizers. Springer, Berlin, pp 69–85. https://doi.org/10.1007/978-3-030-12127-3_5
Ng CWW, Boonyarak TDM (2015) Effects of pillar depth and shielding on the interaction of crossing multitunnels. J Geotech Geoenviron Eng
Niemunis A (2003) Extended hypoplastic models for soils. Dissertation, Ruhr University Bochum, Germany
Niemunis A, Herle I (1997) Hypoplastic model for cohesionless soils with elastic strain range. Mech Cohesive-Frict Mater 2:279–299
Niemunis A, Grandas-Tavera C, Prada-Sarmiento L (2009) Anisotropic visco-hypoplasticity. Acta Geotech 4(4):293–314
Nova R (1994) Controllability of the incremental response of soil specimens subjected to arbitrary loading programmes. J Mech Behav Mater 5(2):193–201
Oliphant TE (2006) A guide to NumPy, vol 1. Trelgol Publishing
Pasculli A, Calista M, Sciarra N (2018) Variability of local stress states resulting from the application of Monte Carlo and finite difference methods to the stability study of a selected slope. Eng Geol 245:370–389. https://doi.org/10.1016/j.enggeo.2018.09.009
Reyes DK, Rodriguez-Marek A, Lizcano A (2009) A hypoplastic model for site response analysis. Soil Dyn Earthq Eng 29:173–184. https://doi.org/10.1016/j.soildyn.2008.01.003
Samarajiva PM (2000) Constitutive modeling of cohesionless granular materials using disturbed state concept. Dissertation, Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge
Samarajiva P, Macari E, Wathugala W (2005) Genetic algorithms for the calibration of constitutive models for soils. Int J Geomech 5(3):206–217. https://doi.org/10.1061/(ASCE)1532-3641(2005)5:3(206)
Shapiro J (2001) Genetic algorithms in machine learning. In: Machine learning and its applications. Springer, Berlin, pp 146–168. https://doi.org/10.1007/3-540-44673-7_7
Tafili M, Triantafyllidis T (2020) AVISA: anisotropic visco-ISA model and its performance at cyclic loading. Acta Geotech 15(9):2395–2413. https://doi.org/10.1007/s11440-020-00925-9
Tamagnini C, Viggiani G, Chambon R (2000) A review of two different approaches to hypoplasticity. In: Kolymbas D (ed) Constitutive modelling of granular materials. Springer, Berlin, pp 107–145
Wang S, Wu W (2020) A simple hypoplastic model for overconsolidated clays. Acta Geotech. https://doi.org/10.1007/s11440-020-01000-z
Wang S, Wu W (2020) Validation of a simple hypoplastic constitutive model for overconsolidated clays. Acta Geotech. https://doi.org/10.1007/s11440-020-01105-5
Wolffersdorff P (1996) A hypoplastic for granular material with a predefined limit state surface. Mech Cohes-Frict Mater 1:251–271
Wu W, Bauer E (1994) A simple hypoplastic constitutive model for sand. Int J Numer Anal Methods Geomech 18(12):833–862. https://doi.org/10.1002/nag.1610181203
Wu W, Kolymbas D (1990) Numerical testing of the stability criterion for hypoplastic constitutive equations. Mech Mater 9:245–253
Wu W, Kolymbas D (2000) Hypoplasticity then and now. Springer, Berlin, pp 57–105. https://doi.org/10.1007/978-3-642-57018-6_4
Wu W, Bauer E, Kolymbas D (1996) Hypoplastic constitutive model with critical state for granular materials. Mech Mater 23(1):45–69. https://doi.org/10.1016/0167-6636(96)00006-3
Wu W, Lin J, Wang X (2017) A basic hypoplastic constitutive model for sand. Acta Geotech 12:1373–1382
Wu W, Bauer E, Niemunis AH(1993) Workshop on modern approaches to plasticity for granular materials, Horton, Greece. In: Kolymbas D (ed) A visco-hypoplastic model for cohesive soils. Elsevier, Amsterdam, pp 365–383
Yin ZY, Jin YF, Shen JSL, Hicher PY (2018) Optimization techniques for identifying soil parameters in geotechnical engineering: comparative study and enhancement. Int J Numer Anal Methods Geomech 42(2):70–94
Acknowledgements
The authors gratefully acknowledge the support and the discussions with the engineer Pierantonio Cascioli, from GEINA srl, and Gabriele Sandro Toro, laboratory technician of the Department of Engineering and Geology of the G. D’Annunzio University, Chieti-Pescara (Italy).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Mendez, F.J., Pasculli, A., Mendez, M.A. et al. Calibration of a hypoplastic model using genetic algorithms. Acta Geotech. 16, 2031–2047 (2021). https://doi.org/10.1007/s11440-020-01135-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11440-020-01135-z