Abstract
The use of finite element calculations to deal with geotechnical problems is therefore limited by poor knowledge of the mechanical parameters of soils. The identification of these parameters characterizing the soil behavior model involves solving the inverse analysis problem. This form of inverse analysis consists in calibrating a numerical soil model on experimental data by iterative modifications of the values of the input parameters of the model until the difference between the result of the numerical calculation and the experimental data is minimal. In this article, we study the use of the principle of inverse analysis for the identification of the parameters of the constitutive soil model Mohr–Coulomb: the shear modulus (G) and the friction angle (φ). The inverse analysis problem posed by the determination of the parameters of the model is solved using an optimization technique based on two stochastic optimization algorithms, the genetic algorithm and the hybrid genetic algorithm with the tabu search method. These two optimization methods have been validated on a pressuremeter test. The results obtained by applying the genetic algorithm method and the hybrid genetic algorithm method for the identification of the two Mohr–Coulomb parameters (G and φ) show that the hybridization process of the genetic algorithm with the tabu search method accelerated the convergence of the algorithm towards the exact solution of the problem whereas the genetic algorithm alone takes a much longer computation time to reach an optimum close to the exact solution of the problem.
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References
Akbarimehr D, Aflaki E (2019) Site investigation et utilisation de réseaux de neurones artificiels pour prédire la perméabilité des roches au barrage de Siazakh. Iran QJ Eng Geol Hydrogeol 52(2):230–239. https://doi.org/10.1144/qjegh2017-048
Akbarimehr D, Aflaki E (2018) An experimental study on the effect of rubber powder on the geotechnical properties of clay soils. Civil Eng J 4(3):594–601. https://doi.org/10.28991/cej-0309118
Brinkgreve RBJ (2003) Plaxis V8 reference manuel. Delft University of Technology & PLAXIS, Pays-Bas
Cambou B, Bahar R (1993) Use of the pressuremeter test for the identification of intrinsic parameters of the behavior of a soil. French Review of Geotechnics 63:39–50
Cambou B, Boubangua A, Bozetto P, Haghgou M (1990) Determination of constitutive parameters from pressuremeter tests. Third Inter. Syrnp. On Pressuremeter, Oxford, Thomas Telford, pp 234–252
Castro CF, Antonio CAC, Sousa LC (2004) Optimisation of shape and process parameters in metal forging using genetic algorithms. J Mater Process Technol 146:356–364
Colliat DJL (1986) Behavior of granular materials under high stresses. Influence of the mineralogical nature of the studied materials. PhD thesis. University of Joseph Fourier Grenoble, pp. 19–44
Cui L, Sheng D (2005) Genetic algorithms in probabilistic finite element analysis of geotechnical problems. Computer and Geotechnics, Elsevier B.V. 32(8)555–563. https://doi.org/10.1016/j.compgeo.2005.11.005
Dano C, Hicher PY, Rangeard D, Marchina P (2007) Interpretation of dilatometer tests in a heavy oil reservoir. Int J Numer Anal Meth Geomech 31(10):1197–1215
De Sousa Coutinho AGF (1990) Radial expansion of cylindrical cavities in sandy soil : application to pressuremeter tests. Can Geotech J 27:737–748
Duncan JM, Chang CV (1970) Non linear analysis of stress strain in soils, Journal of the Soil Mechanics and Foundation Eng. Div., Vol. 96, no SM5, P.1629–1653
Elvira-Ortiz DA, Jaen-Cuellar AY, Morinigo-Sotelo D, Morales-Velazquez L, Osornio-Rios RA, Romero-Troncoso RDJ (2020) Genetic algorithm methodology for the estimation of generated power and harmonic content in photovoltaic generation. Appl Sci 10:542. https://doi.org/10.3390/app10020542
Eslami A, Akbarimehr D (2021) Analysis of the failures of the mixture of waste clay soil and rubber as a durable building material. Constr Build Mater 310:125274. https://doi.org/10.1016/j.jclepro.2020.122632
Eslami A, Akbarimehr D, Aflaki E, Hajitaheriha M (2020) Geotechnical characterization of the Lake Urmia super-soft sediment site using laboratory and CPTu recordings. Mar Georesour Geotechnol 38:10–1223–1234. https://doi.org/10.1080/1064119X.2019.1672121
Gibson RE, Anderson WF (1961) In situ measurement of soil properties with the pressuremeter. Civ Enging Publ Wks Rev 56(658):615–618
Glover F (1986) Future paths for integer programming and links to artificial intelligence. Computers and Operations Research, Elsevier B.V, Vol 13, No. 5, pp. 533–549. https://doi.org/10.1016/0305-0548(86)90048-1
Hajitaheriha MM, Akbarimehr D, Motlagh AH, Damerchilou H (2021) Improvement of the bearing capacity of shallow foundations using a trench filled with granular materials and reinforced with geogrids. Arab Journal of Geosciences 14(15):1–14. https://doi.org/10.1007/s12517-021-07679-y
Hughes JMO, Wroth CP, Windle D (1977) Pressuremeter test in sand. Geotechnique 27(4):455–477
Kajberg J, Lindkvist G (2004) Characterization of materials subjected to large strains by inverse modelling based on in placed displacement fields. International Journal of Solids and Structures, Elsevier B.V, 41(13):3439–3459. https://doi.org/10.1016/j.ijsolstr.2004.02.021
Kiusalaas J (2010) Numerical methods in engineering with matlab. Cambridge university press, 2nd edition
Ladanyi B (1963) Evaluation of pressuremeter test in granular soils, Poc. 2nd Pan-Am. Conf. Soil Mech., p.3–20
Levasseur S (2007) Inverse analysis in geotechnical: development of a method based on genetic algorithms, PhD Thesis, University of Joseph Fourier Grenoble I, France, pp. 20–52
Malécot Y, Levasseur S, Boulon M, Flavigny E (2004) Inverse analysis on in situ geotechnical measurements using a genetic algorithm. In Proceedings of the 9th Int. Symposium on Numerical Models in Geomechanics, pages 223–228, Ottawa, Canada
Marseguerra M, Zio E, Podofillini L (2003) Model parameters estimation and sensitivity by genetic algorithms. Ann Nucl Energy 30:1437–1456
Mehta BJ (1989) Evaluation of subsoil properties by pressuremeter test, 12th International Congress of Soil Mechanics and Foundation Engineering. Rio De Janeiro, Proceedings 1:295–298
Ménard L (1957) In situ measurement of soil physical properties, Annals of Bridges and Roads, p. 357–376
Mladenovic´ N, Dražic´ M, Kovacˇevic-Vujcˇic´ V, Cˇangalovic´ M (2008) General variable neighborhood search for the continuous optimization. Eur J Oper Res 191:753–770
Mokrani L (1991) Physical simulation of the behavior of piles at great depth in a calibration chamber, PhD thesis. National Polytechnic Institute of Grenoble 24–51
Monnet J, Khlif J (1994) Theoretical study of the elastoplastic balance of a powdery soil around a pressuremeter, French Review of Geotechnics, n" 67, p.3–12
Morshed J, Kaluarachchi JJ (1998) Parameter estimation using artificial neural network and genetic algorithm for free-product migration and recovery. Water Resour Res 34:1101–1113
Nabaei A, Hamian M, Parsaei MR, Safdari R, Samad-Soltani T, Zarrabi H, Ghassemi A (2018) Topologies and performance of intelligent algorithms: a comprehensive review. Artif Intell Rev 49:79–103
Park J-S, Ng H-Y, Chua T-J, Ng Y-T, Kim J-W (2021) Unified genetic algorithm approach for solving flexible job-shop scheduling problem. Appl Sci 11:6454. https://doi.org/10.3390/app11146454
Saighi A (1998) Comparison of laboratory and in situ tests: example of the triaxial and the pressuremeter. PhD thesis, Paris Central School, Châtenay Malabry, France
Salençon J (1966) Quasi-static expansion of a spherical or cylindrical cavity in an elastoplastic medium. Annals of Bridges and Roads 3:175–187
Schwaab J, Deb K, Goodman E, Kool S, Lautenbach S, Ryffel A, van Strien MJ, Grêt-Regamey A (2018) Using multi-objective optimization to secure fertile soils across municipalities. Appl Geogr 97:75–84
Shahrour I, Kasdi A, Abriak N (1995) Use of the pressuremeter test for the determination of the mechanical properties of sands obeying the Mohr-Coulomb criterion with a non-associated flow rule. Revue française de géotechnique 73:28–33
Tsai FTC, Sun NZ, Yeh WWG (2003) Global-local optimization for parameter structure identification in the three-dimensional ground water modeling. Water Resour Res 39:1301–1313
Vesic AS (1972) Expansion of cavities in infinite soil mass. J Soil Mech Fdn Eng Div ASCE 98(3):265–290
Worth CP (1984) The interpretation of in situ tests. Geotechnics 34(4):449–489
Zahoor Raja MA, Shah Z, Anwaar Manzar M (2018) A new stochastic computing paradigm for nonlinear Painlevé II systems in applications of random matrix theory. Eur Phys J Plus 133-254. https://doi.org/10.1140/epjp/i2018-12080-4
Zentar R, Hicher PY, Moulin G (2001) Identification of soil parameters by inverse analysis. Comput Geotech 28:129–144
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Moussaoui, M., Bekkouche, S.R., Benzerara, M. et al. Solution of the inverse analysis problem in geotechnics using stochastic methods—application to a pressuremeter test. Arab J Geosci 16, 5 (2023). https://doi.org/10.1007/s12517-022-11075-5
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DOI: https://doi.org/10.1007/s12517-022-11075-5