Reduction of Numerical Model in Some Geotechnical Problems

• Autorzy: Góral Artur , Lefik Marek , Wojciechowski Marek

Identyfikatory

DOI

10.2478/sgem-2023-0016

• Konferencja: 19th KKMGiIG
• Języki publikacji: EN

Abstrakty

EN

The concept of equivalence of the realistic, initial reference model and the simplified, reduced model is proposed. In reduced models, the action of the soil on the structure is replaced by the action of a layer with prescribed properties, defined by a set of parameters. The main difficulty here is to find the parameter values required by the simplified theory. The subject of this work is to find the dependence of the parameters of the reduced model on the parameters of the full model, including realistic soil behavior, in order to ensure the equivalence of both models. We show the potential of the method by presenting two examples: Winkler and Pasternak's model of a plate on the ground. We assume that both models are equivalent if they give identical results (displacements) at a finite number of observation points. An artificial neural network (ANN) is built in order to approximate and record the dependence of the parameters of the reduced model (at the network output) from the parameters of the full model (given at the network input). The complex network acts as a formula that assigns the parameters of the reduced model to a realistic description of the soil structure that is used for finite element method (FEM) modeling. The formalism we propose is quite general and can be applied to many engineering problems. The presented procedure is entirely numerical; it allows to calculate the parameters of the reduced model without resorting to symbolic calculations or additional theoretical considerations.

Słowa kluczowe

EN

ANN; artificial neural network; geotechnics; Winkler model; Pasternak model; reduced models

• Wydawca: De Gruyter
• Czasopismo: Studia Geotechnica et Mechanica
• Rocznik: 2023
• Tom: Vol. 45, nr s1
• Strony: 333--349
• Opis fizyczny: Bibliogr. 37 poz., rys., tab.

Twórcy

autor

Góral Artur

• Division of Geotechnics and Engineering Structures, Department of Concrete Structures Lodz University of Technology, Al. Politechniki 6, 93-590 Łódź

autor

Lefik Marek

• Division of Geotechnics and Engineering Structures, Department of Concrete Structures Lodz University of Technology, Al. Politechniki 6, 93-590 Łódź

autor

Wojciechowski Marek

• Division of Geotechnics and Engineering Structures, Department of Concrete Structures Lodz University of Technology, Al. Politechniki 6, 93-590 Łódź

Bibliografia

• [1] Ataman, M., Zbiciak A., Szcześniak, W.: Drgania własne płyty cienkiej na podłożu Kerra – Jemielity, https://www. researchgate.net/publication/263414439, 2009
• [2] Ataman, M.: Inercyjne, Sprężyste modele podłoża odkształcalnego w zadaniach z mechaniki konstrukcji, Logistyka-nauka, 6, s. 1515, 2014.
• [3] Boso, D.P., Lefik, M. and Schrefler B. A.: Generalised self consistent homogenisation as an inverse problem. Z. Angew. Math. Mech., 90(10-11), pp. 847 – 860, 2010.
• [4] Chen T., Chen H.: Universal Approximation to Non-linear Operators by Neural Networks with Arbitrary Activation Functions and Its Application to Dynamical Systems, IEEE Trans. on Neural Networks, Vol.6, No 4, 911-917, 1995.
• [5] Favre, H.: Sur une loi régissant la déformation d’un sol horizontal sous l’action d’une charge répartie à la surface. Comptes Rendus, Acad. Sci., 252, 1961, 2988–2990.
• [6] Ghavanloo, E., Daneshmand, F. and Rafiei, M.: Vibration and instability analysis of carbon nanotubes conveying fluid and resting on a linear viscoelastic Winkler foundation, Physica E, vol. 42, no. 9, pp. 2218–2224, 2010.
• [7] Gradkowski K.: Nośność podłoży nawierzchni dróg samochodowych wzmacnianych geosyntetykami. Badania doświadczalne, Oficyna Wydawnicza Politechniki Warszawskiej, Warszawa, 2008
• [8] Hertz, J., A. Krogh., A., Palmer G.R.: Introduction to The Theory of Neural Computation, Lecture Notes Volume I, Santa Fe Institute Studies in the sciences of Complexity, Addison- Wesley, 1991.
• [9] Hornik K., Stinchcombe M., White H.: Universal approximation of an unknown mapping and its derivatives using multilayered feedforward networks, Neural Networks, vol. 3, 551-560, 1990.
• [10] Hou Z.Q. and Lucifredi, A.: On the Use of Neural Networks for Identification of Linear and Nonlinear Systems, Meccanica 30, 377-388, 1995.
• [11] Kerr, A.D.: Elastic and viscoelastic foundation models, J. Appl. Mech., 31, 1964, pp.491-498.
• [12] Kerr, A.D.: On the formal development of elastic foundation models, Ing. Arch, 54, 1984, pp. 455–464. https://doi. org/10.1007/BF00537376
• [13] Lefik M.: Przykłady rozwiązań zagadnienia odwrotnego metodą aproksymacji relacji odwrotnej, Wydawnictwo Politechniki Łódzkiej, 2016.
• [14] Lefik M.: Rozwiązanie zagadnienia odwrotnego przy pomocy sztucznych sieci neuronowych. Zastosowanie metod numerycznych w analizie wybranych zagadnień geotechniki i geotechniki środowiska. Wydawnictwo Politechniki Łódzkiej, 2021.
• [15] Lefik M. and Boso D. P.: Identification of parameters of adsorption by approximation of inverse relation and using artificial neural networks, Proceedings Solmech2016 Conference http://solmech2016.ippt.pan.pl /Abstracts/0177. pdf
• [16] Lefik M. and Boso D. P.: Inverse problem - soft solution, in Bytes and Science, edited by G. Zavarise and D. P. Boso (© CIMNE, Barcelona, Spain 2012), pp. 10-34.
• [17] M. Lefik, M. Wojciechowski, M.: Examples of inverse problem in geotechnics: comparative analysis of various strategies of solutions involving artificial neural networks, International Symposium on Geomechanics and Applications for Sustainable Development, SIPS2019, Cyprus. October 2019
• [18] Levinson, M.: On the linear, isotropic, elastic foundation of grade 4. Mech. Res. Com. 6, 1979, pp. 369–378.
• [19] Meier R. W.: Backcalculation of Flexible Pavement Moduli from Falling Weight Deflectometer Data Using Artificial Neural Networks, Report prepared for U.S. Army Corps of Engineers, technical report GL-95-3, Washington DC, 1995.
• [20] Meyer, Z.: Propozycja określania współczynnika podatności podłoża przy projektowaniu płyt fundamentowych, https://docplayer.pl/52076096-Propozycja-okreslania-wspolczynnika-podatnosci-podloza-przy-projektowaniu-plyt-fundamentowych.html
• [21] Nita P.: Budowa i utrzymanie nawierzchni lotniskowych. WKŁ. Warszawa 2008
• [22] Pasternak, P.L.: On a new method of analysis of an elastic foundation by means of two foundation constants, Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstuve i Arkhitekture, Moscow, 1954, (in Russian).
• [23] Reissner, E.: A note on deflections of plates on a viscoelastic foundation, J. Appl. Mech., ASME, 25, 1958, pp.144-145.
• [24] Ruta P., Krawczyk B., Szydło A.: Identification of pavement elastic moduli by means of impact test, Engineering Structures, 100, 2015, ss. 201-211.
• [25] Sadrekarimi J., Akbarzad M.: Comparative study of methods of determination of coefficient of subgrade reaction. The Electronic Journal of Geotechnical Engineering, tom 14/2009, zeszyt E, 2009.
• [26] Suchart Limkatanyu, Woraphot Prachasaree, Nattapong Damrongwiriyan, Minho Kwon, andWooyoung Jung.: Exact Stiffness for Beams on Kerr-Type Foundation: The Virtual Force Approach, Journal of Applied Mathematics, Article ID 626287, p. 13, 2013, http://dx.doi.org/10.1155/2013/626287.
• [27] Szeptyński, P.: Praktyczne zagadnienia interakcji budowli z podłożem, Inżynieria i Budownictwo 72, nr 7 ss. 384-389, 2016.
• [28] Szydło A.: Nawierzchnie drogowe z betonu cementowego. Wydawnictwo Polski Cement, Kraków 2004.
• [29] Świniarski J.: Ocena podatności podłoża przy wymiarowaniu płyt fundamentowych. Inżynieria Morska i Geotechnika, nr 5/2003.
• [30] Tanahashi, H.: Two-dimensional analysis of ground surface displacements using Pasternak Model, J. Struct. Constr. Engrg., AIJ, 530, 2000, pp.85-91
• [31] Terzaghi K.: Evaluation of coefficients of subrade reaction, Inst. of Civil. Eng., London 1956;
• [32] Vallabhan, C.V.G., and Das, Y.C.: Parametric study of beams on elastic foundations, J. Engrg. Mech., ASCE, 114(12), pp.2072- 2082, 1988
• [33] Vlasov, V.Z. and Leont’ev, N.N.: Beams, plates and shells on elastic foundations, Israel Program for Scientific Translations, Jerusalem (Translated from Russian; original Russian version published in 1960). https://archive.org/details/nasa_ techdoc_19670004909/page/n43/mode/2up.
• [34] Winkler, E.: Die Lehre von der Elastizität und Festigkeit, H. Dominicus, Prague, 1867 (in German).
• [35] Wojciechowski, M.: Posadowienie na płycie fundamentowej – ustalanie współczynniów podatności podłoża, Wydawnictwo Politechniki Łódzkiej, 2016.
• [36] Wojciechowski M.: Fempy - finite element method in python, https://github.com/mrkwjc/fempy, http://fempy.org (access: 15, 03, 2021).
• [37] Wojciechowski, M., Lefik, M., D. Boso.: Inverse problems in the light of homogenisation methods: identification

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).