Vol.:(0123456789) 1 3 Engineering with Computers https://doi.org/10.1007/s00366-018-00700-1 ORIGINAL ARTICLE The use of new intelligent techniques in designing retaining walls Mohammadreza Koopialipoor 1  · Bhatawdekar Ramesh Murlidhar 2  · Ahmadreza Hedayat 3  · Danial Jahed Armaghani 2  · Behrouz Gordan 4  · Edy Tonnizam Mohamad 2 Received: 19 November 2018 / Accepted: 31 December 2018 © Springer-Verlag London Ltd., part of Springer Nature 2019 Abstract The stability of retaining walls against overturning is analyzed in this study using artifcial intelligence methods. Five input parameters including wall height, wall thickness, soil friction angle, soil density, and stone cement mixture density were var- ied and 2000 cases were considered in developing the predictive models. Using the artifcial neural network (ANN) method, eight prediction models were developed and evaluated based on the coefcient of determination (R 2 ) and the root mean square error. R 2 values of 0.9740 and 0.9824 for training and testing datasets, respectively (for the best model), indicate the level of ANN capability in predicting safety factor (SF) of retaining walls. After developing the ANN model, the ant colony optimization (ACO) algorithm was used to maximize the safety factor of the wall by varying the input parameters. In fact, the best ANN model was selected to be used as a modeling function in ACO algorithm. The SF result from optimization section was obtained as 3.057 which show a signifcant diference from the mean SF values used in the modeling. It can be concluded that ACO may be used as a powerful optimization algorithm in optimizing SF results of retaining walls. Keywords Stone masonry retaining wall · Safety factor · ANN · ACO · Optimization algorithm 1 Introduction Retaining walls (RWs) are among major structural elements of civil and mining engineering projects and allow for sta- bilizing the soil and rock mass. RWs need to be structur- ally competent to withstand the lateral pressures of the soil and rock masses. This paper outlines the various methods of evaluating the design of RWs and methods of assessing their suitability as needed for a specifc site. The efect of lateral earth pressure and the total force equilibrium were frst investigated using Coulomb’s theory [1] for sliding and frictional RWs. Assuming that the embankment is analogous to incipient rupture, the theory of active pressure on soil has been developed [2], which implies that the embankment is vertical and smooth. This makes designing and analysis of the RWs fairly simple, but in practical terms, RWs are subject to frictional forces and are, therefore, more com- plex to design. To take these into account, Terzaghi [3] proposed a general wedge theory using an arc logarithmic spiral as a failure surface. The main function of an RW is to retain backfll or loose natural soil to create space and enable construction activity. Simple RWs used to support backflls, basically soil-retaining RWs have been used over the years and can be grouped as gravity or semi-gravity * Mohammadreza Koopialipoor Mr.koopialipoor@aut.ac.ir * Danial Jahed Armaghani danialarmaghani@gmail.com Bhatawdekar Ramesh Murlidhar rmbhatawdekar@gmail.com Ahmadreza Hedayat hedayat@mines.edu Behrouz Gordan bh.gordan@gmail.com Edy Tonnizam Mohamad edy@utm.my 1 Faculty of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran 15914, Iran 2 Centre of Tropical Geoengineering (GEOTROPIK), Faculty of Civil Engineering, Universiti Teknologi Malaysia, 81310 Johor Bahru, Malaysia 3 Faculty of Civil and Environmental Engineering, Colorado School of Mines, Golden, CO 80401, USA 4 Department of Geotechnics and Transportation, Faculty of Civil Engineering, Universiti Teknologi Malaysia (UTM), 81310 Skudai, Johor, Malaysia