Vol.:(0123456789) 1 3 Innovative Infrastructure Solutions (2020) 5:96 https://doi.org/10.1007/s41062-020-00348-1 TECHNICAL PAPER Contribution of two artificial intelligence techniques in predicting the secondary compression index of fine‑grained soils Mohammed el Amin Bourouis 1  · Abdeldjalil Zadjaoui 1  · Abdelkader Djedid 2 Received: 14 March 2020 / Accepted: 30 July 2020 © Springer Nature Switzerland AG 2020 Abstract Fine soils have the particularity of producing very slow settlement over time, particularly secondary settlement, also known as creep. The coefficient C α that characterizes the creep phenomenon seems difficult to evaluate in the laboratory and in situ. Two approaches are proposed in this article for a better and faster prediction of that coefficient. The first approach is based on machine learning using multi-gene genetic programming, and the second one uses hybridization of particle swarm opti- mization algorithms and artificial neural networks. A regression analysis allowed identifying the determinant parameters to be used in the calculations. A database from several sites, and containing 203 samples, was utilized. The findings showed that a good agreement exists between the predicted and measured values. This also indicates that these two techniques can be quite interesting for engineers when they have to design works on compressible soils. Keywords Creep · Secondary compression · Genetic programming · Optimization · Neural networks · Particulate swarm Abbreviations MGGP Multi-gene genetic programming NN-PSO Neural network particle swarm optimization PSO Particle swarm optimization QPSO Quantum particle swarm optimization ANN Artificial neural network RMSE Root-mean-square error MAE Mean absolute error Introduction Clayey fine soils have the particularity of producing a set- tlement that can be divided into two phases, a primary set- tlement and a secondary settlement. The first one is more or less rapid and is due to the expulsion of water from the voids of soil. The second one is much slower; it is caused by the deformation of solid particles and takes several years to stabilize. This phenomenon, known as creep, is difficult to study because it raises many difficulties that are mainly related to the complexity of the structure of fine soils and to their behavior as well. The most frequently used param- eter to characterize this creep is the coefficient of secondary compression, generally noted C α (Fig. 1). This index, which is a key parameter for most viscoplastic behavior models applied in the engineering practice [19, 40, 42], is generally obtained by means of conventional oedometric tests. In this article, two novel approaches are suggested to predict this secondary compression index: One is based on multi-gene genetic programming and the other one on hybridization of artificial neural networks and particle swarm optimization algorithms [3]. Secondary compression index In the year 1936, Buisman was the first to use oedometric tests and note that secondary settlement seemed to evolve linearly as a function of the logarithm of time (Fig. 1). He proposed the following expression in which he introduced the coefficient C e , defined as the secondary compression index [6]: (1) Δe = C e × Δ(log t). * Mohammed el Amin Bourouis medamin_bourouis@yahoo.fr 1 Department of Civil Engineering, Faculty of Technology, Aboubekr Belkaid University, BP 230 Chetouane, 13000 Tlemcen, Algeria 2 Department of Architecture, Faculty of Technology, Aboubekr Belkaid University, BP 230 Chetouane, 13000 Tlemcen, Algeria