Application of Machine Learning Technique in Predicting the Bearing Capacity of Rectangular Footing on Layered Sand under Inclined Loading

Document Type : Research Note


Department of Civil Engineering, NIT Hamirpur, Himachal Pradesh, India



The aim of the present study is to apply machine learning technique to predict the ultimate bearing capacity of the rectangular footing on layered sand under inclined loading. For this purpose, a total 5400 data based on the finite element method for the rectangular footing on layered sand under inclined loading were collected from the literature to develop the machine learning model. The input variables chosen were the thickness ratio (0.00 to 2.00) of the upper dense sand layer, embedment ratio (0 to 2), the friction angle of upper dense (410 to 460) sand and lower loose (310 to 360) sand layer and inclination (00 to 450) of the applied load with respect to vertical. The output is the ultimate bearing capacity. Further, the impact of the individual variable on the bearing capacity was also assessed by conducting sensitivity analysis. The results reveal that, the load inclination is the major variable affecting the bearing capacity at embedment ratio 0, 1 and 2. Finally, the performance of the developed machine learning model was assessed using six assessing statistical parameters. The results reveal that the developed model was performing satisfactorily for the prediction of the ultimate bearing capacity of the rectangular footing on layered sand under inclined loading.


Main Subjects

[1]     Kumar J, Chakraborty M. Bearing capacity of a circular foundation on layered sand–clay media. Soils Found 2015;55:1058–68.
[2]     Joshi VC, Dutta RK, Shrivastava R. Ultimate bearing capacity of circular footing on layered soil. J Geoengin 2015;10:25–34.
[3]     Khatri VN, Kumar J, Akhtar S. Bearing Capacity of Foundations with Inclusion of Dense Sand Layer over Loose Sand Strata. Int J Geomech 2017;17.
[4]     Mosadegh A, Nikraz H. Bearing capacity evaluation of footing on a layered-soil using ABAQUS. J Earth Sci Clim Change 2015;6:1000264.
[5]     Panwar V, Dutta RK. Numerical study of ultimate bearing capacity of rectangular footing on layered sand. J Achiev Mater Manuf Eng 2020;1:15–26.
[6]     Rao P, Liu Y, Cui J. Bearing capacity of strip footings on two-layered clay under combined loading. Comput Geotech 2015;69:210–8.
[7]     Mosallanezhad M, Moayedi H. Comparison Analysis of Bearing Capacity Approaches for the Strip Footing on Layered Soils. Arab J Sci Eng 2017;42:3711–22.
[8]     Khatri VN, Singh N, Dutta RK, Yadav JS. Numerical Estimation of Bearing Capacity of Shallow Footings Resting on Layered Sand. Transp Infrastruct Geotechnol 2022.
[9]     Das PP, Khatri VN, Doley R, Dutta RK, Yadav JS. Estimation of bearing capacity of shallow footings on layered sand using finite elements analysis. J Eng Des Technol 2022.
[10]   Zheng G, Zhao J, Zhou H, Zhang T. Ultimate bearing capacity of strip footings on sand overlying clay under inclined loading. Comput Geotech 2019;106:266–73.
[11]   Dutta RK, Khatri VN, Kaundal N. Ultimate Bearing Capacity of Strip Footing on Sand Underlain By Clay Under Inclined Load. Civ Environ Eng Reports 2022;32:116–37.
[12]   Singh SP, Roy AK. Numerical Study of the Behaviour of a Circular Footing on a Layered Granular Soil Under Vertical and Inclined Loading. Civ Environ Eng Reports 2021;31:29–43.
[13]   Panwar V, Dutta RK. Bearing capacity of rectangular footing on layered sand under inclined loading. J Achiev Mater Manuf Eng 2021;108:49–62.
[14]   Nazeer S, Dutta RK. Application of Machine Learning Techniques in Predicting the Bearing Capacity of E-shaped Footing on Layered Sand. J Soft Comput Civ Eng 2021;5:74–89.
[15]   Dutta RK, Gnananandarao T, Sharma A. Application of random forest regression in the Prediction of ultimate bearing capacity of strip footing resting on dense sand overlying loose sand deposit. J Soft Comput Civ Eng 2019;3:28–40.
[16]   Sasmal SK, Behera RN. Prediction of combined static and cyclic load-induced settlement of shallow strip footing on granular soil using artificial neural network. Int J Geotech Eng 2021;15:834–44.
[17]   Gor M. Analyzing the bearing capacity of shallow foundations on two-layered soil using two novel cosmology-based optimization techniques. Smart Struct Syst 2022;29:513–22.
[18]   Moayedi H, Gör M, Kok Foong L, Bahiraei M. Imperialist competitive algorithm hybridized with multilayer perceptron to predict the load-settlement of square footing on layered soils. Measurement 2021;172:108837.
[19]   Moayedi H, Gör M, Khari M, Foong LK, Bahiraei M, Bui DT. Hybridizing four wise neural-metaheuristic paradigms in predicting soil shear strength. Measurement 2020;156:107576.
[20]   Bui, Moayedi, Gör, Jaafari, Foong. Predicting Slope Stability Failure through Machine Learning Paradigms. ISPRS Int J Geo-Information 2019;8:395.
[21]   Dutta RK, Gnananandarao T, Khatri VN. Application of Soft Computing Techniques in Predicting the Ultimate Bearing Capacity of Strip Footing Subjected to Eccentric Inclined Load and Resting on Sand. J Soft Comput Civ Eng 2019;3:30–42.
[22]   Ebid AM, Onyelowe KC, Salah M. Estimation of Bearing Capacity of Strip Footing Rested on Bilayered Soil Profile Using FEM-AI-Coupled Techniques. Adv Civ Eng 2022;2022:1–11.
[23]   Moayedi H, Abdullahi MM, Nguyen H, Rashid ASA. Comparison of dragonfly algorithm and Harris hawks optimization evolutionary data mining techniques for the assessment of bearing capacity of footings over two-layer foundation soils. Eng Comput 2021;37:437–47.
[24]   Nazir R, Momeni E, Marsono K, Maizir H. An Artificial Neural Network Approach for Prediction of Bearing Capacity of Spread Foundations in Sand. J Teknol 2015;72.
[25]   Kabir MU, Sakib SS, Rahman I, Shahin HM. Performance of ANN Model in Predicting the Bearing Capacity of Shallow Foundations, 2019, p. 695–703.
[26]   Sethy BP, Patra CR, Sivakugan N, Das BM. Prediction of Ultimate Bearing Capacity of Eccentrically Loaded Rectangular Foundations Using ANN, 2018, p. 148–59.
[27]   Sethy BP, Patra C, Das BM, Sobhan K. Prediction of ultimate bearing capacity of circular foundation on sand layer of limited thickness using artificial neural network. Int J Geotech Eng 2021;15:1252–67.
[28]   Moayedi H, Moatamediyan A, Nguyen H, Bui X-N, Bui DT, Rashid ASA. Prediction of ultimate bearing capacity through various novel evolutionary and neural network models. Eng Comput 2020;36:671–87.
[29]   Sihag P, Esmaeilbeiki F, Singh B, Ebtehaj I, Bonakdari H. Modeling unsaturated hydraulic conductivity by hybrid soft computing techniques. Soft Comput 2019;23:12897–910.
[30]   Sihag P, Kumar M, Singh B. Assessment of infiltration models developed using soft computing techniques. Geol Ecol Landscapes 2021;5:241–51.
[31]   Boger Z, Guterman H. Knowledge extraction from artificial neural network models. 1997 IEEE Int. Conf. Syst. Man, Cybern. Comput. Cybern. Simul., vol. 4, IEEE; n.d., p. 3030–5.
[32]   Garson DG. Interpreting neural network connection weights 1991.
[33]   Olden JD, Jackson DA. Illuminating the “black box”: a randomization approach for understanding variable contributions in artificial neural networks. Ecol Modell 2002;154:135–50.
[34]   Goh ATC, Kulhawy FH, Chua CG. Bayesian Neural Network Analysis of Undrained Side Resistance of Drilled Shafts. J Geotech Geoenvironmental Eng 2005;131:84–93.
[35]   Bardhan A, Samui P, Ghosh K, Gandomi AH, Bhattacharyya S. ELM-based adaptive neuro swarm intelligence techniques for predicting the California bearing ratio of soils in soaked conditions. Appl Soft Comput 2021;110:107595.
[36]   Meyerhof GG, Hanna AM. Ultimate bearing capacity of foundations on layered soils under inclined load. Can Geotech J 1978;15:565–72.
  • Receive Date: 20 May 2022
  • Revise Date: 01 August 2022
  • Accept Date: 01 October 2022
  • First Publish Date: 01 October 2022