Abstract
Addressing the inherent uncertainties in geotechnical engineering, particularly concerning natural materials, this study focuses on the crucial aspect of reliability analysis in geotechnical structures. The research delves into the Factor of Safety, specifically examining the Moment Ratio, for cantilever sheet pile walls in cohesionless soil. The study employs both the First-Order Reliability Method (FORM) and Second-Order Reliability Method (SORM), integrating various optimization techniques such as Genetic Algorithm, Particle Swarm Optimization, Firefly Algorithm, and Biogeography-Based Optimization. The research systematically evaluates the performance of a model, utilizing the widely-adopted Adaptive Neuro-Fuzzy Inference System (ANFIS) to predict pile moment ratios based on soil properties such as the angle of shearing resistance and unit weight. Rigorous criteria are applied to assess the model's efficacy, revealing the superior predictive capabilities of the hybrid ANFIS and Particle Swarm Optimization (ANFIS-PSO) model. This abstract encapsulates a comprehensive methodology for evaluating and quantifying risk in civil engineering projects related to cantilever sheet pile walls, providing valuable insights for the development and implementation of robust structures in the field.
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The datasets produced or analyzed during the current study can be obtained from the corresponding author upon reasonable request.
References
Bowles J E 1996 Foundation Analysis and Design, The McGrawHill Companies. Inc, Singapore
King G J W 1995 Analysis of cantilever sheet-pile walls in cohesionless soil. J. Geotech. Eng. 121(9): 629–635
Singh A P and Chatterjee K 2020 Influence of soil type on static response of cantilever sheet pile walls under surcharge loading: a numerical study. Arab. J. Geosci. 13: 1–11
Georgiadis M and Anagnostopoulos C 1998 Effect of berms on sheet-pile wall behaviour. Geotechnique. 48(4): 569–574
Viswanadham B, Madabhushi S, Babu K and Chandrasekaran V 2009 Modelling the failure of a cantilever sheet pile wall. Int. J. Geotech. Eng. 3(2): 215–231
Nataraj M S and Hoadley P G 1984 Design of anchored bulkheads in sands. J. Geotech. Eng. 110(4): 505–515
Gopal Madabhushi S P and Chandrasekaran V S 2005 Rotation of cantilever sheet pile walls. J. Geotech. Geoenvironmental Eng. 131(2): 202–212
Pradeep T, GuhaRay A, Bardhan A, Samui P, Kumar S and Armaghani D J 2022 Reliability and prediction of embedment depth of sheet pile walls using hybrid ANN with optimization techniques. Arab. J. Sci. Eng. 47(10): 12853–12871
Day R A 1999 Net pressure analysis of cantilever sheet pile walls. Géotechnique. 49(2): 231–245
Babu G L S and Basha B M 2008 Optimum design of cantilever sheet pile walls in sandy soils using inverse reliability approach. Comput. Geotech. 35(2): 134–143
Kawa M, Puła W and Suska M 2016 Random analysis of bearing capacity of square footing using the LAS procedure. Stud. Geotech. Mech. 38(3)
Basma A A 1991 Reliability-based design of sheet pile structures. Reliab. Eng. Syst. Saf. 33(2): 215–230
Prastings A, Larsson S and Mueller R 2016 Multivariate approach in reliability-based design of a sheet pile wall. Transp. Geotech. 7: 1–12
GuhaRay A and Baidya D K 2015 Reliability-based analysis of cantilever sheet pile walls backfilled with different soil types using the finite-element approach. Int. J. Geomech. 15(6): 6015001
Nazari A, Rajeev P and Sanjayan J G 2015 Offshore pipeline performance evaluation by different artificial neural networks approaches. Measurement. 76: 117–128
Kardani N, Bardhan A, Gupta S, Samui P, Nazem M and Zhang Y 2021 Predicting permeability of tight carbonates using a hybrid machine learning approach of modified equilibrium optimizer and extreme learning machine. Acta Geotech. 1–17
Asteris P G, Mamou A, Hajihassani M, Hasanipanah M, Koopialipoor M, Le T T, Kardani N and Armaghani D J et al. 2021 Soft computing based closed form equations correlating L and N-type Schmidt hammer rebound numbers of rocks. Transp. Geotech. 29: 100588.
Kardani N, Zhou A, Shen S and Nazem M 2021 Estimating unconfined compressive strength of unsaturated cemented soils using alternative evolutionary approaches. Transp. Geotech. 29: 100591
Raja M N A and Shukla S K 2021 Predicting the settlement of geosynthetic-reinforced soil foundations using evolutionary artificial intelligence technique. Geotext. Geomembranes.
Raja M N A, Shukla S K and Khan M U A 2022 An intelligent approach for predicting the strength of geosynthetic-reinforced subgrade soil. Int. J. Pavement Eng. 23(10): 3505–3521
Chang C M, Lin T K and Chang C W 2018 Applications of neural network models for structural health monitoring based on derived modal properties. Measurement. 129: 457–470
Bansal J C, Sharma H and Jadon S S Artificial bee colony algorithm: a survey. Int J Adv. Intell. Paradig. 5(1–2):123–59
Basu M 2013 Artificial bee colony optimization for multi-area economic dispatch. Int J. Electr. Power Energy Syst. 49: 181–187
Maeda M and Tsuda S 2015 Reduction of artificial bee colony algorithm for global optimization. Neurocomputing. 148: 70–74
Shi J, Li X, Khan F, Chang Y, Zhu Y and Chen G 2019 Artificial bee colony Based Bayesian Regularization Artificial Neural Network approach to model transient flammable cloud dispersion in congested area. Process Saf. Environ. Prot. 128: 121–127
Gheysari K, Khoei A and Mashoufi B 2011 High speed ant colony optimization CMOS chip. Expert Syst. Appl. 38(4): 3632–3639
Bououden S, Chadli M and Karimi H R 2015 An ant colony optimization-based fuzzy predictive control approach for nonlinear processes. Inf. Sci. (Ny) 299: 143–158
Nguyen D C H, Ascough II J C, Maier H R, Dandy G C and Andales A A 2017; Optimization of irrigation scheduling using ant colony algorithms and an advanced crop** system model. Environ Model Softw. 97:32–45
Mirjalili S 2015 The ant lion optimizer. Adv. Eng. Softw. 83: 80–98
Dubey H M, Pandit M and Panigrahi B K 2016 Ant lion optimization for short-term wind integrated hydrothermal power generation scheduling. Int. J. Electr. Power Energy Syst. 83: 158–174
Rajan A, Jeevan K and Malakar T 2017 Weighted elitism based Ant Lion Optimizer to solve optimum VAr planning problem. Appl. Soft Comput. 55: 352–370
Kanimozhi G and Kumar H 2018 Modeling of solar cell under different conditions by Ant Lion Optimizer with LambertW function. Appl. Soft Comput. 71: 141–151
Lucas C, Nasiri-Gheidari Z and Tootoonchian F 2010 Application of an imperialist competitive algorithm to the design of a linear induction motor. Energy Convers. Manag. 51(7): 1407–1411
Enayatifar R, Abdullah A H and Lee M 2013 A weighted discrete imperialist competitive algorithm (WDICA) combined with chaotic map for image encryption. Opt. Lasers. Eng. 51(9): 1066–1077
Bek R U and Kosolapov G V 1986 The anodic dissolution of gold in alkaline cyanide solutions. Influence of impurities in solution on rate of process at low overpotentials. Izv Sib Otd Akad Nauk SSSR, Khim. 2: 28–31
Muttil N and Liong S Y 2004 Superior exploration–exploitation balance in shuffled complex evolution. J. Hydraul. Eng. 130(12): 1202–1205
Zhao F, Zhang J, Wang J and Zhang C 2015 A shuffled complex evolution algorithm with opposition-based learning for a permutation flow shop scheduling problem. Int. J. Comput. Integr. Manuf. 28(11): 1220–1235
Rao R V, Savsani V J and Vakharia D P 2012 Teaching–learning-based optimization: an optimization method for continuous non-linear large scale problems. Inf. Sci. (Ny) 183(1): 1–15
Sleesongsom S and Bureerat S 2017 Four-bar linkage path generation through self-adaptive population size teaching-learning based optimization. Knowledge-Based Syst. 135: 180–191
Sivakumar Babu G L and Basha B M 2008 Optimum design of cantilever retaining walls using target reliability approach. Int. J. Geomech. 8(4): 240–252
Hasofer A M and Lind N C 1974 Exact and invariant second-moment code format. J Eng. Mech. Div. 100(1): 111–121
Fiessler B, Neumann H J and Rackwitz R 1979 Quadratic limit states in structural reliability. J. Eng. Mech. Div. 105(4): 661–676
Breitung K 1984 Asymptotic approximations for multinormal integrals. J. Eng. Mech. 110(3): 357–366
Hohenbichler M and Rackwitz R 1988 Improvement of second-order reliability estimates by importance sampling. J. Eng. Mech. 114(12): 2195–2199
Tvedt L 1983; Two second-order approximations to the failure probability. Verit Rep RDIV/20-004083
Tvedt L 1988 Second order reliability by an exact integral. In: Reliability and Optimization of Structural Systems’ 88: Proceedings of the 2nd IFIP WG7 5 Conference London, UK, September 26–28, Springer;. p. 377–84.
Tvedt L 1990 Distribution of quadratic forms in normal space—application to structural reliability. J. Eng. Mech. 116(6): 1183–1197
Cai G Q and Elishakoff I Refined second-order reliability analysis. Struct. Saf. 14(4):267–76
Köylüoǧlu H U and Nielsen S R K 1994 New approximations for SORM integrals. Struct. Saf. 13(4): 235–246
Hong H P 1999 Simple approximations for improving second-order reliability estimates. J. Eng. Mech. 125(5): 592–595
Zhao Y G and Ono T 1999 New approximations for SORM: Part 1. J. Eng. Mech. 125(1): 79–85
Der Kiureghian A, Lin H Z and Hwang S J 1987 Second-order reliability approximations. J. Eng. Mech. 113(8): 1208–1225
Der Kiureghian A and De Stefano M 1991 Efficient algorithm for second-order reliability analysis. J. Eng. Mech. 117(12): 2904–2923
Naess A 1987 Bounding approximations to some quadratic limit states. J. Eng. Mech. 113(10): 1474–1492
Polidori D C, Beck J L and Papadimitriou C 1999 New approximations for reliability integrals. J Eng Mech. 125(4): 466–475
Adhikari S 2004 Reliability analysis using parabolic failure surface approximation. J. Eng. Mech. 130(12): 1407–1427
Armaghani D J and Asteris P G 2021 A comparative study of ANN and ANFIS models for the prediction of cement-based mortar materials compressive strength. Neural Comput. Appl. 33(9): 4501–4532
Mohamed T, Anuar K and Mukhlisin M 2012 Prediction of slope stability using statistical method and fuzzy logic. TOJSAT. 2(4): 68–73
Simon D 2008 Biogeography-based optimization. IEEE Trans Evol Comput. 12(6): 702–713
Alroomi A R, Albasri F A and Talaq J H 2013 Solving the associated weakness of biogeography-based optimization algorithm. Int. J. Soft Comput. 4(4): 1
Yang X S 2010. Nature-inspired metaheuristic algorithms. Luniver press;
Durbhaka G K, Selvaraj B and Nayyar A 2019 Firefly swarm: metaheuristic swarm intelligence technique for mathematical optimization. In: Data Management, Analytics and Innovation: Proceedings of ICDMAI 2018, Volume 2. Springer; p. 457–66.
Holland J H 1992 Genetic algorithms. Sci Am. 267(1): 66–73
Dastanpour A, Ibrahim S, Mashinchi R and Selamat A 2014 Using Genetic Algorithm to Support Artificial Neural Network for Intrusion Detection System. J. Commun. Comput. 11: 143–147
Kennedy J and Eberhart R 1995 Particle swarm optimization. In: Proceedings of ICNN’95-international conference on neural networks. IEEE; p. 1942–8
Roy B and Singh M P 2020 An empirical-based rainfall-runoff modelling using optimization technique. Int. J. River basin Manag. 18(1): 49–67
Umar R, Mohammed F, Deriche M and Sheikh A U H 2015 Hybrid cooperative energy detection techniques in cognitive radio networks. In: Handbook of research on software-defined and cognitive radio technologies for dynamic spectrum management. IGI Global; p. 1–37
Kumar P and Samui P 2022 Design of an Energy Pile Based on CPT Data Using Soft Computing Techniques. Infrastructures. 7(12): 169
Ghani S, Kumari S and Ahmad S 2022 Prediction of the seismic effect on liquefaction behavior of fine-grained soils using artificial intelligence-based hybridized modeling. Arab. J. Sci. Eng. 47(4): 5411–5441
Behar O, Khellaf A and Mohammedi K 2015 Comparison of solar radiation models and their validation under Algerian climate–The case of direct irradiance. Energy Convers. Manag. 98: 236–251
Legates D R and McCabe G J 2013 A refined index of model performance: a rejoinder. Int. J. Climatol. 33(4): 1053–1056
Willmott C J 1984 On the evaluation of model performance in physical geography. In: Spatial statistics and models. Springer; p. 443–60
Wong F S 1985 Slope reliability and response surface method. J. Geotech. Eng. 111(1): 32–53
Bardhan A and Samui P 2022 Probabilistic slope stability analysis of Heavy-haul freight corridor using a hybrid machine learning paradigm. Transp. Geotech. [Internet]. 37(July):100815. Available from: https://doi.org/10.1016/j.trgeo.2022.100815
Kumar R, Rai B and Samui P 2023 Machine learning techniques for prediction of failure loads and fracture characteristics of high and ultra-high strength concrete beams. Innov. Infrastruct. Solut. 8(8): 219
Stone R J 1993 Improved statistical procedure for the evaluation of solar radiation estimation models. Solar Energy. 51(4): 289–291
Ahmad F, Samui P and Mishra S S 2024 Machine learning-enhanced Monte Carlo and subset simulations for advanced risk assessment in transportation infrastructure. J. Mt. Sci. 21: 690–717
Kardani N, Aminpour M, Raja M N A, Kumar G, Bardhan A and Nazem M 2022 Prediction of the resilient modulus of compacted subgrade soils using ensemble machine learning methods. Transp. Geotech. 36: 100827
Eriksson L, Jaworska J, Worth A P, Cronin M T D, McDowell R M and Gramatica P 2003 Methods for reliability and uncertainty assessment and for applicability evaluations of classification-and regression-based QSARs. Environ. Health Perspect. 111(10): 1361–1375
Vighi M, Gramatica P, Consolaro F and Todeschini R 2001 QSAR and chemometric approaches for setting water quality objectives for dangerous chemicals. Ecotoxicol. Environ Saf. 49(3): 206–220
Asadollahi T, Dadfarnia S, Shabani A M H, Ghasemi J B and Sarkhosh M 2011 QSAR models for CXCR2 receptor antagonists based on the genetic algorithm for data preprocessing prior to application of the PLS linear regression method and design of the new compounds using in silico virtual screening. Molecules. 16(3): 1928–1955
Beheshti A, Pourbasheer E, Nekoei M and Vahdani S 2016 QSAR modeling of antimalarial activity of urea derivatives using genetic algorithm–multiple linear regressions. J. Saudi Chem. Soc. 20(3): 282–290
Gandomi A H, Alavi A H, Sahab M G and Arjmandi P 2010 Formulation of elastic modulus of concrete using linear genetic programming. J. Mech. Sci. Technol. 24: 1273–1278
Pradeep T and Samui P 2022 Prediction of Rock Strain Using Hybrid Approach of Ann and Optimization Algorithms. Geotech. Geol. Eng. 40(9): 4617–4643
Golbraikh A and Tropsha A 2002 Beware of q2! J. Mol. Graph. Model. 20(4): 269–276
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Ahmad, F., Samui, P. & Keshav, K.K. Reliability assessment and forecasting of moment ratio/factor of safety for sheet pile walls utilizing hybrid ANFIS enhanced by optimization techniques. Sādhanā 49, 202 (2024). https://doi.org/10.1007/s12046-024-02547-3
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DOI: https://doi.org/10.1007/s12046-024-02547-3