Skip to main content
SpringerLink
Log in

Harnessing Nature-Inspired Soft Computing for Reinforced Soil Bearing Capacity Prediction: A Neuro-nomograph Approach for Efficient Design

  • Original Paper
  • Published:
International Journal of Geosynthetics and Ground Engineering Aims and scope Submit manuscript

Abstract

The bearing capacity of soil in general is considered a key parameter in the field of geotechnical engineering, requiring field investigations and extensive testing to eliminate design errors. Reinforced sand beds, however, present unique complexities for conventional computational techniques, as these methods may fall short in fully capturing the interaction between parameters that control ultimate bearing capacity. Consequently, nature-inspired soft computing (SC) techniques, inspired by the resilience and adaptability inherent in natural systems, have been utilized and evaluated in simulating and predicting the reinforced soil bearing capacity in geotechnical engineering. These include support vectors machines (SVM), ensemble tree (ET), Gaussian’s process regressions (GPR), regression trees (RT), and artificial neural network (ANN). A thorough evaluation of SC techniques was executed for their computational efficiency and prediction accuracy. The hypermeter values of all SC techniques were optimized using Bayesian optimization with the goal of reducing prediction error. The results showed that ANN-SC technique outperformed the other techniques based on three performance measures: mean absolute errors (MAE), coefficients of determination (R2), and root mean square errors (RMSE). Furthermore, normalized importance analysis was conducted using the best-performed model (ANN), and the findings demonstrated that the soil average particle size/reinforcement width (D50/Aw) had the highest relative importance on the ANN-predicted bearing capacity, followed by friction angle and depth of first reinforcement layer. The python code (using PyNomo library) was employed to develop a nomograph to facilitate the application of the ANN model findings. This neuro-nomograph uses the weights and biases from the optimal ANN model to offer a simplified tool to predict reinforced soil bearing capacity. Furthermore, the performance of this novel neuro-nomograph was validated using physical bearing capacity test results. The comparison showed a coefficient of variation (COV) of 0.13 and a mean ratio of test to predicted bearing capacities (UBCtest/UBCpred) of 1.11, which suggests the minimal scatter and, thus, confirm the high precision of the developed neuro-nomograph predictions of the reinforced soil bearing capacities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Data Availability

The data generated/analyzed during the study are available from the corresponding author on reasonable request.

References

  1. Alotaibi E, Nassif N, Barakat S (2023) Data-driven reliability and cost-based design optimization of steel fiber reinforced concrete suspended slabs. Struct Concr 24:1859–1867

    Google Scholar 

  2. Shahin MA (2015) A review of artificial intelligence applications in shallow foundations. Int J Geotech Eng 9(1):49–60

    Google Scholar 

  3. Kurian NP (2005) Design of foundation systems: principles and practices (3 rev. and enl edn.). Alpha Science International, Harrow, Middlesex

    Google Scholar 

  4. Alotaibi E, Omar M, Arab MG, Tahmaz A (2022) Prediction of fine-grained soils shrinkage limits using artificial neural networks. In: 2022 Advances in science and engineering technology international conferences (ASET). IEEE, pp 1–5

  5. Soleimanbeigi A, Hataf N (2005) Predicting ultimate bearing capacity of shallow foundations on reinforced cohesionless soils using artificial neural networks. Geosynth Int 12(6):321–332

    Google Scholar 

  6. Hung CC, Ni SH (2007) Using multiple neural networks to estimate the screening effect of surface waves by in-filled trenches. Comput Geotech 34(5):397–409

    Google Scholar 

  7. Sahu R, Patra CR, Sivakugan N, Das BM (2017) Bearing capacity prediction of inclined loaded strip footing on reinforced sand by ANN. In: International congress and exhibition, sustainable civil infrastructures: innovative infrastructure geotechnology, Springer, Cham, pp 97–109

  8. Sahu R, Patra CR, Sivakugan N, Das BM (2017) Use of ANN and neuro fuzzy model to predict bearing capacity factor of strip footing resting on reinforced sand and subjected to inclined loading. Int J Geosynth Ground Eng 3(3):29

    Google Scholar 

  9. Moayedi H, Hayati S (2018) Modelling and optimization of ultimate bearing capacity of strip footing near a slope by soft computing methods. Appl Soft Comput 66:208–219

    Google Scholar 

  10. Dutta RK, Rao TG, Sharma A (2019) 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 Civil Eng 3(4):28–40

    Google Scholar 

  11. Dutta RK, Khatri VN, Gnananandarao T (2019) Soft computing-based prediction of ultimate bearing capacity of footings resting on rock masses. Inter J Geol Geotech Eng 5(2):1–14

    Google Scholar 

  12. Dal K, Cansiz OF, Ornek M, Turedi Y (2019) Prediction of footing settlements with geogrid reinforcement and eccentricity. Geosynth Int 26(3):297–308

    Google Scholar 

  13. Asghari V, Leung YF, Hsu SC (2020) Deep neural network-based framework for complex correlations in engineering metrics. Adv Eng Inf 44:101058

    Google Scholar 

  14. Chen C, Mao F, Zhang G, Huang J, Zornberg JG, Liang X, Chen J (2021) Settlement-based cost optimization of geogrid-reinforced pile-supported foundation. Geosynth Int 28(5):541–557

    Google Scholar 

  15. Pant A, Ramana GV (2022) Novel application of machine learning for estimation of pullout coefficient of geogrid. Geosynth Int 29(4):342–355

    Google Scholar 

  16. Raviteja KVNS, Kavya KVBS, Senapati R, Reddy KR (2023) Machine-learning modelling of tensile force in anchored geomembrane liners. Geosynth Int. https://doi.org/10.1680/jgein.22.00377

    Article  Google Scholar 

  17. Shahin MA, Jaksa MB, Maier HR (2009) Recent advances and future challenges for artificial neural systems in geotechnical engineering applications. Adv Artif Neural Syst 2009:9

    Google Scholar 

  18. Raja MNA, Shukla SK (2021) Predicting the settlement of geosynthetic-reinforced soil foundations using evolutionary artificial intelligence technique. Geotext Geomembr 49(5):1280–1293

    Google Scholar 

  19. Kumar M, Kumar V, Biswas R, Samui P, Kaloop MR, Alzara M, Yosri AM (2022) Hybrid ELM and MARS-based prediction model for bearing capacity of shallow foundation. Processes 10(5):1013

    Google Scholar 

  20. Samui P, Sitharam TG, Kurup PU (2008) OCR prediction using support vector machine based on piezocone data. J Geotech Geoenviron Eng 134(6):894–898

    Google Scholar 

  21. Kumar M, Samui P (2020) Reliability analysis of settlement of pile group in clay using LSSVM, GMDH. GPR Geotech Geol Eng 38(6):6717–6730

    Google Scholar 

  22. Assadi-Langroudi A, O’Kelly BC, Barreto D, Cotecchia F, Dicks H, Ekinci A, van Paassen L (2022) Recent advances in nature-inspired solutions for ground engineering (NiSE). Int J Geosynth Ground Eng 8(1):3

    Google Scholar 

  23. Sharma R, Chen Q, Abu-Farsakh M, Yoon S (2009) Analytical modeling of geogrid reinforced soil foundation. Geotext Geomembr 27(1):63–72

    Google Scholar 

  24. Chen Q, Abu-Farsakh M (2015) Ultimate bearing capacity analysis of strip footings on reinforced soil foundation. Soils Found 55(1):74–85

    Google Scholar 

  25. Ebid AM (2021) 35 Years of (AI) in geotechnical engineering: state of the art. Geotech Geol Eng 39(2):637–690

    Google Scholar 

  26. Alotaibi E, Omar M, Shanableh A, Zeiada W, Fattah MY, Tahmaz A, Arab MG (2021) Geogrid bridging over existing shallow flexible PVC buried pipe–experimental study. Tunn Undergr Space Technol 113:103945

    Google Scholar 

  27. Aria S, Shukla SK, Mohyeddin A (2019) Behaviour of sandy soil reinforced with geotextile having partially and fully wrapped ends. In: Proc instit civil eng ground improve, pp 1–14

  28. Alotaibi E, Omar M, Arab MG, Shanableh A, Zeiada MY, Tahmaz A, (2019) Experimental investigation of the effect of geogrid reinforced backfill compaction on buried pipelines response. In: The 4th world congress on civil, structural, and environmental engineering

  29. Abu-Farsakh M, Chen Q, Sharma R (2013) An experimental evaluation of the behavior of footings on geosynthetic-reinforced sand. Soils Found 53(2):335–348

    Google Scholar 

  30. Latha GM, Somwanshi A (2009) Bearing capacity of square footings on geosynthetic reinforced sand. Geotext Geomembr 27(4):281–294

    Google Scholar 

  31. Adams MT, Collin JG (1997) Large model spread footing load tests on geosynthetic reinforced soil foundations. J Geotech Geoenviron Eng 123(1):66–72

    Google Scholar 

  32. Das BM, Omar MT (1994) The effects of foundation width on model tests for the bearing capacity of sand with geogrid reinforcement. Geotech Geol Eng 12(2):133–141

    Google Scholar 

  33. Das BM, Shin EC, Omar MT (1994) The bearing capacity of surface strip foundations on geogrid-reinforced sand and clay—a comparative study. Geotech Geol Eng 12(1):1–14

    Google Scholar 

  34. Yetimoglu T, Wu JT, Saglamer A (1994) Bearing capacity of rectangular footings on geogrid-reinforced sand. J Geotech Eng 120(12):2083–2099

    Google Scholar 

  35. Omar MT, Das BM, Puri VK, Yen SC (1993) Ultimate bearing capacity of shallow foundations on sand with geogrid reinforcement. Can Geotech J 30(3):545–549

    Google Scholar 

  36. Omar MT, Das BM, Puri VK, Yen SC, Cook EE (1993) Shallow foundations on geogrid-reinforced sand. Transport Res Rec 1414:59–64

    Google Scholar 

  37. Omar MT, Das BM, Yen SC, Puri VK, Cook EE (1993) Ultimate bearing capacity of rectangular foundations on geogrid-reinforced sand. Geotech Test J 16(2):246–252

    Google Scholar 

  38. Khing KH, Das BM, Puri VK, Cook EE, Yen SC (1993) The bearing-capacity of a strip foundation on geogrid-reinforced sand. Geotext Geomembr 12(4):351–361

    Google Scholar 

  39. Guido VA, Chang DK, Sweeney MA (1986) Comparison of geogrid and geotextile reinforced earth slabs. Can Geotech J 23(4):435–440

    Google Scholar 

  40. Guido VA, Biesiadecki GL, Sullivan MJ (1985) Bearing capacity of a geotextile-reinforced foundation. In: International conference on soil mechanics and foundation engineering. A. A. Balkema, Rotterdam, Netherlands, pp 1777–1780

  41. Junhua W, Haozhe C, Shi Q (2013) Estimating freeway incident duration using accelerated failure time modeling. Saf Sci 54:43–50

    Google Scholar 

  42. Ahmad H, Mahboubi A, Noorzad A (2020) Scale effect study on the modulus of subgrade reaction of geogrid-reinforced soil. SN Appl Sci 2(3):1–22

    Google Scholar 

  43. Mehrjardi GT, Khazaei M (2017) Scale effect on the behaviour of geogrid-reinforced soil under repeated loads. Geotext Geomembr 45(6):603–615

    Google Scholar 

  44. Rasmussen CE, Nickisch H (2010) Gaussian processes for machine learning (GPML) toolbox. J Mach Learn Res 11:3011–3015

    MathSciNet  MATH  Google Scholar 

  45. Abramowitz M, Stegun IA (1965) Handbook of mathematical functions. Dover Publications, New York, p 361

    Google Scholar 

  46. Noble WS (2006) What is a support vector machine? Nat Biotechnol 24(12):1565–1567

    Google Scholar 

  47. Loh WY (2011) Classification and regression trees. Wiley Interdiscip Rev Data Min Knowl Discov 1(1):14–23

    Google Scholar 

  48. Zhou ZH, Tang W (2003) Selective ensemble of decision trees. In: Wang G, Liu Q, Yao Y, Skowron A (eds) International workshop on rough sets, fuzzy sets, data mining, and granular-soft computing. Springer, Berlin, Heidelberg, pp 476–483

    Google Scholar 

  49. The MathWorks, Inc. (2022) Statistics and machine learning toolbox (R2022a). Natick, Massachusetts, United States. Retrieved from https://www.mathworks.com/help/stats/

  50. Nowruzi H, Ghassemi H (2016) Using artificial neural network to predict velocity of sound in liquid water as a function of ambient temperature, electrical and magnetic fields. J Ocean Eng Sci 1(3):203–211

    Google Scholar 

  51. Güven İ, Şimşir F (2020) Demand forecasting with color parameter in retail apparel industry using artificial neural networks (ANN) and support vector machines (SVM) methods. Comput Ind Eng 147:106678

    Google Scholar 

  52. Kumar AR, Goyal MK, Ojha CSP, Singh RD, Swamee PK (2013) Application of artificial neural network, fuzzy logic and decision tree algorithms for modelling of streamflow at Kasol in India. Water Sci Technol 68(12):2521–2526

    Google Scholar 

  53. Moraes R, Valiati JF, Neto WPG (2013) Document-level sentiment classification: an empirical comparison between SVM and ANN. Expert Syst Appl 40(2):621–633

    Google Scholar 

  54. Shahin MA, Maier HR, Jaksa MB (2002) Predicting settlement of shallow foundations using neural networks. J Geotech Geoenviron Eng 128(9):785–793

    Google Scholar 

  55. Evesham HA (1986) Origins and development of nomography. Ann Hist Comput 8(4):324–333

    MathSciNet  MATH  Google Scholar 

  56. Papayannopoulos P (2020) Computing and modelling: analog vs. analogue. Stud Hist Philos Sci A 83:103–120

    Google Scholar 

  57. Omar M, Shanableh A, Hamad K, Tahmaz A, Arab MG, Al-Sadoon Z (2019) Nomographs for predicting allowable bearing capacity and elastic settlement of shallow foundation on granular soil. Arab J Geosci 12(15):485

    Google Scholar 

  58. Mendoza FC, Gisbert AF, Izquierdo AG, Bovea MD (2009) Safety factor nomograms for homogeneous earth dams less than ten meters high. Eng Geol 105(3/4):231–238

    Google Scholar 

  59. Omar M, Hamad K, Al Suwaidi M, Shanableh A (2018) Developing artificial neural network models to predict allowable bearing capacity and elastic settlement of shallow foundation in Sharjah, United Arab Emirates. Arab J Geosci 11(16):464

    Google Scholar 

  60. Douglas J, Danciu L (2020) Nomogram to help explain probabilistic seismic hazard. J Seismol 24(1):221–228

    Google Scholar 

  61. Kashkarov S, Li Z, Molkoy V (2020) Blast wave from a hydrogen tank rupture in a fire in the open: hazard distance nomograms. Inter J Hydro Energy 45(3):2429–2446

    Google Scholar 

  62. Alotaibi E, Mostafa O, Nassif N, Omar M, Arab MG (2021) Prediction of punching shear capacity for fiber-reinforced concrete slabs using neuro-nomographs constructed by machine learning. J Struct Eng 147(6):04021075

    Google Scholar 

  63. Zhang X, Wang M, Li J, Wang Z, Tong J, Liu D (2020) Safety factor analysis of a tunnel face with an unsupported span in cohesive-frictional soils. Comp Geotech 117:103221

    Google Scholar 

  64. Glasser L, Doerfler R (2019) A brief introduction to nomography: graphical representation of mathematical relationships. Int J Math Educ Sci Technol 50(8):1273–1284

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil and Environmental Engineering, College of Engineering, University of Sharjah, P.O. Box 27272, Sharjah, United Arab Emirates

    Maher Omar, Emran Alotaibi, Mohamed G. Arab, Abdallah Shanableh & Ali Tahmaz

  2. Research Institute of Sciences and Engineering, University of Sharjah, Sharjah, United Arab Emirates

    Emran Alotaibi & Abdallah Shanableh

  3. Structural Engineering Department, Faculty of Engineering, Mansoura University, Al-Mansoura, Egypt

    Mohamed G. Arab

  4. Department of Civil and Environmental Engineering, School of Natural Resources Engineering and Management, German Jordanian University, Amman, Jordan

    Dima A. Hussien Malkawi

  5. Department of Applied Physics and Astronomy, College of Science, University of Sharjah, P.O. Box 27272, Sharjah, United Arab Emirates

    Hussein Elmehdi

Authors
  1. Maher Omar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Emran Alotaibi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mohamed G. Arab
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Abdallah Shanableh
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Dima A. Hussien Malkawi
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Hussein Elmehdi
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Ali Tahmaz
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed writing the original draft. Conceptualization: MO, MA, and AT. Data curation: EA and DHM. Formal analysis: EA and AT. Investigation: MO, MA and DHM. Methodology: MO, MA and HE. Project administration: MO and AS. Resources: MO and AS. Software: EA and HE. Supervision: AS, HE and MO validation: AT, MA and DHM. Visualization: EA, MO and AS. Writing—review and editing: MO, MA and EA.

Corresponding author

Correspondence to Maher Omar.

Ethics declarations

Conflict of Interest

The authors declare no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Omar, M., Alotaibi, E., Arab, M.G. et al. Harnessing Nature-Inspired Soft Computing for Reinforced Soil Bearing Capacity Prediction: A Neuro-nomograph Approach for Efficient Design. Int. J. of Geosynth. and Ground Eng. 9, 53 (2023). https://doi.org/10.1007/s40891-023-00472-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40891-023-00472-9

Keywords

Search

Navigation