Evaluation of Uncertainty in Shear-Wave Velocity Based on CPT Records Using the Robust Optimization Method

Document Type : Research Papers

Authors

1 Ph.D. Candidate, Department of Civil Engineering, Memorial University of Newfoundland, Newfoundland, NL, Canada.

2 Assistant Professor, Department of Civil Engineering, Gonbad University, Gonbad, Golestan, Iran.

3 Assistant Professor, Department of Civil Engineering and Construction Management, California Baptist University, California, U.S.

4 Professor, Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.

5 Assistant Professor, Department of Geography and Urban Planning, University of Mazandaran, Babolsar, Mazandaran, Iran.

Abstract

Shear-wave velocity (Vs) is used to evaluate the soil shear modulus and classify the soil type in pseudo-static analysis. Empirical correlations are developed to relate Vs and Cone Penetration Test (CPT) records. However, uncertainty in the input parameter measurements is always a major concern. Therefore, the current research employs a novel method based on robust optimization to study the effect of such uncertainties. To measure the merits of the suggested method, 407 records were collected and categorized for several soil types. The identification procedure employed in this investigation is based on the robust model of least squares, solved using the interior point technique for second-order cone problems. The uncertainty definition is examined against correlation coefficients for empirical models, and optimum values are determined based on the frobenius norm of the data points. A diagram for calculating the shear wave velocity considering uncertainties is also presented. This study suggests that the robust method is the best pattern recognition tool for uncertain datasets compared to previous statistical models. Other power models also have good accuracy compared to the polynomial model, but when uncertainty is taken into account, the accuracy of the other models is lower compared to the polynomial model.

Keywords

References

Alizadeh, F. and Goldfarb, D. (2003). “Second-order cone programming”, Mathematical Programming, 95(1), 3-51, http://doi.org/10.1007/s10107-002-0339-5.
Anagnostopoulos, A., Koukis, G., Sabatakakis, N. and Tsiambaos, G. (2003). “Empirical correlations of soil parameters based on cone penetration tests for Greek soils”, Geotechnical and Geological Engineering, 21, 377-387, http://doi.org/10.1023/B:GEGE.0000006064.47819.1a.
Barrow, B.L. and Stokoe, K.E.I.I. (1983). “Field investigation of liquefaction sites in northern California”, Geotechnical Engineering Thesis, GT 83-1, Civil Engineering Department, University of Texas at Austin, 212 p.
Bayat, M., Saadat, M. and Hojati, A. (2023). “Optimization of dynamic compaction procedure for sandy soils”, Civil Engineering Infrastructures Journal, http://doi.org/10.22059/CEIJ.2023.351287.1889.
Ben-Tal, A., El Ghaoui, L. and Nemirovski, A. (2009). Robust optimization, Princeton University Press, 28, http://doi.org/10.1515/9781400831050.
Chala, A. and Ray, R. (2023). “Machine learning techniques for soil characterization using cone penetration test data”, Applied Sciences Journal, 13(14), 8286,  http://doi.org/10.3390/app13148286.
Comina, C., Foti, S., Passeri, F. Socco, L.V. (2022). “Time-weighted average shear wave velocity profiles from surface wave tests through a wavelength-depth transformation”, Soil Dynamics and Earthquake Engineering, 158, http://doi.org/10.1016/j.soildyn.2022.107262.
Eslami, A., Akbarimehr, D., Aflaki, E. and Hajitaheriha, M.M. (2020). “Geotechnical site characterization of the Lake Urmia super-soft sediments using laboratory and CPTu records”, Marine Georesources and Geotechnology, 38, http://doi.org/10.1080/1064119X.2019.1672121.
Ghose, R. (2004). “Model-based integration of seismic and CPT data to derive soil parameters”, Proceedings of the 10th European Meeting of Environmental and Engineering Geophysics, B019, http://doi.org/10.3997/2214-4609-pdb.10.B019.
Gilder, C.E., Pokhrel, R.M., De Luca, F. and Vardanega, P.J. (2021). “Insights from CPTu and seismic cone penetration testing in the Kathmandu valley, Nepal”, Frontiers in Built Environment, 7, 646009, http://doi.org/10.3389/fbuil.2021.646009.
Golub, G.H. and Van Loan, C.F. (2013). Matrix computations, 3rd Edition, Baltimore, MD: Johns Hopkins, http://doi.org/10.56021/9781421407944.
Hegazy Y.A. and Mayne, P.W. (1995). “Statistical correlations between vs and cone penetration data for different soil types”, Proceedings of the International Symposium on Cone Penetration Testing (CPT'95), Linkoping, Sweden, 4-5 October 1995, Swedish Geotechnical Society, 2, 173-178, https://researchgate.net/publication/283361455_Statistical_correlations_between_Vs_and_CPT_data_fordifferentsoiltypes.
Iyisan, R. and Ansal, A. (1993). “Determination of dynamic soil properties by borehole seismic methods”, 2th National Earthquake Engineering Conference, Proceedings of the Chamber of Civil Engineer’s Turkey (in Turkish).
Jakka, R., Desai, A. and Foti, S. (2022). “Guidelines for minimization of uncertainties and estimation of a reliable shear wave velocity profile using masw testing: A state-of-the-art review”, Advances in Earthquake Geotechnics, 211-253, http://doi.org/10.1007/978-981-19-3330-112.
Kalantary, F., MolaAbasi, H., Salahi, M. and Veiskarami, M. (2013). “Prediction of liquefaction induced lateral displacements using robust optimization model”, Scientia Iranica, 20(2), 242-250, https://doi.org/10.1016/j.scient.2012.12.025.
Kruiver, P.P., de Lange, G., Kloosterman, F., Korff, M., van Elk, J. and Doornhof, D. (2021). “Rigorous test of the performance of shear-wave velocity correlations derived from CPT soundings: A case study for Groningen, the Netherlands”, Soil Dynamics and Earthquake Engineering, 140, 106471, http://doi.org/10.1016/j.soildyn.2020.106471.
Madiai, C., Simoni, G. (2004). “Shear wave velocity-penetration resistance correlation for holocene and pleistocene soils of an area in central italy”, Proceedings ISC-2 on Geotechnical and Geophysical Site Characterization, Viana da Fonseca and Mayne (eds.), Mill Press, Rotterdam, 1687-1694, https://doi.org/10.1400/107037.
Mayne, P.W. and Rix, G.J. (1995). “Correlations between shear wave velocity and cone tip resistance in natural clays”, Soils and Foundations, 35(2), 107-110, https://doi.org/10.3208/sandf1972.35.2107.
Mayne, P.W. (2006). “Undisturbed sand strength from seismic cone tests”, Geomechanics and Geoengineering, London, 1(4), 239-257, https://doi.org/10.1080/17486020601035657.
Mayne, P.W. (2007). Cone penetration testing, national cooperative highway research programme, Synthesis 368, Transportation Research Board, USA, 117pp, https://doi.org/10.17226/23143.
McGann, C.R., Bradley, B.A., Taylor, M.L., Wotherspoon, L.M. and Cubrinovski, M. (2015b). “Development of an empirical correlation for predicting shear wave velocity of Christchurch soils from cone penetration test data”, Soil Dynamics and Earthquake Engineering, 75, 66-75, http://doi.org/10.1016/j.soildyn.2015.03.023.
Meng. F. and Pei, H. (2023). “Quasi-site-specific prediction of shear wave velocity from CPTu”, Soil Dynamics and Earthquake Engineering, 172, http://doi.org/10.1016/j.soildyn.2023.108005.
Mohammadikish, S., Ashayeri, I. and Biglari, M. et al. (2023). “Soil liquefaction assessment by CPT and vs data and incomplete-fuzzy c-means clustering”, Geotechnical and Geological Engineering, https://doi.org/10.1007/s10706-023-02669-1.
Mola‐Abasi, H., Dikmen, U. and Shooshpasha, I. (2015). “Prediction of shear-wave velocity from CPT data at Eskisehir (Turkey), using a polynomial model”,  Near Surface Geophysics, 13(2), 155-167, http://doi.org/10.3997/1873-0604.2015010.
Paoletti, L., Hegazy, Y., Monaco, S. and Piva, R. (2010). “Prediction of shear wave velocity for offshore sands using CPT data Adriatic Sea”, 2nd International Symposium on Cone Penetration Testing, Huntington Beach, CA, USA, 1-8, https://www.geoengineer.org/storage/publication/18372/publication_file/2611/29Paopos.pdf.
Robertson, P.K. (2009). “Interpretation of cone penetration tests, A unified approach”, Canadian Geotechnical Journal, 46(11), 1337-1355, http://doi.org/10.1139/T09-065.
Stolte, A. and Cox, B. (2020). “Towards consideration of epistemic uncertainty in shear-wave velocity measurements obtained via seismic cone penetration testing”, Canadian Geotechnical Journal, 57, http://doi.org/10.1139/cgj-2018-0689.
Sturm, J.F. (1999). “Using Sedumi 1.02. a Matlab toolbox for optimization over symmetric cones”, Optimization Methods and Software,  11(1-4), 625-653, https://doi.org/10.1080/10556789908805766.
Sturm, J. (2002). “Implementation of interior point methods for mixed semidefinite and second order cone optimization problems”, Optimization Methods and Software, 17(6), 1105-1154, https://doi.org/10.1080/1055678021000045123.
Sykora, D.W. and Stokoe, K.H. (1983). “Correlations of in situ measurements in sands of shear wave velocity, soil characteristics and site conditions”, The University of Texas, Austin, Geotechnical Engineering Report, GR83-33.
Tun, M. (2003). “Investigation of the characteristics of Eskisehir soils due to shear wave velocity and determination of their fundamental vibration periods”, Master Thesis, Anadolu University Institute of Science and Technology Department of Physics (in Turkish), http://doi.org/10.13140/RG.2.1.4303.8801.
Tun, M., Ayday, C. (2018). “Investigation of correlations between shear wave velocities and cpt data: A case study at Eskisehir in Turkey”, Bulletin of Engineering Geology and the Environment, 77, 225-236. https://doi.org/10.1007/s10064-016-0987-y.
Wang, J., Hwang, J.  and Lu, C. (2022). “Measurement uncertainty of shear wave velocity: A case study of thirteen alluvium test sites in taipei basin”, Soil Dynamics and Earthquake Engineering, 155, http://doi.org/10.1016/j.soildyn.2022.107195.
Wang, J.S., Hwang, J.H. and Lu, C.C. (2022). “Empirical formulas for shear wave velocity prediction and their uncertainties: a case study of thirteen alluvium test sites in the Taipei basin”, Bulletin of Engineering Geology and the Environment, 81, 450, https://doi.org/10.1007/s10064-022-02949-9.
Wang, T., Xiao, S., Zhang, J. and Zuo, B. (2022). “Depth-consistent models for probabilistic liquefaction potential assessment based on shear wave velocity”, Bulletin of Engineering Geology and the Environment, 81, 255, http://doi.org/10.1007/s10064-022-02754-4.
Yang, H., Liu, Z., Xie, Y. and Li, S. (2023). “A probabilistic liquefaction reliability evaluation system based on catboost-bayesian considering uncertainty using cpt and vs measurements”, Soil Dynamics and Earthquake Engineering, 173, http://doi.org/10.1016/j.soildyn.2023.108101.
Zhai, S., Du, G. and He, H. (2024). “Bayesian probabilistic characterization of the shear-wave velocity combining the cone penetration test and standard penetration test”, Stochastic Environmental Research and Risk Assessment, 38(1), 69-84,  https://doi.org/10.1007/s00477-023-02566-2.
Zhang, Y., Xie, Y., Zhang, Y., Qiu, J. and Wu, S. (2021). “The adoption of deep neural network to the prediction of soil liquefaction based on shear wave velocity”, Bulletin of Engineering Geology and the Environment,  80(6), 5053-5060, http://doi.org/10.1007/s10064-021-02250-1
Zhao, Z., Duan, W. and Cai, G. (2021). “A novel pso-kelm based soil liquefaction potential evaluation system using cpt and vs measurements”, Soil Dynamics and Earthquake Engineering, 150, http://doi.org/10.1016/j.soildyn.2021.106930.
Zhao, Z., Duan, W., Cai, G., Wu, M. and Liu, S. (2022). “CPT-based fully probabilistic seismic liquefaction potential assessment to reduce uncertainty: integrating xgboost algorithm with Bayesian theorem”, Computers and Geotechnics, 149, http://doi.org/10.1016/j.compgeo.2022.104868.
Zhou, J., Huang, S., Wang, M. and Qiu, Y. (2022). “Performance evaluation of hybrid GA–SVM and GWO–SVM models to predict earthquake-induced liquefaction potential of soil: A multi-dataset investigation”, Engineering with Computers, 38, 4197-4215, http://doi.org/10.1007/s00366-021-01418-3.
Civil Engineering Infrastructures Journal
Volume 58, Issue 1
June 2025
Pages 159-171

Files

History

  • Receive Date: 03 October 2023
  • Revise Date: 16 January 2024
  • Accept Date: 12 February 2024

Share

How to cite

Statistics