Simulation of Geological Uncertainty Using Coupled Markov Chain: A Case Study at a Manually Filled Loess Site
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 10, Issue 2
Abstract
Stratigraphic variability contributes significantly to the deformation and stability of geotechnical structures. In this case study, the stratigraphic variability of a typical deep manually filled site in Lanzhou New District, Gansu Province, China is simulated. By applying Walther’s law, the relationship between vertical and horizontal transition counting matrices is established to calculate the vertical and horizontal state-transition probability matrices using a coupled Markov chain model. The Monte Carlo simulation method is used to predict the distribution of soil layers. Based on borehole data, the effects of different borehole layout schemes on the estimation of the transfer probability matrix and prediction of the soil layer distribution are investigated. The results indicate that to obtain accurate estimations for the state transition probability matrix and predictions for the soil layer distribution, more evenly distributed borehole data should be selected. When the values of the diagonal elements in the matrix are high, the sensitivity of the transition probability matrix estimation to the borehole layout scheme is low. Multiple predictions of soil layer distributions using the same borehole layout scheme yield different results primarily because of the significant spacing between the boreholes.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant Nos. 52268058; 51868038); Tianyou Youth Talent Lift Program of Lanzhou Jiaotong University; Special Funds for Guiding Local Scientific and Technological Development by The Central Government (22ZY1QA005). Gansu Provincial Department of Education Industrial Support Program Project, China (2023CYZC-34).
References
Bao, H., M. Tang, H. X. Lan, J. B. Peng, H. Zheng, and G. M. Guo. 2023. “Soil erosion and its causes in high-filling body: A case study of a valley area on the Loess Plateau, China.” J. Mount. Sci. 20 (1): 182–196. https://doi.org/10.1007/s11629-021-7221-5.
Cao, W., A. Zhou, and S. L. Shen. 2021. “An analytical method for estimating horizontal transition probability matrix of coupled Markov chain for simulating geological uncertainty.” Comput. Geotech. 129 (Jan): 103871. https://doi.org/10.1016/j.compgeo.2020.103871.
Cao, Z., Y. Wang, and D. Li. 2016. “Quantification of prior knowledge in geotechnical site characterization.” Eng. Geol. 203 (Mar): 107–116. https://doi.org/10.1016/j.enggeo.2015.08.018.
Chen, G., Y. Zhang, R. Q. Zeng, Z. Yang, X. Chen, F. Zhao, and X. M. Meng. 2018. “Detection of land subsidence associated with land creation and rapid urbanization in the Chinese Loess Plateau using time series InSAR: A case study of Lanzhou New District.” Remote Sens. 10 (2): 270. https://doi.org/10.3390/rs10020270.
Cheng, H. Z., J. Chen, R. P. Chen, and G. L. Chen. 2019. “Comparison of modeling soil parameters using random variables and random fields in reliability analysis of tunnel face.” Int. J. Geomech. 19 (1): 04018184. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001330.
Crisp, M. P., M. B. Jaksa, and Y. L. Kuo. 2020. “Toward a generalized guideline to inform optimal site investigations for pile design.” Can. Geotech. J. 57 (8): 1119–1129. https://doi.org/10.1139/cgj-2019-0111.
Elfeki, A. M. M., and F. M. Dekking. 2001. “A Markov chain model for subsurface characterization: Theory and applications.” Math. Geol. 33 (5): 569–589. https://doi.org/10.1023/A:1011044812133.
Elfeki, A. M. M., and F. M. Dekking. 2005. “Modelling subsurface heterogeneity by coupled Markov chains: Directional dependency, Walther’s law and entropy.” Geotech. Geol. Eng. 23 (6): 721–756. https://doi.org/10.1007/s10706-004-2899-z.
Elkateb, T., R. Chalaturnyk, and P. K. Robertson. 2003. “An overview of soil heterogeneity: Quantification and implications on geotechnical field problems.” Can. Geotech. J. 40 (1): 1–15. https://doi.org/10.1139/t02-090.
Faes, M., and D. Moens. 2019. “Imprecise random field analysis with parametrized kernel functions.” Mech. Syst. Signal Process. 134 (Dec): 106334. https://doi.org/10.1016/j.ymssp.2019.106334.
Gong, W. P., H. M. Tang, H. Wang, X. R. Wang, and C. H. Juang. 2019. “Probabilistic analysis and design of stabilizing piles in slope considering stratigraphic uncertainty.” Eng. Geol. 259 (Sep): 105162. https://doi.org/10.1016/j.enggeo.2019.105162.
He, J., J. Chen, X. Ren, and J. Li. 2021a. “Uncertainty quantification of random fields based on spatially sparse data by synthesizing Bayesian compressive sensing and stochastic harmonic function.” Mech. Syst. Signal Process. 153 (May): 107377. https://doi.org/10.1016/j.ymssp.2020.107377.
He, J., R. Gao, and H. Zhou. 2023. “A nonparametric seismic reliability analysis method based on Bayesian compressive sensing-Stochastic harmonic function method and probability density evolution method.” Mech. Syst. Signal Process. 196 (Aug): 110339. https://doi.org/10.1016/j.ymssp.2023.110339.
He, Y., Y. D. Chen, W. H. Wang, H. W. Yan, L. F. Zhang, and T. Liu. 2021b. “TS-InSAR analysis for monitoring ground deformation in Lanzhou New District, the Loess Plateau of China, from 2017 to 2019.” Adv. Space Res. 67 (4): 1267–1283. https://doi.org/10.1016/j.asr.2020.11.004.
Huang, H. W., L. Xiao, D. M. Zhang, and J. Zhang. 2017. “Influence of spatial variability of soil Young’s modulus on tunnel convergence in soft soils.” Eng. Geol. 228 (Oct): 357–370. https://doi.org/10.1016/j.enggeo.2017.09.011.
Jiang, S. H., I. Papaioannou, and D. Straub. 2020. “Optimization of site exploration programs for slope-reliability assessment.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 6 (1): 04020004. https://doi.org/10.1061/AJRUA6.0001042.
Juang, C. H., T. Dijkstra, J. Wasowski, and X. M. Meng. 2019. “Loess geohazards research in China: Advances and challenges for mega engineering projects.” Eng. Geol. 251 (Mar): 1–10. https://doi.org/10.1016/j.enggeo.2019.01.019.
Kalantari, A. R., A. Johari, M. Zandpour, and M. Kalantari. 2023. “Effect of spatial variability of soil properties and geostatistical conditional simulation on reliability characteristics and critical slip surfaces of soil slopes.” Transp. Geotech. 39 (Mar): 100933. https://doi.org/10.1016/j.trgeo.2023.100933.
Khoshnevisan, S., W. Gong, C. H. Juang, and S. Atamturktur. 2015. “Efficient robust geotechnical design of drilled shafts in clay using a spreadsheet.” J. Geotech. Geoenviron. Eng. 141 (2): 04014092. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001214.
Krumbein, W. C. 1968. “Statistical models in sedimentology.” Sedimentology 10 (1): 7–23. https://doi.org/10.1111/j.1365-3091.1968.tb01908.x.
Lan, H. X., N. M. Tian, L. P. Li, H. J. Liu, J. B. Peng, P. Cui, C. H. Zhou, R. Macciotta, and J. J. Clague. 2022. “Poverty control policy may affect the transition of geological disaster risk in China.” Humanit. Soc. Sci. Commun. 9 (1): 1–7. https://doi.org/10.1057/s41599-022-01096-6.
Li, D. Q., X. H. Qi, Z. J. Cao, X. S. Tang, K. K. Phoon, and C. B. Zhou. 2016a. “Evaluating slope stability uncertainty using coupled Markov chain.” Comput. Geotech.73 (Mar): 72–82. https://doi.org/10.1016/j.compgeo.2015.11.021.
Li, J. H., Y. H. Tian, and M. J. Cassidy. 2015. “Failure mechanism and bearing capacity of footings buried at various depths in spatially random soil.” J. Geotech. Geoenviron. Eng. 141 (2): 04014099. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001219.
Li, P. Y., H. Qian, and J. H. Wu. 2014. “Environment: Accelerate research on land creation.” Nature 510 (7503): 29–31. https://doi.org/10.1038/510029a.
Li, X. A., L. C. Li, Y. X. Song, B. Hong, L. Wang, and J. Q. Sun. 2019. “Characterization of the mechanisms underlying loess collapsibility for land creation project in Shaanxi Province, China—A study from a micro perspective.” Eng. Geol. 249 (Jan): 77–88. https://doi.org/10.1016/j.enggeo.2018.12.024.
Li, Z., X. Wang, H. Wang, and R. Y. Liang. 2016b. “Quantifying stratigraphic uncertainties by stochastic simulation techniques based on Markov random field.” Eng. Geol. 201 (Feb): 106–122. https://doi.org/10.1016/j.enggeo.2015.12.017.
Liang, Y. H., W. H. Shui, and S. F. Lu. 2022. “Field practice and ground settlement behaviors of a land creation case in loess area of China.” Bull. Eng. Geol. Environ. 81 (11): 462. https://doi.org/10.1007/s10064-022-02964-w.
Liu, L. L., Y. M. Cheng, Q. J. Pan, and D. Dias. 2020. “Incorporating stratigraphic boundary uncertainty into reliability analysis of slopes in spatially variable soils using one-dimensional conditional Markov chain model.” Comput. Geotech. 118 (Feb): 103321. https://doi.org/10.1016/j.compgeo.2019.103321.
Liu, W. F., Y. F. Leung, and M. K. Lo. 2017. “Integrated framework for characterization of spatial variability of geological profiles.” Can. Geotech. J. 54 (1): 47–58. https://doi.org/10.1139/cgj-2016-0189.
Phoon, K. K., and J. Ching. 2015. Risk and reliability in geotechnical engineering. New York: CRC Press.
Pu, C. H., Q. Xu, K. Y. Zhao, Y. N. Jiang, L. N. Hao, J. L. Liu, W. L. Chen, and P. L. Kou. 2021. “Characterizing the topographic changes and land subsidence associated with the mountain excavation and city construction on the Chinese loess plateau.” Remote Sens. 13 (8): 1556. https://doi.org/10.3390/rs13081556.
Qi, X. H., D. Q. Li, K. K. Phoon, Z. J. Cao, and X. S. Tang. 2016. “Simulation of geologic uncertainty using coupled Markov chain.” Eng. Geol. 207 (Jun): 129–140. https://doi.org/10.1016/j.enggeo.2016.04.017.
Qi, X. H., W. H. Zhou, and K. V. Yuen. 2017. “Detection of stationary Markovian zones in a geologically heterogeneous area.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 3 (4): 04017026. https://doi.org/10.1061/AJRUA6.0000930.
Schöbi, R., B. Sudret, and S. Marelli. 2017. “Rare event estimation using polynomial-chaos kriging.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 3 (2): D4016002. https://doi.org/10.1061/AJRUA6.0000870.
Shi, C., and Y. Wang. 2022. “Assessment of reclamation-induced consolidation settlement considering stratigraphic uncertainty and spatial variability of soil properties.” Can. Geotech. J. 59 (7): 1215–1230. https://doi.org/10.1139/cgj-2021-0349.
Simões, J. T., L. C. Neves, A. N. Antão, and N. M. Guerra. 2020. “Reliability assessment of shallow foundations on undrained soils considering soil spatial variability.” Comput Geotech. 119 (Mar): 103369. https://doi.org/10.1016/j.compgeo.2019.103369.
Strebelle, S. 2002. “Conditional simulation of complex geological structures using multiple-point statistics.” Math. Geol. 34 (1): 1–21. https://doi.org/10.1023/A:1014009426274.
Tian, N., J. Chen, N. Zhou, and J. Huang. 2023. “Impact of multivariate cross-correlation between soil parameters on maximum longitudinal deformation of an operating tunnel induced by ground surface surcharge.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 9 (4): 04023031. https://doi.org/10.1061/AJRUA6.RUENG-1142.
Vanmarcke, E. H. 1977. “Probabilistic modeling of soil profiles.” J. Geotech. Eng. Div. 103 (11): 1227–1246. https://doi.org/10.1061/AJGEB6.0000517.
Wang, F., and J. E. Chen. 2023. “Efficient modeling of random fields by using Gaussian process inducing-point approximations.” Comput. Geotech. 157 (May): 105304. https://doi.org/10.1016/j.compgeo.2023.105304.
Wang, H., J. F. Wellmann, Z. Li, X. Wang, and R. Y. Liang. 2017a. “A segmentation approach for stochastic geological modeling using hidden Markov random fields.” Math. Geosci. 49 (2): 145–177. https://doi.org/10.1007/s11004-016-9663-9.
Wang, J. D., Y. J. Xu, Y. Ma, S. N. Qiao, and K. Q. Feng. 2018a. “Study on the deformation and failure modes of filling slope in loess filling engineering: A case study at a loess mountain airport.” Landslides 15 (12): 2423–2435. https://doi.org/10.1007/s10346-018-1046-5.
Wang, T. S., F. Liu, Y. T. Yu, and H. E. Cai. 2023. “Numerical analysis of hydrological response in loess excavation and filling area under multi-year precipitation infiltration.” Bull. Eng. Geol. Environ. 82 (10): 1–15. https://doi.org/10.1007/s10064-023-03391-1.
Wang, X. 2021. “Empirical probability distribution models for soil-layer thicknesses of liquefiable ground.” J. Geotech. Geoenviron. Eng. 147 (6): 06021005. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002537.
Wang, X. R., H. Wang, and R. Y. Liang. 2018b. “A method for slope stability analysis considering subsurface stratigraphic uncertainty.” Landslides 15 (5): 925–936. https://doi.org/10.1007/s10346-017-0925-5.
Wang, Y., C. Fu, and K. Huang. 2017b. “Probabilistic assessment of liquefiable soil thickness considering spatial variability and model and parameter uncertainties.” Géotechnique 67 (3): 228–241. https://doi.org/10.1680/jgeot.15.P.219.
Wang, Y., K. Huang, and Z. Cao. 2013. “Probabilistic identification of underground soil stratification using cone penetration tests.” Can. Geotech. J. 50 (7): 766–776. https://doi.org/10.1139/cgj-2013-0004.
Wei, X., and H. Wang. 2022. “Stochastic stratigraphic modeling using Bayesian machine learning.” Eng. Geol. 307 (Sep): 106789. https://doi.org/10.1016/j.enggeo.2022.106789.
Wei, Y. M., X. J. Liu, C. Y. Zhao, R. Tomas, and Z. Jiang. 2021. “Observation of surface displacement associated with rapid urbanization and land creation in Lanzhou, Loess Plateau of China with Sentinel-1 SAR Imagery.” Remote Sens. 13 (17): 3472. https://doi.org/10.3390/rs13173472.
Yao, Y. G., Y. C. Zhang, Y. Zhao, Y. F. Bai, S. N. Zhang, and C. M. Cao. 2021. “The evaluation of artificial filling in loess areas by in-situ tests based on statistical analysis.” Environ. Earth. Sci. 80 (12): 438. https://doi.org/10.1007/s12665-021-09729-w.
Yuen, K. V., and G. A. Ortiz. 2018. “Multiresolution Bayesian nonparametric general regression for structural model updating.” Struct. Control Health Monit. 25 (2): e2077–14. https://doi.org/10.1002/stc.2077.
Zhang, D. M., H. F. Dai, H. Wang, and H. W. Huang. 2021a. “Investigating the effect of geological heterogeneity of strata on the bearing capacity of shallow foundations using Markov random field.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 7 (4): 04021060. https://doi.org/10.1061/AJRUA6.0001182.
Zhang, H. X., R. Q. Zeng, Y. Zhang, S. F. Zhao, X. M. Meng, Y. X. Li, W. C. Liu, X. P. Meng, and Y. P. Yang. 2022a. “Subsidence monitoring and influencing factor analysis of mountain excavation and valley infilling on the Chinese Loess Plateau: A case study of Yan’an New District.” Eng. Geol. 297 (Feb): 106482. https://doi.org/10.1016/j.enggeo.2021.106482.
Zhang, J. Z., H. W. Huang, D. M. Zhang, K. K. Phoon, Z. Q. Liu, and C. Tang. 2021b. “Quantitative evaluation of geological uncertainty and its influence on tunnel structural performance using improved coupled Markov chain.” Acta Geotech. 16 (11): 3709–3724. https://doi.org/10.1007/s11440-021-01287-6.
Zhang, J. Z., Z. Q. Liu, D. M. Zhang, H. W. Huang, K. K. Phoon, and Y. D. Xue. 2022b. “Improved coupled Markov chain method for simulating geological uncertainty.” Eng. Geol. 298 (Mar): 106539. https://doi.org/10.1016/j.enggeo.2022.106539.
Zhang, L. L., J. Zhang, L. M. Zhang, and W. H. Tang. 2010. “Back analysis of slope failure with Markov chain Monte Carlo simulation.” Comput. Geotech. 37 (7–8): 905–912. https://doi.org/10.1016/j.compgeo.2010.07.009.
Zhang, L. X., S. W. Qi, Y. T. Yu, Y. G. Zhang, Z. Q. Li, X. K. Hou, L. N. Ma, Y. Zou, S. F. Guo, and J. B. Peng. 2021c. “A comparative study on the physical properties of natural sedimentary loess and manual filling compacted loess.” Environ. Earth Sci. 80 (21): 721. https://doi.org/10.1007/s12665-021-10047-4.
Zhao, C., W. Gong, T. Li, C. H. Juang, H. Tang, and H. Wang. 2021. “Probabilistic characterization of subsurface stratigraphic configuration with modified random field approach.” Eng. Geol. 288 (Jul): 106138. https://doi.org/10.1016/j.enggeo.2021.106138.
Zhao, L. S., S. Zhuo, and B. Shen. 2023. “An efficient model to estimate the soil profile and stratigraphic uncertainty quantification.” Eng. Geol. 315 (Mar): 107025. https://doi.org/10.1016/j.enggeo.2023.107025.
Zhao, T., and Y. Wang. 2020. “Non-parametric simulation of non-stationary non-Gaussian 3D random field samples directly from sparse measurements using signal decomposition and Markov Chain Monte Carlo (MCMC) simulation.” Reliab. Eng. Syst. Safe 203 (Nov): 107087. https://doi.org/10.1016/j.ress.2020.107087.
Zhu, C. H., and N. Li. 2020. “Ranking of influence factors and control technologies for the post-construction settlement of loess high-filling embankments.” Comput. Geotech. 118 (Feb): 103320. https://doi.org/10.1016/j.compgeo.2019.103320.
Information & Authors
Information
Published In
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 10 • Issue 2 • June 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Oct 20, 2023
Accepted: Jan 2, 2024
Published online: Apr 4, 2024
Published in print: Jun 1, 2024
Discussion open until: Sep 4, 2024
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.