Abstract
Due to their practicability, simple and data-driven empirical models have been extensively developed and applied in practical engineering to predict the run-out distance of landslides. However, the definition of the most appropriate empirical model for specific landslide data is rarely discussed. Moreover, the empirical model is subjected to the high variability of landslide data, which should be quantified into the model to provide more reliable predictions. As such, we propose in this paper, a simple, practical, and probabilistic run-out distance prediction method based on an empirical model and Bayesian method. This method was implemented with a regional landslide inventory compiled from 34 loess landslides in Heifangtai Terrace, Gansu Province, China. In this method, we performed a Bayesian model selection to determine the most appropriate empirical model for the compiled database among the possible candidate models adapted from previous literature. Considering the high variability of data, unknown parameters of the empirical model are regarded as random variables, and their posterior distributions are obtained by Bayesian updating with the compiled database. Then, we developed the probabilistic run-out prediction model to evaluate the run-out distance exceedance probability of landslides based on the most appropriate model and its associated posterior random variable information. We utilized data from two recent landslides that occurred in Heifangtai Terrace to validate the performance of the proposed model. In addition, we produced a run-out distance exceedance probability curve using the proposed method for a potential landslide in Heifangtai Terrace, in which the sliding volume interval is estimated using the slo** local base level (SLBL) method. In general, this study presents a practical method for landslide run-out distance analyses within a probabilistic framework, aiming to provide support for risk-based decisions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adoko AC, Gokceoglu C, Yagiz S (2017) Bayesian prediction of TBM penetration rate in rock mass. Eng Geol 226:245–256. https://doi.org/10.1016/j.enggeo.2017.06.014
Aryal A, Brooks BA, Reid ME (2015) Landslide subsurface slip geometry inferred from 3-d surface displacement fields. Geophys Res Lett 42:1411–1417. https://doi.org/10.1002/2014GL062688
Beguería S, Van Asch TWJ, Malet JP, Gröndahl S (2009) A GIS-based numerical model for simulating the kinematics of mud and debris flows over complex terrain. Nat Hazards Earth Syst Sci 9:1897–1909. https://doi.org/10.5194/nhess-9-1897-2009
Cao Z, Wang Y, Li D (2016) Quantification of prior knowledge in geotechnical site characterization. Eng Geol 203:107–116. https://doi.org/10.1016/j.enggeo.2015.08.018
Chang W, **ng A, Wang P, Zhuang Y, ** K, He J, Chai S (2021) Analysis of dangchuan 5# landslide on january 27, 2021, in yong**g county, gansu province, china. Landslides 18:3615–3628. https://doi.org/10.1007/s10346-021-01743-0
Ching J, Chen YC (2007) Transitional Markov chain Monte Carlo method for bayesian model updating, model class selection, and model averaging. J Eng Mech 133:816–832. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:7(816)
Ching J, Wang JS (2016) Application of the transitional Markov chain Monte Carlo algorithm to probabilistic site characterization. Eng Geol 203:151–167. https://doi.org/10.1016/j.enggeo.2015.10.015
Corominas J (1996) The angle of reach as a mobility index for small and large landslides. Can Geotech J 33:260–271. https://doi.org/10.1139/t96-005
Corominas J, van Westen C, Frattini P, Cascini L, Malet JP, Fotopoulou S, Catani F, Van Den Eeckhaut M, Mavrouli O, Agliardi F, Pitilakis K, Winter MG, Pastor M, Ferlisi S, Tofani V, Hervás J, Smith JT (2014) Recommendations for the quantitative analysis of landslide risk. Bull Eng Geol Env 73:209–263. https://doi.org/10.1007/s10064-013-0538-8
Fan X, Yang F, Siva Subramanian S, Xu Q, Feng Z, Mavrouli O, Peng M, Ouyang C, Jansen JD, Huang R (2020) Prediction of a multi-hazard chain by an integrated numerical simulation approach: The baige landslide, **sha river, china. Landslides 17:147–164. https://doi.org/10.1007/s10346-019-01313-5
Feng X, Jimenez R (2015) Estimation of deformation modulus of rock masses based on bayesian model selection and bayesian updating approach. Eng Geol 199:19–27. https://doi.org/10.1016/j.enggeo.2015.10.002
Feng X, Jimenez R, Zeng P, Senent S (2019) Prediction of time-dependent tunnel convergences using a bayesian updating approach. Tunn Undergr Space Technol 94:103118. https://doi.org/10.1016/j.tust.2019.103118
Finlay PJ, Mostyn GR, Fell R (1999) Landslide risk assessment: Prediction of travel distance. Can Geotech J 36:556–562. https://doi.org/10.1139/t99-012
Geman S, Geman D (1984) Stochastic relaxation, gibbs distributions, and the bayesian restoration of images. IEEE Transac Patt Analys Mach Intel PAMI-6: 721–741. https://doi.org/10.1109/TPAMI.1984.4767596
Guzzetti F, Ardizzone F, Cardinali M, Rossi M, Valigi D (2009) Landslide volumes and landslide mobilization rates in umbria, central italy. Earth Planet Sci Lett 279:222–229. https://doi.org/10.1016/j.epsl.2009.01.005
Hantz D, Vengeon JM, Dussauge-Peisser C (2003) An historical, geomechanical and probabilistic approach to rock-fall hazard assessment. Nat Hazards Earth Syst Sci 3:693–701. https://doi.org/10.5194/nhess-3-693-2003
Hastings WK (1970) Monte Carlo sampling methods using markov chains and their applications. Biometrika 57:97–109. https://doi.org/10.1093/biomet/57.1.97
Hattanji T, Moriwaki H (2009) Morphometric analysis of relic landslides using detailed landslide distribution maps: Implications for forecasting travel distance of future landslides. Geomorphology 103:447–454. https://doi.org/10.1016/j.geomorph.2008.07.009
Huang Y, Li G, **ong M (2020) Stochastic assessment of slope failure run-out triggered by earthquake ground motion. Nat Hazards 101:87–102. https://doi.org/10.1007/s11069-020-03863-7
Hungr O, McDougall S (2009) Two numerical models for landslide dynamic analysis. Comput Geosci 35:978–992. https://doi.org/10.1016/j.cageo.2007.12.003
Hunter G, Fell R (2003) Travel distance angle for “rapid” landslides in constructed and natural soil slopes. Can Geotech J 40:1123–1141. https://doi.org/10.1139/t03-061
Jaboyedoff M, Carrea D, Derron M-H, Oppikofer T, Penna IM, Rudaz B (2020) A review of methods used to estimate initial landslide failure surface depths and volumes. Eng Geol 267:105478. https://doi.org/10.1016/j.enggeo.2020.105478
Jaboyedoff M, Chigira M, Arai N, Derron MH, Rudaz B, Tsou CY (2019) Testing a failure surface prediction and deposit reconstruction method for a landslide cluster that occurred during typhoon talas (japan). Earth Surf Dynam 7:439–458. https://doi.org/10.5194/esurf-7-439-2019
Jaboyedoff M, Couture R, Locat P (2009) Structural analysis of Turtle Mountain (Alberta) using digital elevation model: Toward a progressive failure. Geomorphology 103(1):5–16 S0169555X08001426. https://doi.org/10.1016/j.geomorph.2008.04.012
Jiang S-H, Huang J, Griffiths DV, Deng Z-P (2022) Advances in reliability and risk analyses of slopes in spatially variable soils: a state-of-the-art review. Comput Geotech 141:104498. https://doi.org/10.1016/j.compgeo.2021.104498
Jiang S-H, Wang L, Ouyang S, Huang J, Liu Y (2021) A comparative study of bayesian inverse analyses of spatially varying soil parameters for slope reliability updating. Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 1–20. https://doi.org/10.1080/17499518.2021.2010098
Jimenez R, Feng X, Alonso-Pollán Jose A (2017) Bayesian updating of bearing capacity models for individual stone columns. J Comput Civ Eng 31:04017050. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000691
** YF, Yin ZY, Zhou WH, Horpibulsuk S (2019) Identifying parameters of advanced soil models using an enhanced transitional Markov chain Monte Carlo method. Acta Geotech 14:1925–1947. https://doi.org/10.1007/s11440-019-00847-1
Juang CH, Gong W, Martin JR, Chen Q (2018) Model selection in geological and geotechnical engineering in the face of uncertainty - does a complex model always outperform a simple model? Eng Geol 242:184–196. https://doi.org/10.1016/j.enggeo.2018.05.022
Klar A, Aharonov E, Kalderon-Asael B, Katz O (2011) Analytical and observational relations between landslide volume and surface area. J Geophys Res Earth Surf 116:F02001. https://doi.org/10.1029/2009JF001604
Larsen IJ, Montgomery DR, Korup O (2010) Landslide erosion controlled by hillslope material. Nat Geosci 3:247–251. https://doi.org/10.1038/ngeo776
Legros F (2002) The mobility of long-runout landslides. Eng Geol 63:301–331. https://doi.org/10.1016/S0013-7952(01)00090-4
Li XZ, Kong JM (2010) Runout distance estimation of landslides triggered by "5·12" wenchuan earthquake. J Sichuan Univ (Engineering Science Edition) 42:243–249. https://doi.org/10.15961/j.jsuese.2010.05.011
Lin ML, Chen TW (2020) Estimating volume of deep-seated landslides and mass transport in basihlan river basin, taiwan. Eng Geol 278:105825. https://doi.org/10.1016/j.enggeo.2020.105825
Liu X, Wang Y (2021) Bayesian selection of slope hydraulic model and identification of model parameters using monitoring data and subset simulation. Comput Geotech 139:104428. https://doi.org/10.1016/j.compgeo.2021.104428
Liu X, Wang Y, Li DQ (2019) Investigation of slope failure mode evolution during large deformation in spatially variable soils by random limit equilibrium and material point methods. Comput Geotech 111:301–312. https://doi.org/10.1016/j.compgeo.2019.03.022
McDougall S (2017) 2014 canadian geotechnical colloquium: landslide runout analysis – current practice and challenges. Can Geotech J 54:605–620. https://doi.org/10.1139/cgj-2016-0104
Meier C, Jaboyedoff M, Derron M-H, Gerber C (2020) A method to assess the probability of thickness and volume estimates of small and shallow initial landslide ruptures based on surface area. Landslides 17:975–982. https://doi.org/10.1007/s10346-020-01347-0
Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21:1087–1092. https://doi.org/10.1063/1.1699114
Mitchell A, McDougall S, Nolde N, Brideau MA, Whittall J, Aaron JB (2020) Rock avalanche runout prediction using stochastic analysis of a regional dataset. Landslides 17:777–792. https://doi.org/10.1007/s10346-019-01331-3
Ouyang C, He S, Xu Q, Luo Y, Zhang W (2013) A maccormack-tvd finite difference method to simulate the mass flow in mountainous terrain with variable computational domain. Comput Geosci 52:1–10. https://doi.org/10.1016/j.cageo.2012.08.024
Pan P, Shang Y, Lü Q, Yu Y (2019) Periodic recurrence and scale-expansion mechanism of loess landslides caused by groundwater seepage and erosion. Bull Eng Geol Env 78:1143–1155. https://doi.org/10.1007/s10064-017-1090-8
Peng D, Xu Q, Liu F, He Y, Zhang S, Qi X, Zhao K, Zhang X (2018) Distribution and failure modes of the landslides in heitai terrace, china. Eng Geol 236:97–110. https://doi.org/10.1016/j.enggeo.2017.09.016
Qarinur M (2015) Landslide runout distance prediction based on mechanism and cause of soil or rock mass movement. J Civ Eng Forum 1:29–36. https://doi.org/10.22146/jcef.22728
Qi X, Xu Q, Liu F (2018) Analysis of retrogressive loess flowslides in heifangtai, china. Eng Geol 236:119–128. https://doi.org/10.1016/j.enggeo.2017.08.028
Qiu H, Cui P, Hu S, Regmi AD, Wang X, Yang D (2018) Develo** empirical relationships to predict loess slide travel distances: a case study on the loess plateau in china. Bull Eng Geol Env 77:1299–1309. https://doi.org/10.1007/s10064-018-1328-0
Rickenmann D (1999) Empirical relationships for debris flows. Nat Hazards 19:47–77. https://doi.org/10.1023/A:1008064220727
Stamatopoulos CA, Di B (2015) Analytical and approximate expressions predicting post-failure landslide displacement using the multi-block model and energy methods. Landslides 12:1207–1213. https://doi.org/10.1007/s10346-015-0638-6
Su X, Wei W, Ye W, Meng X, Wu W (2019) Predicting landslide sliding distance based on energy dissipation and mass point kinematics. Nat Hazards 96:1367–1385. https://doi.org/10.1007/s11069-019-03618-z
Sun X, Zeng P, Li T, Wang S, Jimenez R, Feng X, Xu Q (2021a) From probabilistic back analyses to probabilistic run-out predictions of landslides: a case study of heifangtai terrace, gansu province, china. Eng Geol 280:105950. https://doi.org/10.1016/j.enggeo.2020.105950
Sun X, Zeng P, Li T, Zhang T, Feng X, Jimenez R (2021b) Run-out distance exceedance probability evaluation and hazard zoning of an individual landslide. Landslides 18:1295–1308. https://doi.org/10.1007/s10346-020-01545-w
Tian M, Sheng XT (2022) Copula-based probabilistic approaches for predicting debris-flow runout distances in the wenchuan earthquake zone. ASCE-ASME J Risk Uncertai Eng Sys Part a: Civ Eng 8:04021070. https://doi.org/10.1061/AJRUA6.0001197
Wang Y, Huang J, Tang H, Zeng C (2020) Bayesian back analysis of landslides considering slip surface uncertainty. Landslides 17:2125–2136. https://doi.org/10.1007/s10346-020-01432-4
Wang Y, Qin Z, Liu X, Li L (2019) Probabilistic analysis of post-failure behavior of soil slopes using random smoothed particle hydrodynamics. Eng Geol 261:105266. https://doi.org/10.1016/j.enggeo.2019.105266
Xu L, Yan D, Zhao T (2021) Probabilistic evaluation of loess landslide impact using multivariate model. Landslides 18:1011–1023. https://doi.org/10.1007/s10346-020-01521-4
Xu Q, Li H, He Y, Liu F, Peng D (2019) Comparison of data-driven models of loess landslide runout distance estimation. Bull Eng Geol Env 78:1281–1294. https://doi.org/10.1007/s10064-017-1176-3
Yuen KV (2010) Recent developments of bayesian model class selection and applications in civil engineering. Struct Saf 32:338–346. https://doi.org/10.1016/j.strusafe.2010.03.011
Zeng P, Jimenez R, Jurado-Piña R (2015) System reliability analysis of layered soil slopes using fully specified slip surfaces and genetic algorithms. Eng Geol 193:106–117. https://doi.org/10.1016/j.enggeo.2015.04.026
Zeng P, Sun X, Xu Q, Li T, Zhang T (2021) 3D probabilistic landslide run-out hazard evaluation for quantitative risk assessment purposes. Eng Geol 293:106303. https://doi.org/10.1016/j.enggeo.2021.106303
Zeng P, Wang S, Sun X, Fan X, Li T, Wang D, Feng B, Zhu X (2022) Probabilistic hazard assessment of landslide-induced river damming. Eng Geol 304:106678. https://doi.org/10.1016/j.enggeo.2022.106678
Zeng RQ, Meng XM, Zhang FY, Wang SY, Cui ZJ, Zhang MS, Zhang Y, Chen G (2016) Characterizing hydrological processes on loess slopes using electrical resistivity tomography – a case study of the heifangtai terrace, northwest china. J Hydrol 541:742–753. https://doi.org/10.1016/j.jhydrol.2016.07.033
Zhang J, **ao T, Ji J, Zeng P, Cao Z (2021a) Geotechnical reliability analysis: Theories, methods, and algorithms. Tongji University Press
Zhang Y, Meng XM, Dijkstra TA, Jordan CJ, Chen G, Zeng RQ, Novellino A (2020) Forecasting the magnitude of potential landslides based on insar techniques. Remote Sens Environ 241:111738. https://doi.org/10.1016/j.rse.2020.111738
Zhang Z, Zeng R, Meng X, Zhao S, Meng X, Yao Y, Wang H, Guo W, Chen G, Zhang Y (2021b) Estimating landslide sliding distance based on an improved heim sled model. CATENA 204:105401. https://doi.org/10.1016/j.catena.2021.105401
Zhao T, Lei J, Xu L (2021) An efficient bayesian method for estimating runout distance of region-specific landslides using sparse data. Georisk: Assess Manage Risk Eng Syst Geohaz 1–14. https://doi.org/10.1080/17499518.2021.1952613
Zhou WH, Yin ZY, Yuen KV (2021) Practice of bayesian probability theory in geotechnical engineering. Springer
Acknowledgements
This research was supported by the National Natural Science Foundation of China (Project No. 41977224), the Sichuan Science and Technology Program (Project No. 2021JDR0399), the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (Project Nos. SKLGP2020Z013 and SKLGP2021K001), and, partially, by the Spanish Ministry of Science and Innovation, under Grant PID2019-108060RB-I00. Their financial support is greatly appreciated.
