Numerical Modeling of Pumping-Induced Earth Fissures Using Coupled Quasi-Static Material Point Method
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 149, Issue 9
Abstract
Pumping-induced earth fissuring is a typical fluid–solid coupling problem involving fracture evolution. Despite recent advances in the numerical modeling of earth fissures, a holistic approach capable of predicting their evolution and understanding their behavior from fracture mechanisms is absent. This paper presents a coupled numerical method based on the framework of the material point method (MPM) and fracture mechanics for the process-oriented simulation of pumping-induced tensile earth fissures. In this method, fissure behavior is driven by the real-time stress field affected by soil consolidation. After an earth fissure initiates in the region of maximum tensile stress, it propagates in the direction of the maximum circumferential stress around the fissure tip. The great scale difference between a fissure tip and the entire model is addressed with an adaptive refinement strategy. Through the simulation of a physical model experiment reproducing pumping-induced earth fissures with the presence of a bedrock ridge, the complete fissuring process, including initiation, propagation, and arrest, is presented. The simulated fracture time (24 h after drainage), location (directly above the bedrock ridge), final length (165 mm), and morphology evolution (from straight to zigzag) of the main fissure basically were in agreement with the experimental results. The stress intensity factors (SIFs) around fissure tips, which are important fracture parameters that have not been discussed in existing earth fissure analyses, also are captured during the fissure growth. The proposed method quantifies the inhibition of geostatic stress fields in earth fissure development and correlate fissure morphology with the stress field at a fissure tip.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (Nos. 41572250 and 41877216) and the open foundation of Key Laboratory of Earth Fissures Geological Disaster, Ministry of Land and Resources (Geological Survey of Jiangsu Province).
References
Achenbach, J. D., and Z. Li. 1985. “Resistance curves for crack growth under plane-stress conditions in an elastic perfectly-plastic material.” Eng. Fract. Mech. 22 (6): 1073–1078. https://doi.org/10.1016/0013-7944(85)90045-1.
Belytschko, T., and T. Black. 1999. “Elastic crack growth in finite elements with minimal remeshing.” Int. J. Numer. Methods Eng. 45 (5): 601–620. https://doi.org/10.1002/(SICI)1097-0207(19990620)45:5%3C601::AID-NME598%3E3.0.CO;2-S.
Beuth, L., Z. Wieckowski, and P. A. Vermeer. 2011. “Solution of quasi-static large-strain problems by the material point method.” Int. J. Numer. Anal. Methods Geomech. 35 (13): 1451–1465. https://doi.org/10.1002/nag.965.
Biot, M. A. 1941. “General theory of three-dimensional consolidation.” J. Appl. Phys. 12 (2): 155–164. https://doi.org/10.1063/1.1712886.
Bishop, A. W. 1959. “The principle of effective stress.” Tekniske Ukeblad 39 (Apr): 859–863.
Bisht, V., R. Salgado, and M. Prezzi. 2021. “Material point method for cone penetration in clays.” J. Geotech. Geoenviron. Eng. 147 (12): 04021158. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002687.
Broek, D. 1978. Elementary engineering fracture mechanics. New York: Sijthoff & Noordhoff.
Budhu, M. 2008. “Mechanics of earth fissures using the Mohr-Coulomb failure criterion.” Environ. Eng. Geosci. 14 (4): 281–295. https://doi.org/10.2113/gseegeosci.14.4.281.
Bürg, M., L. J. Lim, and R. Brinkgreve. 2017. “Application of a second-order implicit material point method.” Procedia Eng. 175 (Aug): 279–286. https://doi.org/10.1016/j.proeng.2017.01.024.
Ceccato, F., L. Beuth, and P. Simonini. 2016. “Analysis of piezocone penetration under different drainage conditions with the two-phase material point method.” J. Geotech. Geoenviron. Eng. 142 (12): 04016066. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001550.
Chen, X. X., Z. J. Luo, and S. L. Zhou. 2014. “Influences of soil hydraulic and mechanical parameters on land subsidence and ground fissures caused by groundwater exploitation.” J. Hydrodyn. 26 (1): 155–164. https://doi.org/10.1016/S1001-6058(14)60018-4.
Chen, Z., H. Zhou, and D. G. Fredlund. 1999. “Nonlinear model for unsaturated soils and its application.” [In Chinese.] Chin. J. Geotech. Eng. 21 (5): 603–608.
Cheung, S., and A. R. Luxmoore. 2003. “A finite element analysis of stable crack growth in an aluminium alloy.” Eng. Fract. Mech. 70 (9): 1153–1169. https://doi.org/10.1016/S0013-7944(02)00093-0.
Choi, S. R., D. C. Faucett, and B. Skelley. 2015. “Slow crack growth of a pyroceram glass ceramic under static fatigue loading—Commonality of slow crack growth in advanced ceramics.” J. Eng. Gas. Turbines Power-Trans. ASME 2015 (137): 325051–325057. https://doi.org/10.1115/1.4028393.
Duncan, J. M., and C.-Y. Chang. 1970. “Nonlinear analysis of stress and strain in soils.” J. Soil Mech. Found. Div. 96 (5): 1629–1653. https://doi.org/10.1061/JSFEAQ.0001458.
Fletcher, D. I., F. J. Franklin, and A. Kapoor. 2009. “Rail surface fatigure and wear.” In Wheel-rail interface handbook. New York: Woodhead.
Franceschini, A., M. Ferronato, C. Janna, and P. Teatini. 2016. “A novel Lagrangian approach for the stable numerical simulation of fault and fracture mechanics.” J. Comput. Phys. 314 (45): 503–521. https://doi.org/10.1016/j.jcp.2016.03.032.
Frigo, M., M. Ferronato, J. Yu, S. Ye, D. Galloway, D. Carreón-Freyre, and P. Teatini. 2019. “A parametric numerical analysis of factors controlling ground ruptures caused by groundwater pumping.” Water Resour. Res. 55 (11): 9500–9518. https://doi.org/10.1029/2019WR025034.
Gong, X., J. Geng, Q. Sun, C. Gu, and W. Zhang. 2020. “Experimental study on pumping-induced land subsidence and earth fissures: A case study in the Su-Xi-Chang region, China.” Bull. Eng. Geol. Environ. 79 (9): 4515–4525. https://doi.org/10.1007/s10064-020-01864-1.
Guilkey, J. E., and J. A. Weiss. 2003. “Implicit time integration for the material point method: Quantitative and algorithmic comparisons with the finite element method.” Int. J. Numer. Methods Eng. 57 (9): 1323–1338. https://doi.org/10.1002/nme.729.
Hernandez-Marin, M., and T. J. Burbey. 2010. “Controls on initiation and propagation of pumping-induced earth fissures: Insights from numerical simulations.” Hydrogeol. J. 18 (8): 1773–1785. https://doi.org/10.1007/s10040-010-0642-9.
Laborde, P., J. Pommier, Y. Renard, and M. Salaün. 2005. “High-order extended finite element method for cracked domains.” Int. J. Numer. Methods Eng. 64 (3): 354–381. https://doi.org/10.1002/nme.1370.
Li, S., Y. Zhang, J. Wu, J. Yu, and X. Gong. 2021a. “Modeling of crack propagation with the quasi-static material point method.” Eng. Fract. Mech. 245 (2): 107602. https://doi.org/10.1016/j.engfracmech.2021.107602.
Li, Y., P. Teatini, J. Yu, A. Franceschini, M. Frigo, C. Zoccarato, and S. Ye. 2021b. “Aseismic multifissure modeling in unfaulted heavily pumped basins: Mechanisms and applications.” Water Resour. Res. 57 (10): e2021WR030127. https://doi.org/10.1029/2021WR030127.
Li, C., X. Wang, C. He, X. Wu, Z. Kong, and X. Li. 2019. China national digital geological map (public version at 1:200 000 scale) spatial database (V1). Beijing: China Geological Survey.
Liang, W., J. Zhao, H. Wu, and K. Soga. 2021. “Multiscale modeling of anchor pullout in sand.” J. Geotech. Geoenviron. Eng. 147 (9): 04021091. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002599.
Liang, Y., T. Benedek, X. Zhang, and Y. Liu. 2017. “Material point method with enriched shape function for crack problems.” Comput. Methods Appl. Mech. Eng. 322 (5): 541–562. https://doi.org/10.1016/j.cma.2017.05.012.
Liao, M., X. Deng, and Z. Guo. 2018. “Crack propagation modelling using the weak form quadrature element method with minimal remeshing.” Theor. Appl. Fract. Mech. 93 (9): 293–301. https://doi.org/10.1016/j.tafmec.2017.09.012.
Liu, R., Y. Han, J. Xiao, and T. Wang. 2020. “Failure mechanism of TRSS mode in landslides induced by earthquake.” Sci. Rep. 10 (1): 21326. https://doi.org/10.1038/s41598-020-78503-y.
Moës, N., J. Dolbow, and T. Belytschko. 1999. “A finite element method for crack growth without remeshing.” Eng. Fract. Mech. 46 (1): 131–150. https://doi.org/10.1002/(SICI)1097-0207(19990910)46:1%3C131::AID-NME726%3E3.0.CO;2-J.
Nairn, J. A. 2003. “Material point method calculations with explicit cracks.” Comput. Model. Eng. Sci. 4 (6): 649–664. https://doi.org/10.3970/cmes.2003.004.649.
Nardean, S., M. Ferronato, Y. Zhang, S. Ye, X. Gong, and P. Teatini. 2021. “Understanding ground rupture due to groundwater over-pumping by a large lab experiment and advanced numerical modelling.” Water Resour. Res. 57 (Aug): e2020WR027553. https://doi.org/10.1029/2020WR027553.
Pacheco-Martínez, J., M. Hernandez-Marín, T. J. Burbey, N. González-Cervantes, J. Á. Ortíz-Lozano, M. E. Zermeño-De-Leon, and A. Solís-Pinto. 2013. “Land subsidence and ground failure associated to groundwater exploitation in the Aguascalientes Valley, México.” Eng. Geol. 164 (56): 172–186. https://doi.org/10.1016/j.enggeo.2013.06.015.
Peng, J., X. Sun, Q. Lu, L. Meng, H. He, J. Qiao, and F. Wang. 2020. “Characteristics and mechanisms for origin of earth fissures in Fenwei basin, China.” Eng. Geol. 266 (10): 105445. https://doi.org/10.1016/j.enggeo.2019.105445.
Rojas, E., J. Arzate, and M. Arroyo. 2002. “A method to predict the group fissuring and faulting caused by regional groundwater decline.” Eng. Geol. 65 (4): 245–260. https://doi.org/10.1016/S0013-7952(01)00135-1.
Schaap, M. G., and F. J. Leij. 2000. “Improved prediction of unsaturated hydraulic conductivity with the Mualem-van Genuchten model.” Soil Sci. Soc. Am. J. 64 (3): 843–851. https://doi.org/10.2136/sssaj2000.643843x.
Shi, B., Y. Zhang, and W. Zhang. 2019. “Run-out of the 2015 Shenzhen landslide using the material point method with the softening model.” Bull. Eng. Geol. Environ. 78 (2): 1225–1236. https://doi.org/10.1007/s10064-017-1167-4.
Smith, I. M., and D. V. Griffiths. 2004. Programming the finite element method. 4th ed. New York: Wiley.
Su, H., Z. Dang, and J. Cui. 2010. “Duncan-Chang nonlinear elastic model and realization in ANSYS.” [In Chinese.] China Rural Water Hydropower 3 (Apr): 76–79.
Sulsky, D., Z. Chen, and H. L. Schreyer. 1994. “A particle method for history-dependent materials.” Comput. Methods Appl. Mech. Eng. 118 (1): 179–196. https://doi.org/10.1016/0045-7825(94)90112-0.
Teng, Z. H., F. Sun, S. C. Wu, Z. B. Zhang, T. Chen, and D. M. Liao. 2018. “An adaptively refined XFEM with virtual node polygonal elements for dynamic crack problems.” Comput. Mech. 62 (5): 1087–1106. https://doi.org/10.1007/s00466-018-1553-1.
Tuckwell, G. W., L. Lonergan, and R. J. H. Jolly. 2003. “The control of stress history and flaw distribution on the evolution of polygonal fracture networks.” J. Struct. Geol. 25 (8): 1241–1250. https://doi.org/10.1016/S0191-8141(02)00165-7.
Tvergaard, V., and J. W. Hutchinson. 1992. “The relation between crack growth resistance and fracture process parameters in elastic-plastic solids.” J. Mech. Phys. Solids 40 (6): 1377–1397. https://doi.org/10.1016/0022-5096(92)90020-3.
van Genuchten, M. T. 1980. “A closed-form equation for predicting the hydraulic conductivity of unsaturated soils.” Soil Sci. Soc. Am. J. 44 (12): 892–898. https://doi.org/10.2136/sssaj1980.03615995004400050002x.
Wang, B., P. J. Vardon, and M. A. Hicks. 2018. “Rainfall-induced slope collapse with coupled material point method.” Eng. Geol. 239 (11): 1–12. https://doi.org/10.1016/j.enggeo.2018.02.007.
Wang, B., P. J. Vardon, M. A. Hicks, and Z. Chen. 2016a. “Development of an implicit material point method for geotechnical applications.” Comput. Geotech. 71 (13): 159–167. https://doi.org/10.1016/j.compgeo.2015.08.008.
Wang, G., G. You, J. Zhu, J. Yu, X. Gong, and J. Wu. 2016b. “Investigations of Changjing earth fissures, Jiangyin, Jiangsu, China.” Environ. Earth Sci. 75 (6): 502. https://doi.org/10.1007/s12665-015-5163-3.
Wang, Z., Y. Zhang, J. Wu, J. Yu, and X. Gong. 2015. “Numerical simulation of earth fissures due to groundwater withdrawal.” Proc. IAHS 372 (Apr): 95–398. https://doi.org/10.5194/piahs-372-395-2015.
Yang, P., Y. Gan, X. Zhang, Z. Chen, W. Qi, and P. Liu. 2014. “Improved decohesion modeling with the material point method for simulating crack evolution.” Int. J. Fract. 186 (5): 177–184. https://doi.org/10.1007/s10704-013-9925-1.
Ye, S., A. Franceschini, Y. Zhang, C. Janna, X. Gong, J. Yu, and P. Teatini. 2018. “A novel approach to model earth fissure caused by extensive aquifer exploitation and its application to the Wuxi Case, China.” Water Resour. Res. 54 (3): 2249–2269. https://doi.org/10.1002/2017WR021872.
Youssef, A. M., A. A. Sabtan, N. H. Maerz, and Y. A. Zabramawi. 2014. “Earth fissures in Wadi Najran, Kingdom of Saudi Arabia.” Nat. Hazards 71 (3): 2013–2027. https://doi.org/10.1007/s11069-013-0991-5.
Zhang, Y., G. He, J. Wu, J. Yu, and X. Gong. 2022. “Laboratory experimental study on pumping-induced earth fissures.” Hydrogeol. J. 30 (24): 849–864. https://doi.org/10.1007/s10040-022-02473-w.
Zhang, Y., Z. Wang, Y. Xue, J. Wu, and J. Yu. 2016. “Mechanisms for earth fissure formation due to groundwater extraction in the Su-Xi-Chang area, China.” Bull. Eng. Geol. Environ. 75 (2): 745–760. https://doi.org/10.1007/s10064-015-0775-0.
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Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 149 • Issue 9 • September 2023
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© 2023 American Society of Civil Engineers.
History
Received: Jul 6, 2022
Accepted: Mar 21, 2023
Published online: Jun 19, 2023
Published in print: Sep 1, 2023
Discussion open until: Nov 19, 2023
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