Staged Damage Behavior and Acoustic Emission Characteristics of Rock-Like Materials under the Coupled Effects of Clay Mineral Content and Uniaxial Loading
Publication: Journal of Materials in Civil Engineering
Volume 36, Issue 1
Abstract
In this work, we investigated the effects of clay mineral content on the mechanical damage behavior and cracking mechanism of rock-like specimens with different bentonite (montmorillonite) contents by performing uniaxial compression tests. Based on the obtained stress–strain curves, the damage evolution stages and stress thresholds of the specimens were determined. The evolution of internal microcracks and microstructural characteristics of fracture surfaces was analyzed using acoustic emission (AE) technology and scanning electron microscopy. The results showed that the bentonite content remarkably affects the damage behavior and AE patterns of the specimens. With increasing bentonite content from 10% to 40%, the stress thresholds and elastic modulus decreased, the peak strain increased, and the cumulative AE ring count and energy decreased (following a negative power function), indicating that the AE activities were significantly weakened. Moreover, the transformation of AF-RA distribution pattern, the decrease in b-value and increase in proportion of the high peak frequency indicated that the dominant cracking mechanism has been changed from small-scale microtensile modes to large-scale microshear modes. The AE source location results reproduced the formation process of macrofractures. These differences in damage behaviors and AE characteristics caused by bentonite content are closely related to the microstructure features of the specimens. The critical slowing down phenomenon of aforementioned AE parameters can serve for predicting rock instability.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
The data, models, and code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work was funded by the National Natural Science Foundation of China (Grant Nos. 42090052 and 41977249), the National Key Research and Development Program of China (Grant No. 2019YFC1509701), and the China Scholarship Council (File No. 202204910040). Thanks to the eceshi (www.eceshi.com) for the SEM analysis.
References
Aggelis, D. G. 2011. “Classification of cracking mode in concrete by acoustic emission parameters.” Mech. Res. Commun. 38 (3): 153–157. https://doi.org/10.1016/j.mechrescom.2011.03.007.
Aki, K. 1965. “Maximum likelihood estimate of b in the formula log N=a-bM and its confidence limits.” Bull. Earthquake Res. Inst. Univ. Tokyo 43: 237–239.
Brace, W. F., B. W. C. PauldingScholz Jr., and C. Scholz. 1966. “Dilatancy in the fracture of crystalline rocks.” J. Geophys. Res. 71 (16): 3939–3953. https://doi.org/10.1029/JZ071i016p03939.
Bu, F. C., L. Xue, M. Y. Zhai, X. L. Huang, J. Y. Dong, N. Liang, and C. Xu. 2022. “Evaluation of the characterization of acoustic emission of brittle rocks from the experiment to numerical simulation.” Sci. Rep. 12 (1): 498. https://doi.org/10.1038/s41598-021-03910-8.
Cai, M., P. K. Kaiser, H. Morioka, M. Minami, T. Maejima, Y. Tasaka, and H. Kurose. 2007. “FLAC/PFC coupled numerical simulation of AE in large-scale underground excavations.” Int. J. Rock Mech. Min. Sci. 44 (4): 550–564. https://doi.org/10.1016/j.ijrmms.2006.09.013.
Carcione, J. M., D. Gei, T. Yu, and J. Ba. 2019. “Effect of clay and mineralogy on permeability.” Pure Appl. Geophys. 176 (6): 2581–2594. https://doi.org/10.1007/s00024-019-02117-3.
Carpinteri, A., G. Lacidogna, F. Accornero, A. C. Mpalaskas, T. E. Matikas, and D. G. Aggelis. 2013. “Influence of damage in the acoustic emission parameters.” Cem. Concr. Compos. 44 (Nov): 9–16. https://doi.org/10.1016/j.cemconcomp.2013.08.001.
Chen, H. R., Q. Y. Di, W. X. Zhang, Y. Li, and J. R. Niu. 2021a. “Effects of bedding orientation on the failure pattern and acoustic emission activity of shale under uniaxial compression.” Geomech. Geophys. Geo-Energy Geo-Resour. 7 (1): 20. https://doi.org/10.1007/s40948-021-00216-x.
Chen, H. R., S. Q. Qin, L. Xue, B. C. Yang, and K. Zhang. 2018. “A physical model predicting instability of rock slopes with locked segments along a potential slip surface.” Eng. Geol. 242 (Aug): 34–43. https://doi.org/10.1016/j.enggeo.2018.05.012.
Chen, H. R., S. Q. Qin, L. Xue, B. C. Yang, and K. Zhang. 2022. “Universal precursor seismicity pattern before locked-segment rupture and evolutionary rule for landmark earthquakes.” Geosci. Front. 13 (3): 101314. https://doi.org/10.1016/j.gsf.2021.101314.
Chen, H. R., M. Y. Zhai, and L. Xue. 2021b. “Energy characteristics of acoustic emission at the volume-expansion point of a rock bridge: A new insight into the evolutionary mechanism of coastal cliff collapse.” J. Mar. Sci. Eng. 9 (12): 1338. https://doi.org/10.3390/jmse9121338.
Cheng, Y., L. N. Y. Wong, and V. Maruvanchery. 2016. “Transgranular crack nucleation in carrara marble of brittle failure.” Rock Mech. Rock Eng. 49 (8): 3069–3082. https://doi.org/10.1007/s00603-016-0976-2.
Cherblanc, F., J. Berthonneau, P. Bromblet, and V. Huon. 2016. “Influence of water content on the mechanical behaviour of limestone: Role of the clay minerals content.” Rock Mech. Rock Eng. 49 (6): 2033–2042. https://doi.org/10.1007/s00603-015-0911-y.
Du, M. L., F. Gao, C. Z. Cai, S. J. Su, and Z. K. Wang. 2021. “Experimental study on the damage and cracking characteristics of bedded coal subjected to liquid nitrogen cooling.” Rock Mech. Rock Eng. 54 (11): 5731–5744. https://doi.org/10.1007/s00603-021-02584-y.
Eberhardt, E., D. Stead, B. Stimpson, and R. S. Read. 1998. “Identifying crack initiation and propagation thresholds in brittle rock.” Can. Geotech. J. 35 (2): 222–233. https://doi.org/10.1139/t97-091.
Gao, A., C. Qi, R. Shan, and C. Wang. 2022. “Experimental study on the spatial-temporal failure characteristics of red sandstone with a cemented structural surface under compression.” ACS Omega 7 (23): 20250–20258. https://doi.org/10.1021/acsomega.2c02169.
Ge, Z. L., and Q. Sun. 2021. “Acoustic emission characteristics of gabbro after microwave heating.” Int. J. Rock Mech. Min. Sci. 138 (Feb): 104616. https://doi.org/10.1016/j.ijrmms.2021.104616.
Guo, P. Y., M. H. Bu, M. C. He, and Y. W. Wang. 2020. “Experimental investigation on thermal conductivity of clay-bearing sandstone subjected to different treatment processes: Drying, wetting and drying II.” Geothermics 88 (Nov): 101909. https://doi.org/10.1016/j.geothermics.2020.101909.
Gutenberg, B. 1956. “The energy of earthquakes.” Q. J. Geol. Soc. London 112 (1–4): 1–14. https://doi.org/10.1144/GSL.JGS.1956.112.01-04.02.
Gutenberg, B., and C. F. Richter. 1944. “Frequency of earthquakes in California.” Bull. Seismol. Soc. Am. 34 (4): 185–188. https://doi.org/10.1785/BSSA0340040185.
He, M. C., J. Y. Li, and F. Q. Ren. 2020. “Rock burst criterion based on clay mineral content.” Arab. J. Geosci. 13 (4): 185. https://doi.org/10.1007/s12517-020-5199-x.
He, W. H., K. Y. Chen, A. Hayatdavoudi, K. Sawant, and M. Lomas. 2019. “Effects of clay content, cement and mineral composition characteristics on sandstone rock strength and deformability behaviors.” J. Pet. Sci. Eng. 176 (May): 962–969. https://doi.org/10.1016/j.petrol.2019.02.016.
Hoek, E., and C. D. Martin. 2014. “Fracture initiation and propagation in intact rock—A review.” J. Rock Mech. Geotech. Eng. 6 (4): 287–300. https://doi.org/10.1016/j.jrmge.2014.06.001.
Hou, L. H., S. T. Wu, Z. H. Jing, X. H. Jiang, Z. C. Yu, G. L. Hua, L. Su, C. Yu, F. R. Liao, and H. Tian. 2022. “Effects of types and content of clay minerals on reservoir effectiveness for lacustrine organic matter rich shale.” Fuel 327 (Nov): 125043. https://doi.org/10.1016/j.fuel.2022.125043.
Hu, D. W., F. Zhang, J. F. Shao, and B. Gatmiri. 2013. “Influences of mineralogy and water content on the mechanical properties of argillite.” Rock Mech. Rock Eng. 47 (1): 157–166. https://doi.org/10.1007/s00603-013-0413-8.
Hu, X. J., X. N. Gong, H. B. Hu, P. P. Guo, and J. J. Ma. 2022. “Cracking behavior and acoustic emission characteristics of heterogeneous granite with double pre-existing filled flaws and a circular hole under uniaxial compression: Insights from grain-based discrete element method modeling.” Bull. Eng. Geol. Environ. 81 (4): 162. https://doi.org/10.1007/s10064-022-02665-4.
Kamal, M. S., M. Mahmoud, M. Hanfi, S. Elkatatny, and I. Hussein. 2018. “Clay minerals damage quantification in sandstone rocks using core flooding and NMR.” J. Pet. Explor. Prod. Technol. 9 (1): 593–603. https://doi.org/10.1007/s13202-018-0507-7.
Kong, B., E. Y. Wang, Z. H. Li, X. R. Wang, J. Liu, and N. Li. 2016. “Fracture mechanical behavior of sandstone subjected to high-temperature treatment and its acoustic emission characteristics under uniaxial compression conditions.” Rock Mech. Rock Eng. 49 (12): 4911–4918. https://doi.org/10.1007/s00603-016-1011-3.
Lajtai, E. Z., and V. N. Lajtai. 1975. “The collapse of cavities.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 12 (4): 81–86. https://doi.org/10.1016/0148-9062(75)90001-7.
Li, D. X., E. Y. Wang, X. G. Kong, H. S. Jia, D. M. Wang, and M. Ali. 2019. “Damage precursor of construction rocks under uniaxial cyclic loading tests analyzed by acoustic emission.” Constr. Build. Mater. 206 (May): 169–178. https://doi.org/10.1016/j.conbuildmat.2019.02.074.
Li, H. R., R. X. Shen, Y. F. Qiao, and M. C. He. 2021. “Acoustic emission signal characteristics and its critical slowing down phenomenon during the loading process of water-bearing sandstone.” J. Appl. Geophys. 194 (Nov): 104458. https://doi.org/10.1016/j.jappgeo.2021.104458.
Li, L. R., J. H. Deng, L. Zheng, and J. F. Liu. 2017. “Dominant frequency characteristics of acoustic emissions in white marble during direct tensile tests.” Rock Mech. Rock Eng. 50 (5): 1337–1346. https://doi.org/10.1007/s00603-016-1162-2.
Liu, B., Y. D. Sun, J. Wang, and G. Zhang. 2020. “Characteristic analysis of crack initiation and crack damage stress of sandstone and mudstone under low-temperature condition.” J. Cold Reg. Eng. 34 (3): 04020020. https://doi.org/10.1061/(ASCE)CR.1943-5495.0000225.
Liu, D. Q., Z. Wang, X. Y. Zhang, Y. Wang, X. L. Zhang, and D. Li. 2018. “Experimental investigation on the mechanical and acoustic emission characteristics of shale softened by water absorption.” J. Nat. Gas Sci. Eng. 50 (Feb): 301–308. https://doi.org/10.1016/j.jngse.2017.11.020.
Lockner, D. A., J. D. Byerlee, V. Kuksenko, A. Ponomarev, and A. Sidorin. 1991. “Quasi-static fault growth and shear fracture energy in granite.” Nature 350 (6313): 39–42. https://doi.org/10.1038/350039a0.
Martin, C. D., and N. A. Chandler. 1994. “The progressive fracture of Lac du Bonnet granite.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 31 (6): 643–659. https://doi.org/10.1016/0148-9062(94)90005-1.
Michlmayr, G., D. Cohen, and D. Or. 2012. “Sources and characteristics of acoustic emissions from mechanically stressed geologic granular media—A review.” Earth-Sci. Rev. 112 (3–4): 97–114. https://doi.org/10.1016/j.earscirev.2012.02.009.
Moradian, Z. A., G. Ballivy, and P. Rivard. 2012. “Correlating acoustic emission sources with damaged zones during direct shear test of rock joints.” Can. Geotech. J. 49 (6): 710–718. https://doi.org/10.1139/t2012-029.
Naderloo, M., M. Moosavi, and M. Ahmadi. 2019. “Using acoustic emission technique to monitor damage progress around joints in brittle materials.” Theor. Appl. Fract. Mech. 104 (Dec): 102368. https://doi.org/10.1016/j.tafmec.2019.102368.
Nesbitt, H. W., and G. M. Young. 1984. “Prediction of some weathering trends of plutonic and volcanic rocks based on thermodynamic and kinetic considerations.” Geochim. Cosmochim. Acta 48 (7): 1523–1534. https://doi.org/10.1016/0016-7037(84)90408-3.
Ohno, K., and M. Ohtsu. 2010. “Crack classification in concrete based on acoustic emission.” Constr. Build. Mater. 24 (12): 2339–2346. https://doi.org/10.1016/j.conbuildmat.2010.05.004.
Pepe, G., S. Mineo, G. Pappalardo, and A. Cevasco. 2018. “Relation between crack initiation-damage stress thresholds and failure strength of intact rock.” Bull. Eng. Geol. Environ. 77 (2): 709–724. https://doi.org/10.1007/s10064-017-1172-7.
Reches, Z. E., and D. A. Lockner. 1994. “Nucleation and growth of faults in brittle rocks.” J. Geophys. Res.: Solid Earth 99 (B9): 18159–18173. https://doi.org/10.1029/94JB00115.
Reiweger, I., K. Mayer, K. Steiner, J. Dual, and J. Schweizer. 2015. “Measuring and localizing acoustic emission events in snow prior to fracture.” Cold Reg. Sci. Technol. 110 (Feb): 160–169. https://doi.org/10.1016/j.coldregions.2014.12.002.
Senfaute, G., A. Duperret, and J. A. Lawrence. 2009. “Micro-seismic precursory cracks prior to rock-fall on coastal chalk cliffs: A case study at Mesnil-Val, Normandie, NW France.” Nat. Hazards Earth Syst. Sci. 9 (5): 1625–1641. https://doi.org/10.5194/nhess-9-1625-2009.
Sha, S., G. Rong, Z. H. Chen, B. W. Li, and Z. Y. Zhang. 2020. “Experimental evaluation of physical and mechanical properties of geothermal reservoir rock after different cooling treatments.” Rock Mech. Rock Eng. 53 (11): 4967–4991. https://doi.org/10.1007/s00603-020-02200-5.
Shahidan, S., R. Pulin, N. Muhamad Bunnori, and K. M. Holford. 2013. “Damage classification in reinforced concrete beam by acoustic emission signal analysis.” Constr. Build. Mater. 45 (Aug): 78–86. https://doi.org/10.1016/j.conbuildmat.2013.03.095.
Sharma, R. K., B. S. Mehta, and C. S. Jamwal. 2012. “Cut slope stability evaluation of NH-21 along Nalayan-Gambhrola section, Bilaspur district, Himachal Pradesh, India.” Nat. Hazards 66 (2): 249–270. https://doi.org/10.1007/s11069-012-0469-x.
Su, G. S., J. H. Huang, H. J. Xu, and Y. Z. Qin. 2022. “Extracting acoustic emission features that precede hard rock instability with unsupervised learning.” Eng. Geol. 306 (Sep): 106761. https://doi.org/10.1016/j.enggeo.2022.106761.
Tembe, S., D. A. Lockner, and T.-F. Wong. 2010. “Effect of clay content and mineralogy on frictional sliding behavior of simulated gouges: Binary and ternary mixtures of quartz, illite, and montmorillonite.” J. Geophys. Res. 115 (B3): B03416. https://doi.org/10.1029/2009jb006383.
Tham, L. G., H. Liu, C. A. Tang, P. K. K. Lee, and Y. Tsui. 2005. “On tension failure of 2-D rock specimens and associated acoustic emission.” Rock Mech. Rock Eng. 38 (1): 1–19. https://doi.org/10.1007/s00603-004-0031-6.
Ulusay, R., and J. Hudson. 2007. The complete ISRM suggested methods for rock characterization. Lisbon: International Society for Rock Mechanics.
Vitone, C., F. Cotecchia, G. Viggiani, and S. A. Hall. 2012. “Strain fields and mechanical response of a highly to medium fissured bentonite clay.” Int. J. Numer. Anal. Methods Geomech. 37 (11): 1510–1534. https://doi.org/10.1002/nag.2095.
Wang, J. C., G. Q. Chen, Y. F. Chen, and M. Serati. 2022a. “Interrelation analysis method of acoustic emission for failure prediction of brittle failure based on vibration mechanics.” Bull. Eng. Geol. Environ. 81 (6): 247. https://doi.org/10.1007/s10064-022-02752-6.
Wang, Q. S., J. X. Chen, J. Q. Guo, Y. B. Luo, H. Y. Wang, and Q. Liu. 2017. “Acoustic emission characteristics and energy mechanism in karst limestone failure under uniaxial and triaxial compression.” Bull. Eng. Geol. Environ. 78 (3): 1427–1442. https://doi.org/10.1007/s10064-017-1189-y.
Wang, X. Z., H. P. Xie, R. Zhang, G. Z. Zhang, Z. X. Xu, J. H. Deng, D. Wang, C. B. Li, G. Feng, Z. T. Zhang, and L. Ren. 2022b. “Progressive failure characterization of sandstone from yingjinshan area in Qinghai-Tibet Plateau.” Rock Mech. Rock Eng. 55 (11): 6723–6740. https://doi.org/10.1007/s00603-022-02999-1.
Wu, Y. Q., S. L. Li, and D. W. Wang. 2019. “Characteristic analysis of acoustic emission signals of masonry specimens under uniaxial compression test.” Constr. Build. Mater. 196 (Jan): 637–648. https://doi.org/10.1016/j.conbuildmat.2018.11.148.
Xu, C., Y. Cui, L. Xue, H. R. Chen, J. Y. Dong, and H. X. Zhao. 2023. “Experimental study on mechanical properties and failure behaviours of new materials for modeling rock bridges.” J. Mater. Res. Technol. 23 (Mar): 1696–1711. https://doi.org/10.1016/j.jmrt.2023.01.128.
Xu, R. C., Z. Li, and Y. D. Jin. 2022. “Brittleness effect on acoustic emission characteristics of rocks based on a new brittleness evaluation index.” Int. J. Geomech. 22 (10): 04022185. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002562.
Xu, Z. M., R. Q. Huang, Z. G. Tang, and S. D. Wang. 2005. “Clay minerals and failure of slopes.” [In Chinese.] Chin. J. Rock Mech. Eng. 24 (5): 729–740.
Xue, L., M. Qi, S. Qin, G. Li, P. Li, and M. Wang. 2014a. “A potential strain indicator for brittle failure prediction of low-porosity rock: Part I—Experimental studies based on the uniaxial compression test.” Rock Mech. Rock Eng. 48 (5): 1763–1772. https://doi.org/10.1007/s00603-014-0675-9.
Xue, L., M. Qi, S. Q. Qin, G. L. Li, P. Li, and M. M. Wang. 2014b. “A potential strain indicator for brittle failure prediction of low-porosity rock: Part II—Theoretical studies based on renormalization group theory.” Rock Mech. Rock Eng. 48 (5): 1773–1785. https://doi.org/10.1007/s00603-014-0681-y.
Xue, L., S. Q. Qin, Q. Sun, Y. Y. Wang, L. M. Lee, and W. C. Li. 2014c. “A study on crack damage stress thresholds of different rock types based on uniaxial compression tests.” Rock Mech. Rock Eng. 47 (4): 1183–1195. https://doi.org/10.1007/s00603-013-0479-3.
Xue, L., S. Q. Qin, Q. Sun, Y. Y. Wang, and H. T. Qian. 2014d. “A quantitative criterion to describe the deformation process of rock sample subjected to uniaxial compression: From criticality to final failure.” Phys. A 410 (Sep): 470–482. https://doi.org/10.1016/j.physa.2014.05.062.
Yang, B. C., L. Xue, Y. T. Duan, and M. M. Wang. 2021a. “Correlation study between fracability and brittleness of shale-gas reservoir.” Geomech. Geophys. Geo-Energy Geo-Resour. 7 (2): 31. https://doi.org/10.1007/s40948-021-00231-y.
Yang, B. C., W. Zhao, and Y. T. Duan. 2022a. “Critical damage threshold of brittle rock failure based on Renormalization Group theory.” Geomech. Geophys. Geo-Energy Geo-Resour. 8 (5): 135. https://doi.org/10.1007/s40948-022-00441-y.
Yang, J., Z. L. Mu, S. Q. Yang, and W. L. Tian. 2022b. “Experimental investigation of microscopic crack development and damage characteristics of sandstone based on acoustic emission characteristic parameters.” Geomech. Geophys. Geo-Energy Geo-Resour. 8 (2): 51. https://doi.org/10.1007/s40948-022-00361-x.
Yang, J., S. Q. Yang, G. J. Liu, W. L. Tian, and Y. Li. 2021b. “Experimental study of crack evolution in prefabricated double-fissure red sandstone based on acoustic emission location.” Geomech. Geophys. Geo-Energy Geo-Resour. 7 (1): 18. https://doi.org/10.1007/s40948-021-00219-8.
Yu, K., K. D. Zhao, and Y. W. Ju. 2022. “A comparative study of the permeability enhancement in coal and clay-rich shale by hydraulic fracturing using nano-CT and SEM image analysis.” Appl. Clay Sci. 218 (Mar): 106430. https://doi.org/10.1016/j.clay.2022.106430.
Zhai, M. Y., L. Xue, F. C. Bu, B. C. Yang, and H. Ding. 2022. “Microcracking behaviors and acoustic emission characteristics of granite subjected to direct shear based on a novel grain-based model.” Comput. Geotech. 151 (Nov): 104955. https://doi.org/10.1016/j.compgeo.2022.104955.
Zhai, M. Y., L. Xue, H. R. Chen, C. Xu, and Y. Cui. 2021. “Effects of shear rates on the damaging behaviors of layered rocks subjected to direct shear: Insights from acoustic emission characteristics.” Eng. Fract. Mech. 258 (Dec): 108046. https://doi.org/10.1016/j.engfracmech.2021.108046.
Zhang, G. K., F. Gao, Z. Wang, S. L. Yue, and S. X. Deng. 2021. “Quantifying the progressive fracture damage of granite rocks by stress–strain, acoustic emission, and active ultrasonic methods.” J. Mater. Civ. Eng. 33 (12): 04021353. https://doi.org/10.1061/(ASCE)MT.1943-5533.0003962.
Zhang, Z. H., J. H. Deng, J. B. Zhu, and L. R. Li. 2018. “An experimental investigation of the failure mechanisms of jointed and intact marble under compression based on quantitative analysis of acoustic emission waveforms.” Rock Mech. Rock Eng. 51 (7): 2299–2307. https://doi.org/10.1007/s00603-018-1484-3.
Zhao, X. G., M. Cai, J. Wang, P. F. Li, and L. K. Ma. 2015. “Objective determination of crack initiation stress of brittle rocks under compression using ae measurement.” Rock Mech. Rock Eng. 48 (6): 2473–2484. https://doi.org/10.1007/s00603-014-0703-9.
Zhao, X. G., M. Cai, J. Wang, and L. K. Ma. 2013. “Damage stress and acoustic emission characteristics of the Beishan granite.” Int. J. Rock Mech. Min. Sci. 64 (Dec): 258–269. https://doi.org/10.1016/j.ijrmms.2013.09.003.
Zhou, Y., X. Yu, Z. Q. Guo, Y. Yan, K. Zhao, J. Q. Wang, and S. T. Zhu. 2021. “On acoustic emission characteristics, initiation crack intensity, and damage evolution of cement-paste backfill under uniaxial compression.” Constr. Build. Mater. 269 (Feb): 121261. https://doi.org/10.1016/j.conbuildmat.2020.121261.
Information & Authors
Information
Published In
Journal of Materials in Civil Engineering
Volume 36 • Issue 1 • January 2024
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Dec 14, 2022
Accepted: Jun 1, 2023
Published online: Oct 20, 2023
Published in print: Jan 1, 2024
Discussion open until: Mar 20, 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.