Dynamic Response Analysis of Deep-Sea Sediments with Heterogeneity under Moving Nonuniform Mining Collector Loading
Publication: Journal of Engineering Mechanics
Volume 148, Issue 3
Abstract
The dynamic response of heterogeneous deep-sea sediments under moving nonuniform mining collector loading was determined analytically. The heterogeneity of deep-sea sediments is associated with the elastic modulus increasing nonlinearly with depth. The ground pressure of the mining collector with longitudinal eccentricity was assumed to have a trapezoidal distribution. The complex Fourier series method was used to expand the soil displacement and the loading function of the ground pressure with eccentricity. Thus, the governing partial differential equations (PDEs) of motion for the soil were reduced to ordinary differential equations (ODEs) with respect to the horizontal direction and the time . The analytical solution of the ODEs was solved by the method of Frobenius. After verifying the analytical solution by means of comparisons with the Abaqus simulated results for the special cases of homogeneity under uniform load, this analytical solution was utilized to assess the effect of heterogeneity, eccentricity, and pedrail length on the response of deep-sea sediments.
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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 research was funded by the National Natural Science Foundation of China (NSFC 12072309), the Natural Science Foundation of Hunan Province, China (2019JJ50625), the Education Department Foundation of Hunan Province (19B546), the Hunan Innovative Province Construction Project (2019RS1059) and Engineering Research Center of Rock-Soil Drilling & Excavation and Protection, Ministry of Education.
References
Beskou, N. D. 2020. “Dynamic analysis of an elastic plate on a cross-anisotropic and continuously nonhomogeneous viscoelastic half-plane under a moving load.” Acta Mech. 231 (4): 1567–1585. https://doi.org/10.1007/s00707-019-02594-6.
Beskou, N. D., Y. Chen, and J. Qian. 2018. “Dynamic response of an elastic plate on a cross—Anisotropic elastic half-plane to a load moving on its surface.” Transp. Geotech. 14 (Mar): 98–106. https://doi.org/10.1016/j.trgeo.2017.11.003.
Beskou, N. D., J. Qian, and D. E. Beskos. 2017. “Approximate solutions for the problem of a load moving on the surface of a half-plane.” Acta Mech. 229 (4): 1721–1739. https://doi.org/10.1007/s00707-017-2089-8.
Chen, N., L. H. Gong, Q. Wang, and G. S. Zhang. 2003. “Research of trafficability indices of track vehicle on soft soil.” Constr. Mach. 4 (Jan): 25–27.
Chen, Y., N. D. Beskou, and J. Qian. 2018. “Dynamic response of an elastic plate on a cross-anisotropic poroelastic half-plane to a load moving on its surface.” Soil Dyn. Earthquake Eng. 107 (Apr): 292–302. https://doi.org/10.1016/j.soildyn.2018.01.038.
Cheshmehkani, S., and M. Eskandari-Ghadi. 2017. “Three-dimensional dynamic ring load and point load Green’s functions for continuously inhomogeneous viscoelastic transversely isotropic half-space.” Eng. Anal. Boundary Elem. 76 (Mar): 10–25. https://doi.org/10.1016/j.enganabound.2016.12.009.
Chung, J. S. 2005. “Deep-ocean mining technology: Development II.” In Proc., 6th ISOPE Ocean Mining Symp., 9–13. Cupertino, CA: International Journal of Offshore and Polar Engineers.
Deng, Y. H., and G. Y. Wu. 2006. “Influence of the distribution of the normal pressure acting on the pedrail of the mining vehicle in deep ocean to the driving force.” Min. Process. Equip. 34 (12): 18–19.
Ding, L. H., and Y. Q. Gao. 2006. “Research and development of deep-sea mining collector.” Min. Res. Dev. 26 (10): 52–56. https://doi.org/10.13827/j.cnki.kyyk.2006.s1.012.
Han, Z. J., G. Lin, and J. B. Li. 2015. “Dynamic impedance functions for arbitrary-shaped rigid foundation embedded in anisotropic multilayered soil.” J. Eng. Mech. 141 (11): 04015045. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000915.
Handschuh, R., H. Grebe, and J. Panthel. 2001. “Innovative deep ocean mining concept based on flexible riser and self-propelled mining machines.” In Proc., 4th ISOPE Ocean Mining Symp., 99–107. Cupertino, CA: International Journal of Offshore and Polar Engineers.
Hetherington, J. G. 2001. “The applicability of the MMP concept in specifying off-road mobility for wheeled and tracked vehicles.” J. Terramech. 38 (2): 63–70. https://doi.org/10.1016/S0022-4898(00)00010-0.
Itou, S. 2016. “Stresses produced in an orthotropic half-plane under a moving line load.” Int. J. Solids Struct. 100–101 (Dec): 411–416. https://doi.org/10.1016/j.ijsolstr.2016.09.013.
Jan, Q., and M. H. Wang. 1998. “Design of nodule collector for deep ocean mining.” Min. Res. Dev. 1 (1): 37–40. https://doi.org/10.13827/j.cnki.kyyk.1998.01.010.
Khojasteh, A., M. Rahimian, R. Pak, and M. Eskandari. 2008. “Asymmetric dynamic green’s functions in a two-layered transversely isotropic half-space.” J. Eng. Mech. 134 (9): 777–787. https://doi.org/10.1061/(ASCE)0733-9399(2008)134:9(777).
Kreyszig, E. 1983. Advanced engineering mathematics. New York: Wiley.
Lefeuve-Mesgouez, G., D. Le Houédec, and A. T. Peplow. 2000. “Ground vibration in the vicinity of a high-speed moving harmonic strip load.” J. Sound Vib. 231 (5): 1289–1309. https://doi.org/10.1006/jsvi.1999.2731.
Leng, D. X., S. Shao, Y. C. Xie, and H. H. Wang. 2021. “A brief review of recent progress on deep sea mining vehicle.” Ocean Eng. 228 (Apr): 108565. https://doi.org/10.1016/j.oceaneng.2020.108565.
Li, Y. H., T. T. Luo, X. Sun, and W. G. Liu. 2019. “Strength behaviors of remolded hydrate-bearing marine sediments in different drilling depths of the South China Sea.” Energies 12 (2): 1–14. https://doi.org/10.3390/en12020253.
Ma, W. B., Q. H. Rao, K. Feng, and F. Xu. 2015. “Experimental research on grouser traction of deep-sea mining machine.” Appl. Math. Mech. 36 (9): 1243–1252. https://doi.org/10.1007/s10483-015-1979-6.
Man, J. H., K. Z. Yan, Y. Miao, Y. Liu, X. Yang, A. Diab, and L. You. 2021. “3D Spectral element model with a space-decoupling technique for the response of transversely isotropic pavements to moving vehicular loading.” Road Mater. Pavement Des. 1–25. https://doi.org/10.1080/14680629.2021.1986121.
Manolis, G. D., P. S. Divena, T. V. Rangelov, and F. Wuttke. 2017. Seismic wave propagation in non-homogeneous elastic media by boundary elements. Berlin: Springer.
Muho, E. V., and N. D. Beskou. 2019. “Dynamic response of an isotropic elastic half-plane with shear modulus varying with depth to a load moving on its surface.” Transp. Geotech. 20 (Sep): 100248. https://doi.org/10.1016/j.trgeo.2019.100248.
Muravskii, G. 1997. “On time-harmonic problem for non-homogeneous elastic half-space with shear modulus limited at infinite depth.” Eur. J. Mech. A. Solids 16 (2): 227–294.
Pegios, I. P., S. Papargyri-Beskou, Y. Zhou, and P. He. 2019. “Steady-state dynamic response of a gradient elastic half-plane to a load moving on its surface with constant speed.” Arch. Appl. Mech. 89 (9): 1809–1824. https://doi.org/10.1007/s00419-019-01546-9.
Priddy, J. D., and W. E. Willoughby. 2006. “Clarification of vehicle cone index with reference to mean maximum pressure.” J. Terramech. 43 (2): 85–96. https://doi.org/10.1016/j.jterra.2004.10.001.
Qi, C. L., Q. H. Rao, Q. Liu, and W. B. Ma. 2019. “Traction rheological properties of simulative soil for deep-sea sediment.” J. Oceanol. Limnol. 37 (1): 62–71. https://doi.org/10.1007/s00343-018-7258-7.
Rowland, D. 1972. “Tracked vehicle ground pressure and its effect on soft ground performance.” In Proc., 4th Int. ISTVS Conf. 24–28. Stockholm, Sweden: Mechanics of Soil-Vehicle Systems.
Schreiner, B. G. 1967. “A technique for estimating the performance of tracked vehicles in Muskeg.” J. Terramech. 4 (3): 23–29. https://doi.org/10.1016/0022-4898(67)90124-3.
Siddharthan, R., Z. Zafir, and G. M. Norris. 1993. “Moving load response of layered soil. I: Formulation.” J. Eng. Mech. 119 (10): 2052–2071. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:10(2052).
Theodorakopoulos, D. D. 2003. “Dynamic analysis of a poroelastic half-plane soil medium under moving loads.” Soil Dyn. Earthquake Eng. 23 (7): 521–533. https://doi.org/10.1016/S0267-7261(03)00074-5.
Vrettos, C. 1990. “In-plane vibrations of soil deposits with variable shear modulus: I. Surface waves.” Int. J. Numer. Anal. Methods Geomech. 14 (3): 209–222. https://doi.org/10.1002/nag.1610140304.
Welling, C. G. 1981. “An advance design deep sea milling system.” In Proc., Offshore Technology Conf., 247–255. Houston: Offshore Technology Conference.
Wills, B. 1964. “The measurement of soil shear strength and deformation moduli and a comparison of the actual and theoretical performance of a family of rigid tracks.” J. Terramech. 1 (2): 83–88. https://doi.org/10.1016/0022-4898(64)90068-0.
Wu, H. Y., X. M. Chen, Y. Q. Gao, J. S. He, L. H. Ding, and Y. Xu. 2008. “Research on effects of grounding pressure distribution of a type of seabed tracked vehicle on traction force.” In Proc., Int. Offshore and Polar Engineering Conf., 73–77. Cupertino, CA: International Journal of Offshore and Polar Engineers.
Wu, H. Y., S. J. Liu, J. S. He, X. M. Chen, and Y. Q. Gao. 2010. “Research on the effect of grounding pressure distribution on traction force of tracked vehicle.” In Proc., Int. Offshore and Polar Engineering Conf., 197–200. Cupertino, CA: International Journal of Offshore and Polar Engineers.
Yamada, H., and T. Yamazaki. 1998. “Japan’s ocean test of the nodule mining system.” In Proc., 8th Int. Offshore and Polar Engineering Conf., 13–19. Cupertino, CA: International Journal of Offshore and Polar Engineers.
You, L. Y., K. Z. Yan, J. H. Man, and T. W. Shi. 2020. “3D spectral element solution of multilayered half-space medium with harmonic moving load: Effect of layer, interlayer, and loading properties on dynamic response of medium.” Int. J. Geomech. 20 (12): 04020227. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001878.
You, L. Y., K. Z. Yan, T. W. Shi, and J. H. Man. 2019. “Analytical solution for the effect of anisotropic layers/interlayers on an elastic multi-layered medium subjected to moving load.” Int. J. Solids Struct. 172 (Nov): 10–20. https://doi.org/10.1016/j.ijsolstr.2019.05.021.
Zhang, Y., K. T. Gu, and T. Liu. 2012. “Calculation method research on ground pressure of crawler crane.” Constr. Mach. Equip. 43 (11): 39–41.
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Published In
Journal of Engineering Mechanics
Volume 148 • Issue 3 • March 2022
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Aug 2, 2021
Accepted: Oct 22, 2021
Published online: Dec 17, 2021
Published in print: Mar 1, 2022
Discussion open until: May 17, 2022
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