Using Boundary Transform Method to Solve Geotechnical Problems with Mixed-Type Boundary Conditions
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 148, Issue 12
Abstract
In geotechnical engineering, mixed-type boundary problems cannot be solved directly by the integral transform method due to the diversity of boundary conditions. In view of this, the relationships between different boundaries are figured out from the perspectives of physical meaning and mathematical derivation. A novel boundary transform method is then proposed to transform a complex mixed-type boundary into a simple one, and the transform rules for different types of boundaries are graphically presented. Subsequently, the procedures to solve geotechnical problems with mixed-type boundaries are comprehensively elaborated. The application of the proposed boundary transform method for a two-dimensional steady flow problem with mixed-type boundaries is systemically considered. The results show that the boundary transform method can effectively deal with mixed-type boundary problems, rendering accurate solutions when compared with numerical analyses.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
The financial supports from the National Natural Science Foundation of China (51878185, 52078506, and 52178321), the Initial Scientific Research Foundations of Hainan University [KYQD(ZR)-22044], and the Guangxi Scientific and Technological Base and Talent Foundation (2021AC18008) are gratefully acknowledged. The authors also gratefully acknowledge the valuable contributions of Dr. Sujith Mangalathu, who improved the structure and the readability of the final draft of the manuscript.
References
Bau, H. H., and S. Sadhai. 1982. “Heat losses from a fluid flowing in a buried pipe.” Int. J. Heat Mass Transfer 25 (11): 1621–1629. https://doi.org/10.1016/0017-9310(82)90141-7.
Cassiani, G., and Z. Kabala. 1998. “Hydraulics of a partially penetrating well: Solution to a mixed-type boundary value problem via dual integral equations.” J. Hydrol. 211 (1–4): 100–111. https://doi.org/10.1016/S0022-1694(98)00223-6.
Cassiani, G., Z. Kabala, and M. Medina. 1999. “Flowing partially penetrating well: Solution to a mixed-type boundary value problem.” Adv. Water Resour. 23 (1): 59–68. https://doi.org/10.1016/S0309-1708(99)00002-0.
Chai, J., S. Horpibulsuk, S. Shen, and J. P. Carter. 2014. “Consolidation analysis of clayey deposits under vacuum pressure with horizontal drains.” Geotext. Geomembr. 42 (5): 437–444. https://doi.org/10.1016/j.geotexmem.2014.07.001.
Chang, C.-C., and C.-S. Chen. 2002. “An integral transform approach for a mixed boundary problem involving a flowing partially penetrating well with infinitesimal well skin.” Water Resour. Res. 38 (6): 7. https://doi.org/10.1029/2001WR001091.
Chang, C.-C., and C.-S. Chen. 2003. “A flowing partially penetrating well in a finite-thickness aquifer: A mixed-type initial boundary value problem.” J. Hydrol. 271 (1–4): 101–118. https://doi.org/10.1016/S0022-1694(02)00323-2.
Chen, Z., P. Ni, Y. Chen, and G. Mei. 2020a. “Plane-strain consolidation theory with distributed drainage boundary.” Acta Geotech. 15 (2): 489–508. https://doi.org/10.1007/s11440-018-0712-z.
Chen, Z., P. Ni, G. Mei, and Y. Chen. 2020b. “A semi-analytical solution for consolidation of ground with partially penetrating PVDs under the free-strain condition.” J. Eng. Mech. 147 (2): 04020148. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001884.
Chen, Z., T. Xiao, J. Feng, P. Ni, D. Chen, G. Mei, and Y. Chen. 2021. “Mathematical characterization of pile–soil interface boundary for consolidation analysis of soil around permeable pipe pile.” Can. Geotech. J. 58 (9): 1277–1288. https://doi.org/10.1139/cgj-2020-0337.
Cheung, Y. K. 2013. Finite strip method in structural analysis. New York: Elsevier.
Conte, E., and A. Troncone. 2018. “A performance-based method for the design of drainage trenches used to stabilize slopes.” Eng. Geol. 239 (Mar): 158–166. https://doi.org/10.1016/j.enggeo.2018.03.017.
Fabrikant, V. 1991. Mixed boundary value problems of potential theory and their applications in engineering. Dordrecht, Netherlands: Kluwer Academic Publishers.
Gray, H. 1945. Simultaneous consolidation of contiguous layers of unlike compressible soils, 1327–1344. Reston, VA: ASCE.
Huang, S. C., and Y. P. Chang. 1984. “Anisotropic heat conduction with mixed boundary conditions.” J. Heat Transfer 106 (3): 646–648. https://doi.org/10.1115/1.3246729.
Levine, H. 1982. “On a mixed boundary value problem of diffusion type.” Appl. Sci. Res. 39 (4): 261–276. https://doi.org/10.1007/BF00389265.
Mei, G., J. Feng, M. Xu, and P. Ni. 2022. “Estimation of interface parameter for one-dimensional consolidation with continuous drainage boundary conditions.” Int. J. Geomech. 22 (3): 04021292. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002300.
Schneider, G. 1985. “An investigation into the heat loss characteristics of buried pipes.” J. Heat Transfer 107 (3): 696–699. https://doi.org/10.1115/1.3247479.
Sneddon, I. N. 1966. Mixed boundary value problems in potential theory. New York: John Wiley & Sons, Inc.
Stanić, B. 1984. “Influence of drainage trenches on slope stability.” J. Geotech. Eng. 110 (11): 1624–1636. https://doi.org/10.1061/(ASCE)0733-9410(1984)110:11(1624).
Verruijt, A. 2009. An introduction to soil dynamics. Berlin: Springer.
Wang, C., and P. J. Fox. 2020. “Analytical solutions for heat transfer in saturated soil with effective porosity.” J. Geotech. Geoenviron. Eng. 146 (9): 04020095. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002324.
Wang, S., P. Ni, Z. Chen, and G. Mei. 2020a. “Consolidation solution of soil around a permeable pipe pile.” Mar. Georesour. Geotechnol. 38 (9): 1097–1105. https://doi.org/10.1080/1064119X.2019.1655119.
Wang, X., W. Tan, P. Ni, Z. Chen, and S. Hu. 2020b. “Propagation of settlement in soft soils induced by tunneling.” Tunnelling Underground Space Technol. 99 (Sep): 103378. https://doi.org/10.1016/j.tust.2020.103378.
Zeng, C., X. Xue, G. Zheng, T. Xue, and G. Mei. 2018. “Responses of retaining wall and surrounding ground to pre-excavation dewatering in an alternated multi-aquifer-aquitard system.” J. Hydrol. 559 (2): 609–626. https://doi.org/10.1016/j.jhydrol.2018.02.069.
Zeng, C., G. Zheng, X. Xue, and G. Mei. 2019. “Combined recharge: A method to prevent ground settlement induced by redevelopment of recharge wells.” J. Hydrol. 568 (89): 1–11. https://doi.org/10.1016/j.jhydrol.2018.10.051.
Zheng, C., Y. Cai, L. Luan, G. Kouretzis, and X. Ding. 2021. “Horizontal vibration of a rigid strip footing on viscoelastic half-space.” Int. J. Numer. Anal. Methods Geomech. 45 (3): 325–335. https://doi.org/10.1002/nag.3156.
Zheng, C., L. Luan, G. Kouretzis, and X. Ding. 2020. “Vertical vibration of a rigid strip footing on viscoelastic half-space.” Int. J. Numer. Anal. Methods Geomech. 44 (14): 1983–1995. https://doi.org/10.1002/nag.3108.
Zhou, D., Y. K. Cheung, S. H. Lo, and F. T. K. Au. 2005. “Three-dimensional vibration analysis of rectangular plates with mixed boundary conditions.” J. Appl. Mech. 72 (2): 227–236. https://doi.org/10.1115/1.1827250.
Zou, J., A. Wei, and L. Liang. 2020. “Analytical solution for steady seepage and groundwater inflow into an underwater tunnel.” Geomech. Eng. 20 (3): 267–273. https://doi.org/10.12989/gae.2020.20.3.267.
Information & Authors
Information
Published In
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Jul 6, 2021
Accepted: Jul 18, 2022
Published online: Oct 13, 2022
Published in print: Dec 1, 2022
Discussion open until: Mar 13, 2023
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.
Cited by
- Andreas-Nizar Granitzer, Johannes Leo, Franz Tschuchnigg, Particle Swarm Optimization of Interface Constitutive Model Parameters for Embedded Beam Formulations, International Journal of Geomechanics, 10.1061/IJGNAI.GMENG-9429, 24, 11, (2024).