A Semi-Analytical Solution of Two-Dimensional Unsteady Groundwater Flow Outside a Long-Strip Excavation Pit with a Cut-Off Wall
Abstract
:1. Introduction
2. Mathematical Model
2.1. Model Description and Basic Assumptions
- (1)
- The recharge of the overlying unconfined aquifer is not considered;
- (2)
- The head of groundwater is constant at a distance R away from the strip excavation pit;
- (3)
- The cut-off wall is a no-flow boundary;
- (4)
- The entire excavation pit is regarded as a large well.
2.2. Governing Equation and Solving Conditions
3. Solving Procedures
4. Solution Verification
5. Characteristics of Groundwater Seepage
6. Parametric Study
6.1. The Effect of Hydraulic Conductivity Anisotropy
6.2. The Effect of the Penetrating Depth of Cut-Off Wall
6.3. The Effect of Lateral Boundary Distance
7. Case Study and Comparison with the Field Data
7.1. Project Overview
7.2. Conceptualized Groundwater Calculation Model
7.3. Results and Comparison
8. Conclusions
- (1)
- The existence of the cut-off wall has a barrier effect on the distribution of groundwater head, as the cut-off wall increases the seepage path. The groundwater flow in the confined aquifer changes from a simple one-dimensional flow to a two-dimensional flow around the cut-off wall, which indicates the change in the flow velocity and direction.
- (2)
- From the time-domain results, the distribution of drawdown in the horizontal direction changes from a cone-shaped distribution to a straight line over time in a limit confined aquifer, which shows the process of transition from unsteady flow to steady flow. The barrier effect reduces with the increase in pumping time.
- (3)
- The dimensionless drawdown decreases with the increase in anisotropic degree (). The effect of anisotropy is obvious near the cut-off wall, and weakened with the horizontal distance. The effectiveness of excavation dewatering is significantly influenced by the lateral boundary distance, with closer boundaries requiring higher pumping rates to achieve desired drawdown depths, while increased distances result in improved dewatering effects.
- (4)
- The impacts on drawdown in a limited confined aquifer due to the barrier effect are correlated with the penetrating depth of the cut-off wall. When the cut-off wall is not buried deep enough to cut off the confined aquifer completely, it is thought that there is an optimum penetrating depth ratio to achieve a balance between the barrier effect and economy, when determining the parameters.
- (5)
- A case study was conducted on a practical municipal engineering scenario involving the dewatering of a long rectangular excavation. The practical scenario was conceptualized and analyzed using the presented analytical solution, as well as finite element numerical methods. Comparison with field data validates the engineering applicability of the approach proposed in this paper.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Wang, Y.; Li, B.; Chen, C.; Jia, H. Influence of groundwater level fluctuation on lateral deformation of cantilever enclosure structure of pit-in-pit. Mar. Georesources Geotechnol. 2019, 38, 108–113. [Google Scholar] [CrossRef]
- Wu, Y.-X.; Shen, S.-L.; Xu, Y.-S.; Yin, Z.-Y. Characteristics of groundwater seepage with cut-off wall in gravel aquifer. I: Field observations. Can. Geotech. J. 2015, 52, 1526–1538. [Google Scholar] [CrossRef]
- Xu, Y.-S.; Shen, S.-L.; Ren, D.-J.; Wu, H.-N. Analysis of Factors in Land Subsidence in Shanghai: A View Based on a Strategic Environmental Assessment. Sustainability 2016, 8, 573. [Google Scholar] [CrossRef]
- Zhang, L.; Ying, H.; Xie, K.; Huang, D. Effect of Groundwater Fluctuations on Pore Pressures and Earth Pressures on Coastal Excavation Retaining Walls. Mar. Georesources Geotechnol. 2015, 34, 770–781. [Google Scholar] [CrossRef]
- Shen, S.-L.; Wu, Y.-X.; Xu, Y.-S.; Hino, T.; Wu, H.-N. Evaluation of hydraulic parameters from pumping tests in multi-aquifers with vertical leakage in Tianjin. Comput. Geotech. 2015, 68, 196–207. [Google Scholar] [CrossRef]
- Shaqour, F.M.; Hasan, S.E. Groundwater control for construction purposes: A case study from Kuwait. Environ. Geol. 2008, 53, 1603–1612. [Google Scholar] [CrossRef]
- Ervin, M.C.; Morgan, J.R. Groundwater control around a large basement. Can. Geotech. J. 2001, 38, 732–740. [Google Scholar] [CrossRef]
- Pujades, E.; Vàzquez-Suñé, E.; Carrera, J.; Jurado, A. Dewatering of a deep excavation undertaken in a layered soil. Eng. Geol. 2014, 178, 15–27. [Google Scholar] [CrossRef]
- Attard, G.; Winiarski, T.; Rossier, Y.; Eisenlohr, L. Review: Impact of underground structures on the flow of urban groundwater. Hydrogeol. J. 2015, 24, 5–19. [Google Scholar] [CrossRef]
- Wu, Y.X.; Shen, S.L.; Yin, Z.Y.; Xu, Y.S. Characteristics of groundwater seepage with cut-off wall in gravel aquifer. II: Numerical analysis. Can. Geotech. J. 2015, 52, 1539–1549. [Google Scholar] [CrossRef]
- Wang, J.; Feng, B.; Yu, H.; Guo, T.; Yang, G.; Tang, J. Numerical study of dewatering in a large deep foundation pit. Environ. Earth Sci. 2013, 69, 863–872. [Google Scholar] [CrossRef]
- Anderson, E.I.; Mesa, E. The effects of vertical barrier walls on the hydraulic control of contaminated groundwater. Adv. Water Resour. 2006, 29, 89–98. [Google Scholar] [CrossRef]
- Deveughèle, M.; Zokimila, P.; Cojean, R. Impact d’une galerie étanche peu profonde sur l’écoulement d’une nappe. Bull. Eng. Geol. Environ. 2009, 69, 143–152. [Google Scholar] [CrossRef]
- Wu, Y.-X.; Shen, J.S.; Cheng, W.-C.; Hino, T. Semi-analytical solution to pumping test data with barrier, wellbore storage, and partial penetration effects. Eng. Geol. 2017, 226, 44–51. [Google Scholar] [CrossRef]
- Pujades, E.; Carrera, J.; Vázquez-Suñé, E.; Jurado, A.; Vilarrasa, V.; Mascuñano-Salvador, E. Hydraulic characterization of diaphragm walls for cut and cover tunnelling. Eng. Geol. 2012, 125, 1–10. [Google Scholar] [CrossRef]
- Vilarrasa, V.; Carrera, J.; Jurado, A.; Pujades, E.; Vázquez-Suné, E. A methodology for characterizing the hydraulic effectiveness of an annular low-permeability barrier. Eng. Geol. 2011, 120, 68–80. [Google Scholar] [CrossRef]
- Pujades, E.; Vázquez-Suñé, E.; Carrera, J.; Vilarrasa, V.; De Simone, S.; Jurado, A.; Ledesma, A.; Ramos, G.; Lloret, A. Deep enclosures versus pumping to reduce settlements during shaft excavations. Eng. Geol. 2014, 169, 100–111. [Google Scholar] [CrossRef]
- Font-Capo, J.; Pujades, E.; Vàzquez-Suñé, E.; Carrera, J.; Velasco, V.; Montfort, D. Assessment of the barrier effect caused by underground constructions on porous aquifers with low hydraulic gradient: A case study of the metro construction in Barcelona, Spain. Eng. Geol. 2015, 196, 238–250. [Google Scholar] [CrossRef]
- Xu, Y.-S.; Shen, S.-L.; Du, Y.-J.; Chai, J.-C.; Horpibulsuk, S. Modelling the cutoff behavior of underground structure in multi-aquifer-aquitard groundwater system. Nat. Hazards 2013, 66, 731–748. [Google Scholar] [CrossRef]
- Xu, Y.-S.; Shen, S.-L.; Ma, L.; Sun, W.-J.; Yin, Z.-Y. Evaluation of the blocking effect of retaining walls on groundwater seepage in aquifers with different insertion depths. Eng. Geol. 2014, 183, 254–264. [Google Scholar] [CrossRef]
- Xu, Y.-S.; Yan, X.-X.; Shen, S.-L.; Zhou, A.-N. Experimental investigation on the blocking of groundwater seepage from a waterproof curtain during pumped dewatering in an excavation. Hydrogeol. J. 2019, 27, 2659–2672. [Google Scholar] [CrossRef]
- Jie, Y.; Jie, G.; Mao, Z.; Li, G. Seepage analysis based on boundary-fitted coordinate transformation method. Comput. Geotech. 2004, 31, 279–283. [Google Scholar] [CrossRef]
- Wu, Y.-X.; Shen, S.-L.; Yuan, D.-J. Characteristics of dewatering induced drawdown curve under blocking effect of retaining wall in aquifer. J. Hydrol. 2016, 539, 554–566. [Google Scholar] [CrossRef]
- Erduran, K.S.; Kutija, V.; Macalister, C.R. Finite volume solution to integrated shallow surface-saturated groundwater flow. Int. J. Numer. Methods Fluids 2005, 49, 763–783. [Google Scholar] [CrossRef]
- Luo, Z.-J.; Zhang, Y.-Y.; Wu, Y.-X. Finite element numerical simulation of three-dimensional seepage control for deep foundation pit dewatering. J. Hydrodyn. 2008, 20, 596–602. [Google Scholar] [CrossRef]
- Theis, C.V. The relation between the lowering of the Piezometric surface and the rate and duration of discharge of a well using ground-water storage. Trans. Am. Geophys. Union 1935, 16, 519–524. [Google Scholar] [CrossRef]
- Cooper, H.H., Jr.; Jacob, C.E. A generalized graphical method for evaluating formation constants and summarizing well-field history. Eos Trans. Am. Geophys. Union 1946, 27, 526–534. [Google Scholar] [CrossRef]
- Chang, C.-C.; Chen, C.-S. A flowing partially penetrating well in a finite-thickness aquifer: A mixed-type initial boundary value problem. J. Hydrol. 2003, 271, 101–118. [Google Scholar] [CrossRef]
- Chen, Z.; Ni, P.; Chen, Y.; Mei, G. Plane-strain consolidation theory with distributed drainage boundary. Acta Geotech. 2018, 15, 489–508. [Google Scholar] [CrossRef]
- Banerjee, S.; Muleshkov, A. Analytical solution of steady seepage into double-walled cofferdams. J. Eng. Mech. 1992, 118, 525–539. [Google Scholar] [CrossRef]
- Bereslavskii, E. The flow of ground waters around a Zhukovskii sheet pile. J. Appl. Math. Mech. 2011, 75, 210–217. [Google Scholar] [CrossRef]
- Hou, Y.J. Calculation of Mine Water Inflow and Cite Influencing Radius of Hetaoyu Coal with “Virtual Large Diameter Well” Method. Adv. Mater. Res. 2012, 610–613, 2709–2712. [Google Scholar] [CrossRef]
- Li, T.; Song, H.; Huang, G.; Bi, Y.; Li, X. Assessment of groundwater changing trends through the generalized large well method with confined–unconfined flow model in open-pit mine area. Environ. Earth Sci. 2014, 72, 4599–4606. [Google Scholar] [CrossRef]
- Huang, D.Z.; Xie, K.H.; Ying, H.W. Semi-analytical solution for two-dimensional steady seepage around foundation pit in soil layer with anisotropic permeability. J. Zhejiang Univ. (Eng. Sci.) 2014, 48, 1802–1808. [Google Scholar]
- Stehfest, H. Algorithm 368: Numerical inversion of Laplace transforms [D5]. Commun. ACM 1970, 13, 47–49. [Google Scholar] [CrossRef]
- Pujades, E.; López, A.; Carrera, J.; Vázquez-Suñé, E.; Jurado, A. Barrier effect of underground structures on aquifers. Eng. Geol. 2012, 145–146, 41–49. [Google Scholar] [CrossRef]
- He, S.H.; Xia, T.D.; Li, L.X.; Yu, B.Q.; Liu, Z.Y. Influence of groundwater seepage on deformation of foundation pits with suspended impervious curtains. J. Zhejiang Univ. (Eng. Sci.) 2019, 53, 713–723. [Google Scholar] [CrossRef]
- Wan, X.; Ding, J.; Jiao, N.; Sun, S.; Liu, J.; Guo, Q. Observed Performance of Long-Zoned Excavation with Suspended Water-proof Curtain in Yangtze River Floodplain. J. Perform. Constr. Facil. 2022, 36, 04022018. [Google Scholar]
Input Parameters | Value | Dimensionless Parameters | Value |
---|---|---|---|
Strip excavation pit width (2a) | 100 m | Dimensionless thickness of confined aquifer (m) | 2.5 |
Confined aquifer thickness (M) | 20 m | ||
Discharge per unit width (Q) | 2 m2/day | ||
Boundary distance (R) | 500 m | Dimensionless boundary distance (RD) | 10 |
Depth of the cut-off wall in the confined aquifer (d) | 4 m | ||
Specific storage (μe) | 3 × 10−5 m−1 | Penetrating depth ratio of the cut-off wall (n1) | 0.2 |
Horizontal hydraulic conductivities (kh) | 2.5 m/day | ||
Vertical hydraulic conductivities (kv) | 1.5 m/day | Anisotropic (k) | 1.67 |
Soil Layer | Soil Type | Thickness (m) | Unit Weight (kN/m3) | Effective Friction Angle (°) | Effective Cohesion (kPa) | Permeability Coefficient (cm/s) |
---|---|---|---|---|---|---|
I | Silty Clay | 2.0 | 17.5 | 11.5 | 10.0 | 2.0 × 10−6 |
II | Sandy Silt | 2.0 | 19.0 | 30.0 | 1.25 | 2.0 × 10−3 |
III | Silty Clay | 0.5 | 18.0 | 11.0 | 10.0 | 1.0 × 10−6 |
IV | Sandy Silt | 3.70 | 18.5 | 31.5 | 1.0 | 2.0 × 10−3 |
V | Silty Clay | 2.3 | 17.3 | 10.0 | 5.0 | 2.0 × 10−6 |
VI | Fine Sand | 29.5 | 19.0 | 31.5 | 1.0 | 2 × 10−2 |
Calculation Parameters | Value |
---|---|
Length of the calculation model L | 200 m |
Thickness of the aquifer M | 30 m |
Depth of the waterproof curtain embedded lc | 20 m |
Half-width of the foundation pit B | 18 m |
Unit flow rate of dewatering wells Q | 25 m2/day |
Horizontal permeability coefficient Kx | 17.3 m/day |
Vertical permeability coefficient Kz | 17.3 m/day |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Chang, Y.; Lv, L.; Wang, X.; Xu, J. A Semi-Analytical Solution of Two-Dimensional Unsteady Groundwater Flow Outside a Long-Strip Excavation Pit with a Cut-Off Wall. Appl. Sci. 2024, 14, 7367. https://doi.org/10.3390/app14167367
Chang Y, Lv L, Wang X, Xu J. A Semi-Analytical Solution of Two-Dimensional Unsteady Groundwater Flow Outside a Long-Strip Excavation Pit with a Cut-Off Wall. Applied Sciences. 2024; 14(16):7367. https://doi.org/10.3390/app14167367
Chicago/Turabian StyleChang, Yinsheng, Le Lv, Xudong Wang, and Jin Xu. 2024. "A Semi-Analytical Solution of Two-Dimensional Unsteady Groundwater Flow Outside a Long-Strip Excavation Pit with a Cut-Off Wall" Applied Sciences 14, no. 16: 7367. https://doi.org/10.3390/app14167367