Analytical Solution for Steady-State Seepage in Pits During Water Stop Curtain Leakage

doi:10.12068/j.issn.1005-3026.2024.12.013

Abstract

Abstract:

To study the two‑dimensional steady‑state seepage in a pit with isotropic soil during water stop curtain leakage， half the pit’s cross‑section is analyzed due to symmetry. The soil around the water curtain is divided into five regions， and the head distribution is solved using superposition and separation of variables， leading to an explicit analytical solution for the seepage field， considering continuity between regions. Results for head， water pressure， and seepage flow volume at leakage are compared with that of finite element software and references， confirming the analytical solution’s accuracy and efficiency. Parameter analysis shows that vertical leakage crack location and width have minimal impact on head and pressure but significantly affect seepage flow volume.

Key words: two?dimensional steady?state seepage, explicit analytical solution, water pressure, seepage volume, water stop curtain leakage

CLC Number:

TU 43

Jun YU, Wei-jie ZHANG, Dong-kai LI. Analytical Solution for Steady-State Seepage in Pits During Water Stop Curtain Leakage[J]. Journal of Northeastern University(Natural Science), 2024, 45(12): 1778-1786.

Figures/Tables 12

Fig.1 Two‑dimensional seepage modeling of foundation pit during leakage of water curtains

Table 1 Parameters of the pit model

b/m	c/m	h₁/m	h₂/m	a/m	h₃ /m	d₂/mm	k/（m·s^-1）
10	3	16.8	11.2	5	13.45	60	1×10^-9

Fig.2 Finite element model meshing diagram

Fig.3 Comparison of this paper and finite element software head calculation results

Fig.4 Comparison and verification of water pressure calculation results

Fig.5 Comparison of the seepage volume calculation results from literature[17] with the solution in this paper

Fig.6 Effect of d2 on head around the pit

Fig.7 Effect of h3 on head around the pit

Fig.8 Comparison of this paper’s solution with the results of the non‑leakage head calculation of the water stop curtains

Fig.9 Effect of d2 on the surrounding water pressure after the pit reaches steady‑state seepage

Fig.10 Effect of h3 on the surrounding water pressure after the pit reaches steady‑state seepage

Fig.11 Influence of d2 and h3 on the amount of seepage flow at the water stop curtain leakage

References 20

1	Wu Y X， Shen S L， Yuan D J.Characteristics of dewatering induced drawdown curve under blocking effect of retaining wall in aquifer［J］.Journal of Hydraulic Engineering，2016，539：554-566.
2	Wu H N， Xu Y S， Shen S L，et al.Long‑term settlement behavior of ground around shield tunnel due to leakage of water in soft deposit of Shanghai［J］.Frontiers of Architecture & Civil Engineering in China，2011，5（2）：194-198.
3	Shen S L， Wu H N， Cui Y J，et al.Long‑term settlement behaviour of metro tunnels in the soft deposits of Shanghai［J］.Tunnelling and Underground Space Technology，2014，40：309-323.
4	谢志飞.承压含水层中基坑帷幕与降水方案的比较和优选［D］.上海：上海交通大学，2019.
	Xie Zhi‑fei.Optimization and comparation of dewatering method and waterproof curtain in deep‑burried foundation pit［D］.Shanghai：Shanghai Jiao Tong University，2019.
5	Shen S L， Wang Z F， Cheng W C.Estimation of lateral displacement induced by jet grouting in clayey soils［J］.Géotechnique，2017，67（7）：621-630.
6	Shen S L， Han J， Du Y J.Deep mixing induced property changes in surrounding sensitive marine clays［J］.Journal of Geotechnical & Geoenvironmental Engineering，2008，134（6）：845-854.
7	Tan Y， Li X， Kang Z J，et al.Zoned excavation of an oversized pit close to an existing metro line in stiff clay：case study［J］.Journal of Performance of Constructed Facilities，2015，29（6）：04014158.
8	Liu X X， Shen S L， Xu Y S，et al.Analytical approach for time‑dependent groundwater inflow into shield tunnel face in confined aquifer［J］.International Journal for Numerical and Analytical Methods in Geomechanics，2018，42（4）：655-673.
9	Conway B D.Land subsidence and earth fissures in south‑central and southern Arizona，USA［J］.Hydrogeology Journal，2016，24（3）：649-655.
10	Wu Y X， Lyu H M， Han J，et al.Dewatering‑induced building settlement around a deep excavation in soft deposit in Tianjin，China［J］.Journal of Geotechnical and Geoenvironmental Engineering，2019，145（5）：05019003.
11	Pujades E， Jurado A， Carrera J，et al.Hydrogeological assessment of non‑linear underground enclosures［J］.Engineering Geology，2016，207：91-102.
12	Vilarrasa V， Carrera J， Jurado A，et al.A methodology for characterizing the hydraulic effectiveness of an annular low‑permeability barrier［J］.Engineering Geology，2011，120：68-80.
13	Pujades E， Carrera J， Vázquez‑Suñé E，et al.Hydraulic characterization of diaphragm walls for cut and cover tunnelling［J］.Engineering Geology，2012，125：1-10.
14	Wu Y X， Lyu H M， Shen S L，et al.A three‑dimensional fluid‑solid coupled numerical modeling of the barrier leakage below the excavation surface due to dewatering［J］.Hydrogeology Journal，2020，28（4）：1449-1463.
15	Wang D， Feng C L， Mao Z C.Simulation and analysis of the failure for the water stop curtain of building pit in round gravel level［J］.Applied Mechanics ＆ Materials，2015，723：326-329.
16	Wu Y X， Shen S L， Yin Z Y，et al.Characteristics of groundwater seepage with cut‑off wall in gravel aquifer.II：numerical analysis［J］.Canadian Geotechnical Journal，2015，52：1539-1549.
17	Wu Y X， Shen S L， Lyu H M，et al.Analyses of leakage effect of waterproof curtain during excavation dewatering［J］.Journal of Hydrology，2020，583：124582.
18	Thushara A M， Nagaratnam S.Simple solutions for square and rectangular cofferdam seepage problems［J］.Canadian Geotechnical Journal，2018，56：730-745.
19	Yu J， Yang X X， Deng P B，et al.Analytical solution for a steady seepage field of a foundation pit in layered soil［J］.International Journal of Geomechanics，2022，22（10）：04022160.
20	顾樵.数学物理方法［M］.北京：科学出版社，2012.
	Gu Qiao.Mathematical methods for physics［M］.Beijing：Science Press，2012.

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