A 3D sliced-soil–beam model for settlement prediction of tunnelling using the pipe roofing method in soft ground

doi:10.1007/s11709-023-0038-2

Frontiers of Structural and Civil Engineering

2023, Vol. 17

Issue (12): 1934-1948 https://doi.org/10.1007/s11709-023-0038-2

本期目录

A 3D sliced-soil–beam model for settlement prediction of tunnelling using the pipe roofing method in soft ground

Yu DIAO^1,²(

), Yiming XUE^1,², Weiqiang PAN^1,^2,³, Gang ZHENG^1,², Ying ZHANG⁴, Dawei ZHANG⁴, Haizuo ZHOU^1,², Tianqi ZHANG^1,²

¹. Key Laboratory of Coastal Civil Engineering Structure and Safety of Ministry of Education, Tianjin University, Tianjin 300072, China
². Department of Civil Engineering, Tianjin University, Tianjin 300072, China
³. Shanghai Tunnel Engineering Construction Co., Ltd., Shanghai 200032, China
⁴. Tianjin Municipal Engineering Design & Research Institute, Tianjin 300392, China

全文: PDF(10968 KB) HTML

Abstract：

The pipe roofing method is widely used in tunnel construction because it can realize a flexible section shape and a large section area of the tunnel, especially under good ground conditions. However, the pipe roofing method has rarely been applied in soft ground, where the prediction and control of the ground settlement play important roles. This study proposes a sliced-soil–beam (SSB) model to predict the settlement of ground due to tunnelling using the pipe roofing method in soft ground. The model comprises a sliced-soil module based on the virtual work principle and a beam module based on structural mechanics. As part of this work, the Peck formula was modified for a square-section tunnel and adopted to construct a deformation mechanism of soft ground. The pipe roofing system was simplified to a three-dimensional Winkler beam to consider the interaction between the soil and pipe roofing. The model was verified in a case study conducted in Shanghai, China, in which it provided the efficient and accurate prediction of settlement. Finally, the parameters affecting the ground settlement were analyzed. It was clarified that the stiffness of the excavated soil and the steel support are the key factors in reducing ground settlement.

Key words： pipe roofing method soft ground numerical simulation settlement prediction simplified calculation parametric analysis

收稿日期: 2023-02-09 出版日期: 2024-02-05

Corresponding Author(s): Yu DIAO

引用本文:

. [J]. Frontiers of Structural and Civil Engineering, 2023, 17(12): 1934-1948.
Yu DIAO, Yiming XUE, Weiqiang PAN, Gang ZHENG, Ying ZHANG, Dawei ZHANG, Haizuo ZHOU, Tianqi ZHANG. A 3D sliced-soil–beam model for settlement prediction of tunnelling using the pipe roofing method in soft ground. Front. Struct. Civ. Eng., 2023, 17(12): 1934-1948.

链接本文:

https://academic.hep.com.cn/fsce/CN/10.1007/s11709-023-0038-2
https://academic.hep.com.cn/fsce/CN/Y2023/V17/I12/1934

parameter	value	unit
effective cohesion ( $c ′$ )	16.8	kPa
effective internal friction angle ( $φ ′$ )	15.8	(° )
dilation angle ( $ψ$ )	0	(° )
reference secant shear modulus ( $E 50 r e f$ )	5.63	MPa
reference oedometer modulus ( $E o e d r e f$ )	4.88	MPa
reference unloading−reloading modulus ( $E u r r e f$ )	33.56	MPa
reference pressure ( $p r e f$ )	100	kPa
unloading and reloading Poisson ratio ( $ν u r$ )	0.2	–
coefficient of earth pressure at rest ( $K 0$ )	0.68	–
failure ratio ( $R f$ )	0.95	–
reference shear modulus at very small strains ( $G 0 r e f$ )	110.61	MPa
shear strain at corresponding to $0.7 G 0 r e f$ ( $γ 0.7$ )	3.2 × 10⁻⁴	–
power for the stress-level dependency of stiffness (m)	0.65	–

Tab.1

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

item	parameter	value	unit
tunnel	height (H)	7.6	m
	width (L)	7.5	m
	overlying soil layer (C)	5.4	m
steel pipe	outer diameter ( $d 1$ )	1600/1000	mm
	inner diameter ( $d 2$ )	1560/960	mm
	density ( $ρ s$ )	7850	kg/m³
	elastic modulus (E)	206	GPa
	poisson’s ratio ( $ν$ )	0.3	–

Tab.2

soil	$ρ (k N / m 3)$	$c ˙ (k P a)$	$φ ′$ (° )	$E s 1 − 2 (M P a)$	$ν s$
fill soil	17.3	24	16.5	4.92	0.30
silty clay-1	18.6	22	23.1	5.15	0.32
silty clay-2	17.3	10	17.3	3.34	0.33
mucky clay	18.4	12	13.5	2.43	0.37

Tab.3

Fig.9

Fig.10

Fig.11

item	parameter	value
trial tunnel section shrinkage	$V l o s s t r i a l$ (%)	0.05
soil stress and strain	$c u$ (kPa)	varies with depth (see Eq. (14))
	$γ s, f$	0.15
	$β$	1
latticed improvement stiffness	$k s 1$ (MPa/m)	90
layered improvement stiffness	$k s 2$ (MPa/m)	50
inner support stiffness	$k t$ (MPa/m)	500

Tab.4

Fig.12

Fig.13

Fig.14

Fig.15

variable	value
$k s 1$ (MPa/m)	35, 70, 90, 105, 140
$k s 2$ (MPa/m)	$5 / 9 k s 1$

Tab.5

Fig.16

Fig.17

variable	value
$k t$ (MPa)	200, 350, 500, 650, 800

Tab.6

Fig.18

Fig.19

$A$	constant in displacement equations
$[A v]$	general stiffness matrix of the beam
$B$	constant in displacement equations
$c$	effective cohesion
$c u$	undrained shear strength of the soft ground
$C$	thickness of the overlying soil layer
$d t$	diameter of pipe i
$d 1$	outer diameter of a pipe
$d 2$	inner diameter of a pipe
$D$	diameter of the circular-section tunnel
$D t$	diameter of the equivalent tunnel
$E$	pipe elastic modulus
$E s 1 − 2$	soil compression modulus
$E 50 ref$	reference secant shear modulus
$E oed r e f$	reference oedometer modulus
$E u r r e f$	reference unloading–reloading modulus
$G 0 r e f$	reference shear modulus at very low strains
$H$	height of the square-section tunnel
$i z$	settlement trough width
$k s$	foundation reaction coefficient
$k s 1$	latticed improvement stiffness
$k s 2$	layered improvement stiffness
$k t$	inner steel support stiffness
$[k]$	foundation stiffness matrix that is a combination of $k t$ and $k s$
$K 0$	coefficient of earth pressure at rest
$k t$	parameter in the Peck formula
$L$	width of the square-section tunnel
$m$	power for the stress-level dependency of stiffness
$p r e f$	reference pressure
$P p s$	equivalent supporting pressure from the pipe roofing
$P s p$	earth pressure on the pipe roofing
${q i}$	force acting on node i
$R f$	failure ratio
$v m$	maximum ground settlement
$V l o s s s$	soil volume loss
$V l o s s p$	tunnel section shrinkage
$V l o s s t r i a l$	trial tunnel section shrinkage
${w i}$	displacement of each beam
$z$	depth below the ground face
$Z 0$	central depth of the tunnel
$Z m$	maximum depth of the mechanism
$α$	parameter controlling the shape of the mechanism
$β$	power exponent of the stress–strain power curve
$φ ′$	effective internal friction angle
$γ 0.7$	shear strain corresponding to 0.7G₀^ref
$γ s$	shear strain
$γ s, f$	shear strain at maximum shear strength
$v$	Poisson’s ratio of a pipe
$v u r$	Poisson’s ratio of unloading and reloading
$ν s$	Poisson’s ratio of the soil
$ρ$	unit weight of the soil
$ρ s$	density of a pipe
$τ$	shear strength
$ψ$	dilation angle

1	E Ağbay, T Topal. Evaluation of twin tunnel-induced surface ground deformation by empirical and numerical analyses (NATM part of Eurasia tunnel, Turkey). Computers and Geotechnics, 2020, 119: 103367 https://doi.org/10.1016/j.compgeo.2019.103367
2	Klotoé C Hounyevou, E Bourgeois. Three dimensional finite element analysis of the influence of the umbrella arch on the settlements induced by shallow tunneling. Computers and Geotechnics, 2019, 110: 114–121 https://doi.org/10.1016/j.compgeo.2019.02.017
3	W L TanR G Pathegama. Numerical analysis of pipe roof reinforcement in soft ground tunnelling. In: Proceedings of American Society of Civil Engineers (ASCE) Engineering Mechanics Conference. Reston: American Society of Civil Engineers, 2003, 1–10
4	B Lu, J Dong, W Zhao, X Du, C Cheng, Q Bai, Z Wang, M Zhao, J Han. Novel pipe-roof method for a super shallow buried and large-span metro underground station. Underground Space, 2022, 7(1): 134–150 https://doi.org/10.1016/j.undsp.2021.06.003
5	B Lu, W Zhao, W Wang, P Jia, X Du, W Cao, W Li. Design and optimization of secant pipe roofing structure applied in subway stations. Tunnelling and Underground Space Technology, 2023, 135: 105026 https://doi.org/10.1016/j.tust.2023.105026
6	R Hasanpour, H Chakeri, Y Ozcelik, H Denek. Evaluation of surface settlements in the Istanbul metro in terms of analytical, numerical and direct measurements. Bulletin of Engineering Geology and the Environment, 2012, 71(3): 499–510 https://doi.org/10.1007/s10064-012-0428-5
7	C C Chung, C P Lin, C H Chin, K H Chou. Development and implementation of horizontal-plane settlement indication system for freeway health monitoring during underpass construction. Structural Control and Health Monitoring, 2017, 24(11): e1995 https://doi.org/10.1002/stc.1995
8	X Xie, M Zhao, I Shahrour. Experimental study of the behavior of rectangular excavations supported by a pipe roof. Applied Sciences, 2019, 9(10): 2082 https://doi.org/10.3390/app9102082
9	C Yang, Y Chen, Z Guo, W Zhu, R Wang. Surface settlement control in the excavation of a shallow intersection between a double-arched tunnel and a connection tunnel. International Journal of Geomechanics, 2021, 21(4): 04021035 https://doi.org/10.1061/(ASCE)GM.1943-5622.0001983
10	X Q Zhou, J L Pan, Y Liu, C C Yu. Analysis of ground movement during large-scale pipe roof installation and artificial ground freezing of Gongbei tunnel. Advances in Civil Engineering, 2021, 2021: 1–15 https://doi.org/10.1155/2021/8891600
11	H Z Cheng, J Chen, G L Chen. Analysis of ground surface settlement induced by a large EPB shield tunnelling: A case study in Beijing, China. Environmental Earth Sciences, 2019, 78(20): 605 https://doi.org/10.1007/s12665-019-8620-6
12	Y S Fang, J S Lin, C S Su. An estimation of ground settlement due to shield tunneling by the Peck−Fujita method. Canadian Geotechnical Journal, 1994, 31(3): 431–443 https://doi.org/10.1139/t94-050
13	M Y Fattah, K T Shlash, N M Salim. Prediction of settlement trough induced by tunneling in cohesive ground. Acta Geotechnica, 2013, 8(2): 167–179 https://doi.org/10.1007/s11440-012-0169-4
14	L Ma, L Y Ding, H B Luo. Non-linear description of ground settlement over twin tunnels in soil. Tunnelling and Underground Space Technology, 2014, 42: 144–151 https://doi.org/10.1016/j.tust.2014.02.006
15	W Zhao, P J Jia, L Zhu, C Cheng, J Y Han, Y Chen, Z G Wang. Analysis of the additional stress and ground settlement induced by the construction of double-O-tube shield tunnels in sandy soils. Applied Sciences, 2019, 9(7): 1399 https://doi.org/10.3390/app9071399
16	Y Fang, Z Chen, L Tao, J Cui, Q Yan. Model tests on longitudinal surface settlement caused by shield tunnelling in sandy soil. Sustainable Cities and Society, 2019, 47: 101504 https://doi.org/10.1016/j.scs.2019.101504
17	A Mirhabibi, A Soroush. Effects of surface buildings on twin tunnelling-induced ground settlements. Tunnelling and Underground Space Technology, 2012, 29: 40–51 https://doi.org/10.1016/j.tust.2011.12.009
18	I Ocak. A new approach for estimating the transverse surface settlement curve for twin tunnels in shallow and soft soils. Environmental Earth Sciences, 2014, 72(7): 2357–2367 https://doi.org/10.1007/s12665-014-3145-5
19	Q Zhang, K Wu, S Cui, Y Yu, Z Zhang, J Zhao. Surface settlement induced by subway tunnel construction based on modified peck formula. Geotechnical and Geological Engineering, 2019, 37(4): 2823–2835 https://doi.org/10.1007/s10706-018-00798-6
20	C S Wu, Z D Zhu. Analytical method for evaluating the ground surface settlement caused by tail void grouting pressure in shield tunnel construction. Advances in Civil Engineering, 2018, 2018: 1–10 https://doi.org/10.1155/2018/3729143
21	K D Fang, Z Y Yang, Y S Jiang, Z Y Sun, Z Y Wang. Surface subsidence characteristics of fully overlapping tunnels constructed using tunnel boring machine in a clay stratum. Computers and Geotechnics, 2020, 125: 103679 https://doi.org/10.1016/j.compgeo.2020.103679
22	X G Li, X S Chen. Using grouting of shield tunneling to reduce settlements of overlying tunnels: Case study in Shenzhen Metro construction. Journal of Construction Engineering and Management, 2012, 138(4): 574–584 https://doi.org/10.1061/(ASCE)CO.1943-7862.0000455
23	J Y Oh, M Ziegler. Investigation on influence of tail void grouting on the surface settlements during shield tunneling using a stress-pore pressure coupled analysis. KSCE Journal of Civil Engineering, 2014, 18(3): 803–811 https://doi.org/10.1007/s12205-014-1383-8
24	J B An, S J Kang, G C Cho. Numerical evaluation of surface settlement induced by ground loss from the face and annular gap of EPB shield tunneling. Geomechanics and Engineering, 2022, 29(3): 291–300 https://doi.org/10.12989/gae.2022.29.3.291
25	Y J Hou, M Z Zhou, D L Zhang, Q Fang, Z Y Sun, Y H Tian. Analysis of four shield-driven tunnels with complex spatial relations in a clay stratum. Tunnelling and Underground Space Technology, 2022, 124: 104478 https://doi.org/10.1016/j.tust.2022.104478
26	R B Peck. Deep excavations and tunnelling in soft ground. In: Proceedings of the 7th International Society for Soil Mechanics and Foundation Engineering. Mexico: EurekaMeg, 1969, 225–325
27	FLAC3D. Version 7.0. Minnesota: Itasca (Itasca Consulting Group, Inc.). 2019
28	Z G Zhang, M S Huang. Geotechnical influence on existing subway tunnels induced by multiline tunneling in Shanghai soft soil. Computers and Geotechnics, 2014, 56: 121–132 https://doi.org/10.1016/j.compgeo.2013.11.008
29	Y Y Sun, S H Zhou, Z Luo. Basal-heave analysis of pit-in-pit braced excavations in soft clays. Computers and Geotechnics, 2017, 81: 294–306 https://doi.org/10.1016/j.compgeo.2016.09.003
30	K H Chen, F L Peng. An improved method to calculate the vertical earth pressure for deep shield tunnel in Shanghai soil layers. Tunnelling and Underground Space Technology, 2018, 75: 43–66 https://doi.org/10.1016/j.tust.2018.01.027
31	W D Wang, C W W Ng, Y Hong, Y Hu, Q Li. Forensic study on the collapse of a high-rise building in Shanghai: 3D centrifuge and numerical modelling. Geotechnique, 2019, 69(10): 847–862 https://doi.org/10.1680/jgeot.16.P.315
32	L Lan, Q Zhang, W Zhu, G Ye, Y Shi, H Zhu. Geotechnical characterization of deep Shanghai clays. Engineering Geology, 2022, 307: 106794 https://doi.org/10.1016/j.enggeo.2022.106794
33	G Ye, B Ye. Investigation of the overconsolidation and structural behavior of Shanghai clays by element testing and constitutive modeling. Underground Space, 2016, 1(1): 62–77 https://doi.org/10.1016/j.undsp.2016.08.001
34	C Wu, G Ye, L Zhang, D Bishop, J Wang. Depositional environment and geotechnical properties of Shanghai clay: A comparison with Ariake and Bangkok clays. Bulletin of Engineering Geology and the Environment, 2015, 74(3): 717–732 https://doi.org/10.1007/s10064-014-0670-0
35	H ZhouQ HuX YuG ZhengX Liu H XuS Yang J LiuK Tian. Quantitative bearing capacity assessment of strip footings adjacent to two-layered slopes considering spatial soil variability. Acta Geotechnica, 2023, 1–15
36	H Mroueh, I Shahrour. A simplified 3D model for tunnel construction using tunnel boring machines. Tunnelling and Underground Space Technology, 2008, 23(1): 38–45 https://doi.org/10.1016/j.tust.2006.11.008
37	W J Rankin. Ground movements resulting from urban tunnelling: Predictions and effects. Geological Society, 1988, 5(1): 79–92 https://doi.org/10.1144/GSL.ENG.1988.005.01.06
38	R J Mair, R N Taylor, A Bracegirdle. Subsurface settlement profiles above tunnels in clays. Geotechnique, 1993, 43(2): 315–320 https://doi.org/10.1680/geot.1993.43.2.315
39	R J Mair. Centrifugal modelling of tunnel construction in soft clay. Dissertation for the Doctoral Degree. Cambridge: University of Cambridge, 1979
40	A S Osman, M D Bolton, R J Mair. Predicting 2D ground movements around tunnels in undrained clay. Geotechnique, 2006, 56(9): 597–604 https://doi.org/10.1680/geot.2006.56.9.597
41	A S Osman, R J Mair, M D Bolton. On the kinematics of 2D tunnel collapse in undrained clay. Geotechnique, 2006, 56(9): 585–595 https://doi.org/10.1680/geot.2006.56.9.585
42	P Cheng, Y Shen, X Zhao, X Li, H Zhu. Numerical analysis and parameter optimization of pipe curtain excavation method in soft soil subway station. Modern Tunnelling Technology, 2021, 58(S1): 240–250 https://doi.org/10.13807/j.cnki.mtt.2021.S1.031
43	Z F Wang, S L Shen, G Modoni, A Zhou. Excess pore water pressure caused by the installation of jet grouting columns in clay. Computers and Geotechnics, 2020, 125: 103667 https://doi.org/10.1016/j.compgeo.2020.103667
44	S L Shen, P G Atangana Njock, A Zhou, H M Lyu. Dynamic prediction of jet grouted column diameter in soft soil using Bi-LSTM deep learning. Acta Geotechnica, 2021, 16(1): 303–315 https://doi.org/10.1007/s11440-020-01005-8
45	P G Atangana Njock, S L Shen, A Zhou, G Modoni. Artificial neural network optimized by differential evolution for predicting diameters of jet grouted columns. Journal of Rock Mechanics and Geotechnical Engineering, 2021, 13(6): 1500–1512 https://doi.org/10.1016/j.jrmge.2021.05.009
46	S L Shen, Z F Wang, W C Cheng. Estimation of lateral displacement induced by jet grouting in clayey soils. Geotechnique, 2017, 67(7): 621–630 https://doi.org/10.1680/jgeot.16.P.159
47	S L Shen, Z F Wang, J Yang, C E Ho. Generalized approach for prediction of jet grout column diameter. Journal of Geotechnical and Geoenvironmental Engineering, 2013, 139(12): 2060–2069 https://doi.org/10.1061/(ASCE)GT.1943-5606.0000932
48	Z F Wang, S L Shen, G Modoni. Enhancing discharge of spoil to mitigate disturbance induced by horizontal jet grouting in clayey soil: Theoretical model and application. Computers and Geotechnics, 2019, 111: 222–228 https://doi.org/10.1016/j.compgeo.2019.03.012
49	M J Gunn. The prediction of surface settlement profiles due to tunnelling. In: Proceedings of the Wroth Memorial Symposium. Oxford: Thomas Telford Publishing, 1992, 304–316
50	C J Sketchley. Behaviour of Kaolin in Plane-strain. Dissertation for the Doctoral Degree. Cambridge: University of Cambridge, 1973

Viewed

Full text

Abstract

Cited

Shared

Discussed