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

Front. Struct. Civ. Eng.

2023, Vol. 17

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

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

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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.

Keywords pipe roofing method soft ground numerical simulation settlement prediction simplified calculation parametric analysis

Corresponding Author(s): Yu DIAO

Just Accepted Date: 14 November 2023 Online First Date: 24 January 2024 Issue Date: 05 February 2024

Cite this article:

Yu DIAO,Yiming XUE,Weiqiang PAN, et al. A 3D sliced-soil–beam model for settlement prediction of tunnelling using the pipe roofing method in soft ground[J]. Front. Struct. Civ. Eng., 2023, 17(12): 1934-1948.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-023-0038-2
https://academic.hep.com.cn/fsce/EN/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 PH model parameters for typical soft ground in Shanghai

Fig.1 Numerical modeling and fitting results.

Fig.2 Observed displacement vectors of different tunnel shapes in numerical simulations.

Fig.3 Deformation mechanism for square-section tunnels.

Fig.4 CT joint of pipes.

Fig.5 Simplified model of the excavation procedure.

Fig.6 SSB model.

Fig.7 Calculation flow chart.

Fig.8 Geological profile and sectional view of the project.

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 Geometric and mechanical parameters of the tunnel and steel pipes

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 Measured mechanical parameters of the soils

Fig.9 MJS improved zones inside the pipe roofing.

Fig.10 Superposition of the surface settlement distribution.

Fig.11 Fitted line of measured

c u

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 Mechanical parameters of the SSB model

Fig.12 Convergence of the calculation.

Fig.13 3D ground settlement during tunnel excavation at: (a) 25 m; (b) 50 m; (c) 75 m.

Fig.14 Measured and predicted longitudinal settlements of: (a) the pipe roofing; (b) the ground surface in the Shanghai project.

Fig.15 Measured and predicted ground settlements of the soil ground in the Shanghai project.

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

Tab.5 Foundation reaction coefficient of the improved soil

Fig.16 Longitudinal settlement of: (a) the pipe roofing; (b) the ground surface for different stiffness of the improved soil.

Fig.17 Maximum settlement versus the stiffness of the improved soil.

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

Tab.6 Foundation reaction coefficients of the inner supports

Fig.18 Longitudinal settlement of: (a) the pipe roofing; (b) the ground surface for different stiffness of the inner supports.

Fig.19 Maximum settlement versus stiffness of the inner supports.

$A$	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

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