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

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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.

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Data availability statements The data sets generated during and/or analyzed in the current study are available from the corresponding author on reasonable request.

Abbreviations

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 s1−2 :

soil compression modulus

E ref50 :

reference secant shear modulus

E refoed :

reference oedometer modulus

E refur :

reference unloading–reloading modulus

G ref0 :

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 1s :

latticed improvement stiffness

k 2s :

layered improvement stiffness

k t :

inner steel support stiffness

[k]:

foundation stiffness matrix that is a combination of kt and ks

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 ref :

reference pressure

P ps :

equivalent supporting pressure from the pipe roofing

P sp :

earth pressure on the pipe roofing

{q i}:

force acting on node i

R f :

failure ratio

v m :

maximum ground settlement

V sloss :

soil volume loss

V ploss :

tunnel section shrinkage

V trialloss :

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 0.7G0ref

γ s :

shear strain

γ s,f :

shear strain at maximum shear strength

v :

Poisson’s ratio of a pipe

v ur :

Poisson’s ratio of unloading and reloading

v 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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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 52178342), the Tianjin Natural Science Foundation (No. 21JCZDJC00590), and the Shanghai Excellent Academic/Technical Leader Program (No. 20XD1432500).

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Authors and Affiliations

  1. Key Laboratory of Coastal Civil Engineering Structure and Safety of Ministry of Education, Tianjin University, Tianjin, 300072, China

    Yu Diao, Yiming Xue, Weiqiang Pan, Gang Zheng, Haizuo Zhou & Tianqi Zhang

  2. Department of Civil Engineering, Tianjin University, Tianjin, 300072, China

    Yu Diao, Yiming Xue, Weiqiang Pan, Gang Zheng, Haizuo Zhou & Tianqi Zhang

  3. Shanghai Tunnel Engineering Construction Co., Ltd., Shanghai, 200032, China

    Weiqiang Pan

  4. Tianjin Municipal Engineering Design & Research Institute, Tianjin, 300392, China

    Ying Zhang & Dawei Zhang

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  1. Yu Diao
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Correspondence to Yu Diao.

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Diao, Y., Xue, Y., Pan, W. et al. A 3D sliced-soil–beam model for settlement prediction of tunnelling using the pipe roofing method in soft ground. Front. Struct. Civ. Eng. 17, 1934–1948 (2023). https://doi.org/10.1007/s11709-023-0038-2

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