A 3D slicedsoil–beam model for settlement prediction of tunnelling using the pipe roofing method in soft ground
Yu DIAO, Yiming XUE, Weiqiang PAN, Gang ZHENG, Ying ZHANG, Dawei ZHANG, Haizuo ZHOU, Tianqi ZHANG
A 3D slicedsoil–beam model for settlement prediction of tunnelling using the pipe roofing method in soft ground
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 slicedsoil–beam (SSB) model to predict the settlement of ground due to tunnelling using the pipe roofing method in soft ground. The model comprises a slicedsoil 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 squaresection tunnel and adopted to construct a deformation mechanism of soft ground. The pipe roofing system was simplified to a threedimensional 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.
pipe roofing method / soft ground / numerical simulation / settlement prediction / simplified calculation / parametric analysis
[1] 
Ağbay E, Topal T. Evaluation of twin tunnelinduced surface ground deformation by empirical and numerical analyses (NATM part of Eurasia tunnel, Turkey). Computers and Geotechnics, 2020, 119: 103367
CrossRef
Google scholar

[2] 
Hounyevou Klotoé C, Bourgeois E. 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
CrossRef
Google scholar

[3] 
TanW LPathegama R G. 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] 
Lu B, Dong J, Zhao W, Du X, Cheng C, Bai Q, Wang Z, Zhao M, Han J. Novel piperoof method for a super shallow buried and largespan metro underground station. Underground Space, 2022, 7(1): 134–150
CrossRef
Google scholar

[5] 
Lu B, Zhao W, Wang W, Jia P, Du X, Cao W, Li W. Design and optimization of secant pipe roofing structure applied in subway stations. Tunnelling and Underground Space Technology, 2023, 135: 105026
CrossRef
Google scholar

[6] 
Hasanpour R, Chakeri H, Ozcelik Y, Denek H. 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
CrossRef
Google scholar

[7] 
Chung C C, Lin C P, Chin C H, Chou K H. Development and implementation of horizontalplane settlement indication system for freeway health monitoring during underpass construction. Structural Control and Health Monitoring, 2017, 24(11): e1995
CrossRef
Google scholar

[8] 
Xie X, Zhao M, Shahrour I. Experimental study of the behavior of rectangular excavations supported by a pipe roof. Applied Sciences, 2019, 9(10): 2082
CrossRef
Google scholar

[9] 
Yang C, Chen Y, Guo Z, Zhu W, Wang R. Surface settlement control in the excavation of a shallow intersection between a doublearched tunnel and a connection tunnel. International Journal of Geomechanics, 2021, 21(4): 04021035
CrossRef
Google scholar

[10] 
Zhou X Q, Pan J L, Liu Y, Yu C C. Analysis of ground movement during largescale pipe roof installation and artificial ground freezing of Gongbei tunnel. Advances in Civil Engineering, 2021, 2021: 1–15
CrossRef
Google scholar

[11] 
Cheng H Z, Chen J, Chen G L. 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
CrossRef
Google scholar

[12] 
Fang Y S, Lin J S, Su C S. An estimation of ground settlement due to shield tunneling by the Peck−Fujita method. Canadian Geotechnical Journal, 1994, 31(3): 431–443
CrossRef
Google scholar

[13] 
Fattah M Y, Shlash K T, Salim N M. Prediction of settlement trough induced by tunneling in cohesive ground. Acta Geotechnica, 2013, 8(2): 167–179
CrossRef
Google scholar

[14] 
Ma L, Ding L Y, Luo H B. Nonlinear description of ground settlement over twin tunnels in soil. Tunnelling and Underground Space Technology, 2014, 42: 144–151
CrossRef
Google scholar

[15] 
Zhao W, Jia P J, Zhu L, Cheng C, Han J Y, Chen Y, Wang Z G. Analysis of the additional stress and ground settlement induced by the construction of doubleOtube shield tunnels in sandy soils. Applied Sciences, 2019, 9(7): 1399
CrossRef
Google scholar

[16] 
Fang Y, Chen Z, Tao L, Cui J, Yan Q. Model tests on longitudinal surface settlement caused by shield tunnelling in sandy soil. Sustainable Cities and Society, 2019, 47: 101504
CrossRef
Google scholar

[17] 
Mirhabibi A, Soroush A. Effects of surface buildings on twin tunnellinginduced ground settlements. Tunnelling and Underground Space Technology, 2012, 29: 40–51
CrossRef
Google scholar

[18] 
Ocak I. 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
CrossRef
Google scholar

[19] 
Zhang Q, Wu K, Cui S, Yu Y, Zhang Z, Zhao J. Surface settlement induced by subway tunnel construction based on modified peck formula. Geotechnical and Geological Engineering, 2019, 37(4): 2823–2835
CrossRef
Google scholar

[20] 
Wu C S, Zhu Z D. 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
CrossRef
Google scholar

[21] 
Fang K D, Yang Z Y, Jiang Y S, Sun Z Y, Wang Z Y. Surface subsidence characteristics of fully overlapping tunnels constructed using tunnel boring machine in a clay stratum. Computers and Geotechnics, 2020, 125: 103679
CrossRef
Google scholar

[22] 
Li X G, Chen X S. 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
CrossRef
Google scholar

[23] 
Oh J Y, Ziegler M. Investigation on influence of tail void grouting on the surface settlements during shield tunneling using a stresspore pressure coupled analysis. KSCE Journal of Civil Engineering, 2014, 18(3): 803–811
CrossRef
Google scholar

[24] 
An J B, Kang S J, Cho G C. 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
CrossRef
Google scholar

[25] 
Hou Y J, Zhou M Z, Zhang D L, Fang Q, Sun Z Y, Tian Y H. Analysis of four shielddriven tunnels with complex spatial relations in a clay stratum. Tunnelling and Underground Space Technology, 2022, 124: 104478
CrossRef
Google scholar

[26] 
PeckR B. 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

[28] 
Zhang Z G, Huang M S. Geotechnical influence on existing subway tunnels induced by multiline tunneling in Shanghai soft soil. Computers and Geotechnics, 2014, 56: 121–132
CrossRef
Google scholar

[29] 
Sun Y Y, Zhou S H, Luo Z. Basalheave analysis of pitinpit braced excavations in soft clays. Computers and Geotechnics, 2017, 81: 294–306
CrossRef
Google scholar

[30] 
Chen K H, Peng F L. 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
CrossRef
Google scholar

[31] 
Wang W D, Ng C W W, Hong Y, Hu Y, Li Q. Forensic study on the collapse of a highrise building in Shanghai: 3D centrifuge and numerical modelling. Geotechnique, 2019, 69(10): 847–862
CrossRef
Google scholar

[32] 
Lan L, Zhang Q, Zhu W, Ye G, Shi Y, Zhu H. Geotechnical characterization of deep Shanghai clays. Engineering Geology, 2022, 307: 106794
CrossRef
Google scholar

[33] 
Ye G, Ye B. Investigation of the overconsolidation and structural behavior of Shanghai clays by element testing and constitutive modeling. Underground Space, 2016, 1(1): 62–77
CrossRef
Google scholar

[34] 
Wu C, Ye G, Zhang L, Bishop D, Wang J. 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
CrossRef
Google scholar

[35] 
ZhouHHu QYuXZhengGLiuX XuHYangS LiuJTianK. Quantitative bearing capacity assessment of strip footings adjacent to twolayered slopes considering spatial soil variability. Acta Geotechnica, 2023, 1–15

[36] 
Mroueh H, Shahrour I. A simplified 3D model for tunnel construction using tunnel boring machines. Tunnelling and Underground Space Technology, 2008, 23(1): 38–45
CrossRef
Google scholar

[37] 
Rankin W J. Ground movements resulting from urban tunnelling: Predictions and effects. Geological Society, 1988, 5(1): 79–92
CrossRef
Google scholar

[38] 
Mair R J, Taylor R N, Bracegirdle A. Subsurface settlement profiles above tunnels in clays. Geotechnique, 1993, 43(2): 315–320
CrossRef
Google scholar

[39] 
MairR J. Centrifugal modelling of tunnel construction in soft clay. Dissertation for the Doctoral Degree. Cambridge: University of Cambridge, 1979

[40] 
Osman A S, Bolton M D, Mair R J. Predicting 2D ground movements around tunnels in undrained clay. Geotechnique, 2006, 56(9): 597–604
CrossRef
Google scholar

[41] 
Osman A S, Mair R J, Bolton M D. On the kinematics of 2D tunnel collapse in undrained clay. Geotechnique, 2006, 56(9): 585–595
CrossRef
Google scholar

[42] 
Cheng P, Shen Y, Zhao X, Li X, Zhu H. Numerical analysis and parameter optimization of pipe curtain excavation method in soft soil subway station. Modern Tunnelling Technology, 2021, 58(S1): 240–250
CrossRef
Google scholar

[43] 
Wang Z F, Shen S L, Modoni G, Zhou A. Excess pore water pressure caused by the installation of jet grouting columns in clay. Computers and Geotechnics, 2020, 125: 103667
CrossRef
Google scholar

[44] 
Shen S L, Atangana Njock P G, Zhou A, Lyu H M. Dynamic prediction of jet grouted column diameter in soft soil using BiLSTM deep learning. Acta Geotechnica, 2021, 16(1): 303–315
CrossRef
Google scholar

[45] 
Atangana Njock P G, Shen S L, Zhou A, Modoni G. 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
CrossRef
Google scholar

[46] 
Shen S L, Wang Z F, Cheng W C. Estimation of lateral displacement induced by jet grouting in clayey soils. Geotechnique, 2017, 67(7): 621–630
CrossRef
Google scholar

[47] 
Shen S L, Wang Z F, Yang J, Ho C E. Generalized approach for prediction of jet grout column diameter. Journal of Geotechnical and Geoenvironmental Engineering, 2013, 139(12): 2060–2069
CrossRef
Google scholar

[48] 
Wang Z F, Shen S L, Modoni G. 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
CrossRef
Google scholar

[49] 
GunnM J. The prediction of surface settlement profiles due to tunnelling. In: Proceedings of the Wroth Memorial Symposium. Oxford: Thomas Telford Publishing, 1992, 304–316

[50] 
SketchleyC J. Behaviour of Kaolin in Planestrain. Dissertation for the Doctoral Degree. Cambridge: University of Cambridge, 1973

$A$  constant in displacement equations 

$[{A}_{\mathrm{v}}]$  general stiffness matrix of the beam 
$B$  constant in displacement equations 
$c$  effective cohesion 
${c}_{\mathrm{u}}$  undrained shear strength of the soft ground 
$C$  thickness of the overlying soil layer 
${d}_{\mathrm{t}}$  diameter of pipe i 
${d}_{1}$  outer diameter of a pipe 
${d}_{2}$  inner diameter of a pipe 
$D$  diameter of the circularsection tunnel 
${D}_{\mathrm{t}}$  diameter of the equivalent tunnel 
$E$  pipe elastic modulus 
${E}_{\mathrm{s}12}$  soil compression modulus 
${E}_{50}^{\text{ref}}$  reference secant shear modulus 
${E}_{\text{oed}}^{\mathrm{r}\mathrm{e}\mathrm{f}}$  reference oedometer modulus 
${E}_{\mathrm{u}\mathrm{r}}^{\mathrm{r}\mathrm{e}\mathrm{f}}$  reference unloading–reloading modulus 
${G}_{0}^{\mathrm{r}\mathrm{e}\mathrm{f}}$  reference shear modulus at very low strains 
$H$  height of the squaresection tunnel 
${i}_{\mathit{\text{z}}}$  settlement trough width 
${k}_{\mathrm{s}}$  foundation reaction coefficient 
${k}_{\mathrm{s}}^{1}$  latticed improvement stiffness 
${k}_{\mathrm{s}}^{2}$  layered improvement stiffness 
${k}_{\mathrm{t}}$  inner steel support stiffness 
$[k]$  foundation stiffness matrix that is a combination of ${k}_{\mathrm{t}}$ and ${k}_{\mathrm{s}}$ 
${K}_{0}$  coefficient of earth pressure at rest 
${k}_{\mathrm{t}}$  parameter in the Peck formula 
$L$  width of the squaresection tunnel 
$m$  power for the stresslevel dependency of stiffness 
${p}^{\mathrm{r}\mathrm{e}\mathrm{f}}$  reference pressure 
${P}_{\mathrm{p}\mathrm{s}}$  equivalent supporting pressure from the pipe roofing 
${P}_{\mathrm{s}\mathrm{p}}$  earth pressure on the pipe roofing 
$\left\{{q}_{i}\right\}$  force acting on node i 
${R}_{\mathrm{f}}$  failure ratio 
${v}_{\mathrm{m}}$  maximum ground settlement 
${V}_{\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s}}^{\mathrm{s}}$  soil volume loss 
${V}_{\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s}}^{\mathrm{p}}$  tunnel section shrinkage 
${V}_{\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s}}^{\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{l}}$  trial tunnel section shrinkage 
$\left\{{w}_{i}\right\}$  displacement of each beam 
$\mathit{\text{z}}$  depth below the ground face 
${Z}_{0}$  central depth of the tunnel 
${Z}_{\mathrm{m}}$  maximum depth of the mechanism 
$\alpha $  parameter controlling the shape of the mechanism 
$\phantom{\rule{thinmathspace}{0ex}}\beta $  power exponent of the stress–strain power curve 
${\phi}^{\prime}$  effective internal friction angle 
${\gamma}_{0.7}$  shear strain corresponding to 0.7G_{0}^{ref} 
${\gamma}_{\mathrm{s}}$  shear strain 
${\gamma}_{\mathrm{s},\mathrm{f}}^{}$  shear strain at maximum shear strength 
$v$  Poisson’s ratio of a pipe 
${v}_{\mathrm{u}\mathrm{r}}$  Poisson’s ratio of unloading and reloading 
${\nu}_{\mathrm{s}}$  Poisson’s ratio of the soil 
$\phantom{\rule{thinmathspace}{0ex}}\rho $  unit weight of the soil 
$\phantom{\rule{thinmathspace}{0ex}}{\rho}_{\mathrm{s}}$  density of a pipe 
$\tau $  shear strength 
$\psi $  dilation angle 
/
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