doi: 10.3934/dcdss.2020101

Earth pressure field modeling for tunnel face stability evaluation of EPB shield machines based on optimization solution

a. 

School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, China

b. 

School of Management, Guangzhou University, Guangzhou 510006, China

c. 

School of Computer Science and Electronic Engineering, University of Essex, Colchester CO4 3SQ, United Kingdom

* Corresponding author: Yi An (Email: anyi@dlut.edu.cn)

Received  June 2018 Revised  September 2018 Published  September 2019

Earth pressure balanced (EPB) shield machines are large and complex mechanical systems and have been widely applied to tunnel engineering. Tunnel face stability evaluation is very important for EPB shield machines to avoid ground settlement and guarantee safe construction during the tunneling process. In this paper, we propose a novel earth pressure field modeling approach to evaluate the tunnel face stability of large and complex EPB shield machines. Based on the earth pressures measured by the pressure sensors on the clapboard of the chamber, we construct a triangular mesh model for the earth pressure field in the chamber and estimate the normal vector at each measuring point by using optimization solution and projection Delaunay triangulation, which can reflect the change situation of the earth pressures in real time. Furthermore, we analyze the characteristics of the active and passive earth pressure fields in the limit equilibrium states and give a new evaluation criterion of the tunnel face stability based on Rankine's theory of earth pressure. The method validation and analysis demonstrate that the proposed method is effective for modeling the earth pressure field in the chamber and evaluating the tunnel face stability of EPB shield machines.

Citation: Yi An, Zhuohan Li, Changzhi Wu, Huosheng Hu, Cheng Shao, Bo Li. Earth pressure field modeling for tunnel face stability evaluation of EPB shield machines based on optimization solution. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020101
References:
[1]

M. Ahmed and M. Iskander, Evaluation of tunnel face stability by transparent soil models, Tunnelling and Underground Space Technology, 27 (2012), 101-110.  doi: 10.1016/j.tust.2011.08.001.  Google Scholar

[2]

G. Anagnostou and K. Kovári, The face stability of slurry-shield-driven tunnels, Tunnelling and Underground Space Technology, 9 (1994), 165-174.  doi: 10.1016/0886-7798(94)90028-0.  Google Scholar

[3]

G. Anagnostou and K. Kovári, Face stability conditions with earth-pressure-balanced shields, Tunnelling and Underground Space Technology, 11 (1996), 165-173.  doi: 10.1016/0886-7798(96)00017-X.  Google Scholar

[4]

J. H. Atkinson and D. M. Potts, Stability of a shallow circular tunnel in cohesionless soil, Géotechnique, 27 (1977), 203-215.  doi: 10.1680/geot.1977.27.2.203.  Google Scholar

[5]

C. E. AugardeA. V. Lyamin and S. W. Sloan, Stability of an undrained plane strain heading revisited, Computers and Geotechnics, 30 (2003), 419-430.  doi: 10.1016/S0266-352X(03)00009-0.  Google Scholar

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A. BezuijenA. M. TalmonJ. F. W. Joustra and B. Grote, Pressure gradients at the EPBM face, Tunnels and Tunnelling International, 37 (2005), 14-17.   Google Scholar

[8]

R. I. Borja, A finite element model for strain localization analysis of strongly discontinuous fields based on standard Galerkin approximation, Computer Methods in Applied Mechanics and Engineering, 190 (2000), 1529-1549.  doi: 10.1016/S0045-7825(00)00176-6.  Google Scholar

[9]

W. Broere, Tunnel Face Stability and New CPT Applications, Ph.D thesis, Delft University of Technology in Delft, 2001. Google Scholar

[10]

P. Chambon and J.-F. Corté, Shallow tunnels in cohesionless soil: Stability of tunnel face, Journal of Geotechnical Engineering, 120 (1994), 1148-1165.  doi: 10.1061/(ASCE)0733-9410(1994)120:7(1148).  Google Scholar

[11]

R. P. ChenL. J. TangD. S. Ling and Y. M. Chen, Face stability analysis of shallow shield tunnels in dry sandy ground using the discrete element method, Computers and Geotechnics, 38 (2011), 187-195.  doi: 10.1016/j.compgeo.2010.11.003.  Google Scholar

[12]

E. H. DavisM. J. GunnR. J. Mair and H. N. Seneviratne, The stability of shallow tunnels and underground openings in cohesive material, Géotechnique, 30 (1980), 397-416.  doi: 10.1680/geot.1980.30.4.397.  Google Scholar

[13]

M. HuangS. LiJ. Yu and J. Q. W. Tan, Continuous field based upper bound analysis for three-dimensional tunnel face stability in undrained clay, Computers and Geotechnics, 94 (2018), 207-213.  doi: 10.1016/j.compgeo.2017.09.014.  Google Scholar

[14]

E. IbrahimA.-H. SoubraG. MollonW. RaphaelD. Dias and A. Reda, Three-dimensional face stability analysis of pressurized tunnels driven in a multilayered purely frictional medium, Tunnelling and Underground Space Technology, 49 (2015), 18-34.  doi: 10.1016/j.tust.2015.04.001.  Google Scholar

[15]

S. Jancsecz and W. Steiner, Face support for a large Mix-Shield in heterogeneous ground conditions, Tunnelling'94, (1994), 531-550.  doi: 10.1007/978-1-4615-2646-9_32.  Google Scholar

[16]

A. M. Karim, Three-dimensional Discrete Element Modeling of Tunneling in Sand, Ph.D thesis, University of Alberta in Edmonton, 2007. Google Scholar

[17]

S. H. Kim and F. Tonon, Face stability and required support pressure for TBM driven tunnels with ideal face membrane-Drained case, Tunnelling and Underground Space Technology, 25 (2010), 526-542.   Google Scholar

[18]

A. Kirsch, Experimental investigation of the face stability of shallow tunnels in sand, Acta Geotechnica, 5 (2010), 43-62.  doi: 10.1007/s11440-010-0110-7.  Google Scholar

[19]

E. Leca and L. Dormieux, Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material, Géotechnique, 40 (1990), 581-606.  doi: 10.1680/geot.1990.40.4.581.  Google Scholar

[20]

Y. LiF. EmeriaultR. Kastner and Z. X. Zhang, Stability analysis of large slurry shield-driven tunnel in soft clay, Tunnelling and Underground Space Technology, 24 (2009), 472-481.  doi: 10.1016/j.tust.2008.10.007.  Google Scholar

[21]

X. LüY. ZhouM. Huang and S. Zeng, Experimental study of the face stability of shield tunnel in sands under seepage condition, Tunnelling and Underground Space Technology, 74 (2018), 195-205.   Google Scholar

[22]

K. MichaelL. DimitrisV. Ioannis and F. Petros, Development of a 3D finite element model for shield EPB tunnelling, Tunnelling and Underground Space Technology, 65 (2017), 22-34.   Google Scholar

[23]

Q. Pan and D. Dias, Three dimensional face stability of a tunnel in weak rock masses subjected to seepage forces, Tunnelling and Underground Space Technology, 71 (2018), 555-566.  doi: 10.1016/j.tust.2017.11.003.  Google Scholar

[24]

W. J. M. Rankine, On the Stability of Loose Earth, Philosophical Transactions of The Royal Society of London, 147 (1857), 9-27.   Google Scholar

[25]

H. Schuller and H. F. Schweiger, Application of a Multilaminate Model to simulation of shear band formation in NATM-tunnelling, Computers and Geotechnics, 29 (2002), 501-524.  doi: 10.1016/S0266-352X(02)00013-7.  Google Scholar

[26]

C. Shao and D. S. Lan, Tunnel face stability analysis based on pressure field surface's normal vector for earth pressure balanced shield, International Journal of Modelling Identification and Control, 17 (2012), 143-150.  doi: 10.1504/IJMIC.2012.048921.  Google Scholar

[27]

C. Shao and D. S. Lan, Optimal control of an earth pressure balance shield with tunnel face stability, Automation in Construction, 46 (2014), 22-29.  doi: 10.1016/j.autcon.2014.07.005.  Google Scholar

show all references

References:
[1]

M. Ahmed and M. Iskander, Evaluation of tunnel face stability by transparent soil models, Tunnelling and Underground Space Technology, 27 (2012), 101-110.  doi: 10.1016/j.tust.2011.08.001.  Google Scholar

[2]

G. Anagnostou and K. Kovári, The face stability of slurry-shield-driven tunnels, Tunnelling and Underground Space Technology, 9 (1994), 165-174.  doi: 10.1016/0886-7798(94)90028-0.  Google Scholar

[3]

G. Anagnostou and K. Kovári, Face stability conditions with earth-pressure-balanced shields, Tunnelling and Underground Space Technology, 11 (1996), 165-173.  doi: 10.1016/0886-7798(96)00017-X.  Google Scholar

[4]

J. H. Atkinson and D. M. Potts, Stability of a shallow circular tunnel in cohesionless soil, Géotechnique, 27 (1977), 203-215.  doi: 10.1680/geot.1977.27.2.203.  Google Scholar

[5]

C. E. AugardeA. V. Lyamin and S. W. Sloan, Stability of an undrained plane strain heading revisited, Computers and Geotechnics, 30 (2003), 419-430.  doi: 10.1016/S0266-352X(03)00009-0.  Google Scholar

[6]

M. D. Berg, O. Cheong, M. V. Kreveld and M. Overmars, Computational Geometry: Algorithms and Applications, Berlin and Heidelberg: Springer, 2008. doi: 10.1007/978-3-540-77974-2.  Google Scholar

[7]

A. BezuijenA. M. TalmonJ. F. W. Joustra and B. Grote, Pressure gradients at the EPBM face, Tunnels and Tunnelling International, 37 (2005), 14-17.   Google Scholar

[8]

R. I. Borja, A finite element model for strain localization analysis of strongly discontinuous fields based on standard Galerkin approximation, Computer Methods in Applied Mechanics and Engineering, 190 (2000), 1529-1549.  doi: 10.1016/S0045-7825(00)00176-6.  Google Scholar

[9]

W. Broere, Tunnel Face Stability and New CPT Applications, Ph.D thesis, Delft University of Technology in Delft, 2001. Google Scholar

[10]

P. Chambon and J.-F. Corté, Shallow tunnels in cohesionless soil: Stability of tunnel face, Journal of Geotechnical Engineering, 120 (1994), 1148-1165.  doi: 10.1061/(ASCE)0733-9410(1994)120:7(1148).  Google Scholar

[11]

R. P. ChenL. J. TangD. S. Ling and Y. M. Chen, Face stability analysis of shallow shield tunnels in dry sandy ground using the discrete element method, Computers and Geotechnics, 38 (2011), 187-195.  doi: 10.1016/j.compgeo.2010.11.003.  Google Scholar

[12]

E. H. DavisM. J. GunnR. J. Mair and H. N. Seneviratne, The stability of shallow tunnels and underground openings in cohesive material, Géotechnique, 30 (1980), 397-416.  doi: 10.1680/geot.1980.30.4.397.  Google Scholar

[13]

M. HuangS. LiJ. Yu and J. Q. W. Tan, Continuous field based upper bound analysis for three-dimensional tunnel face stability in undrained clay, Computers and Geotechnics, 94 (2018), 207-213.  doi: 10.1016/j.compgeo.2017.09.014.  Google Scholar

[14]

E. IbrahimA.-H. SoubraG. MollonW. RaphaelD. Dias and A. Reda, Three-dimensional face stability analysis of pressurized tunnels driven in a multilayered purely frictional medium, Tunnelling and Underground Space Technology, 49 (2015), 18-34.  doi: 10.1016/j.tust.2015.04.001.  Google Scholar

[15]

S. Jancsecz and W. Steiner, Face support for a large Mix-Shield in heterogeneous ground conditions, Tunnelling'94, (1994), 531-550.  doi: 10.1007/978-1-4615-2646-9_32.  Google Scholar

[16]

A. M. Karim, Three-dimensional Discrete Element Modeling of Tunneling in Sand, Ph.D thesis, University of Alberta in Edmonton, 2007. Google Scholar

[17]

S. H. Kim and F. Tonon, Face stability and required support pressure for TBM driven tunnels with ideal face membrane-Drained case, Tunnelling and Underground Space Technology, 25 (2010), 526-542.   Google Scholar

[18]

A. Kirsch, Experimental investigation of the face stability of shallow tunnels in sand, Acta Geotechnica, 5 (2010), 43-62.  doi: 10.1007/s11440-010-0110-7.  Google Scholar

[19]

E. Leca and L. Dormieux, Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material, Géotechnique, 40 (1990), 581-606.  doi: 10.1680/geot.1990.40.4.581.  Google Scholar

[20]

Y. LiF. EmeriaultR. Kastner and Z. X. Zhang, Stability analysis of large slurry shield-driven tunnel in soft clay, Tunnelling and Underground Space Technology, 24 (2009), 472-481.  doi: 10.1016/j.tust.2008.10.007.  Google Scholar

[21]

X. LüY. ZhouM. Huang and S. Zeng, Experimental study of the face stability of shield tunnel in sands under seepage condition, Tunnelling and Underground Space Technology, 74 (2018), 195-205.   Google Scholar

[22]

K. MichaelL. DimitrisV. Ioannis and F. Petros, Development of a 3D finite element model for shield EPB tunnelling, Tunnelling and Underground Space Technology, 65 (2017), 22-34.   Google Scholar

[23]

Q. Pan and D. Dias, Three dimensional face stability of a tunnel in weak rock masses subjected to seepage forces, Tunnelling and Underground Space Technology, 71 (2018), 555-566.  doi: 10.1016/j.tust.2017.11.003.  Google Scholar

[24]

W. J. M. Rankine, On the Stability of Loose Earth, Philosophical Transactions of The Royal Society of London, 147 (1857), 9-27.   Google Scholar

[25]

H. Schuller and H. F. Schweiger, Application of a Multilaminate Model to simulation of shear band formation in NATM-tunnelling, Computers and Geotechnics, 29 (2002), 501-524.  doi: 10.1016/S0266-352X(02)00013-7.  Google Scholar

[26]

C. Shao and D. S. Lan, Tunnel face stability analysis based on pressure field surface's normal vector for earth pressure balanced shield, International Journal of Modelling Identification and Control, 17 (2012), 143-150.  doi: 10.1504/IJMIC.2012.048921.  Google Scholar

[27]

C. Shao and D. S. Lan, Optimal control of an earth pressure balance shield with tunnel face stability, Automation in Construction, 46 (2014), 22-29.  doi: 10.1016/j.autcon.2014.07.005.  Google Scholar

Figure 1.  Different kinds of shield machines. (a) Earth pressure balance shield machine. (b) Slurry shield machine. (c) Hard rock shield machine. (d) Mixed shield machine. (e) Dual mode shield machine. (f) Rectangle shield machine
Figure 2.  Structure of the EPB shield machine
Figure 3.  Working principle of the EPB shield machine
Figure 4.  Pressure sensors on the clapboard
Figure 5.  Virtual pressure measuring points
Figure 6.  Measuring points used for modeling
Figure 7.  Coordinate system on the clapboard
Figure 8.  Discrete data points
Figure 9.  Normal vector and tangent plane at $ \mathit{\boldsymbol{p}} $
Figure 10.  Projection of the data points onto the tangent plane
Figure 11.  Delaunay triangulation
Figure 12.  Voronoi diagram
Figure 13.  3D triangulation for the data points
Figure 14.  Normal vectors at the data points
Figure 15.  Active and passive earth pressure fields
Figure 16.  Earth pressure fields at six different times (a)-(f). The cyan and blue violet planes denote the active and passive earth pressure fields, the orange and green arrows denote the normal vectors of the active and passive earth pressure fields, the blue triangular meshes denote the earth pressure fields, and the red arrows denote the normal vectors at the measuring points. The units of the axes $ x $ and $ y $ are meter and the unit of the axis $ z $ is bar
Figure 17.  Earth pressure angle with the varying earth pressure at E5
Figure 18.  Earth pressure fields in two cases. (a) The earth pressure at E5 decreases to 50%$ p_{ne} $. (b) The earth pressure at E5 increases to 150%$ p_{ne} $.The units of the axes $ x $ and $ y $ are meter and the unit of the axis $ z $ is bar
Table 1.  Earth pressure angles at the measuring points (unit: $ ^\circ $)
Time No. E1 E2 E3 E4 E5 E6 E7 E8
1 82.1263 79.4182 80.7525 81.1181 79.9521 82.2279 81.4088 79.1411
2 80.8168 79.9801 79.9147 80.0957 79.1641 80.9488 80.3536 78.8670
3 82.6131 81.7718 80.6488 79.9071 79.0446 80.1266 80.7302 81.9452
4 78.8249 77.6968 77.2621 78.0584 79.1200 79.5718 77.7454 76.5422
5 78.5580 79.0929 78.1572 78.2970 79.4725 79.8513 78.4722 77.3459
6 79.7876 79.6536 78.4048 77.4864 78.4145 78.0623 78.3591 79.8496
Time No. E9 A2 A4 D1 D2 D3 D4 D5
1 82.3057 80.8872 81.9276 81.2639 80.2467 80.4916 82.5693 81.9542
2 81.7089 80.2221 80.5088 80.1633 79.8461 79.8634 81.1366 80.1815
3 84.9260 82.4601 79.8087 80.5708 81.6030 81.6349 80.6627 79.5281
4 80.5892 78.1447 78.9757 77.5015 77.4125 77.5080 78.5850 78.0865
5 79.9673 78.5516 79.1212 78.2072 78.6575 78.2354 78.9935 77.9871
6 81.2070 79.9441 77.7178 78.2115 79.841 79.2915 77.8964 77.0773
Time No. E1 E2 E3 E4 E5 E6 E7 E8
1 82.1263 79.4182 80.7525 81.1181 79.9521 82.2279 81.4088 79.1411
2 80.8168 79.9801 79.9147 80.0957 79.1641 80.9488 80.3536 78.8670
3 82.6131 81.7718 80.6488 79.9071 79.0446 80.1266 80.7302 81.9452
4 78.8249 77.6968 77.2621 78.0584 79.1200 79.5718 77.7454 76.5422
5 78.5580 79.0929 78.1572 78.2970 79.4725 79.8513 78.4722 77.3459
6 79.7876 79.6536 78.4048 77.4864 78.4145 78.0623 78.3591 79.8496
Time No. E9 A2 A4 D1 D2 D3 D4 D5
1 82.3057 80.8872 81.9276 81.2639 80.2467 80.4916 82.5693 81.9542
2 81.7089 80.2221 80.5088 80.1633 79.8461 79.8634 81.1366 80.1815
3 84.9260 82.4601 79.8087 80.5708 81.6030 81.6349 80.6627 79.5281
4 80.5892 78.1447 78.9757 77.5015 77.4125 77.5080 78.5850 78.0865
5 79.9673 78.5516 79.1212 78.2072 78.6575 78.2354 78.9935 77.9871
6 81.2070 79.9441 77.7178 78.2115 79.841 79.2915 77.8964 77.0773
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