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June  2020, 13(6): 1721-1741. 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, 2020, 13 (6) : 1721-1741. doi: 10.3934/dcdss.2020101
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##### References:
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
Structure of the EPB shield machine
Working principle of the EPB shield machine
Pressure sensors on the clapboard
Virtual pressure measuring points
Measuring points used for modeling
Coordinate system on the clapboard
Discrete data points
Normal vector and tangent plane at $\mathit{\boldsymbol{p}}$
Projection of the data points onto the tangent plane
Delaunay triangulation
Voronoi diagram
3D triangulation for the data points
Normal vectors at the data points
Active and passive earth pressure fields
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
Earth pressure angle with the varying earth pressure at E5
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
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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