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

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