Deviation correction strategy for the earth pressure balance shield based on shield–soil interactions

Abstract

The control system presently used in shield posture rectification is based on driver experience, which is marginally reliable. The study of the related theory is flawed. Therefore, a decision-making approach for the deviation correction trajectory and posture rectification load for an earth pressure balance (EPB) shield is proposed. A calculation model of posture rectification load of an EPB shield is developed by considering the interactions among the cutter head, shield shell, and ground. The additional position change during the shield attitude correction is highlighted. The posture rectification loads and shield behaviors results can be solved by the proposed method. The influences of the stratum distribution (i.e., bedrock height in the upper-soft and lower-hard strata) on shield behaviors and posture rectification loads are analyzed. Results indicated that the increase of pitch angle in the upper-soft and lower-hard strata causes a sharp rise in vertical displacement. The bedrock height increases the magnitudes of the required posture rectification moments when h_r/D > 0.5. For a tunnel with h_r/D ≤ 0.5, the variation of h_r/D has little effect on the posture rectification moments. Finally, the posture rectifying curves based on the theoretical model are compared with the target ones based on the double circular arc interpolation method. The required results can be obtained regardless of the soil–rock compound stratum distribution. The maximum rectification moment in the rock layer is almost 12.6 times that in the soil layer. Overall, this study provides a valuable reference for moment determination and the trajectory prediction of posture rectification in compound strata.

Graphical abstract

Keywords

additional position change / deviation correction trajectory / earth pressure balance shield / mechanical model / posture rectification

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Nomenclature

ae	Gradient of the ground reaction curve
c	Soil cohesive force
C	A dimensionless parameter of CSM model
d	Wedge amount of the segment
D	Shield diameter
F1	Shield gravity
F2	Reaction force of the tail brush on the inner shield surface
F3	Thrust from jacks
F4	Force acting on the cutter head
F5	Force acting on the shield shell
Fn	Normal resistance forces of a single disc cutter
FM1,FM2	Moments induced by the penetration resistance and earth pressure, respectively
FM21, FM22	Moments caused by the later pressure of soil on the cutter head and rock on the cutter head, respectively
G	Gravity of a shield machine
h	Buried depth of the rock–soil interface
hr	Height of the bedrock in the tunnel face
H	Buried depth of the tunnel center
k	Number of segments
ke	Coefficient of the subgrade reaction
Ke,ij	Coefficient of earth pressure for an element
Ke0, Ke,max,Ke,min	Initial, passive, and active earth pressure coefficients, respectively
l	Segment length
ls	Gravity eccentric distance
L	Shield length
Ldev	Deviation correction mileage
m, n	Numbers of elements along the length and the ring direction of shield, respectively
M1v	Moment with respect to the shield center induced by the eccentric gravity
M4v	Moment with respect to the shield center on the vertical plane caused by the force acting on the cutter head
M5h	Moment with respect to the shield center on the horizontal plane induced by pressure on the shield shell
M5v	Moment with respect to the shield center on the vertical plane induced by pressure on the shield shell
M_{\mathrm{h}}^{\alpha }, M_{\mathrm{v}}^{\beta }	Moments for posture rectification in the horizontal and vertical plane generated by the thrust, respectively
nr	Number of disc cutters
p	Penetration per revolution
P0	Pressure of the broken zone
R	Disc cutter radius
Rc	Radius of the shield shell
Rrec	Radius of deviation correction curve
se	Axis deviation in the horizontal (e = h) or the vertical (e = v) direction
Δs	Vertical subsidence of the circle center induced by the shield gravity
Δsv, Δsh	Vertical and horizontal displacements of the circle center, respectively
S	Spacing between disc cutters
t	Tip width of a disc cutter
Ue,ij	Ground displacement of each element
Δyi	Target deviation correction amount at the ring (i‒1)
zij	Position on the shell of each element
α	Yawing angle
β	Pitch angle
γ1, γ2	Unit weights of soil and rock, respectively
δh, δv	Horizontal and vertical displacements of the circle center caused by posture rectification, respectivley
η	Opening ratio of cutterhend
ηdev	The angle of the shield and positive z-axis
ηi‒1	Angle of the shield down from the z-axis at the deviation correction segment (i‒1)
λ1, λ2	Later pressure coefficients of soil and rock, respectively
σc	Uniaxial compressive strength
σe0,ij	Initial pressure of each element
σh,ij, σv,ij	Horizontal and vertical pressures of each element, respectively
σn	Normal pressure on the shield shell
σt	Tensile strength
φ	Internal friction angle of soil
Φ	Contact angle between the rock and disc cutter
ψ	A model parameter of CSM model
{\omega }_1	Central angle of the first circular arc with a center of O1
{\omega }_2	Central angle of the second circular arc with a center of O2

Acknowledgements

This work was supported by the National Key R&D Program of China (Grant No. 2018YFC1505304), the National Major Scientific Instruments Development Project of China (Grant No. 41627801), the State Key Program of National Natural Science Foundation of China (Grant No. 41731288), and the Open Research Fund Program of State Key Laboratory of Permafrost Engineering of China (Grant No. SKLFSE202015).

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