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

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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 hr/D > 0.5. For a tunnel with hr/D ≼ 0.5, the variation of hr/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.

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Abbreviations

a e :

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

F 1 :

Shield gravity

F 2 :

Reaction force of the tail brush on the inner shield surface

F 3 :

Thrust from jacks

F 4 :

Force acting on the cutter head

F 5 :

Force acting on the shield shell

F n :

Normal resistance forces of a single disc cutter

FM 1, FM 2 :

Moments induced by the penetration resistance and earth pressure, respectively

FM 21, FM 22 :

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

h r :

Height of the bedrock in the tunnel face

H :

Buried depth of the tunnel center

k :

Number of segments

k e :

Coefficient of the subgrade reaction

K e,ij :

Coefficient of earth pressure for an element

K e0, K e max, K e min :

Initial, passive, and active earth pressure coefficients, respectively

l :

Segment length

l s :

Gravity eccentric distance

L :

Shield length

L dev :

Deviation correction mileage

m, n :

Numbers of elements along the length and the ring direction of shield, respectively

M lv :

Moment with respect to the shield center induced by the eccentric gravity

M 4v :

Moment with respect to the shield center on the vertical plane caused by the force acting on the cutter head

M 5h :

Moment with respect to the shield center on the horizontal plane induced by pressure on the shield shell

M 5v :

Moment with respect to the shield center on the vertical plane induced by pressure on the shield shell

\(M_{\rm{h}}^\alpha ,M_{\rm{v}}^\beta \) :

Moments for posture rectification in the horizontal and vertical plane generated by the thrust, respectively

n r :

Number of disc cutters

p :

Penetration per revolution

P 0 :

Pressure of the broken zone

R :

Disc cutter radius

R c :

Radius of the shield shell

R rec :

Radius of deviation correction curve

s e :

Axis deviation in the horizontal (e = h) or the vertical (e = v) direction

∆s :

Vertical subsidence of the circle center induced by the shield gravity

∆s v, ∆s h :

Vertical and horizontal displacements of the circle center, respectively

S :

Spacing between disc cutters

t :

Tip width of a disc cutter

U e,ij :

Ground displacement of each element

∆y i :

Target deviation correction amount at the ring

z ij :

Position on the shell of each element

α :

Yawing angle

β :

Pitch angle

γ 1, γ 2 :

Unit weights of soil and rock, respectively

δ h, δ v :

Horizontal and vertical displacements of the circle center caused by posture rectification, respectivley

η :

Opening ratio of cutterhend

η dev :

The angle of the shield and positive z-axis

η i−1 :

Angle of the shield down from the z-axis at the deviation correction segment

λ 1, λ 2 :

Later pressure coefficients of soil and rock, respectively

σ c :

Uniaxial compressive strength

σ e0,ij :

Initial pressure of each element

σ h,ij, σ v,ij :

Horizontal and vertical pressures of each element, respectively

σ n :

Normal pressure on the shield shell

σ t :

Tensile strength

φ :

Internal friction angle of soil

Φ:

Contact angle between the rock and disc cutter

ψ :

A model parameter of CSM model

ω 1 :

Central angle of the first circular arc with a center of O1

ω 2 :

Central angle of the second circular arc with a center of O2

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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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Authors and Affiliations

  1. School of Civil Engineering, Harbin Institute of Technology, Harbin, 150090, China

    Liang Tang, Xiangxun Kong, Xianzhang Ling, Wenchong Tang & Yifan Zhang

  2. Heilongjiang Research Center for Rail Transit Engineering in Cold Regions, Harbin, 150090, China

    Liang Tang, Xiangxun Kong, Xianzhang Ling, Wenchong Tang & Yifan Zhang

  3. Chongqing Research Institute, Harbin Institute of Technology, Chongqing, 401135, China

    Liang Tang & Xianzhang Ling

  4. Department of Computer Science, University of California, Irvine, CA, 92612, USA

    Yize Zhao

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  1. Liang Tang
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Correspondence to Xiangxun Kong or Xianzhang Ling.

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Tang, L., Kong, X., Ling, X. et al. Deviation correction strategy for the earth pressure balance shield based on shield-soil interactions. Front. Mech. Eng. 17, 20 (2022). https://doi.org/10.1007/s11465-022-0676-4

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