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Comparison and correlation between the laboratory, semi-theoretical and empirical methods in predicting the field excavation performance of tunnel boring machine (TBM)

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Abstract

Many methods have been proposed to predict the field excavation performance of tunnel boring machine (TBM). They can usually predict the general trends of the field rock cutting force and efficiency when cutter penetration depth increases. However, in many cases, the predicted values are not so close (sometimes even very different) to the field values. This study is to check, compare and then correlate the prediction results of three widely used methods in predicting the field TBM excavation performance. These three methods are the laboratory LCM (linear cutting machine) method, the semi-theoretical CSM (Colorado School of Mines) method and the empirical NTNU (Norwegian University of Science and Technology) method. First, the basic procedures of these three methods are reviewed, and their prediction results are obtained concerning the TBM excavation performance in Chongqing Yangtze River Tunnel Project. Then, the quantitative comparison and correlation between the field measured result with the laboratory, semi-theoretical and empirical prediction results are conducted. After that, combined with the previous studies, some empirical formulas are proposed to predict the field TBM excavation performance at the optimum rock cutting condition more reliably and accurately. These empirical formulas can take the laboratory, semi-theoretical and empirical prediction results into comprehensive consideration. Finally, the south lot of the Qinling Tunnel in Yinhanjiwei Water Diversion Project is set as the case study, and the machine parameters and TBM excavation performance in this project are predicted and compared to the field values to verify the applicability and accuracy of the new proposed empirical formulas. Results show that the use of these new proposed empirical formulas can offer more acceptable prediction results for TBM cutterhead design and operation optimization.

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Abbreviations

Ν :

Poisson’s ratio of the rock

Ρ :

Natural density of the rock (g/cm3)

σ c :

Uniaxial compressive strength of the rock (MPa)

σ t :

Brazilian tensile strength of the rock (MPa)

DRI :

Drilling rate index of the rock

E :

Static elasticity modulus of the rock (GPa)

por:

Porosity of the rock (%)

BI :

Rock boreability index (kN/mm)

D :

Diameter of the disc cutter (mm)

FN :

Disc cutter normal force (kN)

FR :

Disc cutter rolling force (kN)

p :

Penetration depth of the disc cutter (mm)

p opt :

Optimum cutter penetration depth (mm)

R :

Radius of the disc cutter (mm)

s :

Spacing of two adjacent disc cutters (mm)

(s/p)opt :

Optimum ratio of cutter spacing to penetration depth

SE :

Rock cutting specific energy (MJ/m3)

T :

Tip width of the disc cutter (mm)

BI LCM :

Rock boreability index obtained by the LCM method (kN/mm)

(BI opt)LCM :

Rock boreability index at the optimum rock cutting condition obtained by the LCM method (kN/mm)

FN LCM :

Disc cutter normal force obtained by the LCM method (kN)

(FN opt)LCM :

Disc cutter normal force at the optimum rock cutting condition obtained by the LCM method (kN)

FR LCM :

Disc cutter rolling force obtained by the LCM method (kN)

(FR opt)LCM :

Disc cutter rolling force at the optimum rock cutting condition obtained by the LCM method (kN)

l :

Sum of the cutting length of every cutting groove in the LCM tests (mm)

M LCM :

Mass of the rock cutting products in the LCM tests (g)

(p opt)LCM :

Optimum cutter penetration depth obtained by the LCM method (mm)

SE LCM :

Rock cutting specific energy obtained by the LCM method (MJ/m3)

(SE opt)LCM :

Optimum rock cutting specific energy obtained by the LCM method (MJ/m3)

θ :

Angle of the studied point referred to the vertical direction (rad)

φ :

Rock-cutter contact angle (rad)

ψ :

Contact pressure distribution constant in the CSM method, usually ranging from − 0.2 to 0.2

BI CSM :

Rock boreability index predicted by the CSM method (kN/mm)

(BI opt)CSM :

Rock boreability index at optimum rock cutting condition predicted by the CSM method (kN/mm)

C :

Constant in the CSM method, usually assumed as 2.12

CC CSM :

Disc cutter cutting coefficient predicted by the CSM method (%)

FN CSM :

Disc cutter normal force predicted by the CSM method (kN)

(FN opt)CSM :

Disc cutter normal force at the optimum rock cutting condition predicted by the CSM method (kN)

FR CSM :

Disc cutter rolling force predicted by the CSM method (kN)

(FR opt)CSM :

Disc cutter rolling force at the optimum rock cutting condition predicted by the CSM method (kN)

FT CSM :

Disc cutter resultant force predicted by the CSM method (kN)

P θ :

Contact pressure within the rock-cutter contact area (MPa)

P 0 :

Base contact pressure immediately beneath the disc cutter (MPa)

(p opt)CSM :

Optimum cutter penetration depth predicted by the CSM method (mm)

SE CSM :

Rock cutting specific energy predicted by the CSM method (MJ/m3)

(SE opt)CSM :

Optimum rock cutting specific energy predicted by the CSM method (MJ/m3)

V CSM :

Rock cutting volume per cutting length in the CSM method (mm2)

b :

Penetration coefficient in the NTNU method

BI NTNU :

Rock boreability index predicted by the NTNU method (kN/mm)

(BI opt)NTNU :

Rock boreability index at optimum rock cutting condition predicted by the NTNU method (kN/mm)

FN 1 :

Critical disc cutter normal force in the NTNU method (kN)

FN ekv :

Equivalent disc cutter normal force in the NTNU method (kN)

FN NTNU :

Disc cutter normal force predicted by the NTNU method (kN)

(FN opt)NTNU :

Disc cutter normal force at the optimum rock cutting condition predicted by the NTNU method (kN)

FR NTNU :

Disc cutter rolling force predicted by the NTNU method (kN)

(FR opt)NTNU :

Disc cutter rolling force at the optimum rock cutting condition predicted by the NTNU method (kN)

k d :

Correction factor for disc cutter diameter in the NTNU method

k DRI :

Correction factor for the DRI of the rock in the NTNU method

k ekv :

Equivalent fracturing factor in the NTNU method

k por :

Correction factor for the porosity of the rock in the NTNU method

k s :

Correction factor for cutter spacing in the NTNU method

k s-tot :

Total fracturing factor in the NTNU method

k si :

Fracturing factor for the ith fracture set in the NTNU method

n :

Number of the fracture sets in the NTNU method, usually less than 3

(p opt)NTNU :

Optimum cutter penetration depth predicted by the NTNU method (mm)

SE NTNU :

Rock cutting specific energy predicted by the NTNU method (MJ/m3)

(SE opt)NTNU :

Optimum rock cutting specific energy predicted by the NTNU method (MJ/m3)

V NTNU :

Rock cutting volume per cutting length in the NTNU method (mm2)

BI field :

Rock boreability index in the field (kN/mm)

(BI opt)field :

Rock boreability index at the optimum rock cutting condition in the field (kN/mm)

D TBM :

Diameter of the TBM cutterhead (mm)

FN field :

Disc cutter normal force in the field (kN)

(FN opt)field :

Disc cutter normal force at the optimum rock cutting condition in the field (kN)

FR field :

Disc cutter rolling force in the field (kN)

(FR opt)field :

Disc cutter rolling force at the optimum rock cutting condition in the field (kN)

N c :

Number of the disc cutter blades mounted on the cutterhead

p rev :

Cutterhead penetration depth per revolution (mm)

(p opt)field :

Optimum cutterhead penetration depth per revolution in the field (mm)

P :

Cutterhead power (kW)

P net :

Net cutterhead power after excluding the frictional loss (kW)

RPM :

Cutterhead rotational speed (r/min)

s avg :

Average cutter spacing of the TBM cutterehead (mm)

SE field :

Rock cutting specific energy in the field (MJ/m3)

(SE opt)field :

Optimum rock cutting specific energy in the field (MJ/m3)

T h :

Cutterhead thrust (kN)

T h, net :

Net cutterhead thrust after excluding the frictional loss (kN)

T q :

Cutterhead torque (kN m)

T q, net :

Net cutterhead torque after excluding the frictional loss, (kN m)

CCS:

Constant cross section

CSM:

Colorado School of Mines

LCM:

Linear cutting machine

NTNU:

Norwegian University of Science and Technology

RCM:

Rotary cutting machine

RMT:

Rock mechanical testing machine

TBM:

Tunnel boring machine

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Acknowledgements

This work was financially supported by National Natural Science Foundation of China under Grant Nos. 41807250, 41907242 and 41702254, China Postdoctoral Science Foundation Program under Grant Nos. 2019T120686 and 2017M622515, and National Key Basic Research Program of China under Grant Nos. 2015CB058102 and 2014CB046903. The authors are grateful for their continuous support, and also grateful to the authors’ colleagues for their valuable help in organizing and improving this article.

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Authors and Affiliations

  1. Key Laboratory of Safety for Geotechnical and Structural Engineering of Hubei Province, School of Civil Engineering, Wuhan University, Wuhan, 430072, Hubei, People’s Republic of China

    Yucong Pan, Quansheng Liu & Yin Bo

  2. Changjiang Institute of Survey, Planning, Design and Research , Wuhan, 430010, Hubei, People’s Republic of China

    Qi Liu

  3. College of Water Conservancy and Hydropower Engineering, Sichuan Agricultural University, Ya’an, 625014, Sichuan, People’s Republic of China

    Jianping Liu

  4. China Railway 11th Bureau Group 4th Engineering Co., Ltd., Wuhan, 430074, Hubei, People’s Republic of China

    Xingxin Peng

  5. China Construction Third Engineering Bureau Co., Ltd., Wuhan, 430064, Hubei, People’s Republic of China

    Tao Cai

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Pan, Y., Liu, Q., Liu, Q. et al. Comparison and correlation between the laboratory, semi-theoretical and empirical methods in predicting the field excavation performance of tunnel boring machine (TBM). Acta Geotech. 17, 653–676 (2022). https://doi.org/10.1007/s11440-021-01228-3

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