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Fig 1.

Schematic diagram of the analysis model and conformal mapping.

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Fig 2.

Cross-section of horseshoe tunnel.

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Table 1.

Calculation parameter values.

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Table 1 Expand

Fig 3.

Finite element model diagram of horseshoe tunnel.

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Fig 4.

Analytical vs numerical solutions for vertical and horizontal displacements around a horseshoe tunnel.

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Fig 5.

Schematic diagram of β sphere in two-dimensional case.

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Table 2.

Calculates parameter statistics.

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Table 2 Expand

Table 3.

Comparison of the calculation results of the four reliability methods.

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Table 3 Expand

Fig 6.

Influence of mean of load parameters on reliability.

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Fig 7.

Influence of variation coefficient of parameters on tunnel reliability.

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Fig 8.

Influence of the correlation coefficient between E and μ on reliability.

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Fig 8 Expand