Abstract
The structural health of operational metro tunnels is closely related to public safety. Prior research has focused on the locations of structural damage, but few researchers have examined both the location of damage and identifying the degree of damage, especially in metro shield tunnels. This paper proposes a new method for identifying structural damage that entails locating and detecting the degradation of tunnel performance, with a special focus on characterizing the degree of damage. First, the dynamic behaviors (modal frequencies and shapes) of different damage levels are obtained from an analytical model of the original tunnel structure. Second, a modal strain energy damage indicator (MSEDI) is introduced to locate the damage, regardless of size. Once the location of the damage is identified using MSEDI, a fuzzy logic-based damage identification (FLBDI) method is used to determine the actual extent of the damage. Finally, a simplified model of the tunnel is created using the Euler-Bernoulli beam theory and Winkler’s foundation, to further test the procedure under an incomplete modal information condition and with differing noise levels. The results reveal that the fuzzy logic- based system can identify the degree of damage and structural degradation with very high accuracy, in which the location of damage and the prediction of performance degradation is satisfactorily confirmed.
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Abbreviations
- F I :
-
Inertia force
- f k :
-
Foundation resistance force
- h :
-
Thickness of compressible stratum
- h i :
-
Thicknesses of the ith layer
- H(x):
-
Heaviside step function
- k :
-
Total foundation resistance modulus
- k i :
-
Foundation resistance modulus of the ith layer
- M(x,t):
-
Moment
- MSE i :
-
ith order MSE for a thin-wall circular shell beam
- \(MSE_{i,k}^0\) :
-
ith MSE of the kth element for the undamaged structure
- \(MSE_{i,k}^d\) :
-
ith MSE of the kth element for damaged tunnel
- MSEDI:
-
Mean damage indicator for the kth element of the structure
- p :
-
Foundation resistance force
- r i,n :
-
Parameter without noise
- r noise :
-
Parameter value with noise
- u(x):
-
Ground deflection
- V(x,t):
-
Shear force
- x d :
-
Damage coordinate along the longitudinal direction
- β :
-
Degradation degree
- Δk :
-
Damage width
- δ(x):
-
Dirac delta function
- ϑ i, k :
-
ith modal order variations of MSE of kth element after damage after damage
- λ :
-
Noise level parameter
- λ :
-
Modal eigenvalue
- \(\lambda _i^1\) :
-
First-order perturbation of the eigenvalue
- ϕ(x):
-
Modal eigenvector
- \(\phi _i^1\) :
-
First-order perturbation of the eigenvector
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Acknowledgments
This work was supported by Natural Science Foundation of Jiangxi Province (20202BABL214041; 20192BAB206032) and Science and technology project of Jiangxi Provincial Transportation Department (2020Z0003; 2020X0013).
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Wan, L., Xie, X., Wang, L. et al. New Damage Identification Method for Operational Metro Tunnel Based on Perturbation Theory and Fuzzy Logic. KSCE J Civ Eng 26, 193–206 (2022). https://doi.org/10.1007/s12205-021-2299-4
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DOI: https://doi.org/10.1007/s12205-021-2299-4