PSI - Issue 47

S. Aiello et al. / Procedia Structural Integrity 47 (2023) 668–674 S.Aiello, V. De Biagi, P. Cornetti, B. Chiaia / Structural Integrity Procedia 00 (2019) 000–000

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tunnel lining's concrete. However, the rock/soil placed at the extrados has a temperature that is almost constant due to geothermal flow, which needs to be considered when assessing the risk of thermal stress-related issues. 3. Analytical model with anomalous thickness reduction The circular plate model and one-dimensional model was created by estimating the schematic of the tunnel's typological section with the anomalous thickness in the key as shown in Fig.1.

Fig. 1. (a) Schematic of tunnel lining with key lining thickness anomaly; (b) Equivalent beam of rectangular cross-section, with anomalous thickness and confined at the ends; (c) Equivalent circular plate, with anomalous thickness and confined at the ends. Its definition was made possible by the following assumptions:  Analyses are limited to the calotte portion  Lining’s curvature is assumed to be infinite (extent of the anomalous thickness reduction is limited)  Lining portions considered are not stressed by compressive forces but only by vertical and thermal ones (permanent load)  Elastic material properties considered constant due to limited temperature variation  Consistent and uniform temperature � of soil  Linear variation of the temperature along the thickness (uniform gradient), given that the internal temperature, � , is higher than the soil temperature and that the difference between the two temperature is 2  Thermal expansion coefficient of the lining material equal to ��� 10 �� ° �� � The thermal variation can be classified into uniform heating and linear (butterfly) thermal variation, in which the bottom flap is heated, and the higher flap is cooled. The uniform thermal variation, , is equal to the linear variation, abbreviated as ∆ . Both values are equal to � (1). � � � �� � � � � (1) The current work is related to the thickness anomaly of the calotte section, which is included in the design thickness portion. Thermal effects are believed to be negligible in the defect-free part (i.e., design thickness lining portion). The one-dimensional model is based on an equivalent beam of rectangular cross-section confined at the ends, with a width of 2 and a thickness anomalous equal to ℎ , which is less than the design value .