PSI - Issue 11

P. Bamonte et al. / Procedia Structural Integrity 11 (2018) 322–330 P. Bamonte and A. Taliercio/ Structural Integrity Procedia 00 (2018) 000–000

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whereas the diameter of the outer wall is comprised between 2.70 and 4.40 m. The base is provided with a door, to access the inside of the chimney for inspection. The base rests of on a massive concrete foundation. The shaft extends up to a height of about 59 m. It has a conical shape, with a taper angle of 0.91°. The cross section is discontinuous at a height of about 42 meters (see Fig.s 2b,c,d). Also the shaft is double-walled: the walls are connected by eight vertical ribs, and by a system of evenly spaced, horizontal diaphragms. The crown consists of a single-walled cylindrical element, with a constant cross section (see Fig. 2e). 2.2. Material properties Four laboratory tests were carried out on bricks extracted from the chimney to evaluate their compressive strength, f b , according to the UNI EN 772-1 standard: an average strength of about 20 MPa was obtained. Nine penetration tests were also carried out on the joints, according to which mortar can be classified as M15. Two double flat-jack tests (labelled MD1 and MD2 hereafter) were carried out to evaluate the macroscopic Young’s modulus ( E ) and Poisson’s ratio (  ) of brickwork. The values reported in Table 1 were obtained. According to the Italian Technical Standards for Constructions (NTC 2008) taking the results of the flat-jack tests into account, brickwork can be classified as “solid brick masonry with lime mortar”; a vertical compressive strength of the order of 8 MPa can be assumed. No indication is provided by the same standards regarding the tensile strength of brickwork. According e.g to Lourenço (2002), the tensile strength when the plane of failure is parallel to the bed joints is approximately 0.2 MPa. When the plane of failure is perpendicular to the bed joints, cracks cross also units and the macroscopic tensile strength is higher: according to Drysdale and Hamid (1982), it can be reasonably assumed to be of the order of 1 MPa. In order to incorporate thermal effects into the numerical analyses of the chimney, the coefficient of thermal expansion (CTE) of masonry,  , has to be estimated. According to the Eurocode 6 (2005), for clay brick masonry  ranges between 4 and 8  10 -6 K -1 . An intermediate value of 6  10 -6 K -1 is here assumed to apply for thermal strains parallel to the bed joint. Perpendicularly to the bed joints, a higher CTE is assumed (  = 12  10 -6 K -1 ), corresponding to that of mortar according to Zeng et al. (2012).. 2.3. Crack pattern Before the restoration work carried out in 2015, the chimney exhibited a crack pattern consisting of horizontal, vertical, and zig-zag cracks. In Fig. 3 cracks are color-coded according to their width. Their depth could not be estimated. The main vertical cracks were surveyed along the south side, from a height of about 18 m up to about 43 m. Thinner vertical cracks of minor length were detected on the other sides, in the lower part of the shaft. Above 43 m, on the west and north sides, zig-zag cracks with an inclination of about 45° and exclusively running along the mortar joints were reported. On the east, west and north sides, horizontal cracks along the bed joints were surveyed from a height of about 50 m up. On the south side, horizontal cracks exist only at the top of the shaft. Other significant cracks affect the entire concrete curb placed at the top of the shaft, but are of lesser structural importance. 3. Numerical model The finite element modeling of the chimney is awkward because of the complex geometry, characterized by the presence of vertical ribs and horizontal diaphragms between the two walls that make up the shaft. An optimum finite elements size must be defined, to balance accuracy in the discretization and computational effort. Two different models were built: the first one, which represents the chimney in its entirety, was used for preliminary global analyses in the presence of non-axisymmetric loads, such as wind; the second one, which represents only one eighth Table 1. Results of the double flat-jack tests. test E (MPa)  MD1 MD2 2383 3143 0.33 0.31