Issue 51

E. Mousavian et alii, Frattura ed Integrità Strutturale, 51 (2020) 336-355; DOI: 10.3221/IGF-ESIS.51.25 350 Depending on if the intersection point locates on Zone 1, 2 or 3, the corresponding equations can be used to define the lock length b , respectively: 3 θ tan φ cot φ 2 2 k d k g b c                (29) cosφ k a b  (30)         3 3 3 tan , cos cos cos cot tan 2 2 2 tan , cos cos cos cot tan 2 2 2 cot tan , c 2 2 k d k k d k k k d c b m g d p c c m m g d p c m c m g d                                                                                                                      os cos p                     (31) where coefficient     1, , 3 1 , ,2 1 ;  k c k k m k         . Sliding resistance of an interlocking interface in a hemispherical dome Fig. 15 presents a generic interlocking interface modelled as a set of failure strips where internal forces are distributed on. These planar strips include dry joints between two interlocking blocks (blue strips) and fracture planes at which the block can crack (red strips). Other kinds of fracture are avoided through considering the main body of the interlocking block rigid enough. A dry joint can be separated, rock, and slide along the locks, while a lock can be cracked at the fracture plane due to bending, shear, torsion or combinations of them. (a) (b) (c) Figure 15 : a) An interlocking interface and its failure planar strips including b) dry joints and c) fracture planes. Convex contact model addressed in [7] idealizes the stress state at an interface to the internal forces at the centre of the interface including the normal force f n , two tangential forces f t 1 and f t 2 normal to each other, two bending moments normal to each other bn 1 and bn 2 and torsion moment t r (Fig. 16a). In this section, instead of the centre of the interface, the internal forces at the intersection point of the meridional thrust-line of a lune and an interface are considered (Fig. 16b and c). A similar approach was previously applied to find the internal forces at the 2D conventional [9] and interlocking interfaces [2] of a semi-circular arch.