Analytical and numerical DDA analysis on the collapse mode of circular masonry arches

Analytical and numerical analysis on the collapse modes of least-thickness circular masonry arches at decreasing friction

“…• non-dimensional horizontal thrust h = H/(w r ) acting in such a limit state of minimum thickness still available to sustain the arch (Couplet-Heyman problem). This classical least-thickness problem in the statics of masonry arches has been revisited by the present authors within a wide research project that has been considering different characteristic aspects, by employing both self-consistent analytical and numerical techniques [5][6][7][8][9][10]. Arches of a general half-angle of embrace 0 <  <  (including for undercomplete and over-complete, horseshoe circular masonry arches) have been systematically analysed in analytical terms.…”

“…Different solutions have been explicitly derived, and numerically explored, which appeared fully consistent with updated outcomes from a re-discussion by Heyman [4], and prior developments by Ochsendorf [11][12], as well as with classical earlier work by Milankovitch [13] (see Foce [14]), and several most recent attempts that meanwhile have appeared [15][16][17][18][19][20][21][22][23][24]. An earlier account on these developments was provided in SAHC10 conference paper [5]; later, a comprehensive analytical treatment with unprecedented closed-form explicit representations was provided in [6], while in [8], consistent comparisons were developed by a Discrete Element Method implementation, in the form of a Discontinuous Deformation Analysis (DDA) tool. Then, first new developments on the role of friction have been preliminarily investigated in such a research mainstream, as initially reported in SAHC12 conference work [7], prodromal to the present one, by releasing Heyman hypothesis 3 of no sliding failure, and accounting for both mixed sliding-rotational and purely-sliding collapse modes (Figs.…”

Horizontal reaction components of pointed vaults

“…Because of its ability to follow the characteristic failure modes and collapse histories of masonry structures in detail, DEM can serve as a tool to check theoretical results with the help of computer-simulated experiments. A characteristic application of DEM can be found in Rizzi, Rusconi and Cocchetti (2014): a discrete element code was used for the comparison of the theoretical predictions for circular arches by Milankovitch (1907), Heyman (1969), and Cochetti, Colasante and Rizzi (2011).…”

Detection of contacts between three-dimensional polyhedral blocks for discontinuous deformation analysis

“…With continuous modifications and improvements, twodimensional (2-D) DDA has been more efficient and suitable to cover practical engineering problems of rockfall, 4-7 landslide, [8][9][10][11][12][13][14][15][16] tunneling and mining, [17][18][19][20][21] cavern and underground opening, [22][23][24][25][26][27] masonry structure, [28][29][30] fracture propagation, 31,32 rock blasting [33][34][35] and many others. [36][37][38][39][40][41][42] However, the applications of 2-D DDA are inappropriate to many practical problems because the majority of discontinuities are not always perpendicular to the cross-section of the model.…”