Abstract
In this paper, the standard formulation for rigid block limit analysis is extended to simulate the effect of innovative strengthening (FRP/FRCM), with a suitable modification of the constitutive constraint that governs the behavior of contact joints. The proposed modeling is applied to both associated and non-associated sliding. The change of the failure surface of a representative contact joint after the reinforcement is first derived. Casting it into a standard matrix form, the constitutive constraint in the lower bound theory is then modified to account for the strengthening effect. After that, the proposed technique is also extended to solve a non-associated problem. Utilizing this technique, the collapse of a 9-block 2D arch with FRP reinforcement is analyzed to compare predictions from associated and non-associated formulations. Detailed parametric studies are carried out to understand the influence of the critical parameters on the difference in the results from these two formulations. The results show that when analyzing the arch with reinforcement, the associated limit analysis may predict an incorrect collapse mechanism as well as an overestimated collapse load. Such overestimation could reach 70.5% in some cases. Employment of non-associated formulation is very necessary for more precise collapse analysis of reinforced masonry arches.
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References
Makris, N., Alexakis, H.: The effect of stereotomy on the shape of the thrust-line and the minimum thickness of semicircular masonry arches. Arch. Appl. Mech. 83(10), 1511–1533 (2013). https://doi.org/10.1007/s00419-013-0763-4
Chiozzi, A., Grillanda, N., Milani, G., Tralli, A.: UB-ALMANAC: an adaptive limit analysis NURBS-based program for the automatic assessment of partial failure mechanisms in masonry churches. Eng Fail Anal 85, 201–220 (2018). https://doi.org/10.1016/j.engfailanal.2017.11.013
Chiozzi, A., Malagù, M., Tralli, A., Cazzani, A.: ArchNURBS: NURBS-based tool for the structural safety assessment of masonry arches in MATLAB. J Comput Civ Eng 30, 4015010 (2016). https://doi.org/10.1061/(asce)cp.1943-5487.0000481
Grillanda, N., Valente, M., Milani, G.: ANUB-Aggregates: a fully automatic NURBS-based software for advanced local failure analyses of historical masonry aggregates. Bull. Earthq. Eng. 18(8), 3935–3961 (2020). https://doi.org/10.1007/s10518-020-00848-6
Portioli, F.P.A.: Rigid block modelling of historic masonry structures using mathematical programming: a unified formulation for non-linear time history, static pushover and limit equilibrium analysis. Bull. Earthq. Eng. 18(1), 211–239 (2019). https://doi.org/10.1007/s10518-019-00722-0
Livesley, R.K.: Limit analysis of structures formed from rigid blocks. Int J Numer Methods Eng 12, 1853–1871 (1978)
Livesley, R.K.: A computational model for the limit analysis of three-dimensional masonry structures. Meccanica 27, 161–172 (1992). https://doi.org/10.1007/BF00430042
Heyman, J.: The stone skeleton. Int. J. Solids Struct. 2, 249–256, IN1–IN4, 257–264, IN5–IN12, 265–279 (1966). https://doi.org/10.1016/0020-7683(66)90018-7
Kooharian, A.: Limit analysis of voussoir (Segmental) and concrete archs. ACI J. Proc. 49, 317–328 (1952). https://doi.org/10.14359/11822
Portioli, F., Casapulla, C., Gilbert, M., Cascini, L.: Limit analysis of 3D masonry block structures with non-associative frictional joints using cone programming. Comput Struct 143, 108–121 (2014). https://doi.org/10.1016/j.compstruc.2014.07.010
Ferris, M.C., Tin-Loi, F.: Limit analysis of frictional block assemblies as a mathematical program with complementarity constraints. Int J Mech Sci 43, 209–224 (2001). https://doi.org/10.1016/S0020-7403(99)00111-3
Gilbert, M., Casapulla, C., Ahmed, H.M.: Limit analysis of masonry block structures with non-associative frictional joints using linear programming. Comput Struct 84, 873–887 (2006). https://doi.org/10.1016/j.compstruc.2006.02.005
Orduña, A., Lourenço, P.B.: Three-dimensional limit analysis of rigid blocks assemblages. Part II: Load-path following solution procedure and validation. Int J Solids Struct 42, 5161–5180 (2005). https://doi.org/10.1016/j.ijsolstr.2005.02.011
Milani, G., Lourenço, P.B., Tralli, A.: Homogenised limit analysis of masonry walls, Part II: Structural examples. Comput Struct 84, 181–195 (2006). https://doi.org/10.1016/j.compstruc.2005.09.004
Chiozzi, A., Milani, G., Tralli, A.: A Genetic Algorithm NURBS-based new approach for fast kinematic limit analysis of masonry vaults. Comput Struct 182, 187–204 (2017). https://doi.org/10.1016/j.compstruc.2016.11.003
Caporale, A., Feo, L., Hui, D., Luciano, R.: Debonding of FRP in multi-span masonry arch structures via limit analysis. Compos Struct 108, 856–865 (2014). https://doi.org/10.1016/j.compstruct.2013.10.006
Caporale, A., Feo, L., Luciano, R., Penna, R.: Numerical collapse load of multi-span masonry arch structures with FRP reinforcement. Compos Part B Eng 54, 71–84 (2013). https://doi.org/10.1016/j.compositesb.2013.04.042
Drucker, D.C.: Coulomb Friction, Plasticity, and Limit Loads. J Appl Mech 21, 71–74 (1954). https://doi.org/10.1115/1.4010821
CNR-DT200 Guide for the design and construction of externally bonded FRP systems for strengthening existing structures. C.N.R., National Research Council, Italy (2013)
Panizza, M., Garbin, E., Valluzzi, M.R.: Peel strength testing of FRP applied to clay bricks. In: Proceedings of the 8th International Conference on Fracture Mechanics of Concrete and Concrete Structures, FraMCoS 2013, pp 562–570 (2013)
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Hua, Y., Milani, G. (2023). Collapse Analysis of Reinforced Masonry Arches: A Comparison of Associated and Non-associated Sliding. In: Capozucca, R., Khatir, S., Milani, G. (eds) Proceedings of the International Conference of Steel and Composite for Engineering Structures. ICSCES 2022. Lecture Notes in Civil Engineering, vol 317. Springer, Cham. https://doi.org/10.1007/978-3-031-24041-6_17
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