Keywords: limit analysis, lower bound, upper bound, finite element analysis, masonry bridges, collapse load.

Model scale and full scale tests [1,2] have shown that arch-fill interaction in masonry bridges often has a fundamental role at bridge collapse, furnishing a large contribution to the strength resources. Two numerical procedures based on the static and kinematical theorem of limit analysis are proposed in order to evaluate lower and upper bounds on the load carrying capacity of multi-span masonry bridges taking into account the arch-fill interaction. The bridge is modelled as a two-dimensional structural system composed by no tensile resistamt (NTR) and ductile in compression masonry arches and piers interacting with a cohesive-frictional fill. Statically admissible stress fields and kinematically admissible velocity fields are obtained via a finite element discretization of the bridge. Arches and piers are modelled by two-noded beam elements based on the assumption of NTR and ductile in compression material. The fill is discretized by triangular and interface elements, as proposed in [3,4,5]. This approach extends the standard finite element limit analysis [6,7] to include discontinuities [8,9] and offers the advantage of increasing the density of the degrees of freedom in the discrete model; this prevents locking phenomena [10] in the compatible model without having to resort to mixed formulations [11,12] or to higher order finite elements [13]. Interface elements are also located between the fill and the arches at their extrados to model possible velocity jumps. Finally, the piecewise linearization of the limit domains has been applied in order to obtain the maximum statically admissible load multiplier and the minimum kinematically admissible load multiplier as solutions of linear programming problems.

In the example the simulation of an experimental collapse test on an existing single span bridge [14] is presented and discussed. The results obtained from the static approach are compared to the results obtained from the kinematic approach. Both the assumptions of plane strain and plane stress fill are considered, in order to evaluate the effects of the out of plane boundary conditions on the collapse load. Finally, the dependence of the load carrying capacity on the mechanical parameters of the fill and of the masonry is analysed and discussed.

1

Page J., Masonry Arch Bridges - TRL State of the Art Review, HMSO, 1993.

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Bottero A., Negre R., Pastor J., Turgeman S., Finite element method and limit analysis theory for soil mechanics problems, Comput. Methods Appl. Mech. Engrg., 22, 131-149, 1980. doi:10.1016/0045-7825(80)90055-9

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Alwis W.A.M., Discrete element slip model of plasticity, Engineering Structures, 23, 1494-1504, 2000. doi:10.1016/S0141-0296(99)00094-2

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Chen J., Yin J.H., Lee C.F., Rigid finite element method for upper bound limit analysis of soil slopes subjected to pore water pressure, J. Engng Mech. ASCE, 130, 886-893, 2004. doi:10.1061/(ASCE)0733-9399(2004)130:8(886)

10

Nagtegaal J.C., Parks D.M., Rice J.R., On numerically accurate finite element solutions in the fully plastic range, Comp. Meth. Appl. Mech. Engng., 4, 153-177, 1974. doi:10.1016/0045-7825(74)90032-2

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Capsoni A., Corradi L., A finite element formulation of the ridid-plastic limit analysis problem, Int. J. Numer. Methods. Engng., 40, 2063-2086, 1997. doi:10.1002/(SICI)1097-0207(19970615)40:11<2063::AID-NME159>3.0.CO;2-#

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Tin Loi F., Ngo N.S., Performace of the p-version finite element method for limit analysis, Int. J. Mech. Sc., 45, 1149-1166, 2003. doi:10.1016/j.ijmecsci.2003.08.004

14

Page J., Load tests to collapse on two arch bridges at Preston, Shropshire and Prestwood, Staffordshire, Department of Transport, TRRL Research Report 110, TRL, Crowthorne, England, 1987.

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