Masonry structures in the presence of foundation settlements and unilateral contact problems

Abstract This paper aims at presenting a new perspective on the modeling of the influence of foundation settlements in masonry structures. We show that it is possible to model in a consistent way the crack pattern and the associated mechanism induced by applied settlements starting from a proper treatment of unilateral contact constraints between contiguous blocks, in which the structure is partitioned after the onset of settlements. We extend two classic variational formulations for the Signorini problem, namely the minimum of the total potential energy and a complementary boundary formulation, to the case of contact between multiple no-tension rigid bodies satisfying Heyman's hypotheses for the limit analysis of masonry structures. The discretization of the proposed variational formulations directly entails two dual linear programming problems. The proposed formulations allow to correctly evaluate the effects of foundation settlements and their influence on the ultimate load bearing capacity of masonry structures.

[1]  Jacques Heyman,et al.  The safety of masonry arches , 1969 .

[2]  Lucrezia Cascini,et al.  Large displacement analysis of dry-jointed masonry structures subjected to settlements using rigid block modelling , 2017 .

[3]  Giuseppe Grioli.  On the stress in rigid bodies , 1983 .

[4]  Lucrezia Cascini,et al.  Assessment of masonry structures subjected to foundation settlements using rigid block limit analysis , 2016 .

[5]  Andrea Chiozzi,et al.  A Genetic Algorithm NURBS-based new approach for fast kinematic limit analysis of masonry vaults , 2017 .

[6]  John Ochsendorf,et al.  The Mechanics of Gothic Masonry Arches , 2010 .

[7]  M. Šilhavý.  Collapse mechanisms and the existence of equilibrium solutions for masonry bodies , 2014 .

[8]  Antonio Gesualdo,et al.  Modelling the cracks produced by settlements in masonry structures , 2018 .

[9]  D. C. Drucker,et al.  A DEFINITION OF STABLE INELASTIC MATERIAL , 1957 .

[10]  Santiago Sánchez-Cervera Huerta,et al.  The Analysis of Masonry Architecture: A Historical Approach , 2008 .

[11]  Paolo Zampieri,et al.  Collapse mechanisms of masonry arches with settled springing , 2018 .

[12]  Paolo Zampieri,et al.  Failure analysis of masonry arch bridges subject to local pier scour , 2017 .

[13]  Matthew Gilbert,et al.  Limit analysis of masonry block structures with non-associative frictional joints using linear programming , 2006 .

[14]  G. Del Piero,et al.  Limit analysis and no-tension materials , 1998 .

[15]  M. Angelillo,et al.  Singular stress fields in masonry structures: Derand was right , 2014 .

[16]  P. Panagiotopoulos.  Inequality problems in mechanics and applications , 1985 .

[17]  Maurizio Angelillo,et al.  Practical applications of unilateral models to Masonry Equilibrium , 2014 .

[18]  G. Milani,et al.  UB-ALMANAC: An adaptive limit analysis NURBS-based program for the automatic assessment of partial failure mechanisms in masonry churches , 2018 .

[19]  S. Alliney,et al.  Boundary variational formulations and numerical solution techniques for unilateral contact problems , 1990 .

[20]  Jacques Heyman,et al.  The stone skeleton , 1995 .

[21]  Zila Rinaldi,et al.  Collapse load of a masonry arch after actual displacements of the supports , 2018 .

[22]  Wout Broere,et al.  A two-stage numerical analysis approach for the assessment of the settlement response of the pre-damaged historic Hoca Pasha Mosque , 2019 .

[23]  Mario Como.  Virtual displacements principle, existence and uniqueness for elastic no tension bodies , 2017 .

[24]  C. Pellegrino,et al.  The masonry buttressed arch on spreading support , 2019, Structures.

[25]  Massimiliano Lucchesi,et al.  A new class of equilibrated stress fields for no-tension bodies , 2006 .

[26]  Thomas E. Boothby.  Analysis of masonry arches and vaults , 2001 .

[27]  Andrea Chiozzi,et al.  ArchNURBS: NURBS-Based Tool for the Structural Safety Assessment of Masonry Arches in MATLAB , 2016, J. Comput. Civ. Eng..

[28]  Gabriele Milani,et al.  Computational Methods for Masonry Vaults: A Review of Recent Results , 2014 .

[29]  Giacomo Tempesta,et al.  The Matlab code of the method based on the Full Range Factor for assessing the safety of masonry arches , 2019, MethodsX.

[30]  M. Angelillo,et al.  Crack patterns identification in masonry structures with a C° displacement energy method , 2018 .

[31]  Zila Rinaldi,et al.  Collapse displacements for a mechanism of spreading-induced supports in a masonry arch , 2015 .

[32]  Michele Paradiso,et al.  Non-Linear Analysis of Masonry Structures Subjected to External Settlements , 2013 .

[33]  Maurizio Angelillo,et al.  The model of Heyman and the statical and kinematical problems for masonry structures , 2019, International Journal of Masonry Research and Innovation.

[34]  P. D. Panagiotopoulos,et al.  The Boundary Integral Approach to Static and Dynamic Contact Problems: Equality and Inequality Methods , 1992 .

[35]  S. Galassi,et al.  Failure modes prediction of masonry voussoir arches on moving supports , 2018, Engineering Structures.

[36]  S. Galassi,et al.  Safety evaluation of masonry arches. A numerical procedure based on the thrust line closest to the geometrical axis , 2019, International Journal of Mechanical Sciences.

[37]  Peter Wriggers,et al.  Computational Contact Mechanics , 2002 .

[38]  Mario Como,et al.  Statics of Historic Masonry Constructions , 2012 .

[39]  V. Gusella,et al.  Collapse displacements of masonry arch with geometrical uncertainties on spreading supports , 2018, Computers & Structures.

[40]  Maurizio Angelillo,et al.  Constitutive relations for no-tension materials , 1993 .

[41]  Mario Como,et al.  Equilibrium and collapse analysis of masonry bodies , 1992 .

[42]  Antonio Gesualdo,et al.  Rigid block models for masonry structures , 2018 .