# LiABlock_3D

**LiABlock_3D: A software tool for collapse mechanism analysis of historic masonry structures**

##### Lucrezia Cascini, Raffaele Gagliardo, Francesco Portioli

*Department of Structures for Engineering and Architecture, University of Naples Federico II, via Forno Vecchio 36, 80134, Naples, Italy*

*Department of Structures for Engineering and Architecture, University of Naples Federico II, via Forno Vecchio 36, 80134, Naples, Italy*

A discrete rigid block model is proposed for collapse mechanism analysis of three-dimensional historic masonry structures subjected to point live loads, seismic induced lateral loads and settlements.

The model is made of polyhedral rigid blocks interacting at no-tension, frictional contact interfaces and can be used to represent complex assemblages and bond patterns.

The formulation and the solution procedure of the underlying limit equilibrium analysis problem were implemented in LiABlock_3D, a MATLAB based tool with Graphical User Interface (GUI).

The software was designed to import the geometric model from commercial Computer Aided Design tools, thus allowing high flexibility of structural configurations and masonry patterns. The graphical interface is also used to define material properties as well as boundary and loading conditions.

Numerical and experimental case studies from the literature were analysed to show the ability of the model developed in predicting the collapse behaviour of a variety of structural typologies. Those include arches, vaults and domes under vertical and horizontal live loads and spreading supports.

A two-storey masonry building with a barrel vault at first level is also analysed under variable lateral loads and support movement. Potentialities and limitations of the proposed formulation and tool are discussed on the basis of the results obtained and also in terms of computational efficiency.

The collapse mechanism limit analysis of masonry structures is based on the discretization of the structure into an assemblage of rigid bodies, usually interacting at no-tension, frictional contact interfaces.

The evaluation of the load factor corresponding to the activation of the rigid block mechanism is carried out through the application of the limit analysis theorems.

A computational tool which is based on a finite element discretization constituted by NURBS rigid elements joined by elasto-plastic interfaces was recently presented in Chiozzi et al.

Software tools based on rigid block modelling for limit analysis are also available. Among those, the LimitState:RING software is devoted to the analysis of 2D masonry bridges under vertical live loads and settlement.

The software is based on the formulation developed by Gilbert et al. and provides as outputs the critical failure modes and the thrust zone at collapse. Examples of applications to masonry vaults.

LiABlock_3D is a novel software tool for the limit equilibrium analysis of masonry structures modelled as assemblages of three-dimensional rigid blocks subjected to live loads and settlements.

The main fields of application are monumental buildings made of large masonry blocks or stones and masonry assemblages with regular or complex bond patterns, such as arched structures and vaults, where the contribution of mortar can be neglected.

LiABlock_3D is deployed as a standalone executable application from MATLAB scripts and functions originated by the first and third author.

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