Designing and Retrofitting Walls for Explosive Effects and Natural Hazards

NATURAL HAZARDS

1. Introduction

a. The use of continuum based numerical models to simulate discontinuous structures, such as masonry, is fraught with difficulty. The introduction of discontinuities such as cracks during the loading event, or because of loading history, has to be wholly or partly predetermined. The use of gap elements allows cracks to open and maintain normal and shear force connection when closed but the crack locations have to be known in advance. Another approach is to avoid explicit representation of discontinuities but instead smear their effect by using a brittle non-linear material model. However, these models fail to predict mechanisms where, for example, initially isolated parts react dynamically together. Continuum methods can give satisfactory results but generally fail to provide a practical method of analysis for masonry.

b. As an alternative to the traditional finite element continuum approach, a discrete element (DE) formulation has been employed to simulate masonry with and without strengthening. So far, the results of the analyses have been applied to parts of buildings and used to help develop remedial design philosophies by providing simulations under ground excitations and explosive effects. A separate project where the engineering analysis has been based on the DE technique has involved the successful strengthening of over sixty masonry arches in Europe, Australia and USA. Predictive verification of full-scale tests underlies this work and has involved calculated collapse loads of masonry arch bridges as well as supplementary load tests on in-service bridges. Results have been shown to correlate very closely with tests (Brookes, Tilly 1999). As the technique is developed it is hoped that the performance of whole buildings can be checked before strengthening systems have been installed.

2. Analytical Requirements

In order to represent masonry with or without retrofitted reinforcement, particularly in seismic engineering where non-linear structural performance defines how ductility and energy absorption characteristics are exhibited, the following types of fundamental behaviour need to be included in the model.

Material and geometric properties of the masonry blocks themselves.
Contact-gap-friction effects along joints between the masonry blocks.
Depending on block and joint properties, the ability to evolve further joints by fracturing which in turn depends on limiting tensile strength and fracture energy.
Full account of stiffness and derived inertia loads which may occur over very short time intervals.
The capability to model post-failure behaviour to help verify simulations against the evidence collected after observed seismic damage and collapse.
To allow stress and initial damage from previous seismic events to be included.
The ability to represent retrofitted reinforcement including materially non-linear behaviour of the steel and the non-linear shear coupling behaviour of the bond with the surrounding masonry.

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