5. ELFEN

5.1 Overview

The use of ELFEN Finite/Discrete Element software provides the opportunities to model the fundamental behaviour of arches in a way that has not before been possible. In particular, the analysis can embrace the following aspects:

1. Representation of the material characteristics (elastic and plastic behaviour) of the brick/stone units and mortar so that buckling, crushing and composite behaviour can be simulated.
    
2. Modelling of contact-gap-friction effects along mortar/dry joints so that limiting tension, cracking, sliding and hinges can be represented.
    
3. Modelling of steel reinforcement including bond failure so that reinforcement based strengthening can be investigated, for example existing reinforced concrete saddles and Cintec anchors.
    
4. Explicit representation of defects such as ring separation, local distortion and mortar loss.
    
5. A solution procedure including the calculation of displacement, strain and stress to efficiently facilitate the modelling of the constitutive behaviour in i), ii) and iii) above and perform global structural analysis.

Crucially it is the ability of ELFEN to model the interaction of the masonry with the retrofitted reinforcement which provides the analytical basis for Archtec.

5.2 Rockfield Software Limited

The ELFEN software has been developed by Rockfield Software Limited over nearly 20 years since the company was founded in 1984. It has been deployed in numerous applications for an international client base with interests in a diverse range of industrial disciplines (including basic engineering, foods, manufacturing, geotechnical, defence, etc).

Rockfield are a high technology company established to provide leading edge numerical based simulation systems and their industrial applications. Their principal aim is to provide industry with support of advanced technology problems through computational modelling.

To meet this objective, the company is committed to computational developments and applications in both existing and emerging disciplines and the undertaking of collaborative research programmes with industry, universities and research organisations. Rockfield is based in Swansea, UK being closely allied to the University of Wales, Swansea, with offices in Australia (Queensland) and in USA (Maryland).

ELFEN undergoes a stringent testing procedure to ensure the software is verified for each application. For example, Rockfield have worked on masonry arches with Gifford to ensure that the software is being correctly applied and have run independent verification exercises to check arch simulations. The software has also been benchmarked for a variety of classes of engineering problems against industry standard tests to ensure that all results are correct.

Rockfield Software Ltd has developed ongoing relationships with leaders in virtually every industry around the world. Some of Rockfield’s ELFEN clients include: BP, Total Fina Elf, Royal Haskoning, Fugro, DML, Corus, Rexam Beverage Can Europe, Crown Cork & Seal, Unilever, Procter & Gamble, DeBeers, Rio Tinto, ORICA, DSTL, QinetiQ, Cintec International, Gifford & Partners and many more.

5.3 The Finite/Discrete Element Algorithm

The algorithm essential for all of the structural analysis undertaken with ELFEN is based on Finite/Discrete Element (DE) method. This is an improvement on the Distinct Element method first developed by Cundall(8) in 1971 in which the concept of individual elements being separate and reacting with their neighbours by contact through friction/adhesion was first successfully applied to geotechnical and granular flow problems. Here elements were considered rigid but later developments for example by Munjiza et al(9) in 1995 included the addition of element deformations and fracturing, with some overlap with traditional finite element theory; the DE method was born.

The DE formulation available in the explicit dynamic version of ELFEN has been adopted for Archtec. Explicit solvers (solution of transient dynamic problems by central difference explicit time integration) are intrinsically dynamic and are well suited to the analysis of structures with discontinuous behaviour such as masonry. Equilibrium difficulties, particularly during softening, often encountered with more traditional implicit solvers are completely avoided although more reliance is required on verification.

5.4 Application to Arch Strength Assessment

Using ELFEN(10) and the DE technique to generically model masonry and fill, this software is used to represent the behaviour of arch barrels allowing prediction of structural behaviour. Simply, each brick or block is modelled and the contact between them automatically calculated as load is applied. Non-linear material models and contact interface models are used to represent the masonry and mortar joints. Stationary loads to reproduce tests or traversing loads to model moving vehicle axles can be easily represented as separate bodies. Unlike specialist arch analysis software and similar to conventional finite element software there is no limit to model complexity. However, for efficient and fully verified operation a carefully controlled modelling approach implemented by a data processing system is always used.

Arches are modelled in two dimensions, with a view to simplifying the analysis as far as possible, using plain strain assumptions. The necessary transverse load distribution criteria for live loading is normally based on rules in BD 21.

Non-linear material models are used to model crushing in the masonry and plastic shearing and tensile behaviour in the fill. The fill material can be modelled either as a non-linear Rankine continua with a tension cut off or as a non-linear Mohr-Coulomb continua, which uses conventional soil parameters angle of internal friction and cohesion. Mobilisation of active and passive pressure effects will be calculated directly by the analysis. Passive and active pressures develop as the barrel deforms with the fill being able to support carriageway loading and develop thrust lines by biaxial compression.

Construction sequence analysis is implicit to the approach with the initial and permanent stress state calculated as a construction event before the introduction of the live loading. Occasionally, depending on the shape of the barrel, formwork has to be represented and used for support until all permanent loads have been applied.

The two pictures in Figure 5.1 show typical ELFEN results, in this case a strength assessment failure. The twin axle loading is moving onto the arch from the left. Red indicates the highest compressive stresses. Significant tensile stresses cannot occur since in the event of tensile forces occurring joints simply open to redistribute them.

Figure 5.1 Typical Numerical Simulation of the Failure of a Masonry Arch
Results shown are Von Mises equivalent stresses