Modelling of fatigue loads

As known, the ISO definition states that fatigue is the progressive, localised and permanent structural change occurring in a material subjected to conditions that produce

fluctuating stresses and strains at some point or points and that may culminate in cracks or complete fracture after a sufficient number of fluctuations.

In engineering structures, fatigue is induced by actions and loads varying with time and/or space and/or by random vibrations. Thus fatigue can be originated by natural events, like waves, wind and so on, or by loads deriving from the normal service of the structure itself.

Among the civil structures exposed to fatigue, bridges occupy a prominent position, as they are subjected to the fluctuating action of lorries or trains crossing the bridges themselves.

The assignment of appropriate fatigue load models is therefore a key topic in contemporary bridge design codes of practice.

In principle, modelling of fatigue loads asks for the complete knowledge of the so-called load spectrum, expressing the load variations or the number of recurrences of each load level during the design working life of the structure. Load spectrum is generally given in terms of an appropriate function, graph, histogram or table.

The load spectrum is often deduced from recorded data, referring to relatively short time intervals. In this case, additional problems must be faced regarding the statistical processing, the reliability over longer periods of the available data and the future trends of traffic.

Whenever the real load spectrum results so complicated that cannot be directly used for fatigue checks, as it happens for bridge, it is replaced by some conventional load spectrum, aimed to reproduce the fatigue induced by the real one.

The evaluation of conventional load spectra is particularly problematic, because it requires to consider the actions also from the resistance point of view. In fact, fatigue depends on the nature of the varying actions and loads, and additionally on structural material details, through the shape and the properties of the relevant S-N curves.

Problems become even tougher when details exhibit endurance (fatigue) limit. As fatigue limits under constant amplitude represents a threshold value for the damaging stress range, it needs to distinguish between equivalent load spectra, aiming to reproduce the actual fatigue damage, and frequent load spectra, aiming to reproducing the maximum load range to be taken into account for fatigue assessments.

Since fatigue verifications are performed in different ways, depending on the necessity to assess fatigue damage or boundless fatigue life, the distinction between equivalent and frequent spectra appears quite obvious.

Moreover, the powerful methods of the stochastic process theory, often used in defining fatigue load spectra in other engineering structures, cannot be applied to bridges, as road traffic loads induce broad band stress histories. All that implies that the link between the action and the effect cannot be expressed by simple formulae, while further difficulties arise when vehicle interactions, whether due to simultaneity or not, become significant.

Nevertheless, provided that vehicle interaction problems can be solved in some way, as shown in the Appendix A to the present chapter, it is intuitive enough to think that fatigue load spectra for bridges are composed by suitable sets of standardized lorries, where each lorry is identified by its own relevant properties, i.e. relative frequency, number of axles, axle loads, axle’s spacing, deduced processing appropriate traffic records.

At this stage, it appears quite evident that definition of load spectra for bridges requires careful consideration of fatigue assessment methodology, to assure that assessments based on conventional spectra or on real spectra lead to the same results.

2.1.1 Fatigue verification methods

The preliminary explanation of fatigue assessment methodology based on conventional load spectra is a crucial question in studying fatigue load models.

It can be easily recognised that fatigue verification methods goes along with a well-defined procedure, characterised by the following steps

1 assignment of fatigue load spectra, discriminating, if necessary, equivalent ones from frequent ones;

2 detection and classification of structural details most vulnerable to fatigue cracking and selection of the appropriate S-N curves;

3 choice of the pertinent partial factors γM;

4 evaluation, for each detail, of the appropriate influence surface.

At this stage, the assessment methodology splits up in two different branches, accordingly as fatigue verification is devoted to compute fatigue damage or to assess boundless fatigue life.

Damage computation procedure

5.a calculation of the design stress history σ⁼σ(t) produced in the detail by the equivalent load spectrum travelling over the influence surface;

6.a analysis of the stress history by means of a suitable cycle counting method, like the reservoir method or the rainflow method, to obtain the stress spectrum, where the number of occurrences of each stress range in the design working life is associated with the stress range itself;

7.a computation of the cumulative damage D using the Palmgren-Miner rule: if D≤1 the fatigue check is satisfied, otherwise, it is necessary to raise the fatigue strength of the detail. Fatigue resistance can be enhanced both reducing the stress range, i.e. enlarging the dimensions, or increasing fatigue category, i.e. adopting more refined workmanship or details.

Boundless fatigue life assessment

5.b calculation of the design stress history σ⁼σ(t) produced in the detail by the frequent load spectrum transiting over the influence surface;

6.b computation of the maximum stress range ∆σmax=σmax-σmin, being σmax and σmin, respectively, the absolute maximum and the absolute minimum of the stress history;

7.b boundless fatigue life assessment. If the verification is not satisfied, it is possible to improve fatigue resistance using the provisions described in 7.a, or to attempt to go through fatigue damage computation.

Obviously, in bridges exposed to high-density traffic, concrete slabs and orthotropic steel deck details are subject to such a huge number of stress cycles, that boundless fatigue life assessment using frequent load spectra becomes quite obligatory.

2.1.2 Reference traffic measurements

Also the fatigue load models of Eurocode 1 have been defined and calibrated on the basis of the two large traffic measurement campaigns carried out in several European countries in years 1977 to 1982 and 1984 to 1988, which have been discussed in Annex A to chapter 3.

Unlike static loads, which depend only on the upper tail of the traffic load distribution, fatigue loads are influenced by the entire distribution.

For this reason, fatigue models have been refined, supplementing the main calibration, based on Auxerre traffic data, with supplementary studies, based on different traffic data, in order to enlarge their field of application,.

These supplementary calibrations regarded not only motorway traffics - Brothal (D), Piacenza, Fiano Romano, Sasso Marconi (I) – but also local traffic on secondary roads (Epone (F)). In effect, long distance traffics, typical of motorways and main roads, are characterised by high percentage of heavy vehicles, while local traffics, typical of secondary roads, are lighter and composed mostly by two axle lorries. Besides, it should be considered that, as confirmed by recent traffic data, European traffics show a trend characterised by

- marked increase of the number of articulated lorries vis-à-vis the simultaneous reduction of the number lorries with trailer;

- reduction of the number of three axle lorries for the benefit of two axle lorries;

- increase of the average load per lorry.