Civil Engineering March 2022 | Vol 30 No 2

32 March 2022 Civil Engineering I t is custom in design codes to specify a Dynamic Amplification Factor (DAF) larger than one, which is multiplied by the static load effects, ε S , to represent the total load effect, ε T . The DAF can be expressed as per Equation 1. DAF = ε T ε S (1) HISTORICAL DESIGN CODE APPROACH Design codes typically specify a DAF based on a study of light and heavy vehi- cles. It has been shown that this approach is conservative as heavier vehicles, which govern the maximum load effects, tend to cause the lowest dynamic amplification. The codes therefore fail to recognise the decreased probability of the maximum static load effects occurring simultane- ously with the maximum dynamic ampli- fication, leading to conservative results. Codes typically determine the DAF for single vehicle events, which are higher than for multiple vehicle events, although multiple vehicle events tend to govern the load effects on short to medium span bridges, leading to further conservatism. ASSESSMENT DYNAMIC RATIO To overcome the historical conservatism, the Assessment Dynamic Ratio (ADR) is introduced to compare the characteristic total load effects, εˆ T , to the characteristic static load effects, εˆ S . The ADR is ex- pressed in Equation 2. ADR = ˆε T ˆε S = G T –1 ( q ) G S –1 ( q ) (2) where G T = cumulative distribution func- tion of the total load effects; G S = cumula- tive distribution function of the static load effects; and q = the quantile of interest. If G T and G S are derived using daily maxima values, then q = 0.999997. Although derived for the assessment of existing structures, the principle is equally applicable to the determination of DAFs for design codes or for the probabi- listic design of new bridges. The ADR ensures that only the dynamic amplification values which occur together with the heaviest vehicles are included in assessment or design. Experimental research has shown that this approach leads to substantially smaller values than prescribed in current design codes. To determine a DAF for a new design code for South Africa would require a fully probabilistic study using measured vehicles from WIM together with a full vehicle bridge interaction software model, taking all influencing factors into account, and using the ADR approach. This is cur- rently not possible due to computational limitations. The purpose of this paper is to investigate the factors influencing DAF and, by comparison to other codes and studies, propose a DAF for the design of bridges in South Africa based on South African characteristics. FACTORS THAT INFLUENCE DYNAMIC AMPLIFICATION The factors the influence the DAF are summarised here. 1. Condition of the road surface Studies have shown that dynamic impact increases as the road surface condition decreases. The relationship between dynamic impact and pavement rough- ness are almost perfectly correlated. Regular pavement maintenance therefore has a beneficial effect on the dynamic amplification and is a cost-effective way to improve bridge safety. The condition of the bridge approaches and position of expansion joints also have a major impact on dynamic amplification. It has been shown that settlement of the bridge approaches, with or without ap- proach slabs, has a significant impact on the dynamic response of a bridge once the vehicle reaches and crosses the spans. Prof. Pierre van der Spuy Pr Eng Associate: Zutari Adjunct Associate Professor: Stellenbosch University pierre.vanderspuy@zutari.com pierrevds@sun.ac.za Dynamic amplification factor for South African bridges It is well known that dynamic effects cause increased load effects in bridge decks due to Vehicle Bridge Interaction. A new free-flow bridge live load model for short to medium span bridges in South Africa was developed by Stellenbosch University which is based on Weigh in Motion (WIM) data collected on National Route 3. As WIM stations are calibrated and the data is post-calibrated to remove dynamic effects, the new model is a static one. Codes typically determine the DAF for single vehicle events, which are higher than for multiple vehicle events, although multiple vehicle events tend to govern the load effects on short to medium span bridges, leading to further conservatism.