CARACTERIZACIÓN DE LAS EMPRESA PETROQUÍMICAS

The moving force model does not allow for the dynamic coefficient due to the track defects. Unfortunately the author has been unable to find any literature that sug- gests how to incorporate this phenomena into a reliability analysis. The dynamic coefficient due to the track defects, ϕ, was therefore taken into account by adjust- ing the results of the moving force model. This dynamic coefficient was estimated using the expression in (UIC, 1979) which can also be found in (CEN, 1995) and is reproduced in Appendix B, see this appendix for the calculation of ϕ. It is assumed that the track quality is of a high standard which allows the lower value to be used. The dynamic factor due to allowance for the effect of track defects will therefore be given by:

Φ_td = 1 + 0.5ϕ (7.1)

The speed of each train was recorded by the WILD system and the first bending frequency was either taken from the 2D bridge model used in the moving force model or the upper frequency of Appendix B, see (B.9), which yields the higher of the two possible values of ϕ.

Results

8.1

General

This chapter shows the results of the simulations, the distribution fitting and the reliability analysis. Descriptions of the methodology and assumptions are given in earlier chapters. However, this introduction briefly recalls some of the main assumptions in order to clarify the presentation of the results.

The track defects were not taken into consideration in the simulations of the trains crossing hypothetical bridges and only the dynamic effects due to constant moving forces were considered. The obtained moments were therefore adjusted to allow for the effects of track defects. This was done using the UIC recommendations, see section 7.4, and was carried out using two different first bending frequency values for each bridge. The first being the same as the bending frequency used during simulation and the other being the upper frequency of the UIC leaflet (UIC, 1979). These three variations will therefore be presented as no defect, defect using actual

frequency and defect using UIC upper frequency in the following tables and figures.

The results are also presented for different load models, those using extreme value theory and those using a Peaks-Over-Threshold method, see Chapter 5. Within the EVT model, the GEV distribution is often used as the distribution for modelling the load effect. The special case of the GEV, the Gumbel distribution, is also used for modelling the load effect and these distinctions should hopefully be clear within the the context of the text. In the case of the POT method, the GPD is used to model the load effect and to calculate return loads. However, in order to perform a reliability analysis using the POT method, the GPD has been converted to a GEV using (5.34–5.36). Although this method ultimately uses the GEV in the reliability analysis it will be referred to as the POT or the GPD method in order to distinguish it from the method using classical extreme value theory.

In the chapter discussing reliability theory and modelling, two assumptions were made as to the modelling of the resistance of the material. The first being that the resistance model is conservatively chosen and represents the 5 % quantile of the real value of resistance, while the other assumes that the resistance model represents the

mean value of resistance. These two different assumptions lead respectively to (4.54) and (4.56) which are used to estimate the mean value of resistance. As an example, the simplified stress block in reinforced concrete beams is used to model the concrete resistance, now is this model conservatively chosen and if so which quantile does it represent? These are referred to in the following sections as the 5 % quantile and the mean value assumption for the resistance model.

All the results presented in this chapter are for a 3.5 month period and for the mixed freight and passenger line at Sannahed close to a marshalling yard called Hallsberg, see section 7.1.1.

The load effects studied in this thesis are the mid-span moments of simply supported bridges. In the presentation, all the moments including the return loads have been divided by the characteristic moment including the dynamic factor M_uic71Φ but ex- cluding the partial safety for traffic load, γq, see section 3.5.5.

The self-weight ratio ν is the load effect of the self-weight of the bridge from the original design expressed as a ratio of the characteristic load effect of the UIC 71 or SW/2 load model including the dynamic amplification factor, see section 4.9. In the following sections the results are often calculated showing two values for each span, e.g. in the reliability analysis and for the return loads. These two results are derived from the range of parameter estimates for the GEV and GPD models. The parameter estimates used for the different calculations are the original estimates obtained directly from the data using one of the parameter estimation methods i.e.

ˆ

ξ, ˆσ, ˆµ. The other set of parameters are those that produced the 95 % quantile

of the 50 year return load using the covariance-variance matrices from the original parameter estimates, see section 5.3.5 and section 5.4.5. These parameter estimates, or the calculations deriving from them, have been referred to as the 95 % quantile value, although strictly speaking these are not 95 % quantiles of the value itself but of that defined above. The parameter estimates in these cases are denoted ˆξ_0.95, ˆ

σ_0.95, ˆµ_0.95.