Rail Ground-Borne Noise and Vibration Prediction Uncertainties

Abstract

On projects where there is limited or only high-level information relating to source, path and receiver components, the uncertainty associated with ground-borne noise and vibration predictions can be large and prediction uncertainties of up to 10 dB(A) have been reported and sometimes applied as a safety factor (engineering margin) on underground railway projects. However, this simplistic and somewhat ad hoc approach is not well founded quantitatively. Furthermore, during the detailed design stage of projects, such large safety factors can be very costly in terms of the required mitigation measures. The uncertainty associated with some modelling input parameters can be quantified and minimised via repeated measurements, however many other parameters and the uncertainty associated with predictions can only be established via published data or engineering judgement. On a recent underground railway tunnel project, a quantitative approach was used with the aim of improving estimates of prediction uncertainties and to better advise the design team of the level of design risk associated with the predictions. Field measurements were also utilised to reduce the uncertainty associated with the ground-borne noise and vibration predictions. Prediction uncertainties were determined on the basis of the methodologies described in the ‘Guide to the expression of uncertainty in measurement’ (GUM) and by establishing an uncertainty budget for each part of the ground-borne noise and prediction process (source, path and receiver). For each modelling input parameter (or source of uncertainty), an estimate of the likely range (minimum and maximum) of values was made on the basis of measurement results, published data and engineering judgement. This paper presents the uncertainty budget calculations where for each parameter, an estimate of the standard uncertainty (uncertainty contribution) has been made on the basis of the half range, the probability distribution and associated distribution divisor. This paper focuses on the results and outcomes at a representative receiver above the railway tunnel which was selected to establish and illustrate the uncertainties in the modelling predictions. The combined standard uncertainty at this location was calculated at 2.5 dB(A) for the source parameters, 2.0 dB(A) for the path parameters and 2.2 dB(A) for the receiver parameters. The combined standard uncertainty for the whole prediction path was calculated to be 3.9 dB(A). A Monte Carlo simulation with 100,000 iterations was also undertaken to provide an independent calculation of the combined standard uncertainty.

In summary, the prediction uncertainty analysis found:

• the predicted ground-borne noise levels are expected to lie within ±3.9 dB(A) [±1σ] of the mean with 68% confidence;

• by adding an engineering margin of 1σ or 3.9 dB(A) to the predicted noise level, the probability of the actual (or true) noise level being less than the predicted noise level is 84%, or conversely, the risk that the actual noise level will be higher than the predicted noise level is 16%; and

• for a 90 and 95% confidence that the actual (or true) noise level will be less than the predicted noise level, the following engineering margins should respectively be added to the modelling results: 5.0 and 6.4 dB(A).