Tunnel lighting calculation model based on bidirectional reflectance distribution function: Considering the dynamic changes in light transmittance in road tunnels

The current tunnel lighting calculation method does not completely consider the dynamic change in light transmittance in a tunnel and reflection characteristics of the tunnel sidewall. Thus, the measured and calculated values of road surface illuminance present a considerable difference, which seriously affects the tunnel lighting design and quality evaluation. To overcome this limitation, in this study, in addition to theoretical analysis and measured experiments, the changing trend in light attenuation is analyzed and a light attenuation model is established. Next, a bidirectional reflectance distribution function that can accurately reflect the reflection characteristics of tunnel sidewall is combined with the light attenuation model and calculation steps based on optical theory to construct a tunnel lighting calculation model considering light transmittance (TLCM-LT). Finally, theoretical calculation and actual measurement verification are conducted via an experimental tunnel simulation, and the results obtained using TLCM-LT are compared with the values calculated based on the Commission Internationale de l'éclairage (CIE), Illuminating Engineering Society of North America (IESNA), and Industry Standards of the People's Republic of China (JTG) specifications. The results show that the average relative error of the TLCM-LT in a smoke-free environment is 1.31 %. In the presence of smoke, the average relative error of the model fluctuates in the range of 2.19–6.8 % with the change in light transmittance in the tunnel, which is significantly lower than the errors obtained based on the CIE, IESNA, and JTG specifications. Compared with a cement sidewall, the average increase rates in road surface illuminance and illuminance uniformity of the highly diffuse reflective sidewall are 23.21 and 3.65 %, respectively.