Eurocode 1 – roughness factor cr(z)
What is the roughness factor for ?
The wind velocity is different depending on whether the building is on the coastline, in a forest or in a city center; the roughness factor is used to model the influence of the building environment on the mean wind speed at a given height and on the turbulence intensity.
How to calculate the roughness factor ?
First of all, the exposure factor method is only valid for a height up to zmax = 200m; beyond this height, the effect of the wind must be specifically studied.
- The terrain factor kr only depend of the roughness length z0
- z0,II is the roughness length for the terrain category II.
- The roughness factor cr at a given height z only depend of the roughness length z0 but with the limitation zmin ⩽ z ⩽ zmax
What are the terrain categories ?
The Eurocode provides five terrain categories with which values are associated:
- z0 is the roughness length in meters corresponding to the height at which the theoretical wind speed would become zero.
- zmin is the minimum height in meters corresponding to the threshold below which the pressure no longer reduces.
| Terrain category | z0 (m) | zmin (m) | |
|---|---|---|---|
| 0 | Sea, coastal area exposed to the open sea | 0.003 | 1 |
| I | Lakes or area with negligible vegetation and without obstacles | 0.01 | 1 |
| II | Area with low vegetation such as grass and isolated obstacles (trees, buildings) with separations of at least 20 obstacle heights | 0.05 | 2 |
| III | Area with regular cover of vegetation or buildings or with isolated obstacles with separations of maximum 20 obstacle heights (such as villages, suburban terrain, permanent forest) | 0.3 | 5 |
| IV | Area in which at least 15% of the surface is covered with buildings and their average height exceeds 15m | 1.0 | 10 |
These terrain categories, the values associated with them and the distance over which they are evaluated can be adapted for each country in their respective national annexes.
The terrain categories must be observed for each wind direction.
For a building with a rectangular base, the surrounding space can for example be divided into 4 sectors of 90° (-45° to + 45° compared to normal to the walls of the building).
Eurocode 1 part 1-4 indicates that the terrain must be observed at an angle of 30°, for each of the angular sectors of 90° it will therefore be necessary to observe the category of terrain on a slippery portion of 30°.
The lowest roughness length within any 30° angular wind sector should be used and small areas (less than 10% of the area under consideration) with deviating roughness may be ignored.
Belgium
France
Italy
Germany
The recommended procedure is not adopted.
Instead of the logarithmic wind profile used in equation (4.4), the power profile applies in Germany.
It also gives correct values of wind speed above a height of z = 200 m up to z = 300 m.
The roughness coefficient cr for the 4 terrain categories in the German appendix NA. B is :
\[c_r = \frac{v_m(z)}{v_m(10)} = 0.19 \times \left( \frac{z_0}{0.05} \right) \ln\left( \frac{10}{z_0} \right) \times \left( \frac{z}{10} \right)^\alpha\]