Initial Deformation of the PETRA3 slab

1. Initial Deformation of the PETRA3 slab Markus Schlösser IWAA 2010, 13.-17. September 2010

2. accuracy requirements (components) old octants: s = 300µm / 150m (transverse & height) new octant: magnet – magnet s = 50µm girder – girder s = 100µm (transverse and height) s = 500µm (longitudinal) (TDR, 2004) • introduction

3. floor of new experimental hall • introduction • Monolithic floor slab made from reinforced concrete • 300m length • 30m width • 1m thickness • (without joint)

4. making of concrete slab concrete delivery and filling of pump • introduction pouring of concrete smoothing of concrete surface

5. cross section of slab top layer, epoxy, t = 15 mm 34.37 34.36 1 (reinforced) concrete with steel fibres (approx. 1% fibers) 49 33.87 1.00 reinforced concrete C30/37 bitumen gliding sheet, t = 3 mm 50 subconcrete 33.37 5 05 3 equalizing layer base layer, concrete-mineral mixture

6. temperature of concrete (2007 – 2009) • temperature setting of concrete 4th epoch 1st epoch 2nd epoch 3rd epoch

7. temperature of concrete (2008) daily variation • temperature 2nd epoch activation of air-condition 1st epoch start of survey in the new hall

8. thermal expansion of concrete slab aconcrete = 10 · 10-6 / K (theoretical value) l = 300m  dl = 3mm / K dT = 22°C – 16°C = 6K  dL16 = 18mm • Problem: • Installation starts at 16°C, final temperature at 22°C • predicted movement is 18mm • accuracy is at the 100µm level • coarse alignment mechanics of most components can notbe moved by more than a few mm • analytical models • Solution: • introduce analytical model • predict position of each network fiducial at 22°C • stakeout coordinates are not affected • independent from the actual temperature

9. models for expansion of slab • 1st approach • network measurement taken at 16.2°C • estimate position of each monument at 22°C from analytical model (linear / circular) • 2nd approach • network measurements taken at 16.2°C and 20.4°C • estimate parameters for analytical model from combination of measurement epochs • 3rd approach • network measurements taken at 16.2°C and 20.4°C • extrapolate position of each monument at 22°C from empirical model • 4th approach • network measurement taken at 22°C • no model necessary • analytical models

10. 1st approach • network measurement taken at 16.2°C • estimate position of each monument at 22°C with analytical model (linear / circular) Each monument gets radial and tangential shift component, Dr = h (r) Dj = x (j) aconcrete from literature • analytical models line of no tangential movement line of no radial movement

11. 2nd approach • network measurements taken at 16.2°C and 20.4°C • estimate parameters of analytical model by combining two measurement epochs Each monument gets radial and tangential shift component, BUT Dr = h (r,j) Dj = x (r,j) estimate aconcrete line of no tangential movement • analytical models line of no radial movement

12. 3rd approach • network measurements taken at 16.2°C and 20.4°C • extrapolate position of each monument at 22°C from empirical model lines of identical tangential movement Each monument gets radial and tangential shift component, Dr = hh (r,j) Dj = xx (r,j) estimate aconcrete • analytical models lines of identical radial movement

13. movements 05/2008 -> 02/2009(16.2 -> 22.0°C) 11.5 3.3 • measure-ments 10.0

14. modell errors 05/2008 -> 02/2009 2.0 3.1 • measure-ments 3.6

15. movements 08/2008 -> 02/2009(20.4 -> 22.0°C) 3.2 0.9 • measure-ments 2.5

16. modell errors 08/2008 -> 02/2009 0.5 0.6 • measure-ments 0.5 (0.8)

17. movements 02/2009 -> 05/2009(22.0 -> 22.0°C) 1.3 • measure-ments 1.2

18. tangential shifts • measure-ments

19. radial shifts • measure-ments

20. height changes • measure-ments

21. high precision measurement, made by civil engineers

22. Summary • empirical thermal expansion coefficient (longitudinal)aconcrete = 12 · 10-6 / K • center line of no radial movement is not in the middle of the slab • height change 05/2008 – 05/2009 approx. 1.5 bis 2.0 mm • deformation seems not to have finished after reaching the final temperature of the slab • result