DYNAMIC BEHAVIOUR OF ROCKFALL SHELTERS

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This paper concerns the application and evaluation of the uncoupled design approach for rockfall protection tunnels that has been recently introduced by the authors.

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DYNAMIC BEHAVIOUR OF ROCKFALL SHELTERS

  1. 1. I  n  t  e  r  d  i  s  c  i  p  l  i  n  a  r  y    R  o  c  k  f  a  l  l    W  o  r  k  s  h  o  p           2  0  1  1  –  I  n  n  s  b  r  u  c  k  -­‐  I  g  l  s   DYNAMIC  BEHAVIOUR  OF  ROCKFALL  SHELTERS  Francesco Calvetti, Claudio di Prisco, Vittorio MoriggiFrancesco Tondini
  2. 2. Rockfall shelter typology: artificial tunnels covered by soil layer Calvetti & di Prisco: An uncoupled approach for the design of rockfall protection shelters WSL Interdisciplinary Workshop on Rockfall Protection 2008 June 23-25, Morschach, CH F1   F2   F3 F1 Impact force  F2 Actions on the shelter  F3 Structural actionsLocal interaction: boulder-soil surface Structural response Stress propagation Calvetti, di Prisco, Moriggi & Tondini
  3. 3. Uncoupled design approach, STEP 1: Impact force CHARTS FORn and F0 as a function of block size (dense sand-gravel soil layer) Calvetti, di Prisco, Moriggi & Tondini
  4. 4. Impact Force: design charts T1,2,3&4 as a function of falling height and block mass (dense sand-gravel soil layer) Calvetti, di Prisco, Moriggi & Tondini
  5. 5. Uncoupled design approach, STEP 2: Actions on shelter Impact wave propagation - dynamic stress diffusion Elastic solution B S ! MAX ( r ) = ! MAX ! f d ! f g r B ! MAXStress  [kPa]   Time  [s]   Calvetti, di Prisco, Moriggi & Tondini
  6. 6. Reference structure: cantilever shelter covered by soil cushion Calvetti, di Prisco, Moriggi & Tondini
  7. 7. FEM model of 1 moduleTendons   “GAP”  elements   (unilateral  contact)   Hinge   Calvetti, di Prisco, Moriggi & Tondini
  8. 8. FEM model of assembled structure •   6  Modules  (10  metres) • 12  Modules  (20  metres) • 18  Modules  (30  metres) • 24  Modules  (40  metres) “GAP” Elements Calvetti, di Prisco, Moriggi & Tondini
  9. 9. Reference impacts: Block mass: 7.8 tons Soil thickness 2-3 m (dense sand-gravel); Impact Energy : E= 1000-2000-5000 kJ (H = 13-26-65 m)   10000 9000 8000 1000 kJImpact force (kN) 7000 6000 2000 kJ 5000 kJ σMAX [kPa] 5000 4000 3000 2000 1000 0 0 0,02 0,04 0,06 0,08 0,1 time (s) r Calvetti, di Prisco, Moriggi & Tondini
  10. 10. Structural response as a function number of modules6 modules 24 modules Comparison 18 – 24 modules E 1000 kJ 2000 kJ 5000 kJ UY -1,8 % -1,9 % -0,06 % UX -6,1 % -7,7 % -10,5 % Calvetti, di Prisco, Moriggi & Tondini
  11. 11. Structural response as a function number of modules Tendon action Comparison   1000  kJ   2000  kJ   5000  kJ    6-­‐24  modules   -­‐38,43  %   -­‐45,58  %   -­‐54,71  %    18-­‐24  modules   -­‐6,42  %   -­‐8,44  %   -­‐11,48  %   Moment  @  C   2,00E+07   1,50E+07   1,00E+07   5,00E+06   T[s]   0,00E+00  M  [N*m]   0   0,05   0,1   0,15   0,2   0,25   0,3   -­‐5,00E+06   -­‐1,00E+07   -­‐1,50E+07   -­‐2,00E+07   -­‐2,50E+07   Calvetti, di Prisco, Moriggi & Tondini
  12. 12. Structural response as a function of distance from impact point Impact point d = 0 [m] Ux [m] d = 8,3 [m] d = 18,26 [m]Uy [m] M [N*m] Calvetti, di Prisco, Moriggi & Tondini
  13. 13. Structural response as a function of impulse shape 2,5   2    Impulse  Factor  [-­‐]   Molto  impulsivo  R  piccoli   2 1,5   Carico  Normale   1 1   0.5 Poco  impulsivo  R  piccoli   0,5   0   0   0,02   0,04   0,06   0,08   0,1   0,12   0,14   T  [s]   2 1 0.5 Ux [m]Uy [m] 2 1 0.5 Calvetti, di Prisco, Moriggi & Tondini
  14. 14. Structural response as a function of distance from impact point Impulse factor 2.0 Vertical displacements @ AUy [m] Impulse factor 0.5 T [s] Uy [m] T [s] Calvetti, di Prisco, Moriggi & Tondini
  15. 15. Structural response: dynamic amplification factors Impulse factor 1.0 1,6   Max. displacement under impulse load 6  ElemenS   1,55   12  ElemenS   1,5   18  ElemenS   Rd  [-­‐]     Static displacement under peak of impulsive force 1,45   24  ElemenS   1,4   1,35   1,3   0   1000   2000   3000   4000   5000   6000   Impact  Energy  [kJ]   Impulse factor 0.5 Impulse factor 1.0 Impulse factor 2.0 Calvetti, di Prisco, Moriggi & Tondini

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