Dr Aïssa Mellal, Civil Engineer STUCKY SA, Switzerland NUMERICS IN GEOTECHNICS AND STRUCTURES 2012 30-31 August 2012, EPFL, Lausanne
Outline o Introduction o Types of Concrete Dams o Purpose of Numerical Analyses of Dams o Investigated Issues o Illustrative Examples Selected Topics o Conclusion
Introduction Dams: Various types: earth, rock-fill, concrete, CVC, RCC, CFRD Complex massive structures: high impact (safety, environment) Evolving structures: rehabilitation/reinforcement (age), heightening Computing capabilities: Various software/tools Modeling of complex phenomena
Types of Concrete Dams Constraints: Valley shape (U, V ) Economical optimization (material availability, transport ) Dam function (storage, hydroelectricity, irrigation, flood control ) Gravity Dams Arch Dams Type Buttress Dams Weir Dams
Grande Dixence gravity dam (H = 285 m) Luzzone arch dam (H = 225 m) Lucendro buttress dam (H = 73 m) Verbois weir dam (H = 34 m)
Purpose of Numerical Analyses of Dams New Construction Project Heightening Project Context Rehabilitation / Strenghtening Project Regulatory Safety Assessment
Construction of Dernier dam Heightening of Cambambe Dam Strenghtening of Les Toules dam Seismic safety assessment of Spitallamm dam
Investigated Issues Topics: Shape/geometry optimization: new structures (feasibility studies) Strength assessment: existing structures Required strength: new structures Transient thermal analyses: early age concrete, model calibration Sliding/overturning stability: dam / potentially detaching blocks Interaction existing/new structures: heightening / strenghtening/ rehabilitation Operation safety of hydromechanical equipments (gates)
Seismic safety assessment of an arch dam
Seismic safety assessment of an arch dam Y Z X Finite element model of the dam (downstream view)
Seismic safety assessment of an arch dam LB RB US face s max = 5.6 MPa @ 21.50 s RB LB DS face s max = 3.6 MPa @ 21.50 s Envelope of dynamic stresses (full reservoir level)
Contrainte [MPa] - Compression / + Traction Seismic safety assessment of an arch dam s max = 5.6 MPa @ 21.50 s 12 Contrainte principale majeure S1 -Lac plein - Séisme 1 CH 8 4 0-4 0 5 10 15 20 25 30 35 40 Contrainte S1 Temps [s] Résistance dynamique à la traction (limite OFEN) Envelope of major principal stresses S1 Time-history of major principal stress S1 Major principal stresses at time t = 21.50 s Directions of principal stresses at time t = 21.50 s
Heightening of an arch dam Investigated topics: Strength assessment: existing concrete Required strength: new concrete Interface existing/new concrete Transient thermal analyses: early age concrete Dam abutment stability
Stress (MPa) Heightening of an arch dam Enveloppe of the principal stresses - Winter 5 3 1-1 -3-5 -7-9 -11-13 (a) (b) (c) (d) (e) -15 0 5 10 15 20 25 30 35 (a) Construction stages (b) Pre-heightening loading (NLWL: 98 masl) (c) Heightening stages (d) Static loads (e) Dynamic load S1 max Time (sec) S3 min S1 max [MPa] S3 min [MPa] Old concrete 2.50-8.93 New concrete 2.55-7.23
Heightening of an arch dam Major (maximum) dynamic principal stress S1 (Winter, OBE) US face LB RB DS face RB LB t = 20.80 s S1 max [MPa] Old concrete 2.43 New concrete 2.55
Heightening of an arch dam Major (maximum) dynamic principal stress S1 (Winter, OBE) US face LB RB DS face RB LB t = 21.97 s S1 max [MPa] Old concrete 2.50 New concrete 2.01
Stability analysis of a detaching block Common practice: Stability analysis is usually carried out considering the block as completely unrestrained on its lateral faces which assumes that the vertical contraction joints remain permanently opened during earthquake. Instantaneous or time-dependent factors of safety are evaluated considering a 2D section of the block. Permanent displacements are obtained from a Newmark sliding block analysis Question: How does the lateral confinement affect the sliding and overturning stability of the block? Is the assumption of permanently opened contraction joints during earthquake too conservative?
Stability analysis of a detaching block Stress resultants on block s faces 1911.24 m Time histories of normal and shear stresses on potential sliding surface 1899.74 m 1900.74 m Time histories of internal N, T and M Time histories of reactions to external loads
Stability analysis of a detaching block Internal forces and moments on the block s faces Integration of stresses on block s faces N Lateral M Lateral T Lateral v T Lateral h T Lateral v T Lateral h N Lateral M Lateral N Base M Base
N [MN] - Compression / + Tension Stability analysis of a detaching block Normal Force - Full Reservoir Level N Lateral M Lateral T Lateral v T Lateral h N Base M Base T Lateral v T Lateral h N Lateral M Lateral 300 200 100 0-100 -200-300 0 5 10 15 20 25 30 Time [s] N lateral N base
T [MN] - DS / + US Stability analysis of a detaching block Shear Force - Full Reservoir Level N Lateral M Lateral T Lateral v T Lateral h N Base M Base T Lateral v T Lateral h N Lateral M Lateral 30 20 10 0-10 -20-30 0 5 10 15 20 25 30 Time [s] T lateral T base
M [MN.m] - DS / + US Stability analysis of a detaching block Moment - Full Reservoir Level N Lateral M Lateral T Lateral v T Lateral h N Base M Base T Lateral v T Lateral h N Lateral M Lateral 90 60 30 0-30 -60-90 0 5 10 15 20 25 30 Time [s] M lateral M base
Stability analysis of a detaching block 1911.24 m 1908.74 m W v Sliding factor of safety: Q v Q h W h G Overturning factor of safety: 1899.74 m U
Factor of Safety Factor of Safety Stability analysis of a detaching block Sliding stability Without lateral confinement (permanently opened contraction joints) With lateral confinement (closed joints if under compression) 100 Sliding Stability - Full Reservoir Level 100 Sliding Stability - Full Reservoir Level 10 10 1 1 0.1 0 5 10 15 20 25 30 0.1 0 5 10 15 20 25 30 Time [s] Time [s]
Factor of Safety Factor of Safety Stability analysis of a detaching block Overturning stability Without lateral confinement (permanently opened contraction joints) With lateral confinement (closed joints if under compression) Overturning Stability - Full Reservoir Level Overturning Stability - Full Reservoir Level 100 100 10 10 1 1 0.1 0 5 10 15 20 25 30 0.1 0 5 10 15 20 25 30 Time [s] Time [s]
Stability analysis of a detaching block For arch dams, the lateral compression due to the pressure of water has a tremendous effect on the overall stability of a potentially detaching block. Neglecting the lateral confinement, assuming permanently opened contraction joints during earthquake, may result in too conservative factors of safety and, in certain cases, to costly and unnecessary retrofit works.
Operation safety of hydromechanical equipments Flap gate Hydraulic jack Outlet gate 5. Seismic safety assessment
Operation safety of hydromechanical equipments
Operation safety of hydromechanical equipments Steel strength assessment Flap gate Outlet gate S1 (traction) S3 (compression) S1 (traction) S3 (compression) vanne-clapet Déplacement Amont-Aval max (mm) temps (s) Contrainte de compression max (MPa) Contrainte de traction max (MPa) Eté Séisme 1 4.35 20.84-35.2 56.4 Hiver Séisme 1 5.11 20.84-35.3 58.7 Séisme 2 5.32 13.28-36.1 64.4 Séisme 3 5.16 7.94-37.1 59.8 vanne-secteur Déplacement Amont-Aval max (mm) temps (s) Contrainte de compression max (MPa) Contrainte de traction max (MPa) 4.81 15.52-217.4 126.0 4.91 15.52-209.2 126.7 5.04 23.22-221.0 134.9 5.70 19.42-220.5 133.1 5. Seismic safety assessment
Déplacement relatif des contreforts [m] - écartement / + rapprochement x 0.001 Déplacement relatif des contreforts [m] - écartement / + rapprochement x 0.001 Operation safety of hydromechanical equipments Operation of gates: jamming hazard Vanne clapet 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 Vanne clapet 0.31 mm @ 11.00 s 0.12 mm @ 11.00 s 0 5 10 15 20 25 30 Temps (s) Dépl. relatif haut Dépl. relatif bas Vanne secteur Vanne secteur Déplacement relatif latéral des contreforts Flap gate Outlet gap Opening width 4.90 5.00 Gate width 4.82 4.92 Wall-gate gap (mm) 40 40 0.06 0.05 0.04 0.03 0.02 0.01 0-0.01 0.05 mm @ 18.62 s 0.01 mm @ 17.88 s 0 5 10 15 20 25 30 Temps (s) Dépl. relatif haut Dépl. relatif bas 5. Seismic safety assessment
Operation safety of hydromechanical equipments Operation of hydraulic jacks: buckling hazard Flap gate jack Outlet gate jack Bar diameter (mm) 150 100 Area (mm2) 17671.5 7854.0 Length (m) 6.35 5.27 Critical Effort N (kn) 1277.3 366.3 Maximal compression (dynamic) of jacks: N critique 2 EI l 2 0 N Compression N max (kn) Vérin vanne-clapet temps (s) Contrainte de compression max (MPa) Compression N max (kn) Vérin vanne-secteur temps (s) Contrainte de compression max (MPa) Eté, Lac plein Séisme 1-418.9 20.84-23.7-123.4 0.01-15.7 Hiver, Lac plein Séisme 1-419.8 20.84-23.8-199.8 0.01-25.4 Séisme 2-432.0 13.28-24.4-199.8 0.01-25.4 Séisme 3-437.2 7.94-24.7-199.8 0.01-25.4 N N Buckling safety afctors: Vérin vanne-clapet Vérin vanne-secteur Eté, Lac plein Séisme 1 3.05 2.97 N Hiver, Lac plein Séisme 1 3.04 1.83 Séisme 2 2.96 1.83 Séisme 3 2.92 1.83 5. Seismic safety assessment
Conclusion Static and dynamic analyses of dams are necessary and powerful tools for the design and the assessment of dam s local and global strength and stability Combined effects of thermal, static and dynamic mechanical loads can be evaluated Main dam s behaviour including early age concrete, crack evolution in time, dynamic oscillations are modeled Sliding and overturning stability are accurately evaluated considering time evolution of all forces acting on the dam or a potentially detaching block Operation safety of hydromechanical equipments is verified, considering gates strength, jamming and buckling.