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14th ICOLD Benchmark Workshop 2017 Theme B – Static and seismic analysis of an arch-gravity dam
Description of the theme
Frédéric ANDRIAN., Pierre AGRESTI, Geoffrey MATHIEU, Alain YZIQUEL (dam expert)
Stockholm, September 6th
Contents
■ Specificities of arch-gravity dams
■ The Janneh dam
■ Models and calculation stages
■ Material parameters
■ Provided data
2
3
Specificities of arch-gravity dams
■ Shear strength by means of self-weight • At the dam / foundation interface • At possible other weak planes
■ Crack opening at the upstream toe generally not
tolerated under normal load cases
■ 2D force equilibrium method (beam theory) • Isostatic model • Coulomb friction approach • (+) Newmark integration (dynamic analysis)
CASE OF STRAIGHT GRAVITY DAMS IN WIDE VALLEYS Lift joints
Dam / foundation interface
Bedrock joints
4
Specificities of arch-gravity dams
■ Arch effect triggered even under normal load cases
• Restricted to dams with low radius of curvature • 7th ICOLD Benchmark, Scalere dam
■ Consequences • Central blocks offloaded, bank blocks overloaded • Bank blocks with upstream toe opening under
normal load cases ■ Need of 3D stress/strain approach
• Hyperstatic model • How to manage the upstream toe opening? • Is sliding a failure mechanism?
CASE OF ARCH-GRAVITY DAMS
Plunging arch – plane view and 3D downstream view
5
Janneh Dam
■ Lebanon, Nahr Ibrahim • Water provision • Hydropower (100 MW)
■ Sound dolomite and dolomitic sandstone
• 25 GPa (rock mass scale) ■ Dead Sea Transform + Mount
Lebanon thrust • 0.37g (975-yr return period) OBE • 0.51g SEE • (0.44g / 0.6g 2017 update)
KEY INFORMATION
6
Janneh Dam
■ RCC arch-gravity dam • Earthquake-resistance
■ Main dimensions • Height: 157m • Crest length: 300m • Thickness: 10m (crest), 66.3m (base) • Radius of curvature: 240m • 0.8/1 downstream slope down to vertical truncation
■ Converging excavation geometry • Plug effect at the dam base • Better incidence angle of the plunging arch at higher
elevations
KEY INFORMATION
7
Models and calculation stages FLOW CHART
Self-weight
Static Analyses
Model 1
Linear elastic, No uplift
Model 2
Non-linear dam / foundation interface,
Bi-linear uplift
Model 3
Non-linear dam / foundation interface,
uplift with crack-related propagation
Dynamic Analyses
Model 4
Non-linear, pseudo-static, spectral
acceleration of the 1st Eigen mode
Models 5 / 7
Linear time history, simplified / advanced dynamic interactions
Models 6 / 8
Non-linear dam / foundation interface, simplified / advanced dynamic interactions
Mandatory stages
Optional stages
■ Subsequent stages with increasing complexity
8
Models and calculation stages
■ RCC dam : horizontal layers ■ Vertical construction joints / thermo-mechanical
effects not considered ■ Staged construction – 10 subsequent layers at
least ■ Non-linear dam / foundation interface if possible ■ Initial state for every models ■ Displacements reset to zero at the end of
construction
SELF-WEIGHT ANALYSIS SPECIFICATIONS
9
Models and calculation stages
■ Dam attached to the foundation ■ Uplift not taken into account
■ Non-linear dam / foundation interface ■ Bi-linear uplift
■ Model 2 + propagation of full uplift at the cracked regions of dam / foundation interface
■ Propagation law to be described by the participants
MODEL 1 SPECIFICATIONS
MODEL 2 SPECIFICATIONS
MODEL 3 SPECIFICATIONS
10
Models and calculation stages
■ X-displacements vs. Elevation for B0 and B5
■ Arch / hoop stresses vs Elevation for B0
■ Resultant shear and normal stresses at the dam / foundation interface for B0 and B5
• Downstream face of interface only for B5 • Shear resultant projected in radial direction for B5
■ Crack-opening along a radial path at the dam /
foundation interface of B5 (models 2 and 3)
REQUESTED RESULTS – STATIC MODELS
11
Models and calculation stages
■ Non-linear dam / foundation interface ■ Pseudo-static approach ■ Spectral acceleration of the 1st Eigen mode ■ Steady uplift ■ Westergaard equivalent pressures ■ Inertia (incl. Westergaard pressures) toward:
• (1st case) Downstream • (2nd case) Upstream
MODEL 4 SPECIFICATIONS
12
Models and calculation stages
■ Time history analysis ■ Dam attached to the foundation
• Non-linear dam / foundation interface (model 6) ■ 5% damping ratio (dam + foundation) ■ Simplified dam / foundation interaction
• Massless foundation • Added mass approach
■ Modal masses ≥ 85% in X-direction (model 5 only)
MODEL 5 (MODEL 6) SPECIFICATIONS
13
Models and calculation stages
■ Recently validated with Japanese dams ■ Time history analysis ■ Dam attached to the foundation
• Non-linear dam / foundation interface (model 8) ■ 5% damping ratio (dam only) ■ Advanced dam / foundation interaction
• Foundation with density + Radiation BC • Water compressibility + Radiation BC • Absorption of bottom waves of reservoir neglected
■ Interaction approaches to be described by the participants
MODEL 7 (MODEL 8) SPECIFICATIONS
14
Models and calculation stages
■ X-displacements at the crest of B0 and B5 ■ For B0 (EL. 764.5 and EL. 839) and B5 (EL. 788.5
and 847) • Histories of x-directed accelerations • Response spectra (5% damping) of the accelerations
■ Histories of opening and sliding at the US and DS toes of B0 and B5
■ Check the progressive effects of • Non-linearities • Use of advanced interaction approaches
REQUESTED RESULTS – DYNAMIC MODELS (1/2)
15
Models and calculation stages
■ Maximum (tensile) vertical stresses of the vertically-truncated toe of B0 (EL. 713.5 and 737)
• Is a horizontal crack starting from DS at these locations possible?
■ Maximum (compressive) arch / hoop stress at the upstream face (EL. 779)
• How far is the arch effect mobilized? ■ Maximum (tensile) arch / hoop stress at the crest of
B0 (EL. 839) • Are the vertical joints expected to open?
■ Check the effects of the progressive approaches
REQUESTED RESULTS – DYNAMIC MODELS (2/2)
16
Material Parameters
Material Density (kg/m3)
Static deformation
modulus (GPa)
Dynamic deformation
modulus (GPa) Poisson’s
ratio p-wave velocity
(m/s) c (kPa) ϕ (°)
Tensile strength
(MPa)
Concrete 2400 20 30 0.2 - - - -
Bedrock 2800 (1) 25 30 0.25 - - - -
Water 1000 0.5 1414(2) - - -
Dam / foundation interface(3)
- - - - 0 45 0
[1] To be used when relevant.
[2] When the compressibility of water needs to be considered. [3] For non-linear calculations.
■ Stiff bedrock • Pessimistic for the dam / foundation interface opening • Pessimistic for the radiation of outer waves for dynamic analysis
17
Provided data
■ 2 Ansys compatible mesh files • 1 for static + simplified dynamic interactions • 1 for advanced dynamic interactions
■ STEP and DXF geometry files per geometry
■ 2 sets of 2 accelerograms (x+z)
• 1 set for simplified interaction • 1 set for advanced interaction (outcrop at the bottom
of the valley, pessimistic)
www.arteliagroup.com
Thank you for your attention!