14th icold benchmark workshop 2017

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

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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

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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

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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

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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

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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

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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

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■ 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



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■ 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

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■ 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


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■ 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

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■ 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

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■ 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)

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■ 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)

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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

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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)

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Thank you for your attention!

14th icold benchmark workshop 2017

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