Evaluation of the behaviour of an arch-gravity dam featuring a pre-existing crack Dr Aïssa Mellal, Civil Engineer STUCKY SA, Switzerland NUMERICS IN GEOTECHNICS AND STRUCTURES - ZSoil Days - 1-2 September 2011, Lausanne
Spitallamm Dam l = 258 m h = 114 m
Objectives 1. Crack Identification 2. Reliable Numerical Model of the Dam (incl. THM calibration) 3. Seismic safety assessment
Crack location and measurements 1900 1880 Cement grout 1860 1840 1820 Cement grout 1800 Section 3a
Crack location and measurements Crack zone 6a 6 5a 5 4a 4 3a 3 2a 2 1a 1 0a 1908.74 m 1900.74 m 1899.74 m Block 3a Block 3a
Depth from dam crest [m] Depth from dam crest [m] Inclinometer measurements Upstream-Downstream Displacements Measures with inclinometer 1900 1880 1860 1840 1820 1800 Initial measure: 01.10.1996 Reservoir level: 1898.90 Reference measure: 04.03.1997 Reservoir level: 1862.36 6 1911.24 Crest 1885.0 RIGHT BANK 1911.24 Crest Borehole B1, Center 5 B3 4 3a B1& B2 3 B4 Downstream view 2 1 LEFT BANK Range 2005 Range 2004 Range 2003 Range 2002 Range 2001 Boreholes B2, B3 and B4-35 -30-25 -20-15 -10-5 0 5 0 5 Borehole B1, CENTER UPSTREAM 25 US Displacement [mm] DS -35-30 -25-20 -15-10 -5 0 5 0 5 10 15 20 Borehole B2, CENTER DOWNSTREAM 25 US Displacement [mm] DS US Displacement [mm] DS 10 15 20 Depth from dam crest [m] Depth from dam crest [m] -35-30 -25-20 -15-10 -5 0 5 0 5 10 15 20 Borehole B3, RIGHT 25 US Displacement [mm] DS -35-30 -25-20 -15-10 -5 0 5 0 5 10 15 20 Borehole B4, LEFT 25 Face concrete "Trog" concrete 1885.0 Mass concrete
Crack location and measurements 1900 1880 1860 1840 1820 1800 Section 3a
Numerical modelling approach 3D FE Model dam incl. crack + foundation 3D Model Transient Thermal analysis Thermal calibration TM Coupling 3D Model Mechanical analysis Displacement calibration Static and dynamic evaluation Stability analysis global and local Retrofit proposal
Geometry and Finite element mesh (3D) Pre-existing crack: Frictional contact Concrete: Linear elastic Solid BC Rock: Linear elastic
Tensile (major principal stress) stress fields Full reservoir No thermal effects Zone of potential horizontal cracking
Progressive crack opening Full reservoir no thermal effects No crack model Horizontal crack model Complete crack model S1=190 kpa S1=80 kpa S1=20 kpa S1: major principal (tensile) stress
Crack configuration at the interface Face / Intermediate concrete 6a 6 5a 5 4a 4 3a 3 2a 2 1a 1 0a 1899.74 m 1900.74 m Pre-existing crack zone 1830 m Section 3a
Loading condition Combined effects Water level + Air-water temperature + solar radiation Air temperature + downstream solar radiation Air temperature + upstream solar radiation Varying level Water temperature
Thermal evolution 2008 February May August November UNIT [ C]
Results of thermal analysis Comparison with the measurements
Temperature ( C) Temperature ( C) Temperature ( C) Temperature ( C) Results of thermal analysis Comparison with the measurements 14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0-2.0-4.0-6.0 Sec. 3a T1 (T1) Measured Model 14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0-2.0-4.0-6.0 Sec. 3a T2.1 (T2) Measured Model Time (date) Time (date) 14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0-2.0-4.0-6.0 Sec. 3a T2.2 (T3) Measured Model 14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0-2.0-4.0-6.0 Sec. 3a T2.3 (T4) Measured Model Time (date) Time (date)
Temperature ( C) Temperature ( C) Temperature ( C) Temperature ( C) Results of thermal analysis Comparison with the measurements 14.0 Sec. 3a T3.1 (T5) Measured Model 14.0 Sec. 3a T3.2 (T6) Measured Model 12.0 12.0 10.0 10.0 8.0 6.0 4.0 2.0 0.0-2.0-4.0-6.0 8.0 6.0 4.0 2.0 0.0-2.0-4.0-6.0 Time (date) Time (date) 14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0-2.0-4.0-6.0 Sec. 3a T3.3 (T7) Measured Model 14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0-2.0-4.0-6.0 Sec. 3a T3.4 (T8) Measured Model Time (date) Time (date)
Thermo-mechanical analysis Model vs. measured displacement
Thermo-mechanical analysis Model vs. measured displacement
Thermo-mechanical analysis Model vs. measured displacement (with assumed linear deviation)
Thermo-mechanical analysis Crack Opening Model vs. joint meter measurements (with assumed linear deviation)
Crack opening Extreme US calculated displacement: 18.65 mm (13.08.2003)
Crack opening Major principal stress at crack tip: (+) Tensile / (-) Compressive stresses
Comments on model validation Thermal calibration using daily temperature measurements leads to good agreement between calculated and measured temperatures at all dam levels Displacement (daily) calibration shows good agreement between calculated and measured diplacements below crack level Calculated displacements of dam s upper arch follow the same trend and order of magnitude as measurements, but irreversible displacements were not reproduced. When a linear deviation is assumed, there is a close correspondance between calculated and measured top displacements Calculated crack opening (max) is close to joint meter measurements (~4 mm) Stresses at lower extremity of the crack (~1830 msm) are permanently compressive under seasonal load variations (hydrostatic pressure) Proposed finite element model reasonably simulates dam s mechanical behaviour under transient static loads (mechanical + thermal). It is therefore considered as suitable to evaluate the dynamic response of the dam
Numerical modelling approach 3D FE Model dam incl. crack + foundation 3D Model Transient Thermal analysis Thermal calibration TM Coupling 3D Model Mechanical analysis Displacement calibration Static and dynamic evaluation Stability analysis global and local Retrofit proposal
Input for dynamic analyses Accelerograms: Friuli Sept. 15, 1976 earthquake, San Rocco station Peak ground acceleration: 0.17 g (OBE) Dynamic elastic modulus: E dyn = 1.25 E stat Damping: 5% Water level: full reservoir level (1908.74 msm) Temperature gradient: Winter: T(15.11.2007) - T(30.04.2007) Concrete strength: f Dyn = 1.5 x f Stat f c (Stat/Dyn), MPa f t (Stat/Dyn), MPa Mass concrete 25 / 37.5 3 / 4.5 Face concrete 49 / 73.5 3 / 4.5 «Trog» concrete 36 / 54 3 / 4.5 Source: Stucky Report no. 4400/4013, July 2003
Spitallamm I MSK = 7.8 Return Period 1 000 years (OBE) log a h = 0.26 I MSK + 0.19 a h = 0.17 g
Seismic safety assessment Accelerograms and corresponding response spectra
Temperature field 30.04.2007 (reference) T air = 6.7 C, T water = 2.6 C, Water level: ~1860 m LB RB US view RB LB DS view
Temperature field 15.11.2007 (Winter) T air = -11.2 C, T water = 3.5 C, Water level: 1901.4 m LB RB US view RB LB DS view
Temperature gradient Winter thermal gradient LB RB US view RB LB DS view
Principal stresses Self-weight LB RB s min = -0.2 MPa s max = 0.1 MPa US view RB LB s min = -1.4 MPa s max = 0.0 MPa DS view
Principal stresses Hydrostatic pressure: full reservoir level (1908.74 msm) LB RB s min = -1.3 MPa s max = -0.1 MPa US view RB LB s min = -0.8 MPa s max = 0.2 MPa DS view
Principal stresses Temperature gradient: DT Winter LB RB s min = -0.1 MPa s max = 1.3 MPa US view RB LB s min = -0.3 MPa s max = 0.0 MPa DS view
Principal stresses Self-weight + Full reservoir level (1908.74 msm) LB RB s min = -1.2 MPa s max = -0.1 MPa US view RB LB s min = -1.3 MPa s max = -0.8 MPa DS view
Principal stresses Self-weight + Full reservoir level (1908.74 msm) + DT Winter LB RB s min = -0.8 MPa s max = 0.9 MPa US view RB LB s min = -1.4 MPa s max = -0.8 MPa DS view
Dynamic analysis Absolute displacement Major principal stress
Displacement (mm) - DS / + US Dynamic upstream-downstream displacement Full reservoir level (1908.74 msm) OBE 5% damping - Winter (+) (-) 50 40 (a) (b) (c) (d) (e) 30 20 10 0 5.6 mm @13.22 s -10-20 -30-40 -50 0 5 10 15 20 25 30 Time (sec) (a) Construction stages (b) Hydrostatic load (1908.74 masl) (c) Temperature gradient (d) Dynamic properties (e) Dynamic load
Absolute crack opening (mm) Dynamic absolute crack opening Full reservoir level (1908.74 msm) OBE 5% damping - Winter 25 (a) (b) (c) (d) (e) 20 15 12.5 mm @13.24 s 10 5 0 0 5 10 15 20 25 30 Time (sec) (a) (b) (c) (d) (e) Construction stages Hydrostatic load (1908.74 masl) Temperature gradient Dynamic properties Dynamic load
Stress evaluation locations D C B A
Stress (MPa) - Compression / + Tension Dynamic major principal stresses S1 Full reservoir level (1908.74 msm) OBE 5% damping - Winter D C B A 6 5 4 3 2 1 0-1 -2 A (1830 m) B (1850 m) C (1880 m) D (1900 m) (a) (b) (c) (d) (e) 3.7 MPa @13.33 s 0 5 10 15 20 25 30 Time (sec) (a) (b) (c) (d) (e) Construction stages Hydrostatic load (1908.74 masl) Temperature gradient Dynamic properties Dynamic load
Dynamic principal stresses at time of extreme S1 (t = 13.33 s) Self-weight + Full reservoir level (1908.74 msm) + Earthquake (OBE) LB RB s min = -0.7 MPa s max = 3.7 MPa US view RB LB s min = -1.2 MPa s max = -0.7 MPa DS view
Stability analysis of a detaching bloc 1899.74 m 1900.74 m Overturning Lift joint opening Sliding Tensile vertical stresses 1830 m
Stability analysis of a detaching bloc 1911.24 msm 1908.74 msm W v Q v Q h W h G SSF = 5.25 (sliding) OSF = 1.43 (overturning) 1899.74 msm U
Comments on stability analysis Both sliding and overturning stability are satisfied for OBE earthquake, with full reservoir level (1908.74 msm) Water pressure has a stabilizing effect against sliding towards upstream (hydrostatic) but a destabilizing effect on overturning (hydrodynamic)
Conclusion 3D finite element of an arch-dam including a crack Combined effects of thermal, static and dynamic mechanical loads Successful evaluation of main dam s behaviour characteristics including crack evolution in time Dynamic analyses show that seismic safety of the dam is guaranteed regarding both concrete strength and stability against sliding and overturning