Safety of Rockfill Dam upon Underwater Explosion Limin Zhang Tianhua Xu

Transcription

1 Wuhan University 26 May 215 Safety of Rockfill Dam upon Underwater Explosion Limin Zhang Tianhua Xu

2 Acknowledgement Breaching mechanisms of earth and rockfill dams under extreme dynamic loading conditions and associated risk assessment (NSFC 海外及港澳学者合作研究基金, ) 2

3 Outline Explosion physics and applications Numerical model Constitutive models Numerical implementation Response of a core-wall dam to upstream underwater explosion Conclusions 3

4 Blasting Civil engineering Mining engineering Military use-bombing Open pit mining blasting Tunnel excavation Slope excavation Demolition Military use 4

5 Blasting Energy release and transformation during an explosion Gas expansion Shock Fragmentation Explosives Detonation Production gas Surrounding materials Acceleration Damage Chemical energy Shock wave Heat, mechanical energy, Plastic deformation 5

6 Introduction to explosion physics Detonation Production gas Reaction zone Unreacted explosive C-J Plane: u CJ, p CJ, r CJ, T CJ, v CJ D u, p, r, T, v C-J Plane: Chapman-Jouget plane Production gas expansion JWL (Jones-Wilkins-Lee) equation of state (e.g. Zukas and Walters 1997) e p A 1 exp RV 1 B 1 exp R2V RV 1 R2V V p is pressure; A, B,, R 1 and R 2 are model coefficients; e is the initial internal energy per unit volume of explosive; and V is the relative volume, which can be calculated by V = v/v, where v and v are the current and initial specific volume, respectively. 6

7 Dams and blasting Dams around the world (Data from ICOLD (214)) dams ( h 15 m) in total Dams under blasting War time or terrorist attack e.g. Möhne Dam and Edersee Dam (German, World War II), Peruca Dam (Croatia, 1993) Engineering practice, disposal of landslide dams e.g. The Swir III dam (Russia, 1935) Earth dams Gravity dams Rockfill dams Others Arch dams Buttress dams Barrages Multiple arch dams (%) Percentage of different kinds of dams in the world Edersee Dam Möhne Dam 7

8 Core rockfill dams Upstream filter 1 Upstream filter 2 Downstream filter 1 Downstream filter 2 Upstream fine rockfill Downstream fine rockfill Mixed rockfill Upstream rockfill transition zone Upstream rockfill 1 Upstream rockfill Gravelly clay 76. Downstream rockfill Downstream rockfill 1 27 May 215 8

9 P ercent finer by w eight (% ) Susceptibility of liquefaction Susceptibility of liquefaction of a core rockfill dam (1) (2) (3) (4) Potentially liquefiable Most liquefiable (Following USNRC 1985) Susceptible to static liquefaction and flow sliding (Following Hunter and Fell 23) G rain size (m m ) Notes: N uozhadu Filter 1 Left N uozhadu Filter 1 R ight N uozhadu Filter 2 Left (1) Nuozhadu core material (Zhang et al. 25); (2) Nuozhadu filter I material (Yuan et al. 212); (3) Nuozhadu filter II material (Yuan et al. 212); (4) Nuozhadu rockfill material (Yuan et al. 212). N uozhadu F ilter 2 R ight N uozhadu R ockfillleft N uozhadu R ockfillright N uozhadu core M aterial 9

10 Research objectives To propose a constitutive model for soil under high strainrate loadings To implement the constitutive model for soil under high strain-rate loadings in a generic numerical platform to solve various engineering problems To study the response of a core/concrete faced rockfill dam to upstream underwater explosion with emphasis on blast wave propagation, pore pressure response and dam deformation 27 May 215 1

11 Outline Explosion physics and applications Numerical model Constitutive models Numerical implementation Response of a core-wall dam to upstream underwater explosion Conclusions 11

12 Dam profile Nuozhadu Dam Yunnan Province, China Height: m Storage capacity of reservoir: 2.37x1 1 m 3 Upstream filter 1 Upstream filter 2 Upstream fine rockfill Downstream filter 1 Downstream filter 2 Downstream fine rockfill Mixed rockfill Upstream rockfill transition zone Upstream rockfill 1 Upstream rockfill Gravelly clay 76. Downstream rockfill Downstream rockfill

13 Numerical model Center of blasting Downstream filter II y x Downstream filter I Air Upstream filter II Upstream filter I Center of blasting Phreatic line Downstream rockfill II Water Upstream rockfill I Upstream rockfill II Gravelly clay Downstream rockfill I 13

14 252 m 19.5 m Numerical model 12 m Center of blasting y x 9 m 14

15 Initial conditions Initial pore water pressure Assumptions: Steady seepage Saturated flow Hydraulic conductivity (m/s): Rockfill 1 & 2: 1.e-3 Filter 1: 5.e-5 Filter 2: 5.e-4 Core: 5.e-8 Phreatic line (kpa)

16 Initial conditions Initial stress state Linear elastic material: E = 1 MPa, n =.25 (MPa) Initial 1 st effective principal stress: Initial 3 rd effective principal stress: (MPa)

17 Outline Explosion physics and applications Numerical model Constitutive models Numerical implementation Response of a core-wall dam to upstream underwater explosion Conclusions 17

18 Explosive C4 Explosive JWL equation of state E p A 1 exp RV 1 B 1 exp R2V RV 1 R2V V A B.1295 E 9e 4 R 4.5 V 1. R High explosive burning model p Fp eos F 1 F max F,1 2tDA 3V el el 1 D*t Typical element l 3v 2A el el 18

19 Water and air Water Null material: deviatoric stress = Gruneisen equation of state 2 2 rc 1 1 / 2 a / 2 p E S1 1 S2 S V Viscosity of water is not considered Air bubbles and turbulent flow are not taken into account Air Null material: deviatoric stress = Equation of state of ideal gas: p r r 1 e C v is the specific heat at constant volume, is the specific heat at constant pressure 19

20 Dam materials Dam materials Rockfill I and II, Filters I and II, Core material (gravelly clay) High strain-rate bounding surface model: cyclic behavior; high strain-rate behavior p Bounding surface Critical surface r 1 =s 1 /p Yield surface n Dilation surface q r 2 =s 2 /p r 3 =s 3 /p T.H. Xu, L.M. Zhang Numerical implementation of a bounding surface plasticity model for sand under high strain-rate loadings in LS-DYNA. Computers and Geotechnics 66,

21 Deviatoric stress (kpa) Volumetric strain (%) Dam materials Model parameters for dam materials Rockfill I & II, gravelly clay: calibrated according to experimental data Filter I & II: use the parameters of a similar material (bedding material in a concrete face rockfill dam) Mechanical behavior Simulation: Rockfill ( 3 =15 kpa) Core ( 3 =5 kpa) Filter ( 3 =8 kpa) Axial strain (%) Test data: Rockfill ( 3 =15 kpa) Core ( 3 =15 kpa) Simulation: Rockfill ( 3 =15 kpa) Core ( 3 =5 kpa) Filter ( 6 3 =8 kpa) Axial strain (%) Test data: Rockfill ( 3 =15 kpa) Core ( 3 =15 kpa) 21

22 Volumetric strain (%) Deviatoric stress (kpa) Dam materials Simulation of high strain-rate triaxial tests Simulation.21%/s.23%/s 1495%/s Experiment.21%/s.23%/s 1495%/s -8 Simulation %/s.23%/s 1495%/s Experiment.21%/s.23%/s 1495%/s Axial strain (%) -2 (Crushed coral sand, 3 = 35 kpa, e in =.93, experimental data after Yamamuro et al. 211) Axial strain (%) 22

23 Undrained analysis The part of dam below the phreatic line is considered undrained Hydro-mechanics coupled analysis is not supported in LS-DYNA Loading duration << Time scale for excessive pore pressure dissipation Implementation of undrained stress integration σ ' D ε σ D ε f σ σ ' σ f f σ' σ' σ' σ σ σ f f f D f is the effective bulk modulus of the pore water/solid mixture, 1-1 times of that of the soil skeleton 27 May

24 Outline Explosion physics and applications Numerical model Constitutive models Numerical implementation Response of a core-wall dam to underwater explosion Conclusions 25

25 Solution loop Numerical platform: LS-DYNA Solution loop Update velocities Update time and check for termination Process kinematic based contact interfaces Update displacements and new geometry Update current time and check for termination START Apply force boundary conditions Process elements Update accelerations; apply kinematic boundary conditions Process penalty based contact interfaces 26

26 Space discretization 8-noded 1-point element 6 5 z 7 8 Discretized equation of motion n i 1 T T T T rnn adv B σdv rn fdv N tds v v v v i Reduced integration: 1-point element x 1 4 h g v g x h z g v J J d d d d 8,,,,

27 Time integration Time integration in LS-DYNA Central difference method Acceleration Ma P F n n n a M P F 1 n n n Geometry x x u n 1 n 1 Velocity v v a t n 1/2 n 1/2 n n Displacement u u v t n 1 n n 1/2 n 1/2 n = current time step (the nth time step) M = diagonal mass matrix; a n = acceleration; P n = external and body forces; F n = internal force, or the stress divergence tensor; v = velocity; u = displacement, respectively; t n+1/2 = ( t n + t n+1 )/2; x = geometry at t = ; and x n+1 = geometry at the (n+1)th time 28

28 Model implementation Stress integration scheme Modified Eulerian scheme with automatic error control (Xu & Zhang, 215) Initial stress state Strain increment Elasto-plastic stress updating Strain increment decomposition Substep initialization Elastic stress updating 1st- and 2nd-order Eulerian estimates of increments of stress and hardening parameters Error calculation and substep refinement Output stress state (all the substeps calculated) 29

29 178 mm Volumetric strain (%) Deviatoric stress (kpa) Model implementation Simulation of high strain-rate triaxial tests Axis of symmetry Simulation.21%/s.23%/s 1495%/s Experiment.21%/s.23%/s 1495%/s Simulation %/s Axial strain (%).23%/s 1495%/s -6 Experiment.21%/s.23%/s %/s mm Axial strain (%) (Crushed coral sand, 3 = 35 kpa, e in =.93, experimental data after Yamamuro et al. 211) 3

30 178 mm Model implementation Simulation of high strain-rate triaxial tests Stress wave propagation in soil specimens Axis of symmetry t 1 = 1x1 4 s t 2 = 5x1 4 s t 3 = 1x1 3 s 35 mm Reference vector: 3.5 m/s 31

31 Outline Explosion physics and applications Numerical model Constitutive models Numerical implementation Response of a core-wall dam to upstream underwater explosion Conclusions 32

32 Pressure (MPa) Water pressure (MPa) Blast-induced water pressure Blast-induced water pressure Distance to center of blasting = 3.4m Distance to center of blasting = 13.7 m Distance to center of blasting = 21.6 m Distance to center of blasting = 27.9m Distance to center of blasting = 34.3 m Distance to center of blasting = 39.8 m Water Time (ms) 1 CRD simulations CRD Simulation Fitted kg/m Fitted 26.8 kg/m Fitted kg/m Fitted 1 Explosive Distance to center of blasting (m) 33

33 Blast-wave propagation Ground velocity at selected instants Refraction Incident wave front 5 ms 125 ms Reference scale: 1 m/s (m/s) Reflection wave front 175 ms 25 ms 35 ms 45 ms 34

34 Blast-wave propagation Ground velocity at selected instants Reference scale: 1.6 m/s (m/s) 65 ms 85 ms 15 ms 125 ms 145 ms 195 ms 35

35 Peak velocity (m/s) Blast-wave propagation Contour of peak ground velocity (m/s) Maximum value: 15.8 m/s Reference scale: 16 m/s Location of blast wave reflection Saturated 4 Part Dry part Distance to center of blasting (m) 36

36 Excessove pore pressure (kpa) Excessove pore pressure (kpa) Excessove pore pressure (kpa) Pore pressure response Time histories of excessive pore pressure EL EL Time (ms) Time (ms) EL Time (ms) 37

37 Pore pressure response Excessive pore pressure at selected instants Unit: MPa ms 125 ms

38 Pore pressure response Excessive pore pressure at selected instants Unit: MPa ms ms ms ms

39 Pore pressure response Peak blast-induced excessive pore pressure (MPa) Maximum value: 62 MPa

40 Pore pressure response Pore pressure ratio u PPR 3 u = excessive pore pressure; 3 = initial 3 rd principal stress Peak pore pressure ratio

41 Pore pressure response Pore pressure ratio u PPR 3 u = excessive pore pressure; 3 = initial 3 rd principal stress Residual pore pressure ratio

42 Blast-induced deformation Residual volumetric strain Residual deviatoric strain (%) (%)

43 Blast-induced deformation Permanent x displacement Permanent y displacement (cm) (cm)

44 Summary and conclusions A rate-dependent bounding surface model for soil under high strain-rate loadings is developed and implemented into an explicit finite element platform, LS-DYNA. Stress waves are observed in soil specimens in high strain-rate triaxial tests. The response of a high-rise core rockfill dam to upstream underwater explosion is simulated. 2 kg/m, C4 explosive. The maximum peak ground velocity occurs nearest to the center of blasting, which is about 15 m/s. The attenuation of blast waves in the dry materials is faster than that in the saturated materials. The upstream filters may be at risk of liquefaction based on the calculated residual pore pressure ratio. The blast-induced permanent horizontal displacement and settlement are 6 cm and 8 cm, respectively. 45

45 Thank you for your attention 46

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