Dynamic failure analysis of concrete dams under air blast using coupled Euler-Lagrange finite element method

doi:10.1007/s11709-018-0465-7

Front. Struct. Civ. Eng.

2019, Vol. 13

Issue (1) : 15-37 https://doi.org/10.1007/s11709-018-0465-7

RESEARCH ARTICLE

Dynamic failure analysis of concrete dams under air blast using coupled Euler-Lagrange finite element method

Farhoud KALATEH(

)

Faculty of Civil Engineering, University of Tabriz, Tabriz 5166616471, Iran

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Abstract

In this study, the air blast response of the concrete dams including dam-reservoir interaction and acoustic cavitation in the reservoir is investigated. The finite element (FE) developed code are used to build three-dimensional (3D) finite element models of concrete dams. A fully coupled Euler-Lagrange formulation has been adopted herein. A previous developed model including the strain rate effects is employed to model the concrete material behavior subjected to blast loading. In addition, a one-fluid cavitating model is employed for the simulation of acoustic cavitation in the fluid domain. A parametric study is conducted to evaluate the effects of the air blast loading on the response of concrete dam systems. Hence, the analyses are performed for different heights of dam and different values of the charge distance from the charge center. Numerical results revealed that 1) concrete arch dams are more vulnerable to air blast loading than concrete gravity dams; 2) reservoir has mitigation effect on the response of concrete dams; 3) acoustic cavitation intensify crest displacement of concrete dams.

Keywords air blast loading concrete dams finite element dam-reservoir interaction cavitation concrete damage model

Corresponding Author(s): Farhoud KALATEH

Just Accepted Date: 12 February 2018 Online First Date: 19 April 2018 Issue Date: 04 January 2019

Cite this article:

Farhoud KALATEH. Dynamic failure analysis of concrete dams under air blast using coupled Euler-Lagrange finite element method[J]. Front. Struct. Civ. Eng., 2019, 13(1): 15-37.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-018-0465-7
https://academic.hep.com.cn/fsce/EN/Y2019/V13/I1/15

Fig.1 Concrete dam-reservoir finite element model subjected to air blast loading. (a) Arch dam-reservoir; (b) gravity dam-reservoir

Fig.2 Schematic of a typical air blast profile

Range $(m/kg 1/3)$	$a 0$	$a 1$	$a 2$	$a 3$
$0.3 ≤ Z ≤ 2.4$	1.769362e–2	–2.032568e–2	5.395856e–1	–3.010011e–2
$2.4 ≤ Z ≤ 12$	–2.251241	1.765820	1.140477e–1	–4.066734e–3
$12 ≤ Z ≤ 500$	–6.852501	2.907447	9.466282e–5	–9.344539e–8

Tab.1 Fitted polynomial coefficients to define the arrival time [²⁸]

Range $(m/kg 1/3)$	$c 0$	$c 1$	$c 2$	$c 3$	$c 4$	$c 5$
$0.3 ≤ Z ≤ 0.95$	308.473000	–2146.9200000	5953.29000000	–8226.0300000	5687.43000000	–1573.41
$0.95 ≤ Z ≤ 2.4$	17.607400	–26.7855000	17.86070000	–5.6555700	0.69416000	0.00
$2.4 ≤ Z ≤ 6.5$	4.432160	–2.7187700	0.74197300	–0.0934132	0.00446971	0.00
$6.5 ≤ Z ≤ 40$	0.711610	–0.0626846	0.00332532	–8.2404900e–5	7.61885000e–7	0.00
$40 ≤ Z ≤ 500$	0.251614	–0.00176758	9.51638000e-6	–2.1971200	1.7913500e–11	0.00

Tab.2 Fitted polynomial coefficients to define the decay coefficient [²⁸]

Parameter	Value
Parameters for EOS
Reference concrete densoity $ρ s$ (kg/m³)	2750
Porous density $ρ 0$ (kg/m³)	2314
Initial sound speed $C 0$ (m/s)	2920
Initial compaction pressure $p e$ (MPa)	23.3
Solid compaction pressure $p s$ (GPa)	6
Polynomia EOS parameters $A 1$ (GPa)	151.3
Polynomia EOS parameters $A 2$ (GPa)	39.58
Polynomia EOS parameters $A 3$ (GPa)	9.04
Polynomia EOS parameters $B 0$	1.22
Polynomia EOS parameters $B 1$	1.22
Polynomia EOS parameters $T 1$ (GPa)	151.3
Polynomia EOS parameters $T 2$ (GPa)	0
Parameters for strength
Damage parameters $α t, α c$	0.5
Static tensile threshold strain in uniaxial tension $ε st0$	$3.5 × 10 − 4$
Static tensile threshold strain in uniaxial compression $ε sc0$	$3.5 × 10 − 3$
Tensile strength $f t$ (MPa)	4
Compressive strength $f c$ (MPa)	50

Tab.3 Material parameter for ordinary concrete [⁴⁶]

Fig.3 (a) Wall structure and fluid domain; (b) ramp base acceleration; (c) finite element discretization

Fig.4 (a) Hydrodynamic pressure time history at the bottom of flexible wall subjected to ramp acceleration; (b) horizontal displacement time history at the top of the flexible wall structure subjected to ramp acceleration

Fig.5 Comparison of results at the bottom of vertical wall subjected to ramp acceleration, using proposed method with analytical solution

Fig.6 (a) One-dimensional of the cavitation model implementation with the Bleich and Sandler problem; (b) finite element model

Fig.7 Velocity response history of a floating structure subjected to a shock wave-effects of cavitation

Fig.8 Finite element model of concrete gravity dam and relevant dimensions and arrangement of target points and target element. (a) Coarse mesh; (b) refined mesh

Fig.9 Finite element model of concrete arch dam and relevant dimensions and arrangement of target points and target element. (a) Coarse mesh; (b) refined mesh

Fig.10 Affected zone of concrete gravity dam by air blast loading. (a) Upper part; (b) middle part

Fig.11 Comparison of Konya concrete gravity dam crest displacement time history subjected to air blast loading for coarse and refined FE meshes

Fig.12 Crest displacement time histories at the Point A for different dam heights subjected to air blast at the upper part of downstream face of gravity dam. (a) H=150 m; (b) H=110 m; (c) H=80 m; (d) H= 50 m

Fig.13 Time history of cavitating nodal point number in the reservoir during air blast shock loading at the upper part of dam: (a) H=150 m; (b) H=110 m

Fig.14 Hydrodynamic pressure time histories at the Point C for different dam heights. (a) Charge at the upper part of gravity dam; (b) charge at the middle part of gravity dam

Fig.15 The damage propagation process of concrete gravity dam subjected to air blast loading close to upper part of downstream face of dam for different height of dam. (a) H=150 m; (b) H = 110 m; (c) H =80 m; (d) H =50 m

Fig.16 Crest displacement time histories at the Point A for different dam heights subjected to air blast located at the middle part of downstream face of gravity dam. (a) H=150 m; (b) H =110 m; (c) H =80 m; (d) H = 50 m

Fig.17 The damage propagation process of concrete gravity dam subjected to air blast loading close to middle part of downstream face of dam for different height of dam. (a) H=150 m, (b) H= 110 m; (c) H=80 m; (d) H=50 m

Fig.18 Affected zone of concrete arch dam by air blast loading. (a) Upper part; (b) middle part

Fig.19 Comparison of Morrow point concrete arch dam crest displacement time history subjected to air blast loading for coarse and refined FE meshes

Fig.20 Crest displacement time histories at the point A for different dam heights subjected to air blast located at the upper part of downstream face of arch dam: (a) H=250 m; (b) H=200 m; (c) H=150 m; (d) H=100 m

Fig.21 The damage propagation process of concrete arch dam subjected to air blast loading close to upper part of downstream face of dam for different height of dam. (a) H=250 m; (b) H= 200 m; (c) H=150 m; (d) H=100 m

Fig.22 Crest displacement time histories at the Point A for different dam heights subjected to air blast located at the middle part of downstream face of arch dam. (a) H=250 m; (b) H=200 m; (c) H=150 m; (d) H=100 m

Fig.23 The damage propagation process of concrete arch dam subjected to air blast loading close to middle part of downstream face of dam for different height of dam. (a) H=250 m; (b) H= 200 m, (c) H=150 m, (d) H=100 m

Fig.24 Hydrodynamic pressure time histories at the Point C for different dam heights. (a) Charge at the upper part of arch dam; (b) charge at the middle of arch dam

Fig.25 Extremes of maximum principal stress due to dynamic response of Morrow Point arch dam to air blast loading close to the upper part of dam for different height. (a) H=250 m; (b) H=200 m; (c) H=150 m; (d) H=100 m

Fig.26 Extremes of maximum principal stress due to dynamic response of Morrow Point arch dam to air blast loading close to the middle part of dam for different height. (a) H=250 m; (b) H=200 m; (c) H=150 m; (d) H=100 m

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