Numerical simulation of nonlinear structural responses of an arch dam to an underwater explosion

Accepted Manuscript Numerical simulation of nonlinear structural responses of an arch dam to an underwater explosion

Qi-Ling Zhang, Duan-You Li, Fan Wang, Bo Li PII: DOI: Reference:

S1350-6307(17)31344-4 doi:10.1016/j.engfailanal.2018.04.025 EFA 3453

To appear in:

Engineering Failure Analysis

Received date: Revised date: Accepted date:

13 November 2017 21 March 2018 12 April 2018

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ACCEPTED MANUSCRIPT Numerical simulation of nonlinear structural responses of an arch dam to an underwater explosion

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Qi-Ling Zhang , Duan-You Li , Fan Wang , Bo Li

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Duan-You Li Changjiang River Scientific Research Institute Jiuwanfang Road, Huangpu Street, Wuhan, China [email protected]

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Qi-Ling Zhang Changjiang River Scientific Research Institute Jiuwanfang Road, Huangpu Street, Wuhan, China [email protected]

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Fan Wang Department of Building and Real Estate, The Hong Kong Polytechnic University Kowloon, Hong Kong, China [email protected]

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Bo Li Changjiang River Scientific Research Institute Jiuwanfang Road, Huangpu Street, Wuhan, China [email protected]

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Corresponding author. Tel.: +86 27 82829860; fax: +86 27 82820548. E-mail addresses: [email protected] (Q.L. Zhang).  Corresponding author. Tel.: +86 27 82829860; fax: +86 27 82820548. E-mail addresses: [email protected] (Q.L. Zhang).

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Abstract This paper is a preliminary attempt to examine nonlinear structural responses of an arch dam to an underwater explosion (UNDEX) shock loading based on numerical simulation. The numerical simulation is based upon the explicit dynamics finite element program ABAQUS/Explicit. Both the dam-reservoir

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interaction and the contraction-joint non-linearity are considered. Our research has underlined the

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importance of the shear keys to the integrity of the arch dam. Failures of the shear keys make each

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monolith more independent and thus the dam structure as a whole more flexible. Two major failure modes of the arch dam have been identified: (a) a break-off failure of the monolith closest to the explosive source,

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and (b) tensile cracking of the dam base concrete. The presented simulation procedure based upon

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ABAQUS/Explicit is time-efficient and relatively undemanding owing to its cut-off computational strategy. We believe that it is more suitable for a large-scale three-dimensional UNDEX simulation involving an

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arch dam than the full-process simulation procedure.

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Keywords: arch dam; underwater explosion; dynamic analysis; contact non-linearity; shear key; concrete

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damage.

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1. Introduction Dams are an integral part of our infrastructure, equal in importance to bridges, roads, and airports. Any failure of them from any means could result in loss of life, significant property damage, lifeline disruption,

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and environmental damage. Consequently, dams are high-priority targets of military strikes in wartime

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[1-3]. In peacetime, dams have become targets of terrorist attacks, especially after the events of September

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11, 2001. The serious terrorism in the last two decades has brought an increased focus on infrastructure protection worldwide, including the security of dams. The Dam Safety and Security Act of 2002

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recognizes the importance of protecting America’s dams against terrorist attacks and the Act has been

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signed into US law [4].

Underwater explosion (UNDEX) may be the easiest and most feasible way to carry out attacks on dams

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for terrorists because of its stealth. Hence in recent years there is a growing body of literature that

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recognizes the importance of anti-UNDEX performance of dams. What we know about anti-UNDEX performance of dams is largely based upon numerical simulation that investigates how dam structures

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vibrate and damage when they experience UNDEX shock loadings. Preliminary work in this field focuses

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primarily on dynamic responses of a gravity dam to an UNDEX at various detonation depths [5]. Linsbauer [6] draws our attention to the stability of a postulated 5-m-long crack spreading perpendicular to the upstream face of a gravity dam, when the dam undergoes earthquake and UNDEX shock loadings. The studies by Zhang and Wang’s group offer probably the most comprehensive numerical analysis of structural performance of gravity dams subjected to UNDEX shock loadings [7-9]. Their use of the hydrocodes AUTODYN [8] and LS-DYNA [7] to predict damage propagation in and failure modes of gravity dams, respectively, seems entirely plausible. In a follow-up comparative study, Wang et al. [9]

ACCEPTED MANUSCRIPT reported that an UNDEX can produce significantly intenser structural responses of a gravity dam than an equivalent air explosion can do. More recent evidence [10] shows that the anti-UNDEX performance of a gravity dam can be over-evaluated when the in-dam spillways are not taken into account in the numerical model.

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Although the numerical studies presented thus far have provided important insights into anti-UNDEX

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performance of dams, a well-known criticism of numerical investigations is the validity of them. An

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experimental attempt has been made [11] aimed at predicting the damage to a gravity dam when the dam experiences far-field UNDEX shock loadings. Their use of a drop-hammer impact method to produce

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shock loadings seems to be acceptable. In a follow-up study, Lu et al. [12] carried out a supplementary

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numerical simulation of their experimental work [11] to better understand the failure process of the model dam. In another major study, Lu et al. [13] have suggested a similarity relationship, and this seems to be an

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innovative approach to quantifying links of physical parameters between a model dam and its prototype.

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The main limitation of the experimental work reviewed here [11-13] is the absence of the impounded water before the model dams. It is thus not yet known whether the absence of the impounded water has a serious

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effect on the experimental results.

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Although in recent years there has been growing interest in anti-UNDEX performance of dams, however, such studies remain narrow in focus dealing only with gravity dams. Compared with a gravity dam, an arch dam of a roughly equal height should have a markedly thinner body. From a qualitative point then, under an UNDEX shock loading an arch dam should perform at least no better than a gravity dam, if not worse. Unfortunately, little is known about anti-UNDEX performance of arch dams. For many years earthquakes have been considered as the biggest threat to arch dams. Consequently seismic performance of arch dams has received much attention over the past few decades. It has been

ACCEPTED MANUSCRIPT generally accepted so far that dam-reservoir interaction [14-17] and contraction-joint non-linearity [18-21] are two important factors which should be considered in seismic (dynamic) analysis of arch dams. This paper is a preliminary attempt to examine nonlinear structural responses of an arch dam to an UNDEX shock loading based on numerical simulation. The above two important factors are taken into consideration

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in the current numerical simulation. It is recognized that calibration of the numerical simulation results

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would require prototype and/or model test data, which are difficult to obtain under the current conditions.

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However, the presented numerical simulation procedure could be at least a practical strategy for preliminary assessment of anti-UNDEX performance of arch dams.

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2. Numerical Methodologies for Simulating UNDEXs

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Research into UNDEXs has a long history and there are two typical numerical methodologies for simulating them: Lagrangian and Eulerian [22]. In a Lagrangian calculation, the mesh is embedded in the

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material domain and the calculation solves for the position of the mesh at discrete points in time. The

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motion of the material is thus inferred from that of the mesh. Since the mass within each element of the mesh remains fixed, a Lagrangian calculation is relatively straightforward and fast. The main disadvantage

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of the Lagrangian calculation methodology for simulating UNDEXs is the low-distortion limitation of it.

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Severe material distortions induced by UNDEXs correspond to Lagrangian mesh distortions, leading to reductions in time steps and/or breakdowns in problem advancements. In a Eulerian calculation, the solution is advanced in time on a mesh fixed in space, instead of that fixed on the material as is done in a Lagrangian calculation. Accordingly the Lagrangian problem of mesh distortions can be avoided and time steps can remain roughly constant in a Eulerian calculation. So it seems that the Eulerian calculation methodology is particularly well suited to large-distortion dynamics simulation, such as UNDEX simulation. However, it is often dismissed as impractical for fluid-structure

ACCEPTED MANUSCRIPT interaction (FSI) analysis due to its high computational cost when handling elements with multiple fluid and/or solid materials. The coupled Eulerian-Lagrangian (CEL) calculation methodology employs both the Eulerian and Lagrangian methodologies in their most advantageous modes in separate (or overlapping) regions of a

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domain [23]. In a CEL calculation, the fluid and solid materials are modeled within their traditional frames

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of reference: Eulerian for fluid dynamics and Lagrangian for structural dynamics. The Eulerian and

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Lagrangian regions continuously interact with each other, allowing true coupling of a fluid and a structure. The Arbitrary Lagrangian-Eulerian (ALE) calculation methodology shares aspects with both Lagrangian

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and Eulerian ones; Lagrangian motion is computed every time step, followed by a remap phase in which

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the spatial mesh is either (a) not rezoned (Lagrangian), (b) rezoned to its original shape (Eulerian) or (c) rezoned to some more “advantageous” shape (between Lagrangian and Eulerian). In this way the spatial

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description of the mesh is neither restricted to following the material motion (Lagrangian) nor remaining

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fixed in space (Eulerian). The ALE method provides a way of coupling fluid dynamics to structural dynamics without interfacing two separate coordinate systems as is done in the CEL method. Consequently,

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the ALE method can be considered a superset of both the Eulerian and Lagrangian methods, but cannot be

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considered a superset of the CEL method. Owing to its capability for analyzing large deformation processes, the ALE method has been incorporated into the LS-DYNA hydrocode, which was frequently employed in different types of FSI analysis [24-25].

3. Current Application of Hydrocodes to Anti-UNDEX Numerical Simulation concerning Dams The CEL methodology has been incorporated in various hydrocodes, which were originally developed for military requirements related to explosives and high-velocity impact [23]. This class of tools has

ACCEPTED MANUSCRIPT recently found applicability to numerical analysis of structural performance of gravity dams subjected to UNDEX shock loadings. So far LS-DYNA [5, 7, 10] and AUTODYN [8-9] are among the most widely used hydrocodes in this field. Using these hydrocodes, researchers have been able to take into account the whole physical process of an UNDEX in numerical analysis, including detonation physics, shock wave

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propagation, bubble dynamics, FSI (if it exists) and large-strain structural plasticity and failure. However,

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the accuracy of such a comprehensive full-process simulation of an UNDEX strongly depends on the mesh

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size used in the Eulerian domain. Consequently, a full-process UNDEX simulation is generally computationally demanding and thus frequently unfeasible when facing a large-scale computational

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problem. This has led authors, for example Wang et al. [26], to investigate how to determine appropriate

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mesh sizes for cost-efficient yet reliable UNDEX numerical simulations. Also for this reason, much of the numerical research on this subject concerning gravity dams up to now has been restricted to limited

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modeling scales; single-monolith models are usually used [5-10].

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Extensive research [18-21] has shown that the three-dimensional effect as regards arch dams is significant when they are undergoing seismic (dynamic) loadings. Hence a full-scale model of an arch dam

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including all the monoliths of it is necessary for numerically predicting nonlinear structural responses of it

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to an UNDEX shock loading. A full-scale arch-dam model should bring about a large modeling scale of the impounded water and thus multiply the computational cost. In this context, it would be best to employ a more practical numerical simulation procedure for preliminary assessment of anti-UNDEX performance of arch dams.

4. Features of UNDEX Simulation in ABAQUS 4.1. Coupled Acoustic-structural Analysis Acoustic analysis in ABAQUS is used to model sound propagation, emission and radiation problems. It

ACCEPTED MANUSCRIPT can include incident wave loadings to model effects such as UNDEX shock loadings on structures interacting with fluids. In this case, fluids are described with acoustic elements and coupled acoustic-structural analysis can model FSI problems. Various boundary conditions can be applied to an acoustic medium. The relationship between the

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pressure of the acoustic medium and the normal motion at its boundary is specified by a boundary

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impedance. The impedance boundary condition at any point along the acoustic medium surface is

uout 

1 1 p p k c

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governed by

(1)

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where uout is the acoustic particle velocity in the outward normal direction of the acoustic medium

1 is the k 1 proportionality coefficient between the pressure and the displacement normal to the surface; is the c

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surface; p is the acoustic pressure; p is the time rate of change of the acoustic pressure;

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proportionality coefficient between the pressure and the velocity normal to the surface. This model can be

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conceptualized as a spring and dashpot in series placed between the acoustic medium and a rigid wall. The spring and dashpot parameters are k and c, respectively, defined per unit area of the interface surface.

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At a fluid-structure interface, there is a transfer of momentum and energy between the media. The

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pressure field modeled with acoustic elements creates normal surface traction on the structure. The acceleration field modeled with structural elements, in turn, creates counterforces at the fluid boundary. In this case the boundary condition can be conceptualized as a spring and dashpot in series placed between the fluid and the structure. The expression (1) for the outward velocity still holds, with uout now being the relative outward velocity of the fluid and the structure: uout  n  (uf  us )

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where us is the velocity of the structure, uf is the velocity of the fluid at the boundary, and n is the

ACCEPTED MANUSCRIPT outward normal to the fluid. The surface-based procedure is the only available method for enforcing acoustic-structural couplings in ABAQUS/Explicit, which is ideally suited for analyzing high-speed dynamic events such as UNDEXs. This method requires that structural and acoustic meshes use separate nodes. At their interface, two

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surfaces should be defined on the structural and acoustic meshes. The interaction between them can be

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defined with a surface-based tie constraint. In general, degrees of freedom common to both surfaces are

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tied, and any other degrees of freedom are unconstrained. However, the case of structural-acoustic constraints is an exception to this rule. In this case appropriate relations between the acoustic pressure on

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structural-acoustic coupling, as mentioned above.

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the fluid surface and the displacements/velocities on the solid surface are formed internally for the

4.2. Incident Wave Loading

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The analysis starting point of a typical UNDEX simulation is usually the detonation of explosive

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charges. The standard Jones, Wilkins, and Lee equation of state is generally preferred for modeling explosive charges. However, UNDEX simulation in ABAQUS tends to focus more on incident wave

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loadings due to detonation of explosive charges rather than detonation physics. As indicated in Fig. 1 [27],

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the incident wave loadings on the acoustic and/or solid meshes depend on the location of the source node, the properties of the propagating fluid and the pulse loading time history specified at the reference (“standoff”) node. The user-defined pulse history at the reference node is assumed to apply with no time delay, phase shift or spreading loss.

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Fig. 1. Incident wave loading model [27]

The reference node should be defined so that it is closer to the source than any point on the solid surface,

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ensuring that the analysis begins before the wave overtakes any portion of the solid surface. To save

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analysis time, the reference node is typically defined on or near the fluid-structure interface where the incoming incident wave would be first deflected. In such an extreme case, the analysis starting point is

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postponed from the detonation of explosive charges to the onset of the loading, namely to the time when

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the incident wave reaches the target structure. In other words, the explosion event and the subsequent shock wave propagation process before the wave impinges on the target structure are ignored.

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Due to the absence of simulation of the explosion event and the subsequent shock wave propagation

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process, initialization of the acoustic field should be performed at the beginning of the first direct-integration dynamic step. All incident wave loading definitions in the first step are considered, and all acoustic-element nodes are initialized to the incident wave field at time zero. This initialization not only saves computational time but also applies the incident wave loading without significant numerical dissipation or distortion, thus reducing the mesh density requirement for the acoustic field.

5. Numerical Simulation 5.1. Numerical Model

ACCEPTED MANUSCRIPT A double-curvature arch dam located in Hubei province, China, is chosen as the study subject of the current numerical simulation. It has a maximum height of 141.00 m and a crest length of 284.61 m. The crest width is 5.50 m and the maximum base width is 22.70 m. The width-to-height ratio of the river valley is 1.89 and the thickness-to-height ratio of the dam is 0.17. The dam consists of six monoliths.

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The current numerical simulation is based upon the explicit dynamics finite element program

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ABAQUS/Explicit. Figure 2 shows the global numerical model of the arch dam-water-foundation rock

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system and the finite element mesh used to model the dam body. The upstream impounded water level is 15 m below the dam crest elevation. The dam and foundation rock are simulated by C3D8 8-node linear

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brick elements. The impounded water is meshed by AC3D4 4-node linear tetrahedron elements. The FSI

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between the water and the dam body, and between the water and the foundation rock, is defined at their common wetted interfaces with surface-based tie constraints. Surface-based contact pairs are defined at the

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monolith-to-monolith interfaces with the Coulomb friction model to simulate the interaction between

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adjacent monoliths. To date there has been little agreement on the value assignment of the kinetic friction coefficient between adjacent monoliths of arch dams. Previous parametric studies on the kinetic friction

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coefficient with regard to arch dams [18] have been exploratory in nature. A key study on the

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concrete-to-concrete friction is that of Tassios and Vintzēleou [28], in which the mechanism of load transfer along unreinforced concrete interfaces was experimentally investigated for different surface roughnesses. It was found that the concrete-to-concrete friction coefficient is approximately 0.4-0.5 when the normal compressive stress is at a 0.50-2.00 MPa level for smooth interfaces. However, for rough interfaces the measured friction-coefficient values are significantly higher. In this study the kinetic monolith-to-monolith friction coefficient is taken as 0.6 as an assumption. It is important to point out that this assumption as regards the friction coefficient is very tentative.

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Fig. 2. Numerical model: (a) Arch dam-water-foundation rock system; (b) Dam body

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It is a common practice in arch dams to have shear boxes or shear keys at contraction joints, which together with friction effect transfers of shear between adjacent monoliths. Shear keys are either beveled or

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unbeveled. An unbeveled shear key of a considerable height can prevent slippage between the joint faces.

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In this case, only opening and closing of contraction joints are considered in numerical analysis [20-21]. In the case of beveled shear keys, the two joint faces can have limited slippage when the joint is only partially

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open. Under the circumstances, not only opening-closing but also sliding behavior at contraction joints

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should be considered in numerical analysis [18]. In the present study, for simplicity the shear keys are not actually modeled in line with their physical shapes, dimensions or locations. Instead, five groups of axial

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spring (SPRINGA) elements are created at the five contraction joints along the radial or vertical (cantilever)

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directions to model the shear keys’ roles in transferring shear between adjacent monoliths, as shown in Fig. 3. Two extreme working conditions of the shear keys (unbeveled) are considered hereon: effective and ineffective. In the effective condition, the shear keys work well and accordingly a huge value of 106 MN/m is assigned to the stiffnesses of the spring elements. In the ineffective condition, the shear keys are assumed to be completely unable to work and thus a zero value is assigned to the stiffnesses of the spring elements. Hereafter the acronyms SK-E and SK-I will be used to refer to the terms ‘shear keys effective’ and ‘shear keys ineffective’ for brevity, respectively.

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Fig. 3. Axial spring elements modeling the shear keys’ roles

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The numerical model consists of 13977 continuum elements for the dam body, 10845 continuum elements for the foundation rock, 27440 acoustic elements for the impounded water, and 43 spring

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elements for the shear keys.

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5.2. Calculation Parameters

The modulus of elasticity of the dam concrete is taken as 28 GPa, the Poisson’s ratio as 0.167, and the

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mass density as 2500 kg/m3. The modulus of elasticity of the foundation material is taken as 20 GPa, the

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Poisson’s ratio as 0.24, and the mass density as 2400 kg/m3. For the water, the bulk modulus is 2.14 GPa, and the mass density is 1000 kg/m3. The speed of sound in the water is assumed to be 1500 m/s, which

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defines the rate of propagation of shock waves.

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The plastic-damage model in ABAQUS is primarily intended to provide a general capability for the analysis of concrete structures under cyclic and/or dynamic loadings. It is based on the models proposed by Lubliner et al. [29] and by Lee and Fenves [30]. It has been demonstrated that the model’s capability for predicting dynamic responses and various failure modes of reinforced concrete beams under blast loadings is satisfactory [31]. The plastic-damage model is thus employed hereon to represent the inelastic behavior of the dam concrete. The tensile strength of the concrete is taken as 1.75 MPa, and the compressive strength as 17 MPa. Figure 4 shows the employed uniaxial stress versus strain and damage variable versus

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strain curves.

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Fig. 4. Employed uniaxial stress versus strain and damage variable versus strain curves for the dam concrete: (a) Tensile; (b) Compressive

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The time period of the numerical analysis is 1 s and the time interval for result output is set to be 0.01 s.

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The explicit central-difference time integration rule in conjunction with the automatic time incrementation scheme [27] is employed for the numerical calculation. The central-difference operator is conditionally

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stable. The stability is maintained by limiting the time increment for each step to a very small value. More

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details on how to estimate the stable time increment size can be found in [27]. It should be noted that as there is no iteration involved in the explicit method, convergence problems are not an issue.

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Publications that concentrate on seismic analysis of arch dams more frequently adopt a constant

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damping mechanism with 5% damping for some or all vibration modes of the dams [14-16, 18]. This modeling strategy has been adopted by Lu et al. [13] in their UNDEX simulation concerning a gravity dam. Omidi et al. [32] call into question the constant damping mechanism and point out that this kind of damping creates artificial damping forces as cracks open with large relative velocity. The damping forces thus restrain the crack opening by transferring artificial stresses across the crack. Compared with seismic responses, UNDEX-induced responses of arch dams are more transient and violent. The damping effect should thus play a less important role in UNDEX-induced responses of arch dams. In this context, the

ACCEPTED MANUSCRIPT current numerical simulation does not take into account the damping effect. It is worth noting that such simplification concerning the damping effect should produce somewhat overestimated simulation results with regard to the UNDEX-induced responses of the arch dam. 5.3. Boundary Conditions

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Zero velocity boundary conditions are enforced for the four sides and bottom of the foundation rock. A

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nonreflecting boundary condition is specified on the upstream surface of the water domain such that

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acoustic waves impinging on this boundary would not be reflected back into the computational domain. The pressure (degree of freedom 8) on the top surface of the water domain is set to zero to enforce a

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free-surface boundary condition.

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5.4. UNDEX Shock Loading

Considering the practicability of UNDEX implementations for terrorists, the explosive source is

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assumed to be located in the mid-cross-section of the No. 3 monolith of the dam, 2 m below the upstream

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impounded water level and 10 m from the upstream face of the dam. The reference node is defined on the upstream face of the dam (the fluid-structure interface). Figure 5 is a schematic diagram showing the

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locations of the source and reference nodes, and their spatial relationships with the No. 3 monolith.

Fig. 5. Locations of the explosive source and reference nodes before the No. 3 monolith of the dam The UNDEX is assumed to be the equivalent of 50 kg of TNT and the explosive-wave propagation type

ACCEPTED MANUSCRIPT be spherical. The peak pressure of the shock wave at the reference node, PR max , is given by [33]

PR max

 13 W  k   R0 



    

(3)

where W is the TNT equivalent weight of the UNDEX in kilograms, R0 is the standoff distance between the

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source and reference nodes in meters, and k and α are empirical coefficients depending on the explosive

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type. For the TNT explosive type herein, the empirical coefficients are as follows: k = 52.27 MPa and α =

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1.13. Thus the calculated PR max at the reference node for the present study is 16.91 MPa. The pressure input at the reference node is a variation on the free-field pressure transducer time record of the UNDEX

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test carried out by Kwon and Fox [34] with an amplification ratio of 16.91/16.30. The raw experimental

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data are obtained by digitizing the Kwon and Fox [34] UNDEX pressure history curve. In the present study, the amplitude of the shock wave is assumed to be inversely proportional to the

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distance from the source. In this context, once the pressure input at the reference node is defined, the

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pressure at any other loaded node on the dam-water interface can be calculated by PL 

R0 PR RL

(4)

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where PL and PR denote the pressure at the loaded and reference nodes, respectively, and RL denotes

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the distance between the source and loaded nodes. Every location on the loaded interface has a phase shift

t in the applied pressure, corresponding to the difference in propagation time between the loaded and reference nodes:

t 

RL  R0 v

(5)

where v denotes the rate of propagation of the shock wave. 5.5. Mesh Sensitivity Analysis Of particular concern in the UNDEX numerical simulation is the water-mesh size effect [26]. To

ACCEPTED MANUSCRIPT examine the mesh dependency of the current numerical model, three additional meshes with different water-grid densities are thus considered. The four water meshes, including the current one shown in Fig. 2a, are presented in Fig. 6 for comparison. The difference between the meshes lies in the number of element divisions along the stream direction. At this stage, for ease of comparison, the material non-linearity

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concerning the concrete and potential failures of the shear keys are not considered. The simulation time

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period is reduced to 0.1 s and the output time interval is adjusted to be 0.001 s.

Fig. 6. Four water meshes with different densities employed for the mesh sensitivity analysis Figure 7 and 8 compare some typical acoustic-pressure and radial-displacement histories at some representative points based on different meshes, respectively. Overall, although there is some inconsistency in the calculation results, no substantial differences are found in their variation trends and ranges. Initially it was believed that the calculation results should tend to converge with the increase in the water-grid density. However, closer inspection reveals relatively significant differences between the WM-10 results

ACCEPTED MANUSCRIPT and the others. The reasons for the differences are not yet completely understood. We should thus sound a note of caution with regard to such findings. Considering that there is satisfactory agreement between the WM-6 and WM-15 results regarding the structural responses of the dam (Fig. 8), which are the focus of this study, we believe that the current WM-6 water mesh would lend itself well for use by this numerical

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investigation.

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Fig. 7. Calculated acoustic-pressure histories at some representative points in the water with different meshes

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Fig. 8. Calculated radial-displacement histories at some representative points on the dam with different meshes (“Positive” denotes radial displacement towards downstream)

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6. Results

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6.1. Radial Acceleration and Displacement

Figure 9 and 10 present the calculated peak radial acceleration and displacement at the crest of each

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monolith, respectively. From the data in Fig. 9 and 10, we can see that the UNDEX shock loading

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generally results in intenser dynamic responses of intermediate monoliths. What stands out in the figures is the significantly higher peak radial acceleration at the No. 3 monolith crest. This result may be explained by the fact that the No. 3 monolith is closer to the explosive source than any other monolith. It is critical to note that the radial acceleration and displacement responses of the No. 3 monolith towards upstream are observably intenser than those towards downstream. The differences in the dynamic responses of the No. 3 monolith in opposite directions could be attributed to the arch action of the dam. The monolith carries the UNDEX shock loading (towards downstream) in part by transmitting it through its adjacent monoliths

ACCEPTED MANUSCRIPT along the arch axis to the abutments. However, it can move upstream more easily because the contraction

(b)

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joints can only hold compression but not tension.

Fig. 9. Peak radial acceleration at the crest of each monolith: (a) Towards upstream; (b) Towards

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downstream

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downstream

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Fig. 10. Peak radial displacement at the crest of each monolith: (a) Towards upstream; (b) Towards

Turning now to the working condition of the shear keys, the influence of it on the radial displacement response of the No. 3 monolith appears to be more significant than that on the radial acceleration response. The peak radial displacement towards upstream at the crest of the No. 3 monolith reaches 23.45 mm in the SK-I condition, 28% higher than that in the SK-E condition. A possible explanation for this might be that the absence of the shear-transferring effect of the shear keys in the SK-I condition makes each monolith more independent and thus the dam structure as a whole more flexible.

ACCEPTED MANUSCRIPT 6.2. Opening-closing Behavior of Contraction Joints Radial dynamic responses of arch dams generally give rise to alternating opening-closing behavior of their contraction joints. Considering that the dynamic responses of the No. 3 monolith are markedly intenser than those of the others, the joint opening histories on both sides of it at the dam crest elevation

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are compared in Fig. 11. As expected, no negative value of the joint opening on either side of the No. 3

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monolith is observed in the SK-E condition. This non-negative joint opening has been found to be typical

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for arch dams with shear keys undergoing seismic loadings [20-21]. The non-negative joint opening could be attributed to the shear keys that ensure the consistency in the radial displacements of the No. 3 and its

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adjacent monoliths.

(a)

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side; (b) On the right side

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Fig. 11. Joint opening histories on the sides of the No. 3 monolith at the dam crest elevation: (a) On the left

In the SK-E condition, the similarity between the joint opening histories on the left and right sides of the No. 3 monolith is worth noting. During the initial 0.2 s, the UNDEX-induced displacement of the No. 3 monolith towards downstream brings about closed states of the joints on the sides of the monolith. In this period, the joints are under compression and the vibrational energy of the No. 3 monolith is transmitted through the joints to its adjacent monoliths and eventually to the abutments at the ends of the dam. During the t=0.2-0.5 s period, the joints on the sides of the No. 3 monolith open up, illustrating that the monolith

ACCEPTED MANUSCRIPT has returned to its equilibrium position and starts to move upstream without transfers of compressive forces between it and its adjacent monoliths at t=0.2 s. Closer inspection of Fig. 11 shows that the trends of the joint opening histories at the upstream and downstream ends on either side of the No. 3 monolith are similar. Compared with the downstream side, the upstream side of the dam is farther from the arch center.

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Consequently, with a few exceptions, the opening at the upstream end is generally greater than that at the

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downstream end on either side of the No. 3 monolith. The peak joint-opening values reach 4.82 mm and

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5.61 mm on the left and right sides, respectively. After t=0.5 s, there is continuing alternating opening-closing behavior of the joints.

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If we now turn to the SK-I condition, similarly, it can be seen that the joints are in closed states during

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the initial 0.2 s even if the shear keys fail. In this period, the static friction effects the transfers of shear between the No. 3 and its adjacent monoliths and thus restrains slippage at the joints. As Fig. 11 shows,

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however, there are significant differences in the joint opening histories between the two working

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conditions of the shear keys after t=0.2 s. The peak joint-opening value reaches 6.86 mm on the left side in the SK-I condition, 42% greater than that in the SK-E condition. On the right side, the peak joint-opening

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value is 5.46 mm in the SK-I condition, slightly less than that in the SK-E condition. The most striking

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result to emerge from the data in Fig. 11 is that the opening state of the left joint, starting at t=0.2 s, lasts markedly longer in the SK-I condition than it does in the SK-E condition. However, for the right joint no significant difference is observed in the joint opening histories between the two working conditions in the t=0.2-0.5 s period. A surprising aspect of the data in Fig. 11 as regards the SK-I condition is in the negative joint-opening values. These negative joint-opening values are somewhat counterintuitive, but do not mean that the No. 3 monolith would penetrate its adjacent monoliths or be penetrated by them in the numerical simulation. The negative joint-opening values could be interpreted as being a result of the shear slippage at

ACCEPTED MANUSCRIPT the contraction joints between the No. 3 and its adjacent monoliths in the SK-I condition, as highlighted in Fig. 12. In this condition, the adjacent monoliths do not always precisely correspond in the arch direction

(b)

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due to the shear slippage.

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Fig. 12. Typical shear slippage at the contraction joints on the sides of the No. 3 monolith in the SK-I condition (deformation scale factor=100): (a) On the left side, t=0.8 s; (b) On the right side, t=0.6 s

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6.3. Damage to Dam Body

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Under the UNDEX shock loading, the dam body may undergo both compressive crushing and tensile cracking. Figure 13 shows the compressive damage to the dam body in the two working conditions of the

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shear keys. Overall, there are no significant differences between the two working conditions in terms of the

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compressive damage. Generally speaking, the compressive damage to the dam body is minor seeing that the calculated maximum compressive-damage variable value is less than 0.03. This relatively low level of

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compressive damage may be explained by the fact that the peak pressure (16.91 MPa) of the shock wave at

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the reference node is very close to the compressive strength (17 MPa) of the dam concrete.

(a)

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(b) Fig. 13. Compressive damage to the dam body in the two working conditions of the shear keys: (a) In the

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SK-E condition; (b) In the SK-I condition

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The single most striking observation to emerge from the damage comparison in Fig. 13 is the local

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compressive damage near the contraction joints at the dam crest elevation in the SK-E condition. The primary cause of the local compressive damage is a consequence of the modeling simplification of the

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shear keys with the axial spring elements, as shown in Fig. 3. Every axial spring element along the radial direction at the dam crest elevation connects the tips of adjacent monoliths. Consequently, as an axial

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spring element is transferring shear in virtue of its tension between the adjacent monoliths it connects, compressive-stress concentrations tend to occur in the dam concrete around the connection points. With the

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No. 3 monolith, for example, there is good agreement between the arising times of the local compressive damage around the top tips of it (Fig. 13a) and the times the joints on the sides of it start to open up (Fig.

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11). It seems possible that the slighter local compressive damage near contraction joints at lower elevations shown in Fig. 13a is due to similar reasons. Given that the present numerical simulation is based on the modeling simplification of the shear keys, the results with regard to the local compressive damage near the contraction joints should thus be treated with considerable caution. In reality, the shear keys play the roles in transferring shear between adjacent monoliths and thus tend to undergo compressive damage. Figure 14 presents the tensile damage to the dam body in the two working conditions of the shear keys. Significantly, compared with the minor compressive damage, the tensile damage to the dam body is much

ACCEPTED MANUSCRIPT more serious. With a few exceptions, the results show that the working condition of the shear keys does not significantly affect the tensile damage on the upstream face of the dam in terms of its level and propagation. The exceptions are concerning the local tensile damage near the contraction joints in the SK-E condition. We believe that the local tensile damage should also be attributed to the employment of the axial spring

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elements, as discussed previously.

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condition; (b) In the SK-I condition

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Fig. 14. Tensile damage to the dam body in the two working conditions of the shear keys: (a) In the SK-E

From Fig. 14, it can be seen that local tensile damage with a medium level arises on the upstream face and near the foundation and left abutment of the dam. Such local tensile damage could be attributed to the radial displacement response towards downstream of the dam under the UNDEX shock loading, which leads to overstress in the cantilever direction at the dam heel. The most striking result in Fig. 14 is the high-level tensile damage on the upstream face of the No. 3 monolith. It can be seen that this damage zone stretches both the width and the thickness of the No. 3 monolith, from Fig. 14 together with Fig. 15 that

ACCEPTED MANUSCRIPT illustrates the tensile damage from a downstream perspective. The damage penetration is likely to be related to the intense radial-swing response of the monolith head induced by the UNDEX shock. This implies that the No. 3 monolith head above the penetrating-damage zone could break off under the

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UNDEX shock loading.

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Fig. 15. Tensile damage to the No. 3 monolith in the two working conditions of the shear keys from a

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downstream perspective: (a) In the SK-E condition; (b) In the SK-I condition It is apparent from Fig. 16 that there are two significant differences in the tensile damage to the dam

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base surface between the two working conditions of the shear keys. First, high-level tensile damage propagates on the No. 3 monolith base surface along its downstream side (dam toe) in the SK-I condition,

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whereas no similar high-level damage is observed in this area in the SK-E condition. Second, local serious tensile damage arises on the No. 1 monolith base surface (near the left abutment) on its downstream side in

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the SK-E condition, while no damage appears in this area in the SK-I condition. The findings highlight that the working condition of the shear keys has a major influence on the energy transfer paths in the dam body. In general, therefore, it seems that in the SK-E condition more impact energy would transfer along the arch direction from the reference node to the abutments owing to the shear-transferring effect of the shear keys, resulting in the local serious tensile damage near the left abutment (Fig. 16a). However, in the SK-I condition more impact energy should transfer along the cantilever direction downwards from the reference node to the No. 3 monolith base due to the absence of the shear-transferring effect of the shear keys,

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leading to the high-level tensile damage at the dam toe (Fig. 16b).

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Fig. 16. Tensile damage to the dam base surface in the two working conditions of the shear keys: (a) In the

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SK-E condition; (b) In the SK-I condition

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7. Discussion

This study set out with the aim of examining nonlinear structural responses of an arch dam to an

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UNDEX shock loading. The current study found that a 50 kg TNT equivalent near-surface UNDEX with a

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standoff distance of 10 m could lead to a break-off of an intermediate monolith of a 100-m-high class arch dam. In our opinion, it should be easy for terrorists to ship 50 kg TNT equivalent explosive materials to a reservoir and implement a near-surface UNDEX close to the dam. Consequently, we believe that there is a clear case for designers to consider anti-UNDEX performance of arch dams and more importantly, for relevant agencies to take anti-terrorism security of arch dams seriously. Another important finding was that an arch dam base is vulnerable to a near-surface UNDEX in view of the long arm of the UNDEX impact force relative to the dam base. It is somewhat surprising that the

ACCEPTED MANUSCRIPT tensile damage to the dam toe is much more serious than that to the dam heel in the SK-I condition (Fig. 16b). This demonstrates just how important the shear keys are to the integrity of the arch dam. It may be the case therefore that once some or all of the shear keys undergo failures by shear due to the inconsistent radial vibrations of the monoliths, the dam toe would become a weak portion of the arch dam. Another

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unanticipated finding was the local serious tensile damage near the left abutment in the SK-E condition,

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but no tensile damage appears near the right abutment (Fig. 16a). It suggests that the impact energy

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propagation and decay in the dam body are complex and thus further assessment of anti-UNDEX performance of arch dams should be case-by-case.

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Together these results provide important insights into the failure modes of the arch dam. The results

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point to the likelihood that the monolith closest to the explosive source might undergo a break-off failure. It would appear that another potential threat to the dam is tensile cracking of the dam base concrete. The

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results suggest that there is an association between the working conditions of the shear keys and the

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tensile-damage level of the dam base concrete. Essentially, failures of the shear keys make each monolith more independent and thus give rise to a redistribution of the energy transfer paths in the dam body from

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the arch to the cantilever direction.

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One of the issues emerging from these findings is that the presented numerical simulation procedure could probably be usefully employed in preliminary assessment of anti-UNDEX performance of arch dams. The presented simulation procedure based upon ABAQUS/Explicit shows two clear advantages over the full-process simulation procedure based upon LS-DYNA [5, 7, 10] or AUTODYN [8-9] when facing a large-scale three-dimensional UNDEX simulation involving an arch dam. First, the presented simulation procedure is time-efficient owing to its cut-off computational strategy, in which acoustic-field initialization is performed at the beginning of the first direct-integration dynamic step. Second, such initialization can

ACCEPTED MANUSCRIPT reduce the mesh density requirement for the acoustic field in that it applies the incident wave loading without significant numerical dissipation or distortion. One downside regarding the current numerical simulation is the simplified modeling of the shear keys with axial spring elements. Due to the modeling simplification, potential failure-evolution processes of the

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shear keys cannot be taken into account in the numerical simulation. However, only two extreme working

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conditions of the shear keys are considered. In addition, the modeling simplification has led to the

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questionable calculation results with regard to the local compressive and tensile damage near the contraction joints, as shown in Fig. 13a and 14a, respectively. A further study with more focus on modeling

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of shear keys is therefore suggested.

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Another negative factor with respect to the current numerical simulation appears to be the employed plastic-damage model. A key problem regarding this model is that it uses concepts of isotropic damaged

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elasticity in combination with isotropic tensile and compressive plasticity to represent the inelastic

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behavior of concrete. Based on this model, the reduction in the stiffness matrix (damage) is isotropic. In reality, the material softening behavior in the direction perpendicular to a crack should be far more

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pronounced than that in the direction parallel to it. In addition, the potential lateral cracking induced by the

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contact [35] between adjacent monoliths cannot be considered with this quite general model. A further study on the current topic with more focus on the physical nature of cracking phenomena in concrete is therefore suggested. It might be possible to use a fixed total strain crack model for describing the inelastic behavior of concrete, in which both normal and shear stresses exist on crack surfaces [36]. A note of caution is due here for the absence of a detailed comparison of the numerical simulation results with some physical data (prototype and/or model test) in this study. Prototype (full-scale model) tests involve elaborate preparations and are very expensive. In addition, they also require the use of

ACCEPTED MANUSCRIPT relatively large amounts of explosives, involving potential risks and need careful handling, which is typically not feasible in civilian research [37]. For now, further reduced scale/enhanced acceleration physical tests (as in centrifuge tests) are required to establish the validity of the proposed modeling strategy, which is of paramount importance to use the strategy to real arch-dam structures. Even so, the capability of

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the spring-based model to account for the two extreme working conditions of the shear keys appears to be

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well supported by the predicted alternating opening-closing behavior of the contraction joints (Fig. 11). We

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believe that the presented numerical simulation procedure could probably be practicably employed in preliminary assessment of anti-UNDEX performance of arch dams.

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8. Conclusions

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The aim of the present research was to examine nonlinear structural responses of an arch dam to an UNDEX shock loading based on numerical simulation. Both the dam-reservoir interaction and the

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contraction-joint non-linearity have been considered in the present study. Our research has underlined the

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importance of the shear keys to the integrity of the arch dam. Failures of the shear keys make each monolith more independent and thus the dam structure as a whole more flexible. Two major failure modes

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of the arch dam have been identified: (a) a break-off failure of the monolith closest to the explosive source,

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and (b) tensile cracking of the dam base concrete. It is crucial to note that failures of the shear keys would significantly intensify the tensile damage to the dam base concrete, thus greatly increasing the dam-failure risk.

We have presented a time-efficient and relatively undemanding numerical simulation procedure for preliminary assessment of anti-UNDEX performance of arch dams. The most important limitation lies in the fact that the shear keys are not actually modeled in line with their physical shapes, dimensions or locations. In addition, the numerical study is limited by the lack of prototype and/or model test validations.

ACCEPTED MANUSCRIPT More prototype and/or model test data would help us to establish a greater degree of accuracy on this matter. Notwithstanding these limitations, this study has gone some way towards enhancing our understanding of nonlinear structural responses of an arch dam to an UNDEX shock loading.

Acknowledgments

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This work was made possible by grants from the National Natural Science Foundation of China

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(51579018, 51409018), the Fundamental Research Funds for Central Public Welfare Research Institutes

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(Changjiang River Scientific Research Institute CKSF2016271/GC, CKSF2016037/GC) and the National Key Research and Development Program of China (2016YFC0401602).

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The original design data of the arch dam chosen as the current study subject were provided by Dr.

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Jun-Jie Hua, who works in Changjiang Institute of Survey, Planning, Design and Research. The provision is hereby gratefully acknowledged. We gratefully acknowledge the constructive comments of the

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anonymous reviewer.

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References

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[1] Jansen, R. B. (1980). Dams and public safety, part IV—Significant accidents and failures, Water and Power Resources Service, U.S. Dept. of the Interior, U.S. Government Printing Office, Washington, D.C. [2] Nonveiller, E., Rupčić, J., and Sever, Z. (1999). “War damages and reconstruction of Peruća dam.” J. Geotech. Geoenviron. Eng., 125(4), 280-288. [3] Charlie, W. A. (2000). “Discussion of ‘War damages and reconstruction of Peruća dam’ by Ervin Nonveiller, Josip Rupčić, and Zvonimir Sever.” J. Geotech. Geoenviron. Eng., 126(9), 854-855. [4] FEMA (Federal Emergency Management Agency). (2003). Dam safety and security in the United States: A progress report on the National Dam Safety Program in fiscal years 2002 and 2003, U.S. Department of Homeland Security, Washington, D.C. [5] Yu, T. (2009). “Dynamical response simulation of concrete dam subjected to underwater contact explosion load.” WRI World Congr. Comput. Sci. Inf. Eng., CSIE, Vol. 1, IEEE Computer Society, Piscataway, NJ, 769-774. [6] Linsbauer, H. (2011). “Hazard potential of zones of weakness in gravity dams under impact loading conditions.” Front. Archit. Civ. Eng. China, 5(1), 90-97. [7] Zhang, S., Wang, G., Wang, C., Pang, B., and Du, C. (2014). “Numerical simulation of failure modes of concrete gravity dams subjected to underwater explosion.” Eng. Fail. Anal., 36, 49-64. [8] Wang, G., and Zhang, S. (2014). “Damage prediction of concrete gravity dams subjected to underwater explosion shock loading.” Eng. Fail. Anal., 39, 72-91. [9] Wang, G., Zhang, S., Kong, Y., and Li, H. (2015). “Comparative study of the dynamic response of concrete gravity dams subjected to underwater and air explosions.” J. Perform. Constr. Facil., 29(4), 10.1061/(ASCE)CF.1943-5509.0000589. [10] Chen, J., Liu, X., and Xu, Q. (2017). “Numerical simulation analysis of damage mode of concrete gravity dam under close-in explosion.” KSCE J. Civ. Eng., 21(1), 397-407. [11] Lu, L., Li, X., and Zhou, J. (2014). “Study of damage to a high concrete dam subjected to underwater shock waves.” Earthquake Eng. Eng. Vib., 13(2), 337-346. [12] Lu, L., Li, X., Zhou, J., Chen, G., and Dong, Y. (2016). “Numerical simulation of shock response and dynamic fracture of a concrete dam subjected to impact load.” Earth Sci. Res. J., 20(1), M1-M6. [13] Lu, L., Kong, X., Dong, Y., Zou, D., and Zhou, Y. (2017). “Similarity relationship for brittle failure dynamic model experiment and its application to a concrete dam subjected to explosive load.” Int. J. Geomech., 17(8), 10.1061/(ASCE)GM.1943-5622.0000889. [14] Hall, J. F., and Chopra, A. K. (1983). “Dynamic analysis of arch dams including hydrodynamic effects.” J. Eng. Mech., 109(1), 149-167. [15] Dowling, M. J., and Hall, J. F. (1989). “Nonlinear seismic analysis of arch dams.” J. Eng. Mech., 115(4), 768-789. [16] Tan, H., and Chopra, A. K. (1995). “Earthquake analysis of arch dams including dam-water-foundation rock interaction.” Earthquake Eng. Struct. Dyn., 24(11), 1453-1474. [17] Omidi, O., and Lotfi, V. (2017). “A symmetric implementation of pressure-based fluid–structure interaction for nonlinear dynamic analysis of arch dams.” J. Fluids Struct., 69, 34-55. [18] Lau, D. T., Noruziaan, B., and Razaqpur, A. G. (1998). “Modelling of contraction joint and shear

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[26]

[27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37]

PT

RI

SC

[25]

NU

[24]

MA

[23]

D

[22]

PT E

[21]

CE

[20]

AC

[19]

sliding effects on earthquake response of arch dams.” Earthquake Eng. Struct. Dyn., 27(10), 1013-1029. Zhou, J., Lin, G., Zhu, T., Jefferson, A. D., and Williams, F. W. (2000). “Experimental investigations into seismic failure of high arch dams.” J. Struct. Eng., 126(8), 926-935. Zhang, C., Xu, Y., Wang, G., and Jin, F. (2000). “Non-linear seismic response of arch dams with contraction joint opening and joint reinforcements.” Earthquake Eng. Struct. Dyn., 29(10), 1547-1566. Omidi, O., and Lotfi, V. (2017). “Seismic plastic–damage analysis of mass concrete blocks in arch dams including contraction and peripheral joints.” Soil Dyn. Earthquake Eng., 95, 118-137. Benson, D. J. (1992). “Computational methods in Lagrangian and Eulerian hydrocodes.” Comput. Methods Appl. Mech. Eng., 99(2-3), 235-394. Mair, H. U. (1999). “Review: hydrocodes for structural response to underwater explosions.” Shock Vib., 6(2), 81-96. Chafi, M. S., Karami, G., and Ziejewski, M. (2009). “Numerical analysis of blast-induced wave propagation using FSI and ALE multi-material formulations.” Int. J. Impact Eng., 36(10-11), 1269-1275. Brunesi, E., Nascimbene, R., Pagani, M., and Beilic, D. (2015). “Seismic performance of storage steel tanks during the May 2012 Emilia, Italy, earthquakes.” J. Perform. Constr. Facil., 29(5), 10.1061/(ASCE)CF.1943-5509.0000628. Wang, G., Wang, Y., Lu, W., Zhou, W., Chen, M., and Yan, P. (2016). “On the determination of the mesh size for numerical simulations of shock wave propagation in near field underwater explosion.” Appl. Ocean Res., 59, 1-9. ABAQUS [Computer software]. (2010). Abaqus analysis user's manual, Dassault Systèmes Simulia Corp., Providence, RI. Tassios, T. P., and Vintzēleou, E. N. (1987). “Concrete-to-concrete friction.” J. Struct. Eng., 113(4), 832-849. Lubliner, J., Oliver, J., Oller, S., and Oñate, E. (1989). “A plastic-damage model for concrete.” Int. J. Solids Struct., 25(3), 299-326. Lee, J., and Fenves, G. L. (1998). “Plastic-damage model for cyclic loading of concrete structures.” J. Eng. Mech., 124(8), 892-900. Huan, Y., Fang, Q., Chen, L., and Zhang, Y. (2008). “Evaluation of blast-resistant performance predicted by damaged plasticity model for concrete.” Trans. Tianjin Univ., 14(6), 414-421. Omidi, O., Valliappan, S., and Lotfi, V. (2013). “Seismic cracking of concrete gravity dams by plastic–damage model using different damping mechanisms.” Finite Elem. Anal. Des., 63, 80-97. Cole, R. H. (1948). Underwater explosions, Dover Publications, New York. Kwon, Y. W., and Fox, P. K. (1993). “Underwater shock response of a cylinder subjected to a side-on explosion.” Comput. Struct., 48(4), 637-646. Cook, R. F., and Roach, D. H. (1986). “The effect of lateral crack growth on the strength of contact flaws in brittle materials.” J. Mater. Res., 1(4), 589-600. Brunesi, E., and Nascimbene, R. (2015). “Numerical web-shear strength assessment of precast prestressed hollow core slab units.” Eng. Struct., 102, 13-30. De, A. (2012). “Numerical simulation of surface explosions over dry, cohesionless soil.” Comput. Geotech., 43, 72-79.

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Highlights The importance of the shear keys to the integrity of the arch dam is underlined.

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Failures of the shear keys make each monolith more independent.

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Two major failure modes of the arch dam have been identified.

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The presented simulation procedure is time-efficient and relatively undemanding.

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