The shock response and dynamic fracture of concrete gravity dams under impact load are the key problems to evaluate the antiknock safety of the dam. This study aims at understanding the effects of impact shock on the elastic response and dynamic fracture of concrete gravity dams. Firstly, this paper uses acceleration records of a concrete gravity dam under impact to establish the correct way to determine the concrete gravity dam of the fundamental frequency and present cut sheets multi-degree-of-freedom dynamic modeling. Under strong impact loading, the constitutive relation of concrete gravity dam and the highest frequency of the impact are uncertain. So, the main advantage of this method is avoiding the use of elastic modulus in the calculation. The result indicates that the calculation method is a reliable computational method for concrete gravity dams subjected to impact. Subsequently, the failure process of dam models was numerically simulated based on ABAQUS commercial codes. Finally, this paper puts forward suggestions for future research based on the results of the analysis. EARTH SCIENCES RESEARCH JOURNAL Earth Sci. Res. J. Vol. 20, No. 1 (March, 2016): M1 -M6 ABSTRACT Keywords: Reservoir, Gravity dam, Underwater explosion, Failure mode, Dynamic analysis. ISSN 1794-6190 e-ISSN 2339-3459 http://dx.doi.org/10.15446/esrj.v20n1.54133 H ID R O L O G Y Lu Lu1,2,3*, Xin Li2, Jing Zhou2, Genda Chen4, Dong Yun1 1 Faculty of management Engineering, Huaiyin Institute of Technology, Huai’an 223001, China 2The State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, 110623, China 3The State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023 China 4 The Center for Infrastructure Engineering Studies, Missouri University of Science and Technology, Rolla, Missouri 65401, USA *Corresponding author. E-mail: llzhxy@aliyun.com Numerical Simulation of Shock Response and Dynamic Fracture of a Concrete Dam Subjected to Impact Load Record Manuscript received: 12/11/2015 Accepted for publication: 05/02/2016 How to cite item Lu, L., Li, X., Zhou, J., & Chen, G. (2016). Numerical Simulation of Shock Response and Dynamic Fracture of a Concrete Dam Subjected to Impact Load. Earth Sciences Research Journal, 20(1). M1-M6. doi: http://dx.doi.org/10.15446/esrj.v20n1.54133 Introduction Recently, the Novosibirsk Hydroelectric Plant after a report about a planted explosive, Russia has declared a state of emergency. So, this event should cause the attention of researchers and administrative departments. Hydraulic dams are critical infrastructure in geotechnical engineering. They are often designed and built to store water for drinking and irrigation in adjacent areas, to add water recreation spaces, to create a water way for the short-distance transport of people and goods across deep canyons in mountainous regions, and to regulate the river during a flood event. A water-filled dam can boost the local economy through various personal and business activities, leading to the establishment of a new community center such as a village or a town, and representing a major capital and long-term investment. On the other hand, the breaching and an accidental damage of a dam can lead to a catastrophic flood event and its chain effects such as engulfing downstream residential areas and washing away agriculture lands. Therefore, design and maintenance of dams are not only a serviceability issue but also a life-threatening matter to millions of people. When extreme events such as earthquakes, tsunamis, hurricanes, and tornadoes took place, concrete dams can be subject to extensive shaking and wave impact. The March-11, 2011, Japan Earthquake event testified the destructive power of the earthquake-induced tsunami. Many scholars have studied the high dam subjected to earthquake action. Among these are Zhou et al. (2000), Mir et al. (1995), Kong et al. (2012). Equally, if not more important, dams are also vulnerable targets for man-made explosion events, particularly with the advent of advanced long-range and precision missile technologies. Since the September 11 attacks by terrorists, there has been increasing public concern about the threat of bomb attacks on dam structures (Federal Emergency Management Agency, 2003). Therefore, protection of dam structures against impact loads is a critical component of homeland security (Lu et al., 2013). Indeed, as respectively studied by Lu et al. (2012, 2014a, 2014b), and Zhang et al. (2014), the risk of a tall concrete dam being subjected to underwater explosion shock wave cannot be neglected. M2 Lu Lu, Xin Li, Jing Zhou, Genda Chen and Dong Yun 0.075 m 0.1 m 0.56 m 0.075 m 0.1 m 0.56 m 0.75M Hammers initial position Water bag Pressure sensor Vertical rope 1#hammer 2#hammer 3#hammer 4#hammer 5#hammer Model dam Moving hammers Fixed point Base Anchorage Hammers initial position Water bag Pressure sensor Vertical rope 1#hammer 2#hammer 3#hammer 4#hammer 5#hammer Model dam Moving hammers Fixed point Base Anchorage Currently, with the development of computational techniques and numerical simulation methods, as well as commercialization of nonlinear dynamic software (e.g. ABAQUS, LY-DYNA), major developments in understanding the structural responses and failure modes of concrete structures under blast load have taken place. Many researchers have conducted comprehensive experimental and numerical investigations related to the effects of explosions on building structures(Tian et al., 2008; Jayasooriya et al., 2011), marine structures (Jin, et al., 2011; Zhang et al., 2011), underground structures (Ma et al., 2011; Li et al., (2013), and bridge structures (Hao et al, 2010; Son et al., 2011). In the modeling of transient loading, it is very critical to describe the propagation velocity of the stress waves correctly. In fact, the value of this velocity depends on the material elastic modulus that is given by the material constitutive relation. From the material point of view, concrete shows an increase in elastic modulus with the strain rate increases, a phenomenon called strain rate effect (Georgin, 2003). The relationship between concrete strength and strain rate was extensively investigated by Bischoff and Perry (1991), Georgin and Reynouard (2003), Grassl(2006) and Tai, Y.S. (2009). Because many problems of the concrete material constitutive parameters and constitutive model have not been a clear understanding, the numerical results obtained by different calculation models are very different. Moreover, the modeling of the strain rate effect on concrete is not very easy to tackle. These problems, to a great extent, comprise the uncertainty existing in the macroscopic numerical simulation. One of the efficient methods to study the failure modes and mechanisms of structures is to carry out a large number of model experiments and obtain data from them. Considering that the experimental study has its limitations, as well as great difficulties and expensive costs for the underwater explosion test, only a small amount of data can be obtained. For example, Lu et al. (2014b) obtained only a small quantity of damage to the relationship between the state and the maximum pressure of the shock wave through model tests. Overall, to the best of our knowledge, experimental investigations of concrete gravity dams under underwater shock wave effects have not yet been conducted to date. Concrete dams are thoroughly studied in this paper both experimentally and numerically to understand their behavior and failure modes. Specifically, this paper is to use acceleration records of the concrete structure under strong impact to establish the correct way to determine the concrete structure of the fundamental frequency and present cut sheets multi-degree-of-freedom dynamic modeling. The dams were numerically modeled to understand further their short- time failure process in the order of msec based on ABAQUS. Examples of model tests The same test setup and test results as presented by Lu (2012), Lu (2014a), Lu (2014b)were used in this paper which will be briefly depicted as follows. The dimension of the model dam and test layout are shown in Figure 1. Figure 1. Dimension of the model dam and test layout (Lu, 2012; Lu, 2014a; Lu, 2014b). -0.01 0 0.01 0.02 0.03 0.04 0.05 0.2 0.3 0.4 0.5 0.6 rT Pr es su re (M Pa ) Time(sec)-0.01 0 0.01 0.02 0.03 0.04 0.05 0.2 0.3 0.4 0.5 0.6 rT Pr es su re (M Pa ) Time(sec) The mechanical properties of the individually tested samples and their average values are given in Table 1. Therefore, the actual material density, Young’s modulus, compressive strength, and tensile strength of the small-scale model are ρm = 2,900 kg/m3, Em = 355 MPa, fcm = 205 kPa, and ftm = 13.2 kPa, respectively. Table 1. Mechanical Properties of Concrete Material for Scale Model Dams (Lu, 2012; Lu, 2014a; Lu, 2014b). -100 -50 0 50 100 150 200 0 0.2 0.4 0.6 0.8 1 St ra in (- ) Time(sec) 610 � -100 -50 0 50 100 150 200 0 0.2 0.4 0.6 0.8 1 St ra in (- ) Time(sec) 610 � The main test results of Model test are shown in Table 2. The pressure, strain recorded and acceleration recorded are shown in Figures 2, 3 and 4. Table 2. Main results of the Model tests (Lu, 2012; Lu, 2014a; Lu, 2014b). -12 -7 -2 3 8 13 18 0.2 0.3 0.4 0.5 0.6 A cc el er at io n( g) Time(sec) 22.521 =ow1#Acceleration sensor -12 -7 -2 3 8 13 18 0.2 0.3 0.4 0.5 0.6 A cc el er at io n( g) Time(sec) -12 -7 -2 3 8 13 18 0.2 0.3 0.4 0.5 0.6 A cc el er at io n( g) Time(sec) 22.521 =ow1#Acceleration sensor Figure 2. Time history of the impact pressure on the dam surface (Lu, 2012; Lu, 2014a; Lu, 2014b). Figure 3. Recorded strain (Lu, 2012; Lu, 2014a; Lu, 2014b). M3Numerical Simulation of Shock Response and Dynamic Fracture of a Concrete Dam Subjected To Impact Load -6 -4 -2 0 2 4 6 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 A cc el er at io n( g) Time(sec) 2#Acceleration sensor -6 -4 -2 0 2 4 6 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 A cc el er at io n( g) Time(sec) 2#Acceleration sensor -3 -2 -1 0 1 2 3 0.2 0.3 0.4 0.5 0.6 A cc el er at io n( g) 3#Acceleration sensor Time(sec) -3 -2 -1 0 1 2 3 0.2 0.3 0.4 0.5 0.6 A cc el er at io n( g) 3#Acceleration sensor Time(sec) -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 0.2 0.3 0.4 0.5 0.6 A cc el er at io n( g) 4#Acceleration sensor Time(sec) -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 0.2 0.3 0.4 0.5 0.6 A cc el er at io n( g) 4#Acceleration sensor Time(sec) -1.5 -1 -0.5 0 0.5 1 1.5 0.2 0.3 0.4 0.5 0.6 A cc el er at io n( g) 5#Acceleration sensor Time(sec) -1.5 -1 -0.5 0 0.5 1 1.5 0.2 0.3 0.4 0.5 0.6 A cc el er at io n( g) 5#Acceleration sensor Time(sec) Figure 4. Recorded Acceleration Time Histories from the Model test (Lu, 2012; Lu, 2014a; Lu, 2014b). As shown in the measured pressure-time curve, the impact load can be simplified to a triangular distribution. The failure mode and damage area are shown in Figure 5. Figure 5. Failure Mode and Damage Area[6-8] Note that the accelerometers and pressure sensor were not synchronized during the test. As a result, the peak accelerations seem to occur before the application of the peak pressure. The maximum time delay among the five accelerometers is 23.44 msec. The time delay was likely caused by different periods when five hammers applied impact forces. Based on the arrival time of peak accelerations, Hammers 4 and 5 were in contact with the model dam later than Hammers 1-3. 3. Cut sheets dynamic modeling For that, the concrete dam is divided into I unites, the governing equation for the system with I freedom is as follows: [M] {a}+[K]{X}={P} (1) where [M],[K] denote the mass matrix and stiffness matrix; {X}, {a} and {P} are the displacement, acceleration and force vectors, respectively. Displacement and acceleration using the vibration mode expand can be got (2) (3) where is {φi} i-th mode vector of the system, ξi is general coordinate corresponding to {φi}. Equation 1 after substituting Equations 2 and 3 becomes (4) This equation left multiplied by {φj}T becomes (5) Use of the orthogonality of the vibration mode on the and , that is (6) By the Equations 5 and 6 can be got (7) The governing equation for ξi is (8) (9) (10) (11) (12) Let M4 Lu Lu, Xin Li, Jing Zhou, Genda Chen and Dong Yun rT P t maxP rT2 P t maxP rT2 P t maxP rT (a) (b) (c) rT P t maxP rT2 P t maxP rT2 P t maxP rT (a) (b) (c) (13) (14) (15) where superscript T denotes transformation of matrix or vector. Pi* is the generalized force the corresponding to i-th vibration mode. Mi* is the generalized masscorresponding to i-th vibration mode. Mii is known quantity, so Mi* can be determined. To give expression of , must be assumed for Pi*(t) .Therefore, three forms of the impact force-time curve were examined, as shown in Figure6 (a-c), with the same Pmax and impulse PmTr. Figure 6. Generalized impact force-time curve Solutions of for Figure 6, a, b, and c, are represented by Equations13, 14 and 15, respectively. Because |Ẍ|t=0 = |Ẍ|max for Equations13 and 14 that are inconsistent with experimental results, Figure 6 (a) and (b) are impossible. To determine the value of must also be determined ω0i and θC from the measured acceleration record. The time of acceleration extremal point(including the maximum and minimum values) tm1, tm2, tm3... tmi and the time of acceleration zero point t01, t02, t03... t0i can be obtained by the measured acceleration records. If Tr infinite,by the first type of the Equation 15, | |max occurs at the following times: , respectively. By the second type of the Equation 15, the following equations can be obtained (16) (17) (18) The specific calculation process is as follows: Let tm1 tm1, then the ω01 and the corresponding Tr is solution. If tm1