ABSTRACT: This paper investigates the effects of near-fault ground motions on the base slipping response of concrete gravity dams. The numerical modeling of the dam-reservoir-foundation system includes the consideration of the nonlinear material behavior of the dam concrete and the foundation rock, the contact interaction between the dam, the reservoir, and the foundation, the unbounded features of the reservoir and foundation domains, and the spatial variation of seismic surface motions. The developed numerical model is then applied to the Koyna Dam, which is subjected to a range of spatially varying near-fault ground motions generated using actual earthquake records. The investigation reveals that spatially non-uniform seismic excitations cause a severer damage behavior of the dam than uniform ones. Specifically, the base slipping response of the dam is found to increase as the apparent propagation velocity decreases. It is also shown that the peak ground acceleration of the near-fault motion is an important parameter that influences the slipping response. Generally, higher peak ground accelerations tend to produce larger permanent slipping displacements.

KEY WORDS: Concrete Gravity Dams; Near-fault Ground Motions; Base Sliding; Dam-Reservoir-Foundation Interaction.

1 INTRODUCTION Seismic ground motions close to an active fault zone are highly influenced by the fault rupture process and mechanism, and, usually, exhibit large velocity pulses and large fault displacements that may differ significantly from typical far-fault ground motions. Although concerns about near-fault ground motions and their damaging potential on structures have been widely recognized, the effects of these impulsive motions on the response of concrete gravity dams still require further scrutiny. Focus has been placed on simple SDOF structures [1-2], frame buildings and structures [3-4], bridges [5-6], and embankment and arch dams [7-8].

To bridge the gap, this paper carries out nonlinear finite element analyses to evaluate the seismic performance of concrete gravity dams subjected to near-fault ground motions. The nonlinear finite element model includes the consideration of a number of important issues present in the computational modeling of concrete gravity dams such as the nonlinear constitutive behavior of concrete and rock, the dam-reservoir-sediment-foundation interaction, the semi-unbounded foundation and reservoir domains, and the spatial variation of earthquake ground motions. The developed nonlinear model is illustrated using the Koyna Dam in India, which is excited by a number of recorded near-fault ground motions. The wave passage effects of spatially varying near-fault ground motions are then investigated.

2 NEAR-FAULT GROUND MOTIONS Near-fault earthquake ground motions refer to the ground motions close to a fault rupture. In the near-fault region, the earthquake motions at a particular site are strongly affected by the fault rupture process. The most salient feature of near-source ground motions is the distinct velocity and

displacement pulses observed in the time histories of these motions, as illustrated in Figure 1a. Such prominent pulse-like characteristics do not appear in ground motions recorded far off the seismic source, as illustrated in Figure 1b.

Near-fault ground motions may occur when the fault rupture propagates towards the site at a velocity nearly as large as the propagation velocity of the shear wave. As a consequence, almost all of the seismic energy from the rupture arrives at the site within a short time, leading to the forward-directivity effect, as shown in Figure 2. Near-fault ground motions can also be caused by permanent static displacement resulting from surface faulting, i.e. fling-step, which is portrayed in Figure 3.

3 STRUCTURAL MODELING OF DAM-RESERVOIR-FOUNDATION SYSTEMS

3.1 Material Behavior of the Dam Concrete, the Reservoir Water, and the Foundation Rock

An important part in the modeling of the dam and foundation domains is their inelastic stress-strain relationship under earthquake loading conditions. Of particular concern is the nonlinear constitutive modeling of the concrete material. In this research, the concrete cracking behavior in the body of the dam is accounted for by the Damaged Plasticity Model [9-12]. In a different way, the nonlinear constitutive behavior of the foundation rock is modeled using the Mohr-Coulomb Model [12], with the near-field domain represented by finite elements and the far-field domain by infinite ones [12]. On the other hand, the water in the reservoir is formulated as a compressible, inviscid, linear medium with different boundary conditions prescribed at its boundaries to emulate energy

Effects of Near-Fault Ground Motions on the Seismic Response of Concrete Gravity Dams

Junjie Huang1

1School of Civil Engineering, Wuhan University, Wuhan, Hubei Province 430072, P.R. China Email: jnjhuang@gmail.com

Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014Porto, Portugal, 30 June - 2 July 2014

A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.)ISSN: 2311-9020; ISBN: 978-972-752-165-4

Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014Porto, Portugal, 30 June - 2 July 2014

A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.)ISSN: 2311-9020; ISBN: 978-972-752-165-4

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radiation at infinity [13] and to simulate wave absorption by the reservoir sediment deposits [14].

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Figure 1. Illustration of near-fault and far-fault ground motions: (a) Ground motion recorded at Station TCU068 during the 1999 Chi-Chi Earthquake (b) Ground motion

recorded at Station USGS 1095 Taft Lincoln School during the 1952 Kern County Earthquake

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3.2 Dam-Reservoir-Foundation Interaction

To appropriately represent the interaction between the dam and the foundation, contact surfaces are enforced at the dam-foundation interface [15]: The contact interaction in the normal direction is characterized by the “hard” contact behavior and the tangential contact interaction by the Coulomb friction law with an allowable slip. The fluid-structure interactions at the dam-reservoir and foundation-reservoir interfaces are modeled using a surface-based coupling procedure [12].

3.3 Spatial Variability of Earthquake Ground Motions

In addition to the aforementioned issues, since concrete gravity dams are long structures situated in environments with complex topography, the spatial distribution of seismic motions may vary considerably at the dam site. Generally, the spatial variability of earthquake ground motions results from three causes, i.e. the local site effect, the incoherence effect, and the wave passage effect [16]. For the sake of simplicity, the present study only concentrates on the latter cause, that is, the wave passage effect due to the differences in time that the seismic wave needs to arrive at different locations.

4 EARTHQUAKE RESPONSE OF CONCRETE GRAVITY DAMS TO NEAR-FAULT GROUND MOTIONS

4.1 The Koyna Dam and the Finite Element Model The Koyna Dam in India is concrete gravity dam of 853 m length and 103 m height. A typical non-overflow section of the dam is displayed in Figure 4. In this research, the Koyna Dam is idealized as a 2D finite element model. The computational modeling is carried out in the finite element software package Abaqus [12]. The 2-D finite element model in Abaqus is shown in Figure 5. The dam is modeled by CPS4R solid elements. The reservoir has a dimension of 385 m length and 91.74 m depth and is modeled by AC2D4 acoustic elements. The finite foundation domain is 840 m long and 420 m deep and is modeled by CPE4R solid elements. In addition, CINPE4 solid infinite elements are employed to simulate the foundation’s far field. The material properties adopted in the analysis, which are mostly based on [10,12,17], are summarized in Table 1. The dam-reservoir-foundation system is first subjected to the static loads including gravity and hydrostatic pressure and then to the dynamic earthquake loading.

66.4

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Figure 4. Configuration of a typical non-overflow cross section of the Koyna Dam

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Figure 5. The finite element model of the Koyna Dam

Table 1. Material parameters for the Koyna Dam model Concrete

Young’s modulus 3.1027×1010 Pa Poisson’s ratio 0.20 Density 2643 kg/m3

Dilation angle 36.31º Compressive initial yield stress 1.26×107 Pa Compressive ultimate stress 2.711×107 Pa Tensile failure stress 2.9×106 Pa Fracture energy 200 N/m

Water Bulk modulus 2.071×109 Pa Density 1000 kg/m3

sediment reflection coefficient 0.5 Rock

Young’s modulus 1.686×1010 Pa Poisson’s ratio 0.18 Density 2701 kg/m3

Cohesion 6.0×105 Pa Angle of friction 41º

5 EARTHQUAKE RECORDS UTILIZED FOR NEAR-FAULT GROUND MOTIONS

To examine the effects of near-fault ground motions on the base slipping response of the dam, a set of 6 representative near-fault ground motion recordings of forward-directivity nature are selected from the PEER Ground Motion Database

[18], which is also consistent with the near-fault ground motion classification criterion proposed by Baker [19]. These recorded ground motions, which originate from the 1979 Imperial Valley Earthquake, the 1983 Coalinga Earthquake, the 1989 Loma Prieta Earthquake, and the 1994 Northridge Earthquake, cover a range of rupture distance from 0.6 km to 9.5 km. The fundamental properties of these ground motion records are listed in Table 2. Figures 6 and 7 plot the acceleration and velocity time histories of these ground motions respectively.

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Table 2. Ground motion parameters for the near-fault records used in this study No. Earthquake Event Station Mw Year Rrup

(km)PGA (g)

PGV (cm/s)

PGD (cm)

1 Imperial Valley-06 Agrarias 6.53 1979 0.7 0.22 42.21 11.6 2 Imperial Valley-06 El Centro Array #7 6.53 1979 0.6 0.46 109.23 44.48 3 Imperial Valley-06 Holtville Post Office 6.53 1979 7.7 0.25 48.75 31.66 4 Coalinga-05 Oil City 5.77 1983 8.5 0.87 42.14 6.14 5 Coalinga-05 Transmitter Hill 5.77 1983 9.5 0.84 44.12 6.81 6 Northridge-01 Sylmar - Converter Sta East 6.69 1994 5.2 0.83 117.52 34.37

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It is worth mentioning that to account for the wave passage effect of earthquake ground motions, a total of four apparent propagation velocities, i.e. 500 m/s, 1000 m/s, 2000 m/s, 4000 m/s, and an infinite velocity are considered for each of the above-mentioned recorded ground motions. The spatially varying near-fault ground motions incorporating the wave passage effect for the five propagating cases are then applied in the horizontal direction of the foundation surface nodes.

5.1 Effects of Near-Fault Ground Motions on the Base Sliding Response of the Dam

To evaluate the earthquake response of the Koyna dam-reservoir-foundation coupled system subjected to spatially propagating near-fault ground motions, this study focuses on the base slipping behavior of the dam. Figure 8 presents the slipping at the base of the dam for different near-fault ground motions and apparent propagation velocities. The permanent sliding displacements for these input excitation cases are summarized in Table 3.

It is first noticed that while the contact slipping responses differ for both uniform and non-uniform excitation cases, these responses share similar “step-like” features. The results also show that in all the cases, the slipping response accumulates in the downstream direction, which is anticipated because it is easier for the earthquake loadings to induce downstream slipping than upstream slipping [20]. The consequences of such transient interfacial behavior are that they temporarily reduce the tensile and shear resistance of the interface, which subsequently tends to lower the response of the dam [21]. On the other hand, the permanent displacement induced by the slipping may impair the functioning of the keys, drains, and grout curtains and, potentially, pave the way for the loss of the reservoir.

It is also found that the peak ground acceleration appears to be an important parameter for the slipping response. For the uniform input motion cases, the jump of the slipping “step” coincides approximately with the occurring time of the peak ground acceleration. The value of the peak ground acceleration also seems to influence the permanent sliding displacement. For instance, the two smallest cases are Ground Motion Nos. 1 and 3. These two cases have peak ground acceleration values below 0.3 g, which are relatively small compared with other cases. On the other hand, the four largest cases come from Ground Motion No. 2, 4, 5, and 6, with

Ground Motion No. 5 being the highest one. In particular, the peak ground accelerations for Nos. 4, 5 and 6 all go above 0.8 g. It is also noticed that although the peak ground acceleration for No. 4 is the largest, its permanent sliding displacement is not the highest. This can be explained by the fact shown in Figure 9 that, although the peak ground acceleration is not the highest, the period corresponding to the peak spectral acceleration for Ground Motion No. 5 (0.61 s) is closer to the fundamental period of the dam-reservoir-foundation system (0.625 s) than that of Ground Motion No. 4 (0.18 s). This is also reflected in Ground Motion No. 2, where the permanent sliding displacement is also comparatively large, as the period corresponding to the peak spectral acceleration is also close to the fundamental period of the dam-reservoir-foundation system.

Regarding the influence of the spatial variability effect of earthquake ground motions, it is clearly shown that the sliding displacements for non-uniform excitations are larger than those for uniform excitations. In particular, the sliding displacements are observed to increase in a descending propagation velocity order. The “jumping” phenomenon is found to be less prominent for the infinite and 4000 m/s propagation velocity cases and more drastic for the slower 2000 m/s, 1000 m/s, and 500 m/s velocity cases. Noticeably, the residual sliding displacements for the slowest velocity are significantly higher than those for other velocity cases.

6 CONCLUSIONS This study investigates the spatial variability effects of near-fault ground motions on the base sliding response of concrete gravity dams. Based on the results obtained from this investigation, the following conclusions and recommendations can be drawn:

(1) Spatially varying near-fault ground motions can have a significant effect on the base sliding response of the dam. The evaluation carried out in this study using a set of 6 recorded near-fault motions incorporating the wave passage effect unveils a clear trend of increasing sliding response with decreasing apparent propagation velocity. This observation raises significant concerns about the safety of concrete gravity dams as the sliding phenomenon can weaken the keys, drains, and grout curtains, and further impact the dam’s equilibrium, which may lead to loss of the reservoir.

Table 3. Permanent slipping displacements of the dam

Ground Motion No. Permanent Slipping Displacements for Different Propagation Velocities (m) Infinity 4000 m/s 2000 m/s 1000 m/s 500 m/s

1 0.0048243 0.010409 0.035493 0.099920 0.157445 2 0.0583219 0.122928 0.179466 0.216863 0.279051 3 0.0132833 0.018845 0.039973 0.103713 0.201220 4 0.0492294 0.058699 0.076424 0.136433 0.154364 5 0.0851348 0.094700 0.128087 0.222524 0.306436 6 0.0578174 0.067735 0.089551 0.185572 0.241303

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Figure 8. Base slipping responses of the dam subjected to spatially varying near-fault ground motions: (a) Ground

Motion No. 1 (b) Ground Motion No. 2 (c) Ground Motion No. 3 (d) Ground Motion No. 4 (e) Ground Motion No. 5

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Figure 9. Response spectra: (a) Ground Motion No. 8 (b) Ground Motion No. 9

(2) For near-fault ground motions of forward-directivity type, the peak ground acceleration appears to be an important parameter for the sliding response. It is found that in general, the higher the peak ground acceleration is, the larger the permanent sliding displacement is.

(3) It should be noted that the forward-directivity and spatial variability effects of earthquake ground motions are fairly complicated. The findings presented herein only apply to the context of the assumptions made in this paper. Generally, the response of the dam is dependent on both the attributes of the ground motions and those of the structural system. Under the same seismic excitation, different dams may exhibit diverse response patterns. On the other hand, for the same dam, different earthquake input motions can induce various structural response behaviors. To rigorously quantify such complex effects, more research efforts are needed in obtaining the solutions using more earthquake input motions and dam models. In the meantime, it is also necessary to consider the non-uniformity in the ground motions due to loss of coherency. Such a comprehensive study is currently underway.

ACKNOWLEDGMENTS This study was supported by the Hubei Provincial Key Laboratory of Safety for Geotechnical and Structural Engineering at Wuhan University under Grant No. HBKLCIV201207 and the China Postdoctoral Science Foundation under Grant No. 2013M540604. The financial support is gratefully acknowledged. The opinions, findings, conclusions, and recommendations disclosed in this work are those of the authors and do not necessarily reflect the views of the funding agencies.

REFERENCES [1] A.K. Chopra and C. Chintanapakdee, Comparing response of SDF

systems to near-fault and far-fault earthquake motions in the context of spectral regions, Earthquake Engineering and Structural Dynamics,30:1769-1789, 2001.

[2] G.P. Mavroeidis, G. Dong, and A.S. Papageorgiou, Near-fault ground motions, and the response of elastic and inelastic single-degree-of-freedom (SDOF) systems, Earthquake Engineering and Structural Dynamics, 33:1023-1049, 2004.

[3] B. Alavi and H. Krawinkler, Behavior of moment-resisting frame structures subjected to near-fault ground motions, Earthquake Engineering and Structural Dynamics, 33:687-706, 2004.

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[4] S. Akkar, U. Yazgan, and P. Gulkan, Drift Estimates in Frame Buildings Subjected to Near-Fault Ground Motions, Journal of Structural Engineering, 131:1014-1024, 2005.

[5] N. Chouw and H. Hao, Significance of SSI and non-uniform near-fault ground motions in bridge response I: Effect on response with conventional expansion joint, Engineering Structures, 30:141-153, 2008.

[6] N. Chouw and Hao H, Significance of SSI and non-uniform near-fault ground motions in bridge response II - Effect on response with modular expansion joint, Engineering Structures, 30:154-162, 2008.

[7] M. Davoodi, M.K. Jafari, and N. Hadiani, Seismic response of embankment dams under near-fault and far-field ground motion excitation, Engineering Geology, 158:66-76, 2013.

[8] A. Bayraktar, A.C. Altuni ik, B. Sevim, M.E. Kartal, T. Turker, and Y. Bilici, Comparison of near- and far-fault ground motion effect on the nonlinear response of dam–reservoir–foundation systems, Nonlinear Dynamics, 58:655-673, 2009.

[9] J. Lubliner, J. Oliver, S. Oller, and E. Onate, A plastic-damage model for concrete, International Journal of Solids and Structures, 25:229-326, 1989.

[10] J. Lee and G.L. Fenves, A Plastic-damage concrete model for earthquake analysis of dams, Earthquake Engineering and Structural Dynamics, 27:937-956, 1998.

[11] J. Lee and G.L. Fenves, Plastic-damage model for cyclic loading of concrete structures, Journal of Engineering Mechanics, 124:892-900, 1998.

[12] Abaqus, Analysis User’s, Examples Problem, and Theory Manuals (Version 6.7). SIMULIA, The Dassault Systèmes, Providence, RI, 2007.

[13] I.S. Sandler, A new computational procedure for wave propagation problems and a new procedure for non-reflecting boundaries, Computer Methods in Applied Mechanics and Engineering, 164:223-233, 1998.

[14] G.L. Fenves and A.K. Chopra, Effects of reservoir bottom absorption on earthquake response of concrete gravity dams, Earthquake Engineering and Structural Dynamics, 11:809-829, 1983.

[15] P.B. Tekie and B.R. Ellingwood, Seismic fragility assessment of concrete gravity dams, Earthquake Engineering and Structural Dynamics, 32:2221-2240, 2003.

[16] A. Zerva, Spatial variation of seismic ground motions: modeling and engineering applications. Boca Raton, Florida: CRC Press, Taylor & Francis Group, 2009.

[17] K.R. Dhawan, D.N. Singh, and I..D. Gupta, Three-dimensional finite element analysis of underground caverns, International Journal of Geomechanics, 4:224-228, 2004.

[18] Pacific Earthquake Engineering Research Center (PEER), 2010 PEER Ground Motion Database BETA Version, accessed 2012.

[19] J.W. Baker, Quantitative classification of near-fault ground motions using wavelet analysis, Bulletin of the Seismological Society of America, 97:1486-1501, 2007.

[20] A.K. Chopra and L. Zhang, Earthquake-induced base sliding of concrete gravity dams, Journal of Structural Engineering, 117:3698-3719, 1991.

[21] P. Leger and M.K. Katsouli, Seismic stability of concrete gravity dams, Earthquake Engineering and Structural Dynamics, 18:889-902, 1989.

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