Dynamic damage evaluation on the slabs of the concrete faced rockfill dam with the plastic-damage model

Computers and Geotechnics 65 (2015) 258–265

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Research Paper

Dynamic damage evaluation on the slabs of the concrete faced rockfill dam with the plastic-damage model Bin Xu, Degao Zou ⇑, Xianjing Kong, Zhiqiang Hu, Yang Zhou The State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China Institute of Earthquake Engineering, Dalian University of Technology, Dalian 116024, China

a r t i c l e

i n f o

Article history: Received 15 September 2014 Received in revised form 24 November 2014 Accepted 5 January 2015 Available online 20 January 2015 Keywords: Plastic-damage model Dynamic analysis Slabs damage Concrete faced rockfill dam Earthquake

a b s t r a c t In this paper, a plastic-damage model for concrete was coupled with the generalized plastic model for rockfill materials and applied to the two-dimensional analysis of a concrete faced rockfill dam (CFRD). First, a plastic-damage model for concrete was programmed in the elastic–plastic dynamic analysis procedure for CFRDs. Previous test simulations were processed to demonstrate the performance and capability of the plastic-damage model and the developed procedure. Numerical simulations of the construction stage, impoundment process, and seismic excitation were conducted to investigate the tensile damage development in the concrete slab of a CFRD during an earthquake. The main tensile damage positions and areas of weakness in the slabs during an earthquake were clarified, which is important for the design of CFRDs. The procedure developed in this study could be adopted in the analysis of interactions between soil and concrete structures. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Due to recent advances in soil and rock engineering, significant progress has been reported in the design and construction of rockfill dams. In China, many concrete faced rockfill dams (CFRDs) with heights over 200 m have been built or designed; for instance, the Shuibuya dam (completed in 2011) is 233 m high [1]. However, in strong seismic regions, earthquakes may cause substantial damage to CFRDs or even cause them to fail, thus endangering lives and causing vast property damage and serious environmental problems. The concrete slabs in CFRDs play the most important role as the main anti-seepage structure. Once the concrete slabs have been damaged during an earthquake, the seepage control system may become impaired or threaten the safety of the dam, i.e., the seepage failure of the Gouhou CFRD in 1993 [2] and the slab dislocation and extruding damage of the Zipingpu CFRD in 2008 [3,4]. Therefore, reliable assessment and a better understanding of the dynamic behavior and seismic response characteristics of these slabs can aid in preventing such catastrophic failures via an improved design of future dams. Currently, the linear elastic model is widely used for the concrete slab, and CFRD construction, impoundment, and earthquake responses analyses have been performed using this approach [4–

⇑ Corresponding author. E-mail address: [email protected] (D. Zou). http://dx.doi.org/10.1016/j.compgeo.2015.01.003 0266-352X/Ó 2015 Elsevier Ltd. All rights reserved.

13]. The results indicated that the tensile strength of the concrete was exceeded. In fact, as a type of quasi-brittle material, concrete can be considered to exhibit linear elastic behavior only under small loads. With increasing tensile strain, cracking and damage will occur, and the concrete will display the characteristics of stiffness degradation and strain softening [14]. Furthermore, the compressive and tensile behaviors of concrete are different and should be considered in investigations of the state of the stress and the cracking behavior of concrete slabs. Considering these characteristics, the results of axial tensile stresses in slabs might greatly exceed the actual concrete tensile strength during strong seismic excitation [13]. Several elastoplastic models of concrete have been established based on damage mechanics and used to simulate the damage process and mechanism of concrete structures [14–21]. For example, the model proposed by Lee and Fenves [17] revealed the independent compressive and tensile damage pattern and the stiffness restoration under reverse loading. The earthquake damage phenomenon of the Koyna gravity dam was successfully numerically simulated with this model [18], and the elastoplastic damage model was also used to analyze the damage-cracking behavior of arch dams [22]. These damage models are primarily used in homogeneous material structures, i.e., arch dams or gravity dams. Few studies have investigated the dynamic responses of CFRDs using a damage model for concrete [23,24]. The main constraints on the use of concrete damage models in the seismic responses analysis of

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CFRDs are as follows: (1) the model of the rockfill materials should be matched with the concrete model. Currently, the nonlinear elastic static and dynamic models are widely used for construction, impoundment, and earthquake simulation of the CFRDs, but the plastic deformation or strain on the rockfill materials cannot be obtained with these models. Therefore, the models based on nonlinear elastic theory do not match the concrete damage model in concept. (2) A plastic interface model that can describe the complex characteristics of the interfacial element between the concrete and rockfill is required to calculate the plastic deformation of the interface. Because of the increase in CFRD heights, the concrete damage should be considered in a seismic analysis of CFRDs, and the following problems should be resolved for damage analyses of the concrete slab of CFRDs using the advanced elastic–plastic model: (1) matching of the elastic–plastic model of rockfill materials, (2) matching of the elastic–plastic interface model and (3) integrating the computational precision, computational efficiency, and stability of the numerical procedure with different plastic models for the concrete, rockfill, and interface. The primary purpose of this study was to investigate the dynamic damage to the concrete slabs during the earthquake period. The plastic-damage model proposed by Lee and Fevens was used to describe the behavior of the concrete. In the previous study by the authors [7,10], a developed generalized plasticity model for rockfill materials that considers the pressure dependency under monotonic and cyclic loading conditions was used to simulate the deformation of the CFRDs during step-by-step construction followed by the subsequent impoundment of the reservoir and seismic responses. An elastic-perfectly-plastic model with pressuredependent shear stiffness was used to simulate the interfaces between the face slabs and cushion gravel [10]. An elastoplastic dynamic analysis procedure for the analysis of CFRD dynamic responses was developed with the described models. Using a 2D plane-strain model with the appropriate constitutive laws for each material of CFRDs, this study was conducted with an emphasis on the following: (1) the effect on stress distribution in the slabs with the use of different models of concrete, (2) the occurrence and development of tensile damage in the slabs during an earthquake, and (3) the seismic damage distribution and areas of weakness in the slabs. 2. Material model This section introduces the models used in the analyses of the CFRD dynamic responses. Compressive stresses are expressed as negative values in this study, and tensile stresses are expressed as positive values.

where k is the plastic invariant, and / is the plastic potential function given by:

/¼

pffiffiffiffiffiffiffi 2J 2 þ ap I1

ð3Þ

 Þ, and J2 ¼ ðs : sÞ=2, where s is the deviatoric effecwhere I1 ¼ trðr tive stress. Furthermore, ap is the material parameter related to the dilatancy of concrete. The extent of damage is represented by the damage state variable j, and its evolution is defined as:

j ¼ kHðr ; jÞ

ð4Þ

The yield function is defined by the effective stress and j:

pffiffiffiffiffiffiffi 1  max iÞ  cðjÞ ðaI1 þ 3J 2 þ bðjÞhr 1a

r  ; jÞ ¼ Fð

ð5Þ

 max is the maximum where a and b are dimensionless parameters, r principle stress, c is the cohesion strength, hi is the McCauley bracket, and a and b are defined as:

a¼

f b0  f c0 2f b0  f c0

ð6Þ

b¼

f c0 ða  1Þ  ð1 þ aÞ f t0

ð7Þ

In the above equations, fc0 and fb0 are the initial uniaxial and biaxial compressive yield stresses, respectively, and ft0 is the initial uniaxial tensile yield stress, as illustrated in Fig. 1. Two independent variables, jt and jc, are introduced to describe the damage state induced by the tensile and compressive stresses, respectively.

jk ¼

1 gk

Z

ep

rk dep ; g k ¼

Z

1

rk dep

ð8Þ

0

0

where k = t represents the tensile state, k = c represents the compressive state, gk is the fracture energy density of concrete, and lk is the characteristic length related to mesh size. The degradation damage variable is expressed as:

 Þ ¼ 1  ð1  st dc ðjc ÞÞð1  sc dt ðjt ÞÞ dðj; r ^ Þ; st ¼ 1  wt rðr

ð9Þ

0 6 wt 6 1

ð10Þ

^ Þ 0 6 wc 6 1 sc ¼ 1  wc rðr

ð11Þ

(

)

1 α I1 + 3 J 2 + β 0σˆ1 = c0 1−α

(

)

1 α I1 + 3J 2 + β 0σˆ 2 = c0 1−α

σˆ 2 f ty

2.1. Plastic-damage model for concrete

σˆ1

This paper adopts the plastic-damage model proposed by Lee and Fenves [17] to simulate the nonlinearity of concrete material during a strong earthquake. The framework of this model is briefly introduced, and details are provided in Refs. [17,19]. The stress tensor is given by:

r ¼ ð1  dÞr ¼ ð1  dÞE0 ðe  ep Þ

ð1Þ

 is the effective stress, E0 is the iniwhere d is the damage variable, r tial elastic stiffness, and e and ep denote the total strain and plastic strain, respectively. During plastic deformation, the normality plastic flow rule is applied as:

Þ @/ðr e_ p ¼ k_  @r

ð2Þ

f cy

( fby , fby )

(

)

1 α I1 + 3J 2 = c0 1−α Fig. 1. Initial yield function in plane stress space of concrete.

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where dt and dc are the uniaxial damage variables; wt and wc are the tensile and compressive stiffness recovery factors, respectively; and ^  Þ is a weight factor with a range from zero to the scalar quantity rðr one. 2.2. Model for rockfill materials and the interface The modified generalized plasticity model was introduced and applied to geomaterials by Mroz and Zienkiewicz [29] and was further developed by Zienkiewicz and Pastor [30,31]. Recently, several improvements to the generalized plasticity model have been proposed [32–34]. In this study, the modified generalized plasticity model by the authors [10] was used for the rockfill materials, and an elastic-perfectly-plastic interface model [10] with pressure-dependent shear stiffness was applied to simulate the interfaces between the face slabs and cushion gravel. For further details, we refer the reader to Refs. [7,10]. Using the modified generalized plasticity model for the rockfill, the residual dam deformation can be obtained directly from the 3D dynamic analysis instead of using a decoupled approach. 2.3. Procedure verification The plastic-damage model for concrete introduced in the previous section was implemented as a component of the finite element program GEODYNA [25] by the second author. This section describes the simulation of several monotonic and cyclic loading experimental tests [26,27] using a single 4-node plane stress isoparametric element. The loads are applied via displacement control. The material properties used in all cases are as follows [17]: elastic modulus, E = 31.0 (tensile) and 31.7 GPa (compressive); Poisson’s ratio, v = 0.18; density, q = 2,400 kg/m3; compression strength, fc0 = 27.6 MPa; tensile strength, ft0 = 3.48 MPa; fracture energy, Gc = 5,690 N/m (compressive) and Gt = 40 N/m (tensile); lc = 82.6 mm; and ap = 0.2.

under alternately applied loading and unloading. The numerical results of two cyclic uniaxial loading cases compared with the experimental data are illustrated in Fig. 3a and b. The results indicate that the model is able to capture the stiffness degradation in each unloading and reloading cycle. However, the hysteresis in reloading is not reflected due to the rate-independent assumption. These simulated results indicate that the plastic-damage constitutive model for concrete was successfully incorporated into the developed procedure, which will guarantee the rationality of the results of the CFRD dynamic responses analysis. 3. Identification of parameters 3.1. Slabs The introduced plastic-damage model was used to model the concrete face slabs. According to the available design information, the following properties were used in the analysis: density q = 2400 kg/m3, modulus of elasticity E = 25.5GPa, and Poisson’s ratio m = 0.167. To describe the plastic-damage behavior of the concrete, certain relevant parameters were used in this analysis based on Ref [17]: compression strength fc0 = 27.6 MPa and tensile strength ft0 = 3.48 MPa. The maximal uniaxial strain ef is assumed to be 5e4 based on the test results [26,27]. The characteristic length lc is determined to be 0.35 m based on the size of the slab element. The fracture energy under tensile stress can be evaluated using the following equation [22]:

Gt ¼

ð12Þ

Because the compressive strength of concrete is considerably higher than the tensile strength, only the tensile damage of the slab concrete is considered in this study. 3.2. Rockfill materials

(1) Monotonic uniaxial loading The existing uniaxial tensile and compressive loading experiments [26,27] were simulated to validate the performance of the model and the finite element program. The simulated results are compared with the corresponding experiments and numerical results from Lee and Fenves [17] and Omidi and Lotfi [28], as shown in Fig. 2a and 2b. The comparison indicates that the numerical simulations correspond well with the experimental results and the solutions from previous studies under uniaxial tensile and compressive loading. (2) Cyclic uniaxial loading

The rockfill material parameters are provided in Table 1 [7]. The model parameters are consistent with those used in the simulation of the static response of the Zipingpu CFRD, and the capacity of the constitutive model in describing the virgin loading, unloading, and reloading responses of the Zipingpu rockfill material is demonstrated in a previous paper by the authors [7]. A comparison of the predicted and tested responses of the same rockfill material in a large-scale cyclic triaxial test is also introduced in the paper [10]. 3.3. Interface

The cyclic uniaxial loading tests [26,27] are also presented to verify the ability of the model to describe the stiffness degradation

The interfaces between the concrete slabs and cushion gravel were investigated experimentally by Zhang and Zhang [35]. The

4

30

(a)

(b) Lee and Fenves Omidi and Lotfi Experimental this study

3

2

Stress/MPa

Stress/MPa

1 ef f lc 2 t

20

Lee and Fenves Omidi and Lotfi Experimental this study

10

1

0 0

0.0001

0.0002

0.0003

Strain

0.0004

0.0005

0 0

0.001

0.002

0.003

Strain

0.004

0.005

Fig. 2. Monotonic uniaxial loading tests simulation with experiment results and previous studies of concrete: (a) tensile test, and (b) compressive test.

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(a)

(b) Experimental this study

Stress/MPa

Stress/MPa

30 3

2

1

0

0

0.0001

0.0002

0.0003

0.0004

20

10

0

0.0005

Strain

Experimental this study

0

0.001

0.002

0.003

Strain

0.004

0.005

Fig. 3. Cyclic uniaxial loading tests simulation with experiment results of concrete: (a) tensile test and (b) compressive test.

Table 1 Rockfill material parameters in the modified generalized plasticity model. G0

K0

Mg

Mf

af

ag

H0

HU0

ms

1000

1400

1.8

1.38

0.45

0.4

1800

3000

0.5

mv

ml

mu

rd

cDM

cu

b0

b1

0.5

0.2

0.2

180

50

4

35

0.022

Table 2 Parameters of the concrete-gravel interfaces of the CFRD. k1

k2

n

u

c

300

1e10

0.8

41.5

0

This approach results in elements and nodes in all of the dam (Figs. 4 and 5), including the slab elements. The upstream slope of the dam is 1(vertical)/1.4(horizontal), whereas the downstream slope is 1/1.5. Prior to seismic loading, the dam was subjected to static loading, including self-weight and hydrostatic pressure. The dam being subjected to static loading is assumed as the initial

elastic-perfectly-plastic interface model parameters were calibrated using their test results and are listed in Table 2 [10]. Acceleration/g

4. Finite element analysis

0.4

4.1. Finite element mesh

0.2 0 -0.2 -0.4 0

5

The ideal CFRD with a height of 200 m used in the static and dynamic analysis is discretized using quadratic plane strain elements with a maximum mesh size of 0.3 m for the slab elements.

10

15

20

25

20

25

Time /s

(a) Transverse direction

Acceleration/g

0.4 0.2 0 -0.2 -0.4 0

5

10

15

Time /s

(b) Vertical direction Fig. 4. Finite element mesh of CFRD.

4

β

3

2

1

0 0.01

0.1

1

T /s

(c) Acceleration amplification response spectrum Fig. 5. Finite element mesh of slab.

Fig. 6. Input ground motion time history and response spectrum.

10

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state, and the damage due to static loading is also considered. Seismic loading is excited on the dam in the initial state, including the static stress field, strain field and displacement field. During the earthquake, the hydrodynamic pressure acting on the face slabs was simulated in the dynamic analysis using the added mass method [36] and the mass element was defined by a single node and concentrated mass components. The simplified Westergaard formula was used, and the added mass intensity on face-slabs can be expressed as:

mwi ¼

u 7 

90 8

q

pffiffiffiffiffiffiffiffiffiffiffiffiffi H 0  yi

ð13Þ

where q is the water density, u is the angle of the upstream slope, H0 is the depth from the position of node i to the bottom of the reservoir, and yi is the depth from the position of node i to the surface of reservoir. During the dynamic analysis, the added mass under the water level during the earthquake can be computed by integrating

mwi on the surface of the face slabs, and there are 5279 added mass elements in total. 4.2. Input ground motions A peak ground acceleration of 0.3 g was considered as the input motions in the upstream–downstream and vertical directions (Fig. 6a and b) and were formulated using the code spectrum (Fig. 6c) of the specifications for the seismic design of hydraulic structures in China [37]. The vertical PGA was two thirds of the horizontal PGA in the stream direction. 4.3. Damping In the developed procedure, the damping matrix was formulated using the assemblage of element-damping matrices and constructed as follows:

Concrete Model

Stress/MPa

200

150

2 0 -2 -4 -6 -8 -10 -12 -14 0

5

10

15

20

25

Time /s 100

Concrete Model

10

Model Elastic Plastic-damage 50

Elastic Plastic-damage

(b)

5

Stress/MPa

Height/m

Elastic Plastic-damage

(a)

0 -5 -10 -15 -20

0

5

10

15

20

25

Time /s

0 0

1

2

3 Fig. 9. The Slop-direction stress history of typical concrete slab elements: (a) without tensile damage; (b) with tensile damage.

Acceleration magnification Fig. 7. Dam axis acceleration magnification.

The tensile strength of concrete £¨3

(a)

8

6

7 5 4

3

1 2 3 4 5 6 7 8

0.00 m 0.06 m 0.12 m 0.18 m 0.24 m 0.30 m 0.36 m 0.42 m

200

150

7 6

8 5 4

1 2 3 4 5 6 3 7 8

0.00 m 0.06 m 0.12 m 0.18 m 0.25 m 0.31 m 0.37 m 0.43 m

Height/m

2

(b)

Model Elastic Plastic-damage

100

50

2 0 0

2

4

6

8

Stress /MPa Fig. 8. Contours of displacements at horizontal direction with different slab concrete model: (a) linear elastic model; (b) plastic-damage model.

Fig. 10. The maximum slope-direction tensile stress of concrete slabs elements.

B. Xu et al. / Computers and Geotechnics 65 (2015) 258–265

½Ce ¼ ae ½Me þ be ½Ke

ð14Þ

According to Rayleigh damping, for each element,

ke ¼

1 a

e

2 x

þ be x



ð15Þ

where x = 2pf is the circular frequency. This method resulted in frequency-dependent damping that did not correspond with the soil damping. Therefore, the range of the frequencies of interest is important for determining the soil damping. Martin et al. [38] proposed a method for determining the values of ae and be based on the predominant frequencies of the structure and the input motion; this method was employed in the QUAD4M procedure:

ae ¼ 2ke

be ¼ 2ke

x1 x2 x1 þ x2

ð16Þ

1

ð17Þ

x1 þ x2

x2 ¼ nx1

ð18Þ

n ¼ closest odded integer greater than xe =x2

ð19Þ

263

5. Results and discussion In this section, the earthquake responses of a 200-m-high CFRD are presented using the elastic and plastic-damage model for concrete. The results of different concrete models are compared to estimate the influence of the concrete model on the acceleration responses and deformation of the dam and the stress in the slabs. Furthermore, the development of the tensile damage in the slabs is analyzed during seismic excitation. This study primarily focuses on the slab performance during an earthquake, and thus, the results of construction and impoundment simulation were not introduced. 5.1. Acceleration responses and deformation of the dam Figs. 7 and 8 illustrate the acceleration responses along the middle axis of the dam and the vertical deformation of the dam after the earthquake using different concrete models. The different concrete models do not change the distribution of the acceleration responses and seismic deformations of the dam considerably, mainly because the acceleration responses and seismic deformations of the dam depend on the properties of the rockfill materials. The contribution of the slabs to the dam’s dynamic performance can be neglected when compared with that of the rockfill zones. 5.2. Slab stress

where x1 and xe are the predominant circular frequencies of the structure and input motion, respectively. In general, if dynamic problems are encountered in soils (or other geo-materials), the damping introduced by the plastic behavior of the material is sufficient to damp out any non-physical or numerical oscillations [38]. In this study, the damping ratio for the concrete slab and rockfill zone was assumed to be 5% in the dynamic analysis [39].

(a) t =11s

(c) t =16s

The stress histories along the slope direction in two typical elements are presented in Fig. 9a and b. For an element without damage (9a), the results from different concrete models provide nearly the same value during the earthquake, which indicates that the plastic-damage model is able to capture the linear behavior of concrete before damage occurs. For an element with serious damage

(b) t =15s

(d) t =17s

Fig. 11. The occurrence and development of the concrete slab’s damage at different moment from 0.6 H to 0.75 H.

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typical moments. Slight damage occurred initially from the slab’s contact with the cushion layer, which subsequently propagated to the surface. Fig. 10 shows that the maximum tensile stress along the slope direction computed by the linear elastic model of the concrete appeared at this elevation. These two results exhibit good agreement and corroborate each other. It could be assumed that the damage from the tensile stress along the slope direction induced the friction between the slabs and cushion layer. During the earthquake, when the dam body shakes toward the downstream direction, tensile damage will appear in the surface due to the stretching of the slabs. The tensile damage developed gradually during the earthquake and exceeded 0.8 in certain elements, which means that the cracking would occur in the slabs [19]. Fig. 12a and b illustrates the tensile damage distribution in the slabs after the earthquake. The main tensile damage occurred intensively at the two positions of 0.65 H and 0.85 H (where H is the dam height). The reason for the tensile damage that occurred at 0.85 H is the whipping effect caused by the earthquake, meaning that these two places are the weak links of the slabs. To improve the aseismic ability of the slabs, the local reinforcement ratio of the slab should be increased during engineering design. In addition, certain measures also should be applied to restrain the whipping effect, i.e., using cement laid stone masonry at the dam crest region or placing the nailed panel at the downstream slope (approximately the top 1/5 of the height).

6. Summary and conclusions In this study, an elastic–plastic dynamic analysis procedure for the CFRD was developed using the plastic-damage constitutive model presented by Lee and Fevens for cyclic loadings of concrete, and the generalized plastic constitutive model for rockfill materials was also applied. Monotonic and cyclic loading tests results of the concrete were simulated, and the results were compared with the experimental results and the results from previous studies to verify the procedure. Furthermore, the dynamic response of the ideal CFRD with a height of 200 m was investigated using the developed procedure with a focus on the tensile damage to the slabs during an earthquake. The following conclusions can be drawn based on the analysis results. Fig. 12. The damage distribution of the concrete slab at the end of earthquake: (a) the whole slabs; (b) from 0.6 H to 0.9 H.

(9b), the maximum tensile stress computed by the plastic-damage model reaches the tensile capacity of the concrete (3.48 MPa). However, the results based on the linear elastic model are greater than 8 MPa and exceed the tensile strength of the concrete. Fig. 10 shows the maximum stress along the slope direction in the slab elements during an earthquake according to different concrete models. The results computed by the linear elastic model exceed the tensile strength of the concrete for dam heights from 80 to 180 m. In contrast, the plastic-damage model showed that the stiffness degradation and stress redistribution occurred after the peak strength of the concrete was reached. Therefore, the results of the stress in the slabs computed from the plastic-damage model are more reasonable. According to this result, the seismic analysis of the high CFRDs should consider the influence of the concrete model on the stress in the slabs even though it might not have a noticeable effect on the dam’s acceleration response and seismic deformation.

5.3. Development of tensile damage in the slabs Fig. 11a–d present the damage in the slabs at the position with an elevation of 130 m (0.65 H, where H is the dam height) at four

(1) The acceleration responses and seismic deformations of the dam depend on the properties of the rockfill, and the use of different concrete models did not substantially change the distribution. (2) The plastic-damage model offers an improvement on the elastic model used in previous investigations in the area of CFRD numerical simulation. The results of the stress in the slabs calculated using the plastic-damage model do not exceed the tensile strength of concrete. The stiffness degradation was considered in the model, and the stress was observed to redistribute after the peak strength of the concrete was reached. (3) The main tensile damage in the slabs occurred intensively at the two positions of 0.65 H and 0.85 H (where H is the dam height) and resulted from the friction between the slabs and the cushion layer and the whipping result, respectively. Particular engineering measures should be applied at these positions to improve the aseismic capability of the slabs. (4) The use of the plastic-damage model for concrete in the analysis of CFRD dynamic responses offers the possibility of qualitative design in engineering. Additionally, the method could be used for damage evaluation of other seepage control structures of the CFRD, i.e., the concrete underground anti-seepage wall, plinth, and junction plate.

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Moreover, the procedure developed in this study could be adopted to analyze the interaction between soil and concrete structures. (5) Although the compressive strength of concrete is considerably higher than the tensile strength, axial extrusion damage took place in the Zipingpu CFRD during the Wenchuan earthquake [10]. Therefore, further work should include 3D numerical analysis to simulate this phenomenon and clarify the mechanism.

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