Evolution law of overall damage of concrete gravity dam under near-fault ground motion

: Strong earthquake cases of concrete gravity dams show that the foundation damage has an important influence on the seismic response and damage characteristics of the dam body. Compared with non-pulse ground motions, pulse-like 9 near-fault ground motions have a wider response spectrum sensitive zone, which will cause more modes of the structure to 10 respond, resulting in more serious damage to the structure. In order to study the real dynamic damage characteristics of 11 concrete gravity dams under the action of near-fault ground motions, this paper takes Koyna gravity dam as the object and establishes a multi-coupling simulation model that can reasonably reflect the dynamic damage evolution process of dam concrete and foundation rock mass. A total of 12 near-fault ground motion records with three types of rupture directivity pulse, fling-step pulse and non-pulse are selected, deep research on the overall damage evolution law of concrete gravity dams. Considering the additional influence of different earthquake mechanisms, different site types and other factors on the study, the selected ground motion records are from the same seismic events (Chi-Chi), the same direction but different stations. The results show that the foundation of the concretes gravity dam often get damaged before the dam body under the action of strong earthquakes. Compared with the near-fault non-pulse ground motion, the structural damage of the gravity dam under the action of the near-fault directivity pulse ground motion is significantly increased, and causes greater damage and displacement response to the dam body. The near-fault fling-step pulse ground motion has the least impact on the dynamic 21 response of the gravity dam structure. 22


Introduction 25
Earthquake disaster survey data show that after an earthquake, major damage often occurs in the zone near the 26 epicenter (Eftekhari et al. 2020). Based on this phenomenon, the seismic engineering community and relevant 27 departments have begun to pay great attention to and study the characteristics of near-fault ground motions. 28 However, due to the uncertainty of earthquake occurrence, there are few near-fault ground motion records 29 obtained from actual records. Therefore, the study of near-fault pulse-type ground motions for a long period construction of high dams and large reservoirs is mainly concentrated in the western region, which is rich in 38 hydropower resources, but faces the inevitable seismic safety problem. Therefore, a correct understanding of 39 the impact of near-fault ground motions on the nonlinear dynamic damage and failure of gravity dams is of 40 great significance to comprehensively and accurately assessing the seismic resistance of large dam projects. 41 Strong earthquakes may cause damage and cracking of the concrete dam, threatening the safety of the 42 dam. In the seismic design and research of high concrete dams, we should break through some traditional 43 concepts and methods that are difficult to reflect reality. For example, in the seismic analysis of traditional 44 high concrete dams, the foundation rock mass is mostly used as linear elastic materials or DP elastoplastic micro-cracks and micro-cracks, resulting in the low tensile properties of the dam foundation material. Under 51 the reciprocating action of earthquakes, the dam foundation rock mass often cracks and fails first, which 52 releases seismic energy to a certain extent, thereby reducing the stress concentration of the dam heel and 53 preventing the dam from cracking and damage. And the measured data of the gravity dam subjected to the 54 earthquake also confirms this (after the earthquake, the Koyna gravity dam foundation interface was drilled 55 and sampled, and it was found that the concrete and the bedrock cemented well, and no signs of cracking at 56 the dam foundation interface were found, and the leakage of the dam foundation did not change significantly 57 after the earthquake) (Chen et al. 2014). The damage analysis of the foundation rock mass is an important part 58 of the damage analysis of multi-coupling system of high concrete dam. However, in the current research on 59 the damage of the high concrete dam system, the damage of the dam body is mostly studied, and the results of 60 the overall damage of the dam foundation are few. In order to truly understand the seismic performance of the 61 concrete gravity dam structure, it is necessary to conduct an in-depth study on the overall dynamic damage 62 evolution process of the dam foundation. references for the seismic design of concrete gravity dams. 87

Near-fault ground motion characteristics and selection methods 88
The long-term accumulation of energy in the crustal rock mass causes the rock formation to rupture and form 89 an earthquake. It is generally believed that the near-fault refers to the zone not more than 20 km away from directional pulse ground motion contains obvious two-way velocity pulses and a larger pulse period (Fig.1), 95 while the fling-step pulse ground motion contain unidirectional velocity and large pulses (Fig. 2). 96 direction. See Table 1 for the characteristics of various types of ground motion parameters. In the Table 1, Tpv  106 is the pulse period, D5-95 represents 5%-95% energy duration, and PGA, PGV, and PGD represent peak 107 ground acceleration, velocity and displacement respectively. 108 In order to avoid the impact of acceleration amplitude, this paper modulates the 12 selected near-fault 110 seismic waves with the acceleration peak value amax=0.2g. Fig.3 shows the average acceleration response 111 spectra of directivity pulse, fling-step pulse and non-pulse near-fault ground motions after amplitude 112 modulation under 5% damping ratio. As shown in the figure, from the peak of the average acceleration 113 response spectrum, the relationship between the three is directivity pulse > non-pulse > fling-step pulse. When 114 the period T < 0.38s, the magnitude order of the average value of the spectral acceleration is non-pulse > 115 directivity pulse > fling-step pulse. When the period T is within the range of 0.38~0.78s, the non-pulse and the 116 directivity pulse ground motion acceleration spectrum increased alternately, and all are greater than the mean 117 value of the fling-step pulse ground motion acceleration spectrum. When the period T ³ 0.78s, the mean value 118 of the directivity pulse acceleration spectrum is significantly greater than that of the non-pulse. Fig.4 shows 119 the average velocity response spectra of directivity pulse, fling-step pulse and non-pulse ground motions after 120 amplitude modulation. It can be seen from the figure that when the period T is small, the average velocity 121 response spectrum of the near-fault directivity pulse and non-pulse ground motions is greater than that of the 122 fling-step pulse ground motions. For long-period, the relationship between the three is fling-step pulse > 123 directivity pulse > non-pulse. 124 curve that the directivity pulse type ground motion velocity time history curve contains obvious long-period, 127 large-value, and short-duration two-way velocity pulse effects. The fling-step type ground motion contains 128 unidirectional speed big pulse. 129

Concrete plastic damage model 130
Because concrete is under complex stress state, the evolution law of tensile damage and compression damage 131 is different. Therefore, this paper uses a dual scalar damage model to simulate the dynamic damage and 132 cracking of concrete, and defines two independent damage variables to describe the material. Deterioration of 133 elastic rigidity caused by damage during tension and compression. Fig.6 and Fig.7 show the schematic 134 diagrams of concrete damage under tension and uniaxial compression respectively. 135 The constitutive relationship of the concrete plastic damage model is as follows: 136 (1) 137 (2) 138 In the formula: st and sc respectively represent the tensile and compressive stresses of the concrete; dt and dc 139 respectively tensile damage factor and compression damage factor;et andec represent tensile and compressive 140 strains respectively; et p and ec p respectively represent plastic strain in tension and plastic strain in compression; 141 E0 is the initial elastic modulus. 142 The Where α and γ are size-independent material constants ( , default value is 3), and are the 148 effective compressive and tensile stress tensors respectively; is the algebraic maximum eigenvalue 149 (maximum effective stress) of the effective stress tensor ; is the effective mises equivalent stress. 150 The flow law of the plastic damage model adopts the non-associated flow law, and its plastic potential 151 function is: 152 Where: x is the eccentricity of the plastic potential function of concrete; st0 is the uniaxial stress at failure;j is 154 the expansion angle of the concrete yield surface during the strengthening process. According to relevant 155 research results, the value of the concrete expansion angle is 36° ~42°. 156

Overall dynamic damage model and verification of gravity dam 157
In order to truly simulate the impact of ground motion on the damage of the overall system of a concrete 158 gravity dam, unlike the traditional model that considers the foundation as linear elastic or DP plastic, this 159 paper extends the concrete plastic damage model (CDP) to the foundation rock based on the similarity of dam 160 body concrete material and rock materials (Guo et al. 2020). Taking the Koyna concrete gravity dam project 161 as an example, the overall damage mechanics model of the concrete gravity dam body-reservoir 162 water-foundation is established. In order to verify its reliability, the measured seismic waves of Koyna dam is 163 used as input, and the Westergaard method is used to simulate hydrodynamic effects. After considering the 164 dissipated energy of the system to the remote ground (Gao et al. 2021), the seismic response damage analysis 165 of the gravity dam body-reservoir-foundation overall damage force system was carried out, and the analysis 166 results were compared with the actual earthquake damage. 167

Dynamic damage finite element model 168
Koyna gravity dam has always been a classic case of concrete dam dynamic analysis. On December 11, 1967, 169 the Koyna gravity dam in India suffered a magnitude 6.5 earthquake. The depth of the reservoir is 91. 75m  170 when the earthquake occurred. The earthquake caused many horizontal cracks on dam body, mainly 171 concentrated near the elevation of 629.0 m (as shown in Fig.8). This paper takes the Koyna gravity dam as the 172 research object and selects a typical retaining dam section of the dam for analysis. The upper, downstream and 173 depth directions of the foundation range are each twice the dam height. The dam body-reservoir-foundation 174 coupling model is shown in Fig.9. 175 wave is 0.474g (Fig.10), and the peak acceleration of the vertical seismic wave is 0.312g (Fig.11). Adopt

Damage evolution characteristics of Koyna gravity dam 189
Under the action of earthquake, the overall damage zone of the gravity dam at different times is shown in 190 Fig.12. After considering the nonlinear damage of the dam body and the foundation, due to the low tensile 191 strength of the dam foundation rock mass, at t=1.92 s, the dam foundation rock mass firstly began to have 192 damage cracks (Fig.12(a)). With the increasing of the duration of ground motion, the damage zone of the 193 bedrock expands about 23.1m in the depth direction, and then begins to expand obliquely downstream. At t 194 =3.64 s, damage cracks began to appear in the dam body, at this time, the depth of the damage cracks in the 195 bedrock is about 34.3 m (Fig.12(b)); After the ground motion is over, the final damage zone of the dam 196 system is shown in Fig.12(d). Dam body damage is mainly concentrated near the elevation of the downstream 197 break slope. The damage of the dam foundation mainly occurred in the bedrock at the heel of the dam, and it 198 extended about 35.2 m in the depth direction, but the impervious curtain was not damaged. It can be seen that 199 after considering the damage of the dam foundation, the foundation part of the concrete gravity dam will be 200 damaged before the dam body under the action of the earthquake. It shows that it is necessary to consider the 201 overall plastic damage of the dam body and the bedrock in the seismic analysis of the concrete gravity dam. 202 (a) t=1.92s (b) t=3.64s (c) t=4.26s (d) t=10s heel. This also shows that only the dam body is considered as a plastic damage model, and the bedrock is 208 considered as a linear elastic or elastoplastic model, which cannot accurately simulate the damage evolution 209 process of a concrete gravity dam multi-coupling system under seismic response. The actual survey after the 210 earthquake also showed that the cracks of the Koyna gravity dam caused by the earthquake were mainly 211 concentrated near the elevation of 629.0 m (Fig.8). Core-drilling sampling at the interface of the dam 212 foundation found that the concrete and bedrock cemented well, no signs of cracking at the interface of the 213 dam foundation were found, and there was no significant change in the leakage of the dam foundation after 214 the earthquake. The simulation results in this paper are in good agreement with the actual earthquake damage. 215

Dynamic response and damage characteristics of gravity dams under near-fault ground motions 216
In order to study the influence of near-fault ground motions on the dynamic damage of the overall system of 217 concrete gravity dams, this paper uses the different types of near-fault ground motion records selected in 218 section 2 to modulate the amplitude of the acceleration peak amax=0.2g as the ground motion input (only 219 consider ground motion horizontal component). The effects of three types of near-fault ground motions on the 220 overall damage evolution of the concrete gravity dam foundation are studied from the aspects of plastic 221 damage zone, dissipated energy and displacement response of the dam. 222

Evolution law of overall damage of dam body and foundation 223
Under the action of near-fault ground motions, the damage and failure process of gravity dam body and 224 foundation material is the deterioration of the mechanical properties of the material caused by the growth, 225 expansion and connection of micro-cracks inside it. It is also an irreversible and energy-consuming evolution 226 process of the internal structure of the material. Fig.13 shows the overall damage distribution of gravity dams 227 under different types of near-fault ground motions. The blue zone indicates that the material is not damaged, 228 and the red zone indicates that the material is damaged by tensile damage. It can be seen from the figure that 229 under the action of the three types of near-fault ground motions, the dam foundation rock mass materials have 230 suffered serious tensile damage. It shows that under the action of earthquake, the dam foundation rock mass is 231 the weak link of the earthquake resistance of the concrete gravity dam. It is necessary to pay more attention to 232 the earthquake resistance analysis of the concrete gravity dam. When the near-fault directivity pulse ground 233 motion is used as input, the overall damage of the gravity dam foundation is shown in Fig.13(a). Both the 234 concrete material of the dam body and the rock material of the foundation suffered serious damage and failure. 235 Among them, the damage of the dam foundation mainly occurred in the bedrock part at the heel of the dam 236 and extended along the depth direction. The concrete damage of the dam body is concentrated in the 237 downstream break slope and spreads upstream. Under the action of the near-fault fling-step pulse ground 238 motion, the overall damage of the gravity dam is shown in Fig.13 (b). It can be seen that there is no damage to 239 the dam body of the concrete gravity dam. Similarly, the damage of the dam foundation mainly occurs in the 240 bedrock part at the heel of the dam and extends in the depth direction. Under near-fault non-pulse ground 241 motions, as shown in Fig.13 (c), similar to the directivity pulse and fling-step pulse ground motions, the dam 242 foundation damage occurs in the bedrock part at the dam heel and extends along the depth direction. 243 Compared with the near-fault directivity pulse ground motion, the dam concrete material is less damaged. 244  has the least impact on the damage and failure of the concrete gravity dam. 257

5.2．dissipated energy characteristics of dam body and foundation 259
The damage and failure of the gravity dam will accumulate in the form of dissipated energy under the action

Analysis of deformation characteristics of gravity dam structure 298
The maximum horizontal displacement of the dam vertex obtained by nonlinear time history analysis is 299 shown in Table 3. It can be seen from the table that under the action of directivity pulse ground motions, the 300 average response of the horizontal displacement of the crest of the dam is the largest. The maximum average 301 displacements in the upstream and downstream directions is 5.78 and 4.87 cm, respectively. The maximum 302 average displacements in the upstream and downstream directions of the dam apex caused by non-pulse 303 ground motions is 5.56 and 3.37 cm, respectively. The displacement response of the dam vertex caused by the 304 fling-step pulse ground motion is 4.30 and 2.51 cm, respectively. From the perspective of the displacement 305 amplitude of the dam vertex caused by ground motions, the relationship between the three working conditions 306 is directivity pulse (10.66cm) > non-pulse (8.93cm) > fling-step pulse (6.81cm). Among them, the average 307 amplitude of the dam vertex displacement caused by the directivity pulse ground motion is 1.19 times of the 308 non-pulse and 1.57 times of the fling-step pulse. 309 In order to facilitate the comprehensive comparison of dam structural deformation caused by different 311 types of near-fault ground motions, the method of expressing the dam deformation characteristics in reference 312 (Liu et al. 2014) is given in the article. In this paper, three displacement angles f1, f1, and f3 are used to 313 represent the residual deformation characteristics of the dam caused by near-fault ground motions. 314 In the formula: u1 and u2 respectively represent the residual horizontal displacement at the vertex and heel of 316 the upstream dam face; u3 and u4 represent the residual horizontal displacement at the vertex of the 317 downstream dam face and the downstream break slope respectively; u5 represents the residual horizontal 318 displacement at the dam toe. Among them, the relative displacement angle f1 reflects the overall deformation 319 of the dam; f2 reflects the overall deformation of the dam head part; and f3 reflects the deformation of the 320 lower structure of the dam. height. This is because after the gravity dam is subjected to near-fault directivity pulse and non-pulse ground 333 motions, the concrete at the downstream break slope has cracked damage, which causes the dam head to tilt in 334 the upstream direction. However, under the action of near-fault sliding type ground motion, the dam concrete 335 did not crack and damage. 336 dam displacement response. The research work has achieved the following understanding: 347 (1)Under the action of three types of near-fault ground motions, the dam foundation of the concrete 348 gravity dam is damaged before the dam body. Among them, the directivity pulse ground motion has the 349 greatest impact on the damage and failure of the concrete gravity dam, followed by the non-pulse ground 350 motion, and the fling-step pulse ground motion is the smallest.

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(2)From the perspective of dissipated energy characteristics. Under the action of near-fault directivity 352 pulse-type ground motions, the plasticity dissipated energy and damage dissipated energy values of the dam 353 body and the dam foundation are close. The dissipated energy caused by near-fault fling-step pulse and 354 non-pulse ground motions is mainly concentrated in the dam foundation. Compared with the near-fault 355 fling-step pulse and non-pulse ground motions, the damage and failure of the dam body caused by the 356 directivity pulse ground motions should be paid more attention.

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(3) From the perspective of the dam body deformation, directivity pulse ground motions can cause larger 358 residual deformation of the dam overall structure and head part. However, the impact on the residual 359 deformation of the lower part of the dam body is relatively small, this is because the directivity pulse ground 360 motion cause larger damage and cracks on the downstream break slope, after the earthquake, the head of the 361 dam tilted in the upstream direction. Under the action of the three types of near-fault ground motions, the 362 average amplitude of the dam crest displacement caused by the directivity pulse ground motion is 1.2 times of 363 the non-pulse and 1.57 times of the fling-step pulse. 364 In summary, compared with the fling-step pulse and non-pulse ground motions, directivity pulse ground 365 motions have a significant impact on the nonlinear seismic response of concrete gravity dams. Therefore, it is 366 necessary to consider the influence of near-fault directivity pulse ground motions when analyzing the seismic 367 safety of concrete gravity dams. There has been the research result enunciation, more significant vertical 368 ground motions in the near-fault area. If the vertical pulse ground motion is also considered, it will 369 undoubtedly further increase the overall damage and failure of the the gravity dam. At present, there are few 370 studies on the seismic response of gravity dam structures under the coupled action of pulse-type two-phase 371 ground motions, and further research is still needed. 372 373