# Nonlinear Dynamic Response of a CC-RCC Combined Dam Structure under Oblique Incidence of Near-Fault Ground Motions

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Characteristics and Selection of Near-Fault Ground Motions

#### 2.1. Characteristics of Near-Fault Ground Motions

#### 2.2. Selection of Near-Fault Pulse and Non-Pulse Ground Motions

## 3. The Input Method of the Obliquely Incident P Wave

#### 3.1. The Viscous-Spring Artificial Boundary

_{T}and K

_{N}represent tangent spring coefficient and normal spring coefficient, G is the shear modulus of the foundation, λ is the lame constant, r is the distance from the scattering wave source to the boundary, A

_{l}represents the area of all the elements containing the node l. C

_{T}and C

_{N}are tangential damping coefficient and normal damping coefficient, ρ is the medium density, c

_{s}is the S wave velocity, and c

_{p}is the P wave velocity. A is the coefficient of 0.8, and B is the coefficient of 1.1.

#### 3.2. P Waves Input Method

_{0}, y

_{0}, z

_{0}) of the model, as shown in Figure 3.

_{1}, the angle between the plane determined by the incident waves and the reflected waves and the xoy plane is α (in order to control a single variable, assuming α is 0° in this research), and the angle between the reflected SV waves and the y-axis positive direction is θ

_{2}. Then, the time-histories of displacement of any point in three directions under the action of free wave field can be expressed as:

_{1}, A

_{2}, and B

_{2}correspond to the amplitude of the potential function of them. Assuming the medium is homogeneous, isotropic, and elastic, and considering the wave theory and stress state of element, the equivalent nodal load in the three directions of the left boundary can be obtained based on Equation (3):

#### 3.3. Numerical Verification on the Input Method

^{3}, the elastic modulus is 32.5 GPa, and Poisson’s ratio is 0.22. A cube finite region of 2000 m × 2000 m × 2000 m was cut out, and the cube was discretized into the solid elements with the side length of 50 m, which meet the requirements of finite element accuracy, and Figure 4 shows the model of the cube. At the side face and bottom face of the cube, the artificial boundary was used. Figure 5 shows the input P wave displacement time-history curve, and the total time is 5.0 s with an interval of 0.005 s.

## 4. CC-RCC Gravity Dam-Foundation Numerical Model

#### 4.1. 3D Dam-Foundation Finite Element Model

#### 4.2. Material Parameters and Loading

## 5. Results and Discussion

#### 5.1. Horizontal Relative Displacements of the Dam Crest

#### 5.2. Damage Distribution of Dam

#### 5.3. Damage Analysis of Interface Structures

#### 5.4. Summary of Results

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**The input of obliquely incident P waves and the model of the viscous-spring artificial boundary.

**Figure 7.**Three-dimensional (3D) gravity dam-foundation system finite element model and the partition diagram of dam body material.

**Figure 9.**The horizontal displacement of point A with respect to point B (under the input angle of 75°).

**Figure 10.**The horizontal displacement of point A with respect to point C (under the input angle of 75°).

**Figure 11.**The maximum absolute value of the relative horizontal displacements (under different input angles).

**Figure 12.**The maximum absolute value of the relative horizontal displacements (under different PGV/PGA ratio).

**Figure 13.**The seismic plastic-damage response of the gravity dam under pulse and non-pulse ground motions.

Earthquake | #1 | #2 | #3 | |||
---|---|---|---|---|---|---|

No. | 1 | 2 | 3 | 4 | 5 | 6 |

Ground motion types | Pulse-like | Non-pulse | Pulse-like | Non-pulse | Pulse-like | Non-pulse |

Station name | PST225 | WP1046 | EDA270 | |||

R_{jb} (km) | 0.95 | 2.11 | 5.09 | |||

Magnitude | 6.54 | 6.69 | 6.53 | |||

Duration (s) | 22.31 | 22.31 | 24.99 | 24.99 | 39.10 | 39.10 |

PGA(g) | 0.2 | 0.2 | 0.2 | 0.2 | 0.2 | 0.2 |

PGV(cm/s) | 61.81 | 23.58 | 56.33 | 29.45 | 52.89 | 21.27 |

PGV/PGA(s) | 0.315 | 0.120 | 0.287 | 0.150 | 0.270 | 0.108 |

Materials | Elasticity Modulus (GPa) | Poisson’s Ratio | Density (kg/m^{3}) |
---|---|---|---|

II-Conventional concrete | 42.6 | 0.167 | 2489 |

I-2-Conventional concrete | 44.3 | 0.167 | 2487 |

Roller compacted concrete | 47.4 | 0.167 | 2476 |

Foundation rock | 30.4 | 0.170 | 2800 |

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**MDPI and ACS Style**

Zhang, J.; Zhang, M.; Li, M.; Min, Q.; Shi, B.; Song, L.
Nonlinear Dynamic Response of a CC-RCC Combined Dam Structure under Oblique Incidence of Near-Fault Ground Motions. *Appl. Sci.* **2020**, *10*, 885.
https://doi.org/10.3390/app10030885

**AMA Style**

Zhang J, Zhang M, Li M, Min Q, Shi B, Song L.
Nonlinear Dynamic Response of a CC-RCC Combined Dam Structure under Oblique Incidence of Near-Fault Ground Motions. *Applied Sciences*. 2020; 10(3):885.
https://doi.org/10.3390/app10030885

**Chicago/Turabian Style**

Zhang, Jiawen, Mengxi Zhang, Mingchao Li, Qiaoling Min, Bowen Shi, and Lingguang Song.
2020. "Nonlinear Dynamic Response of a CC-RCC Combined Dam Structure under Oblique Incidence of Near-Fault Ground Motions" *Applied Sciences* 10, no. 3: 885.
https://doi.org/10.3390/app10030885