# Saturation Effect on the Coherency Loss of Spatially Varying Vertical Ground Motions

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{1}, t

_{2}, and c are set to 6, 10, and 0.5, respectively.

## 3. Numerical Example

_{r}is the saturation degree. Besides, herein, the bulk modulus of the solid skeleton is K

_{b}= 8.67 × 10

^{7}Pa; the bulk modulus of solid grains is K

_{s}= 3.6 × 10

^{10}Pa. Specific cases involved are summarized in Table 1, and fundamental information of simulated seismic motions is shown in Table 2. Simulation points, j and k, with a horizontal spacing distance of 100 m, are set. For every single parameter in each case, 1000 simulations were performed to calculate the mean lagged coherency loss and phase angle of the coherence function between the ground motions. Note that the case with 95% SD in case-1 is equivalent to that with GWL = 0 m in case-2, and the case with GWL = 30 m in case-2 is equivalent to that with WLT = 0 m in case-3.

_{n}, in the water layer can be defined as [13]

_{p}= 2224.7 m/s in fully saturated soil layer, while c

_{p}= 282.79 m/s in a soil layer with SD = 95%) and then the time delay between sites j and k, causing the superposition modes of the wave at sites j and k to be similar, and as thickness of fully saturated soil layer increases, the time delay would become lower and lower. Therefore, to a certain extent, the extra coherency loss due to irregular topography can be made up by an underlying fully saturated soil layer, and this phenomenon tends to be more remarkable as water table becomes higher and higher. At the frequencies where the vertical motion is suppressed significantly by the surface water layer, the value of coherency loss is extremely low. This is because around the frequencies where vertical motion is suppressed significantly by the surface water layer, the frequency content of the motions at j and k is extremely different. Coherency loss function only evaluates the difference between motions. Therefore, the larger the difference between the frequency content of motions, the lower the coherency loss.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Diagrams of site conditions for: (

**a**) the case with varying SD; (

**b**) the case with varying GWL; (

**c**) the case with varying WLT at point k (not to scale).

**Figure 3.**Coherence functions and relevant spectral ratios for varying: (

**a**) site SD; (

**b**) GWL; (

**c**) WLT.

No. of Case | Soil SD/% | GWL for the Whole Site/m | WLT at Point k/m |
---|---|---|---|

Case-1 (the case with varying SD) | 100/98/95/90/0 | - | - |

Case-2 (the case with varying GWL) | above GWL: 95 under GWL: 100 | 0/10/20/30 | - |

Case-3 (the case with varying WLT at point k) | above water layer surface: 95 under water layer surface: 100 | 30 | 0 |

40 | 10 | ||

50 | 20 | ||

60 | 30 |

Incident Angle | Total Duration | Upper Cut-Off Frequency | PGA | Sampling Frequency | No. of Sampling Points |
---|---|---|---|---|---|

60° | 20 s | 25 Hz | 0.2 g | 100 Hz | 2048 |

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**MDPI and ACS Style**

Yao, E.; Yang, Z.; Rao, Y.; Ding, X.; Liu, Z.; Wang, X.; Liu, W.; Li, W. Saturation Effect on the Coherency Loss of Spatially Varying Vertical Ground Motions. *Appl. Sci.* **2023**, *13*, 4302.
https://doi.org/10.3390/app13074302

**AMA Style**

Yao E, Yang Z, Rao Y, Ding X, Liu Z, Wang X, Liu W, Li W. Saturation Effect on the Coherency Loss of Spatially Varying Vertical Ground Motions. *Applied Sciences*. 2023; 13(7):4302.
https://doi.org/10.3390/app13074302

**Chicago/Turabian Style**

Yao, Erlei, Zhaowei Yang, Yu Rao, Xiuli Ding, Zhifang Liu, Xiujie Wang, Wenbo Liu, and Weichao Li. 2023. "Saturation Effect on the Coherency Loss of Spatially Varying Vertical Ground Motions" *Applied Sciences* 13, no. 7: 4302.
https://doi.org/10.3390/app13074302