# Prediction of Dynamic Behavior of Large-Scale Ground Using 1 g Shaking Table Test and Numerical Analysis

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Soil Properties

^{3}and 12.43 kN/m

^{3}, respectively. The optimum moisture content of the soil was determined to be 12.5%. The Atterberg limit test indicated that the Plastic Index (PI) was Non-Plastic (NP). The maximum and minimum void ratios were calculated as 1.123 and 0.443, respectively. The fine content of the soil was measured at 10.8%, and based on the Unified Soil Classification System, the soil was classified as SW-SM. For the dynamic model test, a specimen was selected from the portion of the sample passing through the No. 4 sieve after the physical property tests. The remaining sample retained in the No. 4 sieve was approximately 1%. Table 1 shows the geotechnical index properties of the specimen used in the 1 g shaking table test.

#### 2.2. 1 g Shaking Table Test

#### 2.2.1. Experimental Equipment

^{2}. The data logger used the 24-channel SDL-350R model and was compatible with ARF-20A. The data storage interval is up to 0.005 s. Figure 4b,c show the data logger and accelerometer used in this study.

#### 2.2.2. Experimental Method

#### 2.3. Numerical Analysis

#### 2.3.1. DEEPSOIL Program

#### 2.3.2. Finite Element Analysis

_{max}, h = 0.16 G

_{max}, m = 0.8.

## 3. Results and Discussion

#### 3.1. Acceleration-Time History

#### 3.2. Peak Ground Acceleration

#### 3.3. Spectral Acceleration

#### 3.4. The Stress–Strain Curve of Large-Scale Models

## 4. Conclusions

- By comparing RMSE results, the experimental results were in good agreement with the numerical analysis results in terms of consistency. The dynamic behavior of the slope model from the numerical analysis was consistent with that from the 1 g shaking table test. It was shown that the laminar shear box can minimize the influence of boundaries on the dynamic behavior of soil. The laminar shear box was evaluated to perform well for the slope model. The results of the ABAQUS analysis were in good agreement with those of the experimental analysis for the slope model.
- For different constitutive models, the numerical analysis results were still slightly different. For the flat ground, DEEPSOIL results were closer to the experimental results. For the slope model, the Borja model gave better results than the Mohr–Coulomb model. The input parameters of different constitutive models are different, which is why different numerical analysis results exist.
- Numerical analysis was conducted to obtain stress–strain curves for different constitutive models. The numerical analysis results indicated that the Daredneli model did not accurately capture the behavior under high-strain conditions in the dynamic analysis. On the other hand, the Mohr–Coulomb and Borja models performed better in representing the stress–strain response. It highlights the advantage of using nonlinear and elastoplastic models in their respective applicable regions. The Darendeli model sometimes needs to adequately capture the dynamic behavior of soils under more significant strains, but the Borja model does not.
- The 1 g shaking table test provides a valuable method to evaluate numerical analysis, capture complex behavior, and resolve uncertainties, ultimately leading to more robust and reliable analysis and enhancing the value of the 1 g shaking table test.
- In this study, extensive numerical analysis has been performed to overcome the size limitation of the 1 g shaking table test in predicting the dynamic behavior of real-scale ground. Combining the results of numerical analysis and the 1 g shaking table test, as well as a series of theories, such as the similarity law, the 1 g shaking table experiment can replace the centrifuge test. An equation has been developed to obtain the natural frequency of the real-scale ground. In actual earthquake engineering, the natural frequency can be obtained by this method. The prediction and analysis of the dynamic behavior of large-scale ground by numerical analyses along with the 1 g shaking table test is significant.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Kim, H.; Kim, D.; Lee, Y.; Kim, H. Effect of soil box boundary conditions on dynamic behavior of model soil in 1 g shaking table test. Appl. Sci.
**2020**, 10, 4642. [Google Scholar] [CrossRef] - Saha, R.; Haldar, S.; Dutta, S.C. Influence of dynamic soil-pile raft-structure interaction: An experimental approach. Earthq. Eng. Eng. Vib.
**2015**, 14, 625–645. [Google Scholar] [CrossRef] - Niu, J.; Jiang, X.; Yang, H.; Wang, F. Seismic response characteristics of a rock slope with small spacing tunnel using a large-scale shaking table. Geotech. Geol. Eng.
**2018**, 36, 2707–2723. [Google Scholar] [CrossRef] - Lin, M.L.; Wang, K.L. Seismic slope behavior in a large-scale shaking table model test. Eng. Geol.
**2016**, 86, 118–133. [Google Scholar] [CrossRef] - Kheradi, H.; Nagano, K.; Nishi, H.; Zhang, F. 1-g shaking table tests on seismic enhancement of existing box culvert with partial ground-improvement method and its 2D dynamic simulation. Soils Found.
**2018**, 58, 563–581. [Google Scholar] [CrossRef] - Zarnani, S.; El-Emam, M.M.; Bathurst, R.J. Comparison of numerical and analytical solutions for reinforced soil wall shaking table tests. Geomech. Eng.
**2011**, 3, 291–321. [Google Scholar] [CrossRef] - Pitilakis, D.; Dietz, M.; Wood, D.M.; Clouteau, D.; Modaressi, A. Numerical simulation of dynamic soil–structure interaction in shaking table testing. Soil Dyn. Earthq. Eng.
**2008**, 28, 453–467. [Google Scholar] [CrossRef] - Moghadam, M.R.; Baziar, M.H. Seismic ground motion amplification pattern induced by a subway tunnel: Shaking table testing and numerical simulation. Soil Dyn. Earthq. Eng.
**2016**, 83, 81–97. [Google Scholar] [CrossRef] - Guo, M.Z.; Gu, K.S.; Wang, C. Dynamic response and failure process of a counter-bedding rock slope under strong earthquake conditions. Symmetry
**2022**, 14, 103. [Google Scholar] [CrossRef] - Aldaikh, H.; Alexander, N.A.; Ibraim, E.; Knappett, J. Shake table testing of the dynamic interaction between two and three adjacent buildings (SSSI). Soil Dyn. Earthq. Eng.
**2016**, 89, 219–232. [Google Scholar] [CrossRef] - Shunzo, O. Introduction to Earthquake Engineering; Wiley: Hoboken, NJ, USA, 1973. [Google Scholar]
- Kagawa, T. On the similitude in model vibration tests of earth-structures. In Proceedings of the Japan Society of Civil Engineers; Japan Society of Civil Engineers: Tokyo, Japan, 1978; Volume 1978, pp. 69–77. [Google Scholar]
- Iai, S. Similitude for shaking table tests on soil-structure-fluid model in 1 g gravitational field. Soils Found
**1989**, 29, 105–118. [Google Scholar] [CrossRef] - Zhang, W.; Esmaeilzadeh Seylabi, E.; Taciroglu, E. Validation of a three-dimensional constitutive model for nonlinear site response and soil-structure interaction analyses using centrifuge test data. Int. J. Numer. Anal. Methods Geomech.
**2017**, 41, 1828–1847. [Google Scholar] [CrossRef] - Sadiq, S.; Van Nguyen, Q.; Jung, H.; Park, D. Effect of flexibility ratio on seismic response of cut-and-cover box tunnel. Adv. Civ. Eng.
**2019**, 2019, 4905329. [Google Scholar] [CrossRef] - Kim, H.; Jin, Y.; Lee, Y.; Kim, H.S.; Kim, D. Dynamic response characteristics of embankment model for various slope angles. J. Korean Geosynth. Soc.
**2020**, 19, 35–46. [Google Scholar] [CrossRef] - Darendeli, M.B. Development of a New Family of Normalized Modulus Reduction and Material Damping Curves. Ph.D. Thesis, The University of Texas at Austin, Austin, TX, USA, 2001. [Google Scholar]
- Borja, R.I.; Lin, C.H.; Sama, K.M.; Masada, G.M. Modelling non-linear ground response of non-liquefiable soils. Earthq. Eng. Struct. Dyn.
**2000**, 29, 63–83. [Google Scholar] [CrossRef] - Boore, D.M.; Joyner, W.B. Site amplifications for generic rock sites. Bull. Seismol. Soc. Am.
**1997**, 87, 327–341. [Google Scholar] [CrossRef] - Graves, R.W.; Aagaard, B.T.; Hudnut, K.W.; Star, L.M.; Stewart, J.; Jordan, T.H. Broadband simulations for Mw 7.8 southern San Andreas earthquakes: Ground motion sensitivity to rupture speed. Geophys. Res. Lett.
**2008**, 35, L22302. [Google Scholar] [CrossRef]

**Figure 2.**Simulation of the dynamic behavior and responses of large-scale models through 1 g shaking table test.

**Figure 3.**The experimental system used in this study [16].

**Figure 5.**Acceleration-time history of the input ground motions used in this study: (

**a**) Artificial seismic wave; (

**b**) Hachinohe seismic wave; (

**c**) Ofunato seismic wave.

**Figure 7.**Acceleration-time history of the input ground motions used in this study: (

**a**) A typical shear stress—shear strain relationship of soil; (

**b**) Normalized shear modulus and damping ratio.

**Figure 9.**Part of the acceleration-time history of the artificial seismic wave in flat ground. (

**a**) 2 × 0.6 m (1 time); (

**b**) 4 m × 1.2 m (2 times); (

**c**) 10 m × 3 m (5 times); (

**d**) 20 m × 6 m (10 times); (

**e**) 50 × 15 m (25 times); (

**f**) 100 × 30 m (50 times).

**Figure 10.**Part of the acceleration-time history graph of the artificial seismic wave in the sloping ground. (

**a**) 2 × 0.6 m (1 time); (

**b**) 4 m × 1.2 m (2 times); (

**c**) 10 m × 3 m (5 times); (

**d**) 20 m × 6 m (10 times); (

**e**) 50 × 15 m (25 times); (

**f**) 100 × 30 m (50 times).

**Figure 11.**PGA profile for experiment and numerical analysis with the artificial seismic wave. (

**a**) 2 × 0.6 m (1 time); (

**b**) 4 m × 1.2 m (2 times); (

**c**) 10 m × 3 m (5 times); (

**d**) 20 m × 6 m (10 times); (

**e**) 50 × 15 m (25 times); (

**f**) 100 × 30 m (50 times).

**Figure 12.**The spectral acceleration of Artificial seismic wave in the flat ground. (

**a**) 2 × 0.6 m (1 time); (

**b**) 4 m × 1.2 m (2 times); (

**c**) 10 m × 3 m (5 times); (

**d**) 20 m × 6 m (10 times); (

**e**) 50 × 15 m (25 times); (

**f**) 100 × 30 m (50 times).

**Figure 13.**The spectral acceleration of the artificial seismic wave in the sloping ground (

**a**) 2 × 0.6 m (1 time); (

**b**) 4 m × 1.2 m (2 times); (

**c**) 10 m × 3 m (5 times); (

**d**) 20 m × 6 m (10 times); (

**e**) 50 × 15 m (25 times); (

**f**) 100 × 30 m (50 times).

**Figure 14.**The stress–strain curve of 2 × 0.6 m (1-time) model: (

**a**) Darendeli model; (

**b**) Mohr–Coulomb model; (

**c**) Bojar model.

**Figure 15.**The stress–strain curve of 100 × 30 m (50 times) model: (

**a**) Darendeli model; (

**b**) Mohr–Coulomb model; (

**c**) Bojar model.

Parameter | Value | Parameter | Value |
---|---|---|---|

No. 200 Passing (%) | 10.8 | emax | 1.123 |

Gs | 2.69 | emin | 0.443 |

OMC (%) | 12.5 | rd max (kN/m^{3}) | 18.27 |

PI (%) | NP | rd min (kN/m^{3}) | 12.43 |

USCS | SW-SM |

Item | Specification |
---|---|

Table size (mm) | 2000 × 600 |

Maximum acceleration (g) | 1 |

Full play load (kg) | 1800 |

Payload capacity (kg) | 5000 |

Operating frequency (Hz) | 10 |

Item | Specification | Item | Specification | Item | Specification |
---|---|---|---|---|---|

Mass density | 1 | Length | λ | Acceleration | 1 |

Frequency | λ^{−1} | Shear wave velocity | λ^{−0.5} | Stress | λ |

Modulus | 1 | Time | λ^{0.75} | Strain | 1 |

Parameter | Value |
---|---|

Unit weight (kN/m^{3}) | 17.658 |

OCR | 1 |

N | 10 |

K_{0} | 0.5 |

Frequency | $f={\mathrm{V}}_{\mathrm{s}}/4H$, |

Parameter | Value |
---|---|

Density (kg/m^{3}) | 1800 |

Poisson’s ratio | 0.3 |

Poisson’s ratio | 0.3 |

Internal friction angle (°) | 27.7 |

Cohesion yield stress (kN) | 10 |

Dilatancy angle (°) | 24.4 |

Parameter | Value | Parameter | Value |
---|---|---|---|

Density (kg/m^{3}) | 1800 | Young’s modulus (Pa) | $\mathrm{E}=2\mathsf{\rho}{\mathrm{V}}^{2}(1+\upsilon )$ |

Poisson’s ratio | 0.3 | h | 2 MPa |

m | 0.8 | R | 50 kpa |

Omega | 0.414 | xi | 0.0785 |

H_{0} | 0 |

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**MDPI and ACS Style**

Jin, Y.; Jeong, S.; Kim, D.
Prediction of Dynamic Behavior of Large-Scale Ground Using 1 g Shaking Table Test and Numerical Analysis. *Materials* **2023**, *16*, 6093.
https://doi.org/10.3390/ma16186093

**AMA Style**

Jin Y, Jeong S, Kim D.
Prediction of Dynamic Behavior of Large-Scale Ground Using 1 g Shaking Table Test and Numerical Analysis. *Materials*. 2023; 16(18):6093.
https://doi.org/10.3390/ma16186093

**Chicago/Turabian Style**

Jin, Yong, Sugeun Jeong, and Daehyeon Kim.
2023. "Prediction of Dynamic Behavior of Large-Scale Ground Using 1 g Shaking Table Test and Numerical Analysis" *Materials* 16, no. 18: 6093.
https://doi.org/10.3390/ma16186093