# Assessment of Liquefaction Hazard for Sites in Romania Using Empirical Models

^{1}

^{2}

^{*}

## Abstract

**:**

_{W}≥ 6.0 is employed for the evaluation of the equivalent number of cycles for this seismic source. Several functional forms for the empirical evaluation of the equivalent number of cycles considering various seismological or engineering parameters are tested and evaluated. The regression analysis shows smaller uncertainties for the empirical models based on ground motion engineering parameters. Considering the lack of information in terms of engineering parameters, a simpler empirical model which accounts for the earthquake magnitude, source–site distance and soil conditions is selected for the liquefaction hazard analysis. Based on the proposed empirical model, specific magnitude scaling factors for Vrancea intermediate-depth earthquakes are proposed for the first time as well. The liquefaction hazard analysis is performed for sites whose seismic hazard is generated by either the Vrancea intermediate-depth seismic source or by local shallow crustal seismic sources. In the case of some of the selected sites, liquefaction phenomena were observed during past large-magnitude earthquakes. Unlike previous studies dealing with liquefaction analyses for sites in Romania, in this research, the hazard assessment is performed for various ground motion levels evaluated based on probabilistic seismic hazard assessment. Liquefaction hazard curves are constructed for each analyzed site. The results of the liquefaction hazard analysis show that this phenomenon is more likely to occur in the areas exposed to Vrancea intermediate-depth earthquakes, compared to the areas affected by local shallow earthquakes. In the case of the analyzed soil profiles from Bucharest, Craiova and Ianca, the minimum liquefaction safety factors less than one even for seismic hazard levels having mean return periods of 100 years and less.

## 1. Introduction

## 2. Research Methodology

## 3. Evaluation of the Number of Equivalent Cycles

_{W}≥ 6.0 is compiled for this analysis. The database is a part of the larger ground motion database used in the past studies of Yaghmaei-Sabegh et al. [32] and Pavel and Yaghmaei-Sabegh [33], which deal with the evaluation of the mean period T

_{M}and of the control period T

_{C}for intermediate-depth earthquakes. Only ground motion recordings having a minimum peak ground acceleration (PGA) of 0.05 g [34] are selected for the analysis. The total number of ground motion recordings used for the evaluation of the number of equivalent cycles is 139. Some characteristics of the earthquakes in the database are given in Table 2. Smaller-magnitude Vrancea earthquakes were not considered in the analysis because of the low levels of ground shakings they produce (leading to small macrosiesmic intensities). In this study, the procedure of Seed et al. [35], described also in the study of Castiglia and Santucci de Magistris [34], is employed for the evaluation of the equivalent number of cycles for the ground motion recordings in the database.

_{W}≥ 7.0. A fitted exponential trendline is also shown in the plot. The value of the coefficient of determination R

^{2}for the exponential fit is rather small.

_{M}[36], Arias Intensity [37] and the significant ground motion duration D

_{5-95}[38] are selected as well. It can be observed from Table 3 that the largest correlation coefficients for the equivalent number of cycles are obtained with the earthquake magnitude M

_{W}, hypocentral distance R and significant ground motion duration D

_{5-95}. The same observation holds true also for the logarithm of the equivalent number of cycles, albeit the values of the correlation coefficients can differ substantially for the same considered parameter.

## 4. Empirical Models for the Number of Equivalent Cycles

_{A}; (4) T

_{M}and (5) D

_{5-95}.

_{1}–c

_{5}), (d

_{1}–d

_{7}) and (e

_{1}–e

_{5}) and the model standard deviation are reported in Table 4, Table 5 and Table 6. In Equations (4)–(8), PGA is measured in g and the PGV is in m/s.

## 5. Liquefaction Hazard Analysis for Selected Sites

_{W}≤ 7.5. In addition, the proposed magnitude scaling factors are close to the ones proposed by Seed and Idriss [61].

- The saturated sand deposits are situated at depths larger than 15 m;
- The site design peak ground acceleration is less than 0.15 g, coupled with some other requirements related to the clay or silt content of the sands and the SPT blow count value normalized for overburden effects, and for the energy ratio, N
_{1}(60) is more than 20 or 30.

## 6. Conclusions

_{W}≥ 6.0 is employed in this study for the development of the empirical models. Several empirical models having various dependent parameters are proposed in the study. Specific magnitude scaling factors for liquefaction are proposed for the Vrancea intermediate-depth earthquakes. Subsequently, liquefaction hazard curves are developed for the analyzed sites considering the ground motion input obtained from probabilistic seismic hazard assessment. The most important observations of the study are summarized below:

- The largest correlation coefficients for the equivalent number of cycles are obtained with the earthquake magnitude M
_{W}, hypocentral distance R and significant ground motion duration D_{5-95}; - It was observed that the smallest uncertainty of the proposed empirical models is obtained for the model considering all the engineering parameters;
- The equivalent number of cycles computed using the relation proposed by Seed et al. [35] is larger than the ones obtained using the empirical model from this study, but the difference between the two empirical models decreases with the hypocentral distance;
- The regression coefficients show that the equivalent number of cycles decreases from soil classes A and B to soil class F (deep soft sites);
- The analyzed soil profiles for Bucharest, Craiova and Ianca show minimum liquefaction safety factors less than one even for seismic hazard levels having mean return periods of 100 years and less;
- The results of the liquefaction hazard analysis show that this phenomenon appears more likely in the areas exposed to Vrancea intermediate-depth earthquakes, compared to the areas affected by local shallow earthquakes.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Distribution of the equivalent number of cycles as a function of: (

**a**) hypocentral distance R; (

**b**) peak ground acceleration.

**Figure 2.**Distribution of the equivalent number of cycles as a function of earthquake magnitude. The fitted exponential trendline is shown with the black dashed line.

**Figure 3.**Variation of the equivalent number of cycles as a function of the earthquake magnitude and soil class for: (

**a**) R = 100 km; (

**b**) R = 200 km; (

**c**) R = 300 km [35].

**Figure 4.**Distribution of the residuals as a function of: (

**a**) earthquake magnitude; (

**b**) hypocentral distance R. The fitted linear trendlines are shown with black dashed line.

**Figure 5.**Histograms of residuals as a function of the soil class: (

**a**) soil classes A and B; (

**b**) soil classes C, D and E; (

**c**) soil class F.

**Figure 7.**Seismic hazard curves for peak ground acceleration for the analyzed sites [52].

**Figure 8.**Comparison of the minimum and maximum particle size distribution curves for sands in Romania which liquefied during the Vrancea 1977 earthquake [29].

Step No. | Description | Sites Affected by Crustal Seismic Sources | Sites Affected by Vrancea Seismic Sources |
---|---|---|---|

1 | Evaluation of the equivalent number of cycles | Not necessary | Computed using a ground motion database from Vrancea earthquakes |

2 | Empirical models for the equivalent number of cycles | Not necessary | Developed based on the results from step (1) |

3 | Evaluation of magnitude scaling factors | Not necessary | Developed based on the results from step (2) |

4 | Evaluation of site seismic hazard | Evaluated based on probabilistic seismic hazard assessment from a previous study | |

5 | Liquefaction hazard assessment | Evaluated based on SPT data for the selected sites | |

6 | Liquefaction hazard curves | Evaluated for all the ground motion amplitudes |

Date | Moment Magnitude M_{W} | Focal Depth (km) | No. of Ground Motion Recordings | PGA Range (g) |
---|---|---|---|---|

4 March 1977 | 7.4 | 94 | 2 | 0.10–0.20 |

30 August 1986 | 7.1 | 131 | 33 | 0.05–0.30 |

30 May 1990 | 6.9 | 91 | 47 | 0.05–0.26 |

31 May 1990 | 6.4 | 87 | 19 | 0.05–0.12 |

27 October 2004 | 6.0 | 105 | 38 | 0.05–0.21 |

Parameter | M_{W} | R | PGA | PGV | T_{M} | I_{A} | D_{5-95} |
---|---|---|---|---|---|---|---|

N_{eq} | 0.352 | 0.288 | −0.165 | −0.049 | 0.064 | −0.033 | 0.286 |

ln N_{eq} | 0.368 | 0.281 | −0.196 | −0.084 | 0.049 | −0.044 | 0.230 |

Model | c_{1} | c_{2} | c_{3} | c_{4} | c_{5} | σ |
---|---|---|---|---|---|---|

(1) | −1.342 | 0.465 | - | - | - | 0.52 |

(2) | −2.821 | 0.405 | 0.367 | - | - | 0.51 |

(3) | −2.294 | 0.395 | 0.329 | −0.214 | −0.412 | 0.49 |

Model | d_{1} | d_{2} | d_{3} | d_{4} | d_{5} | d_{6} | σ |
---|---|---|---|---|---|---|---|

(4) | 1.133 | −0.403 | 0.133 | - | - | - | 0.55 |

(5) | −0.626 | −1.440 | −0.424 | 0.942 | - | - | 0.38 |

(6) | −0.933 | −1.907 | 0.094 | 0.926 | −0.633 | - | 0.36 |

(7) | −0.703 | −1.972 | −0.001 | 0.990 | −0.524 | −0.138 | 0.35 |

Model | e_{1} | e_{2} | e_{3} | e_{4} | e_{5} | e_{6} | σ |
---|---|---|---|---|---|---|---|

(9) | −1.651 | 0.447 | 0.149 | - | - | - | 0.52 |

(10) | −3.107 | 0.388 | 0.146 | 0.362 | - | - | 0.51 |

(11) | −0.595 | 0.384 | 0.128 | 0.324 | −0.169 | −0.381 | 0.49 |

Soil Class | Mean | Median | Standard Deviation | Skewness |
---|---|---|---|---|

Soil classes A and B | 0.000 | 0.028 | 0.416 | −0.464 |

Soil classes C, D and E | 0.000 | 0.061 | 0.520 | −0.824 |

Soil class F | 0.000 | −0.034 | 0.484 | 0.082 |

All soil classes | 0.000 | 0.008 | 0.489 | −0.428 |

No. | Site | Layer Name | Layer Depth (m) | Layer Thickness (m) | Average N_{SPT} | Water Table Depth (m) |
---|---|---|---|---|---|---|

1 | Bucharest | medium sand | 4.5–9.5 | 5.0 | 10 | 4.5 |

2 | Bucharest | medium sand | 6.0–8.5 | 2.5 | 11 | 5.5 |

3 | Bucharest | medium sand | 6.5–10.5 | 4.0 | 16 | 5.2 |

4 | Craiova | clayey sand | 0.6–3.4 | 2.8 | 9 | 2.0 |

5 | Craiova | fine sand | 1.9–8.5 | 6.6 | 13 | 2.0 |

6 | Caracal | fine sand | 0.8–6.0 | 5.2 | 16 | 3.5 |

7 | Giurgiu | fine sand | 1.9–4.0 | 2.1 | 14 | 1.5 |

8 | Constanta | medium sand | 0.3–8.5 | 8.2 | 17 | 1.5 |

9 | Ianca | fine sand | 3.7–8.0 | 5.3 | 16 | 5.2 |

10 | Timisoara | medium sand | 0.3–2.6 | 2.3 | 12 | 0.8 |

11 | Timisoara | medium sand | 1.0–3.1 | 2.1 | 9 | 1.1 |

12 | Arad | fine sand | 0.5–5.1 | 4.6 | 15 | 1.0 |

13 | Oradea | fine sand | 0.7–2.5 | 1.8 | 18 | 1 |

14 | Medias | fine sand | 0.2–3.2 | 3.0 | 9 | 1.8 |

15 | Sighisoara | clayey sand | 0.9–4.3 | 3.4 | 8 | 2.0 |

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**MDPI and ACS Style**

Pavel, F.; Vladut, R.
Assessment of Liquefaction Hazard for Sites in Romania Using Empirical Models. *Infrastructures* **2023**, *8*, 133.
https://doi.org/10.3390/infrastructures8090133

**AMA Style**

Pavel F, Vladut R.
Assessment of Liquefaction Hazard for Sites in Romania Using Empirical Models. *Infrastructures*. 2023; 8(9):133.
https://doi.org/10.3390/infrastructures8090133

**Chicago/Turabian Style**

Pavel, Florin, and Robert Vladut.
2023. "Assessment of Liquefaction Hazard for Sites in Romania Using Empirical Models" *Infrastructures* 8, no. 9: 133.
https://doi.org/10.3390/infrastructures8090133