# New Stress Reduction Factor for Evaluating Soil Liquefaction in the Coastal Area of Catania (Italy)

^{*}

## Abstract

**:**

_{d}, which depends on several factors (depth; earthquake and ground motion characteristics; dynamic soil properties). Various relationships of r

_{d}are reported in literature because of the importance of assessment of CSR. Herein, new variations of r

_{d}with depth have been obtained using different deterministic earthquake scenarios as input motion. The relationships are based on large numbers of site response analyses for different site conditions. The new relationships obtained have been used for the evaluation of the liquefaction potential in the area of the Catania Harbour. The liquefaction resistance has been evaluated by the horizontal stress index (K

_{D}) from seismic dilatometer Marchetti tests (SDMTs). Various correlations were developed to estimate the CRR from K

_{D}, expressed in form of CRR-K

_{D}curves to differentiate between liquefiable and non-liquefiable zones. In this study three different CRR-K

_{D}curves have been used.

## 1. Introduction

_{d}.

_{d}relationships are proposed for the eastern coastal plain of Catania area (Italy). The city of Catania, in South-Eastern Sicily, was affected by several destructive earthquakes of about magnitude 7.0 in past times. Extensive liquefaction effects occurred following the 1693 and 1818 strong earthquakes [8,9,10,11].

## 2. Shear Stress Reduction Factor: State-of-Art Review

_{av}= average cyclic shear stress, a

_{max}= peak horizontal acceleration at the ground surface generated by the earthquake, g = acceleration of gravity, σ

_{v0}and σ

_{v0}’= total and effective overburden stresses, and r

_{d}= stress reduction coefficient depending on depth.

_{d}is added to adjust for the flexibility of the soil profile because the soil does not respond as a rigid body [6].

_{d}are estimated from the chart by Seed and Idriss [12] as shown in Figure 1.

_{d}from the surface to a depth of 12 m (~40 ft) [5]. The value of r

_{d}decreases from a value of 1 at the ground surface to lower value at large depths.

_{d}value given in the chart from the surface to a depth 30 m (~100 ft):

_{d}below a depth of 23 m. Indeed, the uncertainty of r

_{d}increases with depth and the simplified procedure is not well verified for depths greater than 15 m [14]. Moreover, the r

_{d}proposal of Seed and Idriss understates the variance and provides biased (generally high) estimation of r

_{d}between 3 and 15 m [1]. Unfortunately, it is the critical soil strata for evaluating soil liquefaction potential [1].

_{d}can be expressed as:

_{S}= uniform soil shear wave velocity, w = frequency of excitation, z = depth. This relationship is plotted in Figure 2.

_{d}is expressed through a linearly decreasing function with depth as:

_{d}relationship that takes into account the effects of earthquake magnitude and depth in the evaluation of r

_{d}.

_{d}calculated using previous equation for M = 5½, 6½, 7½, and 8 are presented in Figure 3. Also shown is the average of the range published by Seed and Idriss [12].

_{d}correlations as a function of depth, earthquake magnitude, intensity of shaking, and site stiffness. They performed a total of 2153 site response analyses by the equivalent linear method. The r

_{d}recommendations proposed by Seed and Idriss [12] are conservatively biased compared to over 80,000 point estimations of r

_{d}from 2153 cases as shown in Figure 4.

_{d}relationship from equivalent-linear site response analyses. Several forms for r

_{d}were examined and the following form was selected for its simplicity and shape:

_{d}at large depths, β = variable that controls the curvature of the function at shallow depths, z = depth in meters and (1-α) = term that scales the exponential.

_{w}) and average shear-wave velocity in the upper 12 m of the profile (V

_{S12}) and the other solely being a function of M

_{W}. The first set of expressions for α and β is:

_{1}-b

_{6}are regression coefficients.

## 3. Seismicity of the Catania Area

_{S}= 7.0–7.3, I

_{o}= X–XI MCS) and 1818 (M

_{S}= 6.2, I

_{o}= IX MCS) strong earthquakes [26].

## 4. Site Response Analysis

_{d}relationships are proposed for the eastern coastal plain of Catania.

_{d}relationships.

_{S}measurements have been incorporated within a Marchetti flat dilatometer (DMT) by placing a velocity transducer in a connecting rod just above the blade. The seismic modulus is an instrumented tube housing two receivers at a distance of 0.50 m [8,30] (Figure 11).

_{d}: material index; M: vertical drained constrained modulus; ϕ: angle of shear resistance; K

_{D}: horizontal stress index; V

_{S}: shear waves velocity; ${\mathrm{G}}_{0}={\mathsf{\delta}\mathrm{V}}_{\mathrm{S}}^{2}$: small strain shear modulus.

_{SPT}-value and S-wave velocity of sands are variables dependent on several parameters such as combinations of effective stress, void ratio, soil fabric, etc. [44].

_{S}, is based on the presence in the literature of several empirical correlations that relate V

_{S}and N

_{SPT}-values.

- (a)
- Ohta and Goto [45]:$${\mathrm{V}}_{\mathrm{S}}=54.33{\left({\mathrm{N}}_{\mathrm{SPT}}\right)}^{0.173}\mathsf{\alpha}\mathsf{\beta}{\left(\frac{\mathrm{z}}{0.303}\right)}^{0.193}$$
_{S}= shear wave velocity (m/s), N_{SPT}= number of blows from SPT, z = depth in meters, $\mathsf{\alpha}$ = age factor (Holocene = 1.000, Pleistocene = 1.303), $\mathsf{\beta}$= geological factor (clays = 1.000, sands = 1.086). - (b)
- Yoshida and Motonori [46]:$${\mathrm{V}}_{\mathrm{S}}=\mathsf{\beta}{\left({\mathrm{N}}_{\mathrm{SPT}}\right)}^{0.25}{\mathsf{\sigma}\u2019}_{\mathrm{V}0}^{0.14}$$
_{S}= shear wave velocity (m/s), N_{SPT}= number of blows from SPT,$\mathsf{\beta}=$geological factor (any soil 55, fine sand 49), σv_{0}’ = effective vertical stress.

^{2}, 196.2 kN/m

^{2}and 294.3 kN/m

^{2}). The plots of shear stresses corresponding to failure versus normal stresses are shown in Figure 15.

_{S}value of 800 m/s (soil type A according to Italian technical regulations [50]). The criterion of choice adopted to evaluate the depth of bedrock consists in the linear interpolation of the shear waves profiles. The depth obtained is approximately 80 m which corresponds to a V

_{S}value of about 800 m/s.

## 5. Shear Stress Reduction Factor r_{d} in the Catania Area (Italy)

_{d}, as a parameter describing the ratio of cyclic stress for a flexible soil column to the cyclic stress for a rigid soil column [5] (Figure 19):

_{d}relationships are proposed for the eastern coastal plain of Catania area (Italy). They have been developed from equivalent-linear site response analyses performed on soil profiles obtained from SPTs date, available for eight boreholes (n. 418–425), and from seismic dilatometer tests (SDMT1-13). The seismic events of 1693 and 1818 have been chosen as scenario earthquakes.

_{d}for sandy saturated soil profiles of eastern coastal Catania area have been determined. They are shown in the Figure 20 and Figure 21.

_{d}from the surface to a depth of 30 m. They can be approximated by Equations (14) and (15).

_{d}relationships obtained for soil profiles of the Catania coastal area are compared to the relationship previously proposed by Iwasaki [16]. As can be seen from the chart, the latter provides slightly higher estimates of r

_{d}.

_{d}values, given in the Figure 20 and Figure 21, from the surface to a depth 30 m:

_{d}relationships are compared to relationships previously proposed by Liao and Whitman [13], and Robertson and Wride [14] from the chart of Seed and Idriss [12]. It is possible to observe that the r

_{d}proposal of Seed and Idriss [12] provides higher estimation of r

_{d}between 0 and 19 m.

## 6. Evaluation of Liquefaction Potential Using the Seismic Dilatometer Marchetti Tests (SDMTs) in the Catania Harbour (Italy)

_{d}relationships, more responsive to soil types examined, have been used for potential liquefaction evaluation in the Catania Harbour (Italy).

_{SL}) profile given by the ratio of the cyclic resistance ratio CRR(z) to cyclic shear stress ratio CSR(z), where z is the depth of the deposit [54].

_{D}curves, approximated by the Equations (19)–(21), have been used.

_{max}. The stress reduction coefficient r

_{d}and the magnitude scaling factor MSF have been given by the Equations (17a,b) and (18), respectively, and the values of the other parameters have been taken from the SDMTs date.

_{D}curves, approximated by Equations (19)–(21), and the horizontal stress index K

_{D}of the 5 SDMTs have been used. Values of K

_{D}versus depth for SDMT4, as example, are shown in Figure 25.

_{D}trends i.e., for SDMT2.

_{D}curves are in good agreement and the level of liquefaction severity is generally high. However, lower LPI values are obtained from the SDMT5 and higher values from the SDMT4. Furthermore, results demonstrate that the ground acceleration is a crucial parameter in the evaluation of liquefaction potential: a 0.1g increase of a

_{max}produces a rise of about 25–50% in LPI.

## 7. Conclusions

_{d}with depth have been obtained from equivalent-linear site response analyses performed on different profiles representative of eastern coastal plain of Catania area. To evaluate the soil profiles and the geotechnical characteristics, in situ and laboratory tests were performed.

_{d}values and the dashed line represents the recommended values of r

_{d}from the surface to a depth of 30 m.

_{d}obtained here are lower.

_{d}relationship is more responsive to soil type examined. The findings can be summarized as follows:

- (1)
- The results obtained from the three CRR-K
_{D}curves are in good agreement. However, it is possible to observe that the equation developed by Monaco provides LPI values slightly larger than those obtained from the equations proposed by Grasso and Maugeri; - (2)
- The results show a high liquefaction potential from the depth of about 3–7 m;
- (3)
- Lower values of the liquefaction potential index are obtained from the SDMT4 and higher values from the SDMT3;
- (4)
- Finally, results demonstrate that the peak horizontal acceleration at the ground surface a
_{max}is an important parameter in the evaluation of liquefaction potential.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Range of values of r

_{d}for different soil profiles (Modified from Seed and Idriss [12]).

**Figure 2.**Stress reduction coefficient versus depth (Modified from Ishihara [15]).

**Figure 3.**Variation of the stress reduction coefficient with depth and earthquake magnitude (from Idriss and Boulanger [6]).

**Figure 8.**Location of standard penetration test (SPT), cone penetration tests (CPT), and seismic dilatometer Marchetti tests (SDMT) in the Saint Giuseppe La Rena site (Eastern coast of Catania, Sicily).

**Figure 10.**Layout of SDMT tests: (

**a**) Catania Harbour area; (

**b**) Nazario Sauro School; (

**c**) National Institute of Geophysics and Volcanology (INGV); (

**d**) Madre Teresa di Calcutta School; (

**e**) STM M6; (

**f**) Bellini Garden; (

**g**) Monte Po.

**Figure 11.**Seismic dilatometer test: (

**a**) SDMT equipment (blade and seismic module); (

**b**) schematic test layout (From Castelli et al. [30]).

**Figure 12.**SDMT equipment (

**a**) at the Saint Giuseppe La Rena site; (

**b**) at the Catania Harbour site; (

**c**) at STM M6 site; (

**d**) at Bellini Garden site; (

**e**) at Monte Po site; (

**f**) at INGV site.

**Figure 13.**Comparison of V

_{S}determined from empirical correlations, Equations (9) and (10), and SDMT1.

**Figure 14.**Horizontal shear stress- horizontal displacement curves under different normal stress conditions (98.1 kN/m

^{2}, 196.2 kN/m

^{2}and 294.3 kN/m

^{2}): (

**a**) S2C2 soil sample (retrieved at 13.20 m in SDMT2 borehole), (

**b**) S4C1 soil sample (retrieved at 8.40 m in SDMT4 borehole).

**Figure 15.**Shear stresses corresponding to failure versus normal stresses (

**a**) S2C2 soil sample (retrieved at 13.20 m in SDMT2 borehole), (

**b**) S4C1 soil sample (retrieved at 8.40 m in SDMT4 borehole).

**Figure 16.**Interactive seismic hazard maps of the city of Catania: (

**a**) 5% probability of exceedance in 50 years (return period of 975 years); (

**b**) 2% probability of exceedance in 50 years (return period of 2475 years).

**Figure 17.**r

_{d}results from response analyses for different soil profiles (SPT1-8 and SDMT1-13) using as input 1693 and 1818 scaled synthetic seismograms to the maximum PGA of 0.3 g.

**Figure 18.**r

_{d}results from response analyses for different soil profiles (SPT1-8 and SDMT1-13) using as input the 1693 and 1818 scaled synthetic seismograms to the maximum PGA of 0.5 g.

**Figure 19.**Schematic for determining maximum shear stress,${\tau}_{max}$, and the stress reduction coefficient, r

_{d}(from Idriss and Boulanger [6]).

**Figure 20.**Range of values of r

_{d}for different soil profiles (SPT1-8 and SDMT1-13) using 1693 and 1818 scaled synthetic seismograms to the maximum PGA of 0.3 g.

**Figure 21.**Range of values of r

_{d}for different soil profiles (SPT1-8 and SDMT1-13) using 1693 and 1818 scaled synthetic seismograms to the maximum PGA of 0.5 g.

**Figure 22.**Comparison of r

_{d}relationship obtained by Iwasaki [16] and relationships proposed in this study.

**Figure 24.**CRS profiles obtained for SDMT2: (

**a**) using the peak horizontal acceleration at the ground surface of 0.4 g; (

**b**) using the peak horizontal acceleration at the ground surface of 0.5 g.

**Figure 25.**Horizontal stress index K

_{D}versus depth of the SDMT4, as example, performed in the Catania Harbour.

**Figure 27.**Liquefaction potential values obtained from: (

**a**) SDMT2 and a

_{max}= 0.4 g; (

**b**) SDMT2 and a

_{max}= 0.5 g; (

**c**) SDMT4 and a

_{max}= 0.4 g; (

**d**) SDMT4 and a

_{max}= 0.5 g.

**Table 1.**Experimental sites and tests used to obtain new r

_{d}relationships in Catania area (Sicily, Italy).

Experimental Sites | Tests |
---|---|

Saint Giuseppe La Rena | SPT 1 (borehole 418) |

Saint Giuseppe La Rena | SPT 2 (borehole 419) |

Saint Giuseppe La Rena | SPT 3 (borehole 420) |

Saint Giuseppe La Rena | SPT 4 (borehole 421) |

Saint Giuseppe La Rena | SPT 5 (borehole 422) |

Saint Giuseppe La Rena | SPT 6 (borehole 423) |

Saint Giuseppe La Rena | SPT 7 (borehole 424) |

Saint Giuseppe La Rena | SPT 8 (borehole 425) |

Saint Giuseppe La Rena | SDMT 1 |

Catania Harbour | SDMT 2 |

Catania Harbour | SDMT 3 |

Catania Harbour | SDMT 4 |

Catania Harbour | SDMT 5 |

Catania Harbour | SDMT 6 |

Nazario Sauro school | SDMT 7 |

Nazario Sauro school | SDMT 8 |

INGV building | SDMT 9 |

Madre Teresa di Calcutta School | SDMT 10 |

STM M6 | SDMT 11 |

Bellini Garden | SDMT 12 |

Monte Po | SDMT 13 |

**Table 2.**Level of liquefaction severity [60]

LPI | Level of Liquefaction Severity |
---|---|

0 | Very low |

0 < LPI ≤ 5 | Low |

5 < LPI ≤ 15 | High |

LPI > 15 | Very high |

**Table 3.**Values of the surface maximum acceleration for the five SDMTs obtained from the site response analysis using the scaled PT1R3 seismogram to the maximum PGA of 0.3g.

Surface Maximum Accelerations | |
---|---|

SDMT2 | 0.44g |

SDMT3 | 0.43g |

SDMT4 | 0.45g |

SDMT5 | 0.49g |

SDMT6 | 0.41g |

**Table 4.**The liquefaction potential index from the five SDMTs for the three different CRR-K

_{D}curves using a

_{max}of 0.4g and 0.5g.

Liquefaction Potential Index | ||||||
---|---|---|---|---|---|---|

a_{max} | 0.4 g | 0.5 g | ||||

CRR-K_{D} curves | 1 | 2 | 3 | 1 | 2 | 3 |

SDMT2 | 13.30 | 9.12 | 9.37 | 17.04 | 12.52 | 12.22 |

SDMT3 | 12.44 | 7.48 | 7.80 | 16.47 | 11.06 | 10.59 |

SDMT4 | 17.13 | 11.97 | 12.01 | 22.50 | 16.06 | 15.78 |

SDMT5 | 7.50 | 3.36 | 3.53 | 11.13 | 6.02 | 5.41 |

SDMT6 | 12.51 | 8.99 | 9.44 | 15.83 | 11.86 | 11.74 |

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## Share and Cite

**MDPI and ACS Style**

Grasso, S.; Massimino, M.R.; Sammito, M.S.V.
New Stress Reduction Factor for Evaluating Soil Liquefaction in the Coastal Area of Catania (Italy). *Geosciences* **2021**, *11*, 12.
https://doi.org/10.3390/geosciences11010012

**AMA Style**

Grasso S, Massimino MR, Sammito MSV.
New Stress Reduction Factor for Evaluating Soil Liquefaction in the Coastal Area of Catania (Italy). *Geosciences*. 2021; 11(1):12.
https://doi.org/10.3390/geosciences11010012

**Chicago/Turabian Style**

Grasso, Salvatore, Maria Rossella Massimino, and Maria Stella Vanessa Sammito.
2021. "New Stress Reduction Factor for Evaluating Soil Liquefaction in the Coastal Area of Catania (Italy)" *Geosciences* 11, no. 1: 12.
https://doi.org/10.3390/geosciences11010012