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

geosciences

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

Salvatore Grasso * , Maria Rossella Massimino and Maria Stella Vanessa Sammito

Department of Civil Engineering and Architecture, University of Catania, 95125 Catania, Italy; [email protected] (M.R.M.); [email protected] (M.S.V.S.) * Correspondence: [email protected]

Abstract: In this paper, a study concerning the soil liquefaction potential in the city of Catania is presented. The stress-based liquefaction analysis framework for cohesionless soil includes a function that describes fundamental aspects of dynamic site response, i.e., the shear stress reduction coefﬁcient,

rd, which depends on several factors (depth; earthquake and ground motion characteristics; dynamic soil properties). Various relationships of rd are reported in literature because of the importance of assessment of CSR. Herein, new variations of rd 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 (KD) from seismic dilatometer Marchetti tests (SDMTs). Various correlations were developed to estimate the CRR from KD, expressed in form of CRR-KD curves to differentiate between liqueﬁable and non-liqueﬁable zones. In this study three different CRR-KD curves have been used.

Keywords: liquefaction; site response analyses; simpliﬁed analysis methods; shear stress reduction factor

Citation: Grasso, S.; Massimino, M.R.; Sammito, M.S.V. New Stress Reduction Factor for Evaluating Soil 1. Introduction Liquefaction in the Coastal Area of Catania (Italy). Geosciences 2021, 11, Soil liquefaction is a major cause of damage during earthquake [1]. Liquefaction is 12. https://doi.org/10.3390/ defined as the transformation of a granular material from solid to a liquefiable state as a geosciences11010012 consequence of increase pore pressure and reduced effective stress [2]. Thus, the evaluation of the susceptibility of a site to seismic-induced liquefaction is an important step in many Received: 23 October 2020 geotechnical investigations. It may be assessed comparing the cyclic resistance ratio (CRR) Accepted: 23 December 2020 to the cyclic shear stress ratio (CSR) due to the ground motion [3–7]. Published: 28 December 2020 Estimates of the in situ CSR can be developed directly, using dynamic response analysis, but it is common in simplified analysis methods to develop estimates of the in Publisher’s Note: MDPI stays neu- situ CSR using empirical relationships [5]. One of the parameters to be evaluated is the tral with regard to jurisdictional clai- stress reduction coefficient rd. ms in published maps and institutio- In this paper, new rd relationships are proposed for the eastern coastal plain of Catania nal affiliations. 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 [8–11]. Copyright: © 2020 by the authors. Li- censee MDPI, Basel, Switzerland. 2. Shear Stress Reduction Factor: State-of-Art Review This article is an open access article The stress-based simplified procedure for evaluating soil liquefaction potential, orig- distributed under the terms and con- inally developed by Seed and Idriss [12], compares the seismic demand of a soil layer ditions of the Creative Commons At- (CSR) with the capacity of the soil to resist liquefaction (CRR). If CSR is greater than CRR, tribution (CC BY) license (https:// liquefaction can occur. The cyclic stress ratio CSR can be calculated by the following creativecommons.org/licenses/by/ equation [3]: 4.0/).

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! 𝜏 𝑎 𝜎 𝐶𝑆𝑅τav = =0.65amax σv0 𝑟 (1) CSR = 0 = 0.65 0 rd (1) 𝜎 𝑔 𝜎 σv0 g σv0 where τav = average cyclic shear stress, amax = peak horizontal acceleration at the ground where τav = average cyclic shear stress, amax = peak horizontal acceleration at the ground surface generated by the earthquake, g = acceleration of gravity, σv0 and σv0'= total and surface generated by the earthquake, g = acceleration of gravity, σv0 and σv0’= total and effective overburden stresses, and rd = stress reduction coefficient depending on depth. effective overburden stresses, and rd = stress reduction coefficient depending on depth. The stress reduction coefficient rd is added to adjust for the flexibility of the soil The stress reduction coefficient rd is added to adjust for the flexibility of the soil profile becauseprofile because the soil doesthe soil not does respond not respond as a rigid as body a rigid [6]. body [6]. ForFor routine routine practice practice the the values values of rofd arerd are estimated estimated from from the chartthe chart by Seed by Seed and Idriss and Idriss [12] as[12] shown as shown in Figure in Figure1. 1.

FigureFigure 1. 1.Range Range of of values values of ofr drdfor for different different soil soil proﬁles profiles (Modiﬁed (Modified from from Seed Seed and and Idriss Idriss [12 [12]).]).

ThisThis chart chart was was determined determined using using a a limited limited number number of of input input strong strong motion motion and and soil soil ± profilesprofiles having having sandsand inin the upper ±1515 m. m. The The dashed dashed line line labeled labeled “Average “Average values” values” rep- represents the recommended values of rd from the surface to a depth of 12 m (~40 ft) [5]. resents the recommended values of rd from the surface to a depth of 12 m (~40 ft) [5]. The The value of rd decreases from a value of 1 at the ground surface to lower value at large value of rd decreases from a value of 1 at the ground surface to lower value at large depths. depths. The following equations can be used to estimate the average rd value given in the The following equations can be used to estimate the average rd value given in the chart from the surface to a depth 30 m (~100 ft): chart from the surface to a depth 30 m (~100 ft): (2.1) rd =𝑟 1.0= 1.0− 0.00765 − 0.00765𝑧z f or 𝑓 z𝑜𝑟≤ 9.15 𝑧 m ≤ 9.15𝑚 (2a) 𝑟 = 1.174 − 0.0267𝑧 𝑓𝑜𝑟 9.15𝑚 < 𝑧 ≤23𝑚 (2.2) rd = 1.174 − 0.0267z f or 9.15 m < z ≤ 23 m (2b) 𝑟 = 0.744 − 0.008𝑧 𝑓𝑜𝑟 23𝑚 < 𝑧 ≤30𝑚 (2.3) rd = 0.744 − 0.008z f or 23 m < z ≤ 30 m (2c) where z = depth below ground surface in meters. where z = depth below ground surface in meters. The Equations (2.1) and (2.2) were proposed by Liao and Whitman [13] and the The Equations (2a,b) were proposed by Liao and Whitman [13] and the Equation (2c) Equation (2.3) was proposed by Robertson and Wride [14]. Youd et al. [7] suggested the was proposed by Robertson and Wride [14]. Youd et al. [7] suggested the Equations (2a,b) Equations (2.1) and (2.2) for noncritical projects and did not recommend values of rd be- for noncritical projects and did not recommend values of rd below a depth of 23 m. Indeed, low a depth of 23 m. Indeed, the uncertainty of rd increases with depth and the simplified the uncertainty of rd increases with depth and the simplified procedure is not well verified procedure is not well verified for depths greater than 15 m [14]. Moreover, the rd proposal for depths greater than 15 m [14]. Moreover, the rd proposal of Seed and Idriss understates of Seed and Idriss understates the variance and provides biased (generally high) estima- the variance and provides biased (generally high) estimation of rd between 3 and 15 m [1]. Unfortunately,tion of rd between it is the3 and critical 15 m soil [1].strata Unfortunately, for evaluating it is the soil critical liquefaction soil strata potential for evaluating [1]. soil liquefaction potential [1]. Several other relationships have been proposed because of the importance of assessment of CSR. Ishihara [15] performed a series of analyses using uniform soil profile and sinusoidal input motions and concluded that the parameter rd can be expressed as:

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Several other relationships have been proposed because of the importance of assessment of CSR. Ishihara [15] performed a series of analyses using uniform soil proﬁle and Geosciences 2019, 9, x FOR PEER REVIEW 3 of 27 sinusoidal input motions and concluded that the parameter rd can be expressed as: 𝑉VS 𝑤𝑧wz rd = sin (3) 𝑟 = wz𝑠𝑖𝑛 VS (3) 𝑤𝑧 𝑉

wherewhere VS V= Suniform= uniform soil soil shear shear wave wave velocity, velocity, w =w frequency= frequency of ofexcitation, excitation, z =z depth.= depth. This This relationshiprelationship is plotted is plotted in Figure in Figure 2. 2 .

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

AnotherAnother simple simple and and widely widely used used relationship relationship is the is the one one proposed proposed by byIwasaki Iwasaki [16] [16 in] in whichwhich the the parameter parameter rd isrd expressedis expressed through through a linearly a linearly decreasing decreasing function function with with depth depth as: as: (4) 𝑟 = 1 − 0.015𝑧 rd = 1 − 0.015z (4) This function was obtained applying six earthquake motions to two alluvial deposits. This function was obtained applying six earthquake motions to two alluvial deposits. IdrissIdriss [17], [17 based], based on on studies studies carried carried out out by by Golesorkhi Golesorkhi [[18],18], performedperformed several several hundred hun- dredparametric parametric site site response response analyses analyses and and proposed proposed a rd relationshipa rd relationship that takesthat takes into account into accountthe effects the effects of earthquake of earthquake magnitude magnit andude depth and depth in the in evaluation the evaluation of rd. of rd. ForFor z ≤z 34≤ m34 the m thefollowing following equation equation was was obtained: obtained: (5) 𝑙𝑛(𝑟) =𝛼(𝑧) +𝛽(𝑧)𝑀 ln(rd) = α(z) + β(z)M (5) where where 𝑧z 𝛼(α𝑧()z)== −1.012−1.012 −− 1.1261.126 𝑠𝑖𝑛 sin ++ 5.1335.133 (5.1)(5a) 11.7311.73 𝑧z 𝛽(β𝑧()z)== 0.1060.106 ++ 0.1180.118 𝑠𝑖𝑛 sin ++ 5.1425.142 (5.2)(5b) 11.2811.28 For z > 34 m the following expression is more appropriate: For z > 34 m the following expression is more appropriate: rd = 0.12 exp(0.22M) (6)(6) r = 0.12exp(0.22M) inin which whichz = z depth= depth in in meters meters and and M M = moment= moment magnitude. magnitude. d PlotsPlots of ofr rcalculatedd calculated using using previous previous equationequationfor for M M = 5=1 /5½,2, 6 1/6½,2, 7 1/7½,2, and and 8 are8 are presented pre- sentedin Figure in Figure3. Also 3. shownAlso shown is the is average the averag of thee of range the range published published by Seed by and Seed Idriss and [Idriss12]. [12].

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Figure 3. Variation of the stress reduction coefficient with depth and earthquake magnitude (from IdrissFigure and 3. 3. VariationVariation Boulanger of ofthe [6]). the stress stress reduction reduction coefficient coefﬁcient with depth with and depth earthquake and earthquake magnitude magnitude (from (from Idriss and Boulanger [6]). Idriss and Boulanger [6]). Cetin and Seed [5], using the Bayesian updating method, suggested new rd correla- Cetin and Seed [5], using the Bayesian updating method, suggested new rd correlations Cetinas a function and Seed of [5 ],depth, using theearthquake Bayesian magnitude, updating method, intensity suggested of shaking, new randcorrelations site stiff- tions as a function of depth, earthquake magnitude, intensity of shaking, and site dstiff- ness.asness. a functionTheyThey performedperformed of depth, a totala earthquaketotal of 2153of 2153 site magnitude, siteresponse response analyses intensity analyses by of the shaking, byequivalent the andequivalent linear site stiffness. linear They performedd a total of 2153 site response analyses by the equivalent linear method. method.method. TheThe r dr recommendations recommendations proposed proposed by Seed by Seedand Idriss and Idriss[12] are [12] conservatively are conservatively biasedThebiasedrd comparedcomparedrecommendations to to over over 80 ,00080 proposed,000 point point estimations by estimations Seed of and rd fromof Idriss rd 2153from [12 cases ]2153 are as cases conservatively shown as inshown Fig- biasedin Fig- urecomparedure 4. to over 80,000 point estimations of rd from 2153 cases as shown in Figure4.

Figure 4. rd results of the site response analyses. Also shown for comparison is the proposed rd range and recommendations of Seed and Idriss [12] (from Cetin and Seed [5]).

Figure 4. rrd resultsresults of the site responseresponse analyses.analyses. AlsoAlso shownshown for for comparison comparison is is the the proposed proposedr rranged Anotherd probabilistic relationship was developed by Kishida et al. [19–20] using d range and recommendations of Seed and Idriss [12] (from Cetin and Seed [5]). andMonte recommendations Carlo simulations. of SeedThe relationship and Idriss [12 wa] (froms based Cetin on about and Seed 23,000 [5]). analyses. The input parameters were PGA, the average shear wave velocity, and the spectral ratio parameter. Another probabilistic relationship relationship was was developed developed by by Kishida Kishida et et al. al. [19–20] [19,20] using Monte Carlo simulations. The relationship wa wass based on about 23,000 analyses. The input parameters were PGA, the average shear wave velocity, andand thethe spectralspectral ratioratio parameter.parameter.

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A recent study was performed by Lasley et al. [21]. They suggested a new rd rela- A recent study was performed by Lasley et al. [21]. They suggested a new rd relation- tionship from equivalent-linear site response analyses. Several forms for rd were exam- ship from equivalent-linear site response analyses. Several forms for r were examined and ined and the following form was selected for its simplicity and shape:d the following form was selected for its simplicity and shape: −z r = (1−α)exp +α (7) −zβ r = (1 − α) exp + α (7) d β where α = limiting value of rd 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 ex- where α = limiting value of rd at large depths, β = variable that controls the curvature of the functionponential. at shallow depths, z = depth in meters and (1-α) = term that scales the exponential. TwoTwo differentdifferent sets sets of of expression expression for forα αand andβ βwere were proposed, proposed, one one being being a a function function of of magnitude (Mw) and average shear-wave velocity in the upper 12 m of the profile (VS12) magnitude (Mw) and average shear-wave velocity in the upper 12 m of the profile (VS12) W andand thethe otherother solelysolely beingbeing aa functionfunction ofof MMW.. TheThe firstfirst setset ofof expressionsexpressions forfor αα andand ββ is:is: (7.1) α =exp(b +bM +bV) α1 = exp(b1 + b2Mw + b3VS12) (7a) (7.2) β =exp(b +bM +bV) and the second set is: β1 = exp(b4 + b5Mw + b6VS12) (7b) (8.1) and the second set is: α =exp(b +bM) α = ( + ) 2 exp b1 b2Mw (8a)(8.2) β =b +bM β = b3 + b4Mw (8b) where b1-b6 are regression coefficients.2 where b1-b6 are regression coefficients. 3. Seismicity of the Catania Area 3. SeismicityThe city ofof theCatania, Catania in South-Eastern Area Sicily (Italy), is subjected to high seismic hazards.The It was city ofshaken Catania, by a in number South-Eastern of strong Sicily earthquakes. (Italy), is subjected In particular to high the seismic events hazards. of Feb- Itruary was shaken1169, December by a number 1542, of strong January earthquakes. 1693, February In particular 1818 and the eventsJanuary of 1848 February produced 1169, Decemberrelevant damages 1542, January [22]. A 1693, repetition February of events 1818 andwith January similar 1848characteristics produced would relevant provide dam- agesthe additional [22]. A repetition risk of a of damaging events with tsunami, similar as characteristics well as liquefaction would phenomena provide the additionalaround the riskcoast of [9–11]. a damaging tsunami, as well as liquefaction phenomena around the coast [9–11]. SeismicSeismic liquefactionliquefaction phenomena phenomena were were reported reported by by historical historical sources sources [23 –[23–25]25] follow- fol- inglowing the 1693the 1693 (MS (M= 7.0–7.3,S = 7.0–7.3, Io = Io X–XI = X–XI MCS) MCS) and and 1818 1818 (M (MS =S = 6.2, 6.2, Io I=o = IXIX MCS)MCS) strongstrong earthquakesearthquakes [[26].26]. FiguresFigures5 5and and6 show6 show the the intensity intensity maps maps for for both both earthquakes. earthquakes.

FigureFigure 5.5.Intensity Intensity map.map. EarthquakeEarthquake ofof 1111 January,January, 1693 1693 (from (from Guidoboni Guidoboni et et al. al. [ 10[10,11]).,11]).

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FigureFigure 6.6.Intensity Intensity map.map. EarthquakeEarthquake ofof 2020 February,February, 1818 1818 (from (from Guidoboni Guidoboni et et al. al. [ 10[10,11]).,11]).

TheThe mostmost significantsignificant liquefactionliquefaction featuresfeatures seemseem toto havehave occurredoccurred inin thethe CataniaCatania area,area, nearnear SaintSaint GiuseppeGiuseppe LaLa RenaRena site,site, situatedsituated inin thethe meisoseismalmeisoseismal regionregion ofof bothboth events.events. TheseThese effectseffects are significantsignificant for for the the implications implications on on hazard hazard assessment assessment mainly mainly for for the the al- alluvialluvial flood flood plain plain just just south south of of the the city, city, where where most most industry and facilities are locatedlocated [[27].27]. TheThe seismicseismic events events that that occurred occurred in January in Janu 1693ary 1693 and February and February 1818 have 1818 been have chosen been aschosen scenario as scenario earthquakes. earthquakes. TheThe ValVal di di Noto Noto earthquake earthquake of 11of JanuaryJanuary, 169311 1693 struck struck a vast a territory vast territory of south- of easternsouth-eastern Sicily andSicily caused and caused the partial, the partial, and in and many in casesmany total,cases destructiontotal, destruction of 57 citiesof 57 andcities60,000 and 60000 casualties casualties [28–31 [28–31].]. The Etna Theearthquake Etna earthquake that took that placetook onplace 20 on February February 1818, 20, was1818, a moderatewas a moderate earthquake, earthquake, but its but effects its effects were noticed were noticed over a over vast areaa vast [9 ,area32–34 [9,32–34]]

4.4. SiteSite ResponseResponse AnalysisAnalysis LocalLocal sitesite responseresponse analyses,analyses, asas wellwell asas dynamicdynamic soil-structuresoil-structure interactioninteraction analyses,analyses, havehave been been performed performed in Cataniain Catania area area (Sicily, (Sicily, Italy), Italy), which which is recognized is recognized as a typical as a Mediter- typical raneanMediterranean city at high city seismic at high risk seismic [35– 40risk]. [35–40]. A database of about 1200 boreholes and water-wells is available in the data-bank of the A database of about 1200 boreholes and water-wells is available in the data-bank of Research Project: Detailed Scenarios and Actions for Seismic Prevention of Damage in the Urban the Research Project: Detailed Scenarios and Actions for Seismic Prevention of Damage in the Area of Catania [41]. The creation of the database provided the basis for the geotechnical Urban Area of Catania [41]. The creation of the database provided the basis for the ge- zonation and seismic microzonation of the city of Catania [42,43]. Based on the geotechnical otechnical zonation and seismic microzonation of the city of Catania [42,43]. Based on the zonation, only the eastern coastal plain of Catania is susceptible to liquefaction because geotechnical zonation, only the eastern coastal plain of Catania is susceptible to liquefac- of the presence of saturated sand deposits in the uppermost 20 m. In this paper, new r tion because of the presence of saturated sand deposits in the uppermost 20 meters. Ind relationships are proposed for the eastern coastal plain of Catania. this paper, new rd relationships are proposed for the eastern coastal plain of Catania. Table1 shows experimental sites and tests used to obtain new rd relationships. Table 1 shows experimental sites and tests used to obtain new rd relationships. The locations of experimental sites are reported in Figure7. In the Saint Giuseppe La Rena site, eight boreholes (No. 418–425 of the database) were made. The depth of the boreholes varies from 8 to 30 m, the water table lies around 2 m below the ground surface and, for all of them, standard penetration tests (SPTs) date are available. Near the borings, eleven cone penetration tests (CPTs) were also made. More recently, at the same site, a seismic dilatometer Marchetti test (SDMT1) was performed. The SDMT1 has an effective depth of 23 m. The subsoil exploration revealed the presence of sand with a content of ﬁne particles less than 30% for a depth of about 10 m. The locations of the SPTs, CPTs, and SDMT1 are reported in Figure8[ 8]. Figure9 shows an example of SPT proﬁle.

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Table 1. Experimental sites and tests used to obtain new rd relationships in Catania area (Sicily, It- Table 1. Experimental sites and tests used to obtain new rd relationships in Catania area (Sicily, Italy). aly). Experimental Sites Tests Experimental Sites Tests Saint GiuseppeSaint Giuseppe La Rena La Rena SPT 1 (borehole SPT 1 (borehole 418) 418) Saint GiuseppeSaint Giuseppe La Rena La Rena SPT 2 (borehole SPT 2 (borehole 419) 419) Saint GiuseppeSaint Giuseppe La Rena La Rena SPT 3 (borehole SPT 3 (borehole 420) 420) Saint GiuseppeSaint Giuseppe La Rena La Rena SPT 4 (borehole SPT 4 (borehole 421) 421) Saint GiuseppeSaint Giuseppe La Rena La Rena SPT 5 (borehole SPT 5 (borehole 422) 422) Saint GiuseppeSaint Giuseppe La Rena La Rena SPT 6 (borehole SPT 6 (borehole 423) 423) Saint GiuseppeSaint Giuseppe La Rena La Rena SPT 7 (borehole SPT 7 (borehole 424) 424) Saint GiuseppeSaint Giuseppe La Rena La Rena SPT 8 (borehole SPT 8 (borehole 425) 425) Saint GiuseppeSaint Giuseppe La Rena La Rena SDMT SDMT 1 1 CataniaCatania Harbour Harbour SDMT SDMT 2 2 CataniaCatania Harbour Harbour SDMT SDMT 3 3 CataniaCatania Harbour Harbour SDMT SDMT 4 4 CataniaCatania Harbour Harbour SDMT SDMT 5 5 CataniaCatania Harbour Harbour SDMT SDMT 6 6 NazarioNazario Sauro Sauro school school SDMT SDMT 7 7 NazarioNazario Sauro Sauro school school SDMT SDMT 8 8 INGVINGV building building SDMT SDMT 9 9 MadreMadre Teresa Teresa di Calcutta di Calcutta School School SDMT SDMT 10 10 STM M6STM M6 SDMT SDMT 11 11 BelliniBellini Garden Garden SDMT SDMT 12 12 MonteMonte Po Po SDMT SDMT 13 13 The locations of experimental sites are reported in Figure 7.

Figure 7. Map of experimental sites in Catania area (Sicily, Italy).Italy).

In thethe CataniaSaint Giuseppe Harbour La area Rena ﬁve site, seismic eight dilatometer boreholes Marchetti (No. 418–425 tests (SDMT2-6)of the database) were performed.were made. They The havedepth an of effective the boreholes depth of varies 30.50 from m, 32.00 8 to m, 30 31.00 meters, m, 30.00 the water m, and table 32.00 lies m. around 2 m below the ground surface and, for all of them, standard penetration tests (SPTs) date are available. Near the borings, eleven cone penetration tests (CPTs) were also made. More recently, at the same site, a seismic dilatometer Marchetti test (SDMT1)

Geosciences 2019, 9, x FOR PEER REVIEW 8 of 27 Geosciences 2019, 9, x FOR PEER REVIEW 8 of 27 was performed. The SDMT1 has an effective depth of 23 m. The subsoil exploration re- wasvealed performed. the presence The SDMT1of sand haswith an a effectivecontent of depth fine particlesof 23 m. lessThe thansubsoil 30% exploration for a depth re- of vealedabout the10 meters. presence of sand with a content of fine particles less than 30% for a depth of about The10 meters. locations of the SPTs, CPTs, and SDMT1 are reported in Figure 8 [8]. Figure 9 showsThe an locations example of of the SPT SPTs, profile. CPTs, and SDMT1 are reported in Figure 8 [8]. Figure 9 Geosciences 2021, 11, 12 8 of 25 shows an example of SPT profile.

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

Figure 9. NSPT test results versus depth (borehole 421-SPT4). Figure 9. NSPT test results versus depth (borehole 421-SPT4). Figure 9. NSPT test results versus depth (borehole 421-SPT4). TwoIn the seismic Catania dilatometer Harbour tests, area indicated five seismic as SDMT dilatometer 7 and SDMT Marchetti 8, were tests conducted (SDMT2-6) from groundwereIn performed. the level Catania to depths They Harbour ofhave 17.5 anarea m effective and five 29.5 seismic depth m, respectively, ofdilatometer 30.50 m, in 32.00 theMarchetti Nazario m, 31.00 tests Sauro m, 30.00(SDMT2-6) school m, site.and wereIn32.00 addition, performed. m. in the They INGV have (National an effective Institute depth of Geophysicsof 30.50 m, 32.00 and Volcanology) m, 31.00 m, 30.00 site, a m, seismic and 32.00dilatometer m.Two seismic test (SDMT dilatometer 9) was tests, performed. indicated It as has SDMT an effective 7 and SDMT depth 8, of were 34.50 conducted m. Other SDMTfromTwo ground tests seismic (SDMT level dilatometer to 10-13) depths were tests, of carried 17.5 indicated m out and in as29.5 Madre SDMT m, Teresarespectively, 7 and di SDMT Calcutta in 8, the Schoolwere Nazario conducted (SDMT Sauro 10, fromdepth ground of 29.50 level m), STMto depths M6 (SDMT of 17.5 11, m depth and 29.5 of 39.94 m, respectively, m), Bellini Garden in the (SDMT Nazario 12, Sauro depth of 30.44 m), and Monte Po (SDMT 13, depth of 12.50 m) sites. Figure 10 shows the location of the SDMTs in each experimental sites.

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school site. In addition, in the INGV (National Institute of Geophysics and Volcanology) site, a seismic dilatometer test (SDMT 9) was performed. It has an effective depth of 34.50 m. Other SDMT tests (SDMT 10-13) were carried out in Madre Teresa di Calcutta School (SDMT 10, depth of 29.50 m), STM M6 (SDMT 11, depth of 39.94 m), Bellini Garden Geosciences 2021, 11, 12 (SDMT 12, depth of 30.44 m), and Monte Po (SDMT 13, depth of 12.50 m) sites. Figure9 of 10 25 shows the location of the SDMTs in each experimental sites.

(a) (b)

(e) (f)

(g)

Figure 10. Layout of SDMTSDMT tests:tests: (aa)) Catania Catania Harbour area; (bb)) Nazario Nazario Sauro Sauro School; (cc)) National National Institute Institute of of Geophysics and Volcanology (INGV); d) Madre Teresa di Calcutta School; e) STM M6; f) Bellini Garden; g) Monte Po. and Volcanology (INGV); (d) Madre Teresa di Calcutta School; (e) STM M6; (f) Bellini Garden; (g) Monte Po.

The SDMTs have been carried out with the aim to evaluate the soil proﬁle of shear wave velocity for the site response analysis. VS 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). Geosciences 2019, 9, x FOR PEER REVIEW 10 of 27

The SDMTs have been carried out with the aim to evaluate the soil profile of shear wave velocity for the site response analysis. VS 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 Geosciences 2021, 11, 12 receivers at a distance of 0.50 m [8,30] (Figure 11). 10 of 25

(a) (b)

FigureFigure 11. 11.Seismic Seismic dilatometer dilatometer test: test: ( a(a)) SDMT SDMT equipment equipment (blade (blade and and seismic seismic module); module); (b (b)) schematic schematic test layout (From Castelli et al. [30]). test layout (From Castelli et al. [30]).

TheThe test test configuration configuration “two "two receivers”/“true receivers"/"true interval”interval" avoidsavoids thethe problemproblem connected connected withwith the the possible possible inaccurate inaccurate determination determination of of the the “first "first arrival” arrival" time time sometimes sometimes met met with with thethe “pseudo "pseudo interval” interval" configurationconfiguration (one(one receiver) receiver) [ 8[8,30].,30]. The The energization energization is is obtained obtained by by aa swinging swinging hammer, hammer, hitting hitting horizontally horizontally a a steel steel parallelepipedal parallelepipedal base. base. The The shear shear wave wave velocityvelocity Vs Vs is is the the ratio ratio between between the the difference difference of of distance distance between between the the energy energy source source and and thethe two two receivers receivers and and the the measured measured delay delay time time of of the the pulse pulse from from the the upper upper to to the the lower lower receiverreceiver [ 8[8].]. SDMTSDMT obtained obtained parameters parameters by by the the equipment equipment shown shown in in Figure Figure 12 12 at at the the sites sites are: are: IIdd: : materialmaterial index; index; M: M: vertical vertical drained drained constrained constrained modulus; modulus;φ :ϕ angle: angle of of shear shear resistance; resistance; K DK:D 2 horizontal: horizontal stress stress index; index; V SV:S shear: shear waves waves velocity; velocity; G 0G= =δVδVS: small : small strain strain shear shear modulus. modulus. Shear wave velocity plays a fundamental role in seismic analyses. It is widely recog-

nized that NSPT-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]. The possibility of using the standard penetration test blowcounts, in order to determine the VS, is based on the presence in the literature of several empirical correlations that relate VS and NSPT-values. The following empirical correlations have been used to obtain the shear wave velocity proﬁles, as a function of depth, for each of the eight boreholes. (a) Ohta and Goto [45]:

z 0.193 V = 54.33(N )0.173α β (9) S SPT 0.303

where VS = shear wave velocity (m/s), NSPT = number of blows from SPT, z = depth in meters, α = age factor (Holocene = 1.000, Pleistocene = 1.303), β = geological factor (clays = 1.000, sands = 1.086). (b) Yoshida and Motonori [46]:

0.25 00.14 VS = β(NSPT) σ V0 (10)

where VS = shear wave velocity (m/s), NSPT = number of blows from SPT, β = geological factor (any soil 55, fine sand 49), σv0’ = effective vertical stress. In Figure 13, the shear wave velocities are shown against depth for borehole 421, as an example, by Equations (9) and (10). Also shown is the shear wave velocity from SDMT1. It is possible to notice that the values obtained with the correlation of Yoshida and Motonori are slightly higher than values determined with the correlation of Ohta and Goto and closer than the values measured from the SDMT1. Thus, it was decided to choose for the seismic response analysis, the values of Vs calculated with the Equation (10), because Geosciences 2021, 11, 12 11 of 25

they are more likely to adhere to the real values. Moreover, Equation (10) better captures Geosciences 2019, 9, x FOR PEER REVIEW 11 of 27 the soil variability because it includes the unit weight of soil.

(a) (b)

(e) (f) Figure 12. SDMT equipment (a) at the Saint Giuseppe La Rena site; (b) at the Catania Harbour site; (c) at STM M6 site; (d) 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 at Bellini Garden site; (e) at Monte Po site; (f) at INGV site. Bellini Garden site; (e) at Monte Po site; (f) at INGV site.

ShearIn addition wave tovelocity situ investigations, plays a fundamental the following role in laboratory seismic analyses. tests were It carriedis widely out rec- on ognizedundisturbed that samples:NSPT-value n. and 6 Resonant S-wave Columnvelocity of tests, sands n.3 are Direct variables shear dependent tests, and n. on 3 Triaxialseveral parameterstests. such as combinations of effective stress, void ratio, soil fabric, etc., [44]. TheResults possibility of direct of shear using tests the are standard presented penetration in Figures test 14 andblowcounts, 15 for S2C2 in order (retrieved to de- at termine13.20 m inthe SDMT2 VS, is based borehole) on the and presence S4C1 (retrieved in the litera at 8.40ture m of in SDMT4several empirical borehole) soilcorrelations samples. thatFigure relate 14 shows VS and the NSPT horizontal-values. shear stress- horizontal displacement curves under different normalThe stress following conditions empirical (98.1 kN/mcorrelations2, 196.2 have kN/m been2 and used 294.3 to kN/mobtain2 ).the The shear plots wave of shear ve- locitystresses profiles, corresponding as a function to failure of depth, versus for normal each of stresses the eight are boreholes. shown in Figure 15. a) Ohta and Goto [45]: z . V = 54.33(N ).α β (9) 0.303

Geosciences 2019, 9, x FOR PEER REVIEW 12 of 27

where VS = shear wave velocity (m/s), NSPT = number of blows from SPT, z = depth in meters, α= age factor (Holocene = 1.000, Pleistocene = 1.303), β = geological factor (clays = 1.000, sands = 1.086). b) Yoshida and Motonori [46]: . . (10) V =β(N) σ

where VS = shear wave velocity (m/s), NSPT = number of blows from SPT, β = geological factor (any soil 55, fine sand 49), σv0' = effective vertical stress. In Figure 13, the shear wave velocities are shown against depth for borehole 421, as an example, by Equations (9) and (10). Also shown is the shear wave velocity from SDMT1. It is possible to notice that the values obtained with the correlation of Yoshida and Motonori are slightly higher than values determined with the correlation of Ohta and Goto and closer than the values measured from the SDMT1. Thus, it was decided to choose for the seismic response analysis, the values of Vs calculated with the equation Geosciences 2021, 11, 12 (10), because they are more likely to adhere to the real values. Moreover, Equation12 (10) of 25 better captures the soil variability because it includes the unit weight of soil.

FigureFigure 13. 13. ComparisonComparison of V ofS determined VS determined from from empirical empirical correla correlations,tions, Equations Equations (9) and (9) (10), and and (10), SDMT1. Geosciences 2019, 9, x FOR PEER REVIEWand SDMT1. 13 of 27 In addition to situ investigations, the following laboratory tests were carried out on undisturbed samples: n. 6 Resonant Column tests, n. 3 Direct shear tests, and n. 3 Triaxial tests. Results of direct shear tests are presented in Figures 14 and 15 for S2C2 (retrieved at 13.20 m in SDMT2 borehole) and S4C1 (retrieved at 8.40 m in SDMT4 borehole) soil samples. Figure 14 shows the horizontal shear stress- horizontal displacement curves under different normal stress conditions (98.1 kN/m2, 196.2 kN/m2 and 294.3 kN/m2). The plots of shear stresses corresponding to failure versus normal stresses are shown in Fig- ure 15.

(a) (b)

Figure 14. Horizontal shear stress- horizontal displacement curves under different normal stress conditions (98.1 kN/m22, Figure 14. Horizontal shear stress- horizontal displacement curves under different normal stress conditions (98.1 kN/m , 196.2 kN/m2 and 294.3 kN/m2): (a) S2C2 soil sample (retrieved at 13.20 m in SDMT2 borehole), (b) S4C1 soil sample (re- 196.2 kN/m2 and 294.3 kN/m2): (a) S2C2 soil sample (retrieved at 13.20 m in SDMT2 borehole), (b) S4C1 soil sample trieved at 8.40 m in SDMT4 borehole). (retrieved at 8.40 m in SDMT4 borehole).

The experimental results of resonant column tests were used to determine the empirical parameters of the equation proposed by Yokota et al. [47] to describe the shear modulus decay with shear strain level:

G(γ) 1 = β (11) G0 1 + αγ(%)

The values of α = 9 and β = 0.815 were obtained.

(a) (b) 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).

The experimental results of resonant column tests were used to determine the empirical parameters of the equation proposed by Yokota et al. [47] to describe the shear modulus decay with shear strain level: G(γ) 1 = (11) G 1+αγ(%) The values of α = 9 and β = 0.815 were obtained. As suggested by Yokota et al. [47], the inverse variation of damping ratio with respect to the normalized shear modulus has an exponential form: G(γ) D(γ)(%) =ηexp−λ (12) G in which D(γ) = strain dependent damping ratio, γ = shear strain, η, λ = soil constants. The values of η = 80 and λ = 4 were obtained [48].

Geosciences 2019, 9, x FOR PEER REVIEW 13 of 27

Geosciences 2021, 11, 12 13 of 25

As suggested by Yokota et al. [47], the inverse variation of damping ratio with respect to the normalized shear modulus has an exponential form:

G(γ) (a) D(γ)(%) = η exp(b) −λ (12) G0 Figure 14. Horizontal shear stress- horizontal displacement curves under different normal stress conditions (98.1 kN/m2, 196.2 kN/m2 and 294.3in whichkN/m2): ( D(a) S2C2γ) = soil strain sample dependent (retrieved at damping13.20 m in SDMT2 ratio, borehole),γ = shear (b) S4C1 strain, soil ηsample, λ = soil(re- constants. The trieved at 8.40 m in SDMT4 borehole). values of η = 80 and λ = 4 were obtained [48].

(a) (b) Figure 15. Shear stresses corresponding to failure versus normal stresses (a) S2C2 soil sample (retrieved at 13.20 m in Figure 15. ShearSDMT2 stresses borehole), corresponding (b) S4C1 soil sample to (retrieved failureversus at 8.40 m normal in SDMT4 stresses borehole). (a ) S2C2 soil sample (retrieved at 13.20 m in SDMT2 borehole), (b) S4C1 soil sample (retrieved at 8.40 m in SDMT4 borehole). The experimental results of resonant column tests were used to determine the em- Localpirical siteparameters response of the analyses equation haveproposed been byperformed Yokota et al. using[47] to 1-Ddescribe linear the equivalentshear code STRATAmodulus [49] decay assuming with shear the strain geometric level: and geological models of substrate as 1-D physical models. G(γ) 1 = (11) The shear wave velocity proﬁlesG used 1+αγ for soil(%) response analyses are obtained from SPTs date, availableThe values for allof α the = 9 and eight β = boreholes0.815 were obtained. (N◦418–425), and from the seismic dilatometer tests (SDMT1-13).As suggested The by valuesYokota et of al. the [47], other the in parametersverse variation were of damping taken ratio from with the re- geotechnical spect to the normalized shear modulus has an exponential form: characterization obtained through in situ and laboratory tests performed. G(γ) The dynamic response modelD( requiresγ)(%) =ηexp− the knowledgeλ of the depth of bedrock.(12) The con- G ventionally adopted depth of the bedrock corresponds to a VS value of 800 m/s (soil type A accordingin which toItalian D(γ) = strain technical dependent regulations damping [ 50ratio,]). Theγ = shear criterion strain, ofη, choiceλ = soil constants. adopted to evaluate The values of η = 80 and λ = 4 were obtained [48]. 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 VS value of about 800 m/s. During strong earthquakes the soil tends to behave as non-linear material. To take into account the soil non linearity, laws of shear modulus and damping ratio against strain

have been inserted in the code. The fourteen 1-D columns have been excited at the base using four seismograms. The chosen input motions are: three seismograms, called B3R3RAD, PT1R3, and PT6R3, evaluated assuming the source to be along the Hyblean-Maltese fault and generating the 1693 seismic ground motion scenario [51,52]; a seismogram evaluated assuming the source to be along the Hyblean-Maltese fault and generating the 1818 seismic ground motion scenario [51]. Based on the interactive seismic hazard maps of the city of Catania [53], the seismograms have been scaled to the maximum PGA of 0.3 g (corresponding to a return period of 975 years) and to the maximum PGA of 0.5 g (corresponding to a return period of 2475 years) by entering the scale factors in the STRATA code [49]. The interactive seismic hazard maps (Figure 16) were obtained by a probabilistic approach [53]. Geosciences 2019, 9, x FOR PEER REVIEW 14 of 27

Local site response analyses have been performed using 1-D linear equivalent code STRATA [49] assuming the geometric and geological models of substrate as 1-D physical models. The shear wave velocity profiles used for soil response analyses are obtained from SPTs date, available for all the eight boreholes (N°418–425), and from the seismic dilatometer tests (SDMT1-13). The values of the other parameters were taken from the geotechnical characterization obtained through in situ and laboratory tests performed. The dynamic response model requires the knowledge of the depth of bedrock. The conventionally adopted depth of the bedrock corresponds to a VS 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 VS value of about 800 m/s. During strong earthquakes the soil tends to behave as non-linear material. To take into account the soil non linearity, laws of shear modulus and damping ratio against strain have been inserted in the code. The fourteen 1-D columns have been excited at the base using four seismograms. The chosen input motions are: three seismograms, called B3R3RAD, PT1R3, and PT6R3, evaluated assuming the source to be along the Hyblean-Maltese fault and generating the 1693 seismic ground motion scenario [51,52]; a seismogram evaluated assuming the source to be along the Hyblean-Maltese fault and generating the 1818 seismic ground motion scenario [51]. Based on the interactive seismic hazard maps of the city of Catania [53], the seismograms have been scaled to the maximum PGA of 0.3 g (corresponding to a return pe- Geosciences 2021, 11, 12 riod of 975 years) and to the maximum PGA of 0.5 g (corresponding to a return period of 14 of 25 2475 years) by entering the scale factors in the STRATA code [49]. The interactive seismic hazard maps (Figure 16) were obtained by a probabilistic approach [53].

(a) (b) Figure 16. Interactive seismic hazard maps of the city of Catania: (a) 5% probability of exceedance in 50 years (return pe- Figure 16. a Interactiveriod of 975 years); seismic (b)hazard 2% probability maps of of exceedance the city of in Catania:50 years (return ( ) 5% period probability of 2475 years). of exceedance in 50 years (return period of 975 years); (b) 2% probability of exceedance in 50 years (return period of 2475 years). Figures 17 and 18 show the results of seismic site response analyses for the seismic Figuresdilatometer 17 testsand (SDMT1-13)18 show the and resultsfor n. 418–425 of seismic boreholes site to responseevaluate the analyses variation of for rd the seismic over a range of soil profiles. dilatometer tests (SDMT1-13) and for n. 418–425 boreholes to evaluate the variation of rd

Geosciences 2019, 9, x FOR PEER REVIEWover a range of soil proﬁles. 15 of 27

Figure 17. rd results from response analyses for different soil profiles (SPT1-8 and SDMT1-13) using as input 1693 and Figure 17.1818rd scaledresults synthetic from seismograms response to analyses the maximum for PGA different of 0.3 g. soil proﬁles (SPT1-8 and SDMT1-13) using as input 1693 and 1818 scaled synthetic seismograms to the maximum PGA of 0.3 g.

Geosciences 2021, 11, 12 15 of 25 Geosciences 2019, 9, x FOR PEER REVIEW 16 of 27

Figure 18. rd results from response analyses for different soil profiles (SPT1-8 and SDMT1-13) using as input the 1693 and Figure 18. rd 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. 1818 scaled synthetic seismograms to the maximum PGA of 0.5 g.

5. Shear5. Stress Shear Reduction Stress Reduction Factor rd Factor in ther Cataniad in the CataniaArea (Italy) Area (Italy) The procedureThe procedure for computing for computing the factor the factor of safety of safety against against liquefaction liquefaction is istermed termed “sim- “simplifiedplified procedure.” procedure.” Since Since its inception its inception in the in the1970s, 1970s, it has it been has been revised revised and andupdated updated by by manymany authors. authors. One Oneof the of theparameters parameters to be to beevaluated evaluated is isthe the stress stress reduction reduction coeffi- coefficient, rd, cient, rd,as as aa parameterparameter describing the ratio of of cyclic cyclic stress stress for for a a flexible flexible soil soil column column to to the the cyclic cyclic stressstress for for a rigid a rigid soil soil column column [5] [5 (Figure] (Figure 19): 19 ):

(τ)(τ ) r = = max deformable soil (13) rd(τ) (13) (τmax)rigid body

Herein, new stress reduction coefﬁcient rd 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

Geosciences 2019, 9, x FOR PEER REVIEW 17 of 27 Geosciences 2021, 11, 12 16 of 25

boreholes (n. 418–425), and from seismic dilatometer tests (SDMT1-13). The seismic events Geosciences 2019, 9, x FOR PEER REVIEWof 1693 and 1818 have been chosen as scenario earthquakes. 17 of 27

Figure 19. Schematic for determining maximum shear stress, 𝜏, and the stress reduction coefficient, rd (from Idriss and Boulanger [6]).

Herein, new stress reduction coefficient rd relationships are proposed for the eastern coastal plain of Catania area (Italy). They have been developed from equivalent-linear Figuresite response 19. Schematic analyses for determining performed maximumon soil prof sheariles stress, obtained 𝜏 , fromand the SPTs stress date, reduction available coeffi- for Figure 19. Schematic for determining maximum shear stress, τmax, and the stress reduction coefﬁcient, cient,eight r boreholesd (from Idriss (n. and 418–425), Boulanger and [6]). from seismic dilatometer tests (SDMT1-13). The seismic rd (from Idriss and Boulanger [6]). events of 1693 and 1818 have been chosen as scenario earthquakes. AccordingHerein,According new to to thestress the approach approach reduction originallyoriginally coefficient proposedproposed rd relationships by Seed areand proposed Idriss Idriss [12], [12 for], the the the ranges ranges eastern of ofcoastalvalues values ofplain of rrdd forforof Cataniasandy sandy saturated saturated area (Italy). soil They proﬁlesprofiles have ofof easternbeeneastern developed coastalcoastal CataniaCatania from equivalent-linear area area have have been been determined.sitedetermined. response They Theyanalyses are are shown shownperformed in in the the on Figures Figures soil prof 20 20 andiles and 21obtained 21.. 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. According to the approach originally proposed by Seed and Idriss [12], the ranges of values of rd for sandy saturated soil profiles of eastern coastal Catania area have been determined. They are shown in the Figures 20 and 21.

FigureFigure 20. 20.Range Range of of values values of ofr rddfor for differentdifferent soilsoil proﬁlesprofiles (SPT1-8(SPT1-8 and SDMT1-13) using using 1693 1693 and and 18181818 scaled scaled synthetic synthetic seismograms seismograms to to the the maximum maximum PGA PGA of of 0.3 0.3 g. g.

The dashed lines labelled “Average values” represent the recommended values of rd from the surface to a depth of 30 m. They can be approximated by Equations (14) and (15).

Figure 20. Range of values of rd for different soil profiles (SPT1-8 and SDMT1-13) using 1693 and 1818 scaled synthetic seismogramsrd = to1 the− 0.018 maximum z PGA of= 0.30.3g g. (14)

rd = 1 − 0.017 z PGA = 0.5g (15)

In the Figure 22, the rd 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 rd.

Geosciences 2019, 9, x FOR PEER REVIEW 18 of 27

Geosciences 2021, 11, 12 17 of 25 Geosciences 2019, 9, x FOR PEER REVIEW 18 of 27

Figure 21. Range of values of rd for different soil profiles (SPT1-8 and SDMT1-13) using 1693 and 1818 scaled synthetic seismograms to the maximum PGA of 0.5 g.

The dashed lines labelled “Average values” represent the recommended values of rd from the surface to a depth of 30 m. They can be approximated by Equations (14) and (15).

r = 1 − 0.018 z PGA = 0.3g (14)

r = 1 − 0.017 z PGA = 0.5g (15)

In the Figure 22, the rd relationships obtained for soil profiles of the Catania coastal Figure 21. Range of values of rd for different soil profiles (SPT1-8 and SDMT1-13) using 1693 and Figurearea are 21. Rangecompared of values to the of rrelationshipd for different previo soil proﬁlesusly (SPT1-8proposed and by SDMT1-13) Iwasaki [16]. using As 1693 can and be 1818 scaled synthetic seismograms to the maximum PGA of 0.5 g. 1818seen scaled from synthetic the chart, seismograms the latter provides to the maximum slightly PGA higher of 0.5 estimates g. of rd.

The dashed lines labelled “Average values” represent the recommended values of rd from the surface to a depth of 30 m. They can be approximated by Equations (14) and (15).

r = 1 − 0.018 z PGA = 0.3g (14)

r = 1 − 0.017 z PGA = 0.5g (15)

In the Figure 22, the rd 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 rd.

FigureFigure 22. 22.Comparison Comparison of ofrd rrelationshipd relationship obtained obtained by by Iwasaki Iwasaki [16 [16]] and and relationships relationships proposed proposed in thisin study.this study.

Moreover, the following two sets of equations can be used to estimate the average rd values, given in the Figures 20 and 21, from the surface to a depth 30 m:

rd = 1.0 − 0.028z for z ≤ 9.15m (PGA = 0.3) (16a)

rd = 0.840 − 0.010z for 9.15m < z ≤ 23m (PGA = 0.3) (16b)

rd = 0.723 − 0.005z for 23m < z ≤ 30m (PGA = 0.3) (16c) Figure 22. Comparison of rd relationship obtained by Iwasaki [16] and relationships proposed in this study.

Geosciences 2019, 9, x FOR PEER REVIEW 19 of 27

Moreover, the following two sets of equations can be used to estimate the average rd values, given in the Figures 20 and 21, from the surface to a depth 30 m:

r = 1.0 − 0.028z for z ≤ 9.15m (PGA = 0.3) (16.1)

Geosciences 2021, 11, 12 r = 0.840 − 0.010z for 9.15m < z ≤ 23m (PGA = 0.3) 18(16.2) of 25

r = 0.723 − 0.005z for 23m < z ≤ 30m (PGA = 0.3) (16.3) = − ≤ ( = ) rdr =1.0 1.0 −0.024z 0.024z for for z z ≤9.15m 9.15m PGA (PGA =0.5 0.5) (17a)(17.1) r = 0.889 − 0.011z for 9.15m < z ≤ 23m (PGA = 0.5) (17b) dr = 0.889 − 0.011z for 9.15m < z ≤ 23m (PGA = 0.5) (17.2) r = 0.677 − 0.002z for 23m < z ≤ 30m (PGA = 0.5) (17c) dr = 0.677 − 0.002z for 23m < z ≤ 30m (PGA = 0.5) (17.3) In the Figure 23, the suggested r relationships are compared to relationships previ- In the Figure 23, the suggestedd rd relationships are compared to relationships pre- ouslyviously proposed proposed by Liaoby Liao and Whitmanand Whitman [13], and[13], Robertson and Robertson and Wride and [14Wride] from [14] the from chart the of Seed and Idriss [12]. It is possible to observe that the r proposal of Seed and Idriss [12] chart of Seed and Idriss [12]. It is possible to observed that the rd proposal of Seed and provides higher estimation of r between 0 and 19 m. Idriss [12] provides higher estimationd of rd between 0 and 19 m.

FigureFigure 23. 23.Comparison Comparison ofof rrdd relationshipsrelationships obtained by Liao and Whitman [13] [13] and and Robertson Robertson and and WrideWride [ 14[14],], and and relationships relationships proposed proposed in in this this study. study.

Lastly,Lastly, itit isis possiblepossible to notice that the the Equations Equations (14), (14) (16.1), and (16a–c) (16.2), provideand (16.3) slopes provide of theslopes straight of the lines straight slightly lines lower slightly than lower that given than bythat Equations given by (15) Equations and (17a–c), (15), respectively.(17.1), (17.2), Thisand is(17.3), due torespectively. the fact that This during is due strong to the motion fact that the during soil tends strong to behave motion as the non-linear. soil tends to behave as non-linear. 6. Evaluation of Liquefaction Potential Using the Seismic Dilatometer Marchetti Tests (SDMTs) in the Catania Harbour (Italy) 6. Evaluation of Liquefaction Potential Using the Seismic Dilatometer Marchetti Tests (SDMTs)The new in therd relationships, Catania Harbour more (Italy) responsive to soil types examined, have been used for potential liquefaction evaluation in the Catania Harbour (Italy). The new rd relationships, more responsive to soil types examined, have been used One way to quantify the potential for liquefaction is through the computation of the for potential liquefaction evaluation in the Catania Harbour (Italy). liquefaction resistance factor (F ) proﬁle given by the ratio of the cyclic resistance ratio One way to quantify the potentialSL for liquefaction is through the computation of the CRR(z) to cyclic shear stress ratio CSR(z), where z is the depth of the deposit [54]. liquefaction resistance factor (FSL) profile given by the ratio of the cyclic resistance ratio The cyclic shear stress ratio CSR is calculated by Equation (1). Moreover, the stress- CRR(z) to cyclic shear stress ratio CSR(z), where z is the depth of the deposit [54]. based analysis framework includes a magnitude scaling factor (MSF). It allows to adjust the induced CSR during earthquake magnitude M to an equivalent CSR for an earthquake magnitude M = 7.5. According to Youd et al. [7], the MSF is given by the following expression:

102.24 MSF = (18) M2.56 Geosciences 2021, 11, 12 19 of 25

The cyclic resistance ratio CRR is commonly evaluated using empirical correlations with SPT and CPT. However, the latter are relatively insensitive to some factors that can inﬂuence the liquefaction resistance such as ageing, stress history, overconsolidation, and horizontal earth pressure coefﬁcient. Instead, the dilatometer test could take better account of these factors in the evaluation of liquefaction resistance [55]. Marchetti [56] and later studies suggested that the horizontal stress index from DMT is a suitable parameter to evaluate the liquefaction resistance of sands [8]. In this paper three CRR-KD curves, approximated by the Equations (19)–(21), have been used.

3 2 CRR = 0.0107KD − 0.0741KD + 0.2169KD − 0.1306 (19)

CRR = 0.0242e(0.6534KD) (20) 2.7032 CRR = 0.0084KD (21) The Equation (19) was proposed by Monaco et al. [57] and the Equations (20) and (21) were developed by Grasso and Maugeri [8]. Then it is possible to evaluate the liquefaction potential index (LPI). The LPI, proposed by Iwasaki et al. [58], provides a depth-weighted index of the potential for triggering of liquefaction at a site [59]. It is computed as:

Z 20 LPI = F(z)w(z)dzm (22) 0 where: F(z) = 0 for FSL ≥ 1 (23)

F(z) = 1 − FSL for FSL < 1 (24) w(z) = 10 − 0.5z (25) According to Iwasaki et al. [60], the level of liquefaction severity with respect to LPI is given in Table2.

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

The LPI framework was used in many recent studies [61–71] In this paper, the procedure described above has been applied to the 5 SDMTs date available in the Catania Harbour area (Figure 10). To evaluate the CSR, the results obtained from the site response analysis using scaled seismograms of 1693 to the maximum PGA of 0.3 g have been taken. The values of the surface maximum accelerations, i.e., for PT1R3 seismogram, are reported in Table3.

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 Geosciences 2019, 9, x FOR PEER REVIEW 21 of 27

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 Geosciences 2021, 11, 12 Thus, it has been decided to choose the values of 0.4g and 0.5g for the peak20 of hori- 25 zontal acceleration at the ground surface amax. The stress reduction coefficient rd and the magnitude scaling factor MSF have been given by the Equations (17.1), (17.2), and (18), Thus, it has been decided to choose the values of 0.4g and 0.5g for the peak horizontal respectively, and the values of the other parameters have been taken from the SDMTs acceleration at the ground surface a . The stress reduction coefﬁcient r and the magni- date. max d tude scaling factor MSF have been given by the Equations (17a,b) and (18), respectively, Typical CSR profiles obtained i.e., for SDMT2 are shown in Figure 24. and the values of the other parameters have been taken from the SDMTs date.

Typical CSR proﬁles obtained i.e., for SDMT2 are shown in Figure 24.

(a) (b)

FigureFigure 24. 24.CRS CRS proﬁles profiles obtained obtained for for SDMT2: SDMT2: (a) ( usinga) using the the peak peak horizontal horizontal acceleration acceleration at the at groundthe surfaceground of surface 0.4 g; (b of) using 0.4 g; the(b) peakusing horizontal the peak horizontal acceleration accelerati at the groundon at the surface ground of 0.5surface g. of 0.5 g.

TheThe CRR-K CRR-KD curves,D curves, approximated approximated by by Equations Equations (19)–(21), (19), (20), and (21), the and horizontal the horizontal stress indexstress K indexD of the KD 5of SDMTs the 5 SDMTs have beenhave used.been used. Values Values of K Dof versusKD versus depth depth for for SDMT4, SDMT4, as as example, are shown in Figure 25. Geosciences 2019, 9, x FOR PEER REVIEWexample, are shown in Figure 25. 22 of 27 The Figure 26 shows the CRR-KD trends i.e., for SDMT2. The liquefaction potential values obtained from SDMT2 and SDMT4 by Equation (22) are reported in Figure 27.

Figure 25. Horizontal stress index KD versus depth of the SDMT4, as example, performed in the Figure 25. Horizontal stress index K versus depth of the SDMT4, as example, performed in the Catania Harbour. D Catania Harbour.

The Figure 26 shows the CRR-KD trends i.e., for SDMT2.

Figure 26. CRR-KD trends obtained from SDMT2 using the Equation (19) proposed by Monaco et al. [57] and the Equations (20) and (21) developed by Grasso and Maugeri [8].

Geosciences 2019, 9, x FOR PEER REVIEW 22 of 27

Geosciences 2021, 11, 12 21 of 25 Figure 25. Horizontal stress index KD versus depth of the SDMT4, as example, performed in the Catania Harbour.

FigureFigure 26.26. CRR-KD trendstrends obtained obtained from from SDMT2 SDMT2 using using the the Eq Equationuation (19) (19) proposed proposed by Monaco by Monaco et al. et al. [57] and[57] the and Equations the Equations (20) (20) and and (21) (21) developed developed by by Grasso Grasso and and Maugeri Maugeri [ 8[8].].

The liquefaction potential values obtained from SDMT2 and SDMT4 by Equation (22) are reported in Figure 27. Geosciences 2019, 9, x FOR PEER REVIEW 23 of 27

(a) (b)

Figure 27. Liquefaction potential values obtained from: (a) SDMT2 and amax = 0.4g; (b) SDMT2 and amax = 0.5g; (c) SDMT4 Figure 27. Liquefactionand amaxpotential = 0.4g; (d) SDMT4 values and obtainedamax = 0.5g. from: (a) SDMT2 and amax = 0.4 g; (b) SDMT2 and amax = 0.5 g; (c) SDMT4 and amax = 0.4 g; (d) SDMT4 and amax = 0.5 g. Based on the results obtained by the SDMT4, the LPI value is higher than 5 (high liquefaction potential) at the depth of about 3 meters; while the results obtained by SDMT2 show a high liquefaction potential from the depth of about 7 meters. The liquefaction potential index at the depth of 20 meters for the 5 SDMTs is summarized in Table 4.

Table 4. The liquefaction potential index from the five SDMTs for the three different CRR-KD curves using amax of 0.4g and 0.5g.

Liquefaction Potential Index amax 0.4g 0.5g CRR-KD 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

Geosciences 2021, 11, 12 22 of 25

Based on the results obtained by the SDMT4, the LPI value is higher than 5 (high liquefaction potential) at the depth of about 3 m; while the results obtained by SDMT2 show a high liquefaction potential from the depth of about 7 m. The liquefaction potential index at the depth of 20 m for the 5 SDMTs is summarized in Table4.

Table 4. The liquefaction potential index from the ﬁve SDMTs for the three different CRR-KD curves using amax of 0.4g and 0.5g.

Liquefaction Potential Index

amax 0.4 g 0.5 g

CRR-KD 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

It is possible to observe that the results obtained from the three CRR-KD 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 amax produces a rise of about 25–50% in LPI.

7. Conclusions

In this paper, new variations of rd 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. Two different charts were determined analytically using a seismogram of 1818 and three seismograms of 1693 with PGA of 0.3g and 0.5g as input motion. The dashed range represents the range of rd values and the dashed line represents the recommended values of rd from the surface to a depth of 30 m. Average values can be approximated by Equations (14), (15), (16a–c) and (17a–c). Comparing the relationships obtained in this study to the relationships previously proposed by Iwasaki, Liao and Whitman and Robertson and Wride, it is possible to notice that the values of rd obtained here are lower. This work has been used for the potential liquefaction evaluation in Catania Harbour because the new rd relationship is more responsive to soil type examined. The findings can be summarized as follows:

(1) The results obtained from the three CRR-KD 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 amax is an important parameter in the evaluation of liquefaction potential.

Author Contributions: Data curation, M.S.V.S.; methodology, S.G.; supervision, M.R.M. All authors have read and agreed to the published version of the manuscript. Geosciences 2021, 11, 12 23 of 25

Funding: This research work was funded by the MIUR (Ministry of Education, Universities and Research [Italy]) through the project entitled “eWAS: an early WArning System for cultural—heritage” (Project code: ARS01_00926/CUP J66C18000390005), financed with the PNR 2015-2020 (National Research Program). Conflicts of Interest: The authors declare no conflict of interest.

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