geosciences

Article One-Dimensional Nonlinear Seismic Response Analysis Using Strength-Controlled Constitutive Models: The Case of the Leaning Tower of ’s Subsoil

Gabriele Fiorentino 1, Camillo Nuti 1,2,* ID , Nunziante Squeglia 3 ID , Davide Lavorato 1 ID and Stefano Stacul 3 ID

1 Department of Architecture, Roma Tre University, 00153 Rome, ; gabriele.fi[email protected] (G.F.); [email protected] (D.L.) 2 College of Civil Engineering, Fuzhou University, Fuzhou 350108, China 3 Department of Civil and Industrial Engineering, University of Pisa, 56122 Pisa, Italy; [email protected] (N.S.); [email protected] (S.S.) * Correspondence: [email protected]; Tel.: +39-06-57332994

 Received: 18 April 2018; Accepted: 19 June 2018; Published: 22 June 2018 

Abstract: The Leaning Tower of Pisa was built between 1173 and 1360 and began to lean at the beginning of its construction. Extensive investigations to reveal the causes of the tilting only began in the early 20th century. Although few have been recorded, there is a renewed interest in the seismic behavior of the tower triggered by the availability of new data and technologies. This paper highlights the influence of using new strength-controlled constitutive models in case of 1D nonlinear response analysis. This is an aspect that has been poorly investigated. Most of the computer codes currently available for nonlinear seismic response analysis (SRA) of soil use constitutive models able to capture small-strain behavior, but the large-strain shear strength is left uncontrolled. This can significantly affect the assessment of a 1-D response analysis and the Leaning Tower’s subsoil can be useful for this study as it represents a well-documented and well-characterized site. After a geological and geotechnical description of the subsoil profile and a synthesis of available data, the seismic input is defined. One-dimensional SRAs were carried out by means of a computer code which considers an equivalent-linear soil modelling and two codes which assume nonlinear soil response and permit to use strength-controlled constitutive models. All the parameters were calibrated on the basis of the same soil data, therefore allowing for a direct comparison of the results.

Keywords: leaning tower; seismic response analysis; seismic input; strength-controlled models

1. Introduction The Leaning Tower of Pisa was built between 1173 and 1360, and many attempts were made during the construction to correct the undesired tilt. The tower is in the form of a hollow cylinder surrounded by six loggias with columns and vaults merging from the base cylinder and surmounted by a belfry. The structure is subdivided into eight levels called ‘orders’. The outer surfaces are made with marble, while the inner ones with various masonry materials. The annulus between the outer and inner surfaces is filled with rubble and mortar. A spiral staircase winds up within the annulus up to the 6th order, while two shorter spiral staircases lead to the floor and top of the belfry. The staircase forms a large opening on the south side just above the level of the first cornice, where the thickness of the masonry suddenly decreases. The high stress within this region was a major cause of concern since it could give rise to an abrupt brittle failure of the masonry.

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Extensive instrumental measurements and investigations started only in the 20th century, as illustrated in [1]. The plane of maximum inclination is approximately coincident with the north-south plane. From 1993 to 2001 the Committee for the Safeguard of Leaning Tower of Pisa carried out several interventions aimed at geotechnical stabilization [2] and structural strengthening [3]. A comprehensive description of the history of the construction of the Tower and interventions is described in [2]. A dynamic monitoring system was installed by the Committee for the Safeguard of the Leaning Tower of Pisa at the end of its activities in 2001. During the last 20 years, several low-intensity earthquakes have been recorded. Although few events and very slight damage related to earthquakes has been observed from the construction of the monument, there is a considerable interest in the seismic behavior of the tower [4–7] triggered by the availability of new data and technologies. Within the chain starting from seismogenic zones and up to the tower, the dynamic response of its subsoil holds a crucial importance, particularly in terms of the frequency content of seismic input. This paper presents some results showing the influence of using new strength-controlled constitutive models in case of 1D nonlinear response analysis. This is an aspect poorly investigated up to now. Most of the codes currently available for nonlinear seismic response analysis use constitutive models able to capture small-strain behavior, but the large-strain shear strength is not controlled. The development of hyperbolic models (for example the Modified Kondner–Zelasko [8]), in the last decades permitted to well capture the backbone stress–strain curve and the unloading-reloading response of the soil. These models are fit to the experimental or reference shear modulus reduction curves and damping ratio curves but are unable to give realistic results in case of medium-large strain levels, resulting in soil layers strength underestimation or overestimation. This fact can significantly affect the assessment of a 1D site response analysis.

2. Subsoil

2.1. Geological Description of the Study Area The current configuration of the Pisa plain comes from the dynamic interaction between erosive and depositional processes developed, starting from the end of the Last Glacial Maximum expansion, first in coastal and transitional marine environments. Then, in the Middle Ages, it evolved mainly in continental fluvial-lake environments. The proximity to the coast provided the environmental conditions, since prehistoric times, to the development of the anthropic settlement in the area on which Pisa will rise and in the entire coastal area. Figure1 shows a geological map of the valley of the Arno river, from to the Tyrrhenian (Ligurian) Sea. The mountains positioned to the east of Pisa consists of formations belonging to the Paleozoic and the Tertiary geological periods and their structures reveal intense tectonic deformations. The main structure is oriented towards NNW-SSE, with faults bordering the western part of the mountains and located 5 km northeast of Pisa. More recent deposits, identified as quaternary continental in the geological map, developed in marine and in fluvial-lacustrine environments and deposited mainly in an estuary environment. The valley of the Arno river crosses a mountainous territory starting from its source, in the Tuscan–Emilian Apennines, up to Florence (Figure1). During the Last Glacial Maximum, in the period between 23,000 and 15,000 years ago, the level of the sea lowered at least 100 m and the river dug a deep valley west of Florence. This valley is now filled with alluvial materials. Pisa rises on these alluvial deposits, at an elevation of 3–4 m above the present mean sea level. The thickness of alluvial sediments near the city is at least 300 m. In the area, at the depth of about 40 m below the ground surface level can be found marine sands deposited during the Flandrian transgression. Geosciences 2018, 8, x FOR PEER REVIEW 3 of 20

deposit,Geosciences which2018 ,was8, 228 formed in a period of rapid eustatic lifting of the sea level. Figure 2 shows the3 of 20 morphological map of the valley of the Arno river.

Geosciences 2018, 8, x FOR PEER REVIEW 3 of 20 deposit, which was formed in a period of rapid eustatic lifting of the sea level. Figure 2 shows the morphological map of the valley of the Arno river.

FigureFigure 1. Geological 1. Geological map map of the of thestudy study area. area. (Adapted (Adapted from: from: Consorzio Consorzio Lamma Lamma Database Database [9]). [ 9]).

Above these dense sands layers, partly rearranged due to wind action, a complex mainly composed by clayey soils can be found. The clay layer close to the surface level is a clayey marine deposit, which was formed in a period of rapid eustatic lifting of the sea level. Figure2 shows the morphologicalFigure 1. Geological map of the map valley of the of study the Arnoarea. (Adapted river. from: Consorzio Lamma Database [9]).

Figure 2. Morphological map of the study area. The scale is the same as the previous figure. (Adapted from: Tuscany Region Database–Geoscopio [10]).

2.2. Geotechnical Model of the Leaning Tower of Pisa Subsoil The soil profile under the tower is shown in Figure 3. It consists of three distinct horizons. Figure 2. Morphological map of the study area. The scale is the same as the previous figure. HorizonFigure A is about 2. Morphological 10‐m thick and map primarily of the study consists area. of The estuarine scale is thedeposits, same aslaid the down previous under figure. tidal (Adapted from: Tuscany Region Database–Geoscopio [10]). conditions(Adapted with from:a rather Tuscany erratic Region sequence Database–Geoscopio of sandy and [10 clayey]). silt layers. Typically of estuarine deposits, there are significant variations over short horizontal distances. At the bottom of horizon A 2.2. Geotechnical Model of the Leaning Tower of Pisa Subsoil there2.2. is Geotechnical a 2‐m thick Modelmedium of the dense Leaning fine Towersand layer of Pisa (i.e., Subsoil upper sand). Horizon B consists primarily of marineThe clay, soil whichprofile extends under downthe tower to a depthis shown of about in Figure 40 m. 3.It isIt subdividedconsists of intothree four distinct distinct horizons. layers. The soil profile under the tower is shown in Figure3. It consists of three distinct horizons. HorizonThe upper A layeris about is soft 10‐ msensitive thick and clay, primarily locally known consists as of Pancone. estuarine It deposits,is underlain laid by down an intermediate under tidal Horizon A is about 10-m thick and primarily consists of estuarine deposits, laid down under tidal conditionslayer of stiffer with clay, a rather which erratic in turn sequence overlies aof sand sandy layer and (the clayey intermediate silt layers. sand). Typically The bottom of estuarine layer of conditions with a rather erratic sequence of sandy and clayey silt layers. Typically of estuarine deposits, deposits,horizon Bthere is a arenormally significant consolidated variations clay over known short horizontal as the lower distances. clay. HorizonAt the bottom B is very of horizon uniform A there are significant variations over short horizontal distances. At the bottom of horizon A there is a therelaterally is a near 2‐m thethick tower. medium dense fine sand layer (i.e., upper sand). Horizon B consists primarily of 2-m thick medium dense fine sand layer (i.e., upper sand). Horizon B consists primarily of marine clay, marineHorizon clay, which C is composed extends down of dense to a sanddepth (the of about lower 40 sand), m. It whichis subdivided extends intodown four to distincta considerable layers. which extends down to a depth of about 40 m. It is subdivided into four distinct layers. The upper Thedepth. upper Based layer on issample soft sensitive descriptions clay, locallyand piezocone known as tests, Pancone. the materials It is underlain to the bysouth an intermediateof the tower layer is soft sensitive clay, locally known as Pancone. It is underlain by an intermediate layer of layer of stiffer clay, which in turn overlies a sand layer (the intermediate sand). The bottom layer of stiffer clay, which in turn overlies a sand layer (the intermediate sand). The bottom layer of horizon horizon B is a normally consolidated clay known as the lower clay. Horizon B is very uniform laterally near the tower. Horizon C is composed of dense sand (the lower sand), which extends down to a considerable depth. Based on sample descriptions and piezocone tests, the materials to the south of the tower

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Geosciencesappear to2018 be ,more8, 228 silty and clayey than to the north, and the upper sand layer is locally thinner.4 This of 20 Geosciences 2018, 8, x FOR PEER REVIEW 4 of 20 is believed to be the cause of the southward tilt of the tower [11]. appearB is a normally to be more consolidated silty and clayey clay than known to the as the north, lower and clay. the Horizonupper sand B is layer very is uniform locally thinner. laterally This near isthe believed tower. to be the cause of the southward tilt of the tower [11].

Figure 3. The subsoil of the Tower. (After Viggiani and Pepe, 2005 [11]).

The water table in horizon A is found at a depth between 1 and 2 m below the ground surface; FigureFigure 3. 3. TheThe subs subsoiloil of of the the Tower. Tower. (After (After Viggiani Viggiani and and Pepe, Pepe, 2005 2005 [11]). [11]). the latter has an average elevation of 3 m above mean sea level. Pumping from the lower sand has resultedTheHorizon waterin downward C table is composed in horizonseepage of A densefrom is found horizon sand at (the a A depth lowerwith betweena sand), pore pressure which 1 and extends2 distributionm below down the with toground a considerabledepth surface; which thedepth.is slightlylatter Based has below an on average hydrostatic sample elevation descriptions (Figure of 4).3 andm above piezocone mean tests,sea level. the materialsPumping from to the the south lower of thesand tower has resultedappearMany toin be downward borings more silty beneath seepage and clayey and from around than horizon to the the tower A north, with show and a pore thethat upperpressure the surface sand distribution layer of the is Pancone locally with thinner. depthclay stretches which This is isbelievedout slightly beneath tobelow be the the hydrostatictower, cause from of the (Figure which southward it4). can be tilt deduced of the tower that the [11]. average settlement of the monument is moreManyThe than water borings 3 m (Figure table beneath in 3). horizon and around A is found the tower at a depth show between that the surface 1 and 2 of m the below Pancone the ground clay stretches surface; outthe beneath latterA comprehensive has the an tower, average from description elevation which it of ofcan 3subsoil mbe above deduced investigations mean that sea the level. average carried Pumping settlementout since from theof the the beginning lower monument sand of has theis moreresulted20th thancentury in 3 downwardm can (Figure be found 3). seepage in [11], from whereas horizon the A dynamic with a pore characterization pressure distribution of subsoil with is the depth focus which of the is slightlypresentA comprehensive belowpaper. hydrostatic description (Figure4 of). subsoil investigations carried out since the beginning of the 20th century can be found in [11], whereas the dynamic characterization of subsoil is the focus of the present paper.

Figure 4. Water head in Horizon A (3), intermediate sand (2) and lower sand (1). (After Viggiani and Pepe,Figure 2005 4. Water [11]). head in Horizon A (3), intermediate sand (2) and lower sand (1). (After Viggiani and Pepe, 2005 [11]).

FigureMany 4. borings Water head beneath in Horizon and around A (3), intermediate the tower show sand that(2) and the lower surface sand of (1). the (After Pancone Viggiani clay and stretches As reported in [12], several tests were performed from the early 1990s to determine the shear out beneathPepe, 2005 the [11]). tower, from which it can be deduced that the average settlement of the monument is wave velocity profile Vs, namely Down Hole (DH) test [13], Cross Hole (CH) test, DH and CH tests more than 3 m (Figure3). [11] and an SDMT test (Seismic Dilatometer Test). The results obtained from these tests show a AsA comprehensivereported in [12], description several tests of were subsoil performed investigations from the carried early out 1990s since to determine the beginning the shear of the satisfactory agreement of the Vs values. All the tests reached a maximum depth of 40 m except for the wave20th centuryvelocity canprofile be found Vs, namely in [11 ],Down whereas Hole the (DH) dynamic test [13], characterization Cross Hole (CH) of subsoil test, DH is the and focus CH oftests the CH test, which reached a depth of 65 m. None of the tests was successful in identifying the seismic [11]presentand paper.an SDMT test (Seismic Dilatometer Test). The results obtained from these tests show a bedrock. satisfactoryAs reported agreement in [12 of], the several Vs values. tests All were the performed tests reached from a maximum the early 1990s depth to of determine 40 m except the for shear the CHwave test, velocity which profile reachedVs ,a namely depth of Down 65 m. Hole None (DH) of the test tests [13], Crosswas successful Hole (CH) in test, identifying DH and CHthe testsseismic [11] bedrock. GeosciencesGeosciences2018 2018,,8 8,, 228 x FOR PEER REVIEW 55 of of 20 20

The bedrock (i.e., Vs ≥ 800 m/s) is presumed to be very deep and some attempts have been made and an SDMT test (Seismic Dilatometer Test). The results obtained from these tests show a satisfactory to increase the knowledge of the subsoil below 65 m depth. An array 2D test has been exploited to agreement of the V values. All the tests reached a maximum depth of 40 m except for the CH test, obtain the shear waves velocity profile down to more than one hundred meters from ground surface which reached a depth of 65 m. None of the tests was successful in identifying the seismic bedrock. [6]. Figure 5 shows the shear velocity profile down to a depth of 100 m. The array 2D test revealed The bedrock (i.e., Vs ≥ 800 m/s) is presumed to be very deep and some attempts have been made the presence of a stiffer layer (i.e., Vs ≈ 500 m/s) at a depth of about 100 m. Another methodology to to increase the knowledge of the subsoil below 65 m depth. An array 2D test has been exploited to investigate about the seismic bedrock depth by using the available H/V ratios is described in [14,15], obtain the shear wave velocity profile down to more than one hundred meters from ground surface [6]. however further studies and investigations have been planned in order to improve the knowledge of Figure5 shows the shear velocity profile down to a depth of 100 m. The array 2D test revealed the subsoil below 100 m depth. presence of a stiffer layer (i.e., V ≈ 500 m/s) at a depth of about 100 m. Another methodology to Many samples have been retrieveds from the ground around the tower. Several of these samples investigate about the seismic bedrock depth by using the available H/V ratios is described in [14,15], have been subjected to laboratory tests to obtain the dynamic characterization of the subsoil. Further however further studies and investigations have been planned in order to improve the knowledge of information can be found in [11]. subsoil below 100 m depth.

Figure 5. Profile of the shear wave velocity. Figure 5. Profile of the shear wave velocity.

3. SeismicMany samplesInput have been retrieved from the ground around the tower. Several of these samples have been subjected to laboratory tests to obtain the dynamic characterization of the subsoil. Further Defining the seismic input is a key step in forecasting the seismic action on a structure. information can be found in [11]. Especially when the bedrock depth is defined, the assessment of the seismic hazard is usually based 3.on Seismic well‐established Input studies [16]. Ancient monumental masonry buildings are particularly vulnerable to vibrations and specificallyDefining to theseismic seismic actions input due is to amany key factors: step in in forecasting the case of the the seismicTower of action Pisa, the on construction a structure. Especiallyprocess lasted when two the centuries, bedrock depth its characteristic is defined, theinclination assessment and ofthe the several seismic changes hazard in is the usually foundation based onsystem well-established occurred during studies its [16 life]. contributed to increase the uncertainty in the dynamic behavior. Therefore,Ancient it monumentalis necessary to masonry define the buildings seismic are input particularly in terms vulnerable of natural toaccelerograms, vibrations and which specifically can be toscaled seismic in order actions to duematch to a many target factors: response in spectrum. the case of In the this Tower context, of Pisa,the use the of construction the design response process lastedspectrum two defined centuries, by its the characteristic Code (e.g., EC8) inclination is not recommended and the several [17], changes as it inhas the no foundation direct relationship system occurredwith a specific during its life contributed characterized to increase by magnitude the uncertainty M and in source the dynamic‐to‐site behavior. distance R, Therefore, necessary it isto necessaryselect sets to of define natural the accelerograms. seismic input To in termsthis aim, of naturalit is appropriate, accelerograms, as reported which canin recent be scaled studies in orderapplied to matchto archeological a target response sites [18] spectrum. to use a In hybrid this context, approach the which use of thecan designbe briefly response summarized spectrum as definedfollows: by the Code (e.g., EC8) is not recommended [17], as it has no direct relationship with a specific earthquake characterized by magnitude M and source-to-site distance R, necessary to select sets1. ofDefinition natural accelerograms. of a Uniform Hazard To this aim,Spectrum it is appropriate, (UHS) obtained as reported by means in recentof a Probabilistic studies applied Seismic to archeologicalHazard Assessment sites [18] to use[19] a using hybrid one approach or more which Ground can Motion be briefly Predictive summarized Equation as follows: (GMPE); 2. Disaggregation of the seismic hazard to obtain the most likely combinations of M and R for a 1. Definitiongiven return of period a Uniform (RP) Hazard [20]; Spectrum (UHS) obtained by means of a Probabilistic Seismic 3. HazardDefinition Assessment of a Scenario [19] usingEarthquake one or selected more Ground from Motionthe seismic Predictive catalogue, Equation compatible (GMPE); with the previously defined UHS, and evaluated with the same GMPEs of point 1.

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2. Disaggregation of the seismic hazard to obtain the most likely combinations of M and R for a given return period (RP) [20]; 3. Definition of a Scenario Earthquake selected from the seismic catalogue, compatible with the Geosciencespreviously 2018, 8, x FOR defined PEER REVIEW UHS, and evaluated with the same GMPEs of point 1. 6 of 20

OnOn the the basis basis of of past past studiesstudies [6[6],], the the target target response response spectrum spectrum was was defined defined for two for returntwo return periods periods(RPs) of(RPs) the of seismic the seismic action, action, namely namely RP = 130 RP = years 130 years (moderate (moderate earthquake) earthquake) and RP and = 500RP = years 500 years (severe (severeearthquake). earthquake). First, First, the disaggregation the disaggregation of the of seismic the seismic hazard hazard was performed, was performed, thus providing thus providing a scenario a scenarioearthquake earthquake for each for return each period.return period. Based on Based the Italian on the seismic Italian catalogueseismic catalogue CPTI15 [ 21CPTI15], two [21], controlling two controllingearthquakes earthquakes were identified were identified [12]: a M W[12]:5.15 a seismicMW 5.15 event seismic with event R (epicentral with R (epicentral distance) distance) = 19 km was= 19 selectedkm was for selected an RP for of 130an RP years of 130 (Livorno years 1742) (Livorno whereas 1742) a whereas MW 5.71 a earthquake MW 5.71 earthquake with R = 21 with km (OrcianoR = 21 kmPisano (Orciano 1846) Pisano was considered 1846) was considered for an RP of for 500 an years. RP of 500 years. TheThe GMPE GMPE proposed proposed by by Akkar Akkar and and Bommer Bommer [22] [22 was] was then then used used to toevaluate evaluate the the target target response response spectraspectra for for a Ground a Ground Type Type B (according B (according to the toEurocode the Eurocode 8 [23] and 8 [ the23] Italian and the Building Italian Code Building NTC Code‐08 [24]),NTC-08 including [24]), the including subsoil theterm subsoil of the equation term of the depending equation on depending the Vs,30 value on the of Vthes,30 site,value which of the is an site, averagewhich shear is an averagewave velocity shear waveof the velocity first 30 ofm. theSeven first accelerograms 30 m. Seven accelerogramswere selected for were each selected return for periodeach from return the period European from Strong the European Motion Database Strong Motion [25], considering Database [ 255 ],< M considering < 5.5 for RP 5 <= M130 < years 5.5 for andRP 5.3 = < 130 M years< 6.2 for and RP 5.3 = 500 < M years. < 6.2 The for RPhorizontal = 500 years. components The horizontal of the selected components accelerograms of the selected were scaledaccelerograms so that a good were match scaled was so thatobtained a good between match the was average obtained spectrum between of the the average seven accelerograms spectrum of the of seveneach set accelerograms and the reference of each target set spectrum and the reference in the range target of spectrumnatural periods in the 0.31–1 range s. of This natural was periodsdone to 0.31–1take into s. Thisaccount was the done natural to take periods into account of the first the two natural bending periods modes of the of firstthe tower two bending and that modes of the of thirdthe mode tower (about and that 0.3 of s), the thus third obtaining mode (abouta scale 0.3factor s), thus(SF) for obtaining each record. a scale Figures factor 6 (SF) and for 7 depict each record. the timeFigures histories6 and of7 thedepict scaled the accelerograms time histories offor the an scaledRP of 130 accelerograms and 500 years, for respectively, an RP of 130 as and well 500 as years, the scalerespectively, factor used as to well obtain as the the scale final factor accelerograms. used to obtain the final accelerograms.

FigureFigure 6. Time 6. Time histories histories of the of the scaled scaled accelerograms accelerograms for for an anRP RP of of130 130 years. years.

Geosciences 2018, 8, 228 7 of 20 GeosciencesGeosciences 2018 2018, 8, x, FOR8, x FOR PEER PEER REVIEW REVIEW 7 of 207 of 20

Figure 7. Time histories of the scaled accelerograms for an RP of 500 years. FigureFigure 7. Time 7. Time histories histories of the of scaledthe scaled accelerograms accelerograms for anfor RP an ofRP 500 of 500years. years.

FigureFigureFigure 8 reports8 8reports reports the the theselected selected selected input input input motion motion motion spectra spectra spectra and and and the the theresults results results in interms in terms terms of ofaverage of average average response response response spectrumspectrumspectrum for for 130for 130 130years years years (left) (left) (left) and and and 500 500 500years years years (right). (right). (right). The The The dispersion dispersion dispersion of the of of the therecords records records (average (average (average spectrum spectrum spectrum (μ)( µ(±μ) 1)± ±standard 11 standard standard deviation deviation deviation (σ ())σ ( ))σis)) is reported reportedis reported for for forthe the the two two cases.cases. cases. ForFor RP ForRP = RP= 130 130 = years, 130years, years, the the dispersion thedispersion dispersion is large,is is large,withlarge, with a maximumwith a maximum a maximum COV COV ( σCOV/ (µσ)/ ofμ (σ) 0.996/ofμ )0.996 of in 0.996 thein the rangein therange 0.31–1range 0.31–1 0.31–1 s, while s, while s, forwhile for RP RPfor = 500 =RP 500 years= 500years thereyears there isthere ais large a is a largedispersionlarge dispersion dispersion too, too, but too, but slightly butslightly slightly lower lower lower compared compared compared to to RP RP to = 130=RP 130 = years, 130years, years, and and a and a maximum maximum a maximum COV COV COV of of 0.643 0.643 of 0.643 in in the in theabove theabove above cited cited cited range. range. range.

(a) (a) (b) (b)

FigureFigureFigure 8. 8.Average 8.Average Average response response response spectrum. spectrum. spectrum. Spectrum-compatibilitySpectrum Spectrum‐compatibility‐compatibility is is assumed assumed is assumed between between between 0.3–1.1 0.3–1.1 0.3–1.1 s. ( as.) Return( as.) (a) ReturnperiodReturn period = period 130 = years;130 = 130years; (b years;) return (b) return(b period) return period = period 500 = years.500 = 500years. years.

4. Site4.4. Site Site Response Response Response Analysis Analysis Analysis TheTheThe subsoil subsoil subsoil model model model adopted adopted adopted for for sitefor site siteresponse response response analyses analyses analyses is is reported is reported inin TableTable in Table1 .1. The The 1. thickness The thickness thickness and and unit and unitweightunit weight weight for for each eachfor lithotypeeach lithotype lithotype were were assumedwere assumed assumed on on the theon basis thebasis ofbasis theof the of data thedata reported data reported reported in [in11 ].[11]. in The [11]. The assumed The assumed assumed shear shearwaveshear wave velocity wave velocity velocity profile profile is profile also is basedalso is also based on based the on outcomes theon theoutcomes outcomes of the 2Dof the seismicof the2D seismic2D array seismic test array [ 6array]. test However, test[6]. [6].However, this However, profile thissatisfactorilythis profile profile satisfactorily satisfactorily matches the matchesV matchess values the measured theVs valuesVs values by measured other measured geophysical by otherby other tests geophysical geophysical in the upper tests part.tests in the Accordingin theupper upper to part.thepart. AccordingVs Accordingprofile, to the the to seismic theVs profile, Vs bedrock profile, the (theseismicVs >seismic 800 bedrock m/s) bedrock is not(Vs >( localizedV 800s > 800m/s) m/s) in is the not is explored notlocalized localized depth in the in range theexplored explored because depthadepthV srangeequal range because to 500because m/s a V sa isequal V reacheds equal to 500 to in 500m/s the m/s loweris reached is reached strata. in Forthe in the thislower lower reason, strata. strata. considering For Forthis this reason, thereason, uncertainties considering considering in thethe theuncertainties location uncertainties of in the the in seismic thelocation location bedrock of the of theseismic (Vs seismic> 800 bedrock m/s), bedrock the(Vs > accelerograms(V 800s > 800m/s), m/s), the theaccelerograms selected accelerograms for the selected site selected response for for the thesite siteresponse response analysis analysis were were recorded recorded at Groundat Ground Type Type B, accordingB, according to Eurocodeto Eurocode 8 definition. 8 definition.

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GeosciencesRegarding2018 the, 8, 228nonlinear properties, most of lithotypes were characterized with resonant column8 of 20 (RC) tests. analysis were recorded atTable Ground 1. Subsoil Type B, model according adopted to for Eurocode site response 8 definition. analysis. Regarding the nonlinear properties, most of lithotypes were characterized with resonant column (RC) tests. USCS ΔH OCR PI φ c‘ U.W. Vs G/G0‐γ & Hor. Layer K0 (‐) Class. (m) (‐) (%) (°) (kPa) (kN/m3) (m/s) D‐γ Curves Table 1. Subsoil model adopted for site response analysis. [26] Average MG MG ‐ 3.0 ‐ ‐ ‐ ‐ ‐ 18.50 ± 0.80 180 curve G/G -γ & Hor. Layer USCS Class. ∆H (m) K (-) OCR (-) PI (%) ϕ (◦) c‘ (kPa) U.W. (kN/m3) V (m/s) 0 RC Test A A1 ML 5.4 0 1.05 3.5 13 34 6.8 18.86 s± 0.72 180D- γ Curves (2016) MG MG - 3.0 - - - - - 18.50 ± 0.80 180 [26] Average[27] curve‐PI = 30, A A1A2 MLSC‐SM 5.4 2.0 1.05 0.88 3.5 132.5 3430 6.834 18.866.8 ± 0.7218.07 ±180 0.85 180 RC Test (2016) σ‘v = 0.55 bar [27]-PI = 30, B A2B1 SC-SMCH 2.03.5 0.88 0.62 2.5 302 3443 6.826 18.072.4 ± 0.8517.00 ±180 0.89 180 RC tests σ‘v = 0.55 bar B2 CH 2.0 0.54 1.5 33 26 7.7 17.49 ± 0.57 180 RC tests B B1 CH 3.5 0.62 2 43 26 2.4 17.00 ± 0.89 180 RC tests B3 CH 4.9 0.42 1.5 41 20 15.9 16.67 ± 0.58 180 RC tests B2 CH 2.0 0.54 1.5 33 26 7.7 17.49 ± 0.57 180 RC tests B3B4 CHCH 4.91.2 0.42 0.61 1.5 411.5 2033 15.930 16.670 ± 0.5819.48 ±180 0.96 230 RC testsRC tests B4B5 CHCL 1.23.0 0.61 0.61 1.5 331.5 3023 030 19.480 ± 0.9619.76 ±230 0.79 230 RC testsRC tests B5 CL 3.0 0.61 1.5 23 30 0 19.76 ± 0.79 230 RC tests[27]‐PI = 8, B6 SC‐SM 2.4 0.88 2.5 8 34 0 19.11 ± 0.49 230 [27]-PI = 8, B6 SC-SM 2.4 0.88 2.5 8 34 0 19.11 ± 0.49 230 σ‘v = 2.0 bar B7 CH 4.6 0.54 1.5 34 26 3.1 18.62 ± 0.97 230σ‘ v = 2.0RC bar tests B7 CH 4.6 0.54 1.5 34 26 3.1 18.62 ± 0.97 230 RC tests B8 CL 1.4 0.54 1.5 23 26 3.1 18.41 ± 0.51 230 RC tests B8 CL 1.4 0.54 1.5 23 26 3.1 18.41 ± 0.51 230 RC tests B9B9 CHCH 4.04.0 0.54 0.54 1.5 311.5 2631 3.126 19.013.1 ± 1.4119.01 ±230 1.41 230 RC testsRC tests B10B10 CHCH 2.62.6 0.54 0.54 1.5 291.5 2629 3.126 19.383.1 ± 0.4419.38 ±230 0.44 230 RC testsRC tests [27]‐PI = 0, C C1 SC‐SM 27.6 ‐ ‐ ‐ ‐ ‐ 20.52 ± 1.29 340[27 ]-PI = 0, C C1 SC-SM 27.6 - - - - - 20.52 ± 1.29 340 σ‘v = 3.50 bar σ‘v = 3.50 bar [27]-PI[27] = 15,‐PI = 15, C2C2 ‐ - 11.111.1 - ‐ ‐ - 15 -15 ‐ ‐ - - ‐ 340 340 σ‘v = 5.0σ‘v bar = 5.0 bar [27]-PI = 0, C3 - 16.3 ------340 [27]‐PI = 0, C3 ‐ 16.3 ‐ ‐ ‐ ‐ ‐ ‐ 340σ‘ = 6.0 bar v σ‘v = 6.0 bar Bedrock Bedrock (C3) - ‐ - ‐ - - ‐ - ‐ - ‐ 21.00‐ 21.00 500 500 ‐ - (C3) Hor. = horizon; ΔH = layer thickness; K0 = at‐rest earth pressure coefficient; OCR = overconsolidation Hor. = horizon; ∆H = layer thickness; K0 = at-rest earth pressure coefficient; OCR = overconsolidation ratio; PIratio;= plasticity PI = plasticity index; ϕ =index; angle ofφ friction;= angle c’ of = friction; effective cohesion;c’ = effective U.W. =cohesion; soil unit weight; U.W. =V ssoil= shear unit wave weight; velocity, Vs = G/Gshear0 = normalizedwave velocity, secant G/G shear0 = modulus;normalizedD = secant damping shear ratio; modulus;γ = shear. D = damping ratio; γ = shear.

TheThe A1A1 lithotype, lithotype, waswas characterized characterized withinwithin thisthis studystudy throughthrough a a recently recently performed performed resonant resonant columncolumn (RC) (RC) test. test. TheThe correspondingcorresponding resultsresults areare reportedreported inin FigureFigure9 9in in terms terms of of normalized normalized secant secant shearshear modulus modulus (Figure(Figure9 a)9a) and and damping damping ratio ratio (Figure (Figure9b) 9b) variation variation as as a functiona function of of the the shear shear strain strain amplitudeamplitude ( (G/GG/G00-‐γγ andand D-D‐γγ curves).curves).

(a) (b)

FigureFigure 9. 9.Resonant Resonant columncolumn testtest (RCT-815;(RCT‐815; 815815 is is the the registration registration number number of of the the soil soil sample) sample) results results (lithotype(lithotype A1): A1): ( a(a)) modulus modulus reduction reduction curve; curve; ( b(b)) damping damping ratio. ratio.

Because of the lack of experimental data, G/G0‐γ and D‐γ curves that have been reported in the Because of the lack of experimental data, G/G0-γ and D-γ curves that have been reported in theliterature literature for forsimilar similar soils soils were were employed employed for forthe the remaining remaining lithotypes: lithotypes: MG, MG, A2, A2, B6, B6, C1, C1, C2 C2and and C3 C3[26,27] [26,27 (Table] (Table 1).1 ).

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These literature curves have been obtained by a huge database of samples and can quantitatively capture the dynamic behavior of the above lithotypes because are based on the grain size distribution, the plasticity index and the soil stress state. Considering the unavailability of the experimental curves, those proposed by Rollins [26] and by Darendeli [27] are a good compromise for the dynamic characterization of the MG and A2, B6, C1, C2, C3, respectively. In order to compare the results obtained with different 1-D SRA models, analyses were carried out by means of three different computer codes: equivalent-linear code STRATA [28], nonlinear code DEEPSOIL [29–31] and nonlinear code ONDA [32,33]. All parameters for the calibration of the models were deduced from the same group of in situ and laboratory tests. The analyses were carried out considering a one-dimensional geometry. This choice is justified by the fact that all the main layers are horizontally stratified, and it can be reasonable to assume a geotechnical subsoil model indefinitely extended horizontally. The seismic wave field was simplified with SH-waves vertically propagating from the bedrock to the soil deposit surface. The input motion was considered as an outcrop motion and was deconvoluted by the computer codes used in this work down to the depth of the base layer.

4.1. Seismic Response Analyses with Equivalent-Linear Models The equivalent-linear (EL) analyses with STRATA were carried out in the frequency domain, and the amplification function was computed. The variation of the shear moduli and of the damping ratios were dependent only on the shear strain level. This means that the material damping has only a frequency independent component. The effective shear strain (γeff) for a given soil layer and for a given stress time history was evaluated following the suggestions in [34] (Equations (1) and (2)).

γe f f = R · γmax (1)

M − 1 R = (2) 10 where R is the effective strain ratio, γmax is the maximum shear strain computed in a layer and M is the magnitude related with the acceleration time history considered. This quantity is representative of the time history duration (i.e., number of cycles). The effective shear strain is needed in order to identify, by an iterative procedure based on G-γ and D-γ curves of each stratum, a strain level which is representative of a given stress time history and therefore to select appropriate values of the shear modulus G and damping ratio D.

4.2. Seismic Response Analyses with Nonlinear Models Nonlinear analyses with ONDA and DEEPSOIL are performed in the time domain with a step-by-step integration of the equations of motion of a multi-degree of freedom lumped parameters model. For that purpose, in ONDA [32] the Wilson-θ time integration method was adopted [35], whereas in DEEPSOIL [29] the dynamic equilibrium equation is solved numerically at each time step using the Newmark-β method [36]. In ONDA, the constitutive law (τ-γ) of the initial loading stress–strain curve (backbone or skeleton curve) is represented by the Ramberg–Osgood model [37]. This model consists of a not invertible relationship that depends on four parameters: α and R represent the position and the curvature of the skeleton curve, respectively, while τmax and G0 represent the soil shear strength and the shear modulus at small strain levels, respectively. ONDA uses a strength-controlled constitutive model. The backbone curve can be written in this form: x = y · (1 + α · |y|R−1) (3) Geosciences 2018, 8, 228 10 of 20 where x and y are the normalized shear strain and shear stress, respectively: γ x = (4) γre f

τmax γre f = (5) G0 τ y = (6) τmax α and R were obtained by a linear interpolation of data collected from Resonant Column tests [11] for lithotypes A1, B1, B2, B3, B4, B5, B7, B8, B9 and B10, while for lithotypes MG, A2, B6, C1, C2 and C3 by a linear interpolation of data based on the modulus reduction curves reported in Table1. For that purpose, the Ramberg–Osgood equation was rewritten as follows:

 G   τ  log 0 − 1 = (R − 1) · log + log(α) (7) G τmax

Considering Equation (7) and performing a linear regression of the experimental and literature curves data, α and R were obtained. In Equation (7), the soil shear strength (τmax) was computed according to Equation (8), as proposed by Hardin and Drnevich [38], nevertheless other relationships can be used.

( )1/2  (1 + K ) 2  (1 − K ) 2 τ = 0 σ0 senϕ + c0 cos ϕ − 0 σ0 (8) max 2 v0 2 v0

In Equation (8) σ’v0 is the vertical effective geostatic stress, K0 is the at-rest earth pressure coefficient, ϕ is the angle of friction, and c’ is the effective cohesion. The values of K0, ϕ and c’ are reported in Table1 for each lithotype. DEEPSOIL can handle mainly two nonlinear constitutive laws (τ-γ) for the initial loading stress–strain curve (backbone or skeleton curve). The most-commonly used stress–strain relationship is the MKZ (Modified Kondner–Zelasko) model [8]. This is a modified hyperbolic model that defines the monotonic shear stress–shear strain law coupled with unloading–reloading behavior and can properly capture the nonlinear soil response in case of small-strain values. Equations (9) and (10) are the basic backbone and the unloading–reloading relationships, respectively, for the MKZ model [8].

γG0 τ =  s (9) 1 + β γ γr

 γ−γrev  2G0 2 τ = + τrev (10)  − s 1 + β γ γrev 2γr where γr is a reference shear strain, β and s are dimensionless factors, τrev and γrev are the shear stress and shear strain at the reversal loading point, respectively. The dimensionless factors are computed by fitting the experimental data. Additional details about the available modulus reduction and damping curve fitting procedures are reported in [29]. Nevertheless, the MKZ model was found to be unable to correctly characterize the nonlinear soil behavior in case of medium-large shear strains because the shear strength at large shear strains are generally left uncontrolled. In 2015, the General Quadratic/Hyperbolic (GQ/H) Strength-Controlled constitutive model [30,31] has been developed and implemented in DEEPSOIL code. This model can consider both the soil shear strength at failure and the small-strain stiffness nonlinearity. The GQ/H model Geosciences 2018, 8, 228 11 of 20 can overcome the above limitations in the MKZ model, related to cases in which the shear strength of the soil is underestimated or overestimated leading to inaccurate site response analysis results. Further details can be found in [30,31]. Compared to the MKZ model, in the GQ/H model both the initial shear stiffness (G0) and the maximum shear strength (τmax) must be defined and inputted, and the backbone curve is represented by the Equation (11).   2 γ τ γr = r (11) τmax   h  i2   1 + γ + 1 + γ − 4θ γ γr γr τ γr

θτ is a curve-fitting parameter defined in the Equation (12).   θ γ 2 γr θτ = θ1 +   ≤ 1 (12) θ + γ 3 γr where θ1, θ2 and θ3 are curve fitting factors. Further details are provided in [30]. In Equation (11), the soil shear strength (τmax) was computed according to Equation (8). In the nonlinear codes (ONDA and DEEPSOIL) used in this work the cyclic behavior of unloading-reloading (hysteretic curves) can be modelled using either the second Masing criterion [39] or the modified second Masing criterion [32,40]. The second Masing criterion states that the unloading–reloading branches of the stress–strain curve have the same shape as the skeleton curve but with a scale factor (n) equal to 2. This function can be expressed with Equations (10) and (13) for the code DEEPSOIL and the code ONDA, respectively.

" R−1# x − xc y − yc y − yc = · 1 + α · (13) n n n where xc and yc are the normalized amplitudes of strain and stress at the stress reversal point, respectively. The hysteretic damping computed using the unloading-reloading stress–strain loops according to the Masing rules may lead to an overestimation of damping at large strains. The modified second Masing criterion [40] assumes that the scale factor can be different from 2. In ONDA to simulate cyclic hardening behavior, the scale factor n should be higher than 2, whereas cyclic softening or material degradation could be modelled by decreasing the values of n (even n < 2). The analyses are conducted in terms of total stresses. The n values should be determined experimentally. If experimental data are lacking, ONDA assumes that n is dependent on the over-consolidation ratio [32], and considers n equal to 5 and 3.5 in NC and OC soil conditions, respectively. When the number of cycles is increased, n decreases. In DEEPSOIL, the modified second Masing criterion is formulated in a different way, as described in [27,31]. We thus compared the site response analysis results obtained with these two codes following the standard second Masing rule. In addition to the hysteretic damping due to the constitutive models adopted, ONDA and DEEPSOIL consider the viscous damping at small strain levels with a damping matrix expressed as a linear combination of the and the stiffness matrixes (i.e., Rayleigh damping formulation). Consequently, even at small strain levels, when the hysteretic damping is null, a viscous damping component is always considered. This overcomes the limitations of other computer codes that result in unrealistic amplifications in the case of low energy earthquakes [32,41]. The Rayleigh damping target frequencies associated to the target soil damping at low strains, used in this work, are those commonly recommended in DEEPSOIL: (a) the natural frequency of the soil profile (0.69 Hz) and (b) 5 times the natural frequency of the soil profile (3.46 Hz). GeosciencesGeosciences 2018 2018, ,8 8, ,x x FOR FOR PEER PEER REVIEW REVIEW 1212 of of 20 20 aa linearlinear combinationcombination ofof thethe massmass andand thethe stiffnessstiffness matrixesmatrixes (i.e.,(i.e., RayleighRayleigh dampingdamping formulation).formulation). Consequently,Consequently, eveneven atat smallsmall strainstrain levels,levels, whenwhen thethe hysteretichysteretic dampingdamping isis null,null, aa viscousviscous dampingdamping componentcomponent is is always always considered. considered. This This overcomes overcomes the the limitations limitations of of other other computer computer codes codes that that result result inin unrealisticunrealistic amplificationsamplifications inin thethe casecase ofof lowlow energyenergy earthquakesearthquakes [32,41].[32,41]. TheThe RayleighRayleigh dampingdamping Geosciencestargettarget frequenciesfrequencies2018, 8, 228 associatedassociated toto thethe targettarget soilsoil dampingdamping atat lowlow strains,strains, usedused inin thisthis work,work, areare12 thosethose of 20 commonlycommonly recommended recommended in in DEEPSOIL: DEEPSOIL: (a) (a) the the natural natural frequency frequency of of the the soil soil profile profile (0.69 (0.69 Hz) Hz) and and (b) (b) 55 times times the the natural natural frequency frequency of of the the soil soil profile profile (3.46 (3.46 Hz). Hz). InIn FiguresFigures 1010 and and 11 1111 the thethe comparison comparisoncomparison between betweenbetween the thethe experimental experimentalexperimental andand the thethe adopted adoptedadopted normalized normalizednormalized modulusmodulus reductionreduction and and dampingdamping ratio ratio curves curves corresponding corresponding to to the the A1 A1 and and UpperUpper Pancone Pancone (B1 (B1-B5)(B1‐‐B5)B5) layerslayers are areare presented. presented.presented. The TheThe damping dampingdamping ratio ratioratio curves curvescurves shown shownshown in Figures inin FiguresFigures 10 and 1010 and11and related 1111 relatedrelated with ONDA withwith ONDAONDA don’t includedon’tdon’t includeinclude the viscous thethe viscousviscous damping dampingdamping at low strainatat lowlow levels strainstrain that levelslevels has thatthat been hashas obviously beenbeen obviouslyobviously included includedincluded in the analyses inin thethe toanalysesanalyses avoid to zeroto avoid avoid damping zero zero damping damping values. ONDAvalues. values. ONDA overestimatesONDA overestimates overestimates the hysteretic the the hysteretic hysteretic damping damping damping at high at at strain high high levelsstrain strain comparedlevelslevels comparedcompared to DEEPSOIL. toto DEEPSOIL.DEEPSOIL. This fact justifiesThisThis factfact the justifiesjustifies slightly thethe lower slightlyslightly spectral lowerlower acceleration spectralspectral values accelerationacceleration obtained valuesvalues with ONDAobtainedobtained and with with shown ONDA ONDA in theand and following shown shown in in section. the the following following section. section.

((aa)) ((bb))

FigureFigure 10. 10. Comparison Comparison between between between the the the experimental experimental experimental and and and the the the adopted: adopted: adopted: ( (aa)) (modulus amodulus) modulus reduction reduction reduction curve; curve; curve; ( (bb)) (dampingbdamping) damping ratio ratio ratio curve curve curve (lithotype (lithotype (lithotype A1). A1). A1).

((aa)) ((bb))

FigureFigure 11. 11. Comparison Comparison between between between the the the experimental experimental experimental and and and the the the adopted: adopted: adopted: ( (aa)) (modulus amodulus) modulus reduction reduction reduction curve; curve; curve; ( (bb)) (dampingbdamping) damping ratio ratio ratio curve curve curve (Upper (Upper (Upper Pancone). Pancone). Pancone). In In Inthis this this Figure, Figure, Figure, triangles triangles triangles represent represent represent the the the best best best-fit‐‐fitfit of ofof the thethe collected collected experimentalexperimental data data related related to to the the Upper Upper Pancone Pancone asas as reportedreported reported inin in [[7]. 7[7].].

4.3. Seismic Response Analysis Results Figure 12 shows the difference between the soil shear strength profile obtained with the commonly used MKZ model and that computed with Equation (8), used to perform the nonlinear analyses with strength-controlled constitutive models (DEEPSOIL GQ/H and ONDA).

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4.3.4.3. Seismic Seismic Response Response Analysis Analysis results results FigureFigure 1212 showsshows thethe differencedifference betweenbetween thethe soilsoil shearshear strengthstrength profileprofile obtainedobtained withwith thethe commonlycommonly usedused MKZMKZ modelmodel andand thatthat computedcomputed withwith EquationEquation (8),(8), usedused toto performperform thethe nonlinearnonlinear Geosciencesanalysesanalyses2018 with with, 8, strength 228strength‐‐controlledcontrolled constitutive constitutive models models (DEEPSOIL (DEEPSOIL GQ/H GQ/H and and ONDA). ONDA). 13 of 20

FigureFigure 12. 12. Implied Implied shear shear strength strength profiles. profiles. Figure 12. Implied shear strength profiles.

TheThe MKZMKZ modelmodel isis notnot ableable toto correctlycorrectly reproducereproduce thethe shearshear strengthstrength profileprofile andand largelylargely overestimateoverestimateThe MKZ thethe model soilsoil resistance isresistance not able atat to failurefailure correctly downdown reproduce toto 44 mm in thein depth,depth, shear while strengthwhile underestimateunderestimate profile and the largelythe soilsoil overestimateresistanceresistance at at thehigher higher soil depths. resistance depths. This This at failureaffects affects downthe the nonlinear nonlinear to 4 m in soil soil depth, response response while analysis underestimateanalysis results. results. the soil resistance at higherTheThe depths.results results for Thisfor a a return affectsreturn period theperiod nonlinear of of 130 130 and soiland 500 response500 years years analysisare are reported reported results. in in Figures Figures 13 13 and and 14 14 in in terms terms of of horizontalhorizontalThe results accelerationacceleration for a return responseresponse period spectraspectra of 130 computed andcomputed 500 years atat groundground are reported surfacesurface in (averaged(averaged Figures 13 overover and all14all theinthe terms inputinput ofmotionsmotions horizontal applied).applied). acceleration AverageAverage response inputinput spectra spectrumspectrum computed atat seismicseismic at ground bedrockbedrock surface andand (averaged amplifiedamplified over spectraspectra all the areare input alsoalso motionsreported.reported. applied). Average input spectrum at seismic bedrock and amplified spectra are also reported.

((aa)) ((bb))

Figure 13. Cont.

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(c) (d) Figure 13. Results of SRA for return period = 130 years with: (a) STRATA (LE); (b) DEEPSOIL Figure 13. Results of SRA for return period = 130 years with: (a) STRATA (LE); (b) DEEPSOIL (NL-MKZ); (c) DEEPSOIL (NL-GQ/H); (d) ONDA (NL). (NL‐MKZ); (c) DEEPSOIL (NL‐GQ/H); (d) ONDA (NL).

(a) (b)

(c) (d)

FigureFigure 14.14. ResultsResults ofof SRASRA forfor returnreturn periodperiod == 500500 yearsyears with:with: (aa)) STRATASTRATA (LE);(LE); ((bb)) DEEPSOILDEEPSOIL (NL-MKZ);(NL‐MKZ); ( c(c)) DEEPSOIL DEEPSOIL (NL-GQ/H); (NL‐GQ/H); ((dd)) ONDAONDA (NL).(NL).

Figure 15a,b show the Fourier spectrum ratios between the ground surface and the base of the FigureFigure 15 15a,ba,b show show the the Fourier Fourier spectrum spectrum ratios ratios between between thethe ground ground surface surface andand the the base base of of the the soil profile for some representative accelerograms at return periods of 130 and 500 years, soilsoil profile profile for for some some representative representative accelerograms accelerograms at return at periodsreturn ofperiods 130 and of 500 130 years, and respectively. 500 years, respectively. In both the Figures and for all the accelerograms, the ratio is generally less than 1 for Inrespectively. both the Figures In both and the for Figures all the accelerograms, and for all the the accelerograms, ratio is generally the lessratio than is generally 1 for frequencies less than above 1 for frequencies above 2 Hz in case of nonlinear analysis. 2frequencies Hz in case ofabove nonlinear 2 Hz in analysis. case of nonlinear analysis.

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(a)

(b)

Figure 15.15. FourierFourier spectrum spectrum ratios ratios between between the the surface surface and and the base the ofbase the of soil the profile soil forprofile some for relevant some inputrelevant motions: input motions: (a) return (a period) return = period 130 years; = 130 (b )years; return (b period) return = period 500 years. = 500 years.

Figure 16 shows the comparisons between the average response spectra, while Figure 17 the average surface-to-bedrocksurface‐to‐bedrock amplification amplification function function for for both both the the return return periods periods considered considered in this in study. this study.

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(a) (b) (a) (b) Figure 16. Comparison between results of different SRA analyses: (a) RP = 130 years; (b) RP = 500 FigureFigureyears. 16. 16. ComparisonComparison between between results results of of different different SRA SRA analyses: analyses: (a) RP (a) = RP 130 = years; 130 years; (b) RP (b =) 500 RP years.= 500 years.

(a) (b) (a) (b) FigureFigure 17. 17.Average Average surface-to-bedrock surface‐to‐bedrock amplification amplification function: function: (a )(a RP) RP = 130= 130 years; years; (b ()b RP) RP = = 500 500 years. years. Figure 17. Average surface‐to‐bedrock amplification function: (a) RP = 130 years; (b) RP = 500 years.

TheThe SRA SRA comparisons comparisons shown shown in in Figures Figures 16 16 and and 17 17 reveal reveal the the importance importance of of the the selected selected analysis analysis methodThe SRA(equivalent comparisons‐linear shown or nonlinear) in Figures in the 16 definitionand 17 reveal of pseudo the importance‐acceleration. of the selected analysis methodmethod (equivalent-linear(equivalent‐linear oror nonlinear)nonlinear) inin thethe definitiondefinition ofof pseudo-acceleration.pseudo‐acceleration. TheThe comparison comparison between between equivalent-linear equivalent‐linear andand nonlinear nonlinear results results revealed revealed more more evident evident differences.The comparison In fact, equivalent between‐ linearequivalent method‐linear overestimates and nonlinear the ordinates results betweenrevealed 0 andmore 1.0 evident s period differences.differences. In fact, equivalent-linearequivalent‐linear method overestimates thethe ordinates betweenbetween 00 andand 1.01.0 ss periodperiod forfor 130 130 years years RP, RP, whereas whereas for 500 for years 500 RPyears ordinates RP ordinates are overestimated are overestimated between 0between and 1.5 s. 0 Maximum and 1.5 s. forMaximum 130 years overestimation RP, whereas isfor above 500 80%years in RPthe intervalordinates 0–0.5 are s.overestimated between 0 and 1.5 s. overestimationMaximum overestimation is above 80% is inabove the interval80% in the 0–0.5 interval s. 0–0.5 s. TheThe equivalent-linear equivalent‐linear models models (e.g., (e.g., STRATA STRATA [28 [28])]) consider consider a a single single elastic elastic modulus modulus referred referred to to a a representativeThe equivalent strain‐linear level models (65% or (e.g., M‐1/10 STRATA of the [28])max considerrange). a single elastic modulus referred to a representativerepresentative strainstrain levellevel (65%(65% oror M-1/10M‐1/10 of the max range). InIn nonlinear nonlinear analyses, analyses, on on the the other other hand, hand, the the elastic elastic modulus modulusG is G updated is updated at each at each time-step time‐step and and is is reducedIn nonlinear considerably analyses, onfor the medium other hand,‐large the deformations, elastic modulus causing G is updated an increase at each intime the‐step deposit and reducedis reduced considerably considerably for medium-large for medium deformations,‐large deformations, causing ancausing increase an in increase the deposit in fundamentalthe deposit periodfundamental and thus period shifting and the thus peaks shifting of the the spectrum peaks of to the higher spectrum periods. to higher periods. fundamentalIn the case period of 130and years thus shiftingRP above the 0.6 peaks s, the of nonlinearthe spectrum analyses to higher practically periods. coincide despite the InIn thethe casecase ofof 130130 yearsyears RPRP aboveabove 0.60.6 s,s, thethe nonlinearnonlinear analysesanalyses practicallypractically coincidecoincide despitedespite thethe factfact that that the the formulation formulation of of the the backbone backbone curve curve adopted adopted in in ONDA ONDA [32 [32,33],33] (Ramberg–Osgood) (Ramberg–Osgood) and and factDEEPSOIL that the [29]formulation (MKZ [8] of and the GQ/H backbone [30,31]) curve is different.adopted in ONDA [32,33] (Ramberg–Osgood) and DEEPSOILDEEPSOIL [[29]29] (MKZ(MKZ [[8]8] andand GQ/HGQ/H [30,31]) [30,31]) is is different. different. InIn the the case case of of 500 500 years years RP RP the the differences differences between between the the commonly commonly used used nonlinear nonlinear MKZ MKZ model model andIn strength the case‐controlled of 500 years constitutive RP the differences models (GQ/H between and theONDA) commonly become used higher nonlinear compared MKZ to modelseismic andand strength-controlledstrength‐controlled constitutiveconstitutive models models (GQ/H (GQ/H and ONDA) become higher compared to seismic motionsmotions for for 130 130 years years RP. RP. The The MKZ MKZ model model overestimates overestimates the the ordinates ordinates obtained obtained with with ONDA ONDA of of motionsabout 10–20% for 130 between years RP. 0 and The 0.8 MKZ s. This model is due overestimates to the different the soil ordinates modelling obtained for medium with ‐ONDAlarge shear of aboutabout 10–20%10–20% betweenbetween 00 andand 0.80.8 s. This is due to the different soil modelling for medium-largemedium‐large shear strainstrain levels. levels. strain Thelevels. latter aspect can be clarified showing in Figure 18 the peak shear strain profiles for 130 and 500 Theyears latter RP seismicaspect can motions. be clarified In case showing of 500 yearsin Figure RP acceleration18 the peak sheartime histories, strain profiles the attained for 130 shearand 500 years RP seismic motions. In case of 500 years RP acceleration time histories, the attained shear

GeosciencesGeosciences2018 2018, 8, ,8 228, x FOR PEER REVIEW 1717 of of 20 20

strain levels are larger compared to 130 years RP input motions. For such a reason becomes relevant to considerThe latter a strength aspect can‐controlled be clarified constitutive showing model in Figure for 18the the soil peak response. shear strain profiles for 130 and 500 yearsThis RP highlights seismic the motions. importance In case of of considering 500 years RP a more acceleration proper and time realistic histories, soil the strength attained profile shear in strainnonlinear levels analysis are larger methods compared starting to 130 from years medium RP input‐severe motions. seismic For suchactions. a reason becomes relevant to consider a strength-controlled constitutive model for the soil response.

(a) (b)

FigureFigure 18. 18. ComparisonComparison between between the the peak peak shear shear strain strain profiles profiles using usingdifferent different SRA analyses: SRA analyses: (a) RP = (a130) RP years–input = 130 years–input motion motionGSA; (b GSA;) RP = (b 500) RP years–input = 500 years–input motion motionAQK. AQK.

5. ClosingThis highlights Remarks the importance of considering a more proper and realistic soil strength profile in nonlinearThe analysispaper shows methods the starting results from of medium-severefree‐field seismic seismic response actions. analyses (SRA) carried out considering the subsoil of Piazza dei Miracoli in Pisa, where the Leaning Tower is located. Given 5. Closing Remarks that this site has been subject to a considerable number of investigations, there is a large number of dataThe available paper showsfor soil the characterization. results of free-field seismic response analyses (SRA) carried out considering the subsoilThe shear of Piazza wave dei velocity Miracoli profile in Pisa, has wherebeen recently the Leaning extended Tower down is located. to more Given than that 100 thism below site has the beenground subject level to a[6]. considerable One‐dimensional number SRA of investigations, were carried there out isby a largemeans number of three of data computer available codes: for soilSTRATA characterization. [28], DEEPSOIL [29] and ONDA [32,33]. TheThe shear first code wave performs velocity the profile analysis has been in the recently frequency extended domain down considering to more an than equivalent 100 m below‐linear thesoil ground model, levelwhereas [6]. DEEPSOIL One-dimensional and ONDA SRA analyze were carried the problem out by in means the time of three domain computer assuming codes: true STRATAnonlinear [28 soil], DEEPSOIL behavior. [All29] the and parameters ONDA [32 ,of33 ].the models were calibrated using the same soil data, thereforeThe first all three code performsmodels can the be analysis considered in the as frequencybeing equivalent. domain considering an equivalent-linear soil model,As discussed whereas in DEEPSOIL [6], seismic and input ONDA is affected analyze by the some problem dispersion in the due time to domain uncertainties assuming related true to nonlinearlack of knowledge. soil behavior. The AllSRA the analyses parameters are also of theaffected models by aleatory were calibrated uncertainty. using the same soil data, thereforeThe all main three target models of can this be paper considered is to asshow being the equivalent. influence of using new strength‐controlled constitutiveAs discussed models in [ 6in], seismiccase of input1D nonlinear is affected response by some analyses. dispersion In duefact, to most uncertainties of computer related codes to lackcurrently of knowledge. available The for SRAnonlinear analyses seismic are also response affected analysis by aleatory use constitutive uncertainty. models able to capture smallThe‐strain main behavior, target of this but paper the large is to show‐strain the shear influence strength of using is left new uncontrolled. strength-controlled This can constitutive affect the modelsassessment in case of of a 1D1‐D nonlinear response response analysis, analyses. as in the In Pisa fact, subsoil most of conditions. computer codes Nonlinear currently models available seem formore nonlinear appropriate seismic in response reproducing analysis the use true constitutive behavior models of the able subsoil, to capture however small-strain calibrating behavior, the butparameters the large-strain seems shearmore strengthdifficult. is left uncontrolled. This can affect the assessment of a 1-D response

Geosciences 2018, 8, 228 18 of 20 analysis, as in the Pisa subsoil conditions. Nonlinear models seem more appropriate in reproducing the true behavior of the subsoil, however calibrating the parameters seems more difficult. In this work, differences between the commonly used nonlinear MKZ model and strength-controlled constitutive models (GQ/H and the model implemented in ONDA) are presented. The MKZ model overestimates the pseudo-acceleration values obtained with ONDA and the GQ/H model, especially in case of 500 years RP seismic input motions. This is due to the different soil modelling for medium-large shear strain levels. In fact, the attained shear strain levels are larger compared to 130 years RP acceleration time histories. This reveals the importance to take into account of a proper soil strength profile in nonlinear analysis methods starting from medium-severe seismic actions. Higher differences were found between equivalent-linear and nonlinear codes. The maximum differences between equivalent-linear and nonlinear models are above 80% in both the 130 and 500 years return periods. For RP = 130 years, the differences decrease and become negligible starting from a period approximately equal to 1 s, whereas the differences remain around 40% for RP = 500 years. The differences among the mean spectra obtained by means of different soil response modelling (equivalent-linear, MKZ model, GQ/H model and ONDA) might be not relevant for a structural designer in case of a new standard building, since it is possible to employ code-defined spectrum or, as an alternative, select the most conservative one. The selection of the appropriate spectrum assumes particular relevance in case of historical buildings or monuments, because in this case structural interventions have to be respectful of construction integrity and a selection of excessively conservative actions could lead to inappropriate operations [17,42]. Moreover, in the case of the Leaning Tower of Pisa, since the fundamental period is about one second, the uncertainties related to nonlinear models seem negligible with respect to the uncertainty related to seismic input. Further studies and investigations have been planned in order to improve the knowledge of subsoil below 100 m depth. This is expected to improve the capabilities of considered models to forecast the ground response.

Author Contributions: G.F., C.N. and D.L. defined the seismic input motions, N.S. described the subsoil model used to perform the seismic response analyses; S.S. analyzed the RC testing data and performed the seismic response analyses; N.S., G.F. and S.S. wrote the paper. Acknowledgments: The authors want to thank the Opera della Primaziale Pisana for supporting this research. Conflicts of Interest: The authors declare no conflict of interest.

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