Mechanical Properties of Historic Masonry Stones Obtained by In Situ Non-Destructive Tests on the St. Agostino Church in Amatrice (Italy)

applied
 sciences
Article
Mechanical Properties of Historic Masonry Stones Obtained by
In Situ Non-Destructive Tests on the St. Agostino Church in
Amatrice (Italy)
Alessandro Grazzini * and Giuseppe Lacidogna

 Department of Structural Geotechnical and Building Engineering, Politecnico di Torino, 10129 Turin, Italy;
 giuseppe.lacidogna@polito.it
 * Correspondence: alessandro.grazzini@polito.it

 Featured Application: The use of non-destructive diagnostic techniques for the in situ and non-
 invasive mechanical characterization of historic stone masonry.

 Abstract: The design of strengthening and securing work for historic buildings requires knowledge
 of the masonry mechanical characteristics, often obtainable through laboratory tests that require
 invasive samples. The non-destructive techniques, applicable in situ in a rapid and non-invasive way,
 represent a valid alternative to estimate mechanical strengths without destructive sampling. In this
 study, a methodology was calibrated which, by combining the results of the ultrasonic and impact
 tests, makes it possible to reach a good estimate of the compression strength and elastic modulus
 of a particular rock: sandstone. Most buildings in Amatrice, the city devastated by the violent
 earthquake of Central Italy in 2016, were built by means of this sedimentary rock. By carrying out a
 



 
 diagnostic campaign on the remaining walls of the St. Agostino church in Amatrice, it was possible to
Citation: Grazzini, A.; Lacidogna, G.
 obtain a correlation, specific for this case study, between the compression strengths from laboratory
Mechanical Properties of Historic tests and the results of the ultrasonic and impact tests. Unlike the traditional Sonreb methods, this
Masonry Stones Obtained by In Situ methodology wanted to favor the use of the impact method instead of the sclerometrer test. In this
Non-Destructive Tests on the St. way, it will be possible to operate on other damaged buildings of similar construction types located
Agostino Church in Amatrice (Italy). in the seismic crater of Amatrice, evaluating the mechanical characteristics of the masonry structures
Appl. Sci. 2021, 11, 6352. https:// be means of in situ non-destructive tests in order to design the safety and strengthening work.
doi.org/10.3390/app11146352

 Keywords: historic building; masonry stone; Amatrice earthquake; structural safety; non-destructive
Academic Editor: Victor Giurgiutiu techniques (NDT); ultrasonic test; impact test

Received: 11 June 2021
Accepted: 7 July 2021
Published: 9 July 2021
 1. Introduction
Publisher’s Note: MDPI stays neutral
 Historic buildings located within seismic areas suffer significant damage and collapse
with regard to jurisdictional claims in
 whenever earthquakes of considerable intensity highlight their structural vulnerabilities.
published maps and institutional affil- The ancient masonry structures are affected by material degradation, high variability in the
iations. quality of the masonry texture, an absence of effective connections between walls and floors,
 an absence of sufficiently rigid floors, and a lack of adequate box behaviour [1–4]. Many of
 these damaged buildings had never received a careful analysis of seismic vulnerabilities
 and adequate seismic improvement interventions [5,6]. In particular, churches are seismi-
Copyright: © 2021 by the authors.
 cally vulnerable buildings due to the presence of very high naves without intermediate
Licensee MDPI, Basel, Switzerland.
 constraints on the walls, as well as being subject to other common structural problems
This article is an open access article
 linked to poor masonry quality [7,8].
distributed under the terms and The 2016 Central Italy earthquake, which caused the total destruction of Amatrice and
conditions of the Creative Commons many other historic villages around it, highlighted the vulnerability of historic buildings
Attribution (CC BY) license (https:// due to decay, an absence of anti-seismic devices and poor maintenance in the masonry
creativecommons.org/licenses/by/ structures. The buildings of Amatrice were characterized by sandstone and marl stones
4.0/). of low strength, but, above all, poor in calcium carbonate. Since the production of lime

Appl. Sci. 2021, 11, 6352. https://doi.org/10.3390/app11146352 https://www.mdpi.com/journal/applsci

Appl. Sci. 2021, 11, x FOR PEER REVIEW 2 of 14

Appl. Sci. 2021, 11, 6352 2 of 14
 masonry structures. The buildings of Amatrice were characterized by sandstone and
 marl stones of low strength, but, above all, poor in calcium carbonate. Since the
 production of lime
 took place with tookquarried
 stones place with stones
 in the samequarried
 sites fromin which
 the same
 the sites fromstones
 building whichwere
 the
 building stones were obtained, they were capable of giving only “poor”
 obtained, they were capable of giving only “poor” lime. From this lime, a mortar, as the lime. From this
 lime,
 bindera of
 mortar, as the binder
 the masonry, of the with
 was obtained masonry, was obtained
 low calcium content,with
 which low calcium
 over content,
 time degraded
 which over time degraded more rapidly, no longer binding the stones
 more rapidly, no longer binding the stones of the masonry. In particular, one of the of the masonry. In
 particular, one of the
 symbolic damaged symbolic
 buildings indamaged
 the historicbuildings
 center ofin the historic
 Amatrice was center
 the St. of Amatrice
 Agostino was
 church,
 the St. Agostino church,
 a Romanesque-Gothic a Romanesque-Gothic
 construction built in 1428construction
 (Figure 1a), built
 whichinsuffered
 1428 (Figure 1a),
 an almost
 which sufferedthat
 total collapse an almost
 occurredtotal
 in collapse
 progressivethatphases
 occurred in progressive
 during phases earthquake
 the long seismic during the
 long
 swarm seismic earthquake
 after the swarm
 first violent after the
 earthquake of 24first violent
 August 2016earthquake
 (Figure 1b)of[9].24The August
 façade2016
 was
 (Figure 1b) [9]. The façade was composed of sandstone, and the interior
 composed of sandstone, and the interior was made from a single nave with a wooden roofwas made from a
 single nave with
 and exposed a wooden roof and exposed trusses.
 trusses.

 (a) (b)
 Figure
 Figure1.1.St.St.Agostino
 Agostinochurch
 churchininAmatrice
 Amatricebefore
 before(a)
 (a)and
 andafter
 after(b)
 (b)the
 theseismic
 seismicearthquake
 earthquakeswarm
 swarmofof2016
 2016ininCentral
 CentralItaly.
 Italy.

 The safeguarding
 The safeguarding ofofthis immense
 this immense artistic heritage
 artistic urgently
 heritage deserves
 urgently careful careful
 deserves knowl-
 edge of the walls’
 knowledge of the mechanical characteristics
 walls’ mechanical in order to better
 characteristics in design
 order strengthening
 to better design work
 (compatible with the monumental buildings) and prepare
 strengthening work (compatible with the monumental buildings) and prepare more more accurate computational
 models with
 accurate different levels
 computational of complexities,
 models with different as described
 levels of incomplexities,
 [10–14], among as others.
 describedIn the
 in
 field of cultural
 [10–14], amongheritage,
 others. non-invasive
 In the fielddiagnostic
 of cultural techniques
 heritage,offer a considerable
 non-invasive contribu-
 diagnostic
 tion to the knowledge
 techniques of the structural
 offer a considerable criticalities
 contribution toofthe
 historic buildings,
 knowledge of partly replacing
 the structural
 the most destructive
 criticalities of historictests that are partly
 buildings, not compatible
 replacingwith the the
 mostconservation
 destructiveoftests
 the architectural
 that are not
 aspects of the
 compatible withhistoric building [15–18].
 the conservation of theNon-destructive tests (NDT)
 architectural aspects of theare the setbuilding
 historic of tests
 and surveys conducted using methods that do not alter the material
 [15–18]. Non-destructive tests (NDT) are the set of tests and surveys conducted using and do not require
 the destruction
 methods that do or notremoval
 alter theofmaterial
 samplesand fromdo the
 not structure,
 require the aimed at searching
 destruction for and
 or removal of
 identifying defects in the structure itself.
 samples from the structure, aimed at searching for and identifying defects in the
 The itself.
 structure determination of the mechanical strength of the historic masonry structures and
 theirThe
 components
 determination(stones, bricks
 of the and mortar)
 mechanical is a very
 strength important
 of the issue for structures
 historic masonry the evaluation
 and
 of the static and seismic safety of the existing building, especially
 their components (stones, bricks and mortar) is a very important issue for the evaluationin consideration of any
 damage
 of already
 the static suffered.
 and seismic Often,
 safety of this determination
 the existing building,takes place through
 especially semi-destructive
 in consideration of any
 tests, such as flat jacks, or through the extraction of samples to be
 damage already suffered. Often, this determination takes place through semi-destructive tested in the laboratory.
 However,
 tests, such asin flat
 the context
 jacks, orof monumental
 through buildings,
 the extraction the destructive
 of samples diagnostic
 to be tested techniques
 in the laboratory.
 must be limited, and can be accompanied (in many cases, partially replaced) by non-
 However, in the context of monumental buildings, the destructive diagnostic techniques
 destructive techniques, which for historical masonry concern precisely the sonic and
 must be limited, and can be accompanied (in many cases, partially replaced) by
 ultrasonic technique, and the impact test [19].
 non-destructive techniques, which for historical masonry concern precisely the sonic and
 One of the non-destructive methods calibrated for evaluating the compression strengths
 ultrasonic technique, and the impact test [19].
 of concrete is the Sonreb method. It is based on calibration curves, obtained from several
 One of the non-destructive methods calibrated for evaluating the compression
 experimental tests, which correlate the compression strength of the concrete with the ultra-
 strengths of concrete is the Sonreb method. It is based on calibration curves, obtained
 sonic speed waves and with the rebound values of the sclerometer, so that only one or both
 from several experimental tests, which correlate the compression strength of the concrete
 non-destructive techniques can be used in situ to estimate the strength of the reinforced
 concrete structure without invasive laboratory tests. Unlike the traditional Sonreb method

with the ultrasonic speed waves and with the rebound values of the sclerometer, so that
 only one or both non-destructive techniques can be used in situ to estimate the strength
Appl. Sci. 2021, 11, 6352 of the reinforced concrete structure without invasive laboratory tests. Unlike3 ofthe 14
 traditional Sonreb method for concrete structures, several authors, such as Vasconcelos et
 al. [20], Vasanelli et al. [21], Cobanoglu et al. [22] and Concu at al. [23], also calibrated and
 validated the application on stone structures. The calibration on stones requires different
 for concrete structures, several authors, such as Vasconcelos et al. [20], Vasanelli et al. [21],
 curves in relation to the different types of lithotypes. The precision of these calibration
 Cobanoglu et al. [22] and Concu at al. [23], also calibrated and validated the application
 curves varies according to the anisotropy that characterizes the different lithotypes.
 on stone structures. The calibration on stones requires different curves in relation to the
 This experimental research has positively evaluated the application of the Sonreb
 different types of lithotypes. The precision of these calibration curves varies according to
 method on a specific case study for the estimation of the mechanical characteristics of
 the anisotropy that characterizes the different lithotypes.
 stone walls damaged by the earthquake: the St. Agostino church in Amatrice. The
 This experimental research has positively evaluated the application of the Sonreb
 purpose was to correlate the compression tests carried out in laboratory on the stones
 method on a specific case study for the estimation of the mechanical characteristics of stone
 taken from the masonry ruins of the church, with the ultrasonic and impact tests
 walls damaged by the earthquake: the St. Agostino church in Amatrice. The purpose was
 performed in situ on the same stones. In fact, unlike the traditional Sonreb methods, this
 to correlate the compression tests carried out in laboratory on the stones taken from the
 methodology
 masonry ruinswanted to favor
 of the church, thethe
 with useultrasonic
 of the impact method
 and impact instead
 tests of theinsclerometer
 performed situ on the
 test, as it is a similar tool that nevertheless offers
 same stones. In fact, unlike the traditional Sonreb methods, this methodology much more information.wanted Theto
 sclerometer test records only the returned elastic energy. On the
 favor the use of the impact method instead of the sclerometer test, as it is a similar tool other hand, the impact
 test
 that also records the
 nevertheless offersgiven
 much energy, the dissipated
 more information. Theenergy, the impact
 sclerometer time, only
 test records and the
 the
 maximum force, energy.
 returned elastic as well as Onbeing able hand,
 the other to estimate and the
 the impact elastic
 test modulus
 also records theofgiven
 the material
 energy,
 [19].
 the dissipated energy, the impact time, and the maximum force, as well as being able to
 The correlation
 estimate and the elastic curves obtained
 modulus in this
 of the experimental
 material [19]. research can be used for further
 diagnostic investigations on other masonry buildings
 The correlation curves obtained in this experimental research and historiccanmonuments in the
 be used for further
 Amatrice
 diagnosticarea, built with on
 investigations the other
 same masonry
 masonry buildings
 texture (Figure 2). It will
 and historic be sufficient
 monuments to
 in the
 calibrate
 Amatricethe curves
 area, builtwithwithreference
 the same to limited
 masonry core samples
 texture or other
 (Figure 2). semi-destructive
 It will be sufficient tests,
 to
 and then estimate
 calibrate the curves inwith
 situ the mechanical
 reference strengths
 to limited by mainly
 core samples or performing non-destructive
 other semi-destructive tests,
 tests for the
 and then benefitinofsitu
 estimate thethe
 conservation
 mechanical of architectural
 strengths artefacts.
 by mainly As a matter
 performing of fact, in
 non-destructive
 Section
 tests for the benefit of the conservation of architectural artefacts. As a matter approach
 11.10.3 of the Italian technical codes for construction [24], insofar as this of fact, in
 is to be11.10.3
 Section considered mainlytechnical
 of the Italian applicable codesforfordimensioned
 constructionsquare stones,
 [24], insofar the approach
 as this legislation is
 provides for themainly
 to be considered possibility of estimating
 applicable for dimensionedthe compression
 square stones, strength of masonry
 the legislation by
 provides
 comparing the strength
 for the possibility of the the
 of estimating individual
 compression materials,
 strength stone blocks by
 of masonry andcomparing
 mortar. The the
 compression
 strength of thestrength
 individual of the mortarstone
 materials, can blocks
 be estimated in situ
 and mortar. Theby means of astrength
 compression Windsor of
 penetrometric
 the mortar cantest or by means
 be estimated in situof by
 smallmeanssamples and the penetrometric
 of a Windsor packing, in the testlaboratory,
 or by means of
 specimens of similar
 of small samples andcomposition
 the packing,tested in theby compression
 laboratory, [25]. In this
 of specimens ofway, both
 similar the design
 composition
 of urgent
 tested by safety work and
 compression [25].post-earthquake
 In this way, both strengthening
 the design ofwork urgent willsafety
 be able
 work to make use
 and post-
 earthquake
 of the mechanicalstrengthening
 strengthwork values will
 ofbetheable
 oldtostones
 make anduse of
 ofthe
 themechanical
 masonry texturesstrengthformed
 values
 of thethem,
 with old stones
 derived and of thethrough
 mainly masonrynon-invasive
 textures formed tests.with
 The them, derived
 mechanical mainlyvalues
 strength throughof
 non-invasive
 the individualtests. stonesThewillmechanical
 be usefulstrength
 for thevalues of the individual
 subsequent estimation stonesof the will be useful
 compression
 for the subsequent
 strength of masonryestimation
 structures.of the compression strength of masonry structures.

 (a) (b)
 Figure
 Figure 2. (a)
 (a) Damaged
 Damaged masonry
 masonry buildings
 buildings in
 in the
 the area
 area around
 around the
 the epicenter
 epicenter of
 of the
 the 2016
 2016 Central
 Central Italy
 Italy earthquake;
 earthquake;(b)
 (b)St.
 St.
 Francesco church in Amatrice, damaged by the same earthquake.
 Francesco church in Amatrice, damaged by the same earthquake.

 2. Materials and Methods
 The experimental tests consisted of:
 - Compression tests on cores obtained by extraction from masonry stones taken in situ
 after the collapse of the St. Agostino church (Figure 3a);

Appl. Sci. 2021, 11, x FOR PEER REVIEW 4 of 14
Appl. Sci. 2021, 11, x FOR PEER REVIEW 4 of 14

 2. Materials and Methods
Appl. Sci. 2021, 11, 6352 2. Materials and Methods 4 of 14
 The experimental tests consisted of:
 The experimental tests consisted of:
 - Compression tests on cores obtained by extraction from masonry stones taken in situ
 - Compression tests on cores obtained by extraction from masonry stones taken in situ
 after the collapse of the St. Agostino church (Figure 3a);
 -- after the collapse
 Ultrasonic of thedetermination
 St. Agostino church (Figuredynamic
 3a);
 Ultrasonic tests
 tests for
 for the
 the determination of of the
 the elastic
 elastic dynamic modulus
 modulusperformed
 performedon on
 - Ultrasonic
 the same tests
 stones for the
 (Figure determination
 4); of the elastic dynamic modulus performed on
 the same stones (Figure 4);
 -- the same stones
 Impact (Figureon 4);
 Impact tests
 tests carried
 carried out
 out on the
 the same
 same stones
 stones (Figure
 (Figure 5).
 5).
 - Impact tests carried out on the same stones (Figure 5).

 (a) (b)
 (a) (b)
 Figure 3.
 Figure 3. (a)
 (a) Extraction
 Extraction of
 of cores
 cores from
 fromstones;
 stones;(b)
 (b)compression
 compressiontest
 teston
 onthe
 thestone
 stonecore
 coresample.
 sample.
 Figure 3. (a) Extraction of cores from stones; (b) compression test on the stone core sample.

 Figure 4. Ultrasonic test setup.
 Figure 4. Ultrasonic test setup.
 Figure 4. Ultrasonic test setup.

Appl.
Appl. Sci.
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 2021,
 2021, 6352 PEER REVIEW
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 5 of 1414

 (a) (b)
 Figure 5. 5.
 Figure (a)(a)
 Electric impact
 Electric hammer;
 impact Pimento
 (b)(b)
 hammer; Pimentomodel
 model multichannel LMS
 multichannel LMS signal
 signal analyzer.
 analyzer.

 2.1.
 2.1. Compression
 Compression Test
 Test
 For
 For theassessment
 the assessmentofofthe
 thestone
 stonemechanical
 mechanicalcharacteristics
 characteristics and
 and the
 the wall
 wall texture
 textureof
 ofthe
 theSt.
 Agostino church, 10 stone samples were taken in situ from the rubble that resulted
 St. Agostino church, 10 stone samples were taken in situ from the rubble that resulted from the
 collapse. For each stone, 2 cylindrical specimens were obtained with a diameter of 50 mm
 from the collapse. For each stone, 2 cylindrical specimens were obtained with a diameter
 and height of 100 mm (Figure 3a). The top and bottom surfaces of the cylindrical specimens
 of 50 mm and height of 100 mm (Figure 3a). The top and bottom surfaces of the
 were mechanically rectified to make them coplanar to the test machine plates, and they
 cylindrical specimens were mechanically rectified to make them coplanar to the test
 were arranged between the press platens without the interposition of friction-reducer
 machine plates, and they were arranged between the press platens without the
 layers. The compression tests were carried out using a Baldwin–Zwick 500 kN material
 interposition of friction-reducer layers. The compression tests were carried out using a
 testing machine, in accordance with the Italian technical code UNI EN 1926: 2007 [26],
 Baldwin–Zwick 500 kN material testing machine, in accordance with the Italian technical
 by applying a monotonically increasing axial load (force control 1 MPa/s) until failure
 code UNI EN 1926: 2007 [26], by applying a monotonically increasing axial load (force
 (Figure 3b).
 control 1 MPa/s) until failure (Figure 3b).
 2.2. Ultrasonic Test
 2.2. Ultrasonic Test
 Ultrasonic tests were also conducted on the same stones to estimate the dynamic elastic
 Ultrasonic
 modulus (Ed ). tests were inspection
 Ultrasonic also conducted on the same stones
 is a non-destructive method,to in
 estimate
 which highthe dynamic
 frequency
 elastic
 sound modulus
 waves are (Edintroduced
 ). Ultrasonicinto inspection is a non-destructive
 the material to be examined, method,
 in order to in highlight
 which high any
 frequency
 surface orsound
 internalwaves are introduced
 defects. Longitudinal into the material
 waves to be examined,
 were produced by means in order
 of an to
 electro-
 highlight any surface or internal defects. Longitudinal waves were produced
 acoustic transducer (emitting probe in piezoelectric or magnetostrictive material) placed by means ofin
 ancontact
 electro-acoustic transducer (emitting probe in piezoelectric or magnetostrictive
 with the stone surface under test; after passing through a path of known length, the
 material)
 train of placed
 waves in wascontact with by
 converted theastone
 secondsurface under test;
 transducer after passing
 (receiving through
 probe) into a path
 an electrical
 ofsignal
 known length, the
 processed train of waves
 by electronic timingwas converted
 circuits by ameasurement
 that allow second transducer of the (receiving
 transit time
 probe)
 of the into an electrical
 impulses. signal test
 The ultrasonic processed by electronic
 device consisted timing Tico
 of: a Proceq ® pulse
 circuits that allow
 generator;
 measurement
 two transducersof theoftransit
 54 kHz time
 (oneofemitting
 the impulses.
 and the The ultrasonic
 other test device
 receiving); a pulseconsisted of:and
 amplifier; a
 Proceq Tico® pulse
 an electronic device generator; two transducers
 for measuring of 54(Figure
 the time interval kHz (one emitting
 4). The speedand thewave
 of the other(v)
 receiving);
 depends on a pulse amplifier;
 the presence anddefects
 of any an electronic
 inside thedevice for measuring
 material, the time
 and is related to theinterval
 value of
 (Figure 4). The elastic
 the dynamic speed of the wave
 modulus (Ed(v) depends
 ) through ondensity
 the the presence
 (ρ) andoftheanyPoisson’s
 defects inside theof
 ratio (ν)
 the material.
 material, and isTherefore,
 related tothe thevalue
 valueofofthe
 thedynamic
 dynamic elastic
 elasticmodulus
 modulus (Ed(E
 ) dof the stonethe
 ) through can
 be obtained
 density (ρ) andusing the following
 the Poisson’s ratio relationship, in accordance
 (ν) of the material. Therefore, with
 thethe technical
 value standards
 of the dynamic
 ASTMmodulus
 elastic D2845 1995 (Ed)and UNIstone
 of the EN 12504-4: 2005 [27,28]:
 can be obtained using the following relationship, in
 accordance with the technical standards ASTM D2845 1995 and UNI EN 12504-4: 2005
 (1 + ν) (1 − 2ν)
 [27,28]: Ed = v2 ρ (1)
 (1 − ν )
 1 + 1 − 2 
 = (1)
 1− 

Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 14

Appl. Sci. 2021, 11, 6352 6 of 14
 In this case, from scientific literature sources [29,30] a ν value equal to 0.20 was
 considered for the sandstone. Three speed measurements were made for each sample.

 2.3. Impact
 In this Test
 case, from scientific literature sources [29,30] a ν value equal to 0.20 was
 considered for the sandstone.
 The impact Threeanother
 test represents speed measurements were madediagnostic
 valid non-destructive for each sample.
 technique,
 capable of evaluating surface detachment phenomena (for example of historical plasters
 2.3. Impact
 [31]) Test
 and of quantifying the static elastic modulus of a material [32]. The methodology is
 The impact
 adaptable to any test represents another valid
 masonry surface, and non-destructive
 has already been diagnostic
 tested technique,
 on historic capable
 stone
 of evaluating
 structures surface
 [33]. detachment
 The electric phenomena
 impact hammer was (for example
 a piezotronicof historical
 PCB, andplasters [31]) and
 the impact was
 of quantifying
 performed onthethestatic elastic
 surface modulus
 material of ainvestigation
 under material [32].by Thea methodology
 10 mm diameter is adaptable
 steel ball
 to anyamasonry
 with total mass surface,
 of 207and has alreadytobeen
 g, connected tested on historic
 a piezoelectric stone structures
 pulse transducer [33].5).The
 (Figure For
 electric
 technical and theoretical details related to the use of the instrumentation, please on
 impact hammer was a piezotronic PCB, and the impact was performed refertheto
 surface material
 the research under investigation
 previously carried outby bya the
 10 mm diameter
 authors steel ball with
 in [19,31–33]. The aanalysis
 total mass of
 of the
 207 g, connected to a piezoelectric pulse transducer (Figure 5). For technical
 diagram (F, t) made it possible to obtain the value of the homogeneous material’s elastic and theoretical
 details
 modulus related to the use
 (Es) through theofHertz’s
 the instrumentation, please using
 impact theory [34,35], refer tothethe researchequations:
 following previously
 carried out by the authors in [19,31–33]. The analysis of the diagram (F, t) made it possible
 ∗
 to obtain the value of the homogeneous material’s = ∗
 elastic, modulus (Es ) through the Hertz’s (2)
 impact theory [34,35], using the following equations:
 where E* was obtained by:
 E∗ E0 1 − ν2
 

 Es = ∗ . 
, (2)
 E0=+ E∗ ν02 − 1 . (3)

 whereThe E* was
 parameters
 obtainedinby:Equations (2) and s (3) were the following: A1 was the area beneath
 the diagram (F, t) corresponding to supplied  energy
 2.87 5 m(see
  3 Figure 6), T represented the time
 ∗
 E
 in which the contact occurs between the two = surfaces;. R was the radius of curvature (3) (10
 T RA1
 mm) of the impact mass m (0.207 Kg), E0 was the mass elastic modulus (222,000 MPa),
 and The parameters
 ν0 was in Equations
 its Poisson’s (2) while,
 ratio (0.2), and (3)with
 wereregard
 the following: A1 was
 to the stone the area
 material, beneath
 a Poisson’s
 the diagram
 ratio (F, t)considered
 of 0.2 was corresponding to supplied energy (see Figure 6), T represented the time in
 [29,30].
 whichThethe ratio
 contact
 between the energythe
 occurs between two surfaces;
 returned (A2) andR was the radius
 the energy of curvature
 supplied (10 mm)
 (A1) represented
 of the impact mass m (0.207 Kg), E
 the restitution coefficient (e). When it was equal to 1, the impact was perfectlyand
 0 was the mass elastic modulus (222,000 MPa), ν0
 elastic
 was its Poisson’s ratio (0.2), while, with regard to the stone material, a Poisson’s
 without dissipated energy. For each stone specimen, 15 impacts (n) were performed to ratio of 0.2
 was considered
 allow [29,30].
 stabilization of the restitution coefficient (e) towards unity.

 Figure6.6.Example
 Figure Exampleof
 offorce–time
 force–timediagram
 diagramininimpact
 impacttest.
 test.

 The ratio between the energy returned (A2 ) and the energy supplied (A1 ) represented
 3. Results
 the restitution coefficient
 The results (e). When
 were related it was
 to the testsequal
 of 20to samples
 1, the impact wasobtained
 (cores), perfectlyfrom
 elastic
 10
 without dissipated energy. For each stone specimen, 15 impacts (n) were performed
 sandstone stones taken from the ruins of the St. Agostino church in Amatrice. The cores to
 allow
 were stabilization
 named by the of letter
 the restitution coefficient
 C, followed (e) towards
 by the number unity.
 of the stone from which they were

Appl. Sci. 2021, 11, 6352 7 of 14

 3. Results
 The results were related to the tests of 20 samples (cores), obtained from 10 sandstone
 stones taken from the ruins of the St. Agostino church in Amatrice. The cores were named
 by the letter C, followed by the number of the stone from which they were extracted, and
 by the letter A and B, which indicated the first and second extraction. Table 1 summarized
 the experimental results, comparing the cylindrical compression strength (fc ) with the
 different values of the elastic modulus: static modulus (Es ) by the secant line of the fc - ε
 diagram during the compression test and by impact tests; and speed waves (v) and dynamic
 modulus (Ed ) obtained by ultrasonic tests.

 Table 1. Results of laboratory tests correlated to non-destructive tests.

 Impact
 Compression Test Ultrasonic Test
 Test
 Specimen fc (MPa) Es (Mpa) Es (Mpa) Ed (MPa) v (m/s)
 C_01_A 65.2 23,866
 75.45 25,624 27,605 28,850 3542
 C_01_B 85.7 27,382
 C_02_A 146.5 35,083
 147.90 36,435 41,722 45,140 4367
 C_02_B 149.3 37,787
 C_03_A 106.7 32,096
 87.05 27,760 27,498 25,831 3343
 C_03_B 67.4 23,425
 C_04_A 150.2 35,670
 167.60 35,616 33,124 44,859 4370
 C_04_B 185.0 35,562
 C_05_A 85.9 28,538
 80.90 24,412 13,163 15,527 2593
 C_05_B 75.9 20,286
 C_06_A 209.4 57,168
 180.85 50,175 42,869 36,627 3943
 C_06_B 152.3 43,183
 C_07_A 119.3 40,919
 117.45 34,863 19,425 32,719 3730
 C_07_B 115.6 28,807
 C_08_A 113.8 34,521
 112.90 34,843 23,171 37,084 4010
 C_08_B 112.0 35,164
 C_09_A 139.3 35,788
 141.55 36,963 52,540 43,872 4347
 C_09_B 143.8 38,139
 C_10_A 137.7 40,605
 140.65 42,249 40,088 43,318 4297
 C_10_B 143.6 43,894
 Average 125.2 34,894 32,121 35,383 3584
 St. dev. 37.0 7359 11,539 9272 544

 The compressive mean strength and the mean strain recorded at peak stress were
 of 125.2 MPa and 3143 µm/m, respectively. The fc - ε diagrams (Figure 7) highlighted an
 expected dispersion of the results due to the anisotropy of material, most likely accentuated
 by any internal microcracks that the stones of masonry walls may have undergone during
 the collapse. The Gauss distribution of cylindrical compression strength (fc), elastic secant
 and dynamic modulus (Es, Ed) of each stone specimen were evaluated in Figures 8–10.

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 Figure7.7.ffcc -- εε diagrams
 Figure diagrams of
 of compression
 compression tests.
 tests.
 Figure7.7.fcfc--εεdiagrams
 Figure diagramsof
 ofcompression
 compressiontests.
 tests.

 Figure 8. Gauss distribution of cylindrical compression strength of stone cores.
 Figure
 Figure 8.8.Gauss
 Figure8. Gaussdistribution
 Gauss distributionofof
 distribution ofcylindrical
 cylindricalcompression
 cylindrical strength
 compression
 compression ofof
 strength
 strength stone cores.
 ofstone
 stone cores.
 cores.

 Figure 9. Gauss distribution of elastic secant modulus of stone cores.
 Figure
 Figure 9.9.Gauss
 Figure9. Gaussdistribution
 Gauss distributionofof
 distribution ofelastic
 elasticsecant
 elastic modulus
 secant
 secant ofof
 modulus
 modulus stone
 of cores.
 stone
 stone cores.
 cores.

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 Figure 10. Gauss distribution of elastic dynamic modulus of stones.
 Figure 10. Gauss distribution of elastic dynamic modulus of stones.
 Figure 10. Gauss distribution of elastic dynamic modulus of stones.
 In order to validate the potential of non-invasive tests only, in the wake
 In order tomade
 contributions validate the potential
 by other authorsof[36–38],
 non-invasive tests only,
 the following in the wake
 exponential contribu- was
 correlation
 tions In order to validate the potential of non-invasive tests only, in the wake
 obtained (Figure 11) between the ultrasonic speed (v), and the cylindrical obtained
 made by other authors [36–38], the following exponential correlation was compression
 contributions
 (Figure madethe
 11)(fcbetween byultrasonic
 other authors
 speed [36–38], thecylindrical
 (v), and the following compression
 exponential strength
 correlation
 (fc ): was
 strength ):
 obtained (Figure 11) between the ultrasonic speed (v), and the cylindrical compression
 0.0004ν.
 strength (fc): f c = 23.131e
 = 23.131 . . (4) (4)
 .
 = 23.131 . (4)

 Figure11.
 Figure 11.Exponential
 Exponentialcorrelation
 correlation between
 between cylindric
 cylindric compression
 compression strength
 strength and ultrasonic
 and ultrasonic speed.speed.
 Figure
 A 11. Exponential
 similar correlation
 relationship between cylindric
 was obtained in Figurecompression strength
 12 by correlating theand ultrasonic
 dynamic speed.
 elastic
 A similar relationship was obtained in Figure 12 by correlating the dynamic elastic
 modulus
 modulus(E (Ed )d)(from
 (fromthe theultrasonic
 ultrasonic speed) and
 speed) thethe
 and cylindrical compression
 cylindrical compressionstrength (fc ). (fc).
 strength
 Finally,A to
 similar
 better relationship
 characterize wasmechanical
 the obtained behavior
 in Figureof12sandstone,
 by correlating
 the the dynamic
 values of the elastic
 static
 Finally, to better characterize the mechanical behavior of sandstone, the values of the
 modulus
 (E s ) and
 (E d ) (from the ultrasonic speed) and the cylindrical compression strength (fc).
 static (Edynamic
 s) and dynamic
 (Ed ) elastic
 (Ed) modules were correlated
 elastic modules in Figurein
 were correlated 13.Figure 13.
 Finally, to better characterize the mechanical behavior of sandstone, the values of the
 static (Es) and dynamic (Ed) elastic modules were correlated in Figure 13.

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 Figure 12.Exponential
 Figure12.
 Figure 12. Exponentialcorrelation
 Exponential correlationbetween
 correlation cylindric
 between
 between compression
 cylindric
 cylindric strength
 compression
 compression and and
 strength
 strength dynamic elasticelastic
 and dynamic
 dynamic elastic
 modulus.
 modulus.
 modulus.

 Figure 13. Exponential correlation between dynamic and static elastic modulus.
 Figure
 Figure 13.
 13. Exponential
 Exponential correlation
 correlation between
 between dynamic
 dynamic and
 and static
 static elastic
 elastic modulus.
 modulus.
 Regarding the impact test, 15 strokes were performed on each stone taken from the
 ruins Regarding
 Regarding
 of the
 the impact
 the St. Agostinoimpact test,
 test,
 church. 15
 15 strokes
 Figure strokes were
 were performed
 14a showed, performed on
 as an example, each
 on the
 each stone
 stone taken
 time–forcetaken from
 from the
 diagram the
 ruins
 ruins
 of of
 of the
 an impact St.
 thetest Agostino
 St.(stone n. 4). church.
 Agostino church. Figure
 Figure
 To fall within 14a
 14a showed,
 a range of greateras
 showed, as an
 an example,
 example,
 stabilization the
 the
 of the time–force
 time–force
 material,
 diagram
 diagram
 the of an
 an impact
 ofthe
 value of test
 test (stone
 impactmodulus
 elastic (Es )n.
 (stone 4).
 n.was To
 To fall
 fall within
 4). obtained within aa range of
 of greater
 range the
 only between greater stabilization
 tenth and the fifteenthof
 stabilization of the
 the
 material,
 material,
 beat the
 the value
 value
 that recorded e >of
 of the elastic
 thewhich
 0.90, elasticwasmodulus
 modulus (E
 (Ess)) was
 considered moreobtained
 was obtained only between
 only 14b)
 stable (Figure [31]. the
 between the tenth
 tenth and
 and
 the
 the fifteenth
 fifteenth beat
 beat that
 that recorded
 recorded ee >> 0.90,
 0.90, which
 which was
 was considered
 considered more
 more stable
 stable (Figure
 (Figure 14b)
 14b)
 [31].
 [31].

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 (a) (b)
 Figure
 Figure14.
 14.Impact
 Impacttest
 teston
 onstone
 stonen.
 n. 4:4:(a)
 (a)time–force
 time–forcediagram
 diagram of
 of the
 the 15
 15 beats; (b) trend of the
 the restitution
 restitution coefficient
 coefficient(e)
 (e)vs.
 vs.
 number
 numberofofbeats
 beats(n).
 (n).

 4.4.Discussion
 Discussion
 Theexperimental
 The experimental campaign
 campaign involved the the calibration
 calibrationand andthe thecombination
 combinationofofvarious various
 in situ
 in situ non-destructive
 non-destructive investigation
 investigation techniques
 techniques through laboratory
 through tests on tests
 laboratory stone onsamples.
 stone
 A variantAofvariant
 samples. the Sonreb method
 of the Sonreb was tested was
 method in the specific
 tested casespecific
 in the study ofcase the study
 stone walls
 of theofstone
 the
 church of St. Agostino in Amatrice, damaged by the 2016
 walls of the church of St. Agostino in Amatrice, damaged by the 2016 Central Italy Central Italy earthquake. More
 specifically, within
 earthquake. More the Sonreb protocol,
 specifically, within the thesclerometric
 Sonreb protocol, test wasthe replaced with thetest
 sclerometric impactwas
 test, which highlighted the accuracy of the ultrasonic test to
 replaced with the impact test, which highlighted the accuracy of the ultrasonic test to evaluate the elastic modulus
 of the stone.
 evaluate In this modulus
 the elastic way, it was of possible
 the stone. to In
 obtain
 this useful
 way, itcorrelations
 was possible to acquire
 to obtain reliable
 useful
 values of the stones’ compression strengths and elastic modulus
 correlations to acquire reliable values of the stones’ compression strengths and elastic only by means of in situ
 non-invasive techniques. The results showed the values
 modulus only by means of in situ non-invasive techniques. The results showed the with an expected dispersion. The
 authors evaluated this dispersion as physiological in the case of stone materials, and this
 values with an expected dispersion. The authors evaluated this dispersion as
 was confirmed in other research studies that are present in the scientific literature [36–39]
 physiological in the case of stone materials, and this was confirmed in other research
 including ongoing experimental studies that demonstrate the anisotropic behavior of the
 studies that are present in the scientific literature [36–39] including ongoing experimental
 stones relative to the different layers. Furthermore, in this specific case, it is also necessary
 studies that demonstrate the anisotropic behavior of the stones relative to the different
 to consider the presence of microcracks inside the stones, generated by the fall during the
 layers. Furthermore, in this specific case, it is also necessary to consider the presence of
 seismic actions.
 microcracks
 The speed inside the stones,
 detected by thegenerated
 ultrasonicby the fall during
 technique showed the seismic
 a good actions. with the
 correlation
 cylindrical compression strength of the same stones (Figure 11). Furthermore, the with
 The speed detected by the ultrasonic technique showed a good correlation impact the
 cylindrical compression strength of the same stones (Figure 11).
 test showed a good precision to estimate the value of the static elastic modulus (Table 1). Furthermore, the impact
 test
 Even showed a good
 for stones, precision
 there to estimate
 was a minimal the value
 difference of thethe
 between static elasticelastic
 dynamic modulus (Table
 modulus (E1).
 d,
 Even for stones,
 obtained there was
 from ultrasonic a minimal
 tests) difference
 and the static one (Ebetween
 s , obtained the bydynamic
 compression elastic modulus
 tests or by
 (E d, obtained
 impact tests).from ultrasonic
 According to thetests) and the
 scientific static one
 literature [38],(E s, obtained
 these differencesby compression
 are variable due tests
 or by impact tests). According to the scientific literature
 the anisotropy that characterizes the sandstone. Even in this specific case study, Ed was [38], these differences are
 variable due the anisotropy that characterizes the sandstone.
 10–15% higher than Es , thus validating the results found with only non-invasive techniques. Even in this specific case
 study,The Edcorrelation
 was 10–15% higher
 can also than Es, for
 be improved thuswallvalidating
 textures differentthe results foundof with
 from those Amatriceonly
 non-invasive techniques. of the number of tests. However, the results obtained so far
 through the intensification
 in theTheAmatrice area showed
 correlation can alsoa be fullimproved
 correlationfor in the
 wall average
 textures values, they are
 different fromapplicable
 those of
 in situ on other similar buildings, and are useful to estimate
 Amatrice through the intensification of the number of tests. However, the results the residual strengths of
 other damaged masonry structures. The correlations between
 obtained so far in the Amatrice area showed a full correlation in the average values, they non-destructive tests and
 laboratory
 are applicable tests
 inwill
 sitube
 oncalibrated
 other similar for the differentand
 buildings, types areofuseful
 historic masonry the
 to estimate walls. The
 residual
 results of this
 strengths of experimental
 other damaged research may alsostructures.
 masonry be useful forThe further specific shear
 correlations tests
 between
 between strengthening
 non-destructive mortars
 tests and and stone
 laboratory structures
 tests will be [40], in orderfor
 calibrated to model the behavior
 the different typesofof
 the mortar-stone composite system, as already carried out
 historic masonry walls. The results of this experimental research may also be usefulin other research studies [41,42],
 for
 further specific shear tests between strengthening mortars and stone structures [40],toin
 and to validate the mechanical compatibility and durability of strengthening materials
 be applied
 order to modelon damaged
 the behaviormasonry
 of thestructures.
 mortar-stone composite system, as already carried out
 in other research studies [41,42], and to validate the mechanical compatibility and
 durability of strengthening materials to be applied on damaged masonry structures.

Appl. Sci. 2021, 11, 6352 12 of 14

 5. Conclusions
 The experimental research validated a rapid technique, based on non-destructive
 techniques, to estimate the compression strength and the elastic modulus of the stones that
 characterize the wall textures of the buildings damaged in the area of Central Italy during
 the 2016 earthquake. From the St. Agostino church in Amatrice, a well-known building
 that symbolizes the damage caused by the 2016 Central Italy earthquake, some sandstones
 were taken and tested in the laboratory under compression test and by ultrasonic and
 impact tests. The average compression strength of Amatrice sandstone was found of about
 125.2 MPa. Moreover, the experimental methodology made it possible to compare the
 average value of the static elastic modulus obtained from the compression tests (34894 MPa)
 with the average one estimated from the impact tests (32121 MPa). Very similar values
 were obtained from the experimental results.
 Subsequently, from these tests, it was possible to elaborate a series of correlations
 between the compression strengths, obtained from the laboratory test, and the values
 offered by the non-invasive tests. In particular, the applied Sonreb methodology replaced
 the sclerometric test obtained with the impact hammer, which accurately estimated the
 value of the elastic modulus in relation to what is already possible with the ultrasonic test.
 In fact, this experimental research validated the possibility of replacing the Schmidt hammer
 with the impact test, which offers more information related to the dissipated energy.
 The results of this research tend to prove that the obtained experimental results can
 be applied in situ for a quick and non-destructive estimate of the residual strengths and
 mechanical characteristics of stones, or other damaged masonry structures with similar
 texture. For different textures, this estimate can be achieved after specific calibration with
 limited sampling of cores and laboratory compression tests. The described methodology
 may have useful applications in the evaluation of the mechanical characteristics of masonry
 damaged by earthquakes and in the design of safety and strengthening works.

 Author Contributions: Conceptualization, A.G. and G.L.; Tests, A.G.; Writing, A.G.; Supervision,
 G.L.; Project administration, A.G. Both authors have read and agreed to the published version of
 the manuscript.
 Funding: This research received no external funding.
 Institutional Review Board Statement: Not applicable.
 Informed Consent Statement: Not applicable.
 Data Availability Statement: Not applicable.
 Acknowledgments: The author greatly thanks the Superintendence Archeology and Fine Arts
 Landscape of Rieti, the Special Superintendent Office for the areas affected by the earthquake of 24
 August 2016, and the Curia of Rieti for providing the opportunity to take the stones and carry out
 the scientific research. The authors would like to thank Antonino Quattrone, Giovanni Bricca and
 Franco Grindatto for their valuable technical support during the execution of the laboratory tests.
 Conflicts of Interest: The authors declare no conflict of interest.

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