# Modulus of Elasticity and Compressive Strength of Tuff Masonry: Results of a Wide Set of Flat-Jack Tests

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Elastic Modulus of Tuff Masonry

_{m}and masonry compressive strength f

_{m}according to the following equation, valid for generic new masonry:

_{m}= 550 f

_{m}, IBC 2003 [63] and MSJC 2002 [64] recommend E

_{m}as 700 times f

_{m}, the Canadian masonry code advises E

_{m}as 850 times f

_{m}(with an upper limit of 20,000 MPa) [65], Eurocode 6 [37] and the Italian standard code (NTC 2018) advise a higher value (E

_{m}=1000 f

_{m}) [19].

_{m}/f

_{m}for tuff masonry ranged between 600 and 800 [40,47]. Some papers highlighted that the usual analytical equations provided values of the modulus of elasticity larger than the ones obtained by experimental tests since they did not consider, or inappropriately considered, the deformations of mortar bed joints [66]. Their deformation, under the average compressive masonry stress (about 33% of masonry strength) could be up to 10 times greater than that of the standard laboratory samples [66].

#### 2.2. Compressive Strength of Tuff Masonry

_{m}are available. They take into account some aforementioned parameters. Frequently, the strength of blocks and mortar is only considered. This could be adequate for brick masonries, and the pseudo-quantitative approaches are merely usable for existing buildings [67,68].

_{m}as a function of block (f

_{b}) and mortar (f

_{j}) strength:

_{m}ranged between 0.92 and 4.34 MPa. This was due to differences in terms of material properties, specimen dimensions, masonry type, and experimental condition. Furthermore, in multi-wythe masonries, the compressive strength was frequently computed on the gross area of the specimen, neglecting the difference in the inner core and surrounding stone wythe. For the above reasons, alternative methods are developing: recently, the masonry’s strength was identified by testing smaller samples (cores) extracted from the wall structure [84]. The procedure allows limiting damage to the masonry structure, but requires specific laboratory tests and interpretation of the results. The technique was verified for brick masonry, while for tuff masonry, it seemed less proper because of the differences in material properties and the larger size of tuff blocks compared to bricks. Within the above framework, double flat-jack tests have spread because of the advantage of testing masonry portions in situ, but they have the limitations listed below, mainly related to the compressive strength measurement [85].

## 3. Remarks on Double Flat-Jack Tests

## 4. Results and Discussion

#### 4.1. Modulus of Elasticity

_{m}was determined as the chord modulus equal to the mean of the values computed between about 5% and 30% of the estimated compressive strength. Table 2 shows the mean value, the standard deviation, and the coefficient of variation as the quality of block squaring varied.

_{m}computed for the entire database of double flat-jack tests (635 tests). The mean value of E

_{m}was equal to 1206 MPa, while the distribution was characterized by a standard deviation equal to 522 MPa and by a coefficient of variation equal to 43.29%.

_{m}was included in the wide range of values provided by laboratory tests on tuff masonry specimens, as reported above. Mostly, it was quite consistent with the values provided by the Italian Building Code for irregular tuff masonry (900–1260 MPa), but lower than those suggested for regular tuff masonry (1200–1620 MPa) [38]. The numerous analyzed flat-jack tests provided an intermediate value between the two code ranges and a mean value lower than the one proposed for regular masonry.

_{sec}and the modulus E

_{m}. The secant modulus was computed at stress equal to about 75% of the compressive strength. Figure 7 shows the frequency distribution of the E

_{sec}/E

_{m}ratio, which had a mean value of 0.58. This was consistent with the values already determined by other authors through compression tests on panels in the laboratory, as reported above. The standard deviation of the distribution was equal to 0.10, while the coefficient of variation was 17.63%.

#### 4.2. Compressive Strength

_{m}computed for the entire set of 635 flat-jack tests. The mean value was equal to 1.96 MPa, while the standard deviation and the coefficient of variation were equal to 0.42 MPa and 21.71%, respectively. The standard error of the mean was equal to 0.0169 MPa, and the confidence interval identified the range of 1.930–1.996 MPa (computed for a confidence level of 95% and assuming Student’s t-distribution).

_{b}and f

_{j}, the masonry strength f

_{m}computed by Equation (2), as provided by Eurocode 6 [37] and NTC 2018 [19], did not envelop all the experimental data.

#### 4.3. Modulus of Elasticity vs. Compressive Strength

_{m}and f

_{m}for all the flat-jack tests. The ratio was quite constant, with the mean value equal to 632. This value was consistent, albeit smaller, with the value determined in [40,47], but was lower than the value frequently advised in building codes (assumed equal to 1000 [19,37]).

_{m}and f

_{m}ranged between 573 and 643, while for regular tuff masonry, it was between 506 and 600. The average value provided by the flat-jack tests was therefore consistent with those of the Italian code [38]. Finally, if it were assumed that flat-jacks provided an underestimation of compressive strength [85], the ratio between E

_{m}and f

_{m}should take lower values than those determined here.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Monaco, M.; Bergamasco, I.; Betti, M. A no-tension analysis for a brick masonry vault with lunette. J. Mech. Mat. Struct.
**2018**, 13, 703–714. [Google Scholar] [CrossRef] - Faella, G.; Giordano, A.; Guadagnuolo, M. Unsymmetric-plan masonry buildings: Pushover vs nonlinear dynamic analysis. In Proceedings of the 9th US National and 10th Canadian Conference on Earthquake Engineering, Toronto, ON, Canada, 25–29 July 2010. [Google Scholar]
- Corradi, M.; Borri, A.; Vignoli, A. Experimental study on determination of strength of Masonry Walls. Constr. Build. Mater.
**2003**, 17, 325–337. [Google Scholar] [CrossRef] - Fonti, R.; Barthel, R.; Formisano, A.; Borri, A.; Candela, M. Rubble masonry response under cyclic actions: The experience of L’Aquila city (Italy). In Proceedings of the 11th International Conference of Computational Methods in Sciences and Engineering, ICCMSE, Athens, Greece, 20–23 March 2015; Volume 1702, p. 160003. [Google Scholar]
- Marghella, G.; Marzo, A.; Carpani, B.; Indirli, M.; Formisano, A. Comparison between in situ experimental data and Italian code standard values. In Brick and Block Masonry: Trends, Innovations and Challenges, Proceedings of the 16th International Brick and Block Masonry Conference, Padova, Italy, 26–30 June 2016; IBMAC: Padova, Italy, 2016; pp. 707–1714. [Google Scholar]
- Simões, A.; Gago, A.; Lopes, M.; Bento, R. Characterization of old masonry walls: Flat jack method. In Proceedings of the 15th World Conference on Earthquake Engineering, Lisbon, Portugal, 24–28 September 2012. [Google Scholar]
- Faella, G.; Frunzio, G.; Guadagnuolo, M.; Donadio, A.; Ferri, L. The church of the nativity in Bethlehem: Non-destructive tests for the structural knowledge. J. Cult. Herit.
**2012**, 1296–2074. [Google Scholar] [CrossRef] - Fiengo, G.; Guerriero, L. Atlante Delle Tecniche Costruttive Tradizionali Napoli terra di lavoro (XVI-XIX); Arte Tipografica: Napoli, Italy, 2008; ISBN 8887375402. [Google Scholar]
- Guadagnuolo, M.; Nuzzo, M.; Faella, G. The corpus domini bell tower: Conservation and safety. In Proceedings of the XIV International Conference on Building Pathology and Constructions Repair—CINPAR 2018, Florence, Italy, 20–22 June 2018. [Google Scholar] [CrossRef]
- Colella, A.; Di Benedetto, C.; Calcaterra, D.; Cappelletti, P.; D’Amore, M.; Di Martire, D.; Graziano, S.F.; Papa, L.; de Gennaro, M.; Langella, A. The neapolitan yellow tuff: An outstanding example of heterogeneity. Constr. Build. Mater.
**2017**, 136, 361–373. [Google Scholar] [CrossRef] - De Vivo, B. Volcanism in the Campania Plain: Vesuvius, Campi Flegrei and Ignimbrites; Elsevier: Amsterdam, The Netherlands, 2006; Volume 9. [Google Scholar]
- Kržan, M.; Gostic, S.; Cattari, S.; Bosiljkov, V. Acquiring reference parameters of masonry for the structural performance analysis of historical buildings. Bull. Earthq. Eng.
**2015**, 13, 203–236. [Google Scholar] [CrossRef] - Jackson, M.; Marra, F. Roman stone masonry: Volcanic foundation of the ancient city. J. Arch. Inst. Am.
**2006**, 110, 403–436. [Google Scholar] [CrossRef] - Guadagnuolo, M.; Monaco, M.; Frunzio, G.; Tafuro, A. Pozzolanic mortars for restoration of sacred tuff masonry structures. In Proceedings of the Utopian and Sacred Architecture, Aversa, Italy, 11–13 June 2019. [Google Scholar]
- Guadagnuolo, M.; Donadio, A.; Faella, G. Out-of-plane failure mechanism of masonry buildings corners. In Proceedings of the 8th International Conference on Structural Analysis of Historical Constructions (SAHC), Wroclaw, Poland, 15–17 October 2012; ISSN 0860-2395. ISBN 9788371252167. [Google Scholar]
- Monaco, M.; Guadagnuolo, M. Out of plane behaviour of unreinforced masonry walls. In Proceedings of the Prohitech-Protection of Historical Buildings—First International Conference, Rome, Italy, 21–24 June 2009; ISBN 9780415558037. [Google Scholar]
- Guadagnuolo, M.; Faella, G. Simplified design of masonry ring-beams reinforced by flax fibers for existing buildings retrofitting. Buildings
**2020**, 10, 12. [Google Scholar] [CrossRef] [Green Version] - Guadagnuolo, M.; Aurilio, M.; Tafuro, A.; Faella, G. Analysis of local mechanisms through floor spectra for the preservation of historical masonries. A case study. In Proceedings of the 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Crete, Greece, 24–26 June 2019. [Google Scholar]
- M.I.T. Aggiornamento delle Norme Tecniche per le Costruzioni; Ministero delle Infrastrutture e dei Trasporti: Rome, Italy, 2018. Available online: https://www.gazzettaufficiale.it/eli/gu/2018/02/20/42/so/8/sg/pdf (accessed on 1 April 2020).
- FEMA, Federal Emergency Management Agency, FEMA 306. Evaluation of Earthquake Damaged Concrete and Masonry Wall Buildings, Basic Procedures Manual; Applied Technology Council: Redwood City, CA, USA, 1999; ATC-43. [Google Scholar]
- Borri, A.; Castori, G.; Corradi, M.; Speranzini, E. Shear behaviour of unreinforced and reinforced masonry panels subjected to insitu diagonal compression tests. Constr. Build. Mater.
**2011**, 25, 4403–4414. [Google Scholar] [CrossRef] - Brignola, A.; Frumento, S.; Lagomarsino, S.; Podestà, S. Identification of shear parameters of masonry panels through the in situ diagonal compression test. Int. J. Archit. Herit.
**2009**, 3, 52–73. [Google Scholar] [CrossRef] - Chiostrini, S.; Galano, L.; Vignoli, A. In Situ Shear and Compression Tests in Ancient Stone Masonry Walls of Tuscany, Italy. J. Test. Eval.
**2003**, 31, 289–303. [Google Scholar] - Calderini, C.; Cattari, S.; Lagomarsino, S. The use of the diagonal compression test to identify the shear mechanical parameters of masonry. Constr. Build. Mater.
**2010**, 24, 677–685. [Google Scholar] [CrossRef] - Buonocore, G.; Gesualdo, A.; Monaco, M.; Savino, M.T. Improvement of seismic performance of unreinforced masonry buildings using steel frames. In Civil-Comp Proceedings: 106, 2014; Topping, B.H.V., Iványi, P., Eds.; Civil Comp Press: Kippen, Stirlingshire, UK; ISBN 978-1-905088-61-4. [CrossRef]
- Guadagnuolo, M.; Faella, G.; Donadio, A.; Ferri, L. Integrated evaluation of the Church of S.Nicola di Mira: Conservation versus safety. NDT & E Int.
**2014**. [Google Scholar] [CrossRef] - Frunzio, G.; Di Gennaro, L.; Guadagnuolo, M. Palazzo Ducale in Parete: Remarks on code provisions. Int. J. Mas. Resear. Inn.
**2019**, 4, 159–173. [Google Scholar] [CrossRef] - Binda, L.; Saisi, A. Application of NDTs to the diagnosis of historic structures. In Proceedings of the Non-Destructive Testing in Civil Engineering, Nantes, France, 30 June–3 July 2009. [Google Scholar]
- Binda, L.; Saisi, A.; Tiraboschi, C. Application of sonic tests to the diagnosis of damage and repaired structures. NDT & E Int.
**2001**, 34, 123–138. [Google Scholar] [CrossRef] - Binda, L.; Saisi, A.; Zanzi, L. Sonic tomography and flat jack tests as complementary investigation procedures for the stone pillars of the temple of S.Nicolo’ l’Arena (Italy). NDT & E Int.
**2003**, 36, 215–227. [Google Scholar] [CrossRef] - Lindqvist, J.E.; Maurenbrecher, P. Testing of hardened mortars, a process of questioning and interpreting. A publication from RILEM TC 203-RHM Repair mortars for historic masonry. Mat. Struct.
**2009**, 47, 853–865. [Google Scholar] - CEN European Committee for Standardization. Non-destructive testing—Ultrasonic examination—Part 1: General Principles, Part 2: Sensitivity and Range Setting, Part 3: Transmission Technique, Part 4: Examination for Discontinuities Perpendicular to the Surface, Part 5: Characterization and Sizing of Discontinuities; CEN: Belgium, Brussels, 2000. [Google Scholar]
- ASTM. Standard Guide for Using the Surface Ground Penetrating Radar Method for Subsurface Investigation; ASTM International: West Conshohocken, PA, USA, 2011; Available online: https://www.astm.org/DATABASE.CART/HISTORICAL/D6432-11.htm (accessed on 1 April 2020).
- BS EN 13187:1999, Thermal Performance of Buildings - Qualitative Detection of Thermal Properties in Building Envelopes - Infrared Method; Infrared Thermography Handbook; Volume 1: Principles and practice, Norman Walker; Volume 2: Applications, A.N. Nowicki; BSI: London, UK, 2005.
- Miranda, L.; Guedes, J.; Rio, J.; Costa, A. Stone masonry characterization through sonic tests. In Proceedings of the VI Congreso International Sobre Patologia y Recuperacion de Estructuras, Cordoba, Argentina, 2–4 June 2010. [Google Scholar]
- ASTM C1196-09. Standard Test Method for In-Situ Compressive Stress Within Solid Unit Masonry Estimated Using Flat-Jack Measurements; ASTM International: West Conshohocken, PA, USA, 2009; Available online: https://www.astm.org/DATABASE.CART/HISTORICAL/C1196-09.htm (accessed on 1 April 2020).
- CEN, European Committee for Standardization. Eurocode 6, EN 1996-1-1: Design of Masonry Structures—Part 1-1: General Rules for Reinforced and Unreinforced Masonry Structures; CEN: Belgium, Brussels, 2005. [Google Scholar]
- M.I.T. Istruzioni per l’applicazione dell’aggiornamento delle Norme Tecniche per le Costruzioni di, Gazzetta Ufficiale: Rome, Italy. 2019. Available online: https://www.gazzettaufficiale.it/eli/gu/2019/02/11/35/so/5/sg/pdf (accessed on 1 April 2020).
- Bernardini, A.; Mattone, R.; Modena, C.; Pasero, G.; Pavano, M.M.; Pistone, G.; Roccati, R.; Zaupa, F. Determinazione delle capacità portanti per carichi verticali e laterali di pannelli murari in tufo. Atti II Congr. Naz, 1984, pp. 345–360. Available online: http://www.reluis.it/mada/foto/026.pdf (accessed on 1 April 2020).
- Faella, G.; Manfredi, G.; Realfonzo, R. Experimental evaluation of mechanical properties of old tuff masonry panels subjected to axial loadings. In Proceedings of the 9th International Brick/Block Masonry Conference, Berlin, Germany, 13–16 October 1991. [Google Scholar]
- Prota, A.; Marcari, G.; Fabbrocino, G.; Manfredi, G.; Aldea, C. Experimental in-plane behaviour of tuff masonry strengthened with cementitious matrix—Grid composites. ASCE J. Comp. Constr.
**2006**, 10, 223–233. [Google Scholar] [CrossRef] - Augenti, N.; Romano, A. Preliminary experimental results for advanced modelling of tuff masonry structures. In Proceedings of the Structural Analysis of Historical Constructions, SAHC08, Bath, UK, 2–4 July 2008. [Google Scholar]
- Augenti, N.; Parisi, F. Mechanical characterization of tuff masonry. In Proceedings of the 1st International Conference on Protection of Historical Buildings, Rome, Italy, 21 June 2009; pp. 1579–1584. [Google Scholar]
- Calderoni, B.; Cordasco, E.A.; Guerriero, L.; Lenza, P.; Manfredi, G. Mechanical behaviour of postmedieval tuff masonry in the Naples area. Mason. Int.
**2009**, 21, 85–96. [Google Scholar] - Grande, E.; Romano, A. Experimental investigation and numerical analysis of tuff-brick listed masonry panels. Mat. Struct.
**2012**, 46, 63–75. [Google Scholar] [CrossRef] - Miccoli, L.; Garofano, A.; Fontana, P.; Müller, U. Experimental testing and finite element modelling of earth block masonry. Eng. Struct.
**2015**, 104, 80–94. [Google Scholar] [CrossRef] - Marcari, G.; Basili, M.; Vestroni, F. Experimental investigation of tuff masonry panels reinforced with surface bonded basalt textile-reinforced mortar. Compos. Part B Eng.
**2017**, 108, 131–142. [Google Scholar] [CrossRef] - Alecci, V.; Stipo, G.; La Brusco, A.; De Stefano, M.; Rovero, L. Estimating elastic modulus of tuff and brick masonry: A comparison between on-site and laboratory tests. Constr. Build. Mater.
**2019**, 204, 828–838. [Google Scholar] [CrossRef] - Sandoli, A.; Ferracuti, B.; Calderoni, B. FRP-confined tuff masonry columns: Regular and irregular stone arrangement. Compos. Part B Eng.
**2019**, 162, 621–630. [Google Scholar] [CrossRef] - Gesualdo, A.; Calderoni, B.; Sandoli, A.; Monaco, M. Minimum energy approach for the in-plane shear resistance of masonry panels. Ing. Sismica
**2019**, 36, 42–53. [Google Scholar] - Gesualdo, A.; Calderoni, B.; Iannuzzo, A.; Fortunato, A.; Monaco, M. Minimum energy strategies for the in-plane behaviour of masonry. Frat. Ed Int. Strut.
**2020**, 14, 376–385. [Google Scholar] [CrossRef] - Ceroni, F.; Pecce, M.; Manfredi, G.; Marcari, G.; Voto, S. Analisi e caratterizzazione meccanica di murature di tufo. In Proceedings of the 15th CTE Congress, Bari, Italy, 4–6 November 2004. [Google Scholar]
- Binda, L.; Papayianni, I.; Toumbakari, E.; Van Hees, R. Mechanical tests on mortars and assemblages. In Characterisation of Old Mortars with Respect to their Repair - Final Report of RILEM TC 167-COM; RILEM Publications SARL: Bagneux, France, 2004; Volume 28, pp. 57–76. [Google Scholar] [CrossRef]
- Degryse, P.; Elsen, J.; Waelkens, M. Study of ancient mortars from Sagalassos (Turkey) in view of their conservation. Cem. Concr. Res.
**2002**, 32, 1457–1463. [Google Scholar] [CrossRef] - Lanas, J.; Pérez Bernal, J.L.; Bello, M.; Alvarez-Galindo, J.I. Mechanical properties of natural hydraulic lime-based mortars. Cem. Concr. Res.
**2004**, 34, 2191–2201. [Google Scholar] [CrossRef] [Green Version] - Drdácký, M.; Masin, D.; Mekonone, M.D.; Slizkova, Z. Compression tests on non-standard historic mortar specimens. In Proceedings of the 1st Historical Mortar Conference, Lisbon, Portugal, 24–26 September 2008; pp. 24–26. [Google Scholar]
- Drougkas, A.; Roca, P.; Molins, C. Compressive strength and elasticity of pure lime mortar masonry. Mat. Struct.
**2015**, 49, 983–999. [Google Scholar] [CrossRef] [Green Version] - Brook, J.J.; Abu Baker, B.H. The modulus of elasticity of masonry. Mason. Int.
**1998**, 12, 58–63. [Google Scholar] - Tassios, T.P. Meccanica Delle Murature; EPC: Napoli, Italy, 1988; Available online: https://www.epc.it/contenuti/bufarini_mecc_murature_sito.pdf (accessed on 1 April 2020).
- Wolde-Tinsae, A.M.; Atkinson, R.H.; Hamid, A.A. State-of-the-art: Modulus of elasticity. In Proceedings of the 6th North American Masonry Conference, Philadelphia, PA, USA, 1 June 1993; The Masonry Society: Boulder, CO, USA; pp. 1209–1220. [Google Scholar]
- Drysdale, R.G.; Hamid, A.A.; Baker, L.R. Masonry Structures: Behaviour and Design; Prentice-Hall: Englewood Cliffs, NJ, USA, 1994. [Google Scholar]
- Brooks, J. Concrete and Masonry Movements; Butterworth-Heinemann Elsevier: Oxford, UK, 2015. [Google Scholar]
- ICC, International Code Consortium. International Building Code; IBC: Falls Church, VA, USA, 2003. [Google Scholar]
- Masonry Standards Joint Committee (MSJC). Building Code Requirements for Masonry Structures; ACI 530-02/ASCE 5-02/TMS 402-02; American Concrete Institute, Structural Engineering Institute of the American Society of Civil Engineers, The Masonry Society: Detroit, MI, USA, 2002. [Google Scholar]
- Canadian Standards Association (CSA). Design of Masonry Structures, S304.1; CSA: Mississauga, ON, Canada, 2004. [Google Scholar]
- Zavalis, R.; Jonaitis, B.; Lourenco, P.B. Analysis of bed joint influence on masonry modulus of elasticity. In Proceedings of the 9th International Masonry Conference, Guimarães, Portugal, 7–9 July 2014. [Google Scholar] [CrossRef]
- De Matteis, G.; Corlito, V.; Guadagnuolo, M.; Tafuro, A. Seismic vulnerability assessment and retrofitting strategies of Italian masonry churches of the Alife-Caiazzo Diocese in Caserta. Int. J. Archit. Herit.
**2019**. [Google Scholar] [CrossRef] - Guadagnuolo, M.; Aurilio, M.; Faella, G. Retrofit assessment of masonry buildings through simplified structural analysis. Frat. E Int. Strut.
**2020**, 14, 398–409. [Google Scholar] [CrossRef] - Costigan, A.; Pavía, S.; Kinnane, O. An experimental evaluation of prediction models for the mechanical behaviour of unreinforced, lime-mortar masonry under compression. J. Build. Eng.
**2015**, 4, 283–294. [Google Scholar] [CrossRef] [Green Version] - Kaushik, H.B.; Rai, D.C.; Jain, S.K. Stress-strain characteristics of clay brick masonry under uniaxial compression. ASCE J. Mat. Civil. Eng.
**2007**, 19, 728–739. [Google Scholar] [CrossRef] - Marotta, A.; Liberatore, D.; Sorrentino, L. Estimation of unreinforced tuff masonry compressive strength based on mortar and unit mechanical parameters. In Proceedings of the 16th International Brick and Block Masonry Conference, Padova, Italy, 26–30 June 2016. [Google Scholar]
- CEN, European Committee for Standardization. EN 1015-11:1999, Methods of Test for Mortar for Masonry: Determination of Flexural and Compressive Strength; CEN: Brussels, Belgium, 2006. [Google Scholar]
- CEN, European Committee for Standardization. EN 772-1:2011, Methods of Tests for Masonry Units: Determination of Compressive Strength; CEN: Belgium, Brussels, 2011. [Google Scholar]
- Nicotera, P.; Lucini, P. La costituzione geologica del sottosuolo di Napoli nei riguardi dei problemi. In Proceedings of the VIII Convegno di Geotecnica, Cagliari, Italy, 1967. [Google Scholar]
- Faella, C.; Martinelli, E.; Nigro, E.; Paciello, S. Tuff masonry walls strengthened with a new kind of cfrp sheet: Experimental tests and analysis. In Proceedings of the 13th World Conference on Earthquake Engineering, Vancouver, BC, Canada, 1–6 August 2004. [Google Scholar]
- Domède, N.; Pons, G.; Sellier, A.; Fritih, Y. Mechanical behaviour of ancient masonry. Mat. Struct.
**2008**, 42, 123–133. [Google Scholar] [CrossRef] - Page, A.W. The biaxial compressive strength of masonry. Proc. Inst. Civ. Eng.
**1981**, 71, 893–906. [Google Scholar] [CrossRef] - Vermeltfoort, A.T.; Martens, D.R.W.; Van Zijl, G.P.A.G. Brick–mortar interface effects on masonry under compression. Can. J. Civ. Eng.
**2007**, 34, 1475–1485. [Google Scholar] [CrossRef] - Chagneau, F.; Levasseur, M. Contrôle des matériaux de construction par dynamostratigraphie. Mat. Struct.
**1989**, 22, 231–236. [Google Scholar] [CrossRef] - Gucci, N.; Barsotti, R. A non-destructive technique for the determination of mortar load capacity in situ. Mat. Struct.
**1995**, 28, 276–283. [Google Scholar] [CrossRef] - RILEM TC 177–MDT. Test method recommendations of RILEM TC 177–MDT Masonry durability and on-site testing–D.1: Indirect determination of the surface strength of unweathered hydraulic cement mortar by the drill energy method. Mater. Struct.
**2004**, 37, 485–487. Available online: https://www.rilem.net/images/publis/1617.pdf (accessed on 1 April 2020). - RILEM TC 177–MDT. Test method recommendations of RILEM TC 177–MDT Masonry durability and on-site testing–D.4: In–situ stress tests based on the flat jack. Mater. Struct.
**2004**, 37, 491–496. Available online: https://www.rilem.net/images/publis/1619.pdf (accessed on 1 April 2020). - RILEM TC 177–MDT. Test method recommendations of RILEM TC 177–MDT Masonry durability and on-site testing–D.5: In-situ stress-strain behaviour tests based on the flat jack. Mater. Struct.
**2004**, 37, 497–501. Available online: https://www.rilem.net/images/publis/1620.pdf (accessed on 1 April 2020). - Pelà, L.; Roca, P.; Benedetti, A. Mechanical characterization of historical masonry by core drilling and testing of cylindrical samples. Int. J. Archit. Herit.
**2016**, 10, 360–374. [Google Scholar] [CrossRef] [Green Version] - Cescatti, E.; Dalla Benetta, M.; Modena, C.; Casarin, F. Analysis and evaluations of flat jack test on a wide existing masonry buildings sample. In Proceedings of the 16th International Brick and Block Masonry Conference, Padova, Italy, 26–30 June 2016. [Google Scholar]
- British Standards Institution. BS 5628-1: Code of Practice for the Use of Masonry. Structural Use of Unreinforced Masonry; British Standards Institution: London, UK, 2005. [Google Scholar]
- Valluzzi, M.R.; Munari, M.; Modena, C.; Binda, L.; Cardani, G.; Saisi, A. Multilevel approach to the vulnerability analysis of historic buildings in seismic areas Part 2: Analytical interpretation of mechanisms for the vulnerability analysis and the structural improvement. Restor. Build. Monum.
**2007**, 13, 427–441. [Google Scholar] [CrossRef] - ASTM C1197-14A. Standard Test Method for In-Situ Measurement of Masonry Deformability Properties Using the Flat-Jack Method; ASTM International: West Conshohocken, PA, USA, 2014; Available online: https://www.astm.org/Standards/C1197.htm (accessed on 1 April 2020).
- Kingsley, G.R.; Noland, J.L. A note on obtaining in-situ load-deformation properties of unreinforced brick masonry in the united states using flatjacks, evaluation and retrofit of masonry structures. In Proceedings of the Second Joint USA-Italy Workshop on Evaluation and Retrofit of Masonry Structures, Boulder, CO, USA, August 1987; pp. 215–223. [Google Scholar]
- Andreini, M.; De Falco, A.; Giresini, L.; Sassu, M. Mechanical characterization of masonry walls with chaotic texture: Procedures and results of in-situ tests. Int. J. Archit. Herit.
**2014**, 8, 376–407. [Google Scholar] [CrossRef] - Almeida, C.; Guedes, J.; Arêde, A.; Costa, C.Q.; Costa, A. Physical characterization and compression tests of one leaf stone masonry walls. Constr. Build. Mater.
**2012**, 30, 188–197. [Google Scholar] [CrossRef] - Binda, L.; Tiraboschi, C. Flat-jack test as a slightly destructive technique for the diagnosis of brick and stone masonry structures. Restor. Build. Monum.
**1999**, 5, 449–472. [Google Scholar] [CrossRef] - Manning, E.C.; Ramos, L.F.; Fernandes, F. Tube-jack testing: Regular masonry wall testing. In Proceedings of the SAHC2014—9th International Conference on Structural Analysis of Historical Constructions, Mexico, Mexico, 14–17 October 2014. [Google Scholar]
- Porco, F.; Uva, G. Alcune considerazioni sull’applicazione della tecnica dei martinetti piatti su murature caotiche. In Proceedings of the Atti della XII Conferenza Nazionale sulle Prove non Distruttive, Monitoraggio, Diagnostica Milano, 11–13 October 2007. [Google Scholar]
- Ramos, L.F.; Manning, E.C.; Fernandes, F.; Fangueiro, R.; Azenha, M.; Cruz, J.; Sousa, C. Tube-jack testing for irregular masonry walls: Prototype development and testing. NDT & E Int.
**2013**, 58, 24–35. [Google Scholar] - Simões, A.; Bento, R.; Gago, A.; Lopes, M. Mechanical characterization of masonry walls with flat-jack tests. Exp. Tech.
**2015**, 40, 1163–1178. [Google Scholar] - Uranjek, M.; Bosiljkov, V.; Žarni´c, R.; Bokan-Bosiljkov, V. In situ tests and seismic assessment of a stone-masonry building. Mat. Struct.
**2012**, 45, 861–879. [Google Scholar] [CrossRef] - Alecci, M.; De Stefano, M.; Luciano, R.; Marra, A.; Stipo, G. Numerical investigation on the use of flat-jack test for detecting masonry deformability. J. Test. Eval.
**2020**. [Google Scholar] [CrossRef] - Binda, L.; Cardani, G.; Saisi, A.; Valluzzi, M.R.; Munari, M.; Modena, C. Multilevel approach to the vul-nerability analysis of historical buildings in seismic areas, Part 1: Detection of parameters for vulnerability analysis through on site and laboratory investigation. Restor. Build. Monum.
**2007**, 13, 413–426. [Google Scholar] [CrossRef] - Parivallal, S.; Kesavan, K.; Ravisankar, K.; Sundram, B.A.; Ahmed, A.K.F. Evaluation of in situ stress in masonry structures by flatjack technique. In Proceedings of the National Seminar & Exhibition on Non-destructive Evaluation, Chennai, India, 8–10 December 2011. [Google Scholar]
- Gregorczyk, P.; Lourenço, P.B. A review on flat-jack testing. Eng. Civil.
**2000**, 9, 39–50. [Google Scholar] - Valluzzi, M.R. Consolidamento E Recupero Delle Murature; Gruppo Editoriale: Faenza, Italy, 2003. [Google Scholar]
- Noland, J.L.; Atkinson, R.H.; Schaller, M.P. A review of the flat-jack method for Nondestructive evaluation. In Proceedings of the Nondestructive evaluation of civil structures and Materials, Boulder, CO, USA, 15–17 October 1990. [Google Scholar]
- Ronca, P.; Tiraboschi, C.; Binda, L. In-situ flat-jack tests matching new mechanical interpretations. In Proceedings of the 11th International Brick/Block Masonry Conference, Shanghai, China, 4–16 October 1997. [Google Scholar]
- Saisi, A.; Gentile, C.; Cantini, L. Post-earthquake assessment of a masonry tower by on-site inspection and operational modal testing. In Proceedings of the ECCOMAS Thematic Conference- COMPDYN 2013: 4th International Conference on Computat, Kos Island, Greece, 12–14 June 2013. [Google Scholar]
- Hendry, A.W. Structural Brickwork; The Macmillan Press: London, UK, 1981. [Google Scholar]
- Witzany, J.; Čejka, T.; Zigler, R. The analysis of nonstress effects on historical stone bridge structures (monitoring, theoretical analysis, maintenance). In Proceedings of the the 10th East Asia Pacific Conference on Structural Engineering and Construction (EASEC-10), Bangkok, Thailand, 3–5 August 2006; Volume 6, pp. 21–26. [Google Scholar]
- Witzany, J.; Čejka, T.; Zigler, R. Failure resistance of the historic stone bridge structure of Charles Bridge. I: Susceptibility to nonstress effects. J. Perf. Constr. Facil.
**2008**, 22, 71–82. [Google Scholar] [CrossRef] - Proske, D.; van Gelder, P. Safety of Historical Stone Arch Bridges; Springer: Berlin, Germany, 2009. [Google Scholar]
- Vasconcelos, G.; Lourenço, P.B. Experimental characterization of stone masonry in shear and compression. Constr. Build. Mater.
**2009**, 23, 3337–3345. [Google Scholar] [CrossRef]

**Figure 5.**Frequency distribution of (

**a**) the modulus of elasticity and (

**b**) compressive strength of smoothly- and roughly-squared block masonry.

**Figure 10.**Frequency distribution of the ratio between the modulus of elasticity and compressive strength.

Reference | Tuff Strength | Mortar Strength | Masonry | ||||
---|---|---|---|---|---|---|---|

Specimen Size | Modulus of Elasticity | Compressive Strength | |||||

L | H | t | |||||

(MPa) | (MPa) | (cm) | (cm) | (cm) | (MPa) | (MPa) | |

Bernardini et al. 1984 [39] | 4.98–6.46 | 1.73–5.78 | 82–104 | 83–104 | 12–25 | 1650–2100 | 3.05–4.26 |

Faella et al. 1991 [40] | 3.50 | 2.0–3.0 | 130 | 125 | 50 | 991–1110 | 1.23–1.53 |

Prota et al. 2006 [41] | 2.00 | 5.00 | 103 | 103 | 25 | 680 | 2.30 |

Augenti, Romano 2007 [42] | 4.13 | 7.14 | 62 | 62 | 15 | 1980 | 4.31 |

Augenti, Parisi 2009 [43] | – | – | 61 | 65 | 15 | 2222 | 3.96 |

Calderoni et al. 2009 [44] | 3.49–4.30 | 1.56–3.76 | 100–133 | 82–95 | 42–67 | 743–1252 | 2.55–4.34 |

Grande, Romano 2012 [45] | 4.13 | 7.14 | 61 | 60 | 15 | 781 | 1.97 |

Miccoli et al. 2015 [46] | 5.21 | 3.32 | 50 | 50 | 11.5 | 587–1071 | 2.71–3.77 |

Marcari et al. 2017 [47] | 8.00 | 6.60 | 100 | 100 | 25 | 1495–1869 | 2.67–2.70 |

Alecci et al. 2019 [48] | 4.22 | 0.99 | 57 | 61 | 19 | 818 | 0.92–1.20 |

Sandoli et al. 2019 [49] | 4.60 | 1.93 | 13.5–22 | 30–40 | 16.5–22 | 385–393 | 2.36–2.39 |

Elastic Modulus | Compressive Strength | |||
---|---|---|---|---|

Blocks | Squared | Roughly Squared | Squared | Roughly Squared |

Mean value (MPa) | 1209 | 1197 | 2.01 | 1.71 |

Standard deviation (MPa) | 489 | 672 | 0.42 | 0.36 |

Coefficient of variation (%) | 40.45 | 56.16 | 20.92 | 21.06 |

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**MDPI and ACS Style**

Guadagnuolo, M.; Aurilio, M.; Basile, A.; Faella, G.
Modulus of Elasticity and Compressive Strength of Tuff Masonry: Results of a Wide Set of Flat-Jack Tests. *Buildings* **2020**, *10*, 84.
https://doi.org/10.3390/buildings10050084

**AMA Style**

Guadagnuolo M, Aurilio M, Basile A, Faella G.
Modulus of Elasticity and Compressive Strength of Tuff Masonry: Results of a Wide Set of Flat-Jack Tests. *Buildings*. 2020; 10(5):84.
https://doi.org/10.3390/buildings10050084

**Chicago/Turabian Style**

Guadagnuolo, Mariateresa, Marianna Aurilio, Andrea Basile, and Giuseppe Faella.
2020. "Modulus of Elasticity and Compressive Strength of Tuff Masonry: Results of a Wide Set of Flat-Jack Tests" *Buildings* 10, no. 5: 84.
https://doi.org/10.3390/buildings10050084