The Toughness of Imperial Roman Concrete

The toughness of imperial roman concrete

P. Brune & R. Perucchio University of Rochester, Rochester, New York, USA A.R. Ingraffea Cornell University, Ithaca, New York, USA M.D. Jackson Northern Arizona University, Flagstaff, Arizona, USA

ABSTRACT: The concrete composites used to realize the monumental structures of Imperial Rome are remarkable engineering materials. While the endurance of intact constructions such as the Pantheon evinces the concretes’ durability, such durability mostly serves to preserve the mechanical properties, which are responsible both for the monuments’ original creation and continued survival. Despite their prominent role in the engineering achievements of the empire, these mechanical properties – particularly in tension and fracture – have not been comprehensively assessed. We first review the mechanical properties obtained through various experimental programs conducted on both authentic ancient composite core samples and their components, summarizing the major findings and outlining the remaining gaps in knowledge. We then qualitatively discuss the fracture of Roman concrete within the context of our own testing program, which will test both re- fabricated and authentic materials, with the aim of characterizing the fracture behavior that has contributed to the preservation of a significant component of engineering heritage.

1 INTRODUCTION fragmented brick and volcanic rock coarse aggregate of decimeter-scale dimensions bonded by a poz- Between 60-160CE, Imperial Roman engineers zolanic mortar, based on altered volcanic ash ini- honed their usage of concrete to create spanned mo- tially mixed with hydrated lime. The mortar has a numental structures with designs that would violate relatively low compressive strength as compared present-day Civil Engineering building safety codes with Portland cement mortars. The published me- (ACI 318-08 2008). And yet a surprising number of chanical testing data is sparse, and provides only these buildings are still extant today, some in excel- scattered compressive strength values that are not lent states of preservation and covered by their orig- accompanied by full load-displacement curves. Va- inal unreinforced concrete vaults. Scholarly investi- riability in mortar and coarse aggregate composi- gations tend to emphasize the architectural tions further reduces the applicability of these re- significance of the monuments instead of exploring sults, particularly as they pertain to fracture of the the structural considerations invoked by the creation concretes and the buildings realized therein. All told, and survival of these daring constructions. Those describing the fracture behavior of these highly het- rare studies that analyze structural behavior have erogeneous composites with widely varying con- been constrained by limited knowledge of the me- stituents presents remarkable challenges. However, chanical behaviors of the constituent concretes. In- its characterization is vital to accurately assessing deed, not a single analysis has incorporated the frac- the safety of surviving structures, and understanding ture mechanics of Roman concrete as a quasi-brittle their extraordinary durability in response to a com- material. Such analyses are critical for both preserv- bination of differential settling on weakly consoli- ing deteriorating structures and understanding the dated bedrock and seismic ground motions over their endurance of those still intact, as well as studying nearly 2000-year life spans. the ancient design conventions responsible for their We begin with an exploration of published and conception and construction. unpublished mechanical test data for both the con- Fracture mechanics has not previously been ap- glomeratic concretes and their assorted constituents. plied to Roman concretes, mainly because little is Examination of results for authentic historic speci- known of their physical behavior as cementitious mens, modern laboratory-fabricated re-productions, composites. The conglomeratic fabric contains and raw geologic materials provides initial insights into the potential application of modern concrete The structural Jfabric= −D (ofh,T Roman)∇h concretes can be (1) explicitly accounts for the evolution of hydration fracture mechanics to describe the fracture behavior described on several length scales. On the structural reaction and SF content. This sorption isotherm of the ancient cementitious composites. From this scale, the material Theoccupies proportionality large volumes coefficient – the D(h,T) is called reads 3 review, we formulate several hypotheses about the Great Hall encompassesmoisture anpermeability excess of and 3000m it is a ofnonlinear function fracture mechanisms of the concretes. We include a concrete – as a heterogeneousof the relative composite humidity hcontinuum. and temperature T (Bažant ⎡ ⎤ preliminary description of our proposed testing On the meso level, a pozzolanic mortar bonds deci- ⎢ 1 ⎥ & Najjar 1972). The moisture mass balance requires w ()()h,α ,α = G α ,α 1 − + program, which will employ a novel experimental meter-sized coarsethat aggregates the variation (caementa in time). of Various the water mass per unit e c s 1 c s ⎢ ∞ ⎥ ⎢ 10(g α − α )h ⎥ configuration to measure the fracture properties of materials were usedvolume as caementa of concrete, with (water builders content often w ) be equal to the ⎣ e 1 c c ⎦ (4) laboratory-reproductions of an Imperial pozzolanic vertically gradingdivergence the aggregates of the by moisture mass density flux J to mortar, before culminating in the fracture testing of reduce the self-weight of upper sections of struc- ⎡ 10(g α ∞ − α )h ⎤ K ()α ,α ⎢e 1 c c − 1⎥ a significant volume of authentic ancient core sam- tures, especially in vaults.∂w 1 c s ⎢ ⎥ ples from the Great Hall of the Markets of Trajan − = ∇ • J (2) ⎣ ⎦ ∂t (c.110CE). where the first term (gel isotherm) represents the The water content w can be expressed as the sum physically bound (adsorbed) water and the second of the evaporable water w (capillary water, water e term (capillary isotherm) represents the capillary 2 DESCRIPTION OF ROMAN CONCRETES vapor, and adsorbed water) and the non-evaporable water. This expression is valid only for low content (chemically bound) water w (Mills 1966, n of SF. The coefficient G represents the amount of The meaningful discussion of Roman concretes is Pantazopoulo & Mills 1995). It is reasonable to 1 water per unit volume held in the gel pores at 100% necessarily intertwined with the structures it real- assume that the evaporable water is a function of relative humidity, and it can be expressed (Norling ized. Accordingly, to provide context for a review of relative humidity, h, degree of hydration, α , and c Mjornell 1997) as the mechanical properties of ancient concretes, we degree of silica fume reaction, α , i.e. w =w (h,α ,α ) s e e c s first examine the Great Hall in terms of its concretes = age-dependent sorption/desorption isotherm to view Imperial Roman monumental concretes c s (Norling Mjonell 1997). Under this assumption and G ()α ,α = k α c + k α s (5) through the lens of an exemplary structure. The by substituting Equation 1 into Equation 2 one 1 c s vg c vg s Great Hall is an appropriate choice because, through obtains the generosity of those charged with its care, we c s where k vg and k vg are material parameters. From the have been able to meaningfully study the mechanical ∂w ∂w ∂w maximum amount of water per unit volume that can behavior and material composition of its structure in e ∂h e e Figure 2. Computational− solid model+ ∇ • ( ofD the∇h )Great= Hall,α& show-+ α& + w& (3) fill all pores (both capillary pores and gel pores), one unprecedented depth (Jackson et al. 2009, Brune & ∂h ∂t h ∂α c ∂α s n ing the three structural-scale materials. c s can calculate K1 as one obtains Perucchio, in prep.).

When approaching the Great Hall, one sees main- The wall and vault concretes of the Great Hall ⎡ ⎛ ∞ ⎞ ⎤ where ∂we/∂h is the slope of the sorption/desorption 10⎜ g α −α ⎟h ly the brick facing that clads the concrete nucleus of ⎢ ⎝ 1 c c ⎠ ⎥ (Fig. 2) feature atisotherm least two (also distinct called aggregate moisture mix- capacity). The w − 0.188α s + 0.22α s − G ⎢1− e ⎥ standard Imperial Age wall construction (Fig. 1). tures (Jackson et al. 2009). The caementa of the wall 0 c s 1⎢ ⎥ governing equation (Equation 3) must be completed ⎣ ⎦ (6) The considerable dimensions of monumental build- K ()α ,α = concrete include byfragmented appropriate bricks boundary (~1600kg/cu.m) and initial conditions. 1 c s ⎛ ∞ ⎞ ings, combined with the tenacious bond between 10⎜ g α −α ⎟h and two tuffs: the Thecompact relation and betweenrelatively the durable amount of evaporable ⎝ 1 c c ⎠ core and cladding, consign the facing to curing and e −1 Tufo Lionato (~1700kg/cu.m)water and relative and thehumidity porous is and called ‘‘adsorption weather protection functions while ensuring that the weakly durable isotherm”Tufo Giallo if measureddella Via withTiberina incr easing relativity The material parameters kc and ks and g can conglomeratic core acts as a structural skeleton. Al- vg vg 1 (~1500kg/cu.m). humidityThe lighter and vau ‘‘desorptionlt concrete isotherm”contains in the opposite be calibrated by fitting experimental data relevant to though hidden from view, the concretes at the center almost exclusivelycase. Tufo Neglecting Giallo della their Via difference Tiberina. (Xi et al. 1994), in free (evaporable) water content in concrete at of Imperial monuments were hardly afterthoughts. The wall mortar thewas following, produced ‘‘sorption by combining isotherm” hy- will be used with various ages (Di Luzio & Cusatis 2009b). Indeed, these are remarkably complex materials, in- drated lime with referencePozzolane to Rosseboth sorption altered andvolcanic desorption conditions. corporating a diverse mixture of constituents from ash aggregate, mainlyBy the in smallway, gravel-if the tohystere sand-sizedsis of the moisture Rome’s rich geologic surroundings to form a versa- scoriae, and veryisotherm small quanti wouldties be of taken ground, into sand-account, two different 2.2 Temperature evolution tile and durable building material. sized Tufo Lionatorelation, aggregate. evaporable The binding water matrixvs relative of humidity, must Note that, at early age, since the chemical reactions

the wall mortarbe contains used according alumina- to the and sign alkali- of the variation of the associated with cement hydration and SF reaction cement gels and relativitysträtlingite. humidity. In contrast, The theshape vault of the sorption are exothermic, the temperature field is not uniform mortar contains isotherm notable foramounts HPC is(~33 infl uencedvolume%) by many parameters, for non-adiabatic systems even if the environmental of light grey pumiceespecially (~800kg/cu.m), those that a influencesmaller quan- extent and rate of the temperature is constant. Heat conduction can be tity (~15% volume%)chemical of heavierreactions Pozzolane and, in Rosseturn, determine pore described in concrete, at least for temperature not (~1700kg/cu.m), structureand a very and small pore quantitysize distribution (<5 vol- (water-to-cement exceeding 100°C (Bažant & Kaplan 1996), by ume%) of groundratio, Tufo cement Lionato. chemical The cements composition, are SF content, Fourier’s law, which reads as yet unknown. curingTaken time togeth ander, method, the two temperature, concrete mix additives, formulations evince Roman builders’ sophisticated etc.). In the literature various formulations can be q = −λ∇T (7) and intentional deploymentfound to describe of available the sorption materials isotherm of normal towards the controlling of self-weights. But how did concrete (Xi et al. 1994). However, in the present where q is the heat flux, T is the absolute Figure 1. Photo of brick-faced concrete wall (bottom left) with the diverse materialpaper combinations the semi-empirical translate intoexpression me- proposed by schematic showing concrete nucleus. A typical facing brick is chanical properties? temperature, and λ is the heat conductivity; in this about 15cm wide. Norling Mjornell (1997) is adopted because it

Proceedings of FraMCoS-7, May 23-28, 2010 3J =PREVIOUS−D(h,T )∇h EXPERIM ENTAL TESTING OF (1) gate;explicitly relative accounts proportions for the were evolution not recorded. of hydration Uniax- ROMAN CONCRETES & COMPONENTS ialreaction compression and SF tests content. recorded This both sorption the compressive isotherm The proportionality coefficient D(h,T) is called strengthreads (mean=3.60MPa, stdev=1.96MPa) and elas- Themoisture numerous permeability confections and itof is Imperial a nonlinear Roman function con- tic modulus (mean=2.9GPa, stdev=1.8GPa) of the creteof the are relative marked humidity by widely h and divergent temperature aggregate T (Bažant con- samples. Several complete⎡ stress-strain curves⎤ were stituents. Due to the general unavailability of au- also obtained. Also, significantly,⎢ 1modulus⎥ of rup- & Najjar 1972). The moisture mass balance requires w ()()h,α ,α = G α ,α 1 − + thenticthat the specimens variation inand time the challengeof the water of laboratorymass per unit re- turee testsc measureds 1 c thes ⎢bending tensile∞ strength⎥ for ⎢ 10(g α − α )h ⎥ fabrication,volume of concrete no comprehensive (water content experimental w) be equal testing to the two Hadrian’s Villa samples⎣ e 1(0.68,c 0.78c ⎦ MPa). (4) ofdivergence these various of the materials moisture hasflux beenJ executed to ro- However, no additional information concerning spe- bustly characterize their overall mechanical behav- cimen size or complete⎡ load-displacement10(g α ∞ − α )h ⎤ curves K ()α ,α ⎢e 1 c c − 1⎥ ior.∂ wThe experimental programs to date have focused was provided for1 thec bendings ⎢ tests. ⎥ largely− = ∇on• Jcompressive strength. These findings con-(2) In addition, samples from⎣ the Basilica of ⎦Maxen- ∂t firm the expected variation in performance among tius included cores from a large section of the col- where the first term (gel isotherm) represents the the Thedifferent water formulations, content w can which be expressed encourages as the an sumex- lapsed main vault, two of the barrel vault base walls, physically bound (adsorbed) water and the second aminationof the evaporable of the mechanics water w of (capillary the constituent water, aggre-water and the foundation. Specific information about the e term (capillary isotherm) represents the capillary gatevapor, components. and adsorbed water) and the non-evaporable cores is limited to their geometry and bulk density. water. This expression is valid only for low content (chemically bound) water w (Mills 1966, The aggregate constituents were not recorded. All n of SF. The coefficient G represents the amount of Pantazopoulo & Mills 1995). It is reasonable to samples were cylinders with1 15cm diameters and 3.1 Testing of ancient roman concretes water per unit volume held in the gel pores at 100% assume that the evaporable water is a function of heights between 30 and 38cm, except for three pris- relative humidity, and it can2 be expressed (Norling Forrelative samples humidity, cored hfrom, degree Ancient of hydration, structures, α Lam-, and matic blocks of 35x35cm cross section and 45cm c Mjornell 1997) as prechtdegree (1984)of silica published fume reaction, the first α modern, i.e. w = mechanicalw (h,α ,α ) height. The samples were extracted along an axis s e e c s test= age-dependentresults in the formsorption/desorp of compressivetion strengths,isotherm perpendicular to the stratification of the aggregate with a single measurement of the elastic modulus layers. The volumetricc s proportion of mortar in the (Norling Mjonell 1997). Under this assumption and G ()α ,α = k α c + k α s (5) (18GPa).by substituting Cores Equationwere obtained 1 into fro Equationm a variety 2 oneof concrete1 c swas vgsaidc to fallvg sbetween 40-60%, with the sites,obtains structures (from a roughly 250-year range), additional remark that the lowest proportions of and locations within the structures. Lava, tuff (type mortar appearc ins the zones of the structure where the where k vg and k vg are material parameters. From the unspecified), basalt, sandstone, quartz, and slate are building process was executed “most carefully.” Un- ∂w ∂w ∂w maximum amount of water per unit volume that can all mentionede ∂h as coarse aggregate.e Diversee composi- iaxial tests measured the compressive strength of − + ∇ • (D ∇h) = α& + α& + w& (3) fill all pores (both capillary pores and gel pores), one tions∂h of∂t mortar hwere also∂α observed,c ∂α withs ndifferent nine samples (mean=4.6MPa, stdev=1.4MPa) and c s can calculate K1 as one obtains types of limestone – either dolomitic or pure – iden- the elastic modulus of three (mean=2.7GPa, stdev= tified as the quicklime source and pozzolana (prove- 0.9GPa). No complete load-displacement⎡ ⎛ ∞ ⎞curves⎤ where ∂we/∂h is the slope of the sorption/desorption 10⎜ g α −α ⎟h nance, color, alteration facies, and maximum grain were reported (Giavarini et al. 2006).⎢ ⎝ 1 c c ⎠ ⎥ isotherm (also called moisture capacity). The w − 0.188α s + 0.22α s − G ⎢1− e ⎥ size were not noted) only identified for certain sam- As a whole,0 previousc smechanical1⎢ testing of⎥ an- governing equation (Equation 3) must be completed ⎣ ⎦ (6) ples. No information about the relative percentages cientK ()α ,αconcrete= cores provides scattered compressive by appropriate boundary and initial conditions. 1 c s ⎛ ∞ ⎞ of coarse aggregate and mortar was provided. Lim- strengths over statistically10⎜ g α insignificant−α ⎟h and highly The relation between the amount of evaporable ⎝ 1 c c ⎠ ited information about the dimensions of the pris- varying populations. eSpecimen size−s1 were generally water and relative humidity is called ‘‘adsorption matic test samples was included, usually in the form only two or three times larger than the caementa, the isotherm” if measured with increasing relativity The material parameters kc and ks and g can of an edge length (mean=6.7cm), except for two cy- largest heterogeneity, further rvgestrictingvg the applica-1 humidity and ‘‘desorption isotherm” in the opposite be calibrated by fitting experimental data relevant to lindrical samples of 15cm diameter. The wide vari- bility of the strength results to structural-scale be- case. Neglecting their difference (Xi et al. 1994), in free (evaporable) water content in concrete at ability in composition and provenance of the sam- havior. Furthermore, aggregate constituents were the following, ‘‘sorption isotherm” will be used with various ages (Di Luzio & Cusatis 2009b). ples is evident in the considerable scatter of the seldom catalogued with sufficient rigor. Altogether, reference to both sorption and desorption conditions. measured compressive strengths, with a mean of it seems that the composite nature of the ancient ma- By the way, if the hysteresis of the moisture 12.9MPa (stdev=5.5MPa) over 52 samples. terial and the source of its vulnerability in structures isotherm would be taken into account, two different 2.2 Temperature evolution Samuelli Ferretti (1996) oversaw mechanical test- – mainly tensile fracture – were not sufficiently well relation, evaporable water vs relative humidity, must Note that, at early age, since the chemical reactions ing of Ancient Roman concrete cores obtained from understood to inform the experimental programs’ be used according to the sign of the variation of the associated with cement hydration and SF reaction the Port of Trajan at Fiumicino and Hadrian’s Villa goals. Only two small samples were used to measure relativity humidity. The shape of the sorption are exothermic, the temperature field is not uniform in Tivoli. The Fiumicino cores were taken from the tensile strength, and no measurement of fracture isotherm for HPC is influenced by many parameters, for non-adiabatic systems even if the environmental foundations of a warehouse and measured 15cm in properties has been published. especially those that influence extent and rate of the temperature is constant. Heat conduction can be diameter and between 25.5 and 28cm in height, with chemical reactions and, in turn, determine pore described in concrete, at least for temperature not alternating strata of brick and tuff (unspecified) structure and pore size distribution (water-to-cement exceeding 100°C (Bažant & Kaplan 1996), by coarse aggregate. The relative proportions of brick, 3.2 Component testing ratio, cement chemical composition, SF content, Fourier’s law, which reads tuff, and mortar were measured by area from maps The variability evident in the composite responses curing time and method, temperature, mix additives, of the exterior core surfaces as (35, 20, 45), (2.5, 35, asserts the importance of the component mechanical etc.). In the literature various formulations can be q = −λ∇T 62.5), and (19, 16, 65). The samples from Hadrian’s behaviors to achieving a more robust estimation (7) of found to describe the sorption isotherm of normal Villa consisted of two prismatic blocks of the overall composite response. Several testing pro- concrete (Xi et al. 1994). However, in the present 10x10x14cm3 and one that was 11x11x22cm3. Both gramswhere haveq is made the valuableheat flux, contributions T is the by absolutemeasur- paper the semi-empirical expression proposed by blocks were taken from the collapsed vaulting of the ingtemperature, the mechanical and λ propertiesis the heat of cond mortaructivity; and coarsein this Norling Mjornell (1997) is adopted because it Sala a Tre Esedre and contained only brick aggre- aggregate constituents of the ancient concretes.

Proceedings of FraMCoS-7, May 23-28, 2010 3.2.1 Ancient roman bricks indicate quite scatteredJ = −D (materialh,T )∇h characteristics and (1) explicitly accounts for the evolution of hydration Samuelli Ferretti (1996) tested ancient bricks, com- rock strengths. reaction and SF content. This sorption isotherm monly used in fragmented form as caementa. Bricks The proportionality coefficient D(h,T) is called reads of widely varying provenance and quality, generally moisture permeability and it is a nonlinear function taken from wall facings, were sawed to create 29 of the relative humidity h and temperature T (Bažant ⎡ ⎤ sample sets. From these, prismatic specimens meas- & Najjar 1972). The moisture mass balance requires ⎢ 1 ⎥ 3 w ()()h,α ,α = G α ,α 1 − + uring 15x15x30mm were subjected to compression that the variation in time of the water mass per unit e c s 1 c s ⎢ ∞ ⎥ ⎢ 10(g α − α )h ⎥ (mean=17MPa, stdev=5.9MPa) and direct tension volume of concrete (water content w) be equal to the ⎣ e 1 c c ⎦ (4) tests (mean=3.33MPa, stdev=1.25MPa). The elastic divergence of the moisture flux J modulus (mean=13.4GPa, stdev=4.7GPa) was also ⎡ 10(g α ∞ − α )h ⎤ K ()α ,α ⎢e 1 c c − 1⎥ measured along with a ductility ratio, defined to be ∂w 1 c s ⎢ ⎥ the quotient of the strain at ultimate failure (after − = ∇ • J (2) ⎣ ⎦ ∂t softening) and the strain corresponding to the peak where the first term (gel isotherm) represents the stress. This ratio averaged 2.26 (stdev=0.35); a few The water content w can be expressed as the sum physically bound (adsorbed) water and the second complete stress-strain curves are described as “char- of the evaporable water w (capillary water, water e term (capillary isotherm) represents the capillary acteristic of a fragile material”. vapor, and adsorbed water) and the non-evaporable water. This expression is valid only for low content (chemically bound) water w (Mills 1966, n of SF. The coefficient G represents the amount of 3.2.2 Ancient roman mortars Pantazopoulo & Mills 1995). It is reasonable to 1 water per unit volume held in the gel pores at 100% Samuelli Ferretti (1996) created pozzolanic mortar assume that the evaporable water is a function of relative humidity, and it can be expressed (Norling samples using hydrated lime and sieved Pozzolane relative humidity, h, degree of hydration, α , and c Mjornell 1997) as Rosse combined in Vitruvian proportions (1:3, by degree of silica fume reaction, α , i.e. w =w (h,α ,α ) s e e c s volume). Only ash particles smaller than 2mm were = age-dependent sorption/desorption isotherm used; in contrast, the mortars in the Great Hall in- c s (Norling Mjonell 1997). Under this assumption and G ()α ,α = k α c + k α s (5) clude Pozzolane Rosse scoriae up to 1.5cm. The by substituting Equation 1 into Equation 2 one 1 c s vg c vg s amount of Roman tap-water used was specified ac- Figure 3. Strength dataobtains for Tufo Lionato and Tufo Giallo della cording to a volumetric ratio with lime of (1.39:1); it Via Tiberina. Each column corresponds to a different quarry. c s where k vg and k vg are material parameters. From the was not stated how much water was used to initially Large markers represent the mean for each type of test result. maximum amount of water per unit volume that can After De Casa et al. (1999,∂w 2007) and Jackson et ∂al.w (2005). ∂w hydrate the lime, making a water to cement ratio un- e ∂h e & e & & fill all pores (both capillary pores and gel pores), one 3 − + ∇ • (D ∇h) = α c + α s + wn (3) available. Prismatic beams of 40x40x160mm were ∂h ∂t h ∂α ∂α can calculate K as one obtains The variation in results (Fig. 3), likely inc part dues 1 cast, de-molded after an unspecified amount of time, to dissimilar experimental setups, occurs not just be- and cured in a lime-water solution. After curing at 7, ⎡ ⎛ ∞ ⎞ ⎤ tween quarries butwhere also ∂w fore/∂h different is the slope locations of the and sorption/desorption 10⎜ g α −α ⎟h 28, 90, 180, and 360 days, modulus of rupture tests ⎢ ⎝ 1 c c ⎠ ⎥ stratigraphic levelsisotherm in a single (also quarry. called The moisturescattered capacity). The w − 0.188α s + 0.22α s − G ⎢1− e ⎥ were followed by compression tests on the broken 0 c s 1⎢ ⎥ strengths of the twogoverning tuffs reflect equation their (Equationheterogeneous, 3) must be completed ⎣ ⎦ (6) halves. The results indicate a marked reduction in K ()α ,α = by appropriate boundary and initial conditions. 1 c s ⎛ ∞ ⎞ flexural (30%) and compressive strength (10%) be- pyroclastic fabrics, which are composed of variable 10⎜ g α −α ⎟h The relation between the amount of evaporable ⎝ 1 c c ⎠ tween the 90-day and 180/360-day samples. This proportions of vitric, lithic, and crystal fragments e −1 water and relative humidity is called ‘‘adsorption suggests a complex hardening process, perhaps due bound by zeolite (and calcite) cements. Furthermore, isotherm” if measured with increasing relativity The material parameters kc and ks and g can to chemical phase transitions in the pozzolanic ce- weathering of pumice glass in some tuff specimens vg vg 1 humidity and ‘‘desorption isotherm” in the opposite be calibrated by fitting experimental data relevant to ments during curing. For the 360-day samples, a produces clay mineral that weakens the cohesion case. Neglecting their difference (Xi et al. 1994), in free (evaporable) water content in concrete at mean flexural strength of 0.95MPa (stdev=0.10MPa) of the tuff, thereby reducing mechanical strength and the following, ‘‘sorption isotherm” will be used with various ages (Di Luzio & Cusatis 2009b). and mean compressive strength of 12.07MPa durability (Jackson et al. 2005). reference to both sorption and desorption conditions. (stdev=1.02MPa) were measured. The mean elastic Tuff coarse aggregates can form 50 volume% of By the way, if the hysteresis of the moisture modulus, measured during compression tests, was the concrete fabric of monumental walls and vaults. isotherm would be taken into account, two different 2.2 Temperature evolution 3GPa (stdev=0.1GPa). Therefore the characterization and inclusion of the mechanical behaviorsrelation, of theevaporable Roman watertuff lithologies vs relative humidity, must Note that, at early age, since the chemical reactions be used according to the sign of the variation of the associated with cement hydration and SF reaction 3.2.3 Roman volcanic tuffs is central to an accurate composite material model relativity humidity. The shape of the sorption are exothermic, the temperature field is not uniform Various tuffs from the Roman region were fre- describing the fracture of Imperial concretes. The isotherm for HPC is influenced by many parameters, for non-adiabatic systems even if the environmental quently used as caementa in monumental construc- widespread variability tuff mechanical properties, especially those that influence extent and rate of the temperature is constant. Heat conduction can be tions. While heavier leucititic lavas and travertine along with their dependence upon petrographic-scale chemical reactions and, in turn, determine pore described in concrete, at least for temperature not were used in foundations and lighter pumice and characteristics, highlights the importance of using structure and pore size distribution (water-to-cement exceeding 100°C (Bažant & Kaplan 1996), by scoriae were sometimes used in vaults, volcanic data appropriate to either a specific tuff provenance ratio, cement chemical composition, SF content, Fourier’s law, which reads tuffs (and brick fragments) comprise the majority of or a well-documented petrographic analogue. curing time and method, temperature, mix additives, coarse aggregates in Imperial conglomeratic wall etc.). In the literature various formulations can be q = −λ∇T concretes. Numerous tests by De Casa et al. (1999, (7) 3.3 Synopsis of Experimentalfound to describe Results the sorption isotherm of normal 2007) and Jackson et al. (2005) on two commonly concrete (Xi et al. 1994). However, in the present used tuffs – Tufo Giallo della Via Tiberina and Tufo The accumulated experimental data identifies sev- where q is the heat flux, T is the absolute paper the semi-empirical expression proposed by Lionato (those found in the Great Hall concretes) – eral obstacles to understanding the mechanical be- temperature, and λ is the heat conductivity; in this havior of Roman Norlingconcretes. Mjornell First, there (1997) is the is famil- adopted because it

Proceedings of FraMCoS-7, May 23-28, 2010 iarJ = difficulty−D(h,T )∇ hwith concrete constructions in travers- (1) explicitlyAdditionally, accounts the impossibilityfor the evolution of obtaining of hydration suffi- ing from the structural scale (~m) to the experimen- cientlyreaction large and and SF isolated content. mortar This specimens sorption fromisotherm an- tal Thescale proportionality(~cm). For Roman coefficient concretes, D(h,T) this difficultyis called cientreads concretes requires all tests to occur on repro- ismoisture compounded permeability by the factand that,it is agiven nonlinear typical function coarse ductions fabricated in the laboratory. Even when aggregateof the relative dimensions, humidity ah sufficientland temperaturey representative T (Bažant informed by the best (but⎡ inevitably limited)⎤ under- experimental scale is on the order of decimeters or standing of Roman materials⎢ and1 practices,⎥ re- & Najjar 1972). The moisture mass balance requires w ()()h,α ,α = G α ,α 1 − + eventhat themeters. variation The instrongly time of heterogeneous the water mass fabric per unit of createde c mortars samples1 c s ⎢lose a vital∞ degree ⎥of accu- ⎢ 10(g α − α )h ⎥ thevolume concretes of concrete further (water complicates content w the) be analysisequal to theof racy from differences in⎣ curinge and1 c aging.c ⎦Further- (4) fracturedivergence behavior. of the moisture Furthermore, flux J the scattered me- more, a third element in the Roman concrete com- chanical and unknown fracture behaviors of the posite, the interfacial ⎡ transition10(g α ∞ − αzones)h ⎤ (ITZs) K ()α ,α ⎢e 1 c c − 1⎥ coarse∂w aggregates, combined with the length-scale between mortar and1 c coarses ⎢ aggregate and within⎥ the on− which= ∇ • Jthey appear in the concretes, presents (2) a pozzolanic mortar, seems⎣ to substantially influence⎦ ∂t major source of variability. Finally, the mortar is a the initiation and propagation of microcracks. While where the first term (gel isotherm) represents the compositeThe water material content in wand can of be itself. expressed The particle as the sizesum it is not yet known how the ITZs surrounding physically bound (adsorbed) water and the second distributionof the evaporable of the Pozzolanewater w Rosse(capillary aggregate water, ranges water caementa, possibly at the same decimeter length- e term (capillary isotherm) represents the capillary fromvapor, coarse and adsorbedsilt- to medium water) gravel-sizedand the non-evaporable in the poz- scale, affect fracture propagation, the millimetric water. This expression is valid only for low content zolanic(chemically mortars bound) of the Greatwater Hallw and ( Millsother monu-1966, zones around scoriaceous mortar aggregate have n of SF. The coefficient G represents the amount of mentsPantazopoulo (Jackson & et Millsal., 2007). 1995 )These. It is fragments reasonable have to been observed to impact 1fracture trajectories (Jack- water per unit volume held in the gel pores at 100% beenassume shown that tothe redirect evaporable crack watpropagationer is a function in the ce- of son et al. 2009). relative humidity, and it can be expressed (Norling mentitiousrelative humidity, binding matrixh, degree (Fig. of 4). hydration, α , and c Mjornell 1997) as degree of silica fume reaction, α , i.e. w =w (h,α ,α ) s e e c s = age-dependent sorption/desorption isotherm 4 THE FRACTURE OF IMPERIAL ROMAN CONCRETEc s (Norling Mjonell 1997). Under this assumption and G ()α ,α = k α c + k α s (5) by substituting Equation 1 into Equation 2 one 1 c s vg c vg s obtains The mechanical behavior, particularly in fracture, of Roman concretesc s is central to understanding how the where k vg and k vg are material parameters. From the daring monumental structures were initially con- ∂w ∂w ∂w maximum amount of water per unit volume that can e ∂h e e ceived, according to the empirical processes widely − + ∇ • (D ∇h) = α& + α& + w& (3) fill all pores (both capillary pores and gel pores), one ∂h ∂t h ∂α c ∂α s n thought to govern Imperial Roman design, and how c s can calculate K1 as one obtains they have endured for nearly two millennia in an ac-

tive seismic zone on relatively⎡ poorly⎛ consolidated∞ ⎞ ⎤ where ∂we/∂h is the slope of the sorption/desorption 10⎜ g α −α ⎟h bedrock (Molin et al. 1995, Rovelli⎢ et⎝ 1al.c 1995).c ⎠ ⎥ isotherm (also called moisture capacity). The w − 0.188α s + 0.22α s − G ⎢1− e ⎥ Our experimental0 c programs 1 ⎢aims to characterize⎥ governing equation (Equation 3) must be completed ⎣ ⎦ (6) theK ()α mechanical,α = behavior on length scales that are by appropriate boundary and initial conditions. 1 c s ⎛ ∞ ⎞ appropriate for the constituent10⎜ g α −α ⎟hmaterials and ex- The relation between the amount of evaporable ⎝ 1 c c ⎠ trapolate as accuratelye as possible this−1 description to water and relative humidity is called ‘‘adsorption the structural scale, on which the formation of struc- Figureisotherm” 4. Photomicrograph if measured ofwith the curvingincreasing trajectory relativity of a The material parameters kc and ks and g can debonding crack that follows the perimeters of Pozzolane tural-scale macrofractures thatvg imperilvg surviving1 humidity and ‘‘desorption isotherm” in the opposite be calibrated by fitting experimental data relevant to Rosse scoriae in a mortar sample from the Great Hall, pro- monuments occurs (Fig. 5). Accordingly, our pro- case. Neglecting their difference (Xi et al. 1994), in free (evaporable) water content in concrete at duced by a point source load test (after Jackson et al. 2009). gram will measure fracture properties of the diverse the following, ‘‘sorption isotherm” will be used with various ages (Di Luzio & Cusatis 2009b). constituents of Roman concrete and use the results reference to both sorption and desorption conditions. to characterize an appropriate fracture model for the By the way, if the hysteresis of the moisture composite. For example, the fracture energy of the isotherm would be taken into account, two different 2.2 Temperature evolution composite, G , could be found to depend on the relation, evaporable water vs relative humidity, must Note that, at f_compearly age, since the chemical reactions fracture energies and tensile strengths of the mortar be used according to the sign of the variation of the associated with cement hydration and SF reaction and coarse aggregates, and the tensile strengths of relativity humidity. The shape of the sorption are exothermic, the temperature field is not uniform the interfaces: isotherm for HPC is influenced by many parameters, for non-adiabatic systems even if the environmental especially those that influence extent and rate of the temperature is constant. Heat conduction can be GGf=⋅ξχmortar +⋅ mortar ++... χ ⋅ f ITZbrick (1) chemical reactions and, in turn, determine pore describedfcomp_1 in concrete, f 1at tleast for temperature n t not structure and pore size distribution (water-to-cement exceeding 100°C (Bažant & Kaplan 1996), by th ratio, cement chemical composition, SF content, whereFourier’s ξi =law, the which i fracture reads energy influence coeffi- th curing time and method, temperature, mix additives, cient; and χi = i tensile strength influence coeffi- etc.). In the literature various formulations can be cient.q = − λThe∇T model for the fractu re properties of (7)the found to describe the sorption isotherm of normal composite, parametrized as in equation 1 in terms of concrete (Xi et al. 1994). However, in the present thewhere component q is theproperties, heat flux, may beT furtheris the informedabsolute paper the semi-empirical expression proposed by Figure 5. Survey of macrofractures afflicting Pantheon’s dome bytemperature, fractographic and observations λ is the heat that cond identifyuctivity; additional in this atNorling the time ofMjornell a restoration (1997) (after Terenziois adopted 1934). because it physical parameters describing the fracture of the

Proceedings of FraMCoS-7, May 23-28, 2010 composite material. The model will then be opti- ever, limit the applicabilityJ = −D(h,T of)∇ hpoint-source results to (1) explicitly accounts for the evolution of hydration mized (i.e., the values for χi, ξi, determined) based understanding fracture on the structural scale. At this reaction and SF content. This sorption isotherm on both experimental results and numerical model- scale, the formation Theof fracture proportionality process zones coefficient (FPZs) D(h,T) is called reads ing of the fracture processes of the cores of ancient surrounding nucleatingmoisture and permeability propagating and fracturesit is a nonlinear function conglomeratic concrete. Indeed, the program will could, conceivably,of thesubstantially relative humidity reduce h anda monu- temperature T (Bažant ⎡ ⎤ focus on testing numerous 20cm-diameter drill cores ment’s overall stability by weakening load paths in ⎢ 1 ⎥ & Najjar 1972). The moisture mass balance requires w ()()h,α ,α = G α ,α 1 − + of the wall concrete of the Markets of Trajan, which highly stressed regionsthat the or, variation equivalently, in time reducing of the thewater mass per unit e c s 1 c s ⎢ ∞ ⎥ ⎢ 10(g α − α )h ⎥ cores have been generously entrusted to our research local tensile strengthsvolume of load-carryingof concrete (water regions. content w) be equal to the ⎣ e 1 c c ⎦ (4) program by the Sovraintendenza Archeologica di In modern concretes,divergence the of FPZ the moisturegrows as flux distrib- J Beni Culturali di Roma. As described above, the uted microcracks converge on increasingly larger ⎡ 10(g α ∞ − α )h ⎤ K ()α ,α ⎢e 1 c c − 1⎥ pozzolanic mortar and caementa are similar to many length scales ranging∂w from voids in the cementitious 1 c s ⎢ ⎥ Imperial constructions. Ideally, the parametrized matrix (10e-6m) −to the= ∇ average• J aggregate particle (2) ⎣ ⎦ ∂t fracture model derived from the Great Hall wall (10e-3m), depending on the local morphology and where the first term (gel isotherm) represents the concretes could then be particularized to describe the stress field (van MierThe 1997). water contentAs the wcrack can drivingbe expressed as the sum physically bound (adsorbed) water and the second behavior of other Imperial concretes. energy increases,of the the bridging evaporable microcracks water w in(capillary the water, water e term (capillary isotherm) represents the capillary The careful evaluation of the fracture energies of process zone eventuallyvapor, andreach adsorbed a length water) scale andlarger the non-evaporable water. This expression is valid only for low content components of the composite concrete is a first step than that of the aggregate(chemically particles, bound) and a watermacrofrac- w (Mills 1966, n of SF. The coefficient G represents the amount of towards the derivation of such a model. Such meas- ture may form/advance.Pantazopoulo & Mills 1995). It is reasonable to 1 water per unit volume held in the gel pores at 100% urements would supplement test data already ob- The larger rangeassume of com thatponent the evaporablelength scales wat (uper is a function of relative humidity, and it can be expressed (Norling tained from the concretes of the Great Hall. Jackson to 10e-1m) in Romanrelative concretes humidity, makes h, degreethe develop- of hydration, α , and c Mjornell 1997) as et al. (2009) used point source tests on discs 3.5cm ment of the FPZdegree difficult of silicato intuit fume qualitatively. reaction, α ,In i.e. w =w (h,α ,α ) s e e c s in diameter and 1.5cm thick to approximate tensile stead, we introduce= age-dependentHillerborg’s non-dimensionalsorption/desorp tion isotherm strengths of the components of the wall concrete. brittleness number to explore the process zone quan- c s (Norling Mjonell 1997). Under this assumption and G ()α ,α = k α c + k α s (5) The preparation of test specimens isolated specific titatively: by substituting Equation 1 into Equation 2 one 1 c s vg c vg s elements of the composite concrete fabric, so that the obtains point-load tensile strengths were measured for 2 c s β =⋅()/()D fEG ⋅ (2) where k vg and k vg are material parameters. From the caementa (brick, Tufo Lionato, Tufo Giallo della Via tF ∂w ∂w ∂w maximum amount of water per unit volume that can Tiberina), the pozzolanic mortar, and each of the re- e ∂h e e where D = any −structural+ ∇dimension;• (D ∇h) = f =α &tensile+ α& + w& (3) fill all pores (both capillary pores and gel pores), one spective caementa interfaces (Fig. 6). ∂h ∂t h ∂αt c ∂α s n strength; E = elastic modulus; and G = fracturec en-s can calculate K1 as one obtains F ergy. Modern dam concretes may present a rough ⎡ ⎛ ∞ ⎞ ⎤ analog to Romanwhere concretes. ∂we/∂h The is irthe coarse slope aggregate of the sorption/desorption 10⎜ g α −α ⎟h ⎢ ⎝ 1 c c ⎠ ⎥ sizes approach thoseisotherm of typical(also Romancalled caementamoisture , capacity). The w − 0.188α s + 0.22α s − G ⎢1− e ⎥ 0 c s 1⎢ ⎥ while experimentalgoverning measure equation of their composite(Equation 3)frac- must be completed ⎣ ⎦ (6) K ()α ,α = ture behavior recordsby appropriate demonstrably boundary larger and fracture initial conditions. 1 c s ⎛ ∞ ⎞ 10⎜ g α −α ⎟h energies compared toThe typically-graded relation between modern the amount con- of evaporable e ⎝ 1 c c ⎠ −1 cretes (Deng et al.water 2008). and This relative agrees humidity with a general is called ‘‘adsorption c s trend of increasingisotherm” fracture ifenergy measured with maximumwith incr easing relativity The material parameters k vg and k vg and g1 can aggregate size (Eliceshumidity & Roccoand ‘‘desorption 2008). In isotherm”modern in the opposite be calibrated by fitting experimental data relevant to concretes, one cancase. envision Neglecting the propagating their difference fracture (Xi et al. 1994), in free (evaporable) water content in concrete at requiring increasedthe energy following, to produce ‘‘sorption a more isotherm” tortu- will be used with various ages (Di Luzio & Cusatis 2009b). ous path around referenceand/or a tougherto both sorptionpath through and desorption the conditions. larger aggregate Byparticles, the way, but ifstill the following hystere sisthe of the moisture same general trajectory,isotherm with would varia betions taken occurring into account, on two different 2.2 Temperature evolution a smaller (~mm)relation, scale. This evaporable is not necessarilywater vs relative the humidity, must Note that, at early age, since the chemical reactions case for Roman beconcretes, used according where theto thelarger sign aggre- of the variation of the associated with cement hydration and SF reaction gate constituentsrelativity could significan humidity.tly alterThe fractureshape of the sorption are exothermic, the temperature field is not uniform propagation pathsisotherm and characteristics. for HPC is influenced by many parameters, for non-adiabatic systems even if the environmental A simple two-dimensionalespecially those schematic that influence (Fig. 7) extent il- and rate of the temperature is constant. Heat conduction can be lustrates several pochemicalssibilities. reactions The composite and, in fracture turn, determine pore described in concrete, at least for temperature not Figure 6. Tensile strengths of components from the wall con- energy for cases (A-C)structure can and be expressedpore size distributionas follows: (water-to-cement exceeding 100°C (Bažant & Kaplan 1996), by crete of the Great Hall, as measured by point source tests. ratio, cement chemical composition, SF content, Fourier’s law, which reads

()A curing time and method, temperature, mix additives, GGLLFIc=⋅()/_1 (3) The point source strengths supplement, in an ap- etc.). In the literature various formulations can be q = −λ∇T (7) proximate sense, the extremely limited data on the found to describe the sorption isotherm of normal tensile strength of Imperial concretes and make im- GGLGLL()B =⋅+()/ ⋅ (4) FITZ11concrete 1|21|2 (Xi et al. 1994). However, in the present where q is the heat flux, T is the absolute portant suggestions of elements in the composite paper the semi-empirical expression proposed by concrete fabric in which fractures may nucleate. The temperature, and λ is the heat conductivity; in this GGLGLGLGLL()C =⋅+⋅+()/Norling Mjornell ⋅+⋅ (1997) is adopted(5) because it small sample size and complicated stress fields, how- FITZ11 22 1|31|344

Proceedings of FraMCoS-7, May 23-28, 2010 J = −D(h,T )∇h where GIc_1 = G F_1 = G 1 = the fracture energy of (1)the theexplicitly ability accountsof the monuments for the evolution to absorb of changes hydration in mortar; L1|2 = the length of the crack path along the externalreaction andand internal SF content. energies This over sorptionmany centuries. isotherm interfaceThe proportionality between the mortar coefficient and a TufoD(h,T) Giallo is called della readsWhile much study is needed to explore this phe- Viamoisture Tiberina permeability caementa andfragment it is a (Fig.nonlinear 8); G functionITZ1|3 the nomenal endurance, our initial hypothesis posits the fractureof the relative energy humidity of the interfaceh and temperature between brickT (Bažant and dissipation of energy into⎡ the development of⎤ widely mortar; and so on. In the absence of any measured distributed but relatively⎢ weakly1 coalesced⎥ or & Najjar 1972). The moisture mass balance requires w ()()h,α ,α = G α ,α 1 − + data,that theextremely variation rough in time approximations of the water for mass the perrespec- unit bridgede c processs 1 zones.c s ⎢These zones∞ of dispersed,⎥ ⎢ 10(g α − α )h ⎥ tivevolume fracture of concrete energies (water could content compute w) bea “composite” equal to the small-scale (with respect⎣ eto the1 c meso-structure)c ⎦ (4) fracturedivergence energy of the that moisture increases flux by J around 50% in case cracking effectively delay the localization necessary B, and almost doubles in case C, illustrating the po- for the nucleation, linkage,⎡ 10(g αand∞ − αpropagation)h ⎤ of K ()α ,α ⎢e 1 c c − 1⎥ tential∂w of the large aggregates and interfaces to alter fractures on structurally1 c s ⎢ perilous scales. This⎥ hy- composite− = ∇ • Jfracture properties. The estimates assume (2) pothesis introduces further⎣ questions: at what⎦ point ∂t a homogeneous mortar and do not take into account does the accumulation of these potentially isolated where the first term (gel isotherm) represents the centimeter-scaleThe water content scoria w canand belava expressed aggregate, as the which sum microstructural damage zones imperil the building physically bound (adsorbed) water and the second canof the impact evaporable fracture waterpropagation w (capillary (Figs. 4, water, 7d&e). water on a structural scale? And how suddenly? What role e term (capillary isotherm) represents the capillary vapor, and adsorbed water) and the non-evaporable do the unusual and highly durable alumina- and al- water. This expression is valid only for low content (chemically bound) water w (Mills 1966, kali-rich pozzolanic cements of the Roman mortars n of SF. The coefficient G represents the amount of Pantazopoulo & Mills 1995). It is reasonable to play in the resistance of the1 concrete fracture? And, water per unit volume held in the gel pores at 100% assume that the evaporable water is a function of more globally, could conglomeratic composite con- relative humidity, and it can be expressed (Norling relative humidity, h, degree of hydration, α , and cretes, perhaps characterized by the ability to absorb c Mjornell 1997) as degree of silica fume reaction, α , i.e. w =w (h,α ,α ) energy via widely distributed, weakly coalesced s e e c s = age-dependent sorption/desorption isotherm process zones, have applications for sustainable concrete constructionc in seismicallys active areas? (Norling Mjonell 1997). Under this assumption and G ()α ,α = k α c + k α s (5) by substituting Equation 1 into Equation 2 one 1 c s vg c vg s obtains c s where k vg and k vg are material parameters. From the maximum amount of water per unit volume that can ∂w ∂h ∂w ∂w − e + ∇ • (D ∇h) = e α& + e α& + w& (3) fill all pores (both capillary pores and gel pores), one ∂h ∂t h ∂α c ∂α s n can calculate K as one obtains c s 1

⎡ ⎛ ∞ ⎞ ⎤ where ∂we/∂h is the slope of the sorption/desorption 10⎜ g α −α ⎟h ⎢ ⎝ 1 c c ⎠ ⎥ isotherm (also called moisture capacity). The w − 0.188α s + 0.22α s − G ⎢1− e ⎥ 0 c s 1⎢ ⎥ governing equation (Equation 3) must be completed ⎣ ⎦ (6) K ()α ,α = by appropriate boundary and initial conditions. 1 c s ⎛ ∞ ⎞ 10⎜ g α −α ⎟h The relation between the amount of evaporable e ⎝ 1 c c ⎠ −1 water and relative humidity is called ‘‘adsorption c s Figureisotherm” 7. Schematic if measured showing withpossible incr meso-scaleeasing (A-C)relativity and The material parameters k vg and k vg and g1 can micro-scalehumidity and(d-e) ‘‘desorptionmechanisms of isotherm” fracture in ain Roman the opposite concrete be calibrated by fitting experimental data relevant to vault.case. Neglecting their difference (Xi et al. 1994), in free (evaporable) water content in concrete at the following, ‘‘sorption isotherm” will be used with various ages (Di Luzio & Cusatis 2009b). referenceIt seems to reasonableboth sorption to andpostulate desorption relatively conditions. large fractureBy the energiesway, if forthe Roman hystere concretes.sis of the Combining moisture thisisotherm with theirwould lower be taken tensile into strengths account, (Fig. two 6),different equa- 2.2 Temperature evolution tionrelation, 2 suggests evaporable large, water possibly vs relative meter-scale, humidity, process must Note that, at early age, since the chemical reactions zonesbe used preceding according stru to ctural-scalethe sign of themacrofractures variation of thein associated with cement hydration and SF reaction Romanrelativity concretes. humidity. How The such shape a process of the zone sorption might are exothermic, the temperature field is not uniform influenceisotherm forthe HPCpropagation is influenced of fracture by many and parameters,consequent for non-adiabatic systems even if the environmental structural-scaleespecially those destabithat influencelization extentof a monument and rate of is the a temperature is constant. Heat conduction can be complexchemical question.reactions However, and, in inturn, view determine of the extraor- pore described in concrete, at least for temperature not dinarystructure survival and pore of sizemany distribution Imperial (waterage monuments,-to-cement exceeding 100°C (Bažant & Kaplan 1996), by exposedratio, cement to two chemicalmillennia ofcomposition, differential groundSF content, sub- Fourier’s law, which reads sidencecuring time and andseismic method, ground temperature, motions, wemix tentatively additives, suggest here that the mechanical strength of the con- etc.). In the literature various formulations can be q = −λ∇T (7) cretes, likely modest but certainly sufficient, is of found to describe the sorption isotherm of normal Figure 8. Top: photograph of wall concrete core with compo- secondary importance. Perhaps far more relevant to nents outlined: 1-pozzolanic mortar; 2-Tufo Giallo della Via concrete (Xi et al. 1994). However, in the present where q is the heat flux, T is the absolute thepaper structures’ the semi-empirical continued stabilexpressionity are proposedthe fracture by Tiberina; 3-brick fragment; 4-Tufo Lionato. The outer core di- energies of their concretes, empirically evident in ametertemperature, is 20cm. andBottom: λ is schematic the heat of condtest design.uctivity; D = 20cm;in this r Norling Mjornell (1997) is adopted because it = 5cm.

Proceedings of FraMCoS-7, May 23-28, 2010 We begin exploring these questions with the frac- behavior, incorporatingJ = −D( h,variaT )∇htions in component (1) explicitly accounts for the evolution of hydration ture testing of laboratory re-productions of Impe- properties and their relative importance in the com- reaction and SF content. This sorption isotherm rial Roman mortar. The geometry of the Great Hall posite response. The proportionality coefficient D(h,T) is called reads drill cores – eccentric, hollow, thin-walled cylinders moisture permeability and it is a nonlinear function – motivates a novel test design that loads arc-shaped of the relative humidity h and temperature T (Bažant ⎡ ⎤ specimens in three-point bending (Fig. 8). The ob- ACKNOWLEDGEMENT ⎢ 1 ⎥ & Najjar 1972). The moisture mass balance requires w ()()h,α ,α = G α ,α 1 − + jectives are to observe the microstructures of the that the variation in time of the water mass per unit e c s 1 c s ⎢ ∞ ⎥ ⎢ 10(g α − α )h ⎥ mortar reproductions before testing, to record the We acknowledgevolume the generous of concrete assistance (water content of L. w ) be equal to the ⎣ e 1 c c ⎦ (4) microstructural nucleation, coalescence, and propa- Ungaro and M. divergenceVitti from ofthe the Sovraintendenza moisture flux J ai gation of fractures on specific length scales during Beni Culturali del Comune di Roma, Ufficio Fori ⎡ 10(g α ∞ − α )h ⎤ K ()α ,α ⎢e 1 c c − 1⎥ testing, and to produce estimates for the fracture en- Imperiali. ∂w 1 c s ⎢ ⎥ ergy and tensile strength of the re-fabricated mortars − = ∇ • J (2) ⎣ ⎦ ∂t based on measurements recorded on the experimen- where the first term (gel isotherm) represents the tal scale. Specimens will be tested after 7, 28, 90, REFERENCES The water content w can be expressed as the sum physically bound (adsorbed) water and the second 180 days, and at multi-year curing periods to ob- of the evaporable water w (capillary water, water A.C.I. 318 Building Code Requirements for Structurale term (capillary isotherm) represents the capillary serve how the strength and fracture properties de- vapor, and adsorbed water) and the non-evaporable Concrete and Commentary. Farmington Hills, MI: ACI. water. This expression is valid only for low content velop as cementitious phases advance. Details con- (chemically bound) water w (Mills 1966, Brune, P. & Perucchio, R. in prep. Roman Concrete Vaultingn of SF. The coefficient G represents the amount of cerning sample fabrication, testing, and data Pantazopoulo & Mills 1995). It is reasonable to 1 in the Great Hall of Trajan’s Markets. Journal of Structural water per unit volume held in the gel pores at 100% reduction, will be published along with experimental Engineering. assume that the evaporable water is a function of relative humidity, and it can be expressed (Norling results and analysis as the project proceeds. De Casa, G. & Lombardi,relative G. 2007.humidity, Caratteri h ,Fisico-Meccanici degree of hydration, α , and c Mjornell 1997) as del Tufo Giallo degreedella Via of silicaTiberina fume (Roma). reaction, Rendiconti α , i.e. w =w (h,α ,α ) Lincei 18(1): 5-25. s e e c s = age-dependent sorption/desorption isotherm 5 SOME PRELIMINARY CONCLUSIONS De Casa, G. et al. 1999. Il Tufo Lionato Dei Monumenti c s Romani. Geologica(Norling romana 35:Mjonell 1-25. 1997). Under this assumption and G ()α ,α = k α c + k α s (5) 1 c s vg c vg s Deng, Z. et al. 2008.by substituting Comparison Equationbetween Mechanical 1 into Equation 2 one The fracture testing of the mortar reproductions will Properties of Damobtains and Sieved Concretes. Journal of contribute the first measurement of the fracture en- c s Materials in Civil Engineering. where k vg and k vg are material parameters. From the ergy of Imperial Roman concrete, which is likely a Elices, M. & Rocco, C. 2008. Effect of aggregate size on the ∂w ∂w ∂w maximum amount of water per unit volume that can fundamental component in the formulation of a frac- fracture and mechanicale ∂ hproperties of a simplee concrete.e fill all pores (both capillary pores and gel pores), one Engineering Fracture− Mechanics+ ∇ • 75:(D 3839-3851.∇h) = α& + α& + w& (3) ture description for the composite material. Past me- ∂h ∂t h ∂α c ∂α s n Giavarini, C. et al. 2006. Mechanical Characteristicsc of Romans can calculate K1 as one obtains chanical characterizations of Roman concretes have ‘Opus Caementicium.’ In S. Kourkoulis (ed.), Fracture and focused on compressive strength. Test results show Failure of Natural Building Stones. Dordrecht: Springer. ⎡ ⎛ ∞ ⎞ ⎤ where ∂we/∂h is the slope of the sorption/desorption 10⎜ g α −α ⎟h considerable scatter, which attests to the highly het- Jackson, M.D. et al. 2005. The Judicious Selection and ⎢ ⎝ 1 c c ⎠ ⎥ isotherm (also called moisture capacity). The w − 0.188α s + 0.22α s − G ⎢1− e ⎥ erogeneous nature of the composite material and the Preservation of Tuff and Travertine Building Stone in 0 c s 1⎢ ⎥ governing equation (Equation 3) must be completed ⎣ ⎦ (6) importance of understanding the length scales on Ancient Rome. Archaeometry 47(3): 485-510. K ()α ,α = Jackson, M.D. et byal. appropriate 2009. Assessment boundary ofand materialinitial conditions. 1 c s ⎛ ∞ ⎞ which particular mechanical and fracture properties 10⎜ g α −α ⎟h characteristics of ancientThe concretes,relation Grandebetween Aula, the Markets amount of evaporable ⎝ 1 c c ⎠ should be measured. Still, the reported strengths, e −1 of Trajan, Rome.water Journal and of relativeArchaeological humidity Science is 36:called ‘‘adsorption however dispersed, in conjunction with the structural Lamprecht,2481-2492. H.O. 1984.isotherm” Opus caementicium: if measured Bautechnik with incrder easing relativity The material parameters kc and ks and g can analysis of Imperial monuments generally indicate Römer. Düsseldorf: Beton-Verlag. vg vg 1 humidity and ‘‘desorption isotherm” in the opposite be calibrated by fitting experimental data relevant to that the concretes have strength sufficient for the Molin, D. et al. 1995. Sismicità di Roma. In Memorie case. Neglecting their difference (Xi et al. 1994), in free (evaporable) water content in concrete at static loads of the extant architectural designs (c.f., Descrittive della Carta Geologica d'Italia: La Geologia di Roma I, edited bythe R. following, Funiciello, ‘‘sorption331-407. Rome: isotherm” Istituto will be used with various ages (Di Luzio & Cusatis 2009b). Brune & Perucchio in prep.). Poligrafico e Zeccareference dello Stato. to both sorption and desorption conditions. Mechanical analyses to determine the factors be- Rovelli, A. et al. 1995.By thePrevisione way, delif themoto hysteredel suolosis eof the moisture hind the survival of these designs – and the cementi- modellazione degli effetti locali. In Memorie Descrittive isotherm would be taken into account, two different 2.2 Temperature evolution tious materials that preserved them while subjected della Carta Geologica d'Italia: La Geologia di Roma I, relation, evaporable water vs relative humidity, must Note that, at early age, since the chemical reactions to centuries of seismic and subsidence events – edited by R. Funiciello,416-432. Rome: Istituto Poligrafico e Zecca dello Stato.be used according to the sign of the variation of the associated with cement hydration and SF reaction requires investigation into how microcracks in the Samuelli Ferretti, A.relativity 1996. Rapporto humidity. sulle prove The di laboratorioshape of the sorption are exothermic, the temperature field is not uniform composite concrete nucleate, propagate, and poten- ed in situ effettuateisotherm sui forcomponenti, HPC is inflin uencedMateriali by da many parameters, for non-adiabatic systems even if the environmental tially resist fracture at the structural scale. The wide costruzione e especiallytecnologie thosecostruttive that influencedel patrimonio extent and rate of the temperature is constant. Heat conduction can be variation of aggregate compositions and consequent archeologico e monumentale romano con particolare chemical reactions and, in turn, determine pore described in concrete, at least for temperature not mechanical properties of the conglomeratic compos- riferimento al tipo laziale ed all'opus latericium. Roma. structure and pore size distribution (water-to-cement exceeding 100°C (Bažant & Kaplan 1996), by ites and their components makes the identification of Terenzio, A. 1934. La restoration du Pantheon de Rome. Conservation des ratio,monuments cement d’art &chemical d’historie: composition,280-285. SF content, Fourier’s law, which reads structural-scale material properties by direct experi- Van Mier, J.G. 1997.curing Fracture time and Processes method, of temperature, Concrete: mix additives, mental testing extremely difficult. Instead, our ap- Assessment of Materialetc.). In Parameters the literature for Fracture various Models. formulations can be q = −λ∇T proach will be to measure relevant fracture and me- Boca Raton, FL: CRC Press. (7) found to describe the sorption isotherm of normal chanical properties on the micro- and meso- scales. concrete (Xi et al. 1994). However, in the present These data will inform a parametrized model for the where q is the heat flux, T is the absolute paper the semi-empirical expression proposed by composite that will aim to create a reasonably temperature, and λ is the heat conductivity; in this Norling Mjornell (1997) is adopted because it bounded envelope for the structural-scale fracture

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