materials

Article A Computational Study of the Shear Behavior of Reinforced Concrete Beams Affected from Alkali–Silica Reactivity Damage

Bora Gencturk 1,* , Hadi Aryan 1, Mohammad Hanifehzadeh 1, Clotilde Chambreuil 2 and Jianqiang Wei 3

1 Sonny Astani Department of Civil and Environmental Engineering, University of Southern California, 3620 S. Vermont Avenue, KAP 210, Los Angeles, CA 90089-2531, USA; [email protected] (H.A.); [email protected] (M.H.) 2 LMT—Laboratoire de Mécanique et Technologie, University Paris-Saclay, ENS Paris-Saclay, CNRS, 91190 Gif-sur-Yvette, France; [email protected] 3 Department of Civil and Environmental Engineering, University of Massachusetts, Lowell, MA 01854-5104, USA; [email protected] * Correspondence: [email protected]; Tel.: +1-(213)-821-1036; Fax: +1-(213)-744-1426

Abstract: In this study, an investigation of the shear behavior of full-scale reinforced concrete (RC) beams affected from alkali–silica reactivity damage is presented. A detailed finite element model (FEM) was developed and validated with data obtained from the experiments using several metrics, including a force–deformation curve, rebar strains, and crack maps and width. The validated FEM was used in a parametric study to investigate the potential impact of alkali–silica reactivity (ASR)



 degradation on the shear capacity of the beam. Degradations of concrete mechanical properties were correlated with ASR expansion using material test data and implemented in the FEM for Citation: Gencturk, B.; Aryan, H.; different expansions. The finite element (FE) analysis provided a better understanding of the failure Hanifehzadeh, M.; Chambreuil, C.; mechanism of ASR-affected RC beam and degradation in the capacity as a function of the ASR Wei, J. A Computational Study of the expansion. The parametric study using the FEM showed 6%, 19%, and 25% reduction in the shear Shear Behavior of Reinforced capacity of the beam, respectively, affected from 0.2%, 0.4%, and 0.6% of ASR-induced expansion. Concrete Beams Affected from Alkali–Silica Reactivity Damage. Keywords: reinforced concrete; shear failure; alkali–silica reactivity; finite element modeling Materials 2021, 14, 3346. https://doi.org/10.3390/ ma14123346

Academic Editors: Bahman Ghiassi 1. Introduction and Dario De Domenico The durability of concrete is an important consideration for reinforced concrete (RC) structures. One of the major concerns is the degradation of concrete from alkali–silica Received: 25 March 2021 reaction (ASR), which is a slowly occurring chemical process between the hydroxyl ions Accepted: 10 June 2021 available in the pore water of concrete and the aggregate containing reactive silica. The Published: 17 June 2021 chemical product, named ASR gel, is highly expansive in the presence of moisture. The gel expansion develops an internal pressure and induces micro-cracking, which degrades the Publisher’s Note: MDPI stays neutral mechanical and physical properties of the concrete [1]. As micro-cracks build up throughout with regard to jurisdictional claims in the concrete volume, the negative effects of the ASR on the macro-scale properties of published maps and institutional affil- concrete are observed. Substantial damage in the form of both micro and macrocracking iations. has been reported in various types of structures in the United States, including bridges, roadways, dams and nuclear power plants due to ASR [2–4]. The initial sign of ASR is mapping cracks on the exposed concrete surfaces. Mapping cracks are a pattern of hairline cracks with random orientation on the surface of a concrete member. Over time, additional Copyright: © 2021 by the authors. symptoms, including volumetric expansion, relative movement, localized crushing and Licensee MDPI, Basel, Switzerland. spalling, and surface discoloration may be observed. In extreme cases, the rupture of This article is an open access article the reinforcement due to excessive expansion strains has been reported [5]. The rate of distributed under the terms and expansion is largely a function of the reactivity of the aggregate, the alkali content of the conditions of the Creative Commons cement, the confinement level of the structural element, and the environmental conditions, Attribution (CC BY) license (https:// i.e., moisture and temperature [6,7]. In some cases, up to 0.6% expansion was observed creativecommons.org/licenses/by/ in a period of 10 years in the field [7]. The expansion and cracking eventually result 4.0/).

Materials 2021, 14, 3346. https://doi.org/10.3390/ma14123346 https://www.mdpi.com/journal/materials Materials 2021, 14, 3346 2 of 23

in a reduction in the service life of the structure. In addition to the field evidence and experimental studies, numerical models have been developed to simulate the concrete expansion and deterioration due to ASR. Recently, ASR degradation has been implemented in lattice discrete particle models (LDPM), which can simulate the heterogenous nature of concrete at the coarse aggregate scale. This approach enables an accurate modeling of the volumetric expansion of the ASR gel, concrete cracking and the degradation of concrete strength and stiffness due to ASR [8–10]. The shear failure of RC beams is relatively less understood; particularly, for damaged infrastructure components. Sucharda [11] presented a procedure to identify the fracture properties of concrete through inverse analysis of multicriteria decision analysis, stochastic modelling and nonlinear simulations. The identified parameters were then used to perform a parametric study on the shear behavior of concrete beams with no shear reinforcement. The basic mechanical properties of concrete were defined through laboratory tests and a number of concrete beams with different longitudinal reinforcement ratios were tested in shear. In addition to determining the fracture energy, the shear capacity as a function of longitudinal reinforcement ratio was derived. Conforti and Minelli [12] performed a numerical study on the shear behavior of fiber-reinforced concrete deep beams using the modified compression field theory and disturbed stress field model. Particular attention was given to the modeling of nonlinear properties of concrete such as tension softening. After validating the models with experimental results, the influence of size effect on the shear behavior of the beams was investigated. Nine beams without shear reinforcement were studied in three groups of no fiber, and 50 kg/m3 and 75 kg/m3 of hooked-end steel fibers. All beams were 250 mm wide, and each group included three beams each with 500 mm, 1000 mm, and 1500 mm height and an effective depth 60 mm less than the beam height. The shear span for each beam was three times the effective depth of the beam. The results showed that the modified compression field theory and disturbed stress field model accurately predict the shear behavior of different size beams with and without fibers. Wu and Hu [13] presented an experimental method to quantify the contributions of concrete and transverse reinforcement to the shear strength of RC beams. The developed approach was based on measuring the strains along the entire length of each stirrup without affecting the bond between the reinforcement and the concrete. It was concluded that not all the stirrups intersecting a major diagonal shear crack yield at the verge of shear strength. Additionally, the peak contributions of concrete and transverse reinforcement do not occur when the beam reaches its strength. Domenico and Ricciardi [14] presented an upgraded truss model in which the upper compression strut may show lower inclination compared to the lower compression strut. This is mechanically induced by the increase in shear stress in the upper part of beam close to the crack tip. It was shown that the proposed model accurately estimates the experimental shear strength of RC beams. A number of studies have been performed on the shear behavior of bridge decks affected by ASR [15,16]. Schmidt et al. [15] presented a test method for concrete bridges without disturbing the traffic. Their approach included collecting concrete cylinder samples and unreinforced beams from parts of the slab that were damaged and less damaged by ASR for comparative load testing in the laboratory. Barbosa et al. [16] presented results of tests on 18 RC beams sawn from a flat bridge slab significantly damaged from ASR. The test results showed that the crack distribution and moment capacity of the beams were affected by ASR and the beams failed in flexure under three-point bending but the prestressing effect of the ASR-induced expansion compensates for degraded concrete properties. ASR, being one of the most prevalent damage mechanisms in RC structures, deserves further investigation with regards to its influence on the shear capacity of RC beams. This study aims to fill this gap of scarce data and analysis on the shear capacity of ASR-damaged beams. First, a comprehensive literature review has been performed to synthesize the available data in terms of the reduction in concrete mechanical properties as a function of ASR expansion. Then, the results of two full-scale shear tests on a RC beam have been presented in terms of maximum shear capacity, crack maps and widths, and strains in the Materials 2021, 14, 3346 3 of 23

reinforcement. The two shear spans had the same geometry and reinforcement details such that the repeatability of the experiments could be verified. The results from the second shear test in which the beam was pushed to ultimate strength and failure have been used to validate a finite element model (FEM), which was later used to simulate the long-term structural behavior of the beam affected from ASR. The reduction in the mechanical properties of the concrete was estimated using relationships obtained from data synthesized from the literature and then used as inputs to the FEM in a parametric study. The reduction in the shear capacity of the beam was predicted as a function of the concrete ASR expansion.

2. Literature Synthesis Numerous studies have reported the effect of ASR on the mechanical properties of concrete; particularly, on the compressive and tensile strength, and Young’s modulus. However, the effect on the compressive strength is disputed among researchers [17,18]. Most of the studies reported that the effect of ASR on the tensile strength and Young’s modulus is higher than that on the compressive strength, as further discussed below. A comprehensive experimental program was performed by the authors of this study on the effect of ASR on the mechanical properties of concrete using accelerated aging [19]. A 0.8% sodium hydroxide by weight of cement was added to concrete and degradation was evaluated over time. Increasing the alkaline dosage is a well-known method in which the long-term behavior of the material is simulated in a short period of time [20–22]. Over a 210-day period of accelerated aging, 16% and 21% reduction, respectively, was observed in the split tensile strength and elastic modulus of the concrete. However, the reduction in compressive strength was not significant (about 5%). Sanchez et al. [17] prepared 20 concrete mixtures with three target strengths of 25 MPa, 35 MPa, and 45 MPa, and ten different reactive aggregates to study the damage caused by alkali–aggregate reaction (AAR). AAR refers to the general class of reactions between the alkali hydroxides in the concrete pore solution and the mineral phases of the aggregates. ASR is one of the most common types of AAR [23]. Thirty-five cylinder specimens, 100 mm by 200 mm in size, from each mixture were tested at different expansion levels with a maximum expansion of 0.3%. All 20 concrete mixtures had the same amount of cement and aggregate volume for comparison purposes. The cylinders were kept at 38 ◦C and 100% relative humidity. The highest reduction in elastic modulus was about 67%, and the lowest was about 40% at 0.3% expansion for the 35 MPa mixture. The reduction in tensile strength was between 45% and 80%, depending on the aggregate type at the 0.2% expansion level. The compressive strength was the least affected parameter, with a reduction between 20% and 35% at the 0.2% expansion level. Esposito et al. [24] studied the effect of ASR on concrete and developed a correlation between mechanical properties and expansion. Two different concrete mixtures from Dutch and Norwegian aggregates were used. The Norwegian aggregates were expected to have a higher reactivity than Dutch ones. The two concretes were designed with similar aggregate gradation and 28-day compressive strength. The samples from both mixtures were stored at 38 ◦C and 96% relative humidity. The test data showed a 28-day compressive strength between 60 MPa and 68 MPa. The expansions were measured on 75 × 75 × 280 mm prisms and the compressive testing was performed on 150 mm cubes. The last test was conducted at 365 days of concrete age. The approximate expansion obtained after 365 days was 0.11% and 0.18% for the mixtures using the Dutch and Norwegian aggregates, respectively. A slight increase in the mechanical properties was observed in the first 90 days, and then the degradation began. The variation of the static elastic modulus of the concrete with Dutch aggregates was insignificant (less than 7%), while that with Norwegian aggregates showed a 35% reduction. Both concretes showed an increase in the compressive strength while the split tensile strength exhibited a 23% and 26% decrease for the concretes with Dutch and Norwegian aggregates, respectively. In conclusion, the elastic modulus was found to be the most sensitive parameter to ASR and the second most affected parameter was found Materials 2021, 14, 3346 4 of 23

to be the split tensile strength. It was concluded that the increase in the concrete strength with increased maturity overshadows a potential decrease due to ASR. Fan and Hanson [25] performed three-point flexural tests on 152 × 254 × 1524 mm concrete beams affected by ASR over the one-year accelerated aging period. The beams were immersed in an alkali solution that was cyclically heated between 38 ◦C and room temperature. The alkali solution contained 10 g of sodium hydroxide (NaOH), 14 g of potassium hydroxide (KOH), and 0.1 g of calcium oxide (CaO) per liter of tap water. The expansion in the cylinders was measured using a mechanical dial gage as the change in the distance between the studs placed on the sides of the specimen. It was found that the mechanical properties of nonreactive cylinders do not change significantly over time. However, tests showed about 24%, 38%, and 31% percent reduction in the compressive strength, splitting tensile strength, and dynamic modulus, at an age of 6 months and expansion of 2300 microstrain compared to the 28-day values. It was concluded that, despite visible cracks, the flexural strength of the reactive beams is about the same as those of the nonreactive beams. Gautam et al. [26] performed an experimental study to identify the degradation in material properties of concrete under multi-axial state of stress. The triaxial expansion of 254 mm cubic specimens, prepared with reactive coarse aggregates, and restrained with rods in uniaxial and biaxial conditions up to 9.6 MPa pressure, was measured. 1.3 kg/m3 of NaOH pallets were added to the concrete mixtures to accelerate ASR. To accelerate aging, the specimens were cured in an environmental chamber at 50 ◦C and 100% relative humidity for 8 months. Compression and splitting tension tests were performed at different ages on 75 mm diameter cores drilled from the specimens. It was observed that the expansion was significantly lower in the restrained directions while the volumetric expansion remained relatively constant. Fifteen percent less volumetric expansion for the biaxially stressed specimens was measured compared to the unstressed specimens. The splitting tensile strength for the unrestrained non-reactive specimens increased by 60% while the reactive concrete showed a 50% reduction. The increase in the strength was attributed to the continuing hydration of the anhydrous cement in the samples. No statistically meaningful change was observed in the compressive strength while an average of 20% reduction was observed in the elastic modulus. The confinement increased the compressive strength while the elastic modulus was similar both in restrained and unrestrained samples. Ahmed et al. [27] investigated the material properties of concrete subjected to a 12-month accelerated aging regimen. The compressive strength of 100 mm cubes, the split tensile strength of 100 × 100 mm cylinders, and direct tensile strength, according to BS 6319 [28], of dumb-bell briquette-shaped specimens were evaluated. Fused silica (as reactive aggregates) and Portland cement with a high alkali content of 4.9 kg/m3 were used in the concrete. Additional Na2SO4 and K2SO4 were added to the mixture to increase the alkali content to 7 kg/m3. After curing, the specimens were kept in water at 38 ◦C to accelerate the chemical reactions. Expansions in 100 × 100 × 500 mm prisms and 150 × 300 mm cylinders were measured using a digital Vernier scale. The reduction in the compressive strength was 59% after 12 months at 1.6% expansion. The losses in the split tensile and direct tensile strength were found to be 60% and 80%, respectively. Sargolzahi et al. [29] evaluated two concrete mixtures, one with Spratt limestone as a reactive aggregate source and the other with Limeridge limestone as a non-reactive aggregate source. Four prisms, 75 × 75 × 285 mm, for expansion measurements and 24 cylinders, 100 × 200 mm, for mechanical testing, were prepared. NaOH pellets were added to the reactive concrete mixture to increase the alkali content to 4.5 kg/m3. The specimens were stored at 38 ◦C in a high humidity environment according to the Canadian CSA A23.2-14A Standard [30]. The compressive strength of the reactive concrete was 14% lower than that of the non-reactive mixture after 23 months of aging and at 0.14% expansion. This reduction was 37% for the static modulus of elasticity under the same conditions. Saint-Pierre et al. [31] applied accelerated aging on concrete by submerging the speci- mens made with reactive aggregate in a 1 mol L−1 NaOH solution at 38 ◦C for 3.5 months. Materials 2021, 14, 3346 5 of 23

3 The alkali content (Na2O equivalent) of the reactive concrete was 5.25 kg/m . Ten prisms, 75 × 75 × 300 mm, with reference studs for expansion measurement and 40 cylinders, 100 × 200 mm, for mechanical tests were prepared. The maximum expansion in the reactive and non-reactive concretes was measured as 0.19% and 0.02%, respectively. While the difference between compressive strength for the reactive and non-reactive mixtures was insignificant, a 13% reduction in the elastic modulus was observed. Smaoui et al. [32] evaluated the mechanical and durability properties of concrete affected by accelerated ASR. Low-alkali and high-alkali content mixtures were prepared with 0.6% and 1.25% Na2O by mass of cement, respectively. The high-alkali mixture was prepared by dissolving NaOH pellets in the mixing water. Non-reactive coarse limestone and fine granitic aggregates were used for both concretes with a water-to-cement (w/c) ratio of 0.41. The specimens were kept at 23 ◦C and 100% relative humidity until testing. Prisms 50 × 75 × 350 mm in size and 100 × 200 mm cylinders were tested at various ages up to 180 days. The results revealed the difference between the properties of concrete samples made from high-alkali and low-alkali mixtures. At an age of six months, the high- alkali concrete specimens showed 12% lower compressive strength, 7% lower modulus of elasticity, 15% lower direct tensile strength, 14% lower split tensile strength, and 3% lower modulus of rupture compared with the low-alkali concrete specimens. Multon et al. [33] performed material testing as a part of an investigation on the effect of moisture gradient on ASR. Potassium hydroxide (KOH) was dissolved in the mixing water to increase the Na2O equivalent content of the mixture to 1.25%. Cylinders with measurements of 160 × 320 mm were tested for mechanical properties. The samples were kept at 38 ◦C for 12 months in sealed conditions. The elastic modulus of the reactive concrete was 20% lower at 12 months compared to the 28-day value and 27% lower compared to the non-reactive concrete. The tensile strength was 3% higher after 12 months compared to the 28-day value but 9% lower compared to the non-reactive concrete of the same age. The reactive concrete also had a 10% increase in compressive strength after 12 months but the difference with the non-reactive concrete was indistinguishable. Giannini and Folliard [34] used El Paso, Texas sand and New Mexico gravel to prepare two reactive concretes. Cylinders with measurements of 100 × 200 mm were prepared for compressive testing. Type I cement was used and NaOH was added to the mixture 3 to increase the alkaline content to a Na2O equivalent of 5.25 kg/m . The cylinders were initially wrapped with plastic to prevent moisture loss and then stored at 38 ◦C and 95% relative humidity. In the El Paso sand concrete, the compressive strength and elastic modulus showed a 13% and 45% reduction, respectively, after one year of aging and 0.6% expansion compared to their 28-day values. The New Mexico gravel concrete showed a 10% increase and a 19% reduction in the compressive strength and elastic modulus, respectively, after one year of aging and 0.85% expansion. More than 50 data points for elastic modulus, and compressive and tensile strength were extracted from the literature, as listed in Table1 and plotted in Figures1–3. The data points indicated as “current study” in Table1 were obtained by the authors, as presented in [24]. The data points were normalized with respect to the 28-day strength value of each mixture. Exponential trendlines were obtained for each set of data and presented in the figures. The equations for these trendlines are summarized in Table2. These equations are used to estimate material degradation as inputs to the parametric study performed using the FEM. Materials 2021, 14, x FOR PEER REVIEW 6 of 23

Table 1. List of the studies on ASR-affected concrete properties.

Alkaline Maximum Cement Con- Reference Reactive Aggregate Type w/c 1 Ratio Dosage Expansion tent (kg/m3) 2 Materials 2021, 14, 3346 (%) (%6) of 23 Current study El Paso Sand 291 0.52 1.25 0.18 Attar et al. [19] El Paso sand 427 0.33 1.25 0.10 Smaoui et al. [35] Texas sand 420 0.4 1.25 0.39 Table 1. List of the studies on ASR-affected concrete properties. Smaoui et al. [35] Québec City limestone 420 0.4 1.25 0.17 Esposito et al. [24] Quartzite, quartz, chert, volcanicCement rock Content w/c3801 Alkaline0.45 Dosage Maximum1.17 Expansion0.11 Reference Reactive Aggregate Type 3 2 Esposito et al. [24] Quartz, quartzite, gneiss, metarhyolite(kg/m ) Ratio380 (%)0.45 1.17 (%) 0.18 SargolzehiCurrent study et al. [29] El PasoSpratt Sand limestone 291345 0.52 1.250.5 1.25 0.18 0.08 Attar et al. [19] El Paso sand 427 0.33 1.25 0.10 3 4 SmaouiFan et et al. al. [3 [356]] Gold Texas Hill sand coarse aggregate 420403 0.4 1.250.47 - 0.39 0.17 SaintSmaoui-Pierre et al. et [ 35al.] [31] Québec CitySpratt limestone limestone 420350 0.4 1.250.5 5.25 5 0.17 0.2 Esposito et al. [24] Quartzite, quartz, chert, volcanic rock 380 0.45 1.175 0.11 GiaccioEsposito etet al. al. [24 [3] 7] Quartz, quartzite,Crushed gneiss, quartzitic metarhyolite sandstone 380380 0.45 1.170.42 4.0 0.18 0.22 SargolzehiGiaccio et et al. [29[3]8] Granitic Spratt stone limestone with feldspars, quartz, 345etc. 420 0.5 1.250.42 1.24 0.08 0.28 3 4 MultonFan et al.et [al.36] [33] Gold Hill coarseLimestone aggregate 403410 0.47 - 0.5 1.25 0.17 0.26 Saint-Pierre et al. [31] Spratt limestone 350 0.5 5.25 5 0.2 GianniniGiaccio et et al. al. [37 ][34] Dolomite, Crushed quartzitic carbonat sandstonee, siliceous volcanics 380 420 0.42 4.00.425 1.25 0.22 0.14 Granitic stone with feldspars, quartz, GianniniGiaccio et et al. al. [38 ][34] El Paso sand 420 0.42_ 1.24_ _ 0.28 0.42 etc. Swamy and Al-Asali Multon et al. [33]Amorphous Limestone fused silica sand 410520 0.5 1.250.44 1.00 0.26 0.62 [39] Dolomite, carbonate, siliceous Giannini et al. [34] 420 0.42 1.25 0.14 Larive [40] volcanicsTournaisis limestone 410 0.44 1.25 0.21 Giannini et al. [34] El Paso sand _ _ _ 0.42 SwamyMonette and Al-Asali [41] [ 39] AmorphousSiliceous fused silica limestone sand 520423 0.44 1.000.61 1.25 0.62 0.35 Larive [40]Thames Tournaisis Valley limestonesand (50% chert) and fused 410 0.44 1.25 0.21 AhmedMonette et [41al.] [27] Siliceous limestone 423400 0.61 1.250.5 1.75 0.35 0.15 Thames Valley sand (50%silica chert) and Ahmed et al. [27] 400 0.5 1.75 0.15 Multon [42] Calcareousfused silica stones with silica 410 0.5 1.25 0.1 Multon [42] Calcareous stones with silica 410 0.5 1.25 0.1 ChloriteChlorite interleaved interleaved with quartzwith quartz and and feld- BenBen HahaHaha [43 [4] 3] _ 0.46_ 0.40.46 0.4 0.16 0.16 feldspar spar Ottersbo cataclasite with crypto and LindgårdLindgård [44 [4] 4] Ottersbo cataclasite with crypto and quartz550 550 0.3 0.670.3 0.67 0.08 0.08 quartz Lindgård [44] OttersboOttersbo cataclasite cataclasite with with crypto crypto and and quartz 400 0.45 0.93 0.23 Lindgård [44] 400 0.45 0.93 0.23 Lindgård [44] Ottersbo cataclasitequartz with crypto and quartz 315 0.6 1.17 0.28 Ottersbo cataclasite with crypto and Lindgård [44] 315 0.6 1.17 0.28 Sanchez et al. [45] Volcanicsquartz and chert sand 314 0.61 1.25 0.3 SanchezSanchez et et al. al. [45 [4]5] Volcanics Volcanics andand chert chert sand coarse aggregate 314 314 0.61 1.250.61 1.25 0.3 0.2 Sanchez1 Water et-to al.-cement [45] ratio; Volcanics 2 by weight and chert of coarsecement; aggregate 3 the specimens were 314 submerged 0.61 in 0.5 N concentration 1.25 alkali solution 0.2 for 1 6Water-to-cement months; 4 maximum ratio; 2 expansionby weight ofon cement; reinforc3 theed beam; specimens 5 the were total submerged alkali content in 0.5 in N the concentration mixture (kg/m alkali3) solution. for 6 months; 4 maximum expansion on reinforced beam; 5 the total alkali content in the mixture (kg/m3).

2 1.8 Literature This study 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 Normalized CompressiveStrength Normalized 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Expansion (%)

FigureFigure 1. 1.Normalized Normalized compressive compressive strength strength versus versus ASR ASR expansion. expansion.

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2 2 1.8 Literature 1.8 ThisLiterature study 1.6 This study 1.6 1.4 1.4 1.2 1.2 1 1 0.8 0.8 0.6 0.6 0.4 0.4 Normalized Tensile Strength Tensile Normalized 0.2 Normalized Tensile Strength Tensile Normalized 0.2 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.1 0.2 0.3 Expansion0.4 (%) 0.5 0.6 0.7 0.8 Expansion (%)

Figure 2. Normalized tensile strength versus ASR expansion. FigureFigure 2. 2.Normalized Normalized tensile tensile strength strength versus versus ASR ASR expansion. expansion.

2 2 1.8 Literature 1.8 ThisLiterature study 1.6 This study 1.6 1.4 1.4 1.2 1.2 1 1 0.8 0.8 0.6 0.6 0.4

Normalized ElasticModulus Normalized 0.4

Normalized ElasticModulus Normalized 0.2 0.2 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.1 0.2 0.3 Expansion0.4 (%) 0.5 0.6 0.7 0.8 Expansion (%) Figure 3. Figure 3. Normalized modulusmodulus ofof elasticityelasticity versusversus ASRASR expansion.expansion. Figure 3. Normalized modulus of elasticity versus ASR expansion. TableTable 2.2. NormalizedNormalized equationsequations forfor estimatingestimating ASRASR damagedamage asas aa functionfunction ofof expansion.expansion. Table 2. Normalized equations for estimating ASR damage as a function of expansion. MechanicalMechanical Property, Property, y yProperty, Property, y as a Function y as a Function of Expansion of Expansion Percentage, Percentage, x x Mechanical Property, y Property, y as a Function of Expansion Percentage, x ElasticElastic Modulus Modulus y = 1.0189y = 1.0189 × 10×−1.224x10− 1.224x Elastic Modulus −1.224x−1.068x TensileTensile Strength Strength yy = = 0.9830 1.0189y = 0.9830 × × 10 10×−1.068x10 −0.482x TensileCompressive Strength Strength y = 0.9830y = 1.011110×−110.068x Compressive Strength y = 1.0111 × × 10 −0.482x Compressive Strength y = 1.0111 × 10−0.482x 3. Experimental Program 3. Experimental Program 3. ExperimentalThe experimental Program program and the results are described in detail in a recent study by The experimental program and the results are described in detail in a recent study by the authors [46]. Since the validation of the computational model in this study is based on the authorsThe experimental [46]. Since the program validation and ofthe the results compu aretational described model in detail in this in study a recent is based study on by thethe results authors of [4 these6]. Since experiments, the validation a brief of summary the compu oftational the pertinent model parts in this of thestudy experimental is based on program and results are presented in this section.

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Concrete with a w/c ratio of 0.52, a slump of 190 mm and an average 28-day strength of 27.5 MPa was designed as shown in Table3.

Table 3. Concrete mixture proportions.

Material Amount Mixing Water, kg/m3 154 Type II Low Alkali Portland Cement, kg/m3 291 19 mm Coarse Aggregate, kg/m3 1038 9.5 mm Coarse Aggregate, kg/m3 208 Reactive Sand from El Paso, Texas, kg/m3 727 Pozzolith 8 1, g/m3 1187 Glenium 3400 NV 1, g/m3 1557 1 Pozzolith 8 and Glenium 3400 NV are water-reducing admixtures produced by BASF Corporation (Ludwigshafen, Germany) [47].

To obtain the mechanical properties of the concrete, standard material tests were performed at 28 days and 210 days after casting, the latter of which being when the beam was tested. Table4 shows the results obtained from these tests. As presented in Table4, the split tensile strength of concrete decreased as a result of early-stage ASR degradation. The scatter of the test results in Table4 can be found in the figures of [6].

Table 4. Mechanical properties of concrete.

Age No. of Tests at Property Standard 28 Days 210 days Each Age Compressive Strength (MPa) 38.5 40.0 3 ASTM C39 [48] Split Tensile Strength (MPa) 4.6 3.5 3 ASTM C496 [49] Elastic Modulus (GPa) 17.7 19.0 3 ASTM C469 [50] Modulus of Rupture (MPa) 4.7 1 4.8 2 ASTM C78 [51] 1 Testing performed at 3 months of age.

A full-scale RC beam, 6.4 m in length with a rectangular cross-section 0.6 m deep and 0.3 m wide, was fabricated. The volumetric ratio of the gross longitudinal reinforcement was constant at 4.2% over the length of the beam, while a light transverse reinforcement with a volumetric ratio of 0.13% was provided in the two shear spans with a span-to- depth ratio of about 2.9, as shown in Figure4. To calculate this ratio, the span length was measured between the center of the loading plate and the center of the support plate. At the center of the beam and above the supports at the ends, a heavy shear reinforcement with a volumetric ratio of 1.3% was used to prevent failure in these regions. Figure4 also shows the locations of supports and loading points during the first and second tests as well as the string potentiometers, SPi, for deflection measurements under the loading points. Additionally, the strain gauges installed on the stirrups and longitudinal reinforcement are shown in Figure4. The actuator load and displacement were also, respectively, obtained from the actuator load cell and actuator linear resistance transducer (LRT). All the sensors, including load cells, LRT, and string and linear potentiometers, were calibrated and verified prior to testing. No calibration is required for the strain gauge sensors and these strain gauges were installed on the reinforcement by grinding and polishing a smooth surface on the steel and then, attaching and sealing the sensors. Materials 2021, 14, 3346 9 of 23 Materials 2021, 14, x FOR PEER REVIEW 9 of 23

FigureFigure 4. 4.As As built built dimensions dimensions of of the the full-scale full-scale beam, beam, loading loading and and support support locations locations and and instrumentation instrumentation (all (all dimensions dimensions are inare mm). in mm).

TheThe testtest setupsetup consisted of the components shown shown in in Figure Figure 55.. The supports at at the the twotwo endsends allowed allowed beam beam displacement displacement in inthe the longitudinal longitudinal direction direction and androtation rotation about about the thestrong strong axis. axis. A loading A loading frame frame and a and servo a servo-hydraulic-hydraulic actuator actuator with 670 with kN 670 capacity kN capacity were wereused usedto apply to applyload to load the toshear the span. shear Restraints span. Restraints were placed were on placed either on side either of the side beam of theto beamrestrict to the restrict movement the movement of the beam ofthe to the beam vertical to the direction vertical within direction the within test plane. the testExternal plane. Externalclamps were clamps installed were installed in the shear in the span shear that span was that not wasbeing not tested being to tested protect to it protect from crack- it from crackinging and damage, and damage, and to and allow to allow for a second for a second test on test the on same the beam. same beam.A total A of total 890 ofkN 890 post kN- post-tensioningtensioning force forcewas applied was applied through through these theseclamps, clamps, which whichwere pre were-analyzed pre-analyzed to be suffi- to be sufficientcient to prevent to prevent cracking cracking in this in region. this region. The clamps The clamps were werealso used also usedduring during the second the second test, test,but this but thistime time on the on thealready already tested tested and and cracked cracked span span,, so sothat that a acomplete complete failure failure in in the the alreadyalready testedtested spanspan could be prevented and the the shear shear deformation deformation could could be be focused focused into into thethe spanspan beingbeing tested.tested. The tests were conducted under quasi-static loading. As described in [46] in detail, the loading protocol included multiple steps of loading, pauses to conduct crack measurements, and unloading. The loading protocol consisted of load control and displacement control segments. Only during the displacement control segment that was performed at the final stage of the second test to push the beam to failure, was there a direct relation between the load rate and the beam deflection. In the other segments, the deflection of the beam was a function of the tangent stiffness of the beam at that stage of the loading and the load increment or decrement. Load–deflection diagrams for the first and the second shear tests performed on the two ends of the beam are presented in Figure6. During the first shear test, the beam was not loaded to complete failure and the test was terminated at 556 kN load to prevent damage to the other shear span. In the second test, the loading was continued up to 578 kN in load-control mode and then switched to displacement control and the test was continued up to complete failure. The maximum capacity of the beam was obtained as 635 kN in the second test and the residual shear strength of the beam after failure was found to be 369 kN. Figure6 shows that in the second shear test, the beam retains a slightly higher stiffness past 8 mm deflection. This slight difference is attributed to the uncertain clamping force applied to the other span during each test, and the influence of the cracks caused by the first test on the second test.

Figure 5. Test setup.

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Figure 4. As built dimensions of the full-scale beam, loading and support locations and instrumentation (all dimensions are in mm).

The test setup consisted of the components shown in Figure 5. The supports at the two ends allowed beam displacement in the longitudinal direction and rotation about the strong axis. A loading frame and a servo-hydraulic actuator with 670 kN capacity were used to apply load to the shear span. Restraints were placed on either side of the beam to restrict the movement of the beam to the vertical direction within the test plane. External clamps were installed in the shear span that was not being tested to protect it from crack- ing and damage, and to allow for a second test on the same beam. A total of 890 kN post- tensioning force was applied through these clamps, which were pre-analyzed to be suffi- cient to prevent cracking in this region. The clamps were also used during the second test, Materials 2021, 14, 3346 but this time on the already tested and cracked span, so that a complete failure 10in ofthe 23 already tested span could be prevented and the shear deformation could be focused into the span being tested.

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The tests were conducted under quasi-static loading. As described in [46] in detail, the loading protocol included multiple steps of loading, pauses to conduct crack meas- urements, and unloading. The loading protocol consisted of load control and displace- ment control segments. Only during the displacement control segment that was per- formed at the final stage of the second test to push the beam to failure, was there a direct relation between the load rate and the beam deflection. In the other segments, the deflec- tion of the beam was a function of the tangent stiffness of the beam at that stage of the loading and the load increment or decrement. Load–deflection diagrams for the first and the second shear tests performed on the two ends of the beam are presented in Figure 6. During the first shear test, the beam was not loaded to complete failure and the test was terminated at 556 kN load to prevent damage to the other shear span. In the second test, the loading was continued up to 578 kN in load-control mode and then switched to dis- placement control and the test was continued up to complete failure. The maximum ca- pacity of the beam was obtained as 635 kN in the second test and the residual shear strength of the beam after failure was found to be 369 kN. Figure 6 shows that in the sec- ond shear test, the beam retains a slightly higher stiffness past 8 mm deflection. This slight difference is attributed to the uncertain clamping force applied to the other span during each test, and the influenceFigure 5. of Test the setup. cracks caused by the first test on the second test.

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FigureFigure 6. 6.Load–deflection Load–deflection diagrams diagrams for for the the shear shear tests. tests. The The deflection deflection was was measured measured under under the the loading loading point. point.

AlthoughAlthough bothboth teststestsresulted resulted in in a a shear shear failure, failure, since since during during the the second second test test the the beam beam waswas pushedpushed toto thethe completecomplete failure,failure, forfor brevity,brevity, thethe resultsresults ofof thethe second second shearshear testtest areare presentedpresented inin thethe following.following. FigureFigure7 7presents presents the the crack crack maps maps and and major major crack crack widths widths at at thethe peakpeak loadload ofof 635635 kN.kN. TheThe widthswidths ofof thethe crackscracks werewere largerlarger close close to to the the middle middle of of the the shearshear span.span. FigureFigure7 7only only presents presents the the crack crack pattern pattern and and crack crack widths widths at at select select locations. locations. TheThe crackcrack width is is not not presented presented to to scale. scale. Crack Crack widths widths were were manually manually measured measured at selec att selectlocations locations,, as shown as shown in the in figure the figure,, that have that havebeen beenvisually visually identified identified to be tothe be largest the largest crack crackopening. opening.

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Figure 7. Crack maps and width at the peak load of 635 kN. FigureFigure 7. 7.Crack Crack maps maps and and width width at at the the peak peak load load of of 635 635 kN. kN. Figure 8 presents the results of stirrups strain versus load. The strain gauges #2 and Figure 8 presents the results of stirrups strain versus load. The strain gauges #2 and #3, whichFigure 8 were presents installed the results on the of middle stirrups stirrups strain versus of the load. span, The experienced strain gauges significantly #2 and #3, which were installed on the middle stirrups of the span, experienced significantly #3,higher which strains were compared installed to on the the other middle two stirrups strain gauges. of the This span, is experiencedconsistent with significantly the results higher strains compared to the other two strain gauges. This is consistent with the results higherpresented strains in Figure compared 7 for to the the crack other widths two strain in the gauges. middle This of the isconsistent span. with the results presentedpresented in in Figure Figure7 for7 for the the crack crack widths widths in in the the middle middle of of the the span. span.

Figure 8. Load versus stirrup strains. FigureFigure 8. 8Load. Load versus versus stirrup stirrup strains. strains. 4. Finite Element Modeling and Analysis 4.4. Finite Finite Element Element Modeling Modeling and and Analysis Analysis 4.1.4.1. Material Material Models Models 4.1. Material Models AsAs mentioned mentioned earlier,earlier, a a FEM FEM is is created created for for the the shear shear failure failure of of the the RC RC beam beam using using As mentioned earlier, a FEM is created for the shear failure of the RC beam using ATENAATENA 3D 3D [52 [5].2 The]. The selected selected constitutive constitutive model model for concrete, for concrete, CC3DNonLinCementitious2, CC3DNonLinCementi- ATENA 3D [52]. The selected constitutive model for concrete, CC3DNonLinCementi- istiou baseds2, is on based fracture on fracture in tension in andtension plasticity and plasticity in compression. in compression. The parameters The parameters used for thisused tious2, is based on fracture in tension and plasticity in compression. The parameters used modelfor this are model summarized are summarized in Table in5. Table Some 5. parameters Some parameters such as such elastic as elastic modulus, modulus, Poisson’s Pois- for this model are summarized in Table 5. Some parameters such as elastic modulus, Pois- ratio,son’s tensileratio, tensile strength, strength, and compressive and compressive strength strength were obtainedwere obtained from materialfrom materia tests,l andtests, son’s ratio, tensile strength, and compressive strength were obtained from material tests, theand remaining the remaining parameters, parameters including, including specific specific energy, energy, tension tension stiffening, stiffening, and crack and shear crack and the remaining parameters, including specific energy, tension stiffening, and crack stiffnessshear stiffness factor, werefactor determined, were determined through through the model the tuning model and tuning validation and validation using the datausing shear stiffness factor, were determined through the model tuning and validation using fromthe data the from beam the experiment. beam experiment. The definitions The definitions of the parametersof the parameters given given in Table in 5Table for the5 for the data from the beam experiment. The definitions of the parameters given in Table 5 for CC3DNonLinCementitious2the CC3DNonLinCementitious2 concrete concrete model model are presented are presented in detail in detail in ATENA in ATENA program pro- the CC3DNonLinCementitious2 concrete model are presented in detail in ATENA pro- documentationgram documentation [52]. The [5 value2]. The of v 1alue for theof 1 fixed for the crack fixed model crack coefficient model coefficient in Table5 indicatesin Table 5 thatgram this documentation is the active mode [52]. forThe concrete value of cracking. 1 for the Infixed this crack model, model the crackcoefficient distribution in Table is 5

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uniform within the material volume and cracking occurs when the principal stress exceeds the tensile strength of concrete. In the fixed crack model, the direction of crack during loading remains fixed, as given by the principal stress direction at the moment of crack initiation. The crack width is calculated based on the crack opening strain over the crack band in the finite elements representing the concrete.

Table 5. Parameters of the concrete model.

Parameter Symbol Unit Value Elastic Modulus E MPa 1.896 × 104 Poisson’s Ratio µ - 0.20 Tensile Strength ft MPa 4.00 Compressive Strength fc MPa −40.00 −4 Specific Fracture Energy GF MN/m 2.000 × 10 Tension Stiffening cts - 0.04 −3 Critical Compressive Displacement Wd m −1.050 × 10 −3 Plastic Strain at Compressive Strength εcp - −3.200 × 10 Reduction of Compressive Strength Due to Cracks rc,lim - 0.80 Crack Shear Stiffness Factor SF - 20.00 Aggregate Size - m 0.019 Failure Surface Eccentricity - - 0.52 Multiplier for The Plastic Flow Direction β - 0.00 Specific Material Weight ρ MN/m3 2.30 × 10−2 Fixed Crack Model Coefficient - - 1.00

A bilinear model with strain hardening, CCReinforcement, was used to model the steel reinforcing bars. The input parameters were derived from the uniaxial rebar testing for different steel reinforcements in the beams as presented in Table6.

Table 6. Parameters of the reinforcement model.

Material Characteristic Unit #5 Stirrup #5 Longitudinal Rebar #8 Longitudinal Rebar #3 Stirrup Elastic Modulus, E MPa 200,000 200,000 200,000 200,000 Yield Strength, σy MPa 483 500 490 517 Maximum Stress, σt MPa 680 676 672 648 Maximum Strain, εlim - 0.2 0.2 0.3 0.1 Specific Material Weight, ρ MN/m3 0.0785 0.0785 0.0785 0.0785

4.2. Geometry The geometry of the model is based on the dimensions of the beam presented earlier. The model is composed of three parts: the concrete beam, reinforcement, and the steel plates for the supports, loading plate and the clamps. The concrete was meshed with iso-parametric 3D linear brick elements (see Figure9). To model the post-tensioning force of the clamps, a discrete rigid object with the same contact area of the clamps was created on the top and bottom of the beam, and a compression force, equal in magnitude to that was used in the experiments, was applied, as shown in Figure9. The embedded discrete reinforcement (shown in Figure 10) had displacement compatibility with the surrounding concrete. Table7 presents the mesh information of the FE model for concrete, steel (supports and loading points), and rebar components. MaterialsMaterials2021 2021, 14, 14, 3346, x FOR PEER REVIEW 1313 of of 23 23 Materials 2021, 14, x FOR PEER REVIEW 13 of 23

FigureFigure 9.9.Finite Finite elementelement meshmesh and post-tensioningpost-tensioning force. Figure 9. Finite element mesh and post-tensioning force.

Figure 10. Flexure and shear reinforcement in the FEM. Figure 10. FlexureFlexure and and shear shear reinforcement reinforcement in in the the FE FEM.M. Table 7. Mesh information of the FEM. Table 7. MeshTable information 7. Mesh ofinformation the FEM. of the FEM. Model Component Element Shape Element Size Element Type No. of Elements Model Component Element Shape Element Size Element Type No. of Elements Concrete ModelBrick Component Element60 Shapemm Element SizeLinear Element Type No.5300 of Elements Concrete Brick 60 mm Linear 5300 Steel TetrahedralConcrete Brick12 mm 60 mmLinear Linear50436 5300 Steel Tetrahedral 12 mm Linear 50436 Rebar LineSteel Tetrahedral60 mm 12 mm2-D truss Linear3290 50,436 Rebar LineRebar 60 Line mm 60 mm2-D truss 2-D truss3290 3290 4.3. Loading and Boundary Conditions 4.3. Loading and Boundary Conditions 4.3. LoadingThe load and was Boundary simulated Conditions by applying a 25.4 mm prescribed deformation, for a com- The load was simulated by applying a 25.4 mm prescribed deformation, for a com- pleteThe analysis, load was at increments simulated byof 0.01 applying mm displacement a 25.4 mm prescribed in the neg deformation,ative Z, vertical, for adirection. complete plete analysis, at increments of 0.01 mm displacement in the negative Z, vertical, direction. analysis,The supports at increments were free of to 0.01 rotate mm about displacement the transverse in the axis negative of the Z,beam vertical, and they direction. were There- The supports were free to rotate about the transverse axis of the beam and they were re- supportsstricted to were move free in tothe rotate vertical about direction. the transverse Surface axissprings of the were beam placed and under they were the supports restricted stricted to move in the vertical direction. Surface springs were placed under the supports toto moverepresent in the the verticalbehavior direction. of elastomeric Surface pad springsof the supports were placed shown under in Figure the 5, supports and a 890 to to represent the behavior of elastomeric pad of the supports shown in Figure 5, and a 890 representkN load was the behaviorapplied to of simulate elastomeric the padeffect of of the the supports clamps shownin the farther in Figure shear5, and span a 890 of the kN kN load was applied to simulate the effect of the clamps in the farther shear span of the loadbeam. was applied to simulate the effect of the clamps in the farther shear span of the beam. beam. 4.4.4.4. Solution Solution Method Method 4.4. Solution Method TheThe Newton–Raphson Newton–Raphson method method with with the line the search line optimizationsearch optimization approach andapproach tangent typeThe stiffness Newton was used–Raphson for solving method the governing with the equations. line search The optimization line search strategy approach adjusts and tangent type stiffness was used for solving the governing equations. The line theand displacement tangent type increments stiffness w toas optimize used for the solving required the work governing and reduces equations. the out-of-balance The line search strategy adjusts the displacement increments to optimize the required forces.search Table strategy8 presents adjusts the the iteration displacement limit and increments different error to tolerances optimize for the the required solution work and reduces the out-of-balance forces. Table 8 presents the iteration limit methodwork and along reduces with the the parameters out-of-balance of the lineforces. search Table approach. 8 presents the iteration limit and different error tolerances for the solution method along with the parameters and different error tolerances for the solution method along with the parameters of the line search approach. of the line search approach. Table 8. Solution parameters. Table 8. Solution parameters. Title Parameter Value Title Parameter Value General Iteration limit per analysis step 500 General Iteration limit per analysis step 500

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Table 8. Solution parameters.

TitleDisplacement Parameter error tolerance Value0.010000 IterationResidual limit error per analysis tolerance step 5000.010000 AbsoluteDisplacement residual error error tolerance tolerance 0.0100000.010000 General Residual error tolerance 0.010000 Energy error tolerance 0.000100 Absolute residual error tolerance 0.010000 UnbalancedEnergy error energy tolerance limit 0.0001000.800 Limit of line search iterations 2 Line Search Unbalanced energy limit 0.800 LimitLine of search line search limit iterations—min. 2 0.010 Line Search LineLine search limit—min.limit—max. 0.0101.000 Line search limit—max. 1.000 4.5. Model Validation 4.5. ModelThe FEM Validation is validated using the experimental data from the second test. Like the sec- ondThe shear FEM test, is the validated first test usingalso resulted the experimental in shear failure data but from thethe shear second failure test. of the Like second the secondtest included shear test,the ultimate the first shear test also load resulted capacity in and shear the failure load drop but thesince shear the failuretest continued of the secondto capture test th includede entire failure. the ultimate The primary shear load step capacitytaken for and validation the load is dropto compare since thethe testload continuedversus deflection to capture diagrams, the entire which failure. is shown The primary in Figure step 11. taken Despite for validation some differences is to compare in the thestiffness load versus and the deflection ultimate diagrams, strength, whichan acceptable is shown agreement in Figure 11was. Despite obtained. some differences in the stiffness and the ultimate strength, an acceptable agreement was obtained.

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FigureFigure 11. 11.Load Load versus versus deflection deflection diagrams diagrams of of the the experiment experiment and and the the FEM. FEM.

ForFor further further evaluation evaluation of of the the FEM, FEM, the the crack crack patterns patterns corresponding corresponding to to the the peak peak load load areare compared, compared,as as shown shown in in Figure Figure 12 12.. SimilarSimilar toto FigureFigure7 ,7, Figure Figure 12 12bb presents presents the the crack crack pattern,pattern, and and the the concentration concentration and and widths widths of of the the cracks cracks are are not not presented presented to to scale. scale. Overall,Overall, thethe crack crack patterns patterns show show a a good good correlation correlation between between the the FEM FEM and and the the experiment. experiment. In In both both patterns,patterns, the the major major shear shear crack crack was was located located diagonally diagonally between between the the loading loading point point and and the the support.support. TheThemaximum maximum crackcrackwidth widthat atpeak peak load load was was obtained obtained as as 4.1 4.1 mm mm from from the the FEM FEM andand 4.4 4.4 mm mm from from the the experiment. experiment. The FEM was also validated by comparing the reinforcement strains. From four #3 stirrups, the ones close to the middle of the span showed a significant strain. Therefore, in Figure 13, the stress versus strain diagrams of the stirrup close to the middle of the shear span are compared. The experiment stirrup strain at the peak load was 0.019, while the strain from the FEM was about 0.025. Figure 14 presents the stress versus strain diagrams of the bottom longitudinal rebar. It is noted that the stress values for the experimental data were obtained from the material tests of the rebar and using the rebar strains recorded

Figure 12. Crack patterns of the (a) FEM and the (b) experiment at peak load.

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Displacement error tolerance 0.010000 Residual error tolerance 0.010000 Absolute residual error tolerance 0.010000 Energy error tolerance 0.000100 Unbalanced energy limit 0.800 Limit of line search iterations 2 Line Search Line search limit—min. 0.010 Line search limit—max. 1.000

4.5. Model Validation The FEM is validated using the experimental data from the second test. Like the sec- ond shear test, the first test also resulted in shear failure but the shear failure of the second test included the ultimate shear load capacity and the load drop since the test continued to capture the entire failure. The primary step taken for validation is to compare the load versus deflection diagrams, which is shown in Figure 11. Despite some differences in the stiffness and the ultimate strength, an acceptable agreement was obtained.

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Figure 11. Load versus deflection diagrams of the experiment and the FEM. Materials 2021, 14, 3346 15 of 23 For further evaluation of the FEM, the crack patterns corresponding to the peak load are compared, as shown in Figure 12. Similar to Figure 7, Figure 12b presents the crack Materials 2021, 14, x FOR PEER REVIEW 15 of 23 frompattern the, and strain the gage. concentration Additionally, and widths the diagrams of the cracks in Figures are not 13 presented and 14 are to sketched scale. Overall, up to the crack strain patterns corresponding show a togood the correlation peak load. between These figures the FEM indicate and the acceptable experiment. agreement In both betweenpatterns, thethe resultsmajor ofshear the crack experiment was located and FEM. diagonally Additionally, between the the bottom loading longitudinal point and steel the reinforcementsupportThe. TheFEM maximum was showed also 0.0019 validatedcrack width strain by atcomparing peak the peak load the load was reinforcement duringobtained the as experiment, 4.1 strains. mm fromFrom while the four FEM this #3 stirrups,valueand 4.4 was mm the 0.0024 fromones inclosethe the experiment. to FEM. the middle of the span showed a significant strain. Therefore, in Figure 13, the stress versus strain diagrams of the stirrup close to the middle of the shear span are compared. The experiment stirrup strain at the peak load was 0.019, while the strain from the FEM was about 0.025. Figure 14 presents the stress versus strain diagrams of the bottom longitudinal rebar. It is noted that the stress values for the experimental data were obtained from the material tests of the rebar and using the rebar strains recorded from the strain gage. Additionally, the diagrams in Figures 13 and 14 are sketched up to the strain corresponding to the peak load. These figures indicate acceptable agreement between the results of the experiment and FEM. Additionally, the bottom longitudinal Figuresteel 12. Crackreinforcement patterns of showed the (a)) FEM 0.0019 and thestrainthe ((bb)) experimentatexperiment the peak atat load peakpeak during load.load. the experiment, while this value was 0.0024 in the FEM.

Figure 13. ComparisonComparison of of the the experimental experimental and and numerical numerical stress stress–strain–strain diagrams diagrams in inthe the stirrup stirrup close close to the to themiddle middle of the of thespan. span.

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FigureFigure 14.14.Comparison Comparison of of the the experimental experimental and and numerical numerical stress–strain stress–strain diagrams diagrams of of the the bottom bottom longitudinal longitudinal rebar rebar close close to theto the loading loading point. point.

4.6.4.6. ParametricParametric StudyStudy InIn thisthis section, section, the the validated validated FEM FEM is usedis used to evaluate to evaluate the influencethe influence of ASR of onASR the on shear the performanceshear performance of the of beam. the beam. Thisinvestigation This investigation is based is based on the on degradation the degradation in the in concrete the con- mechanicalcrete mechanical properties properties due to due ASR. to The ASR. mechanical The mechanical properties properties affected affected by ASR by are ASR chosen are aschosen the concrete as the concrete compressive compressive and split and tensile split strength, tensile andstrength, elastic and modulus. elastic Themodulus. equations The extractedequations from extracted the literature, from the as literature, presented as in presented Table2, were in Table used to2, were estimate used the to degradation estimate the indegradation these properties. in these In properties. addition, the In reduction addition, inthe the reduction fracture energy,in the fracture which is energy, an important which propertyis an important of the concrete property constitutive of the concrete model constitutive used in the model FEM, used has been in the also FEM, calculated has been using also calculated using 0.18 GF = 73 fcm (1) . = 73 (1) where GF is the fracture energy (N/m) and fcm is the mean compressive strength (MPa) [53]. Threewhere cases GF isare the defined fracture based energy on ( ASRN/m expansion) and fcm is levelsthe mean of 0.2%, compressive 0.4%, and strength 0.6%. Accordingly, (MPa) [53]. theThree normalized cases are valuesdefined of based the concrete on ASR properties expansion are leve calculatedls of 0.2%, for 0.4%, different and expansions, 0.6%. Accord- as presentedingly, the innormalized Table9. values of the concrete properties are calculated for different expan- sions, as presented in Table 9. Table 9. Different cases of ASR and corresponding percentage remained in concrete mechanical properties. Table 9. Different cases of ASR and corresponding percentage remained in concrete mechanical properties. Case Properties 1 2Case 3 0.2% Expansion 0.4% Expansion 0.6% Expansion Properties 1 2 3 Compressive Strength 92% (36.8 MPa) 83% (33.2 MPa) 76% (30.4 MPa) 0.2% Expansion 0.4% Expansion 0.6% Expansion Elastic Modulus 80% (15.2 GPa) 62% (11.8 GPa) 49% (9.3 GPa) CompressiveTensile Strength Strength 79%92% (3.2 ( MPa)36.8 MPa) 64%83% (2.6 (33.2 MPa) MPa) 52%76% (2.1 (30.4 MPa) MPa) FractureElastic EnergyModulus 98.5%80% (0.197 (15.2 kN/m) GPa) 96.7%62% (0.193 (11.8 kN/m) GPa) 95.1%49 (0.190% (9.3 kN/m) GPa) Tensile Strength 79% (3.2 MPa) 64% (2.6 MPa) 52% (2.1 MPa) FigureFracture 15 Energy presents the98.5% effect ( of0.197 ASR kN/m on the) 96.7% shear ( performance0.193 kN/m) 95.1% of the ( RC0.190 beam kN/m in) terms of load versus deflection. The reference model and the models representing concrete degradationFigure 15 due presents to ASR the are effect shown. of ASR According on the to shear Figure performance 15, ASR Cases of the 1 toRC 3 beam cause in a terms of load versus deflection. The reference model and the models representing concrete

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degradegradationdation due due to toASR ASR are are shown. shown. According According to toFigure Figure 15, 15, ASR ASR Cases Cases 1 to1 to3 cause3 cause a a reductionreduction in inthe the shear shear strength strength by by 6.3%, 6.3%, 19.4%, 19.4%, and and 25.4%, 25.4%, respectively. respectively. It isIt isnoted noted that that reduction in the shear strength by 6.3%, 19.4%, and 25.4%, respectively. It is noted that thesethese shear shear strength strength reductions reductions are are merely merely the the result result of ofdegradation degradation of ofconcrete concrete propert propertiesies these shear strength reductions are merely the result of degradation of concrete properties obtainedobtained at atdifferent different ASR ASR expansions. expansions. The The potential potential self self-stressing-stressing of ofconcrete concrete as asa resulta result obtained at different ASR expansions. The potential self-stressing of concrete as a result of ofASR ASR expansion expansion in inthe the presence presence of ofinternal internal reinforcement, reinforcement, which which may may act act to torecover recover the the of ASR expansion in the presence of internal reinforcement, which may act to recover strengthstrength reduction reduction, is, isnot not considered. considered. Therefore, Therefore, these these shear shear strength strength reductions reductions for for dif- dif- the strength reduction, is not considered. Therefore, these shear strength reductions for ferentferent ASR ASR cases cases are are conservative conservative estimates. estimates. different ASR cases are conservative estimates.

700 700 ReferenceReference Model Model ASRASR Case Case 1 1 - 6.3% 600600 - 6.3% ASRASR Case Case 2 2 ASR Case 3 - 19.4% 500 ASR Case 3 - 19.4% 500 - 25.4%- 25.4%

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0 0 0 0 5 5 1010 1515 2020 2525 3030 3535 4040 4545 DeflectionDeflection (mm) (mm)

Figure 15. Load versus deflection diagram for different levels of ASR degradation. FigureFigure 15.15. LoadLoad versusversus deflectiondeflection diagramdiagram forfor differentdifferent levelslevels ofof ASRASR degradation.degradation.

FigureFigureFigure 16 16 16presents presentspresents the thethe maximum maximummaximum crack crackcrack width widthwidth at atatpeak peakpeak load loadload for forfor different differentdifferent levels levelslevels of of ofASR ASRASR degradation.degradation.degradation. According According to tothis this figure, figure,figure, the thethe maximum maximummaximum crack crackcrack width widthwidth at atatpeak peakpeak load loadload for forfor ASR ASRASR CasesCasesCases 1 1and1 and and 2 2 is2 is isless less than than thatthat that ofof the ofthe referencethe reference reference model. model. model. For For Case For Case 3,Case the 3, 3, maximumthe the maximum maximum crack crack width crack widthatwidth peak at atpeak load peak isload slightlyload is isslightly slightly higher higher thanhigher thethan than crack the the widthcrack crack width in width the referencein inthe the reference reference model. model. This model. result This This is resultattributedresult is isattributed attributed to the deflection to tothe the deflection deflection corresponding corresponding corresponding to the peak to tothe load the peak for peak each load load model. for for each each For model. example, model. For For as example,shownexample, inas Figureasshown shown 15 in, comparedinFigure Figure 15, 15, tocompared thecompared reference, to tothe ASRthe reference, reference, Case 1 ASR has ASR smaller Case Case 1 deflection has1 has smaller smaller at de- peak de- flectionload.flection Forat atpeak higher peak load. load. ASR For expansions,For higher higher ASR ASR the expansions, deflectionexpansions, atthe peakthe deflection deflection load increases, at atpeak peak load which load increases, resultsincreases, in whichlargerwhich results maximumresults in inlarger larger crack maximum widthsmaximum corresponding crack crack widths widths corresponding to corresponding the peak load. to tothe the peak peak load. load.

5 5 4.5 4.5 4 4 3.5 3.5 3 3 2.5 2.5 (mm) (mm) 2 2 1.5 1.5 1 1 0.5 0.5 Maximum Crack Width at Peak Load Load Peak at Width Crack Maximum Maximum Crack Width at Peak Load Load Peak at Width Crack Maximum 0 0 ReferenceReference Model Model ASRASR Case Case 1 1 ASRASR Case Case 2 2 ASRASR Case Case 3 3

Figure 16. Maximum crack width at peak load for different cases of ASR. FigureFigure 16. 16. Maximum Maximum crack crack width width at peakat peak load load for for different different cases cases of ASR.of ASR.

Materials 2021, 14, 3346 18 of 23

Table 10 presents the maximum strain values corresponding to peak load at the bottom and top longitudinal rebar as well as the four stirrups in the shear span for different cases of ASR. The stirrup strain gauge numbers in Table 10 refer to those in Figure4. A full bond between the reinforcement and the concrete was assumed in the FEM. The results from Table 10 indicate the relation between the maximum reinforcement strains at peak load and different levels of concrete degradation. Accordingly, a low level of ASR degradation reduces the stirrup strains. At higher levels of ASR degradation, the stirrup strains increase and, in most cases, exceed the strain values from the reference model. This is related to the deflection at the peak load. As shown in Figure 15, the deflection at peak load for low and high levels of ASR damage is smaller and higher, respectively, than that of the reference model. ASR Case 1 applies a lower degradation in concrete mechanical properties than that of other cases which do not significantly change the beam shear performance. This results in a similar but smaller stiffness in the load–deflection diagram and consequently slightly smaller peak load and the corresponding deflection. With an increase in the ASR degradation of concrete mechanical properties, the significant reduction in the maximum load and the stiffness affects the shear performance of the beam. This reduction results in an increase in the deflection at lower peak loads. Table 10 also shows that the strain of top longitudinal reinforcement remains almost unchanged for different levels of ASR. However, for the bottom longitudinal reinforcement, as the ASR becomes worse, the strain value drops. Unlike the stirrup strains, which depend on the deflection at peak load, the strain of the bottom longitudinal reinforcement at peak load is more dependent on the value of the load. As the load capacity decreases due to ASR, the strain of the bottom longitudinal rebar at the peak load drops. The reason for this is that in shear failure, the plastic shear deformation develops disproportional to the load and determines the strain of the resisting stirrups. Meanwhile, due to shear failure occurring prior to any flexural yielding, the bottom longitudinal reinforcement strains are almost proportional to the load. Table 10 shows this relation between the strain values in the reinforcement and the ASR level. This table also shows that, unlike the longitudinal steel reinforcement, all the indicated stirrups in all the FEM yield at the peak load. This confirms that, as desired, the nonlinear shear behavior governed the beam response while the beam stayed in the linear range until the peak load was achieved.

Table 10. Maximum reinforcement strain at peak load for different levels of ASR degradation (refer to Figure4 for numbering of stirrup strain locations).

Maximum Strain (×10−3) FE Model Bottom Top Longitudinal Stirrup No. 1 Stirrup No. 2 Stirrup No. 3 Stirrup No. 4 Longitudinal Rebar Rebar Reference 1.96 −1.34 6.56 17.30 25.14 5.38 Case 1 1.85 −1.35 4.50 15.25 14.43 2.96 Case 2 1.73 −1.32 9.94 22.41 23.62 10.10 Case 3 1.60 −1.34 9.82 22.43 22.86 9.37

Additionally, for different ASR cases, Figures 17 and 18 illustrate the variation of strain at peak load along the length of the bottom longitudinal rebar and the height of the middle stirrup, respectively. The experimental results are also shown using circular markers at the strain gauge locations. It is noted that the peak values in these plots correspond to the results of Table 10. Materials 2021, 14, 3346 19 of 23 Materials 2021, 14, x FOR PEER REVIEW 19 of 23 Materials 2021, 14, x FOR PEER REVIEW 19 of 23

Figure 17. Strain along the length of the bottom longitudinal rebar at peak load. FigureFigure 17.17. StrainStrain alongalong thethe lengthlength ofof thethe bottombottom longitudinallongitudinal rebarrebar atat peakpeak load.load.

FigureFigure 18.18. StrStrainStrainain along along thethe heightheight ofof #3#3 stirrup stirrup atat peakpeak load.load.

5.5. Conclusions Conclusions AsAs aa partpartpart of ofof this thisthis study, study,study, a large-scaleaa largelarge--scalescale beam beambeam was waswas constructed constructedconstructed and testedandand testedtested to study toto studystudy its shear itsits shearperformance.shear performance.performance. The beam TheThe beambeam was designed waswas designeddesigned to fail toto in failfail shear inin shearshear prior priorprior to any toto flexural anyany flexuralflexural yielding. yielding.yielding. Two TwoshearTwo shearshear tests tests weretests wewe conductedrere conductedconducted by applying byby applyingapplying a load aa toloadload each toto sheareacheach shearshear span ofspanspan the ofof beam, thethe beam,beam, with span- withwith spanto-depthspan--toto--depthdepth ratios ratiosratios of about ofof aboutabout 2.9 at 2.92.9 each atat end.eacheach Theend.end. shear TheThe shearshear tests wereteststests werewere conducted conductedconducted under underunder quasi-static quasiquasi-- staticloading.static loading.loading. The acquired TheThe acquiredacquired data were datadata processed,werewere processed,processed, and the andand experimental thethe experimentalexperimental results, resultsresults including,, includingincluding shear shearloadshear versus lloadoad versusversus deflection deflectiondeflection diagram, diagram,diagram, reinforcement reinforcementreinforcement strains, strains,strains, crack crack mapscrack maps andmaps maximum andand maximummaximum crack crackwidthcrack widthwidth at peak atat load peakpeakwere loadload usedwerewere to usedused validate toto validatevalidate a detailed aa detaileddetailed FEM ofFEMFEM the ofof beam. thethe beam.beam. The validated TheThe validatedvalidated FEM FEMwasFEM in waswas turn inin used turnturn to usedused study toto thestudystudy effect thethe of effecteffect different ofof differentdifferent levels of levelslevels ASR degradationofof ASRASR degradationdegradation corresponding corre-corre- spondtospond 0.2%,inging 0.4%, toto 0.2%,0.2%, and 0.4%,0.4%, 0.6% andand of the 0.6%0.6% concrete ofof thethe concrete expansion.concrete expansion.expansion. The reduced TheThe reducedreduced concrete concreteconcrete compressive com-com- pressivepressive strength,strength, tensiletensile strength,strength, modulusmodulus ofof elasticity,elasticity, andand fracturefracture energyenergy werewere calcu-calcu- latedlated basedbased onon ASRASR expansionexpansion andand usedused inin thethe FEM.FEM. TheThe followingfollowing conclusionsconclusions areare mademade::

Materials 2021, 14, 3346 20 of 23

strength, tensile strength, modulus of elasticity, and fracture energy were calculated based on ASR expansion and used in the FEM. The following conclusions are made: • The shear tests indicated that the nonlinear shear behavior governed the response of the beams with span to depth ratios of 2.9, a shear reinforcement ratio of 0.13%, and a longitudinal reinforcement ratio of 4.2%. This was confirmed based on the data from the strain gauges installed on the shear and longitudinal reinforcement. • The major diagonal shear cracks were from the top corner loading point towards the bottom corner support. Some secondary diagonal shear cracks also occurred between the top corner loading point and the middle of the span at the bottom and between the bottom corner support and the middle of the span at the top. • The major shear cracks were more concentrated in the middle of shear span than towards the ends. Similarly, the stirrups close to the middle of shear span yielded while the stirrups close to the loading point and support remained elastic throughout the test. • According to the parametric study using the validated FEM, 0.2%, 0.4%, and 0.6% of ASR expansion induced 6.3%, 19.4%, and 25.4% reduction in the shear capacity of the beams. • For ASR degradation less than 0.4% expansion, the maximum crack width at peak load decreased compared to the reference model but as the ASR degradation progressed, the maximum crack width at peak load increased. For the highest level of ASR degradation with 0.6% expansion, the maximum crack width at peak load slightly exceeded that of the reference model. This happened due to the significant reduction in the beam stiffness, which caused higher deflection at a much lower peak load. • For ASR degradation less than 0.2% expansion, the stirrup strain at peak load is reduced compared to the no ASR case. However, for higher levels of ASR with 0.4% and 0.6% expansion, the strains of the stirrups exceeded the strains in the reference model. This is because the stirrup strain is related to the deflection. The deflection at peak load is smaller at the early stages of ASR but then it increases as the ASR further develops due to further reduction in the material properties. Early-stage ASR results in a slightly lower peak load and corresponding deflection. Higher ASR degradation considerably affects the beam shear performance and reduces the peak load and stiffness. This causes more deflection in the beam and higher stirrups strain. • For different levels of ASR degradation, no significant variation in the top longitudinal reinforcement strain at peak load was observed. On the other hand, as the level of ASR degradation increased, the strain of the bottom longitudinal reinforcement at peak load decreased. Unlike the stirrup strains, which were correlated to the deflection at peak load, the strain of the bottom longitudinal reinforcement was correlated to the peak load. The computational models in this study were developed to capture the degradation of beam shear strength as a result of degradation of the concrete mechanical properties from ASR. The relation between the concrete degradation and ASR expansion was derived from the literature and implemented in the models but the models did not consider the influence of the self-prestressing effect as a result of concrete expansion. Therefore, further research is needed to quantify the self-prestressing effect as a function of the ASR expansion, reinforcement size and ratio, and concrete properties, and if significant implement this effect in modeling the behavior of reinforced concrete members affected from ASR.

Author Contributions: Conceptualization, B.G., H.A., M.H. and J.W.; methodology, B.G., H.A., M.H., C.C. and J.W.; software, H.A., M.H. and C.C.; validation, H.A., M.H., C.C. and J.W.; formal analysis, H.A., M.H., C.C. and J.W.; investigation, B.G., H.A., M.H., C.C. and J.W.; resources, B.G.; data curation, H.A., M.H., C.C. and J.W.; writing—original draft preparation, B.G., H.A. and M.H.; writing—review and editing, B.G. and H.A.; visualization, H.A., M.H., C.C. and J.W.; supervision, B.G.; project administration, B.G.; funding acquisition, B.G. All authors have read and agreed to the published version of the manuscript. Materials 2021, 14, 3346 21 of 23

Funding: United States Department of Energy through the Nuclear Energy University Program (Award No. DE-NE0008438). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available upon reasonable request from the corresponding author. Acknowledgments: The financial support for this project was provided by the United States Depart- ment of Energy through the Nuclear Energy University Program under the Award No. DE-NE0008438. The findings presented herein are those of the authors and do not necessarily reflect the views of the sponsor. Conflicts of Interest: The authors declare no conflict of interest.

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