Constitutive model for plain and fiber‐reinforced lightweight concrete under compression

In this research work, experimental investigations of the compressive behavior of plain and fiber‐reinforced lightweight‐aggregate concrete have been carried out (this formed part of a wider study, which also examined tensile and flexural behaviors). Compression mechanical properties were established in the studies and a generic constitutive compressive σ–ε model for both plain and fibrous lightweight concrete was derived and validated against experimental results from the present studies and previous research in the literature involving different types of lightweight aggregates, concrete strengths, and steel fibers. The reliability of predictions of the constitutive model was also checked against existing fibrous concrete models. A fiber‐reinforcing factor was also introduced taking into account the fiber volume fraction, fiber length and diameter, the number of fiber bends, and concrete compressive strength. As such, this was considered a better descriptor of the material than simply using the fiber volume fraction. The lightweight aggregates examined in the experimental study were recycled from fly ash waste and the fibers were hooked‐ended with single, double, and triple bends (corresponding to DRAMIX steel fibers 3D, 4D, and 5D types, respectively). The fibers were added at volume fractions Vf of 1% and 2% and the experimental studies were carried out using standard cube and cylinder uniaxial compression test specimens. It was concluded that the higher the number of bends and fiber content, the more pronounced the enhancement provided by the fibers to the compressive strength and ductility responses. All steel fibers used in the present studies were found to significantly improve the compressive toughness, while only 4D and 5D fibers (i.e., those with double and triple end bends) enhanced the compressive strength by up to 12% and 15%, respectively. It was also found that the elastic properties of plain lightweight concrete remained unaffected by the addition of fibers.


| INTRODUCTION
The use of structural lightweight aggregate concrete (LWAC) as a replacement to conventional normal-weight aggregate concrete (NWAC) is essentially aimed at decreasing gravity and inertial loads and increasing the strength-to-weight ratio. 1 This in turn leads to a reduction in cross-sectional sizes required for key elements such as columns, beams, slabs, and foundations and an increase in building space, 2 which promotes overall savings in materials, transport costs, and construction time.This has environmental benefits.In addition, the porous nature of LWAC brings several other advantages such as increased thermal insulation, noise absorption, and fire resistance. 3,4Besides, the lightweight aggregate used in the present experimental investigations is from recycled waste and thus offers further reduction in CO 2 emissions as well as being an alternative to the depleting gravel and quarried natural resources. 5The lightweight aggregates used are recycled fly ash waste (commercially known as LYTAG), which is a by-product of coal-fired electricity power stations. 6Fly ash, also termed Pulverized Fuel Ash (PFA), is the ash resulting from the burning of pulverized coal in these power stations.A study on LYTAG in 2014 showed that it can bring about 34% savings in CO 2 with reduction of up to 48% of concrete and reinforcement when compared to conventional gravel concrete. 7][10][11] Modern structural applications of LWAC also include bridges and towers.However, these advantages are tempered by the increased brittleness of lightweight concrete.The latter is thought to be the product of the more porous concrete matrix and poorer aggregate interlock mechanism in LWAC as compared to NWAC, which translates into lack of natural toughening mechanism post-crack. 53][14][15] Structural PFA-LWAC (i.e., LYTAG) has been around since the 1960s; however, limited comprehensive research has been carried out on its mechanical properties. 16,17Moreover, equations to define the material and structural properties of LWAC are usually adapted from studies in the last century based on NWC. 13,15,18,19he brittle nature of lightweight concrete can be addressed normally by incorporating traditional steel reinforcement.However, the latter solution can become increasingly impractical when reduction in structural element sizes is sought by employing LWAC, especially at critical zones such as joints.1][22][23][24] The earliest work examining the advantages of the usage of steel fibers in lightweight concrete have been reported several years ago. 257][28] Thus, the present comprehensive experimental investigations of fibrous recycled LWAC are beneficial for the rapidly developing concrete technology, since coal-fired power generation remains the largest contributor of energy in the world. 29Furthermore, it should be noted that, at present, there is no international standards specific for steel fiber-reinforced lightweight concrete (SFRLC) with current guidelines being usually adapted from their steel fiber-reinforced normal-weight concrete (SFRC) counterparts.So the findings of the present research study will help provide an insight into the structural responses of SFRLC and proposing a semiempirical constitutive model to predict the compressive stresses and strains of both LWAC and SFRLC.The research also serves to quantify the influence of multiple bend fibers on the pre-and post-peak compressive behavior of fibrous concrete.

| LITERATURE REVIEW
1][32][33] However, some disparity in results were reported concerning the influence of steel fiber reinforcement on the compressive behavior of lightweight concrete.This can be due to the different parameters inspected such as the target compressive strength, aggregate type, steel fiber type, its geometry, shape, and content.Some researchers who carried out compressive tests on SFRLC reported a negative influence on the compressive strength and modulus of elasticity and a positive influence on the compressive ductility as compared to plain LWAC.For instance, an experimental study on expanded clay lightweight concrete reinforced with straight micro steel fibers with volume fraction V f ≤ 1.25% in compression, reported a maximum decrease of 12% in compressive strength. 28Similarly, another study measured a decrease of 15% in the compressive strength of expanded clay lightweight concrete reinforced with hooked-end steel fibers with V f ≤ 0.5%. 24In addition, compressive tests were carried out on oil palm shell lightweight concrete reinforced with hooked-end steel fibers and found a decrease in compressive strength of 6.7% when V f > 0.5%, and an increase of 6% when V f < 0.5%. 11Finally, tests on shale ceramic reinforced with steel fibers with V f ≤ 0.9%, revealed that a maximum decrease of compressive strength of 18%. 2 Some researchers blamed the decrease in compressive strength of SFRLC on the reduction in fibrous specimens density caused by the presence of air voids due to the addition of fibers, especially noticeable when V f > 0.5%. 11,24On the other hand, some researchers observed an increase in both the compressive strength and ductility of expanded clay lightweight concrete as the fiber content was increased, while pumice lightweight concrete exhibited a reduction in compressive strength and increase in ductility as fiber content was increased. 34In the study, 34 the differences in the behavior of both types of lightweight concrete were attributed to the fiber length to maximum aggregate size ratio, which was lower and hence more favorable for the expanded clay aggregate as compared to the pumice aggregate.The aggregate size and type from different literature were used to validate findings of the present research.Similar to the expanded clay concrete responses reported in, 34 another study found an increase in compressive strength and ductility of oil palm shell concrete (OPSC) as fibers were added. 31They reported beneficial impact of steel fiber reinforcement on lightweight concrete, however, seems to be varied.5][36][37][38] Other researchers reported a drastic increase in compressive strength of lightweight concrete of up to 61% $ 72% with steel fiber reinforcement volume fractions of up to 2%. 8,32,33enerally, no detailed explanation was provided as to why steel fibers result in an increase in compressive strength, and merely observations were reported.The present research work will attempt to provide explanation to such behavior in Section 4. It was found that the increase in compressive strength is due to the activation of the fiber confinement effect on the concrete specimen, as the fibers bridge the lateral crack develping due to tension in the orthogonal direction.Moreover, it was observed that the effect of steel fiber reinforcement on compressive strength became more prominent as the lightweight aggregate content was increased. 39,40Scarce research was found on fibrous recycled fly-ash based LWAC such as LYTAG; so for instance, the latter was tested with V f ≤ 1% and found no particular pattern in relation to the compression strength when fibrous and plain lightweight concrete were compared. 26,41,42Further testing was also carried out to examine the effect of polypropylene (provided at a volume fraction V f = 0.56%) and steel (at V f = 1.7%) fibers on LYTAG fly-ash based high strength lightweight aggregate concrete and it was reported that a reduction in compressive strength of up to 11% was observed. 30Given the scatter in the results of SFRLC reported herein, there is an urgent need for further investigations on the compression behavior of SFRLC, particularly steel fiber-reinforced fly-ash based lighweight concrete.This work serves to offer more clarity and understanding on this key fundemental material behavior.The present experimental studies also culminate in deriving a compressive constitutive σ-ε model for SFRLC based on different hooked-end steel fiber types, geometries, contents, and plain concrete compressive strengths.Validation of the proposed model using experimental tests performed in the present studies as well as those found in the literature is also carried out.
There are different types of steel fibers including both engineered and natural/recycled ones.There is currently a rapid increase in the development of concrete utilizing different waste fibers due to potential economic and environmental benefits. 43Several studies were reviewed by Kalpana and Tayu 43 examining waste steel from steel reinforcement and formworks, which were mixed with structural light-weight concrete incorporating various fiber contents and this has resulted in preventing brittle failure in lightweight concrete.Improvements to strength were also reported, which were linked to optimum fiber dosages.Karalar et al. 44 experimentally examined beams with different amounts of longitudinal reinforcement and volume fractions of waste lathe scraps ranging from 1% to 3% and reported improvement in bending performance and also in compressive strength.Similar results were also reported on a study by Elik et al. 45 investigating the performance assessment of fiber-reinforced concrete produced with waste lathe fibers.Zeybek et al. 46 carried out experimental investigations to evaluate the performance of concrete reinforced with steel fibers extracted from waste tires with volume fractions 1%, 2%, and 3% (with compression, splitting tensile, and flexure tests carried out).It was found that the mechanical properties were improved with the addition of fibers; however, workability was significantly reduced with the addition of more than 2% volume fraction of fibers.Furthermore, empirical equations were developed to predict the compressive and splitting tensile strengths and strains.Limited experimental studies were carried out on lightweight concrete reinforced with steel fibers with multiple end hooks (i.e., 4D and 5D fibers), despite their increased use in normal weight concrete applications.Dehghani and Aslani 47 experimentally examined the effect of 3D, 4D, and 5D hooked-end type on the pull-out behavior of fibers embedded in cementitious composites and it was found that the use of more bends at hooked-end (i.e., 5D vs. 3D) significantly enhances the bond strength of fibers.Guler and Funda 48 carried out experimental work to examine the compressive and flexural strengths and toughness capacities of 3D, 4D, and 5D fibers under high temperatures and it was found that these capacities reduced significantly as temperature increased.Mohamed et al. 49 carried out a comprehensive review of research on the performance of steel fiber-reinforced lightweight concrete.It was found that the load-carrying capacity of SFRLC is increased by the addition of steel fibers, which also limits the spread of cracks and reduces their width.It was also concluded that, by making the concrete lighter, it is possible to provide economical solutions while limiting its deformation.

| Aggregate
LYTAG recycled sintered pulverized fly ash aggregates were used as the coarse aggregate of the lightweight concrete in the present experimental study.LYTAG aggregates (4-14 mm) are brown, roughly spherical with a honeycomb structure of interconnected voids, and sometimes irregular in shape as can be seen in Figure 1.LYTAG is fire resistant and highly stable at elevated temperatures with a specific gravity of about 1.8 and water absorption of up to 15%.Furthermore, LYTAG void ratio of about 40% makes it ideal in freeze and thaw conditions.Natural sharp sand with a maximum aggregate size of 4.75 mm was used as the fine aggregate of the concrete.The sand had a water absorption of 0.09% and specific gravity of 2.65 complying with BS EN 12620. 52Sieve analysis for both LYTAG and sand can be found in Figure 2. The percentage passing through 600 μmm of fine aggregate was found to be 51.2% in the sieve analysis.

| Fibers
DRAMIX hooked-end steel fibers with single-bend (3D), double-bend (4D), and triple-bend (5D) were used in the present experimental study. 53The fibers were essentially used to address the brittleness of lightweight aggregates and as conventional reinforcement replacement.It has been estimated that two thirds of the fibers used in the industry are hooked-end 3D steel fibers. 54For this reason, hooked-end 3D fibers were regarded as the control fibers during the experimental program, while the rest of the fibers were used for the purpose of evaluating the effects of different fiber geometries on the behavior of lightweight concrete.The three fiber types considered in the present experimental program are shown in Figure 3.The modulus of elasticity of these steel fibers is 210 GPa, while the tensile strength varies. 55The precise geometrical properties of the fibers and their hooks are illustrated in Table 1, which is adapted from Abdallah et al. 54,55 who electronically scanned identical fibers and processed the geometrical properties of the hooks using a computer software.The definitions of symbols L1, L2, L3, L4, θ1, and θ2 in Table 1 are shown in Figure 4.In order to F I G U R E 2 Sieve analysis for sand and LYTAG aggregates.
prevent the possibility of fibers balling during mixing, DRAMIX fibers were supplied collated together with a type of water dissolvable glue from the manufacturer.Collation was successful at reducing the possibility of fibers balling, thus allowing better fiber dispersion (in a similar manner to that reported by Balaguru and Foden 36 ).The comparison between the performance of these fibers offered an understanding of the contribution of extensive mechanical anchorage systems (hooks) on the compressive strengths and ductility of SFRLC.

| Mix proportions
A total of four mixes were cast with the design proportions shown in Table 2.These were adopted from LYTAG manuals 6 and the extensive experimental studies by Lambert. 16The quantity of fibers was calculated to be 78.5 and 157 kg per 1 m 3 of lightweight concrete for fiber contents of V f = 1 and 2%, respectively.It was opted not to use any superplasticisers or water reducers since the w/c of the mixes was relatively high, while fiber dosage was generally low (V f <2%).This further avoids adding an extra variable or limitation to the study.It is important to note that the quantities in Table 2 were increased by a factor of 15% upon mixing to account for any possible freshly mixed concrete losses during workability tests, casting, leveling, and vibration.Based on the mix designs provided by the manufacturer, 6 as the concrete target strength is increased, the quantity of sand is reduced, while that of cement is increased.The calculated dry density expected was around 1800 kg/m 3 .It should be noted that LYTAG mix design manual 6 recommends an effective water quantity of 180 kg/m 3 ; however, it was observed that this quantity contributes to an overly workable mix.Hence, it was suggested that the effective water was reduced to 175 kg/m 3 , which also agrees with recommendations from Lambert. 16A B L E 1 Properties of hooked-end fibers used 53 and geometrical properties of hooks are adapted from Abdallah et al. 54,55 Fiber type σ u (MPa)

3D 4D 5D
F I G U R E 3 Fibers used in this work.

| Specimen preparation
Average values for air dry, oven dry, and saturated surface dry (SSD) loose densities, along with those for the water content and maximum water absorption for LYTAG aggregates, were measured in the laboratory using 10 samples (Table 3).Measuring the water content of LYTAG was of utmost importance as LYTAG aggregates were found to absorb water of approximately 15% of their weight, which also agrees with LYTAG manual. 6Water absorption was determined based on BS EN 1097-6:2013. 56For this reason, LYTAG aggregates were completely submerged in water for 24 h prior to mixing to ensure maximum water absorption of the aggregates.On the day of mixing, LYTAG aggregates were then taken out of the water and surface dried for 10 min using a dry towel to achieve SSD state, then directly added to the mix.This is considered to be an effective way to achieve SSD as revealed in previous studies. 57This method guaranteed that the fresh concrete was workable at all stages, the compressive strength adequate, and surface finishing satisfactory.Sand was ovendried for 1 day at 100 C prior to mixing.It should be noted that a preliminary study requiring aggregates to be submerged in water 30 min before mixing with an effective water of 180 kg/m 3 as suggested by Lyag 6 resulted in overly high slump values and difficulty in finishing. 57,58he materials were mixed in a power-driven rotatory mixer with a capacity of 75 L using recommendations from the lightweight aggregate manufacturer's manual (Figure 5).Following mixing, the concrete was poured in molds in 3-5 layers depending on the size of the specimen and fiber content.Depending on the volume of the mix and its water/cement ratio, the time taken to vibrate the specimens varied from one mix to another, although good quality was ensured for surface finishing and even distribution of coarse LYTAG aggregates throughout the casting process.After casting, the specimens were wrapped with plastic sheets to prevent water evaporation and left in the concrete laboratory for 24 h at a temperature of 20 ± 2 C and humidity of 50 ± 5%.Finally, the specimens were demolded and cured in a water tank for 28 days prior to mechanical testing in accordance with BS EN 12390-2. 59

| Test methods
This work highlights crushing cube tests and uniaxial compression cylinder tests.Each mix included three repeated specimens per V f for both cubes and cylinders.This led to a total of nine cubes and nine cylinders per mix.Cylinders with height of 200 mm and diameter of 100 mm were used, while the cubes tested had a width of 100 mm.

| Compressive crushing cube test
In the present experimental studies, compressive crushing cube tests were an indicative of the consistency and quality of the mix design.These quick and simple tests were carried out (Figure 6) to directly measure the crushing strength of plain and fibrous lightweight concrete at 28 days.The loading rate used for these tests was 2.3 kN/s according to C39/C39M. 60

| Uniaxial compression cylinder test
Due to their uniform stress distribution, cylinders were chosen to evaluate the complete compressive stressstrain behavior of LWAC and SFRLC, including static modulus of elasticity and Poisson's ratio.A calibrated compressometer-extensometer steel ring designed according to ASTM C 469 61 was clamped onto the concrete cylinders as shown in Figure 7.The compressometer consisted of two yokes.The top one was free to rotate as it was pinned in two opposite points aligned with the center of the cylinder, while the bottom one was fully attached onto the cylinder using three bolts in a way that a straight line passing through a bolt and the center of the cylinder made an angle of 120 with the line passing through the neighboring bolt and the center of the cylinder.A pivot rod was used to maintain a constant distance between the two compressometer yokes.At mid-height of the cylinder, there was a relaxed Linear Variable Differential Transformer (LVDT), which measured the vertical displacement of the specimen.
To calculate the vertical deformation based on Figure 8, the following formula was used: where d, g, e r , and e g are the total deformation of the specimen (measured in mm), vertical LVDT gauge reading (measured in mm), the perpendicular distance between the clamped point of the rotating yoke and location of the pivot, and the perpendicular distance between the gauge and clamped point of the rotating yoke, respectively.Since distances e r and e g were set to be equal then: As shown in Figure 7, an extensometer was mounted circumferentially at opposite points.A pivot rod was also provided to maintain a constant distance between the bottom and middle yokes.The extensometer yoke was open in a way to allow an initially fully compressed LVDT at the middle height of the cylinder to be set up.This LVDT measured the transverse deformation.
By adopting a similar diagram to the one shown in Figure 7, the transverse deformation of the diameter can be calculated using: Mixing process for plain and fibrous lightweight concrete.
where d' and g' are the transverse deformation of the specimen diameter (mm) and the transverse LVDT gauge reading (mm), respectively.
To calculate the modulus of elasticity 61 : where S 1 , S 2 , ε 1 , and ε 2 are the stress at ε 1 (MPa), the stress at 40% of peak load (MPa), the strain of 0.000050 and the longitudinal strain at S 2 , respectively.
To calculate Poisson's ratio 61 : where ε t2 and ε t1 are the mid-height transversal strains at S 2 and S 1 , respectively.The exact placement of the compressometerextensometer ring along the height of the cylinder is shown in Figure 9. Before testing, a neoprene pad with a steel retainer was used according to ASTM C1231/ C1231M 62 to cap the cylinders and ensure a uniform distribution of the load at the uneven top surface of the cylinders.The neoprene capping method brought several advantages when compared to the classic sulfur capping method such as time saving in preparation of specimen, reduction in cost and safety of engineer and environment. 63In addition, unbounded neoprene capping does not alter the strength at the top surface of the concrete in comparison with other types of capping (such as sulfur and gypsum capping) provided that the correct hardness of the neoprene cap is chosen.In this work, neoprene pads of 60 shore hardness for strengths ranging between 10 and 48 MPa were used.Moreover, the caps can be applied easily and immediately unlike in the case for the common capping compounds, which also require safety equipment and experience in surface finishing.It should be noted that to ensure a nearly perfect contact between the loading platens and the top surface of the cylinders, a fine layer of cement not exceeding 5-mm thickness was mixed and applied on the top surface of the cylinders 2 days before testing to allow it to dry and gain a similar concrete strength (30-40 MPa).The purpose of this layer was to further cover any aggregates and fibers at the top surface of the cylinder, which could otherwise potentially cause damage to the neoprene cap and lead the load to be applied at an unfavorable angle resulting in premature failure.Hence, this fine cement layer ensured a better function of the neoprene pads, which resulted in better evaluation of the compressive σ-ε relationship, concrete strength f lcm , modulus of elasticity E lcm , and Poisson's ratio μ.A displacement-controlled loading rate of 1.2 mm/min was adopted as it was found to be the most suitable following trial tests to assess the effect of fibers on the brittle lightweight concrete and derive the full compressive σ-ε relationship.

| Workability
Slump tests according to BS EN 12390-2 59 were carried out immediately after mixing the concrete with the results reported in Table 4.For plain lightweight concrete, the mix proportion and specimen preparation techniques, detailed in Sections 3.2 and 3.3 of the present work, yielded satisfactory slump values and surface finishing of specimens.This agrees with previous work on plain LYTAG concrete. 16,64It can be seen that the addition of fibers drastically reduced workability.This was also observed by Swamy and Jojagha 65 who carried out workability tests on steel fiber-reinforced LYTAG concrete and Zeybek et al. 46 who carried out experimental investigations on concrete strengthened with recycled fibers from waste tires.At fiber dosage of V f = 2%, it was observed that the finishing process became challenging, the possibility for balling of fibers high, and inhomogeneity of concrete likely.This further emphasizes that for fibrous mixes, fiber dosage should not exceed V f = 1.5%-2% based on workability challenges if no superplasticizers or water reducing agents are used.Furthermore, this agrees with other researchers such as Düzgün et al. 39 who reported workability issues with V f > 1.5%.It also appears that the mixes having fibers with more extensive hooks held the slump together more tightly, which led to lower slump values than those mixes having fibers with less extensive hooks.It should be noted that the mixing and vibration time was increased as workability reduced owing to the increased need for compaction (this agrees with Düzgün et al. 39 ).

| Density
The average water-saturated density of the lightweight concrete produced was measured for each mix at 28 days after curing based on three cubes each with a width of 100 mm according to BS EN 12390-7. 65Oven-dry density was also measured for plain LYTAG according to BS EN 12390-7. 65,66The water-saturated densities were in the range of 1900-2000 kg/m 3 , while the oven-dry densities were in the range of 1700-1780 kg/m 3 for all specimens.The difference between densities of LWAC and SFRLC specimens appeared to be negligible, which may suggest the need of a better vibration technique and larger specimens to measure density to avoid potential size-effects with the usage of macro fibers.This agrees with several researchers. 2,11,28,33,41,67,68

| Crushing cube compressive strength
The mean compressive strength based on the crushing cube tests is shown in Table 5.The compressive strength values of fibrous cubes were identical or similar to those of plain cubes.Therefore, fiber reinforcement has little to no influence on the compressive strength of lightweight concrete.This observation was in line with Swamy et al.'s 26 findings who carried out compressive cube tests on fibrous LYTAG lightweight concrete.All failure patterns were satisfactory according to BS EN 12390-3. 69his was the case since all cubes' side faces failed due to lateral tensile expansion with little damage to top and bottom faces of the cubes confined by the platens (Figure 10).As previously discussed, little to no effect of any types of fibers was seen on the crushing compressive strength of lightweight concrete; however, a longer duration of time was recorded for the cube load to drop to 80% of the peak load at which point the test was stopped.This observation implied an increased ductility of the fibrous lightweight concrete cubes.Upon releasing the crushing machine steel plates, it was apparent that the cubes had been storing energy throughout the test via steel fibers and abruptly moved as an initially compressed spring.Further inspection of fibrous specimens revealed that the fibers acted as lateral confining elements for the cubes by bridging the cracks thus preventing the load from dropping instantly as in the case of plain concrete.The effect of fibers on ductility is further inspected by studying the uniaxial compressive stress-strain behavior of cylinders.orthogonal direction to the axial compressive load).The curves clearly show the enhancements provided by the fibers in comparison to the plain concrete samples, which will be discussed in detail in the following sections.Unlike normal weight concrete, which remains largely linear up until 30%-45% of maximum load, 70 plain PFA lightweight concrete's stress-strain tested in this work remained linear up until 60%-70% of peak load with fibrous specimens having the least linearity due to steel fibers presence initiating micro cracking in the concrete.Domagala 42 reported a stress-strain linearity of up to 90%-95% of the peak load for LWAC and 85% of the peak load for SFRLC specimens.The difference between the two results could be attributed to the more homogeneity of the lightweight concrete used in Domagala 42 due to its smaller PFA coarse aggregates of 4-8 mm with water absorption of 25%, in comparison to the present work's PFA coarse aggregates of 4-14 mm with water absorption of 15%.Overall, the rough surface and porous coarse lightweight aggregates seem to enable a better bond with cement, which makes it act as a monolithic material prolonging the linear behavior in the ascending portion of the compressive stress-strain curve, which is the case in Domagala's work.It also causes it to fail in a brittle pronounced manner once fracture develops due to the poor aggregate interlock mechanism, as also reported in Grabois et al., 24 Kayali et al., 30 and Domagala 42 as the aggregates themselves are fractured through unlike normal-weight aggregates, which fracture at the interface with mortar.Similar behavior was reported in pumice concrete as coarse aggregates develop high bond with cement due to their rough surface and increased porosity and water absorption. 21,33Expanded clay concrete with lower water absorption and smoother aggregates is less homogenous, which causes earlier cracking and less monolithic behavior, leading to fibers influencing the modulus of elasticity more effectively. 20,34he behavior of lightweight concrete can be split into three stages.During stage A, both LWAC and SFRLC cylinders experience a progressive linear load increase up to a load of 60%-70% of peak load corresponding to a strain of about 0.95‰, at which macro-cracking starts to take place in the middle section of the cylinder.This slightly reduces the secant modulus of elasticity and marks the start of stage B. As soon as a larger crack is formed, the cylinder specimens for plain lightweight concrete mixes collapse in a sudden manner (Figure 12a).This is attributed to the nature of lightweight aggregate, which  was observed to be sheared through at failure.This behavior agrees with several researchers. 24,30,42For fibrous lightweight concrete, however, stage B initiates a plateau-like behavior, which lasts up to a strain of within the interval of 2.5-3.2‰depending on the fiber dosage.The higher the V f , the larger the strain at peak.The macro cracking at the end of stage A initiated by the presence of fibers leads to the activation of fiberbridging mechanism preventing the formation of a larger shear crack at stage B. Furthermore, this causes redistribution of stresses via energy dissipation of multiple cracks unlike in the case of plain lightweight concrete.At stage C, as extensive lateral cracking dominates the post-peak behavior of the cylinders, the compressive load finally begins to decline in a ductile manner for the fibrous mixes.
It is interesting to note that upon inspection of cracking in the tested cylinder specimens, it was apparent that the cracks ran parallel to the direction of loading causing eventual splitting of the LWAC cylinders (as can be seen in Figure 12a), while a network of interconnected cracks being bridged by steel fibers was a typical cracking pattern of SFRLC cylinders (as shown in Figure 12b).Domagala 42 also reported similar cracking paths, although some instances where fibers failed to bridge cracks were reported.The latter was not observed in the current work probably due to the higher V f dosages used (1% and 2%) as compared to Domagala's work where the highest V f was 0.8%. 42Since none of the fibers were seen to rupture or break during the compression tests, the different maximum tensile strength of 3D, 4D, and 5D fibers was never reached, and thus did not take part in the behavior of SFRLC specimens.Hence, provided that fibers are normally activated following cracking, it is safe to assume that the extensive hooks or bends are only responsible for bridging the crack during phase B and providing a lateral confinement to the cylinder, which prevents the expansion of tensile cracking, therefore increasing the compressive strength.While 3D fibers with the basic mechanical hook (single bend) end up being pulled out more easily, 4D (double bend) and 5D (triple bend) fibers bond better to the brittle lightweight concrete increasing confinement and thus upgrading LWAC peak compressive strength.

| Elastic properties in compression
For LWAC and SFRLC specimens, Young's modulus of elasticity was calculated to be an average of 20.1, 19.7, 20.1, and 22.1 GPa for mixes 1, 2, 3, and 4, respectively, with no noticeable difference between LWAC and SFRLC specimens of the same mix (as can be seen in Figure 13).Kayali et al. 30 who carried out compression tests on high strength fibrous and plain lightweight concrete also reported a trivial influence on the modulus of elasticity as steel fibers were added, while Domagala 42 who carried out compression tests on plain and fibrous PFA concrete reported a similar trend in results as this work's for cubic and cylindrical compressive strengths and modulus of elasticity.These values remain somewhat lower than Eurocode 2 provisions, 69 which suggest 22.1, 22.8, and 23.4 GPa for LC30, LC35, and LC40, respectively.SFRLC cylinders did not exhibit a tangible variation in the elastic values of neither the modulus of elasticity nor Poisson's ratio from the plain concrete cylinders.
The measured Poisson's ratio values ranged between 0.15 and 0.20 for all LWAC and SFRLC specimens (Figure 14).These were also consistent with findings reported by Lambert who carried compression tests on plain PFA lightweight concrete. 16Therefore, modulus of elasticity and Poisson's ratio remained unaffected with the addition of hooked-end fibers to the lightweight concrete mix, whereas post-peak ductility substantially increased.This finding is consistent with work by Li et al. in which random hooked-end fibers in SFRC were found to have little to no effect on the modulus of elasticity, while slight favorable or unfavorable effect of fiber reinforcement on compressive strength can be seen. 71

| Cylinder compressive strength
From Figure 15, it is observed that (compared to 3D fibers), 4D and 5D fibers with extensive hooks were capable of further increasing the mean compressive strength of the cylinders regardless of the plain concrete's strength.On the other hand, there is an insignificant change in the compressive strength 3D fibers were used.The compressive strength for plain concrete of Mix 2 was increased by 5% and 12.2% when 4D fibers were added to LC30 with dosages of V f = 1% and 2%, respectively.Similarly, for Mix 4, the compressive strength for plain concrete was increased by 7.8% and 15% when 5D fibers were incorporated in the LC40 mix with dosages of V f = 1% and 2%, respectively.As reported earlier in Section 4.3 of the present study, the SFRLC cube compressive crushing strength was found to have no practical difference to that of LWAC counterparts.Nevertheless, there was a slight apparent increase in SFRLC cylinder compressive strength compared to that of corresponding LWAC samples.This can be attributed to the size effect of cylinder specimens in comparison to the length of fibers and the casting direction to loading direction, which is perpendicular for cubic specimens and parallel for cylindrical specimens.The latter's casting-loading arrangement is known to encourage favorable alignment of steel fibers to arrest cracks more efficiently.This concept was also discussed by Domagala. 42

| Compression toughness
The compression toughness was chosen to evaluate the energy absorption and post-peak ductility of SFRLC in compression.Similar to Liu et al. 2 who based their estimation of compression toughness on ASTM C 1018 72 approach, the compression toughness was calculated by dividing the total area up to a strain three times larger than the peak strain by the area up to the peak strain, under the compression σ-ε curve.Since plain lightweight concrete failed once compression peak was reached, the toughness was 1 for these specimens.Despite the little increase in compressive strength, especially for 3D fibers, the ductility was significantly enhanced by more than 2.5 times for Vf = 1% and close to three times for Vf = 2% (as depicted in Figure 16).It is interesting to see that the compressive toughness calculated for different concrete strengths with identical fiber reinforcement differed.While it is clear that the random distribution of fibers play an important factor in the latter, it is well established that the stronger the mix, the more brittle the concrete, which in turn lowers ductility. 30,73,74his is confirmed by the compression tests carried out.For instance, Mix 4 with the highest compressive strength f lck = 40 MPa reinforced with the triple bend 5D fibers provided the lowest compressive toughness when V f = 1% of all the cylinders of the same V f .However, for the same mix, when V f = 2% of 5D fibers were added to plain lightweight concrete cylinders, the increase in compression toughness was 18% higher than that of V f = 1%, which is the highest increase amongst all the cylinders tested.The latter comes as no surprise since 5D fibers were expected to offer more lateral confinement than the rest of the fibers, especially while having a stronger bond strength due to being mixed with stronger concrete.4D and 3D fibers led to 4% and 6% increase in compression toughness, respectively, when V f was increased from 1% to 2%.Since the compression toughness was increased by an average of 260% by adding fiber dosage of Vf = 1% and a sight further increase with Vf = 2%, it was concluded that the benefit of fiber reinforcement on compressive ductility is perhaps optimized at V f = 1%, with more benefit being reported with the highly brittle stronger concrete grades.

| Relationship between cylinder f lcm and cube f lcm,cube strengths
Due to the difference in confinement and slenderness, a higher compressive strength was calculated for cubes f lcm,cube than cylinders f lcm .Comparing the results from both plain and fibrous cylinders and cubes, the following relationship can be derived using linear regression analysis (with strengths measured in MPa) with R 2 = 0.94: One equation was deemed sufficient for both plain and fibrous PFA aggregate concrete as there was practically no difference in the compressive strength due to fibers, as discussed earlier.Based on table 11.3.1 from Eurocde 2 70 The Eurocode equation overestimates the mean cylinder strength by over 10% for stronger mixes with an overall average of $6% overestimation, while the proposed equation predicts the mixes' mean cylinder strength reasonably well with an average underestimation of $1%.

| Static modulus of elasticity
Modulus of elasticity appears to be connected to concrete compressive strength.This is also supported by Eurcodes and fib models. 70,75Based on linear regression analysis for both plain and fibrous lightweight concrete (with the modulus of elasticity measured in GPa), the following equation was derived to link E lcm to f lcm with R 2 = 0.96.
As observed from the compressive tests, it should be borne in mind that fibers have practically no effect on the elastic behavior of lightweight concrete.However as previously discussed, if the aggregate-cement bond is weak, the contribution of fibers can take place early on during loading due to fibers crack initiation, thus affecting the modulus of elasticity in a positive or a negative manner depending on fiber dosage and type.These lightweight aggregates are thought to be less rough or smooth with a lower water absorption.A comparison between the ratios of the predicted-to-experimental values of the moduli of elasticity can be found in Table 6.This is based on a total of 36 plain and fibrous cylinders tested in the present experimental investigations as well as using the most relevant equations derived by previous researchers.
As expected, Lambert's equation based on plain LYTAG predicted E lcm with good accuracy.Slate et al., 78 ACI318-89, 79 and Liu et al. 2 equations, which take into consideration the density of concrete, also predict E lcm of this work's tested specimens with high accuracy.Eurocode 2 63 overestimates E lcm , while the rest of the models appear to underestimate E lcm .
To check the validity of Equations ( 1) and ( 2) using experimental data established outside this work, the predictions of the proposed equations were compared with the results of these experiments as shown in Table 7.It should be noted that in some instances where only crushing cube strength was given, Equation ( 1) was used to derive f lcm , which was in turn input in Equation ( 2) to finally calculate E lcm (for instance: in the work of Liu et al. 2 where no compressive testing of cylinder was carried out).Overall, the regression power Equation (2) suggested was successful at predicting E lcm values for lightweight concrete of different lightweight aggregate types (such as expanded clay, expanded shale, pumice, PFA), different cement strengths (i.e., 42.5 and 52.5 MPa), plain compressive cube strengths (ranging from 19.5 MPa 16 to 87 MPa 20 ), fiber types (hooked end, crimped, opposite end), fiber materials (plastic, carbon, steel) and fiber volume fractions (ranging from 0.25% to 2%).Equation 2slightly overestimated E lcm of SFRLC specimens with aggregates that were smooth, had low water absorption, or developed too many air voids due to poor compaction. 30

| Poisson's ratio
Similar to the findings reported by Lambert, 16 Poisson's ratio appeared to be random between 0.15 and 0.20 (as can be seen in Figure 14).No particular relation linking Poisson's ratio to concrete strength, modulus of elasticity, fiber type, and dosage was formulated (although the general trend of both axial and lateral strains can be seen in Figure 11b).This behavior is identical to that of plain lightweight concrete and stems from the fact that fibers have no impact on the elastic behavior of lightweight concrete as discussed previously.In order for Poisson's ratio to be altered for fibrous concrete materials, fibers have to intervene earlier to provide either confinement to change the lateral strain or reinforcement similar to vertical rebars to change the axial strain.This does not occur until cracking has developed at stage B, as explained earlier in Section 4.4.1 of the present study.

| Fiber-reinforcing factor ρ f
Several researchers defined the fiber factor (or fiber- ][83][84][85] Although, this factor was used to develop empirical and semi-empirical equations for fibers of different shapes and material properties in the past, it has some shortcomings due to its generic and simplistic nature.For example, with regards to the hooked-end steel fibers used in this work, the fiber-reinforcing index does not quantify the effect of the different extensive mechanical hooks or bends on the properties of concrete.So, if a hooked-end fiber and a straight fiber shared identical aspect ratio L f /d f , the fiber-reinforcing index would be identical for both fibers.This translates to both fibers influencing the mechanical properties of a similar concrete in the same way, which is not accurate since the mechanical hooks in bent fibers enhance the mechanical properties of brittle concrete more than straight fibers.Khuntia et al. 86 defined a shape factor β to adjust the fiber-reinforcing index based on their geometry as follows V f (L f /d f ) β, with β = 1, 2/3, and 3/4 for SFRC with hooked-end or crimped steel fibers, plain, or round steel fibers and SFRLC with hooked-end or crimped steel fibers, respectively. 86While the latter equation is considered to be more comprehensive in comparison with the classical fiber reinforcing index, it does not take into consideration the geometrical and mechanical differences within the same fiber group such as the case between hooked-end 3D and 5D hooks, which enable the latter to display an improved performance under loading.Besides, it does not distinguish between fibers of different materials.For instance, plastic fibers and carbon fibers, which are usually straight and come in filaments exhibit bond strengths with concrete different to that of steel fibers.Hence, a new fiberreinforcing factor is proposed in the present research work to quantify the improvement in the behavior of SFRLC both in tension (in related experimental work) and compression, while considering different fiber types, geometries, aspect ratios, and materials; as expressed in Equation 3.
where V f is the fiber volume fraction (%), L f is the fiber length, L e is the effective fiber length, d f is fiber diameter, δ is the shape factor, and κ is the material factor.The shape factor δ is taken as 0.8 for straight fibers, 0.9 for crimped fibers, 1 for single hooked-end fibers (or fibers with n b = 1, such as 3D), 1.5 for double hooked-end fiber (or fibers with n b = 2, such as 4D), and 2 for triple hooked-end fiber (or fibers with n b = 3, such as 5D) with n b as the number of bends.The shape factors are chosen based on the maximum possible strength that can be developed from pull-out studies on DRAMIX 3D, 4D, and 5D fibers found in this work and also by Abdallah et al. 54,55,85,87 who used similar fibers in their study.The material factor κ is 1 for steel, 0.3 for plastic, and 0.1 for carbon fibers.These were based on comparison of the literature followed by inverse analysis.The effective fiber length L e is defined as the length required to develop the maximum pull-out strength of fiber based on pull-out tests, which are detailed elsewhere, with preliminary study found in Al-Naimi and Abbas. 58L e is calculated from the following expression: where L h is the fiber hook length for hooked-end fibers.L h is taken as 0 for both crimped and straight fibers.The fiber-reinforcing factor ρ f , which is a way to quantify the fiber-matrix interfacial bond, was used in the present work to derive the SFRLC uniaxial compressive σ-ε relationship.The fiber-reinforcing factors and fiberreinforcing index with V f = 1% for the different hookedend fibers used in this work are summarized in Table 8.
The second column in Table 8 refers to the proposed modified reinforcing factor and it is demonstrating the allowance for the number of fiber bends (unlike the last column showing the conventional factor, which remain unchanged for different fiber number of bends).Table 8 shows that, unlike the proposed fiberreinforcing factor ρ f , the conventional fiber-reinforcing index is incapable of assessing the effect of increasing the number of bends between 3D, 4D, and 5D on concrete.For this reason, ρ f appears to be a better estimate for quantifying the effect of fiber reinforcement on concrete.Thus, the fiber factor ρ f will be incorporated into material equations to derive a σ-ε constitutive model compressive using the experimental results of LWAC and SFRLC specimens tested in this work as well as those tested in previous research.

| Proposed constitutive compressive σ-ε model
The proposed compressive stress-strain model is depicted in Figure 17.For the tested LWAC specimens, the strain at peak load ε lc1 was equal to the strain at ultimate load ε lcu since concrete failed in a sudden brittle manner once it reached the peak strength.This also agrees with several researchers 24,42 and Eurocode 2. 70 This is the case because once the load has reached its peak strength, the lightweight aggregates end up being sheared through providing no resistance against cracking unlike in the case for normal weight aggregate concrete.Using the results from the uniaxial compressive cylinder tests, the strain at peak of plain lightweight concrete can be written as: where f lcm,p is the peak mean cylinder compressive strength of plain lightweight concrete.
For SFRLC specimens, however, the strain at peak strength and at ultimate strength were seen to be influenced by concrete strength and fiber-matrix interfacial bond, which is affected by fiber type, geometry, and dosage.Using regression analysis, the maximum concrete cylinder strength for both LWAC and SFRLC can be calculated using the following proposed expression: where ρ f is the fiber-reinforcing factor discussed earlier in the previous section.
Figure 18 shows the influence of fiber reinforcement on compressive strength of LWAC using Equation (6).It can be seen that when ρ f < 0.3 (corresponding to V f = 0.4% for 3D fibers), the influence of fibers on the compressive strength is trivial.The limit is shown herein using ρ f rather than V f to take into consideration the fiber shape, material, type, and geometry.Furthermore, to calculate the strain at peak of SFRLC with E lcm (MPa) calculated from Equation (2): This equation takes into account the increased brittleness when concrete strength grade is higher and so it adds a realistic concept of compression toughness and ductility.Adopting a second-order equation form, commonly used by several researchers such as Soroushian and Lee, 88 the complete compressive stress-strain for lightweight concrete can be derived from: Equation (8) for the calculation of the ascending part of the compressive stress-strain relationship, includes the definition of a plateau when f lc = f lcm depending on the value of factor α (Equation 11), which is based on the composite material peak elastic modulus calculated from E lcm,f = f lcm /ε lcf and the base composite material peak elastic modulus E b,f : E b,f is a constant that was empirically determined from the uniaxial cylinder compression tests in the present study and found to be equal to 21,150 MPa.
The slope of the descending branch z in Equation ( 9) can be determined from the following equation: f lcm,ult in Equation ( 10) is the ultimate residual post-peak axial compressive stress calculated using the following regression analysis equation: the comparisons between the experimental and predicted compressive stress-strain curves from mixes of different strengths, V f , and fiber types up to a strain of 0.014.Although generally conservative during the post-peak, the suggested model is seen to be successful at predicting the compressive strength and strain at peak.The predicted stress values remained accurate at all strain levels, while that of the peak compressive strength was predicted within 96% for all the tested specimens.
To further verify the adequacy of the proposed compressive stress-strain model for plain and fibrous lightweight concrete, the results of uniaxial compression tests on LWAC and SFRLC cylinders reported by Domagala 42 were predicted using compression models of other researchers 2,69,88,89 as well as the proposed compression model derived in the present study (and depicted in Figure 17) and the results are shown in Figures 23 and   24.It should be borne in mind that currently there is a scarcity in the compression stress-strain data for SFRLC, which prompted the current experimental research study.Besides, some existing data reported a decrease rather than an increase in compressive strength with fiber addition stemmed from poor bond (such as the case of plastic fiber) and poor compaction or mixing and thus they were not considered in the validation exercise. 30igures 23 and 24 show that the proposed model accurately predicted the modulus of elasticity (within 2% for both LWAC and SFRLC), peak compressive strengths (1% overestimation for LWAC and 5% underestimation for SFRLC), strains at peak (1% overestimation for LWAC and 3.5% underestimated for SFRLC) and post-peak ductility with good accuracy for both plain and fibrous cylinders in consideration.It should be noted that Eurocode 2 63 prediction clearly overestimated the modulus of elasticity and underestimated the strain at peak for LWAC.This is due to Eurocode 2 assumption for strain at peak of LWAC being lower than that of normal weight concrete.Such assumption has been shown to be inaccurate throughout the experimental tests of this work and others since the lower modulus of elasticity for LWAC results in   having a higher strain at peak than NWC for similar strengths.Liu et al. 2 also confirmed the latter based on 842 tests of plain and fibrous lightweight concrete cylinders.While Soroushian and Lee 88 and Ezeldin and Balaguru 89 stress-strain models seem to be more suitable for plain and fibrous normal weight concrete since they highly overestimated the modulus of elasticity for LWAC and SFRLC, Liu et al. 2 model prediction for plain and fibrous lightweight concrete is considered reasonable.Liu et al. 2 model predicted the modulus of elasticity within 1% for both SFRLC and LWAC, slightly underestimated the peak strength of SFRLC by 7% and overestimated the strain at peak of LWAC by 8%.Nonetheless, the strain at peak for SFRLC was overestimated by 20% and as a result, the ductility was overestimated.This is the case because unlike the proposed model, Liu et al. 2 model does not allow for the increased brittleness associated with higher concrete strength grades and simply an additional strain is derived based on the fiber-reinforcing index.This was also noticed in the rest of the models examined in the comparison where a factor of the fiberreinforcing index is added linearly to SFRLC concrete strength.This was proven to be too simplistic in this work, since the proposed constitutive model derives the peak compressive strengths and strains for fibrous concrete, while considering the improved fiber-matrix interfacial bond as well as the increased brittleness, as the concrete grade becomes higher.Based on the preceding discussion, the proposed compressive σ-ε for LWAC and SFRLC models are regarded as a viable and accurate predicting tool for the compressive behavior of plain and fibrous lightweight concretes with various concrete strengths, fiber types, geometries, and fiber volume fractions.

| CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK
In the present research work, experimental studies were carried out to examine the compressive behavior of recycled lightweight aggregate concrete reinforced with single and multiple-bend steel fibers.Consequently, the following conclusions and recommendations were made: • A unique generic constitutive compressive stressstrain model capable of predicting accurately the behavior of SFRLC composites was proposed.Due to the nature of the constitutive model and its related equations that depend mainly on fiber-reinforcing factor ρ f and plain concrete compressive strength, the model is deemed flexible and adaptable to other fibrous composites.• The proposed model's predicted pre-peak stress values remained accurate at all strain levels with the compressive strength being predicted within 96% for all the tested specimens, whilst the post-peak predictions were slightly conservative.Using a case study of LWAC and SFRLC, it was found that the proposed constitutive model is more reliable than some of the most established fibrous concrete models available in the literature.• In the present study, a new fiber-reinforcing factor ρ f is proposed, which is affected by concrete compressive strength, number of fiber bends, and fiber volume fraction.Due to this versatility and taking into account all the key parameters affecting the fiber-concrete interaction, the new fiber-reinforcing factor is considered to be more accurate and representative compared to the somewhat simplistic volume fraction V f usually used.• The uniaxial compressive behavior of fibrous concrete was found to be proportional to the fiber-reinforcing factor.• Due to the absence of an aggregate interlock mechanism, it was confirmed that LWAC, which acts as a monolithic material, fails in a brittle sudden manner once the peak strength is reached, due to the shearing through the coarse lightweight aggregate.This pronounced brittleness was the key reason for introducing lc MPa) ε Plain LWAC cylinder in compression F I G U R E 2 3 of LWAC with V f = 0%. 42MPa) ε SFRLC in compression V f = 0.8% F I U R E 4 of SFRLC compressive with V f = 0.8%.42 fibers to provide ductility.The effect of the incorporation of fiber reinforcement on lightweight concrete in compression was found to be more pronounced with the increase in plain concrete compressive strength, number of fiber bends, and fiber volume fraction.
• The addition of fibers to lightweight concrete was found to add compressive strength as the number of bends n b and fiber volume fraction V f were increased.The increase in peak compressive strength was insignificant for specimens with 3D fibers; however, those with 4D and 5D fibers exhibited an increase of up to 15% moving from V f = 0% to V f = 2%.This behavior is attributed to the capability of multiple hook fibers to bend more efficiently and provide confinement to the concrete specimens tested.• The compression toughness used to quantify ductility was found to increase as V f was increased.The compression toughness of plain lightweight concrete was increased by an average of 260% upon adding fiber dosage of 1% for all fiber types.A further insignificant increase of compression toughness of 5% on average was recorded at V f = 2% as compared to V f = 1% for both 3D and 4D specimens, while that of 5D specimens was increased by about 18%.• No practical effect on Poisson's ratio was found with the addition of fibers to the lightweight concrete mix, which was measured to be between 0.15 and 0.20.This was also the case for modulus of elasticity, which remained constant up to approximately 70% of peak strength.• Regression equations linking cube and compressive strengths, and static modulus of elasticity for both plain and fibrous lightweight concrete were derived based on the experimental program detailed in the present research work.These equations were also validated and were preceded an examination of a vast literature of SFRLC, which included different lightweight aggregate types, cement strengths, plain concrete compressive strengths, fiber types, fiber materials, and fiber volume fractions.The compression behavior proposed model main characteristics can serve to enrich codes and guidelines of plain and fibrous lightweight concrete.• While negligible influence of fibers was reported on density, workability of LWAC was found to be negatively affected by the addition of fibers especially with multiple-bend fibers (for example 5D) and at high fiber dosages such as V f > 1%.To address the latter issue, it is recommended that the lightweight concrete's coarse aggregates are mixed after achieving the SSD state with sand being fully oven-dried.Furthermore, the use of superplasticizers is recommended for mixes with V f > 1% as that will enhance the mixing process and mitigate risks of having voids and non-homogeneity in the mix.Another recommendation to enhance workability and avoid size effects would be to use bigger sections such 150 mm 3 cubes rather than 100 mm 3 .
Recommendations for future work are also made below.
• Further studies describing the stress-strain behavior of PFA lightweight fibrous concrete in compression.These should also serve to further validate the work in the present paper.• Validation of the constitutive models suggested in this paper using finite element analysis especially for different fiber types, volumes, and materials.• Carrying out experiments on both the material and structural levels on multiple bend fibers (described here as 4D and 5D fibers).• Using the fiber factor to investigate the effect of fibers on the tensile and shear behavior of lightweight concrete.

F
I G U R E 9 Instrumentation and test set-up for uniaxial compression cylinder test.F I G U R E 8 Calculation of deformations (adapted from ASTM C46955 ).

4. 4 |
Figure 11 depicts the complete uniaxial stress-strain curves of cylinders under compression, with both axial and lateral strains measured (the latter demonstrating the confinement effect provided by the fibers as they bridge the cracks developing due to tension in the

Note:
The values between brackets show the percentage change in strength in each mix compared to the plain concrete control specimen.a Average compressive strength from the test.b Manufacturer's characteristic strength.Satisfactory crushing failures of (a) LWAC cube and (b) SFRLC cube.
curves and (b) lateral tensile strain (shown alongside the axial compressive strain).

2 4 F I G U R E 1 3 4 F I G U R E 1 4
Typical crack patterns at failure of (a) plain cylinder and (b) fibrous cylinder LWAC.Measured modulus of elasticity values for the four mixes tested.Measured Poisson's ratio values for the four mixes tested.

4 F I G U R E 1 5 4 F I G U R E 1 6
Measured cylinder compressive strengths for the four mixes tested.Calculated compression toughness for the four mixes tested.flcm ¼ 1:75f 0:80 lcm,cube

1 F
G U R E 1 9 versus experimental compression σ-ε curves of Mix 1.

3 F I G R E 2 1 4 F I G R E 2 2
Predicted experimental uniaxial compression σ-ε curves of Mix 3. Predicted versus experimental uniaxial compression σ-ε curves of Mix 4.
Design of the four different mixes used in the experimental studies.
T A B L E 2 Note: Standard deviation values are shown between brackets.
T A B L E 5 Average values from crushing cube tests based on three cubes per V f .
Validation of E lcm values for both LWAC and SFRLC predicted using the proposed Equations (1) and (2) against the experimental data established by other researchers.
T A B L E 7 Note: Average values shown between brackets.a Plastic fiber-reinforced LWAC.b Medium strength and high strength cements are used.
T A B L E 8 Fiber reinforcing factor and fiber reinforcing index for the fibers used in this work.
Percentage increase of compressive strength with the addition of fibers as function of the fiber reinforcing factor ρ f .