Shaking Table Test of U-Shaped Walls Made of Fiber-Reinforced Foamed Concrete

Fiber-reinforced foamed concrete (FRFC) is a lightweight material that has the potential to perform well in seismic applications due to its low density and improved mechanical properties. However, studies focused on the seismic assessment of this material are limited. In this work, U-shaped wall specimens, made of FRFC reinforced with henequen fibers and plain foamed concrete (PFC) with a density of 900 kg/m3, were subjected to shaking table tests. PFC and FRFC were characterized using compression and tension tests. FRFC exhibited enhanced mechanical properties, which were attributed to the fibers. The dynamic tests showed that U-shaped walls made of FRFC performed better than those made of PFC. The time period prior to the collapse of the FRFC U-shaped walls was longer than that of the PFC specimens, which was attributed to the enhanced specimen integrity by the fibers. Finite element simulations of the shaking table test allowed for the prediction of the stress concentration and plastic strain that may lead to the failure of the U-shaped wall. These results showed that U-shaped walls made of FRFC have the potential to perform well in seismic applications, however, these results are preliminary and further studies are needed to support the findings of this work.


Introduction
Unreinforced masonry (URM) structures, such as those made of adobe, clay, bricks, or blocks, are used in many parts of the world because they are inexpensive, relatively easy to build and utilize locally available materials. However, in many cases, URM structures are unregulated, and are built using simple technology and low-quality construction practices [1]. One major concern is that URM construction is still widely used in areas prone to seismic activity. URM structures are highly susceptible to damage from earthquakes [2], meaning that a major earthquake could cause significant human and economic losses. URM structures are particularly vulnerable to seismic events because they are not capable of dissipating energy through large plastic deformations during an earthquake, due to their lack of ductility [3]. Moreover, URM buildings may also have insufficient strength to resist seismic load due to the absence of connections between wall leaves, poor adhesion of the mortar and the presence of voids [1]. The failure of earthen buildings during an earthquake is mainly due to its low growing because it is possible to obtain materials with low density and good mechanical properties that promote sustainability [41]. In addition, natural fibers are low-cost renewable materials that can be found in abundant supply in many countries [42]. Recent investigations performed on foamed concrete reinforced with natural fibers, such as kenaf [33], coir [43], sisal [44], and henequen [45] fibers, among others, have found that there is an enhancement of the compressive, tensile, and flexural strengths when compared to non-reinforced foamed concrete.
Based on the aforementioned literature, fiber-reinforced foamed concrete (FRFC) has the potential to perform well in structural and seismic applications due to its low density and improved toughness and ductility by the fibers, effectively reducing the risk of earthquake damage, however, studies focusing on the seismic assessment of this type of material are limited in the literature. Hence, the objective of the present study is to investigate the seismic performance of FRFC with a density of 900 kg/m 3 , reinforced with the natural fiber henequen (Agave fourcroydes Lem.), which is one of the main cultivated species of Agave used to produce fibers in the south of Mexico. For this investigation, the dynamic cyclic loading response of U-shaped wall model specimens made of FRFC was studied by means of shaking table tests with a sinusoidal excitation, and the results were compared with those of non-reinforced foam concrete specimens. The mechanical characterization of the foamed concrete was performed using compression and tension tests. Finite-element (FE) simulations of the dynamic loading of U-shaped walls were performed to predict stress concentration that may lead to failure and improve the design of the U-shaped walls.

Fiber-Reinforced Foam Concrete
The foamed concrete mixture used in this study to fabricate the U-shaped wall specimens was prepared using the pre-foaming method [35], which consisted of 3 stages: (1) preparation of the mortar, (2) preparation of the foam, and (3) mixing of mortar and foam. A target dry density of 900 kg/m 3 was used. The mixture was prepared using the following constituents for 1 m 3 : Portland cement CPC 30R EXTRA (CEMEX, Merida, Mexico) with a minimum strength of 30 MPa at 28 days (427 kg), dry sand (214 kg), water (299 kg), and foam (EABASSOC foaming agent, EAB Associates, Altrincham, UK) (24 kg). The materials were mixed in a 60-L mixer STARK (Stark Tools USA, Chino, CA, USA) until a homogeneous mixture was obtained. The mixture without fibers is referred to as plain foamed concrete (PFC). For the fiber-reinforced foamed concrete (FRFC), henequen fibers were gradually distributed, at random, by hand in small amounts into the mixture at the end of stage 3, at a fiber volume fraction of 0.5%. Henequen fibers were supplied by local producers (Desfibradora La Lupita, Baca, Mexico). A fiber length of~4 mm was used ( Figure 1a). As a reference, the reported mechanical properties of henequen fibers are: density of 1400 kg/m 3 , elastic modulus of 13.2 GPa, tensile strength of 500 MPa, and diameter of 170 µm [46]. Since the main purpose of this work was to evaluate the effect of the presence of fibers on the dynamic response of the U-shaped walls made of FRFC, fiber treatment to improve durability was not performed.
Materials 2020, 13, x FOR PEER REVIEW 3 of 17 materials that can be found in abundant supply in many countries [42]. Recent investigations performed on foamed concrete reinforced with natural fibers, such as kenaf [33], coir [43], sisal [44], and henequen [45] fibers, among others, have found that there is an enhancement of the compressive, tensile, and flexural strengths when compared to non-reinforced foamed concrete. Based on the aforementioned literature, fiber-reinforced foamed concrete (FRFC) has the potential to perform well in structural and seismic applications due to its low density and improved toughness and ductility by the fibers, effectively reducing the risk of earthquake damage, however, studies focusing on the seismic assessment of this type of material are limited in the literature. Hence, the objective of the present study is to investigate the seismic performance of FRFC with a density of 900 kg/m 3 , reinforced with the natural fiber henequen (Agave fourcroydes Lem.), which is one of the main cultivated species of Agave used to produce fibers in the south of Mexico. For this investigation, the dynamic cyclic loading response of U-shaped wall model specimens made of FRFC was studied by means of shaking table tests with a sinusoidal excitation, and the results were compared with those of non-reinforced foam concrete specimens. The mechanical characterization of the foamed concrete was performed using compression and tension tests. Finite-element (FE) simulations of the dynamic loading of U-shaped walls were performed to predict stress concentration that may lead to failure and improve the design of the U-shaped walls.

Fiber-Reinforced Foam Concrete
The foamed concrete mixture used in this study to fabricate the U-shaped wall specimens was prepared using the pre-foaming method [35], which consisted of 3 stages: (1) preparation of the mortar, (2) preparation of the foam, and (3) mixing of mortar and foam. A target dry density of 900 kg/m 3 was used. The mixture was prepared using the following constituents for 1 m 3 : Portland cement CPC 30R EXTRA (CEMEX, Merida, Mexico) with a minimum strength of 30 MPa at 28 days (427 kg), dry sand (214 kg), water (299 kg), and foam (EABASSOC foaming agent, EAB Associates, Altrincham, UK) (24 kg). The materials were mixed in a 60-L mixer STARK (Stark Tools USA, Chino, CA, USA) until a homogeneous mixture was obtained. The mixture without fibers is referred to as plain foamed concrete (PFC). For the fiber-reinforced foamed concrete (FRFC), henequen fibers were gradually distributed, at random, by hand in small amounts into the mixture at the end of stage 3, at a fiber volume fraction of 0.5%. Henequen fibers were supplied by local producers (Desfibradora La Lupita, Baca, Mexico). A fiber length of ∼4 mm was used ( Figure 1a). As a reference, the reported mechanical properties of henequen fibers are: density of 1400 kg/m 3 , elastic modulus of 13.2 GPa, tensile strength of 500 MPa, and diameter of 170 µm [46]. Since the main purpose of this work was to evaluate the effect of the presence of fibers on the dynamic response of the U-shaped walls made of FRFC, fiber treatment to improve durability was not performed.

Mechanical Properties of Foamed Concrete
To evaluate the mechanical behavior of the foamed concrete mixtures, uniaxial compression tests were performed according to the BS-EN-12390 using cubical specimens with dimensions of 100 mm × 100 mm × 100 mm (Figure 1b). The specimens were tested in a Shimadzu AG-1 universal

Mechanical Properties of Foamed Concrete
To evaluate the mechanical behavior of the foamed concrete mixtures, uniaxial compression tests were performed according to the BS-EN-12390 using cubical specimens with dimensions of 100 mm × 100 mm × 100 mm (Figure 1b). The specimens were tested in a Shimadzu AG-1 universal testing machine (Shimadzu Corporation, Kyoto, Japan), equipped with a load cell of 100 kN, at a crosshead speed of 2.4 mm/min. The tensile behavior of the foamed concrete mixtures was also evaluated in accordance with the ASTM C307 (ASTM International, West Conshohocken, PA, USA) using dog-bone shaped specimens with a length of 76 mm and a cross-section area of 25.4 mm × 25.4 mm. The specimens were placed in a Shimadzu AG-1 universal testing machine, equipped with a load cell of 20 kN, and loaded in direct uniaxial tension at a displacement rate of 1 mm/min until failure ( Figure 1c). All specimens were left to cure for at least 28 days before testing. Figure 2a shows typical stress-strain curves for the PFC and FRFC specimens obtained from the compression tests. It can be seen in Figure 2a that the foamed concrete specimens exhibit an initial elastic response at very low strains, until a peak strength is reached at a strain of~0.014, followed by a sudden drop in stress, which corresponds to the initial failure of the specimen. After the elastic regime, both PFC and FRFC specimens can withstand a percentage of the maximum strength at increasing strains (39% and 50% of the maximum strength for PFC and FRFC specimens, respectively, at a strain of 0.15). This percentage is higher for the FRFC, which is attributed to the enhanced integrity and toughness of the specimens by the fibers. Figure 2b shows typical stress-strain curves from the uniaxial tension tests for both PFC and FRFC. For PFC, an elastic regime is observed until the peak strength is reached at a strain of 0.023, which is followed by a sudden failure of the specimen. For FRFC, the fibers prevented a sudden failure of the specimen; after the peak strength is reached at strain of 0.027, specimens can withstand a percentage of the maximum strength as the displacement increases (9.2% of the maximum strength at a strain of 0.05). Moreover, an increase of 37% in the tensile strength was observed for the FRFC specimens when compared to the PFC. evaluated in accordance with the ASTM C307 (ASTM International, West Conshohocken, PA, USA) using dog-bone shaped specimens with a length of 76 mm and a cross-section area of 25.4 mm × 25.4 mm. The specimens were placed in a Shimadzu AG-1 universal testing machine, equipped with a load cell of 20 kN, and loaded in direct uniaxial tension at a displacement rate of 1 mm/min until failure ( Figure 1c). All specimens were left to cure for at least 28 days before testing. Figure 2a shows typical stress-strain curves for the PFC and FRFC specimens obtained from the compression tests. It can be seen in Figure 2a that the foamed concrete specimens exhibit an initial elastic response at very low strains, until a peak strength is reached at a strain of ∼0.014, followed by a sudden drop in stress, which corresponds to the initial failure of the specimen. After the elastic regime, both PFC and FRFC specimens can withstand a percentage of the maximum strength at increasing strains (39% and 50% of the maximum strength for PFC and FRFC specimens, respectively, at a strain of 0.15). This percentage is higher for the FRFC, which is attributed to the enhanced integrity and toughness of the specimens by the fibers. Figure 2b shows typical stress-strain curves from the uniaxial tension tests for both PFC and FRFC. For PFC, an elastic regime is observed until the peak strength is reached at a strain of 0.023, which is followed by a sudden failure of the specimen. For FRFC, the fibers prevented a sudden failure of the specimen; after the peak strength is reached at strain of 0.027, specimens can withstand a percentage of the maximum strength as the displacement increases (9.2% of the maximum strength at a strain of 0.05). Moreover, an increase of 37% in the tensile strength was observed for the FRFC specimens when compared to the PFC. Table 1 shows the mechanical properties of the foamed concrete mixtures, obtained from the compression and tension tests, which include the compressive and tensile strengths. The results are presented as mean ± standard deviation of at least three repetitions. It can be seen that, in general, the fiber-reinforcement enhanced the mechanical properties of the FRFC when compared to those of the PFC, which is attributed to the enhanced specimen integrity produced by the fibers [35]. It is noted that compressive elastic strain was not accurately measured due to the lack of strain gauges. For a foamed concrete with a density of 900 kg/m 3 , the elastic modulus is in the range of 1.5-2 GPa [47,48]. The density ρ of the mixtures shown in Table 1 was calculated using ρ = W/V, where W (kg) is the weight of the cubical specimens, measured using an analytical balance Ohaus EB6 (Ohaus Corporation, Parsippany, NJ, USA), and V (m 3 ) is their volume. V was calculated using the dimensions measured by a digital caliper with a resolution of 0.05 mm (Truper, Mexico City, Mexico).   Table 1 shows the mechanical properties of the foamed concrete mixtures, obtained from the compression and tension tests, which include the compressive and tensile strengths. The results are presented as mean ± standard deviation of at least three repetitions. It can be seen that, in general, the fiber-reinforcement enhanced the mechanical properties of the FRFC when compared to those of the PFC, which is attributed to the enhanced specimen integrity produced by the fibers [35]. It is noted that compressive elastic strain was not accurately measured due to the lack of strain gauges. For a foamed concrete with a density of 900 kg/m 3 , the elastic modulus is in the range of 1.5-2 GPa [47,48]. The density ρ of the mixtures shown in Table 1 was calculated using ρ = W/V, where W (kg) is the weight of the cubical specimens, measured using an analytical balance Ohaus EB6 (Ohaus Corporation, Parsippany, NJ, USA), and V (m 3 ) is their volume. V was calculated using the dimensions measured by a digital caliper with a resolution of 0.05 mm (Truper, Mexico City, Mexico).

U-Shaped Wall Specimens
To investigate the dynamic cyclic behavior of foamed concrete walls, 1:7.5 scaled U-shaped wall models were fabricated. The scaled U-shaped wall structure is intended to represent a wall section of a typical house, in the rural areas, in the state of Oaxaca, Mexico [49,50]. The geometrical details of the U-shaped wall with a cross-section thickness of 20 mm are described in Figure 3a. Although a preliminary study showed that adequate fiber dispersion can be achieved in the mixtures for fiber volume fractions of up 1%, a fiber volume fraction of 0.5% was selected for this work to ensure adequate fiber dispersion and workability of the mixture, considering the thickness of the U-shaped walls. However, further studies should be performed using different fiber volume fractions to find a balance between workability and mechanical properties. To fabricate the U-shaped walls, a mold was manufactured as shown in Figure 3b. The foamed concrete mixture was prepared as aforementioned and cast into the mold (Figure 3c). The U-shaped wall specimens were left to cure for at least 28 days at room temperature before testing. In total, six U-shaped wall specimens were fabricated, i.e., three specimens using the PFC mixture and three specimens using the FRFC mixture ( Figure 3d). The average mass of the U-shaped wall specimens made of PFC and FRFC was 5.09 and 5.44 kg, respectively.

U-Shaped Wall Specimens
To investigate the dynamic cyclic behavior of foamed concrete walls, 1:7.5 scaled U-shaped wall models were fabricated. The scaled U-shaped wall structure is intended to represent a wall section of a typical house, in the rural areas, in the state of Oaxaca, Mexico [49,50]. The geometrical details of the U-shaped wall with a cross-section thickness of 20 mm are described in Figure 3a. Although a preliminary study showed that adequate fiber dispersion can be achieved in the mixtures for fiber volume fractions of up 1%, a fiber volume fraction of 0.5% was selected for this work to ensure adequate fiber dispersion and workability of the mixture, considering the thickness of the U-shaped walls. However, further studies should be performed using different fiber volume fractions to find a balance between workability and mechanical properties. To fabricate the U-shaped walls, a mold was manufactured as shown in Figure 3b. The foamed concrete mixture was prepared as aforementioned and cast into the mold (Figure 3c). The U-shaped wall specimens were left to cure for at least 28 days at room temperature before testing. In total, six U-shaped wall specimens were fabricated, i.e., three specimens using the PFC mixture and three specimens using the FRFC mixture ( Figure 3d). The average mass of the U-shaped wall specimens made of PFC and FRFC was 5.09 and 5.44 kg, respectively.

Shaking Table Test and Instrumentation
The U-shaped wall specimens were subjected to dynamic cyclic loading using a single-axis shaking  table Quanser Shake Table II (Quanser Consulting Inc., Markham, ON, Canada) [51]. Figure 4a shows the test set-up, in which, the U-shaped wall specimen is mounted on a wooden base, with dimensions of 800 mm × 500 mm × 18 mm, using steel slotted angles. The wooden base is then attached to the shaking table using screws and nuts. A mass of 1.4 kg was mounted at the top of each flange using steel strips (Figure 4b), to simulate the mass of a roof [52]. Slotted angles were used to connect the steel strips to the flanges. The average total mass of the structure (base, wall, steel strips and connectors) was 13.25 kg. The U-shaped wall specimens were subjected to a 4-Hz sinusoidal base motion with an amplitude of 20 mm, parallel to the web segment (Figures 3d and 4a), until failure occurred. A linear variable differential transformer (LVDT) Micro Measurements HS100 (Vishay Precision Group, Malvern, PA, USA), with a displacement range of 100 mm, was used to record the displacement of the left flange ( Figure 4b). A single-axis accelerometer Kistler 10 g PiezoBeam (Kistler Group, Winterthur, Switzerland), with a range of ±98 m/s 2 , was attached to the right flange to record its acceleration history during the test (Figure 4b). A fast camera Sony Cyber-shot DSC-RX100 IV (Sony Corporation, Tokyo, Japan) recording at 120 frames per second was used to capture the failure of the U-shaped wall specimens during the shaking table test (Figure 4a).

Shaking Table Test and Instrumentation
The U-shaped wall specimens were subjected to dynamic cyclic loading using a single-axis shaking  [51]. Figure  4a shows the test set-up, in which, the U-shaped wall specimen is mounted on a wooden base, with dimensions of 800 mm × 500 mm × 18 mm, using steel slotted angles. The wooden base is then attached to the shaking table using screws and nuts. A mass of 1.4 kg was mounted at the top of each flange using steel strips (Figure 4b), to simulate the mass of a roof [52]. Slotted angles were used to connect the steel strips to the flanges. The average total mass of the structure (base, wall, steel strips and connectors) was 13.25 kg. The U-shaped wall specimens were subjected to a 4-Hz sinusoidal base motion with an amplitude of 20 mm, parallel to the web segment (Figures 3d and 4a), until failure occurred. A linear variable differential transformer (LVDT) Micro Measurements HS100 (Vishay Precision Group, Malvern, PA, USA), with a displacement range of 100 mm, was used to record the displacement of the left flange (Figure 4b). A single-axis accelerometer Kistler 10g PiezoBeam (Kistler Group, Winterthur, Switzerland), with a range of ±98 m/s 2 , was attached to the right flange to record its acceleration history during the test (Figure 4b). A fast camera Sony Cyber-shot DSC-RX100 IV (Sony Corporation, Tokyo, Japan) recording at 120 frames per second was used to capture the failure of the U-shaped wall specimens during the shaking table test (Figure 4a). Figure 5a,b show the acceleration-time and displacement-time histories, respectively, measured by the built-in sensors of the shaking table. A 10-Hz low-pass digital filter was applied to the acceleration signal in order to eliminate noise. It can be seen in Figure 5 that after ∼1.5 s, the maximum acceleration and displacement of the shaking table are around ±12.5 m/s 2 and ±19.8 mm, as expected, for the abovementioned sinusoidal excitation parameters.

Numerical Simulations
The numerical simulations of the U-shaped wall, subjected to dynamic cyclic loading, were performed using the finite-element (FE) software Abaqus/Explicit (Version 2016, Dassault Systèmes Simulia Corp., Providence, RI, USA) [53]. The FE simulation was employed as a tool to investigate localized stress concentration and plastic strain that may lead to cracking and failure during the dynamic loading. The geometry of the 3D FE model was based on the U-shaped wall and shaking table test described in Section 2.3 and 2.4, respectively. The FE model consisted of a U-shaped wall, wooden base, steel angles, and steel strips (Figure 6a). The mesh comprised 8-node brick elements (C3D8R) with reduced integration formulation. The base, steel strips and angles were modelled as rigid bodies. A global element size of 10 mm was used. For the U-shaped wall, an average element size of 7 mm was used, giving a total of 11,520 elements. The steel angles were tied to the base, steel strips and wall using the Tie Constraint option (fully bonded).
Steel parts and wooden base were modelled using densities of 7800 and 500 kg/m 3 , respectively. The elastic behavior of the foamed concrete material used for the U-shaped wall was modelled using a compression elastic modulus of E = 2 GPa, Poisson's ratio of ν = 0.05 and density of ρ = 900 kg/m 3 .
The plastic behavior was modelled using the Crushable Foam material model with the following parameters: compression yield stress ratio k = 1 and hydrostatic yield stress ratio kt = 0.1 [35]. For the Crushable Foam model hardening tabular data, experimental curves from the uniaxial quasi-static compression test (Figure 2a) were used [54]. A failure criterion, to simulate failure of the material, was not implemented due to the lack of fracture parameters.
Gravity load was applied to the entire model as a vertical acceleration field (−9.806 m/s 2 ). To simulate the dynamic cyclic loading of the shaking table, the displacement-time history curve from Figure 5b was input in tabular form and applied to the wooden base as a prescribed displacement boundary condition. The total time of the simulated dynamic loading was 3 s. To investigate the effect of the shape of the wall corners on the stress concentration, in addition to the wall with flat corners (Figure 6b), a wall with round corners (inner and outer radii of 20 and 40 mm, respectively) was also modelled (Figure 6c).
A mesh sensitivity analysis was carried out using three different element sizes: 10 mm (coarse mesh), 7 mm (intermediate mesh) and 5 mm (fine mesh), resulting in 2, 3, and 4 through-thickness elements, and a total of 4374, 11,520, and 34,556 elements, respectively. Figure 7 shows the contour plots of the predicted maximum principal stress for the U-shaped wall with flat corners subjected to dynamic loading (t = 1.89 s) using different element sizes. It is noted that in Figure 7, for illustration purposes, the deformation in the direction of motion has been scaled up by a factor of 50 to visualize the bending of the specimens. It can be seen that the stress contours are similar for the intermediate (Figure 7b) and fine (Figure 7c) meshes, while for the course mesh, the stress contour is different (Figure 7a). The model using the intermediate mesh predicted a maximum stress value ∼18% higher than that of the model using the fine mesh, while the model using the course mesh predicted a

Numerical Simulations
The numerical simulations of the U-shaped wall, subjected to dynamic cyclic loading, were performed using the finite-element (FE) software Abaqus/Explicit (Version 2016, Dassault Systèmes Simulia Corp., Providence, RI, USA) [53]. The FE simulation was employed as a tool to investigate localized stress concentration and plastic strain that may lead to cracking and failure during the dynamic loading. The geometry of the 3D FE model was based on the U-shaped wall and shaking table test described in Sections 2.3 and 2.4, respectively. The FE model consisted of a U-shaped wall, wooden base, steel angles, and steel strips (Figure 6a). The mesh comprised 8-node brick elements (C3D8R) with reduced integration formulation. The base, steel strips and angles were modelled as rigid bodies. A global element size of 10 mm was used. For the U-shaped wall, an average element size of 7 mm was used, giving a total of 11,520 elements. The steel angles were tied to the base, steel strips and wall using the Tie Constraint option (fully bonded).   Steel parts and wooden base were modelled using densities of 7800 and 500 kg/m 3 , respectively. The elastic behavior of the foamed concrete material used for the U-shaped wall was modelled using a compression elastic modulus of E = 2 GPa, Poisson's ratio of ν = 0.05 and density of ρ = 900 kg/m 3 . The plastic behavior was modelled using the Crushable Foam material model with the following parameters: compression yield stress ratio k = 1 and hydrostatic yield stress ratio k t = 0.1 [35]. For the Crushable Foam model hardening tabular data, experimental curves from the uniaxial quasi-static compression test (Figure 2a) were used [54]. A failure criterion, to simulate failure of the material, was not implemented due to the lack of fracture parameters.
Gravity load was applied to the entire model as a vertical acceleration field (−9.806 m/s 2 ). To simulate the dynamic cyclic loading of the shaking table, the displacement-time history curve from Figure 5b was input in tabular form and applied to the wooden base as a prescribed displacement boundary condition. The total time of the simulated dynamic loading was 3 s. To investigate the effect of the shape of the wall corners on the stress concentration, in addition to the wall with flat corners (Figure 6b), a wall with round corners (inner and outer radii of 20 and 40 mm, respectively) was also modelled (Figure 6c).
A mesh sensitivity analysis was carried out using three different element sizes: 10 mm (coarse mesh), 7 mm (intermediate mesh) and 5 mm (fine mesh), resulting in 2, 3, and 4 through-thickness elements, and a total of 4374, 11,520, and 34,556 elements, respectively. Figure 7 shows the contour plots of the predicted maximum principal stress for the U-shaped wall with flat corners subjected to dynamic loading (t = 1.89 s) using different element sizes. It is noted that in Figure 7, for illustration purposes, the deformation in the direction of motion has been scaled up by a factor of 50 to visualize the bending of the specimens. It can be seen that the stress contours are similar for the intermediate (Figure 7b) and fine (Figure 7c) meshes, while for the course mesh, the stress contour is different (Figure 7a). The model using the intermediate mesh predicted a maximum stress value~18% higher than that of the model using the fine mesh, while the model using the course mesh predicted a maximum stress value~36% lower than that of the model using the fine mesh. The fine mesh could improve the accuracy of the solution; however, this results in a significant increase in the computational cost. Based on this analysis, the intermediate mesh size was deemed sufficient for convergence and used throughout this work to increase the computational efficiency.     Figure 8a,c that there are large acceleration values (>20 m/s 2 ), which indicate the collapse of the right flange. In Figure 8b,d, displacements larger than 20 mm correspond to the collapse of the left flange. For the PFC Specimen #1, the test stopped prematurely, after the collapse of the right flange. It is noted that for some specimens, the right flange (RF) was the first to fail, while for other specimens, the left flange (LF) was the first to fail. It is also noted that for some specimens both flanges collapsed during the test, while for other specimens, only one flange collapsed. Table 2 shows the period of time from the beginning of the test to the formation of the first visible crack, and then to the time of collapse of the first flange. In the cases where a second flange failed, Table 2 also shows the period of time from the beginning of the test to   Figure 8a,c that there are large acceleration values (>20 m/s 2 ), which indicate the collapse of the right flange. In Figure 8b,d, displacements larger than 20 mm correspond to the collapse of the left flange. For the PFC Specimen #1, the test stopped prematurely, after the collapse of the right flange. It is noted that for some specimens, the right flange (RF) was the first to fail, while for other specimens, the left flange (LF) was the first to fail. It is also noted that for some specimens both flanges collapsed during the test, while for other specimens, only one flange collapsed. Table 2 shows the period of time from the beginning of the test to the formation of the first visible crack, and then to the time of collapse of the first flange. In the cases where a second flange failed, Table 2 also shows the period of time from the beginning of the test to the formation of the first visible crack on the second flange, and then to the time of collapse of the second flange. The time periods were calculated based on the video recording of each test. The data presented in Table 2 show that the FRFC specimens performed better than the PFC specimens during the dynamic tests. This can be seen by comparing the time periods prior to the collapse of the first flange, which in most cases is longer for the FRFC specimens when compared to the PFC specimens (on average 16.2 s longer). It is also noted that the time period between the formation of the first visible crack on the first flange and the collapse of that same flange was longer in all cases for the FRFC specimens when compared to the PFC specimens (on average 2.3 s longer). This is attributed to the fiber-reinforcement, which enables a distributed growth of micro-cracks in the specimen [55] prior to the development of macro-cracks, however, microscopic studies should be performed to confirm this assumption. It can also be seen in Table 2 that most PFC specimens exhibited failure of the second flange, while for the FRFC specimens, this only occurred in the FRFC specimen #3 after more than 16 s. This confirms the enhanced integrity of the FRFC specimens by the fibers when compared to the PFC specimens. It is important to note that there were large variations in the time of collapse of the first flange for the FRFC specimens when compared to the PFC specimens. It is believed that although every precaution was taken to achieve adequate fiber dispersion in the matrix, it is possible that fiber bundles and large air-voids could have formed in some parts of the specimens, which in turn, may have led to the initial cracking, however, microscopic studies should be conducted to verify this supposition.  Table 2 show that the FRFC specimens performed better than the PFC specimens during the dynamic tests. This can be seen by comparing the time periods prior to the collapse of the first flange, which in most cases is longer for the FRFC specimens when compared to the PFC specimens (on average 16.2 s longer). It is also noted that the time period between the formation of the first visible crack on the first flange and the collapse of that same flange was longer in all cases for the FRFC specimens when compared to the PFC specimens (on average 2.3 s longer). This is attributed to the fiber-reinforcement, which enables a distributed growth of micro-cracks in the specimen [55] prior to the development of macro-cracks, however, microscopic studies should be performed to confirm this assumption. It can also be seen in Table 2 that most PFC specimens exhibited failure of the second flange, while for the FRFC specimens, this only occurred in the FRFC specimen #3 after more than 16 s. This confirms the enhanced integrity of the FRFC specimens by the fibers when compared to the PFC specimens. It is important to note that there were large variations in the time of collapse of the first flange for the FRFC specimens when compared to the PFC specimens. It is believed that although every precaution was taken to achieve adequate fiber dispersion in the matrix, it is possible that fiber bundles and large air-voids could have formed in some parts of the specimens, which in turn, may have led to the initial cracking, however, microscopic studies should be conducted to verify this supposition.    Figures 9 and 10 show the collapse sequence captured by the camera of the first flange of the PFC specimen #1 and FRFC specimen #1, respectively. These two specimens had similar failure modes and for both specimens a main diagonal crack was observed on the right flange. Figure 9b-d shows the initiation of the first visible crack (indicated by a red arrow), the subsequent crack development and the collapse of the flange, respectively. For the PFC specimen #1, the time between the initiation of the first visible crack on the right flange and the collapse of that flange was 0.92 s. Figure 10b-f shows the initiation of the first visible crack, the subsequent crack development and the collapse of the flange, respectively. It can be seen in Figure 10d that a secondary diagonal crack developed on the right flange of the FRFC specimen #1. For this specimen, the time between the initiation of the first visible crack and the collapse of right flange was 3.59 s. As aforementioned, this longer time period between the initiation of the first visible crack and the collapse of the flange for the FRFC specimen is attributed to the enhanced integrity of the specimen, provided by the fibers. This enhancement of specimen integrity and mechanical properties of fiber-reinforced cement-based materials has been observed for different types of fiber-reinforcements, including natural [33,56], synthetic [32,57] and metallic fibers [58], and carbon nanotubes [59]. It has been reported that in fiber-reinforced concrete, the fibers prevent the concrete from cracks growing by forming connection bridges [60]. It is noted that in most cases, the video recording allowed for the identification of the moment when the first visible crack formed. It occurred when there was a change in the direction of motion of the shaking table, causing the maximum peaks of acceleration.  Figures 9 and 10 show the collapse sequence captured by the camera of the first flange of the PFC specimen #1 and FRFC specimen #1, respectively. These two specimens had similar failure modes and for both specimens a main diagonal crack was observed on the right flange. Figure 9b-d shows the initiation of the first visible crack (indicated by a red arrow), the subsequent crack development and the collapse of the flange, respectively. For the PFC specimen #1, the time between the initiation of the first visible crack on the right flange and the collapse of that flange was 0.92 s. Figure 10b-f shows the initiation of the first visible crack, the subsequent crack development and the collapse of the flange, respectively. It can be seen in Figure 10d that a secondary diagonal crack developed on the right flange of the FRFC specimen #1. For this specimen, the time between the initiation of the first visible crack and the collapse of right flange was 3.59 s. As aforementioned, this longer time period between the initiation of the first visible crack and the collapse of the flange for the FRFC specimen is attributed to the enhanced integrity of the specimen, provided by the fibers. This enhancement of specimen integrity and mechanical properties of fiber-reinforced cement-based materials has been observed for different types of fiber-reinforcements, including natural [33,56], synthetic [32,57] and metallic fibers [58], and carbon nanotubes [59]. It has been reported that in fiber-reinforced concrete, the fibers prevent the concrete from cracks growing by forming connection bridges [60]. It is noted that in most cases, the video recording allowed for the identification of the moment when the first visible crack formed. It occurred when there was a change in the direction of motion of the shaking table, causing the maximum peaks of acceleration.    Figure 11a,b shows the failure modes of the PFC and FRFC specimens, respectively. The red arrows indicate the direction of the crack growth. It can be seen in Figure 11 that the majority of the specimens exhibited one main diagonal crack that originated from the top corners of the wall. Some specimens exhibited a secondary crack on the same flange, and in one case, a third crack was also observed (Figure 11a, PFC #2, left flange).  Figure 12 shows contour plots of the predicted maximum principal stress, for both U-shaped walls with flat corners and with round corners, at different times of the dynamic loading. The chosen  Figure 11a,b shows the failure modes of the PFC and FRFC specimens, respectively. The red arrows indicate the direction of the crack growth. It can be seen in Figure 11 that the majority of the specimens exhibited one main diagonal crack that originated from the top corners of the wall. Some specimens exhibited a secondary crack on the same flange, and in one case, a third crack was also observed (Figure 11a, PFC #2, left flange).  Figure 11a,b shows the failure modes of the PFC and FRFC specimens, respectively. The red arrows indicate the direction of the crack growth. It can be seen in Figure 11 that the majority of the specimens exhibited one main diagonal crack that originated from the top corners of the wall. Some specimens exhibited a secondary crack on the same flange, and in one case, a third crack was also observed (Figure 11a, PFC #2, left flange).  Figure 12 shows contour plots of the predicted maximum principal stress, for both U-shaped walls with flat corners and with round corners, at different times of the dynamic loading. The chosen  Figure 12 shows contour plots of the predicted maximum principal stress, for both U-shaped walls with flat corners and with round corners, at different times of the dynamic loading. The chosen times correspond to a full cycle (one wavelength) and show when the specimens were subjected to a change in direction, i.e., maximum acceleration. It is noted that in Figure 12, for illustration purposes, the deformation in the direction of motion has been scaled up by a factor of 50 to visualize the bending of the specimens [61]. It can be seen in Figure 12 that in most cases, the stress contour shows a diagonal band with high levels of stress at the flanges, and stress concentration at the top corners of the wall. These predicted observations are in agreement with the experimentally observed locations where the cracks formed (Figures 9 and 10), and the diagonal cracks observed in the majority of the specimens ( Figure 11). It can also be seen in Figure 12 that for the U-shaped wall with round corners, the levels of stress are lower than those observed in the U-shaped walls with flat corners. Figure 12 also shows that although there is stress concentration at the top corners of the U-shaped wall with round corners, the stress concentration is more evenly distributed throughout the specimen.

Numerical Results
Materials 2020, 13, x FOR PEER REVIEW 12 of 17 times correspond to a full cycle (one wavelength) and show when the specimens were subjected to a change in direction, i.e., maximum acceleration. It is noted that in Figure 12, for illustration purposes, the deformation in the direction of motion has been scaled up by a factor of 50 to visualize the bending of the specimens [61]. It can be seen in Figure 12 that in most cases, the stress contour shows a diagonal band with high levels of stress at the flanges, and stress concentration at the top corners of the wall. These predicted observations are in agreement with the experimentally observed locations where the cracks formed (Figures 9 and 10), and the diagonal cracks observed in the majority of the specimens (Figure 11). It can also be seen in Figure 12 that for the U-shaped wall with round corners, the levels of stress are lower than those observed in the U-shaped walls with flat corners. Figure 12 also shows that although there is stress concentration at the top corners of the U-shaped wall with round corners, the stress concentration is more evenly distributed throughout the specimen. Figure 13 shows contour plots of the maximum principal plastic strain for both U-shaped walls with flat corners and with round corners at 1.5 and 3 s. It can be seen in Figure 13a that at t = 1.5 s, there is plastic strain at the top corners of the U-shaped wall with flat corners, while for the U-shaped wall with round corners, there is no plastic strain (Figure 13b). At t = 3.0 s, there is plastic strain in both types of U-shaped walls, however, the predicted value of the plastic strain for the U-shaped wall with round corners (0.0008) (Figure 13d) is much lower than that for the U-shaped wall with flat corners (0.024) (Figure 13c). These locations, in which there are large values of plastic strain, are more likely to develop cracks [62].   Figure 13 shows contour plots of the maximum principal plastic strain for both U-shaped walls with flat corners and with round corners at 1.5 and 3 s. It can be seen in Figure 13a that at t = 1.5 s, there is plastic strain at the top corners of the U-shaped wall with flat corners, while for the U-shaped wall with round corners, there is no plastic strain (Figure 13b). At t = 3.0 s, there is plastic strain in both types of U-shaped walls, however, the predicted value of the plastic strain for the U-shaped wall with round corners (0.0008) (Figure 13d) is much lower than that for the U-shaped wall with flat corners (0.024) (Figure 13c). These locations, in which there are large values of plastic strain, are more likely to develop cracks [62]. Materials 2020, 13, x FOR PEER REVIEW 13 of 17

Discussion
The experimental results presented here have shown that henequen fiber-reinforcement can be used to improve the mechanical performance of U-shaped wall model specimens made of FRFC. This material has the potential to perform well in structural and seismic applications, and to be used for the fabrication of precast wall panels. However, we acknowledge that our results are preliminary and further experimental and numerical research has to be carried out to support the findings of this work. Further studies should include strategies to assess the effect of different fiber volume fractions and foamed concrete densities on the mechanical properties of the FRFC, an assessment of the durability of the henequen fibers in the cement-based foamed concrete, and further mechanical testing to fully understand the toughening mechanisms of the foamed concrete reinforced with natural fibers. For the U-shaped walls, it is necessary to test large scale models with different walling configurations, such as L-shaped walls. Dynamic testing should include different cyclic loadings and earthquakes excitations, and be performed using different loading directions. Although the experimental results presented here are limited, they provide useful knowledge about the behavior of fiber-reinforced materials and structures subjected to dynamic loading. These results could also be useful to validate numerical models that are used to predict seismic and dynamic behavior.
The numerical results showed that the design of the U-shaped wall is crucial to reduce stress concentration that may lead to the formation of plastic strain, cracking and subsequent failure. The FE simulations presented here are important from a design viewpoint because they show that material properties and geometrical characteristics can potentially be tailored to improve seismic performance. These FE simulations could be extended to predict the seismic response of FRFC walls with more complex geometries, including the simulation of a full-scale U-shaped wall or a complete house. However, more mechanical testing is needed to obtain a complete set of parameters for material model calibration and numerical simulation validation. Finally, robust material models, that include failure criterion, should be employed to obtain more accurate predictions.

Conclusions
In this work, the mechanical performance of U-shaped wall model specimens subjected to dynamic cyclic loading, by means of shaking table tests, was investigated. The U-shaped walls were made of foamed concrete without fiber-reinforcement (PFC) and with fiber-reinforcement (PFC). Both PFC and FRFC, with a target dry density of 900 kg/m 3 , were characterized using compression and tensile tests. These tests showed that the fiber-reinforcement improved the mechanical properties, toughness and ductility of the foamed concrete, which was attributed to the enhanced specimen integrity produced by the inclusion of the fibers. For the dynamic testing, the U-shaped walls were subjected to a 4-Hz sinusoidal base motion with an amplitude of 20 mm. The results

Discussion
The experimental results presented here have shown that henequen fiber-reinforcement can be used to improve the mechanical performance of U-shaped wall model specimens made of FRFC. This material has the potential to perform well in structural and seismic applications, and to be used for the fabrication of precast wall panels. However, we acknowledge that our results are preliminary and further experimental and numerical research has to be carried out to support the findings of this work. Further studies should include strategies to assess the effect of different fiber volume fractions and foamed concrete densities on the mechanical properties of the FRFC, an assessment of the durability of the henequen fibers in the cement-based foamed concrete, and further mechanical testing to fully understand the toughening mechanisms of the foamed concrete reinforced with natural fibers. For the U-shaped walls, it is necessary to test large scale models with different walling configurations, such as L-shaped walls. Dynamic testing should include different cyclic loadings and earthquakes excitations, and be performed using different loading directions. Although the experimental results presented here are limited, they provide useful knowledge about the behavior of fiber-reinforced materials and structures subjected to dynamic loading. These results could also be useful to validate numerical models that are used to predict seismic and dynamic behavior.
The numerical results showed that the design of the U-shaped wall is crucial to reduce stress concentration that may lead to the formation of plastic strain, cracking and subsequent failure. The FE simulations presented here are important from a design viewpoint because they show that material properties and geometrical characteristics can potentially be tailored to improve seismic performance. These FE simulations could be extended to predict the seismic response of FRFC walls with more complex geometries, including the simulation of a full-scale U-shaped wall or a complete house. However, more mechanical testing is needed to obtain a complete set of parameters for material model calibration and numerical simulation validation. Finally, robust material models, that include failure criterion, should be employed to obtain more accurate predictions.

Conclusions
In this work, the mechanical performance of U-shaped wall model specimens subjected to dynamic cyclic loading, by means of shaking table tests, was investigated. The U-shaped walls were made of foamed concrete without fiber-reinforcement (PFC) and with fiber-reinforcement (PFC). Both PFC and FRFC, with a target dry density of 900 kg/m 3 , were characterized using compression and tensile tests. These tests showed that the fiber-reinforcement improved the mechanical properties, toughness and ductility of the foamed concrete, which was attributed to the enhanced specimen integrity produced by the inclusion of the fibers. For the dynamic testing, the U-shaped walls were subjected to a 4-Hz sinusoidal base motion with an amplitude of 20 mm. The results showed that the U-shaped wall specimens made of FRFC performed better than those made of PFC because the time period prior to the collapse of the U-shaped walls was longer for the FRFC specimens, which was attributed to enhanced integrity of the specimens by the fibers. The finite element simulations proved to be a useful tool to improve the design of the U-shaped walls and predict stress concentration and the formation of plastic strain that may lead to cracking and failure during the dynamic cyclic loading. The results presented here showed that U-shaped walls made of FRFC have the potential to perform well in structural and seismic applications. However, these results are preliminary and further experimental and numerical research should be carried out to support the findings of this work.