3.1. Load-Midspan Displacement Behavior and Failure Modes
shows the load-midspan displacement responses of the concrete beams to the flexural bending. Two replicate specimens were tested for both the unreinforced and geogrid-reinforced beams. The averaged maximum load is 3.7 kN and 3.5 kN for unreinforced and geogrid-reinforced beams, respectively, indicating that the geogrid in this study does not necessarily contribute to improving the peak flexural strength of plain concrete. However, in looking at Figure 4
, it can be seen that the geogrid-reinforced beams carried additional load after the crack was initiated, reaching a maximum post-cracking load of 0.8 kN, or about 23% of the maximum load. It is noted that the maximum post-cracking load is relatively low compared to the maximum peak load. Unlike other unconventional discrete types of reinforcements such as fibers whose bonding with concrete is the primary contributor to the reinforcement, geogrids are continuous and planar-type reinforcements, and carry the majority of the post-crack load upon the initiation of cracks in concrete. Thus, for geogrid-reinforced concrete, its post-crack load-carrying capacity relies on the ultimate tensile strength of the geogrids embedded in the concrete. The polypropylene (PP) type of geogrid used in this study typically has a relatively low ultimate tensile strength compared to other types of geogrids materials such as polyester (PET) or high-density polyethylene (HDPE) [29
]. It is expected that the post-crack load would increase substantially when multiple layers of geogrids are installed in the concrete.
also indicates that geogrid-reinforced specimens exhibit significant deformation before ultimate failure, most likely due to the geogrid’s ductility, while the deformation of the control specimen is minimal, as expected. Table 3
summarizes the results of the flexural four-point testing for the plain and geogrid-reinforced beams.
Based on the four-point bending tests, the flexural strength, also known as modulus of rupture, R
can be determined according to the following equation [30
is the maximum total load measured, units in kN; l
is the support span length, 712 mm; b
is the specimen width, 152 mm; h
is the specimen height, 152 mm. It should be noted that the above equation was modified from the flexural strength equation for four-point loading where the loading span was exactly one third of the support span. As listed in Table 3
, the averaged flexural strength for plain and reinforced concrete beams is 300 kPa and 284 kPa, respectively. It is noted that the single layer of geogrid used in this particular study did not necessarily increase the flexural strength of the concrete.
The area under the load-deflection curve in Figure 4
represents the static flexural energy absorption capacity of the concrete beams. The accumulated flexural energy for plain and geogrid-reinforced concrete is 6.8 J and 22.1 J, respectively. Embedding geogrids in the concrete results in a substantial improvement in the total energy-absorption capacity and the post-peak ductility under flexure. It is worth noting that, similar to carbon fiber ropes used for shear strengthening of reinforced concrete beams or steel fibers used in shear-dominated beams [31
], limited past studies have demonstrated that geogrids as shear reinforcement in a hybrid form with steel fibers can enhance shear capacity and alter the failure mechanisms of beams from a brittle shear failure to a ductile flexural failure [19
Observations from images of beams during loading and at failure show that, for the reinforced concrete beams, there was extensive crack propagation, with a wide crack mouth opening before failure (Figure 5
); in contrast, the plain concrete beam failed instantly. For geogrid-reinforced beams, as shown in Figure 5
, the geogrid was able to hold the concrete beam with a macrocrack, suggesting that embedding geogrids in plain concrete delay collapse failure. The geogrid-reinforced specimens exhibit more ductility, delayed cracking, and an increased strength after cracking. On the other hand, the failure mode and mechanism of the unreinforced control beam was observed to follow a brittle and sudden failure due to the lack of any reinforcement. The extensive post-cracking deformation of the geogrid-reinforced concrete beams shows that the inclusion of geogrids provides a certain degree of post-cracking ductility, which is desirable in most applications.
After the initial cracking, load is redistributed to the geogrids embedded at the lower portion of the beam. Based on pullout tests for geogrids embedded in concrete cement, a past study found that geogrids with roughened surfaces were able to provide surface frictional resistance force to cause a fracture failure of the geogrid instead of a pullout failure [33
]. For the concrete specimens consisting of coarse aggregates in this study, in addition to frictional resistance along the geogrid’s surface, the developed passive stress against the geogrid’s bearing rib can provide pullout resistance. Geogrids were fractured at both the junctions and ribs, as depicted in Figure 6
. No signs of slippage or pullout of geogrids were found upon a close examination of the geogrid surfaces post failure. This is further confirmed by the strain measurements in geogrids that are presented later.
A clip-on gage was used to measure the crack mouth opening displacement (CMOD) at the notch of the beams. Figure 7
shows the CMOD measurements until collapse failure of the beams. The sudden drop of load, along with a significant increase of CMOD, indicates the initiation of cracking. As can be seen in Figure 7
, extensive CMOD occurs for geogrid-reinforced concrete beams after the initial cracking, whereas the plain concrete beams exhibited very little CMOD, indicating an abrupt, brittle failure. This resembles the observations from images of beams during loading and at failure (Figure 5
). As the load is redistributed to the geogrids after the initial cracking in concrete, the load increases gradually as geogrids elongate until a rupture of ribs or junctions occurs.
In contrast to the relatively low post-crack load of geogrid-reinforced concrete shown in Table 3
, the significantly greater CMOD exhibited by geogrid-reinforced concrete suggests the promising potential of using geogrids for enhancing post-crack ductility of plain concrete. This also indicates the need to examine both the strength and deformation characteristics of the geogrids used in this study. A close examination of the stress-strain behavior of both the geogrids and concrete would shed light on the flexural behavior of geogrid-reinforced concrete, and help us better understand the effectiveness of using geogrids for reinforcing plain concrete. In addition, with properly defined stress-strain relationships for geogrids and concrete, it would enable sectional analysis of geogrid-reinforced concrete under flexure. Further, it has been established that the addition of fiber reinforcement in concrete in the form of fiber grids [16
] or discrete fibers [34
] significantly improves the overall post-cracking response, and the implementation of this favorable behavior in numerical simulations provides rational and accurate analytical results concerning the curvature ductility and the resisting bending moment of flexural structural members.
3.3. Strain Developed in Geogrids
Strain gauges were installed in pairs on the top and bottom surfaces of a geogrid rib, and the measurements were averaged in order to take into consideration strain measurements caused by flexural bending, and to obtain the tensile strain in geogrids. Strain gages were installed at the center and at various distances from the center: 25 mm, 51 mm, and 76 mm. Figure 8
shows the tensile strain developed in geogrids during loading for both geogrid-reinforced specimens. It was observed from both of the geogrid-reinforced specimens that no measurable strains developed at 76 mm from the center of the beam. Thus, it is likely that geogrids were not mobilized at locations whose distances are greater than 76 mm from the center along the longitudinal direction. As the loading span of the test setup is 152 mm or 76 mm from each side of the center in longitudinal direction (Figure 3
a), it appears that the geogrids were mobilized to exhibit measurable strains only within the area under the loading span or the zone of the maximum bending moment.
Additionally, as shown in Figure 8
, all of the geogrids were activated and mobilized instantly upon the application of the flexural load. With the exception of the location that is 25 mm from the center in specimen 1, for each respective concrete beam, the strain measurements at all locations are approximately the same until the peak load or the initial cracking. This suggests that the geogrids in each of the concrete beams were uniformly mobilized, and that the geogrids embedded in concrete acted as a whole without slippage or pullout from the concrete. After the peak load or the initial cracking, most of the tensile force is transferred to the geogrids, and strains were not uniformly developed or distributed, as seen in Figure 8
. As expected, more strains developed in geogrids at locations closer to the center after the initial cracking.