4.2. Effect of Installation Conditions on the Fracture Mode
Next, in order to make a basic consideration of the effects of anchor bolt installation conditions (bolt diameter, embedding depth, joint strength between bolt and concrete) on pull-out strength and fracture pattern, an analysis model with the same dimensions as the specimens used in the previous study [
6] was examined. An analysis model was created in which anchor bolts were embedded in the center of a concrete block, and analysis was performed by constraining the vertical displacement of the particles at the four corners, as shown in
Figure 10. Here, assuming anchor bolts used to attach seismic retrofitting members to concrete blocks, we examined load-bearing performance when the embedding depth is not sufficient or when chemical adhesives with different adhesive strengths are used.
Table 3 shows the material parameters used in the analysis, and
Table 4 shows the condition parameters for anchor installation. In this study, 0.5 m/s was selected as the pull-out speed given to the anchor bolts according to the maximum speed level assumed for ordinary seismic wave.
First, the crack growth process of concrete with the increase of pull-out displacement of anchor bolts was investigated, and the adhesive stress distribution that changed, at the same time, was analytically considered.
Figure 11 show the final crack pattern of Case 1, 2, and 3, respectively. With the increase of adhesive stress limit, the fracture pattern changed from bond fracture, bond-cone combined fracture, to cone fracture.
As shown in
Figure 11, there are many small cracks around the anchor bolt, and a major crack can be found at the bottom of the anchor bolt. In the case of adhesive stress limit is 16 MPa, the major crack developed to the surface of the concrete, forming a cone shaped fracture pattern.
The bond stress development are shown in
Figure 12. Due to the mechanical symmetry of the loading condition, the resulting figure shows only zoomed half of the analysis area. Focusing on the result of
Figure 12a,b with the adhesive stress limit set to 8 MPa, when the pull-out displacement reaches
x = 75
m, fine cracks are seen near the anchor bolt, and the bond stress rises to about 5 MPa in the entire circumference of the anchor bolt. When pull-out displacement
m, a major crack that could lead to cone fracture can be found at the bottom of the anchor bolt. In addition, adhesive fracture was confirmed in the concrete area with a depth of 10 to 15 mm around the anchor bolt. Regarding the adhesive stress distribution, it was found that the stress decreased to zero at the bottom and at about 10–15 mm depth of the concrete. This phenomenon indicate that the bond stress can be influenced by cracks. At the upper part, the constraint from the surrounding concrete is relatively low. Micro cracks and major radial cracks can both be found in this area. Thus, the bond stress in this area decreases at an earlier stage [
12,
15].
In
Figure 12c,d, where the adhesive stress limit is 12 MPa, crack development and bond stress distributions are similar to the previous case. With the increase of adhesive stress limit, the cone area at the upper part of the anchor bolt when
m is larger than that in Case 1. The final fracture pattern changed from bond fracture to bond-cone complex fracture. In
Figure 12e,f, where the bond stress is 16 MPa, the crack development and the bond stress distribution of
m is similar to previous cases. When
m, the crack reaches the surface of the concrete block, and the bond stress on the lower part of the anchor bolt decreases, forming a cone shaped fracture pattern.
The load-displacement relationship of Case 1, 2, and 3 is shown in
Figure 13, where it shows that, with the increase of the maximum bond stress, the maximum load is increasing. For the case with bond stress of 8 MPa where the fracture pattern is bond fracture, the shape of the load-displacement curve is similar to the bond-stress curve mentioned in
Figure 3b. For the case with bond stress of 12 MPa where the fracture pattern is compound fracture, it can be found that the area of the load-displacement curve is larger than the previous curve, indicating that the energy consumed in compound fracture is larger than in bond fracture. For the case with bond stress of 16 MPa, the maximum load is larger than the previous cases, and the area of the load-displacement curve, or the energy consumed, is even larger. Because of concrete cracks generated in this process, more noise can be observed in the curve.
For case 2, 6, and 7, when increasing the diameter of the anchor bolt, the damage pattern changed from bond damage to cone damage, shown in
Figure 14, and the load-displacement relationship is shown in
Figure 15. When the diameter of the anchor bolt increases, more bond force is provided by the increased interface area between anchor bolt and concrete. This bond force is subjected to the same amount of concrete in a cone-shaped area; thus, more concrete is damaged with more bond force by the pull-out process.
For case 2, 4, and 5, when changing the embedment depth of the anchor bolt from shallow to deep, the damage pattern changed from cone damage to bond damage, shown in
Figure 16, and the load-displacement relationship is shown in
Figure 17. When the embedment depth of the anchor bolt increases, the volume of the cone-shaped area also increases. Although more bond force is provided by the increased interface area, the fracture pattern changes from cone fracture to bond fracture due to more concrete participating in resisting the bond force.
To summarize, the analysis cases with bond stress of 12 MPa and their final crack pattern are listed in
Table 5 and
Figure 18. In this figure, the horizontal axis is the ratio between embedment depth
and the anchor bolt diameter
d, while the vertical axis is the maximum load
P in the pull-out process. When
, the fracture pattern is cone fracture; when
, the fracture pattern is bond fracture; and, when
, the fracture pattern is cone-bond complex fracture. This figure shows the tendency that, in this study, with the increase of the value of
, the fracture pattern changes from cone fracture to bond fracture.
4.3. Influence of the Spacing between Anchor Bolts
Then, the influence of spacing between anchor bolts to the load capacity of the anchor bolt is investigated. The analysis model is shown in
Figure 19, with different spacing between anchor bolts
s, from 234 mm to 25 mm. The sides of the upper surface of the concrete block are fixed, and the material parameters are the same with previous analysis. The development process of the cracks during the pull-out process is shown in
Figure 20,
Figure 21 and
Figure 22.
In the case where the spacing is 234 mm, the development process is similar to the case with a single anchor bolt. Inclined cracks generate from the bottom of the anchor bolt and, finally, reach the surface of the concrete block. Two separate cone areas are formed. When the spacing s is 150 mm, the inclined cracks also generate at the bottom of the anchor bolt. When the pull-out displacement m, the cracks located between the two anchor bolts joint with each other, forming a long crack connecting the two anchor bolts. When m and m, the cracks reach the surface of the concrete, and a complicated double-cone fracture surface is obtained. When the spacing s is 25 mm, cracks generate from the bottom of the anchor bolt. The cracks outside the anchor bolts are long and inclined, and the cracks between the anchor bolts are short and horizontal. When m and m, the inclined cracks reach the surface of the concrete block. The shape and the area of the emerged cone shape becomes more like the cone shape of a single anchor bolt.
The load-displacement curves are shown in
Figure 23. In the case where the spacing
s is 150 mm, the total area of the emerged cone shape changed little compared to the two separate cone shapes, and the maximum load remains same for spacing of 200 mm and 150 mm. When the spacing
s is 25 mm, the two anchor bolts just behave as a single anchor bolt, and the maximum load is about half of the previous cases. To make the tendency more clear, relationship between the ratio between the total maximum load and the maximum load of a single anchor bolt
and the spacing
s is shown in
Figure 24a, and the relationship between the ratio between the total maximum load and the maximum load of a single anchor bolt
and the ratio between spacing and embedment depth
is shown in
Figure 24b. In
Figure 24a, it is found that the maximum load remains unchanged when the spacing
s is larger than a certain value in different case, which is also described in Reference [
28]. In
Figure 24b, it is clear that the load decrease is not noticeable until
reaches 2.0. Compared to existing studies that considered the effect of anchor bolt diameter on sufficient embedment depth [
28], this study investigated the effect on pull strength of adjacent bolt spacing at relatively shallow embedding depths. As a result, it is confirmed that an interval of 2.0 times of the embedment depth is needed as a minimum distance of adjacent bolt spacing to keep the pull-out strength. This result indicates that a minimum spacing of 2.0 times of the embedment depth should be ensured for anchor bolts to provide sufficient resistance against pull-out load.
4.4. Influence of the the Distance from Free Edge
The influence of distance between the edge of the concrete block and the anchor bolt is investigated. The analysis model is shown in
Figure 25. The embedment depth
is 48 mm, and distance
s between the edge of the concrete and the anchor bolts varies from 100 mm to 17 mm. As a boundary condition, the vertical displacement of the black color area (along 3 sides) in the upper surface are fixed, and the other side is not fixed.
Figure 26 show the principal strain distribution in half the region of the analysis model in consideration of mechanical symmetry under the 0.45 mm pull-out displacement level.
From the final crack pattern, it was found that, when there is enough distance from the edge of concrete block, a cone-shaped crack pattern can be observed. However, the cone-shaped crack becomes incomplete with the decrease of distance
s. In particular, the crack at the bottom of the anchor bolt extended to the lateral surface of the concrete without changing direction in the case of
, while, in other cases, the cracks turned. From the load-displacement relationship shown in
Figure 27 and the relationship between the maximum load and the ratio of distance to free edge and embedment depth
shown in
Figure 28, it can be recognized that the maximum pull-out strength decreased when
is lower than
, and the maximum pull-out strength in case of
decreased around 40% compared with other cases. As a reference, about 50% of the maximum load drop can be found in the experiment [
8,
16]. Compared to the existing studies [
8] that showed the influence of the anchor bolt diameter under sufficient embedment depth, we investigated the minimum distance from the free end to keep the pull-out strength of the anchor bolt, and it has been found that maintaining proper pull-out strength requires a distance from the free end that is greater than 1.0 times the anchor bolt embedding depth. This is also shown by the tendency of the experiments conducted in Reference [
16]. Thus, it indicates that
should be guaranteed when installing anchor bolts at the edges of the concrete structures. In addition, compared to the analysis results in the previous section, it can be found that the analysis model with insufficient distance between the anchor bolt and the free edge is similar to a half model of cases with insufficient intervals between anchor bolts considering symmetricity. When sufficient valid base concrete around a single anchor bolt is not guaranteed, the pull-out performance of this single anchor bolt is limited. When installing anchor bolts under these conditions, it is necessary to avoid densely placed rebar areas to ensure sufficient embedding depth for the bolts and the surrounding concrete area. In the next section, we will consider an example of countermeasures when a sufficient concrete area cannot be secured around the anchor bolt.
4.5. Measures against Insufficient Distance from the Free End with PCM
As clarified in the previous section, if the anchor bolt installation position is close to the free end, the pull-out strength will decrease. We investigated a method that does not reduce the pull-out strength as much as possible, even when anchor bolts are unavoidably attached near the free end by using PCM (Polymer Cement Mortar).
PCM is a simple method of spraying reinforced mortar onto the existing concrete of an aged RC structure, and it has already been used in many ways [
23,
24]. In this study, we calculated how much the anchor bolt pull-out strength can be prevented from decreasing by PCM method when the anchor installation position is close to the free end.
The analysis model of this simulation is shown in
Figure 29, where a PCM reinforcement layer with 3-mm or 6-mm thickness is added to the existing concrete surface. In
Figure 29a, the PCM area is smaller, but it is able to cover the projection of the anchor bolt on the lateral surface of the concrete block, while, in
Figure 29b, the PCM area is sufficient to cover sufficient the corn failure domain. The material parameters of PCM is shown in
Table 6. The boundary conditions are the same as the previous section, where the three sides of the upper surface displayed in black in the figure are fixed.
Figure 30 shows the crack pattern obtained in SPH analysis, and
Figure 31 shows the load-displacement relationship. It is recognized from
Figure 30a,b that, since the strength of the PCM material is higher than that of existing concrete, the cracks can be seen growing under the PCM area. Thus, this change in the crack growth path causes a slight increase in the pull-out strength of the anchor bolt.
On the other hand, in the case of
Figure 30c,d, when the PCM reinforcement area is wide, a crack occurred in the PCM layer, which has a high tensile strength than that of existing concrete, and a clear effect was seen, such as an improvement in pull-out strength of about 40%. To summarize these results, it is possible to improve the pull-out strength of anchor bolts with insufficient distance from free end by using the PCM method. To achieve a better performance of the PCM reinforcement layer, the reinforced area by PCM should be large enough to cover the assumed cone failure domain of the concrete.