Introduction
Various types of fastening systems, including cast-in-place and postinstalled anchors, are often used in structural engineering and construction applications to transfer external loads to concrete structures. A tensile-loaded mechanical anchor fails, in general, via concrete-related failure modes, such as concrete cone breakout and concrete splitting. Concrete splitting failure may occur when an anchor is placed in a relatively thin concrete member or very close to adjacent anchors or concrete free edges. Concrete cone breakout failure is characterized by the formation of a cone-shaped fracture surface in the concrete at the anchoring zone. This failure mode is fairly common at tensile stresses lower than the tensile capacity of the steel in the anchor. Previous theoretical and experimental studies on single cast-in-place anchor bolts under tension loads showed that the concrete cone circumferential cracking initiates at approximately 30% of the ultimate load (
Eligehausen et al. 2006). These cracks initiate from the anchor head and propagate toward the concrete surface as the load increases. The crack propagation remains stable up to anchor peak load, at which the length of concrete cone crack is up to approximately 50% of the total length of a full cone. As the deformation at peak load is exceeded, the crack propagation becomes unstable, and a complete failure cone forms.
In general, concrete cone breakout and splitting failures are characterized as brittle-failure modes, because, beyond the peak load, the load-displacement curves associated with these failures decline sharply due to rapid and unstable propagation of concrete cracks. In these modes, the full tensile capacity of the concrete is expended, thereby resulting in concrete cracks at the anchoring zone. Nevertheless, if the steel in the anchor experiences a tensile stress that exceeds its ultimate tensile strength, steel failure may occur, but the concrete remains undamaged. The steel in the anchor undergoes ductile failure, which is rarely observed but may occur if the steel is ductile and the anchor embedment depth is extremely large compared to the shank diameter of anchor.
As depicted in Fig.
1, concrete-material neighboring fastening systems operated via a mechanical bearing head often experience two stress fields: (1) a local stress field resulting from the interaction between the anchor bearing head and the concrete, and (2) a global stress field resulting from concrete-member bending induced by the anchor transverse load. This bending induces concrete tensile stresses, which lead to concrete cracking, at the anchoring zone. The magnitude of these stresses can be reduced by increasing the global bending stiffness of the member. The global bending stiffness of a concrete member depends mainly on the concrete properties (i.e., concrete strength and Young’s modulus), member thickness, and amount of surface reinforcement; hence, these parameters may affect the tensile breakout resistance of the anchors. Also, the size of the bearing part of anchors has an effect on the local stresses in the vicinity of the anchors; the concrete local stresses under the anchor bearing part decrease with increasing head size.
Unfortunately, current design models for predicting the tensile breakout capacity of anchors are based on the simplifying assumption that member thickness, surface reinforcement, and size of the anchor bearing part have no effect on the anchorage capacity and performance. Recently, however, the role of the global bending stiffness of the concrete member and size of the anchor bearing part in the tensile breakout capacity of headed anchors has been considered.
Nilforoush et al. (
2017a,
b) performed extensive numerical studies to evaluate systematically the influence of member thickness, anchor-head size, and orthogonal surface reinforcement on the tensile breakout capacity of headed anchors at various embedment depths. Those studies revealed that the capacity of the anchors increases with increasing member thickness, increasing size of the anchor head, or in the presence of orthogonal surface reinforcement. Based on their numerical results, three modification factors were proposed to account for the influence of the aforementioned parameters. In addition, the concrete capacity (CC) method for predicting the tensile breakout capacity of anchors was modified and extended by incorporating their proposed modification factors.
In the present study, the influence of member thickness, anchor-head size, and orthogonal surface reinforcement on the anchorage capacity and performance is experimentally evaluated for cast-in-place headed anchors under monotonic tensile loads in uncracked concrete. A total of 19 single cast-in-place headed anchors were tested in plain and reinforced concrete members of various thicknesses. The tested headed anchors had various head sizes (i.e., small, medium, and large). The experimental results are presented in terms of (1) anchorage ultimate load, (2) anchor displacement at ultimate load and at a load corresponding to the initiation of concrete cone circumferential cracking (considered as 30% of the ultimate load), (3) anchorage load-displacement relationship, (4) anchorage stiffness and ductility, and (5) failure mode and geometry. Furthermore, the validity of the proposed modified CC method incorporating the recently proposed modification factors is discussed.
Experimental Results and Discussions
Experimental results, such as the ultimate load of the tested anchors
, anchor displacement at peak loads
, anchor displacement at the initiation of concrete cone cracks
(i.e., considered as the displacement at 30% of the ultimate load), and the concrete cube compressive strength
on the day of testing, are summarized in Table
4. As the table indicates,
varies from 37.70 to 41.03 MPa. The CC method [Eq. (
1)] stipulates that the tensile breakout capacity is proportional to the square root of the concrete compressive strength. Therefore, a normalized ultimate load
to a concrete compressive strength of
(corresponding to a concrete cylinder compressive strength of
) was calculated by multiplying the measured ultimate loads
with a normalizing factor of
.
Table
4 also provides the mean normalized ultimate load associated with each test category
, observed failure mode, and failure load predicted by the CC method [Eq. (
1)] and the proposed model [Eq. (
4a)].
In addition, a corresponding bending cracking failure load
for the tested concrete slabs was evaluated based on the yield line theory and is presented in Table
4. According to Nielsen and Hoang (
2016), the bending failure load for a simply supported circular slab subjected to a concentrated load at its center can be determined as follows:
where
= crack (yield) moment per unit width of slab. For the plain concrete slabs,
may be considered as the concrete bending cracking moment
, whereas for the reinforced concrete slabs, it can be considered as the reinforcement yield moment
. Based on the theory of elasticity, the crack (yield) moment
and
per unit width of concrete slab can be determined as follows:
where
= characteristic flexural tensile strength of concrete;
= elastic section modulus per unit width of slab;
= slab height;
= characteristic yield strength of reinforcement;
= reinforcement area per unit width of concrete slab; and
= distance from the most extreme concrete compression fiber (i.e., compression face) to the centroid of tension reinforcement. According to EN 1992-1-1 (
CEN 2004),
may be considered as
, where
is the mean flexural tensile strength of concrete, which can be determined as follows:
where
= mean axial tensile strength of concrete, which is related to
. The calculated bending cracking failure loads based on the yield line theory are the upper bound in the sense that the actual failure load will never be higher, but may be lower than the load predicted.
Moreover, the anchorage ductility was evaluated by defining a ductility factor (DF), which was considered as the ratio of the displacement at ultimate load to the displacement at the initiation of concrete cone cracks (
). The mean values of ductility factor for the tested headed anchors are shown in Fig.
7(a). The anchorage stiffness was also measured as the secant stiffness to 30% of the ultimate load (
) and to the ultimate load (
). The mean values of
and
for the tested headed anchors are presented in Figs.
7(b and c), respectively.
Influence of Member Thickness
Fig.
8 shows the load-displacement curves of headed anchors in PC members of various thicknesses. As can be seen, the anchor ultimate load and the anchor displacement at ultimate load increase slightly with increasing thickness of the concrete member. In addition, the anchorage stiffness decreases slightly with increasing member thickness, whereas the anchorage ductility improves slightly (Fig.
7). The postpeak anchorage behavior reveals that the anchors, especially those in the thinnest members, are quite brittle. This is evidenced by the sharp decline in the load-displacement curves, after peak loads, attributable to the development of rapid and unstable concrete cracks.
Fig.
9 shows the crack patterns at failure for the headed anchors embedded in PC members of various thicknesses. The anchors failed via concrete cone breakout, except for those in the thinnest members, which underwent mixed-mode concrete cone and splitting/bending failure. In fact, concrete cone circumferential cracking is initiated at the head of these anchors and propagate toward the concrete surface as the load increases. However, concrete bending/splitting cracking dominates the failure at anchor peak load and divides the concrete block into several separate pieces. This mixed-mode failure mechanism gives rise to more brittle behavior for headed anchors in the thinnest concrete members compared with those in thicker members.
With increasing member thickness and consequent increased global bending stiffness of the member, the failure mode changed from the mixed-mode concrete cone and splitting failure (observed in the thinnest PC members) to pure concrete cone breakout. This increase in member thickness prevents bending/splitting cracking but promotes circumferential concrete cone cracking, as previously indicated by Nilforoush et al. (
2017a,
b). Based on Eqs. (
6) and (
7), a critical member thickness (
) at which the concrete bending cracking occurs for the plain concrete members can be evaluated
To calculate the critical bending cracking member thickness
, the corresponding measured anchor failure loads
in plain concrete members of various thicknesses (i.e., Series 1) is substituted for
in Eq. (
10). This equation gives
values of 346, 375, and 422 mm, respectively, for the PC members with the thicknesses of
, 440, and 660 mm. Because the thickness of the thinnest concrete slabs (
) is lower than its critical thickness (
), the concrete bending cracking, therefore, dominates the failure of these slabs. This indicates that the thickness of the thinnest slabs has to be increased to larger than 346 mm to prevent the concrete bending/splitting failure of these slabs.
Influence of Anchor-Head Size
The load-displacement curves of headed anchors with different head sizes are compared in Fig.
10(a). As Figs.
7 and
10(a) show, the anchorage stiffness and capacity increase significantly with increasing size of the anchor head, whereas the anchorage ductility and anchor displacement at peak load decrease considerably. In addition, the curves of the large-headed anchors are quite linear compared with those of medium-headed and small-headed anchors. A comparison of the postpeak behavior (i.e., after the peak load is reached) revealed that the large-headed anchors are quite brittle, undergoing sudden failure without prior noticeable anchor displacement, whereas the small-headed anchors are rather ductile, undergoing large deformations. To better understand the behavior of headed anchors with various head sizes, the relative capacity of anchors (
) are plotted in Fig.
10(b) as a function of relative anchor displacement (
). The relative capacities and displacements were determined by dividing the load-displacement curves of anchors with different head sizes to their corresponding peak loads and displacements at peak loads. As the figure shows, it seems that the concrete cone crack growth is stable up to anchor peak load for all head sizes. However, when anchor displacement exceeds the displacement at peak load, the crack growth becomes unstable for the medium-headed and large-headed anchors. This is evidenced by the sharp decline in the relative capacity of the medium-headed and large-headed anchors. On the contrary, the small-headed anchors showed larger relative capacity and displacement after peak load compared with their medium-headed and large-headed counterparts. This is because the concrete under the head of small-headed anchors was subjected to a high bearing stress of
at ultimate load, which causes local crushing of the concrete under the anchor head and a consequent gradual anchor pullout
According to ACI 318 (
ACI 2014), the characteristic bearing stress under the anchor head is limited to
for the failure mode associated with the concrete cone breakout in cracked concrete. For anchors located in a region of a concrete member where no cracking is expected at service load levels, the characteristic bearing stress can be increased to
(
). The characteristic value is equivalent to 5% fractile of the mean value, which is taken as
of the mean value [ACI-318 (
ACI 2014)]. If the characteristic bearing stress under the head is divided by 0.75, a mean allowable bearing stress of
is obtained for anchors in uncracked concrete. If the mean bearing stress under the anchor head becomes larger than
, then the anchorage may be governed by pullout failure rather than concrete cone breakout failure.
Fig.
11 shows the crack patterns at failure for headed anchors with various head sizes. As the figure shows, all anchors (irrespective of head size) undergo failure via concrete cone breakout. The average concrete cone angle with respect to the loading direction increases with increasing head size. In addition, the diameter of the cone at the concrete surface is
for anchors with small and medium heads and
for anchors with large heads. This finding concurs with the results of the numerical study conducted by Nilforoush et al. (
2017b).
Furthermore, in the case of large-headed anchors [Fig.
11(c)], the formation of concrete cone cracks is hindered by the vertical support, and the failure mode changes to bending cracking. The same behavior was observed in experimental and numerical studies on influence of size of the anchor head by Eligehausen et al. (
1992) and Nilforoush et al. (
2017b), respectively. This behavior gives rise to the postpeak brittleness of the large-headed anchors (Fig.
10). It should also be emphasized that the change in the failure mode occurred after reaching the peak load, so it does not seem to affect the anchorage capacity, although it does affect the postpeak anchorage behavior. The observed brittle postpeak anchorage behavior for anchors with the large head could have been prevented if the concrete member had been reinforced.
Influence of Surface Reinforcement
Fig.
12 shows the load-displacement curves of headed anchors in RC and PC members of various thicknesses, and the failure load predicted by the CC method [Eq. (
1)].
During pullout loading of Specimen RC-440-M1, the loading rod detached from the coupling nut at a load of
. Therefore, this test was aborted before capturing the actual peak load of the headed anchor. In a subsequent attempt, the loading rod was fastened to the anchor and loaded again. The load-displacement curve obtained in the second attempt is shown by a broken line in Fig.
12(b). As the figure shows, the anchor ultimate load during this attempt is lower than that of its companion specimen. This is attributable to the fact that the concrete surrounding the anchor had already cracked when the anchor was loaded for the second time.
Compared with the headed anchors in PC members, the anchorage ductility and failure load improve for the headed anchors in RC members. In addition, the anchor displacement at peak load and postpeak load increases when surface reinforcement is present. The same behavior was observed in an experimental study by Nilsson et al. (
2011) on anchor bolts in RC members.
The ratio of ultimate load in RC members to that in PC members is shown in Fig.
13 for various member thicknesses. As the figure shows, the surface reinforcement has a more favorable influence on the tensile breakout resistance of headed anchors in thin members than in thick members. The same tendency was reported by Nilforoush et al. (
2017a) for the simulated headed anchors at various embedment depths in RC members of various thicknesses.
Fig.
14 shows the crack pattern of the headed anchors in RC members of various thicknesses. The tested anchors, even in the thinnest members, failed primarily via concrete cone breakout. As shown in Fig.
14(a), the orthogonal surface reinforcement prevents the bending cracks observed in the thinnest PC members. This reinforcement enhances the global bending stiffness of the member, thereby preventing the occurrence of splitting/bending cracks. Nevertheless, concrete cone cracks develop even in the presence of surface reinforcement and dominate the failure of the tested anchors. Similar-shaped concrete cones formed in RC members of various thicknesses. However, the cone surface formed in RC members is shallower than that formed in PC members.
Validity of Numerically Proposed Modification Factors
To check the validity of the numerically proposed modification factors, three modification factors were extracted respectively from the experimental results of headed anchors in Series 1–3 and compared with the numerically proposed modification factors by Nilforoush et al. (
2017a,
b).
Fig.
15(a) shows the relationship between the relative anchorage capacity
and relative member thickness
for the tested and simulated headed anchors in plain concrete members of various thicknesses. Trend lines fitted to the test and simulation results coincide and confirm that the relative anchorage capacity increases with increasing relative member thickness. The trend lines fitted to the test and simulation results indicate that the increase rate is proportional to
and
, respectively.
In addition, Fig.
15(b) shows the relationship between relative capacity of headed anchors with various head sizes to the capacity of an anchor bolt with a code-equivalent head size (
) and normalized bearing areas (
). The code-equivalent anchorage capacity (
) represents the capacity of a headed anchor that has a code-equivalent bearing area (i.e., corresponding to a bearing stress of
under the anchor head at peak load). Trend lines fitted to the test and simulation results stipulate that the relative capacity increases with increasing the relative bearing area. The increase rate at tests is proportional to
, which is slightly larger than the numerically obtained increase rate of
.
Moreover, the relative capacity of headed anchors in reinforced concrete to the capacity in unreinforced concrete (
) are plotted in Fig.
15(c) as a function of a relative member thickness (
) for the tested and simulated anchors. This figure shows that the relative capacity increases by decreasing the relative member thickness. Trend lines fitted to the test and simulation results indicate that the increase rate at test and simulation is proportional to
and
, respectively.
In all these figures, the trend lines fitted to the test results correspond closely to those fitted to the numerical results, thereby confirming the validity of the proposed modification factors for member thickness (), anchor-head size (), and surface reinforcement ().
Comparison of Experimental Results and Predictions
The measured anchorage capacities of headed anchors in Series 1–3 are compared with the values predicted by the CC method [Eq. (
1)] and proposed model [Eq. (
4a)]. The ratio of the measured capacity of headed anchors in PC members of various member thicknesses (i.e., Series 1) to the capacity predicted by the CC method [Eq. (
1)] and proposed model [Eq. (
4a)] is shown in Fig.
16(a). As the figure shows, the ratio of the measured failure loads to that predicted by the CC method increases with increasing member thickness. Ratios of 1.0, 1.08, and 1.17 are obtained for anchors with member thicknesses of 330, 440, and 660 mm, respectively, indicating that the CC method underestimates the mean tensile breakout capacity of the anchors housed in thick members.
Compared with the CC method, the proposed method [Eq. (
4a)] more accurately predicts the failure load of tested anchors in plain members of various thicknesses. For example, values of 1.05, 1.05, and 1.04, corresponding to members with thicknesses of 330, 440, and 660 mm, respectively, are obtained for the ratio of the measured failure load to the value predicted by Eq. (
4a).
Fig.
16(b) shows the ratio of the measured failure loads to those predicted by the CC method [Eq. (
1)] and the proposed model [Eq. (
4a)] for headed anchors with various head sizes (i.e., Series 2). As the figure shows, values of 1.08, 1.17, and 1.44, corresponding to small-headed, medium-headed, and large-headed anchors, are obtained, respectively, for the ratio of the measured capacity to that predicted by the CC method. This implies that the CC method significantly underestimates the tensile breakout strength of the large-headed anchors. Underestimation of anchorage capacity (by the CC method) associated with anchors of various head sizes results partly from to the fact that the tested anchors were embedded in thick concrete members (
).
The ratios of the measured failure load to that predicted by Eq. (
4a) for anchors with small, medium, and large heads are 1.02, 1.04, and 1.09, respectively, indicating that the proposed model [Eq. (
4a)] better predicts the failure load of anchors with various head sizes compared with the CC method.
Fig.
16(c) shows the ratio of capacities measured for headed anchors in RC members of various thicknesses (i.e., Series 3) to those predicted by the CC method [Eq. (
1)] and proposed method [Eq. (
4a)]. As the figure shows, the ratio of failure load to that predicted by the CC method for tested anchors in RC members with thicknesses of 330, 440, and 660 mm is 1.17, 1.22, and 1.24, respectively, whereas values of 1.03, 1.05, and 1.07, corresponding to RC members with thicknesses of 330, 440, and 660 mm, respectively, are obtained for the ratio of the measured failure loads to that predicted by Eq. (
4a). This confirms that the CC method underestimates the concrete cone breakout resistance of headed anchors in RC members, whereas the proposed model [Eq. (
4a)] more accurately predicts the tensile breakout resistance in RC members.
To further evaluate the validity of Eq. (
4a) in predicting the capacity of single anchor bolts with various head sizes in unreinforced and reinforce concrete members of various thicknesses, the results of 124 pullout tests from the literature (
Eligehausen et al. 1992;
Zhao 1993;
Lee et al. 2007;
Nilsson et al. 2011) and 19 tests of this study are plotted in Fig.
17 and compared with predictions according to the CC method [Eq. (
1)] and the proposed model [Eq. (
4a)]. In these experiments, anchor bolts were tested in concrete specimens of different strengths; the concrete cube compressive strength (
) varied from 19.1 to 45.1 MPa. Eqs. (
1) and (
4a) predict the mean tensile breakout capacity of anchors based on the concrete cylinder compressive strength; thus the measured concrete cube compressive capacities at tests were converted to concrete cylinder compressive strength (
). Then, failure loads observed at tests were normalized to a concrete cylinder compressive strength equivalent to
using a normalizing factor of
.
In addition, headed anchors were tested in concrete members of different relative thicknesses (
). Therefore, failure loads at tests were also normalized to a relative member thickness of
using a normalizing factor of
. Moreover, the relative bearing area (
) of tested anchors varied from approximately 0.8 to 8.1. Therefore, failure loads at tests were further normalized to a relative bearing area of
using a normalizing factor of
. The applied normalizing factors are obtained based on the proposed model [Eq. (
4a)], which stipulates that the tensile breakout capacity is proportional to
,
, and
. The reinforcement content of the tested concrete slabs also varied from 0 to 1.16%, which, depending on the thickness of concrete members at tests, gives different values for the proposed modification factor
. Therefore, the
modification factor for the tested concrete members was evaluated, and then the failure loads at tests were further normalized to
using a normalizing factor of [
]. The normalized capacities were then plotted as a function of anchor embedment depth in Fig.
17(a) for anchor embedment depths up to 525 mm and in Fig.
17(b) for anchor embedment depths up to 1,143 mm.
As the figure shows, the CC method [Eq. (
1)] considerably underestimates the tensile breakout capacities of deep anchors. In contrast, Eq. (
4a) provides the best description of the normalized anchorage capacities at tests for the embedment depths up to 635 mm. For embedment depths
, however, it seems that the proposed model [Eq. (
4a)] slightly overestimates the tensile breakout capacity. Therefore, the proposed model [Eq. (
4a)] should be used only for the maximum embedment depths given in ACI 349 [Appendix D (
ACI 2006)] and ACI 318 (
ACI 2014), i.e.,
. To extend the application of Eq. (
4a) for
and better clarify the influence of member thickness, anchor-head size, and surface reinforcement on the tensile capacity and performance of very deep anchors, further systematic numerical and experimental evaluations of deep anchor bolts are required.