1. Introduction
Reinforced concrete slabs subjected to concentrated loads near linear supports are commonly found in practice, such as in bridge deck slabs [
1]. The structural elements are characterized by high shear forces concentrated in the region between the concentrated loads and the linear support. Due to the increasing traffic loads and heavy truck loads close to supports, the existing bridge deck slabs could fail due to shear. Thus, more massive constructions or shear reinforcements are now required in bridge deck slabs [
2]. This raises the question of whether there is a lack of safety for existing bridge deck slabs that were built mainly without shear reinforcement, or whether deck slabs under concentrated wheel loads exhibit reserves of shear capacity, which are neglected in current design codes [
3].
Shear strengthening techniques based on the use of fibre reinforced polymer (FRP) materials have been proposed and developed in the past thirty years [
4,
5]. Externally bonded (EB) FRP is the most commonly used method for strengthening concrete structures using FRP material. To increase the shear behaviour of reinforced concrete structures, FRP sheets are generally applied on the side surface of concrete elements. Additionally, the near-surface-mounted (NSM) FRP rod method is another technique used to increase the shear resistance. In the NSM method, FRP rods are embedded grooves intentionally prepared on the concrete cover of the side faces of concrete structures. The efficiency of these strengthening schemes relies on the bond performance of concrete-adhesive-FRP interfaces. However, those two strengthening methods cannot be applied to increase the shear capacity of concrete deck slabs due to an inaccessible web of structures. Therefore, a new strengthening approach is adopted (see
Figure 1): vertical holes are drilled into the deck slabs upwards from the soffit in the shear zones, high-viscosity epoxy resin is injected, and then FRP bars are embedded in place. This strengthening method is called deep embedment strengthening [
6] or embedded through-section (ETS) strengthening [
7]. Previous research [
8,
9,
10] revealed that this strengthening technique provided higher strengthening efficiency compared to the EB and NSM strengthening methods. In addition, the shear capacity of strengthened concrete beams can be enhanced by this strengthening method [
8,
9,
10].
The aim of this paper is to study the structural behaviour of one-way reinforced concrete slabs in bridge deck structures strengthened with deep embedment FRP bars, see
Figure 2. A series of experimental tests were carried out to investigate some structural variables on the behaviours of those slabs, which included deep embedment strengthening materials, spacing and diameter of deep embedment strengthening FRP bars, and the drilling of holes. After comparing the results of different test specimens, the influence of the deep embedment strengthening scheme on ultimate strength and failure mode was discussed and presented. An understanding of the effect of deep embedment shear strengthening method on the behaviour of concrete deck slabs can be extended. In addition, a nonlinear finite element analysis (NLFEA) model was developed simulate the behaviour of test slabs. The results from this NLFEA model showed good convergence ability and gave good agreement with test results in the validation analysis. Finally, a tow-way design approach for the prediction of ultimate capacity of concrete slabs strengthened with deep embedment FRP bars is proposed. The loading-carrying capacity predicted by this method showed good correlation with the test results.
6. Loading-Carrying Capacity Prediction Method
In this study, a design model is proposed to predict the loading-carrying capacity of concrete slabs shear strengthened with deep embedment FRP bars. It was found in the test that the failure mode of concrete slabs could be varied from brittle shear failure to ductile flexural failure by using the deep embedment strengthening method. As a result, a two-way prediction approach, including bending and shear ultimate strengths, is adopted in this paper as shown below:
Flexural Capacity:
The flexural capacity of concrete slabs is predicted by using the equations in a bridge structure design code named BS5400 [
35], which is given by:
In Equation (13), is the steel reinforcement percentage, b and d are width and effective depth of concrete slabs respectively, and are yield strength of steel bars and concrete strength, respectively. In order to relate the bending moment (Mb) to the applied load (Pb), relevant elastic analysis is adopted as shown in Equation (14).
Shear Capacity:
The shear capacity of concrete slabs shear strengthened with deep embedment FRP bars is considered as the combination of the contribution of concrete and deep embedment FRP bars. In this study, the contribution of concrete to shear capacity is predicted by the design method in BS 5400 [
35], due to the consideration of the influence of longitudinal steel reinforcement in this theoretical model, which is given by Equation (15) [
35].
A theoretical model proposed by Mofidi et al. [
20] is adopted to predict the shear capacity contributed by the application of deep embedment FRP shear strengthening method, as shown in Equation (16).
where
is deep embedment FRP bar cross-sectional area,
is effective shear depth (the greater of 0.72 h and 0.9 d),
is inclination angle of FRP bars (90 degrees for this test),
is spacing between FRP bars.
is effective strain in FRP bars, which can be calculated as below:
In Equation (16),
is diameter of FRP bars used in deep embedment strengthening,
is elastic modulus of FRP bars.
,
, and
are coefficients in the BPE (Eligehausen, Popov, and Bertero Model) modified bond-slip model [
36] using in this theoretical model. The values of those coefficients are shown in
Table 4 based on the bonding test results. In addition,
is a decreasing coefficient (
) that represents the effect of FRP bars having an anchorage length shorter than the minimum anchorage length needed (
Leff as shown in Equations (19) and (20)). The effective anchorage length coefficient (
) can be determined using the following equations:
Additionally,
accounts for the effect of the internal stirrup on the effective strain of strengthening FRP bars. Due to no stirrup used in this test,
can be set to 1 [
20]. Therefore, the shear capacity of the concrete slabs shear strengthened with deep embedment FRP bars can be determined as:
Based on the calculation procedure discussed above, the loading-carrying capacity of the test slabs in this study can be expressed as below:
Table 6 presents the comparison of the loading-carrying capacities from the test results and the theoretical models discussed above. It can be noted that the adopted theoretical method yielded accurate and reliable predictions with an average Pp/Pt of 0.96 and a corresponding COV (Coefficient of variation) of 3%. Additionally, using the deep embedment strengthening scheme results in increasing shear strength of the concrete slabs, which is enhanced to be equal to or more than the flexural strength of those slabs in this theoretical prediction (see
Table 6). This indicates that the failure mode is varied from brittle shear failure to ductile flexural failure, which corresponds to the test results.