1. Introduction
Through the segmental construction method was said firstly used in China on arch bridges in the 7th century and was used in Europe until the 12th century, the first segmental precast concrete bridge was Choisy-Le-Roi, built in 1962 by Eugène Freyssinet and Jean Muller, crossed the Seine River in France [
1,
2,
3]. After that, with the development of prestressing techniques, segmental precast bridges are used in highway bridges, urban viaducts, and some railway bridges more and more [
4,
5,
6,
7]. In recent decades, due to the advantages of less traffic disturbance, low environmental pollution, and short construction period, segmental precast bridges are vigorously promoted in China, especially for the application in urban viaducts and transit railway [
8,
9,
10].
Segmental precast bridges are defined as bridges consisted of discrete segments stressed together by prestressed tendons to form bridge superstructure and substructure [
2,
11]. Connected through the mechanical interlocking of multiple keys in the web section of the segments, segmental precast bridges are expected to behave as a monolithic structure and maintain allowable stress state for the serviceability limit state. In AASHTO (American Association of State Highway and Transportation Officials) bridge design specifications [
12,
13,
14,
15], it is emphasized allowable compression and tension stresses for segmental precast bridges depending on the type of joint and the presence or absence of bonded reinforcing across the joints. Without epoxy and temporary post-tensioning, dry joints are designed with smaller reduction factor for the shear capability and higher residual compression. These may result in thicker web walls or greater amounts of post-tensioning steel. But compared with undesirable brittle failure in epoxied joints, segmental precast bridges with dry joints are more favorable, moreover, cost-saving in epoxy construction [
15,
16,
17,
18]. Multiple keys distributed over the height of the web and flanges of the segments play important roles in the following three aspects, (1) aligning segments during erection, (2) transferring the shear force between segments during service, (3) ensuring durability by protecting the prestress tendons against corrosion where the tendons pass through the joints. According to AASHTO LRFD (Load Resistance Factor Design)-17 [
12], shear keys between segments should be utilized to prevent relative sliding between adjacent segments in segmental precast bridges. In conclusion, the behavior of segmental precast bridges is dependent on the behavior of the joints between segments [
19,
20].
Through experiments and finite element analysis, researchers have demonstrated that the prestress value, shape, and number of the keys, concrete strength, friction coefficient, etc., are all significant parameters affecting the shear capacity of the dry joints. Based on the research results, the different shearing capacity formula of dry joints were proposed and discussed.
As early as in 1983, through experiments on different types of joints, including no keys, single large key, and multiple keys, Koseki and Breen [
21] investigated the shear transfer strength across these types of joints used between adjacent segments of segmental precast bridges. Experimental results showed that the failure mode of the dry joint specimen is a direct shear failure at the key root. According to the test results, the formula of the shear bearing capacity
of dry joint was proposed, namely,
is the sum of
, and
. Here,
is the friction resistance of the keys,
is the shear resistance at the concrete key root. The formula was later adopted by AASHTO [
15]. 1990, Buyukozturk [
22] conducted direct shear tests on keyed joints, considering parameters, such as a number of keys, prestressing level, and the epoxy thickness. It was found that the shear capacity
of the joints increased with the increase of lateral pre-compression stress
. Consequently, the shear bearing capacity of the keyed joints is proposed as
is equal to the product of
(area of the key root) and
(average shear stress at the key root). In which,
is linearly related to the lateral prestress
and the concrete tensile strength
.
In 2002, after verifying finite element model through test results, Rombach [
23,
24] conducted numerical parametric study on the shear bearing capacity of dry joints with various number and shapes of shear keys, concrete qualities etc. On this basis, the shear capacity
of the keyed dry joint was considered a combination of a frictional and a shear part [
23]. However, different from the recommendation in AASHTO [
15], the frictional part included the total area of the joint and not only the smooth parts. The load-bearing capacity of the keys depends on the concrete compressive strength and the area of the failure plane of the keys. Meanwhile, a safety coefficient was considered. Based on the direct shear test results of the keyed dry joints, Turmo [
17,
18] compared the predictions of ultimate joint strength in terms of the provisions in ATEP [
2,
25] and AASHTO [
15]. It was shown that results obtained by the provisions in AASHTO were more consistent with test results. Taking concrete compressive strength higher than 50 MPa with comparatively lower tensile strengths into consideration, Turmo [
17] proposed a new formula be included in the Euro-code. Liu [
26] proposed a formula for evaluating the shear bearing capacity of UHPC joints. It was found to have better agreement with the shear test results than that in the AASHTO provisions.
Aiming to the existing formulas, further investigations were carried out by researchers. Comparing experimental results with the AASHTO [
15] and another design criterion, Zhou [
27] found that the provisions in AASHTO [
15] and Rombach formula [
23] underestimated the shear bearing capacity of the single-keyed joint by a value up to 40%, but greatly overestimated the shear capacity of dry multiple-keyed dry joints. Hence, it was suggested to introduce strength reduction factors for multiple-keyed dry joints. Subsequently, to investigate the structural behavior of the keyed dry joints under the direct shear, a numerical analysis model was established by Shamass [
28], and a parametric study was carried out on predicting the shear capacity of multiple-keyed dry joints. Results showed that the shear capacity predicted by the AASHTO code equation diverges from that predicted by numerical analysis at high confining pressure. This is because the contribution of friction in the total shear capacity decreased with an increase in confining pressure. The same conclusions were demonstrated by Jiang [
29,
30,
31]. Meanwhile, Jiang [
32] also investigated the influence of key depth on the shear resistance of the dry joint. Results showed that the predicted results, according to the provisions in AASHTO [
15], are more applicable for dry joints with key depth in 35 mm and 40 mm. Ahmed [
2] demonstrated through experiments that the average shear transfer of a single key is higher for specimens with a smaller number of keys. Four flange shear keys are capable of increasing the shear capacity by 14% and the elastic stiffness of the joints by 73%. Compared with simulating results, Jiang [
33] demonstrated AASHTO standard overestimated the shear capacity of single-keyed dry joints with fixing imperfections at the lower surface of the key by up to 0.602–22.0%, but greatly underestimated that of the rest, and proposed a modified formula with a strength reduction factor.
Regarding the shear capacity of the keyed joints in segmental precast bridges, the following points could be summarized according to the above researches. Firstly, concrete compressive strength, friction resistance of keys are the critical influence factors of the shear capacity of the keyed joints. But as the contribution and influence coefficient of each part to be concerned, especially due to the lack of detailed explanation from the failure mechanism of the keyed dry joint, the conclusions of different studies are quite different. Secondly, lateral prestress, number, and structural geometry of the keys affect the shear capacity of the keyed dry joint to some extent. Still, no clear influence regularity about these factors is presented yet. Thirdly, though the provisions in AASHTO are not well applicable to all kinds of joints in segmental precast bridges, the applicability of other existing formulas is also limited to some extent. Therefore, it is necessary to investigate further about the influence law of different influencing factors, and accordingly to obtain a universal calculation formula for the shear capacity of joints in segmental precast bridges.
For the above research purposes, with the finite element simulation analysis method considering the plastic damage of concrete, the influence laws of different factors on the ultimate shear capacity of the single-key dry joints are studied in this paper. The factors include lateral prestress, concrete strength, structural geometry of the keys (depth, inclination angle, aspect ratio), etc. Based on the numerical results and comprehensive evaluation of the existing formula, the shear capacity calculation formula of the single-key dry joint was proposed in terms of the maximum principal stress failure criterion. And the applicability of the proposed formula was verified by comparing it with the existing experimental results and numerical results.