Experimental investigation on the deformation capacity of lap splices under cyclic loading

Abstract

Correct detailing and positioning of lap splices is essential in order to prevent premature failure of reinforced concrete structural members. Especially before the introduction of capacity design guidelines, lap splices were often placed in member regions that undergo inelastic deformations under earthquake loading. When assessing the seismic performance of such members, not only the lap splice strength, which was assessed in previous studies, but also information on the deformation capacity of lap splices is required. This paper analyses the results of a recently concluded experimental programme on spliced RC wall boundary elements tested under uniaxial tension–compression cyclic loading. The study aimed at investigating the influence of lap splice length, confining reinforcement and loading history on the deformation capacity of lap splices. The latter is defined as the average strain, at the onset of splice failure, ascribed to deformations originating from the lap splice zone. Analysis of the test results showed that the deformation capacity of lap splices: (1) increases with lap splice length; (2) increases with confining reinforcement but the effectiveness of the confining reinforcement is dependent on the lap splice length; (3) decreases with larger imposed compression levels; (4) is larger for bottom-casted with respect to top-casted lap splices. Finally, an empirical model is proposed to estimate the strain capacity of lap splices, which provides a good fit with the experimental results.

Appendix: Mechanical interpretation and calibration of the parameters α

The discussion of the calibration process for the parameters α₁ and α₂ requires some considerations based on the observed pre-failure cracking behaviour of the test units:

(1) In the TUs with continuous reinforcement, the width of the cracks located at the foundation and top-beam interfaces is approximately equal. However, a similar width is also observed for cracks located along the member, as illustrated in Fig. 2d. This implies that the contribution to the crack width due to anchorage strain penetration (w_anc) is, for the current test units, approximately equal to the one given by the steel–concrete slip accumulated along half of the average crack spacing distance. Note that, considering a reference TU as a tension chord (Marti et al. 1998), the width of a crack along the column height can be expressed as:

$$w = \mathop \smallint \limits_{{ - \frac{srm}{2}}}^{{\frac{srm}{2}}} \left( {\varepsilon_{s} - \varepsilon_{c} } \right) dx$$

(13)

where srm represents the average crack spacing, and ε_s and ε_c are the steel and concrete strains. On the other hand, the width of a top beam or foundation interface crack in the unit with continuous reinforcement (denoted respectively by w_TBI and w_FI) is the sum of two contributions:

$$w_{TBI} = \mathop \smallint \limits_{0}^{{l_{anc} }} \varepsilon_{s} dx + \mathop \smallint \limits_{{ - \frac{srm}{2}}}^{0} \left( {\varepsilon_{s} - \varepsilon_{c} } \right)dx$$

(14)

$$w_{FI} = \mathop \smallint \limits_{{ - l_{anc} }}^{0} \varepsilon_{s} dx + \mathop \smallint \limits_{0}^{{\frac{srm}{2}}} \left( {\varepsilon_{s} - \varepsilon_{c} } \right) dx$$

(15)

where l_anc is the anchorage length. The first integral term for each crack refers to the anchorage strain penetration (the concrete is assumed to be unstrained), while the second term refers to the steel–concrete slip in the column. When the anchored rebar is bent inside the foundation (such as in the current TUs), l_anc can be estimated as l_anc = l₀ + 5Ø_l, where l₀ is the straight anchored length (Sezen and Setzler 2008). From the two equations above, and building on the observation that w ≈ w_TBI ≈ w_FI the following Eq. (16) can be derived:

$$\mathop \smallint \limits_{0}^{{l_{anc} }} \varepsilon_{s} dx = \mathop \smallint \limits_{{ - l_{anc} }}^{0} \varepsilon_{s} dx \approx \mathop \smallint \limits_{0}^{{\frac{srm}{2}}} \left( {\varepsilon_{s} - \varepsilon_{c} } \right)dx = \mathop \smallint \limits_{{ - \frac{srm}{2}}}^{0} \left( {\varepsilon_{s} - \varepsilon_{c} } \right) dx$$

(16)

It is underlined that the approximation above is not valid in general for other configurations of rebar diameters (which is the quantity that mainly governs srm) and/or anchorage configurations.

(2) In the TUs with lap splices, up until lap splice failure and independently of the lapped length or the confining reinforcement content, the top and bottom splice-end cracks showed a comparable width (i.e. w_TOP ≈ w_BOT), which was also similar to cracks located outside the lapped zone (e.g. see Fig. 2b). While the latter width can be expressed through Eq. (13), w_TOP and w_BOT are described by the following Eqs. (17) and (18).

$$w_{TOP} = \mathop \smallint \limits_{{ - \frac{{srm^{ls} }}{2}}}^{0} \left( {\varepsilon_{s}^{ls} - \varepsilon_{c}^{ls} } \right) dx + \mathop \smallint \limits_{0}^{{\frac{srm}{2}}} \left( {\varepsilon_{s} - \varepsilon_{c} } \right) dx$$

(17)

$$w_{BOT} = \mathop \smallint \limits_{{ - l_{anc} }}^{0} \varepsilon_{s} dx + \mathop \smallint \limits_{0}^{{\frac{{srm^{ls} }}{2}}} \left( {\varepsilon_{s}^{ls} - \varepsilon_{c}^{ls} } \right) dx$$

(18)

where the appendix l_s indicates that the quantity refers to the lap splice region. The observation above (w_TOP ≈ w_BOT ≈ w) implies that the contribution to w_TOP and w_BOT coming from the lap splice zone (w_ls) is approximately equal to the one due to deformations occurring above (w_TOP,out) or below (w_BOT,out) the lapped region:

$$w_{ls} = \mathop \smallint \limits_{0}^{{\frac{{srm^{ls} }}{2}}} \left( {\varepsilon_{s}^{ls} - \varepsilon_{c}^{ls} } \right)dx = \mathop \smallint \limits_{{ - \frac{{srm^{ls} }}{2}}}^{0} \left( {\varepsilon_{s}^{ls} - \varepsilon_{c}^{ls} } \right)dx \approx w_{{TOP},{out}}= \mathop \smallint \limits_{0}^{{\frac{srm}{2}}} \left( {\varepsilon_{s} - \varepsilon_{c} } \right) dx \approx w_{{BOT},{out}} = \mathop \smallint \limits_{{l_{anc} }}^{0} \varepsilon_{s} dx$$

(19)

It can be noted that, given a similar crack spacing within and outside the lap-splice region (srm^ls ≈ srm), Eq. (18) turns into Eq. (15). In other words, for the current test units and at the same level of applied axial force, the rebar steel strain integral (slip) of the splice loaded-end contributing to the end crack width (w_ls) is similar to the one provided by a continuous bar (w_TOP,out). This fact (w_ls ≈ w_TOP,out) is not surprising since at a lap splice end the entire load is carried by a single bar while the contiguous cut-off rebar is unloaded.

(3) Within the lapped region, horizontal cracks cross the spliced rebars that do not share the same amount of stress. In each pair, one bar is more stressed than the other; from equilibrium considerations, the stress sum has to equal the input stress at each rebar loaded end. If bond is degraded by the more stressed bar (with eventual stress loss), causing slip and crack opening, the less stressed rebar is forced to accommodate the increased crack width (Tastani et al. 2015) and take over the eventual stress shed by the companion bar. The crack width, which results from the slip accumulation over both crack edges, is thus governed by the more stressed bar of the pair.

From the considerations above, a relation α₁ ≈ α₂ ≈ 0.5 can be expected for the present TUs. A validation was performed by comparing Δ_proc, as computed according to the procedure of Sect. 4.1, with the displacement Δ_int obtained by integrating, along the lap splice length, the envelope of the top and bottom anchored rebar strains (i.e. equation (20) for the case depicted in Fig. 4c).

$$\Delta_{int} = \varepsilon_{TE} \cdot l_{E} + \varepsilon_{AB}^{TA} \cdot l_{0,AB} + \varepsilon_{BC}^{TA} \cdot l_{0,BC} + \varepsilon_{CD}^{TA} \cdot l_{0,CD} + \varepsilon_{DE}^{BA} \cdot l_{0,DE} + \varepsilon_{EF}^{BA} \cdot l_{0,EF} + \varepsilon_{BE} \cdot l_{E}$$

(20)

The strain envelope (black thick line in Fig. 4c) is used in view of consideration (3) and it is computed by means of the optical markers directly glued on the spliced rebars, which are represented in Fig. 4b and c. The displacement Δ_int includes contributions from the splice-end strains (ε_BE and ε_TE), which, due to the unavailability of a measurement point, were retrieved from the experimental (monotonic) steel stress–strain law. The input quantity to the constitutive law was the bar-loaded-end stress, derived from the global imposed axial force N (Fig. 4c). A simplified constant integration weight l_E = 12.5 mm was associated to both strains ε_BE and ε_TE, roughly corresponding to half the distance between the closest LED and the end crack. It is noted that since the largest deformations occurred at the lap-ends, neglecting the contribution due to ε_BE and ε_TE would result in a non-negligible underestimation of Δ_int, especially for imposed displacement demands beyond yielding of the longitudinal reinforcement. Although from a theoretical viewpoint Δ_int is the measure best representing the pure lap splice deformation, it was comparatively more difficult to obtain than Δ_proc because: (1) the detachment of one or more markers glued on the spliced rebars was more likely than the detachment of those glued on the concrete; and (2) after the failure of the first lap splice the calculation of the steel stresses at the lap loaded end was highly unreliable. In fact, they depended on the unknown residual force carried by the failed lap splices as well as on the force redistribution between the still-holding splices. Note that, after rebar yielding, any miscalculation of the rebar stress would yield big differences in the estimated strain. For the cases in which the calculation of Δ_int was indeed possible, the validation of the assumption α₁ ≈ α₂ ≈ 0.5 was carried out and is depicted in Fig. 4d.