## 1 Introduction  
Precast concrete structures have the advantages of convenience in construction and environmental friendliness [1]. Recently, the use of precast concrete members has increased [2]. The sleeve grouting connector plays a decisive role in determining whether a precast structure can perform its prescribed function. At present, most sleeve grouting connectors are grouted splice connectors. To fabricate a grouted splice connector, two steel bars are placed and spliced at the centre of the sleeve, and grouting material is poured into the sleeve to fill the volume of the sleeve and left to cure until it reaches its final strength. A sketch of this type of connector is shown in Figure 0(a). There have been many studies on grouted splice connectors [3; 4; 5; 6; 7]. The results of an experimental study conducted by [PERSON] et al. [8] showed that the bearing capacity of the connector was increased by reducing the inner diameter of the sleeve and increasing the embedded length. [PERSON] et al. [9] showed in an experimental study that the stiffness of the connectors was increased with the increase in the embedded length. [PERSON] et al. [10] conducted uniaxial tension tests of connectors with the lapping length and diameter of the sleeve as the research parameters. [PERSON] et al. [11] proposed that the ultimate bearing capacity of the connector was higher than that of the steel bar when the lapping length was no less than eight times the diameter of the steel bar. [PERSON] et al. [12] showed that the existence of internal defects reduced the bearing capacity, rigidity, ductility, and energy dissipation capacity of the connector. Furthermore, there have also been many studies of grouted splice connectors under repeated load [13; 14; 15; 16; 17]. [PERSON] et al. [18] carried out tests of grouted splice connectors under uniaxial tension, high stress, and large deformation during repeated tension and compression, and they analysed the effects of the steel bar diameter, sleeve form, and deflection of the steel bar on the mechanical properties of the connectors. [PERSON] et al. [19] found that there was no significant effect on the connector performance under high-stress repeated tension and compression loading. [PERSON] et al. [20] showed that the peak loads of grouted sleeve connectors were reduced after cyclic loading. [PERSON] et al. [21] carried out tests of grouted sleeve connections under cyclic loading, and the results showed that buckling of steel occurred for all grouted sleeve connections under cyclic loads. A shear key and notch needs to be set in the inner wall of the grouted splice connector to improve the force transmission performance of the connector, which requires high performance material and accurate casting. Moreover, the sleeve diameter must be small to obtain a larger bearing capacity, so it is difficult to insert steel bars when members are in place. In addition, the grouting material is not easy to compact, which leads to security problems. Due to the disadvantages of grouted splice connectors, [PERSON] developed a grouted sleeve lapping connector for which the vertical members could be fully prefabricated after the connector was used. [PERSON] named this connector the APC (all vertical members precast in concrete structures) connector [22]. A sketch of the grouted sleeve lapping connector is shown in Figure 1b. To create this connector, two steel bars are lapped and placed in the sleeve while the grouting material is poured in, and the sleeve is used to constrain the steel bars, which greatly improves the bearing capacity of the connector. Importantly, the grouted sleeve lapping connector is under a strong constraint and the force directions of two steel bars lapped in the sleeve are opposite; thus, the direction of the force that it provides to the sleeve (grouting material) is opposite, and the force is diminished, which is known as the interlock phenomenon (Figure 2).