## 1 Introduction  
Fully-grouted bolts are extensively applied in the support of mines, tunnels, and slopes due to their advantages, including their low price, ease of installation, and good reinforcement effect. The fully-grouted bolt is surrounded by grouts, the cementation effect of which combines bolts and surrounding rocks. This, on the one hand, improves the integrity of the surrounding rock and enhances the self-supporting capacity thereof [1; 2]; on the other hand, the tensile property of bolts can inhibit the deformation of the surrounding rock and then improve the surrounding rock stability [3; 4]. Giving play to the mechanical properties of fully-grouted bolt support is vital for anchorage design and anchorage effect. To this end, numerous scholars have conducted relevant research through theoretical analysis, field monitoring, laboratory tests, and numerical simulation [5; 6; 7; 8; 9]. Existing research mainly focuses on two aspects: the stress distribution on and around such bolts under different conditions and the corresponding theoretical or numerical model; the other is to study influences of different factors on the anchoring strength, including the bolt length and diameter, grout strength, and confining pressure of the rock mass. With regard to the stress distribution law of fully-grouted bolts, [PERSON] [10] found that the axial stress of bolts attenuates exponentially from the loading point to the tail of the bolts under a small pullout load based on pullout tests and evinced by theoretical analysis and laboratory tests. [PERSON] and [PERSON] [11] established three stress distribution models of bolts through theoretical analysis and proposed that failure occurs near the loading point at first and gradually develops to depth when the tensile load exceeds a certain value. According to the mechanical behaviors of bolts in pullout tests, some researchers found that the peak stress on bolts is in the vicinity of the pullout load point, and then the stress gradually declines along the bolts [12; 13; 14]. [PERSON] et al. [15] conducted numerical simulations to simulate pullout tests and found that the zone with grout defects leads to a plateau on the stress distribution curve. By performing numerical simulations of constant-resistance large-deformation bolts, [PERSON] et al. [16] revealed the distribution of normal stress and shear stress on the bolt-surrounding-rock interface. [PERSON] et al. [17] provided a viscoelastic semi-analytic solution to the axial force of bolts via theoretical analysis and explored the influences of other factors on the axial force. The anchoring strength of bolts Is Important for the stability of the surrounding rock, and a low anchoring strength may cause failure of the surrounding rocks even under small deformation. At present, the anchoring strength of bolts has been mainly studied through pullout tests on bolts, in which the maximum pullout load of bolts serves as the major evaluation index. By conducting pullout tests, [PERSON] et al. [18] stated that enlarging the bolt length and diameter and improving the grout strength can improve the maximum pullout load of bolts, and they constructed an empirical equation governing this behavior. [PERSON] et al. [19] found in laboratory tests that the maximum pullout load of bolts has a non-linear relationship with the confining pressure. [PERSON] et al. [20] and [PERSON] et al. [21] also conducted pullout tests to study the critical anchorage length of bolts; that is, the maximum pullout load does not increase any longer when the bolt length is increased to a certain value. [PERSON] and [PERSON] [22] found that although improving the grout strength does not change the stress distribution on such bolts, it increases their maximum pullout load. By performing laboratory pullout tests, [PERSON] et al. [23] found that the sample diameter and confining pressure affect the maximum pullout load of bolts and the failure mode of anchorage systems. [PERSON] et al.