## 1 Introduction
[12] conducted PO tests on rock bolts with the EL ranging between 150 mm and 320 mm. They found that there was a linear relationship between the largest anchorage force and the EL. [PERSON] [13] investigated how the EL influenced the anchorage force of three diverse rock bolts: weld grip, single Arapree and double Arapree. It showed that the largest anchorage force increased linearly with the EL. [PERSON] et al. [14] investigated the critical EL with laboratory tests. The tested bolt had a diameter of 20 mm. It showed that the critical EL was directly related to the water-cement ratio. With this ratio increasing, the critical EL also increased. [PERSON] et al. [15] compared the reinforcement performance of rock bolts when the EL increased from 100 mm to 300 mm. They found that with the EL increasing, the rock bolts were likely to show yielding behaviour under the PO environment. [PERSON] et al. [16] tested the reinforcement performance of a bamboo rock bolt. The EL ranged between 800 mm and 3000 mm. It showed that the largest anchorage force increased linearly with the EL. [PERSON], [PERSON] and [PERSON] [1] investigated the reinforcement performance of rock bolts under diverse loading conditions. During testing, the EL was changed from 100 mm to 1000 mm. They found that the EL was the key factor in determining the reinforcement performance of rock bolts. Moreover, they found that critical EL was around 430 mm. [PERSON] et al. [17] compared the reinforcement performance of rock bolts when the EL was 0.1 m and 0.2 m. Apparently, the EL had an apparent influence on the largest anchorage force of rock bolts. No matter which hole diameter was used, the rock bolts had a higher anchorage force when the EL was longer. [PERSON] et al. [18] conducted laboratory tests to investigate the reinforcement performance of rock bolts when the EL increased from 100 mm to 200 mm. In this case, a constant borehole diameter of 28 mm was used. It showed that the largest anchorage force increased directly with the EL. [PERSON] et al. [19] conducted laboratory PO tests on rock bolts to reveal the critical EL. They indicated that the critical EL was composed of three parts: the cone broken length, the plastic deformation length and the elastic deformation length. The above experimental study exerts a paramount role in helping underground operators to better understand the rock reinforcement mechanism. However, compared with that, when referring to the EL influence, much less work has been conducted with the numerical modelling method. Recently, modified pile elements have been proposed to investigate the reinforcement performance of rock bolts [20]. The advantages of modified pile elements are that there is a rock bolt flag. Once this rock bolt flag is turned on, it can be used to model point-anchored rock bolts and full-grouting rock bolts. Moreover, modified pile elements accept the revision of the original constitutive model. Therefore, users can revise the original constitutive model of the modified pile elements. The credibility of the modified pile elements has been validated with experimental PO tests in previous research [21]. However, until now, little research has been conducted to use the modified pile elements with an elastic debonding law to investigate the reinforcement performance of rock bolts. Therefore, the research gap is that little research has been conducted to use this numerical modelling method to study the reinforcement performance of rock bolts. To solve this gap, this paper used the numerical software of FLAC3D 6.0 to conduct the numerical simulation. The modified pile elements were used to simulate the rock bolts. More importantly, an elastic debonding law was substituted into the modified pile elements to replace the original constitutive model. The task of this paper is to reveal the relationship between the EL and anchorage force of full-grouting rock bolts with modified pile elements.