BSCR structure
BSCR is a composite reinforcement composed of bamboo, composite fillers, and steel strands. The manufacturing process of BSCR involves several steps. Initially, a bamboo with a diameter of approximately 100 mm is chosen and then split into two sections along the radial direction, which are subsequently filled with a composite filler. Next, the two halves of the bamboo are brought together with a steel strand positioned at the center, and bundled with steel straps at intervals of 0.5 m. Finally, the bundled bamboo is wrapped with glass cloth and coated with epoxy resin to enhance corrosion resistance. A diagram and photograph of the cross-section of BSCR are displayed in Fig. 3. The mechanical properties of BSCR are derived from the high strength and toughness of bamboo, the reinforcing function of the inner steel strand, and the composite filler, which serves to bond the bamboo and steel strand together and transfer loads from the bamboo to the steel strand. (Ren et al., 2010; Zhang et al., 2015).
Centrifuge model tests
To investigate the anchorage mechanism of rockbolts under the coupled effect of tensile and shear stress, a series of centrifugal model tests on bolted slopes were performed at 18 gravities using a centrifuge facility at Tongji University, Shanghai, China. The details of this centrifuge facility were described in detail by Huang et al. (2020). To ensure the results of centrifuge model tests are comparable to those of a prototype, it is crucial to correctly scale down the parameters of the centrifuge model experiment based on the similitude laws and select appropriate materials (Ren et al., 2020). The details of the scaling laws adopted for the centrifuge model tests are listed in Table 1. The model slopes in the tests were 500 mm high, equivalent to a 9 m high slope in prototype. A mixture of silica sand, clay, cement and water with a mass ratio of 8: 2: 0.9: 2.18 was selected as the soil of the slope model. During the casting process of slope models, a fissure (72° from the bottom, 370 mm in length), consisting two-layer poly tetra fluoro ethylene (PTFE) films coated with lubricating oil, was pre-embedded at a distance of 130 mm from the top of the slope surface. Two types of rockbolts, made of organic glass (polymethyl methacrylate) and steel wire, were employed to simulate BSCR and CR respectively. It should be noted that the two kinds of rockbolts have the same axial stiffness but different bending stiffness, that is to say, BSCR can bear much more lateral shear stress than CR. The loading system was composed of a load plate (dimensions: 130 mm×130 mm×25 mm) and a load motor with a constant loading rate of 15 mm/min.
The top settlement and lateral deformation of the slope face were measured by two laser displacement transducers. The particle image velocity (PIV) technique was used to determine the global deformation of the slope by comparing high-definition digital camera photos captured before and after loading (Li and Jing, 2008). In addition, the strains of rockbolts were measured using strain gauges. The layout of the slope with locations of measurement sensors and the centrifuge model are shown in Fig. 4. Five tests were carried out to investigate the anchorage mechanism of rockbolts with different parameters as listed in Table 2. A detailed description of the centrifuge tests and the analysis of the results can be found in Refs (Ren et al., 2018).
Table 1
Main scaling laws adopted for centrifuge model tests.
Parameters | Prototype | Model |
Soil of slope | | |
Density (ρs) | 1 | 1 |
Young’s modulus (Es) | 1 | 1 |
Cohesion (c) | 1 | 1 |
Friction angle (ϕ) | 1 | 1 |
Rockbolts | | |
Bending stiffness (B) | 1 | 1/N |
Tensile strength (T) | 1 | 1/N |
Diameter (D) | 1 | 1/N |
Note: N = model ratio
Table 2
Summary of model configurations.
Test name | Rockbolts material | Number of layers |
Case NR | —— | —— |
Case 1 | steel wires | 1 |
Case 2 | organic glass | 1 |
Case 3 | steel wires | 2 |
Case 4 | organic glass | 2 |
Finite element simulation
The finite element program PLAXIS was employed to simulate the aforementioned centrifuge model test. In order to investigate the anchorage mechanism of the rockbolts subjected to the coupled effect of lateral tensile and shear stress in practice engineering, the scale of the numerical model was consistent with the prototype of the centrifuge test. That is, a 9 m high and 10.8 m long slope was numerically built, with the bottom fixed and the sides set to be horizontally fixed, as shown in Fig. 5. BSCR was simulated by plate elements, and the anchor cable was simulated by spring elements, and the structural plane was simulated by interface elements. The plate elements can bear tensile stress and shear stress, while the spring elements can only bear tensile stress. In this investigation, the plate elements and spring elements were assumed to be elastic-plastic and linear elastic, respectively. The Mohr-Coulomb failure criterion was used for modelling the behaviour of soil and structural plane in this study, a technique widely utilized by scholars in finite element analysis (Ardakani et al., 2014; Argani and Gajo, 2021; Jia et al., 2010). Material properties of the slopes and rockbolts used in the numerical model were determined through laboratory testing, and are summarized in Table 3 and Table 4.
Table 3
Material parameters of slope.
Materials | Elastic modulus E (Mpa) | Poisson's ratio ν | Cohesion c (kPa) | Internal friction angle ϕ (°) |
Slope soil | 40 | 0.25 | 148 | 30 |
Structural plane | 0.35 | 0.35 | 2 | 10 |
Table 4
Material parameters of BSCR and CR.
Materials | Axial stiffness EA (kN) | Bending stiffness EI (kN·m2) | Diameter D (cm) |
BSCR | 3.18×104 | 4.96 | 10 |
CR | 3.18×104 | 0.042 | 2 |
Verification of the finite element model
To ensure the validity of the finite element model and effectively simulate the mechanical behavior of BSCR, it is necessary to verify its accuracy. In this study, combined with the results of the centrifugal model tests (Ren et al., 2018), the verification of the finite element model was conducted by means of a comparative analysis involving the slope bearing capacity, deformation and axial stresses along the rockbolt.
Bearing capacity
The load-displacement relationship plays a vital role in evaluating the load-bearing capacity of bolted slopes and the effectiveness of rockbolts, making it a significant parameter in engineering practices. Through a comparison between the load-displacement curves obtained from five centrifuge test results and the corresponding calculated results presented in Fig. 6, the numerical results are good agreement with the centrifuge test results. In addition, the load-displacement curves of the bolted slopes (Case 1 - Case 4) in centrifuge tests, as shown in Fig. 6b-e, can be characterized by three consecutive stages: elastic, plastic and failure. Initially, during the elastic stage at the initial loading phase, there is a rapid increase in the vertical load, leading the bolted slopes to reach the plastic point with a minimal vertical displacement of approximately 0.05 m. Subsequently, as the plastic stage commences, the growth rate of the vertical load diminishes significantly with the progressive increase in vertical displacement, indicating the onset of yielding in the rockbolts. Towards the end of the plastic stage, there is a sharp decline in loading corresponding to the increase in vertical displacement, marking the transition of the slopes into the failure stage, characterized by rockbolt yield failure. In contrast, the load-displacement curve of the slope without any reinforcement (Case NR), as shown in Fig. 6a, can be roughly divided into two stages of elastic and damage. Following the elastic stage, the fractured soil entered directly into the damage stage, aligning with the inherent characteristics of the soil. Moreover, by comparing Fig. 6a and b, it is also clear that BSCR has a higher load bearing capacity than CR, implying that compared with CR, BSCRs with larger bending stiffness and diameter could bear more load, and that the bolted slope with BSCRs is more stable.
Deformation and failure mode
As mentioned in the section of Centrifuge model tests, the global deformation of slopes could be obtained by the PIV technology. However, due to the limitation of the observation window size of the model box, only the area within the red dotted box shown in Fig. 7a was taken for analysis. In addition, as the anchorage mechanism of BSCR is the main focus of this research, the centrifuge test of Case 2, which replicated BSCR in prototype, was chosen for numerical comparison. Figures 7b and c show the deformation and shear strain of the centrifugal slope model at failure in Case 2 respectively. It can be seen that the slope deformation mainly occurs in the sliding soil body on the right side of the structural plane. The shear strain at the lower structural surface is significantly greater than that at the upper structural surface, reflecting the reinforcing effect of the upper anchor. The deformation and shear strain nephograms of the numerical results are shown in Fig. 7d and e, which are similar to the experimental results in terms of tendency and magnitudes. In other words, the numerical simulation agrees well with the centrifuge test on the whole.
Axial stress of rockbolt
Figure 8 presents a comparison between the measured and calculated axial stress distribution along the rockbolt under a vertical load of 250 kPa, where positive values indicate tensile stress and negative values indicate compression stress. It can be observed that the calculated results are slightly lower than the measured results, but the overall distribution of axial stress is nearly identical. It should be noted that the axial strain of rockbolt, obtained from the strain gauge readings, may be influenced by various factors such as installation and calibration-strain relationship, as mentioned by Ren et al. (2016). Therefore, the difference between the measured and the calculated axial stress of rockbolt in this study is still acceptable. This analysis further substantiates the higher precision of the finite element analysis employed in this study, thereby providing a solid foundation for conducting further investigations into the anchorage mechanism of BSCR.
Parametric analysis
Although the results of model tests are generally reliable, the testing process can be both time-consuming and costly, making it arduous to perform a considerable number of tests. With the development of computer technology, the alternative method of finite element analysis has been widely used by many scholars and achieved good results. To further investigate the influence of anchorage factors, a parametric study was performed using the finite element analysis in this study, in which the centrifugal test of Case-2 was chosen as the benchmark group. This approach allowed for a comprehensive exploration of the impact of various anchorage factors, while leveraging the benefits of computational analysis.
Effect of the rockbolt inclination angle
The inclination angle α, which represents the angle between rockbolt and structural plane (as shown in Fig. 4a), is a significant factor influencing the mechanical characteristics of rockbolts. This has been approved by numerous researchers (Chen, 2014; Cui et al., 2020; Li et al., 2016). In this study, the impact of different rockbolt inclination angles on slope deformation under a load of 250 kPa was investigated, and the results are presented in Fig. 9. It can be observed that the slope deformation increases as the inclination angle becomes larger, with this trend becoming more pronounced for angles exceeding 90°. This phenomenon can be attributed to the fact that BSCR is more flexible and has a significantly greater capacity for tension than compression. Thus, BSCR performs better in terms of tensile strength when the rockbolt inclination angle is less than 90°. However, if the anchorage angle exceeds 90°, the rockbolt is subjected to higher compressive stress. These findings are supported by the distribution of axial stress along the rockbolt for different inclination angles, as illustrated in Fig. 10a. At an inclination angle of 60°, the axial stress values are predominantly positive, while at an anchoring angle of 135°, the values are entirely negative. This indicates that as the inclination angle of the rockbolt changes from 60° to 135°, it undergoes a gradual transition from tension to compression.
However, it is not suggested to reduce the inclination angle of the rockbolt too much, as this will make it difficult to fully utilize BSCR's lateral shear capacity. As shown in Fig. 10b, when the inclination angle is 90°, the maximum positive and negative values of the shear stress of the rockbolt are at a higher level, indicating that the shear capacity of BSCR is completely exerted in this state. Moreover, the two images depicting angles α = 60° and α = 75° in Fig. 9 demonstrate that reducing the inclination angle may not necessarily result in a significant reduction in slope deformation. Therefore, in practical engineering applications, it is advisable to choose an inclination angle slightly less than 90° to facilitate grouting operations while still maintaining a satisfactory level of performance.
Effect of the number of rockbolt layers
Figure 11 illustrates the effect of the number of BSCR layers on slope deformation under a vertical load of 250 kPa. The results demonstrate a decrease in slope deformation with an increase in the number of rockbolt layers. This observation aligns with expectations, as a greater number of rockbolt layers enhances the overall stiffness of the bolted slope, thereby increasing its resistance to deformation (Lin et al., 2020). Figure 12a and b depict the distribution of lateral displacement and settlement of the slopes with varying numbers of rockbolt layers. Notably, increasing the number of rockbolt layers from two to three results in only a 4.7% reduction in lateral displacement and a 13.8% reduction in settlement compared to increasing from one to two. Therefore, considering the principle of minimizing damage to earthen heritage sites, it is recommended to avoid excessive use of rockbolts while ensuring safety and effective deformation control.
Effect of the rockbolt length
Figure 13 shows the deformation of bolted slopes with varying rockbolt lengths. The slope deformation is the greatest with the smallest rockbolt length of 3 m, whereas there is no discernible difference between the slopes with rockbolt lengths of 7.6 m and 5 m. It is observed that reducing the rockbolt length from 5 m to 3 m leads to a ten-fold increase in slope deformation compared to a reduction from 7.6 m to 5 m. This indicates that increasing the rockbolt length can enhance slope stability, but excessively long rockbolts do not significantly improve it.
Figures 14a and b compare the axial stress and shear stress of rockbolts of various lengths. The axial stress distribution range of the shortest rockbolt is smaller than that of other rockbolts, indicating that it is too short to provide complete anchoring force. The axial stress distribution of the 7.6 m and 5 m rockbolts is nearly identical, meaning that the axial stress is very small beyond 5 m for the 7.6 m rockbolt. This finding suggests that the BSCR has an effective anchorage length of approximately 5 m, as supported by previous studies (Ren et al., 2018; Ren et al., 2020). In addition, the length of the rockbolt has little effect on the distribution of shear stress, which is mainly concentrated near the structural plane.
In conclusion, the stability of bolted slopes could be improved by increasing the length of BSCR. However, due to the limitation of the effective anchorage length of the rockbolt, excessive lengthening of the rockbolt is wasteful. On the other hand, reducing the drilling depth of the rockbolt can be a way to preserve earthen heritage sites. However, considering the presence of cracks within the earthen heritage sites that continue to propagate internally, as indicated by the multi-layer crack structure in Fig. 1a, it is crucial to ensure a sufficient safety length of the rockbolt.