Guojian Cui, Chuanqing Zhang,*, Yibin Pan, Liang Deng, Hui Zhou

a State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Sciences, Wuhan,430071,China

b University of Chinese Academy of Sciences, Beijing,100049, China

c PowerChina Huadong Engineering Corporation Limited, Hangzhou, 310014, China

d College of Civil Engineering and Architecture, China Three Gorges University, Yichang, 443002, China

Keywords:Bolt profile Constant normal stiffness (CNS)Shear test Interface failure characteristics Shear behaviors

A B S T R A C T Rock bolts have been widely used for stabilizing rock mass in geotechnical engineering. It is acknowledged that the bolt profiles have a sound influence on the support effect of the rock bolting system.Previous studies have proposed some optimal rib parameters (e.g. rib spacing); unfortunately, the interface shear behaviors are generally ignored. Therefore, determination of radial stress and radial displacement on the bolt-grout interface using traditional pull-out tests is not possible.The load-bearing capacity and deformation capacity vary as bolt profiles differ, suggesting that the support effect of the bolting system can be enhanced by optimizing bolt profiles. The aim of this study is to investigate the effects of bolt profiles(with/without ribs,rib spacing,and rib height)on the shear behaviors between the rock bolt and grout material using direct shear tests. Thereby, systematic interfacial shear tests with different bolt profiles were performed under both constant normal load (CNL) and constant normal stiffness(CNS)boundary conditions.The results suggested that rib spacing has a more marked influence on the interface shear behavior than rib height does, in particular at the post-yield stage. The results could facilitate our understanding of bolt-grout interface shear behavior under CNS conditions, and optimize selection of rock bolts under in situ rock conditions.

1. Introduction

Failure of rock bolting system frequently occurs in practical engineering (Hyett et al., 1992; Cai et al., 2015). Load transfer mechanism of fully encapsulated rock bolt is critical for understanding the reinforcement effect and support capacity of bolted rock mass, and optimizing of support design scheme for rock bolting systems in different rock masses. The load transfer mechanism is generally governed by many factors, including the mechanical properties of two interface(i.e.bolt-grout and grout-rock interfaces), bolt, and grout material (Yokota et al., 2019). Amongst them,the strength of the bolt-grout interface is critical because the failure of the rock bolting system is more likely to occur at this interface, resulting in decoupling between the rock bolt and grout material when subjected to axial loading (Thenevin et al., 2017).Understanding the shear behaviors of the bolt-grout interface is also essential to develop a constitutive model in numerical simulation (Ma et al., 2016).

The interfacial shear behaviors and reinforcement mechanism of rock bolting system under constant pressure and stiffness boundary conditions have been intensively investigated using pullout and shear tests in laboratory (Hyett et al., 1992; Kilic et al.,2002a, b; Aziz and Webb, 2003; Moosavi et al., 2004; Aziz et al.,2008; Blanco Martín et al., 2013; Cao et al. 2014a; Chen et al.2014, 2016; Li et al. 2014; Wu et al. 2017). It should be noted that constant stiffness boundary conditions can better reflect the actual interfacial shear behavior,compared to constant pressure boundary conditions, because shear dilatancy would be inhibited by surrounding rock mass, which subsequently increase the pressure on the interface in practical engineering(Hyett et al.,1992;Shrivastava and Rao, 2018; Zhang et al., 2020a). Three dominant mechanisms concerning the interfacial bond strength were identified, i.e.chemical adhesion, friction, and mechanical interlock associated with ribs, in which the shear resistance resulting from chemical adhesion is negligible (Satola, 2007). Compared to the friction,mechanical interlock mobilizes the predominant bond capacity before the failure of the rock bolting system(Cao et al.,2013). The effect of mechanical interlock is mainly related to the mechanical characteristics of the grout materials, surrounding rock mass conditions,and bolt profiles(i.e.rib shape,rib height,and rib spacing),which is generally evaluated by experimental studies. Hyett et al.(1992) investigated the effect of radial wall stiffness on the shear strength of cable bolts and found that higher radial wall stiffness can lead to larger load-bearing capacity.Aziz et al.(2008)suggested that the bonding capacity of the rock bolt increases with increasing rib spacing. Nevertheless, the shear behavior and failure mechanism are difficult to be predicted accurately using pull-out tests due to the lack of measured lateral displacement and radial stress during the pull-out processes.

To overcome abovementioned difficulties, direct shear test is generally used (Aziz et al., 2001; Yokota et al., 2018). For example,Aziz et al. (2001) studied the effects of initial normal stress (σn0)and bolt types on the interface shear behavior under a 8.5 kN/mm normal stiffness. Yokota et al. (2018) studied crack propagation mechanism accompanied by debonding process of the bolt-grout interface with various rib parameters and grout strengths under constant normal load (CNL) conditions. Unfortunately, the actual radial stiffness of the in situ borehole wall or that of steel tubes in the laboratory pull-out tests is significantly greater than that in the shear tests, suggesting insufficient normal stiffness applied on the bolt-grout interface in previous direct shear tests. It is therefore indispensable to conduct constant normal stiffness(CNS)tests with higher normal stiffness for the bolt-grout interface.

In addition to experimental studies, analytical model and numerical analysis have also been used to evaluate the interface shear behavior (e.g. Yazici and Kaiser,1992; Benmokrane et al.,1995; Li and Stillborg, 1999; Blanco Martín et al., 2011; Cao et al., 2013,2014b;Ma et al.,2014;Chen et al.,2016;Li et al.,2017;Shang et al.,2018; Yokota et al. 2019; Saadat and Taheri, 2020; Wang et al.,2020). Benmokrane et al. (1995) proposed a trilinear constitutive model for bond stress-slip relation at the bolt-grout interface.Cao et al.(2014b)analytically investigated the interaction between bolt profile and surrounding rock mass.Shang et al.(2018)constructed a discrete element method (DEM) model to explore the micromechanism of mortar-bolt interface when shearing. Yokota et al.(2019) investigated the effects of the typical rib parameters on mortar-bolt interface behavior using discontinuous deformation analysis (DDA) under CNL conditions. It can be noted that most analytical models and numerical analysis ignored the effect of normal stiffness on the interfacial behavior as well.

In view of the limitations of previous studies, the CNS direct shear tests under high normal stiffness conditions for bolt-grout interface were performed in this context. This study is in an attempt to understand the shear behavior and failure mechanism of the bolt-grout interface with different bolt profiles for various rock masses upon selection and optimization of the bolt configuration.Thereby, the effect of bolt profiles and normal stiffness on the interfacial behaviors in terms of the ultimate shear strength, ultimate shear displacement, and absorbed deformation energy were discussed. Additionally, interface failure characteristics were identified.

2. Specimen preparation and experimental set-up

2.1. Experimental methodology

In laboratory and in situ pull-out tests, the radial confinement applied at the outside of the bolt-grout interface can be considered as constant radial stiffness conditions in most cases.When rock bolt is subjected to axial load in the pull-out test,the interfacial shearing between the rock bolt and grouting material occurs.Therefore,CNS direct shear test can also be used to evaluate the interfacial behavior during pulling,where the natural bolt-grout interface for shearing could be obtained by unfolding the cylinder interface of pull-out specimen along its axial direction. According to Blanco Martín (2012)’s assumption, rotational invariance can be assumed in the radial direction of borehole. Therefore, in this study, the interfacial shearing was further simplified as two-dimensional(2D)(see Fig.1a)shearing under CNS conditions.Cao(2013)and Yokota et al.(2018)also used the simplified 2D steel plate to simulate rock bolt in their shear tests. Similar methods have been applied by Benmokrane et al. (1994) and Gu et al. (2003) in terms of rocksocketed piles, which illustrates the consistency between the results of CNS shear and pull-out tests.

2.2. Specimen preparation

The steel plate with tensile strength and elastic modulus of 630 MPa and 200 GPa was manufactured to simulate rock bolt,and then grout material was cast on the surface of steel plate to produce the well-matched unbonded bolt-grout specimen for direct shear test, because the adhesion of bolt-grout interface barely influenced the mechanical properties during shearing(Satola,2007,Yokota et al.,2018;Ho et al.,2019).Both steel plate and grout specimen have dimensions of 100 mm×50 mm×50 mm(length×width×height).The specification of the prototypical steel plate is from a type of threadbar with 10 mm rib spacing(s),1.2 mm rib height(h),and 50°rib angle(θ)(Zhang et al.,2020a).The rib face angle of steel plate is set as 90°for simplification. As the varied bolt profiles can lead to different bolt-grout interface shear behaviors, load-bearing capacities, and deformation capacities, the effect of bolt profiles (with/without ribs, rib spacing, and rib height) were investigated subsequently.The surface profiles of steel plates used in the shear test are summarized in Fig.1a.The influence of rib angle is neglected in this study because rib angle isa secondary influencefactorcomparedwith rib spacing and rib height(Yokota et al.,2018).

The grout specimen was prepared using 32.5R Portland cement,river sand, tap water, and calcium formate early strength agent with a ratio of 1:1:0.4:0.03 by weight and cured in a standard concrete curing box for 3 d before conducting tests(see Fig.1c).The average uniaxial compressive strength (UCS), Poisson’s ratio, and elastic modulus of the grout specimens are 29.64 MPa, 0.25, and 7.54 GPa, respectively.

2.3. Test apparatus and parameters

The direct shear tests were carried out using a self-developed test equipment (Model RJST-616) in the Institute of Rock and Soil Mechanics(IRSM),Chinese Academy of Sciences(CAS).It consists of vertical and horizontal loading jacks with a maximum load capacity of 200 kN and 300 kN,respectively.This equipment can apply both CNL and CNS boundary conditions on the bolt-grout specimen using a servo-controlled system in which the normal stress is updated in real time according to input normal stiffness and shear dilatancy.Note that zero normal stiffness represents CNL boundary conditions. More details about the CNS boundary conditions during shearing have been documented by Jiang et al.(2004).The applied normal stiffness knis within 1-1000 GPa/m for the tested specimens.The load can be measured by load cells connected to loading jacks, and the displacement can be monitored with linear variable differential transformers (LVDTs) mounted on the shear box, with an accuracy of 0.001 mm.

Fig.1. Bolt-grout specimens: (a) Specification of steel plates (a and b are the rib top and base width of the bolt, respectively), (b) Steel plate, and (c) Grout specimens.

The matched bolt-grout specimen was mounted into a shear box prior to shearing. During the tests, 2.5 kN normal load was first applied on the specimen at a load rate of 0.1 kN/s. Once the prescribed normal load was reached, the normal load would remain constant in the CNL tests and would vary with shear dilatancy according to the input stiffness value in the CNS tests.Then,the shear load was applied by moving horizontal piston at a displacement rate of 0.3 mm/min until the end of direct shear test.

The experimental scheme is tabulated in Table 1.For the planar bolt-grout interface, i.e. smooth bolt, only the CNL shear test was performed because the dilation or compression deformation resulting from shearing is approximately zero for a planar interface,which means that the results of the CNS tests are basically the same as those in the CNL tests (Shrivastava and Rao, 2018). As for the bolt-grout interface with ribs, both CNL and CNS shear tests were performed. In the CNS tests, the normal stiffnesses of 10 GPa/m,50 GPa/m, and 100 GPa/m were adopted before shearing to investigate the effect of surrounding rock mass confinement on the interfacial shear behavior.According to the in situ results reportedby Hyett et al.(1992),the range of applied stiffness was found to be representative of a series of rock masses from the soft coal to shale.

Table 1 Experimental scheme of the shear tests for the bolt-grout interface.

2.4. Verification of applied boundary conditions

To verify application of the normal stiffness for the shear test equipment, comparison between the actual normal stiffness and the input normal stiffness is presented in Fig.2.The actual normal stiffness is defined as the slope of the fitting formula of normal stress-normal displacement curve. As shown in Fig. 2, the actual normal stiffness value is nearly equal to the input value, and the error is no more than 0.5%. The results confirmed that the equipment could apply both CNL and CNS boundary conditions accurately.

Fig. 2. Normal stress-normal displacement curves for the bolt-grout interface under different normal stiffnesses and the corresponding fitting formulae.

3. Results

3.1. Shear behaviors of the bolt-grout interface

To investigate the bolting effect of bolts with different bolt profiles under different surrounding rock mass confinements, a series of bolt-grout interface direct shear tests was carried out under various experimental conditions. Typical laboratory test results are shown in Figs. 3-8, in which the curves of shear stress,normal displacement, normal stress, and friction coefficient with shear displacement are included.The results indicate that both bolt profiles and normal stiffness(surrounding rock mass confinement)can significantly influence the interface shear behaviors.

3.1.1. Shear stress-shear displacement curves

Fig. 3. Shear stress-shear displacement curves of the bolt-grout interface with different bolt profiles under the CNL conditions: (a) Rib spacings, and (b) Rib heights.

Fig. 4. Shear stress-shear displacement curves of the bolt-grout interface with different bolt profiles under the CNS conditions: (a) Rib spacings, kn =10 GPa/m,(b)Rib spacings,kn = 100 GPa/m, (c) Rib heights, kn = 10 GPa/m, and (d) Rib heights, kn = 100 GPa/m.

Fig. 5. Normal displacement-shear displacement curves of the bolt-grout interface with and without ribs (rib spacings of 10-40 mm) under normal stiffness of (a) 0 GPa/m, (b)10 GPa/m, and (c) 100 GPa/m.

Figs. 3 and 4 show the shear stress-shear displacement curves of the interface with different bolt profiles under CNL and CNS conditions, respectively. The shear stress-shear displacement curves of the planar interface under CNL conditions are also illustrated in Fig. 3a for comparison. For planar bolt-grout interface without ribs,it shows that the shear stress increased linearly until the peak shear strength was reached. After that, the shear stress almost kept constant, and a slight stick-slip phenomenon was observed in the post-peak friction sliding stage, as shown in the enlarged view(see Fig.3a).Similar phenomenon has been reported by Cao et al.(2014b),who investigated the interface shear behavior between the smooth bolt and grout in the pull-out tests.However,in the case of bolt-grout interface with ribs, the shape of shear stress curves were related to the applied normal boundary conditions and bolt profiles, especially in the post-yield deformation region.The yield shear strength refers to as the characteristic point where the shear stress curves cease to be elastic with a sharp change in curvature.Thereby,the yield shear strength corresponds to the peak shear strength in the CNL tests.

For the shear stress-shear displacement curves of the boltgrout interface with various rib spacings under CNL conditions(see Fig. 3a), it shows that the interfacial shear strength of threadbar is much higher than that of smooth bolt.All shear stress curves display a distinct strain-softening characteristic where the shear stress first increases almost linearly until reaching the peak shear strength within 1 mm shear displacement. Subsequently, it drops sharply, resulting in brittle failure in the interface, and finally decreases slowly to a stable residual shear stress with increasing shear displacement. A reduction in the degree of brittleness with increasing rib spacing was noticed, due to fewer cracks being generated in the grout specimens for the bolt-grout interface with larger rib spacing. The results of the bolt-grout interface with different rib heights further confirmed the correlation between brittleness and cracks, where bolt with larger rib height would cause more cracks generated in the grout specimens and thus lead to a more abrupt post-peak stress drop(see Fig.3b).Moreover, the peak shear displacements of the bolt-grout interface with different rib spacings and rib heights are nearly constant,basically in the range of 0.6-1 mm. However, the shear displacement corresponding to the residual shear strength increases with increases of rib spacing and rib height.

From Fig.4,it can be seen that the rib spacing has a more sound influence on the shear stress curves under CNS conditions.For the bolt-grout interface with rib spacing of 10 mm, brittle failure is dominant,and the shape of the shear stress curve is similar under both boundary conditions. However, the degree of brittleness is smaller under CNS conditions than that under CNL conditions due to the increased normal stress on the interface resulting from shear dilatancy.

When rib spacing is witnin 20-40 mm, the shear stress curves at the post-yield region under CNS conditions are distinctly different from that under CNL conditions.This shows a clear stress yield-hardening behavior prior to the ultimate shear strength and subsequently strain-softening behavior rather than complete strain-softening behavior at the post-yield deformation region,demonstrating that ductile failure is dominant. In the post-yield region, the shear stress first decreased slightly, and a reduction in the stress drop after the yield shear strength with increasing rib spacing was observed when the rib spacing was 20-40 mm. This scenario is consistent with that under CNL conditions, which is always much smaller than that with 10 mm rib spacing under the same boundary conditions. Additionally, the stress drop also declined gradually or even disappeared with increasing normal stiffness. Followed by an approximate stress yield-hardening behavior, where the shear stress increased gradually as shearing progressed which was accompanied by some slight fluctuation before reaching ultimate shear strength. The ultimate shear strength referred to as the shear stress before a sudden drop which represented the onset of complete asperity shearing and therefore the ultimate shear strength was sometimes slightly smaller than the maximum value obtained from the shear stress curves due to the existing fluctuation. When the rib spacing increased from 20 mm to 40 mm, the degree of stress yield-hardening became weaken. However, the shear displacement between the yield strength and the ultimate shear strength increased with increasing rib spacing, suggesting that the rock bolt with larger rib spacing could induce larger deformation capacity before the shear stress dropped. Finally, the shear stress rapidly reduced again with a lower brittleness as compared with that after the yield shear strength.The difference was related to the failure mode,where the first stress drop is due to part cohesion loss and the latter is due to the decreased normal stress on the interface due to the compression deformation. Similar shear stress curves have been obtained by Aziz et al. (2008) in their pull-out tests, and by Johnston et al.(1987) in the shear tests, although different interface shear test methods, various types of rock joints, and different normal stiffnesses were applied in their tests. A comparison between Fig.4a and b demonstrates that normal stiffness can also affect the interfacial behavior. Both the stress drop values and the shear displacement between the yield and ultimate shear strengths decreased with increasing normal stiffness.

Fig. 6. Normal displacement-shear displacement curves of the bolt-grout interface with rib heights of 0.9-1.8 mm under normal stiffness of (a) 0 GPa/m, (b) 10 GPa/m, and (c)100 GPa/m.

Fig.7. Normal stress-shear displacement curves of the bolt-grout interface under CNL and CNS conditions.(a) Normal stiffness:0 and 10 GPa/m,rib spacing:10-40 mm;and(b)Normal stiffness: 0 and 100 GPa/m, rib height: 0.9-1.8 mm.

Fig.8. Friction coefficient-shear displacement curves of the bolt-grout interface with different bolt profiles under CNS conditions:(a)Rib spacings,kn=0 GPa/m;(b)Rib spacings,kn = 10 GPa/m; and (c) Rib heights, kn = 10 GPa/m.

The steel plate with rib spacing of 30 mm was also used to investigate the influencee of rib height on the interface shear behavior because it showed optimal performance when rib spacing is 30 mm, which will be discussed in Section 3.2. Fig.4c and d depicts the interfacial shear stress-shear displacement curves at various rib heights under CNS conditions,suggesting that rib height barely affected the shape of shear stress curves. However, the rib height affected the stress drop values and the shear displacement between the yield shear strength and the ultimate shear strength.As shown in Fig. 4c and d, increase in the rib height tended to diminish the shear displacement between the yield shear strength and the ultimate shear strength,and increase the stress drop values.

3.1.2. Normal displacement (stress)-shear displacement curves

Since the magnitudes of normal displacement and normal stress of the bolt-grout interface in the direct shear tests depend on the bolt surface profile configurations and applied boundary conditions, the evolutions of normal displacement and normal stress with shear displacement are used to evaluate the interfacial shear behavior.

Fig. 5a-c depicts the normal displacement-shear displacement curves under rib spacings of 10-40 mm, initial normal stress of 0.5 MPa,and normal stiffnesses of 0 GPa/m,10 GPa/m,and 100 GPa/m, respectively. The normal displacement curve for the planar interface is also presented in Fig. 5a. This clearly shows that the normal displacement for the planar interface is negligible in the CNL test. The normal displacement curves generally showed similar change trends for the bolt-grout interface with ribs under both CNL and CNS conditions. The normal displacement almost remained stable in the initial shear deformation region, followed by a rapid increase in normal displacement accompanied by decreased variation rate. Once the peak normal displacement was reached, the normal displacement would remain stable again for the CNL tests,and sharply decreased in the CNS tests.It can be speculated that the normal displacement would diminish again when the grout specimens ride up and over the steel rib in the CNL tests. However, the peak dilation angle differs significantly with bolt profile configurations under the same boundary conditions. Generally, the peak dilation angle tended to decrease with the increasing rib spacing and increase with the increasing rib height, as shown in Figs. 5 and 6,respectively.

The normal stress-shear displacement curves are horizontal lines under CNL conditions (see Fig. 7). Under CNS conditions, the shape of normal stress curves is consistent with that of normal displacement curves.A comparison among Figs.3,5 and 7 indicated that the shear stress curves correlated well with the normal displacement and normal stress curves.Under CNL conditions,the peak normal displacement point lagged behind the peak stress point, which revealed that the normal displacement continued to increase after the peak stress point. Under CNS conditions, the normal displacement also continued to increase when rib spacing was 10 mm. However, the ultimate shear strength point approximately coincided with the peak points of normal displacement when rib spacings were 20-40 mm.The results also suggested that rib height did not change the abovementioned relationship.

3.1.3. Friction coefficient-shear displacement curves

The friction coefficient is defined as the ratio of shear stress(τ)to normal stress (σ), which reflects the relative interfacial shear resistance. Fig. 8 illustrates the friction coefficient-shear displacement curves under various bolt profiles, initial normal stress of 0.5 MPa,and normal stiffnesses of 0 and 10 GPa/m,respectively.

For the planar interface, the characteristics of the friction coefficient curve and the shear stress curve are almost the same.For the bolt-grout interface with ribs, unlike the shear stress curves,the shape of the friction coefficient curves is independent of the bolt profiles and boundary conditions. The friction coefficient curve underwent three stages: (1) pre-peak stage: the friction coefficient increased with shear displacement before the peak friction coefficient; (2) strain-softening stage: the friction coefficient gradually decreased until reaching residual value; and (3)friction sliding stage: the friction coefficient kept almost constant.The shear displacement corresponding to the peak friction coefficient is about 1 mm for all the tests. A comparison between Figs. 3 and 8 suggests that the yield shear strength point approximately corresponds to the peak friction coefficient point.In addition, it is indicative that both the bolt profiles and normal stiffness influence the peak friction coefficient, while they barely influence the residual value.

3.2. Influence of bolt profiles on the typical shear parameters

The ultimate shear strength τu, peak friction coefficient μp, ultimate friction coefficient μu, ultimate normal displacement nu,ultimate shear displacement su,and absorbed deformation energy E obtained from the shear curves are tabulated in Table 2. The absorbed deformation energy E refers to the area between the shear stress curves and shear displacement axis prior to the ultimate shear strength, because the shear displacements when the tests terminated are not the same for all the tests.

3.2.1. Influence of rib spacing

The variations of ultimate shear strength, peak and ultimate friction coefficients, ultimate normal displacement, ultimate shear displacement,and absorbed deformation energy with rib spacings of the bolt-grout interface under different normal stiffnesses are shown in Fig.9.The results revealed that both normal stiffness and rib spacing influenced the above-mentioned parameters.

Fig. 9a depicts the influence of rib spacing on the ultimate shear strength under different normal stiffnesses. The ultimate shear strength reduced with increasing rib spacing under CNL conditions. However, under CNS conditions, the ultimate shear strength showed a nonlinear change trend, where it increased first and then decreased, and the maximum value was obtained when rib spacing was 30 mm. For example, under normal stiffness of 10 GPa/m, the ultimate shear strength first increased by 50%from 2.92 MPa to 4.38 MPa when the rib spacing increased to 30 mm and then decreased to 3.39 MPa when the rib spacing increased to 40 mm. The results indicated that the load-bearing capacity of the bolt-grout interface could be improved by optimizing the rib spacing and optimal rib spacing is within 30-40 mm for the tested rock bolt. Meanwhile, the ultimate shear strength increased continuously with increasing normal stiffness irrespective of the rib spacing,implying that the bolt can bear the higher load in harder rock, while the increasing rate gradually decreased.

Table 2 Results of shear tests between bolt and grout material with different bolt profiles under the CNS conditions.

Fig.9. Variations of shear parameters with rib spacing under different normal stiffnesses:(a)Ultimate shear strength,(b)Peak and ultimate friction coefficients,(c)Ultimate normal displacement, (d) Ultimate shear displacement, and (e) Absorbed deformation energy. Unit of kn is GPa/m.

Fig. 9b depicts the variation of the peak and ultimate friction coefficients with rib spacing under different normal stiffnesses.In Fig. 9b, the solid and hollow legends represent the peak and ultimate friction coefficients, respectively. Both of them declined with increasing rib spacing, and the influence of rib spacing was more pronounced on the peak friction coefficient compared with that on the ultimate friction coefficient. It is noted that the ultimate friction coefficient was equal to the peak friction coefficient under CNL conditions because solid and hollow marks overlapped and was always less than the peak friction coefficient under CNS conditions. When rib spacings is within 20-40 mm, the ultimate friction coefficient under different normal stiffnesses was almost constant, ranging from 0.85 to 1. Generally, the difference between the peak and ultimate friction coefficients of the bolt-grout interface with 10 mm rib spacing was smaller than that with larger rib spacing, due to brittle failure occurring when the rib spacing was 10 mm and ductile failure occurring when rib spacing was between 20 mm and 40 mm.Moreover,the peak and ultimate friction coefficients also decreased with increasing normal stiffness.

Ultimate normal displacement is a critical parameter in the CNS tests because it determines the actual interfacial normal stress. Fig. 9c depicts the relationship between the ultimate normal displacement and rib spacing under different normal stiffnesses. The ultimate normal displacement in the CNL tests increased when the rib spacing was within 10-20 mm and then declined. Meanwhile, in the CNS tests, a positive correlation between the ultimate normal displacement and the ultimate shear strength was observed.It is apparent that higher normal stiffness would result in less ultimate normal displacement.

For rock bolting system, it should be both strong and deformable (Li et al., 2014). Therefore, we also focused on the interfacial deformation capacity in addition to its load-bearing capacity. Fig. 9d presents the influence of rib spacing on the ultimate shear displacement under different normal stiffnesses.Under CNL conditions, the ultimate shear displacement was within 0.6-1 mm. However, under CNS conditions, the ultimate shear displacement increased quickly with increasing rib spacing and was significantly greater than that under CNL conditions for the interface with the same rib spacing except for rib spacing was 10 mm. The ultimate shear displacement was approximately equal under both CNL and CNS conditions when the rib spacing was 10 mm. The phenomena suggested that the deformation capacity of rock bolt could be improved by optimizing the rib spacing. The ultimate shear displacement mainly depended on the interface failure characteristics. Ductile failure would cause larger ultimate shear displacement than brittle failure does. A comparison of the ultimate shear displacement under different normal stiffnesses indicated that the ultimate shear displacement was generally reduced with increase of normal stiffness within the testing range.

The absorbed deformation energy can reflect the load-bearing and deformation capacities of the rock bolting system simultaneously. Under CNL conditions, the effect of rib spacing on the absorbed deformation energy can be neglected. However, the rib spacing apparently influences the absorbed deformation energy under CNS conditions (see Fig. 9e), where the absorbed deformation energy increases as rib spacing increases. Therefore, the energy-absorbing capacity of the conventional threadbar can be enhanced easily by optimizing rib spacing.

3.2.2. Influence of rib height

Fig. 10a illustrates the influence of the rib height on the ultimate shear strength under different normal stiffnesses. The ultimate shear strength tended to increase as both the rib height and normal stiffness increased. Fig. 10b depicts the influence of rib height on the peak and ultimate friction coefficients under different normal stiffnesses. The solid and hollow legends represent the peak and ultimate friction coefficients, respectively. Solid and hollow black marks overlapped under CNL conditions. It has to be noted that the ultimate friction coefficient is almost constant at different rib heights under CNS conditions, while it increases with increase of rib height in the CNL tests. The peak friction coefficient generally increased as rib height increased and decreased as normal stiffness increased.Fig. 10c illustrates the influence of rib height on the ultimate normal displacement under different normal stiffnesses. Overall,the ultimate normal displacement tended to decrease and increase with the rib height under CNL and CNS conditions,respectively, but the difference was small under CNS conditions.Fig. 10d illustrates the influence of rib height on the ultimate shear displacement under different normal stiffnesses. Under CNL conditions, the brittle failure was dominated, and the ultimate shear stress was mobilized at the shear displacement of 0.8-1 mm approximately when the rib height was between 0.9 and 1.8 mm. Meanwhile, under CNS conditions, the ductile failure holds. The ultimate shear displacement was larger than that under CNL conditions, and it reduced as the rib height and normal stiffness increased. The energy-absorbing capacity increased as the rib height increased under CNL conditions,while it decreased under CNS conditions (see Fig. 10e). Generally, higher normal stiffness resulted in less energy-absorbing capacity when the normal stiffness was between 10 and 100 GPa/m.

Fig. 10. Variations of shear parameters with rib height under different normal stiffnesses: (a) Ultimate shear strength; (b) Peak and ultimate friction coefficients; (c) Ultimate normal displacement; (d) Ultimate shear displacement; and (e) Absorbed deformation energy. Unit of kn is GPa/m.

Fig. 11. Typical interface shear failure modes: (a) Slip failure (σ = 0.5 MPa, without ribs); (b) Dilational slip failure (σ = 0.5 MPa, kn = 0 GPa/m, L = 30 mm); (c) Shearedcrushed failure (σ = 0.5 MPa,kn = 50 GPa/m,L = 30 mm); and (d) Sheared-off failure(σ = 0.5 MPa, kn = 50 GPa/m, L = 10 mm).

3.3. Interface failure characteristic

As the strength and stiffness of steel plate are much higher than that of grout specimen, failure can occur in the grout specimen.Fig.11 displays the typical failure characteristics of grout asperities at the end of the direct shear tests for the bolt-grout interface with different bolt profiles under both CNL and CNS conditions. The damage of the planar bolt-grout interface was minor(see Fig.11a),due to the fact that pure friction sliding occurred on the interface.On the other hand,the damage induced in the grout specimens was severe for the bolt-grout interface with ribs where the grout asperities were partially or completely cut off or crushed as shearing progresses. Three types of dominant interface failure modes were observed, i.e. dilational slip failure (see Fig.11b), sheared-crushed failure (see Fig.11c), and sheared-off failure (see Fig.11d).

For the dilational slip failure, the inclined cracks with an angle smaller than the rib angle were generated from the tip of the ribs,and the grout specimens would override and slide along the newly generated inclined crack surface during shearing, revealing the dominant inclined cracks. However, the horizontal cracks were dominated for the sheared-off and sheared-crushed failure. The difference between the sheared-off and sheared-crushed failure is that the grout asperities were cut off directly for the sheared-off failure mode, while the grout asperities were persistently crushed until a critical point was reached for the sheared-crushed failure mode.The asperity could not be completely cut off as there existed stress concentration for grout asperities adjacent to the steel ribs when the rib spacing was large enough.Subsequently,the strength of grout material was first reached and then crushed. In addition,some grout debris was also noted on the sides of grout specimens along the shear direction for the sheared-crushed failure mode resulting from tension effect.Generally,amongst the three types of failure modes,the sheared-crushed failure mode showed the most severe surface damage, followed by sheared-off failure mode, and the dilational slip failure mode had the least surface damage.

A comparison between Fig.11b and c indicated that the normal stiffness influenced the interface failure mode and degree of surface damage. This is due to the factor that higher normal stiffness can lead to higher normal stress on the interface.The asperity tended to be sheared off rather than sliding up or overriding the steel plate along the newly generated slip surface under high normal stress condition. The difference in the failure modes of the bolt-grout interface with the same surface parameters is negligible under higher normal stiffness conditions.

Fig.12a and b presents the influence of rib spacing on the failure modes under both CNL and CNS conditions. The results suggested that the rib spacing of the bolt affected the interface failure mode and degree of surface damage.Under CNL conditions,dilational slip failure was dominant; however, grout asperities near loading end were locally cut off when the rib spacing was 10 mm. In the CNS tests,the sheared-off failure dominated at rib spacing of 10 mm;as the rib spacing increased, the sheared-crushed failure gradually played a role. Fig.12c and d displays the influence of rib height on the failure modes under both CNL and CNS conditions. It can be concluded that rib height barely affected interface failure modes.

4. Discussion

4.1. Comparison of test results in direct shear and pull-out tests with different rib spacings

Direct shear and pull-out tests could be used to determine the interfacial shear strength, where the direct shear test was characterized by a planar interface shear and the pull-out test was by a ring interface shear.Since the pull-out test method has been widely recognized, it is used to compare CNS test results.

Fig.12. Influence of bolt profile on the interface failure modes: (a) Rib spacing under CNL conditions; (b) Rib spacing under CNS conditions; (c) Rib height under CNL conditions;and (d) Rib height under CNS conditions.

Aziz et al.(2008)conducted pull-out tests to compare the effect of rib spacing, and they concluded that the load-bearing capacity increased by 97.5%when rib spacing was increased to 37.5 mm and then decreased by 6.5%when it was decreased to 50 mm.This is in agreement with our results in the CNS shear tests, although the optimal rib spacing and growth rate are slightly different. The discrepancy can be attributed to the differences in grout material and rib parameters. As discussed in Section 3.1.1, the shear stress curves and pull(axial)force curves showed similar characteristics.It should be emphasized that only axial force-axial displacement curves can be obtained directly in most pull-out tests. However,variations of the normal displacement and normal stress during shearing can be measured in the CNS tests,as shown in Figs.5-7.As for interface failure modes,both dilational slip failure and shearedoff failure were identified for two types of tests(Cao et al.,2014b),while sheared-crushed failure was only revealed in the shear tests.Additionally,the failure process can be visualized in the shear tests.Therefore,CNS direct shear test is more suitable for evaluating the interfacial shear behavior and failure process compared with pullout tests.

4.2. Effect of normal stiffness on the interfacial shear behaviors

It is recognized that normal stiffness applied on the shear plane affected the interfacial shear behaviors (Shang et al., 2018;Shrivastava and Rao,2018;Zhang et al.,2020b).Both CNL and CNS shear tests of bolt-grout interface were performed in this study. It can be seen that both load-bearing and deformation capacities of the bolt-grout interface were underestimated when ignoring the normal stiffness, and the influences of bolt profiles on them were different under different boundaries.Overall,the variation in loadbearing and deformation capacities with different rib spacings and rib heights was small in the CNL tests (see Figs. 9 and 10). Shang et al. (2018) presented similar change trends in their DEM simulation. However, under CNS conditions, the variation in loadbearing and deformation capacities with rib spacings and rib heights was significant (see Figs. 9 and 10). This conclusion emphasized the importance of CNS shear tests of bolt-grout interface.

Fig.13 shows the relationship between shear stress and corresponding normal stress at the yield and ultimate shear stress points under normal stiffness of 0-100 GPa/m for the bolt-grout interface with different rib spacings. The corresponding CNL shear strength envelopes were also plotted in the same figure for comparison(Zhang et al.,2020a).All yield shear stress points were close to the CNL strength envelope. Ultimate shear stress points were close to the CNL strength envelope when the rib spacing was 10 mm,while they were below the CNL strength envelopes when the rib spacing was within 20-40 mm. The difference is likely related to the asperity damage of grout specimen. Under the same applied normal stress for CNL and CNS shearing, accumulated asperity damage of grout specimen was observed due to shear history in the CNS tests, and the damage could be negligible at the yield point when the rib spacing was larger than 10 mm, but it could not be ignored at the ultimate point which tended to reduce the shear resistance of the bolt-grout interface.

Fig.13. Comparison of yield and ultimate shear stress points obtaining from CNS tests with CNL strength envelopes of the bolt-grout interface with different rib spacings.

4.3. Optimization and suggestions for support design

The rock bolt with different specifications showed totally different interface shear behaviors, which suggested that there existed an optimal rock bolt profile in the support design of rock bolting system.As for the standardized rock bolt used in this study,increasing rib spacing can enhance bearing and deformation capacities under CNS conditions. As the rib spacing increased, the load-bearing capacity first increased and then decreased,while the deformation capacity increased monotonously. In addition,increasing rib height can lead to an increase in bearing capacity and a reduction in deformation capacity.Aziz et al.(2008)and Lin et al.(2014) recorded similar behaviors in their pull-out tests.

The selection of rib profile parameters is associated with the failure modes of rock masses. For soft and weak rock masses, the time-dependent squeezing deformation is notable, thus rock bolt needs to accommodate large rock deformation with the proper load-bearing capacity,which means that the load-bearing capacity can be reduced to some extent to achieve greater deformation capacity.Thereby,the rock bolt with larger rib spacing and lower rib height is suggested to use when load-bearing capacity is sufficient.On the other hand, in hard rock masses, spalling failure and rockburst are the two main types of failure modes. When spalling failure occurs, the rock bolt is used to suppress crack growth, and the bearing capacity is more important than deformation capacity,revealing that the deformation demand and the load demand of rock bolt reduced and increased for the optimal rib profile parameters, respectively. Thereby, the rock bolt with optimal rib spacing(e.g.30 mm in this study)and larger rib height is suggested.For potential rockburst occurrence, the rock bolt must be both strong and deformable to absorb enormous energy prior to failure.Thereby,the rock bolt with optimal rib spacing and lower rib height is suggested. However, the optimal rib profile parameters of different rock bolts in various rock masses must be determined experimentally for site-specific purpose due to the difference in the bolt profile, grout,and rock mass.

4.4. Limitations

(a) The effects of grout specimens(e.g.the type of grout material(resin,plaster,and cement),mixture design,and curing time)were not comprehensively understood. In addition, the influences of the rib face angle, rib angle, and rib shape were also not considered.

(b) More realistic simulation of bolt profiles is needed to obtain more accurate results.

(c) Univariate analysis cannot reflect the combined effect of bolt profile and grout specimens since these parameters are all inter-correlated.

(d) Only initial normal stress of 0.5 MPa was applied on the boltgrout interface. CNS shear tests under higher initial normal stress are needed in the future.

(e) Dynamic and cyclic interface shear behavior was ignored.

In order to obtain more general conclusions on the shear behavior of the bolt-grout interface to guide support design,more experiments with different experimental parameters are needed in the future.

5. Conclusions

The aim of this study was to investigate the influence of rock bolt profile on the bolt-grout interface shear behavior in various rock types. Accordingly, a series of shear tests of the simplified 2D bolt-grout interface with varied surface parameters under different normal stiffnesses was performed. The main conclusions are summarized as follows:

(1) It shows that the interface shear behavior is associated with the bolt profile and applied normal stiffness. Approximately ideal elastoplastic shear stress curve accompanied by a slight stick-slip phenomenon was observed for the planar interface without ribs.For the bolt-grout interface with ribs,the shear stress curves showed strain-softening characteristic when the rib spacing was 10 mm or under CNL conditions,whereas these curves showed a post-yield hardening behavior when the rib spacing was 20-40 mm under CNS conditions.

(2) The curves of normal stress and normal displacement versus shear displacement showed similar shapes in all the tests,regardless of the bolt profile and boundary conditions.In CNS shear,the normal stress and normal displacement increased first until the ultimate shear strength was reached,and then gradually declined as shearing progressed.

(3) The mechanical parameters varied as bolt profile and normal stiffness changed. Therefore, the support effect of the bolting system can be optimized by changing the bolt profile under different surrounding rock mass conditions. The ultimate shear strength of the bolt-grout interface with ribs was significantly larger than that without ribs and increased as higher normal stiffness was applied. With the increase of rib spacing, the ultimate shear strength decreased under CNL conditions,whereas it tended to increase first and then reduce under CNS conditions.Additionally,an increase in the ultimate shear strength as a function of rib height was observed.Rock bolt with larger rib spacing and less rib height were capable of accommodating large deformation before failure.The energyabsorbing capacity of the bolting system can be enhanced by increasing rib spacing and diminishing rib height.

(4) The slip failure occurred for the planar bolt-grout interface without ribs. In the case of bolt-grout interface with ribs,dilational slip failure was dominant under the CNL conditions.As the normal stiffness increased, the normal displacement was restricted, the sheared-off failure would occur when rib spacing was low, and subsequently the sheared-crushed failure was likely to occur when rib spacing was high.

Declaration of competing interest

The authors wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.

Acknowledgments

This study is supported by the key projects of the Yalong River Joint Fund of the National Natural Science Foundation of China(Grant No.U1865203),the National Key Research and Development Program of China(Grant Nos.2019YFC0605103,2019YFC0605100),and the National Natural Science Foundation of China (Grant No.51279201). The partial support from the Youth Innovation Promotion Association CAS is gratefully acknowledged.

List of symbols

L Length of specimen

W Width of specimen

H Height of specimen

a Rib top width of the bolt

b Rib base width of the bolt

s Rib spacing of the bolt

h Rib height of the bolt

θ Rib angle of the bolt

σn0Initial normal stress applied on the bolt-grout interface

knNormal stiffness applied on the bolt-grout interface

σ Normal stress on the bolt-grout interface

v Normal displacement of the bolt-grout interface

R2Coefficient of determination of the fitting curve