Experimental study on the shear performance of quasi-NPR steel bolted rock joints

Manhao He ,Shulin Ren ,Haotian Xu ,Senlin Luo ,Zhigang Tao,* ,Chun Zhu

a State Key Laboratory for Geomechanics and Deep Underground Engineering,China University of Mining and Technology,Beijing,100083,China

b School of Mechanics and Civil Engineering,China University of Mining and Technology,Beijing,100083,China

c School of Earth Sciences and Engineering,Hohai University,Nanjing,210098,China

Keywords:Energy absorption bolt Quasi-NPR (Negative Poisson’s ratio) steel Bolted rock joints Shear test Shear performance

ABSTRACT Quasi-NPR (negative Poisson’s ratio) steel is a new type of super bolt material with high strength,high ductility,and a micro-negative Poisson’s effect.This material overcomes the contrasting characteristics of the high strength and high ductility of steel and it has significant energy-absorbing characteristics,which is of high value in deep rock and soil support engineering.However,research on the shear resistance of quasi-NPR steel has not been carried out.To study the shear performance of quasi-NPR steel bolted rock joints,indoor shear tests of bolted rock joints under different normal stress conditions were carried out.Q235 steel and #45 steel,two representative ordinary bolt steels,were set up as a control group for comparative tests to compare and analyze the shear strength,deformation and instability mode,shear energy absorption characteristics,and bolting contribution of different types of bolts.The results show that the jointed rock masses without bolt reinforcement undergo brittle failure under shear load,while the bolted jointed rock masses show obvious ductile failure characteristics.The shear deformation capacity of quasi-NPR steel is more than 3.5 times that of Q235 steel and #45 steel.No fracture occurs in the quasi-NPR steel during large shear deformation and it can provide stable shear resistance.However,the other two types of control bolts become fractured under the same conditions.Quasi-NPR steel has significant energy-absorbing characteristics under shear load and has obvious advantages in terms of absorbing the energy released by shear deformation of jointed rock masses as compared with ordinary steel.In particular,the shear force plays a major role in resisting the shear deformation of Q235 steel and#45 steel,therefore,fracture failure occurs under small bolt deformation.However,the axial force of quasi-NPR steel can be fully exerted when resisting joint shear deformation;the steel itself does not break when large shear deformation occurs,and the supporting effect of the jointed rock mass is effectively guaranteed.

1.Introduction

Bolt support has been widely used in geotechnical engineering because of its significant reinforcement benefits,convenient construction technology,and low cost.It is one of the mostly used methods to control the surrounding rock in underground engineering(Huang et al.,2002;Li,2010a;Lin et al.,2014).However,the gradual increase in burial depth has led engineers to perform works in more deteriorated deeper environments as compared to shallower environments,and deep rock masses often have characteristics of high ground stress,large deformation,and strong time effect(He et al.,2005;Liu et al.,2016).The elongation and strength of traditional ordinary bolt materials are not sufficient to meet the supporting requirements of deep rock masses(Li,2010b;He et al.,2014,2021;Li et al.,2019).In addition,deep rock masses often exist in a block system composed of many irregularly distributed joints,cracks,faults,and other weak structural surfaces that cut the rock masses into blocks.The mechanical behavior,deformation characteristics,and instability modes of deep rock masses are controlled by structural planes.The bolt support system plays a key role in restraining the displacement and deformation of unstable blocks along the structural plane.However,most of the existing studies on the bolting mechanism and performance evaluation of bolts only consider the effect of bolts in the pure tension state,and the lateral shear effect of the bolt is often ignored.In fact,field engineering has shown that the failure of anchor bolts in deep support projects is often caused by the combined effects of tensile and shear forces(Fig.1) (Li,2010a;Liu et al.,2018).Therefore,studies on the shear resistance of bolts are of great significance in support engineering.With the increasing demand for resources and continuous expansion of the scope of human activities (Liu et al.,2018;Jiang et al.,2019;Wu et al.,2019a),geotechnical activities such as energy mining and the construction of traffic tunnels have gradually moved to deeper locations,and increasingly more attention has been paid to the study of bolt materials and their shear performance in deep support engineering.

In response to the support problems encountered during deep geotechnical engineering,scholars at home and abroad have attempted to develop a new type of bolt that can provide constant resistance during the deformation stage of the surrounding rock and that has good extension properties,i.e.bolts with energyabsorbing properties.The concept of energy-absorbing bolts was first proposed by Ortlepp (1992) in the early 1990s.These bolts have been studied for nearly 30 years and rich results have been obtained.The first real energy-absorbing bolt,called the cone bolt,was developed by Jager (1992).It is mainly composed of a smooth steel rod and a flattened conical flaring forged at the distal end of the bolt.The maximum deformation of the cone bolt can reach more than 200 mm,and it can absorb energy of more than 16-39 kJ.However,the cone bolt is mainly anchored by grouting,and it takes a long time for the grout to solidify to reach an adequate supporting strength.The Canadian Norand Company improved the cone bolt and developed the modified cone bolt (MCB),which is a new type of bolt with resin anchoring ability(Cai and Champaigne,2012).MCB38 and MCB33 are two typical representatives of the MCB,which have a deformation range of 300-900 mm and an energy absorption capacity of 35 kJ.In 2006,the D-bolt was developed by Chunlin Li (2010b).It is composed of a smooth steel bar and three or more anchoring elements(Li,2010b;2012;Li and Doucet,2012).The D-bolt has the characteristic of large deformation that is achieved by the plastic deformation of the steel between the anchoring elements.The yield strength of the D-bolt is 450 MPa,and the elongation is 12%-20%.In addition,other types of energy-absorbing bolts,such as the Garford dynamic bolt,the Roofex bolt,and the tension and compression-coupled (TCC) yield bolt (Wu et al.,2019a),have been used for support in deep excavations.However,these bolts are mainly made of ordinary steel materials with a Poisson’s effect(referred to as Poisson’s ratio(PR)materials),i.e.small deformation materials that break and fail due to necking deformation during tension.In addition,although they have improved energy-absorption performance obtained through structural combinations or rod designs,the nature of the PR materials is the same.On the contrary,due to the particularity of the PR material’s structure,it is necessary to expand the hole or use special tools for installation in actual engineering applications,which leads to a complex construction process and high costs.

Fig.1.Deep jointed rock mass support engineering:(a) Schematic diagram of support engineering;and(b)Field failure phenomenon of bolted jointed rock mass(Li,2010a).

In 2009,a macro-negative Poisson’s ratio (NPR) structural bolt was developed by the State Key Laboratory of Geomechanics and Deep Underground Engineering of China University of Mining and Technology (Beijing).This bolt is also known as 1G-NPR,representing the first generation of NPR products developed in the laboratory (He et al.,2014).In contrast to the traditional bolts that undergo necking during tension,the structure of the macro-NPR bolt expands when subjected to tensile load,and it has the valuable characteristics of high constant resistance,large deformation,and energy absorption.Fig.2a shows the composition and mechanical characteristic curves of the macro-NPR bolt (He et al.,2021).The constant resistance of the two types of macro-NPR bolts can reach 350 kN and 850 kN,and the maximum deformation is 1000 mm and 2000 m,respectively.Their mechanical properties are significantly better than other types of energyabsorbing bolts.Accordingly,the macro-NPR bolts are widely used for tunnel deformation control,surrounding rock support of roadways,slope reinforcement,landslide monitoring,and other engineering fields (He et al.,2012,2021;Ren et al.,2020;Wang et al.,2020;Tao et al.,2021).However,similar to the other types of bolts,the macro-NPR bolt is also made of a combination of various PR materials.Based on the research of macro-NPR bolts,in 2014,the first author’s team performed research on quasi-NPR materials,integrating the idea of the NPR effect to develop a metallic material not only with a similar geometric shape to an ordinary rebar,but also with high strength,large deformation,and high energy absorption properties.The static tension curve of quasi-NPR steel is shown in Fig.2b.It can be observed that the strength of the quasi-NPR bolt can reach 900-1100 MPa,and the corresponding elongation is 68%-36%.There is no yield platform during the stretching process,and no obvious necking occurs after the steel bar is broken (Gu et al.,2021;He et al.,2021).Tang et al.(2021) found that the high strength and high toughness of the quasi-NPR bolt were also maintained at strain rates from 0.1 s-1to 1000 s-1.Quasi-NPR material,also known as 2G-NPR,which represents the second generation of NPR products developed in our laboratory,overcomes the contrasting characteristics of the high strength and high ductility of traditional PR materials,and extraordinary energy absorption characteristics are realized from the nature of the material rather than the structure.

Fig.2.Macro-NPR structural bolt and quasi-NPR bolt:(a)The composition and mechanical characteristic curves of macro-NPR bolts;and(b)The mechanical characteristic curve of quasi-NPR bolts (He et al.,2021).

Many factors influence the shear performance of bolted rock joints,such as bolting angle,joint surface roughness,bolting method,and loading conditions,and these have been extensively studied.A direct shear test of bolted rock joints was first carried out by Bjurstrom (1974),where the shear performance of fully encapsulated rebar bolts with different bolting angles to strengthen a granite body with continuous joints was studied.The results showed that the bolting angle has a significant influence on the‘dowel effect’of the bolts.When the bolting angle is less than 35º,the bolt exhibits tensile failure characteristics,and its transverse shear effect is negligible.However,Liu and Li (2018) showed that when the bolting angle is smaller than the friction angle of the joint surface,the transverse shear resistance of the bolt is close to zero.Li and Liu (2019) carried out an experimental study on the influence of bolting angle and grouting strength on the shear performance of a bolt and concluded that the bolt shear effect is the best when the bolting angle is 40º-50ºand the grouting strength is 50 MPa.Grasselli (2005) also performed related studies on the bolting angle,and he pointed out that there is an optimal bolting angle to optimize the shear effect of bolts,which is generally between 30ºand 60º.Cui et al.(2020)studied the effects of two different normal boundary conditions,constant normal load (CNL) and constant normal stiffness(CNS),on the shear performance of bolted jointed rock masses,and the results illustrated that under CNS conditions,the joint surface showed more obvious failure characteristics during the shear process.Chen et al.(2018) studied the influence of joint surface roughness on the deformation characteristics of bolts and revealed that when the joint surface roughness increases,the length of the transverse shear deformation section of the bolt gradually increases.Wu et al.(2018) stated that compared with unbolted jointed rock masses,bolts can effectively suppress the dilatancy effect of joints.Li et al.(2016) compared the effects of fiberglass bolts,rebar bolts,and anchor cables on the shear resistance of joints through indoor shear tests,and pointed out that the shear stiffness of a bolted rock mass is significantly affected by the stiffness of the bolt material.Wu et al.(2019b) studied the failure characteristics and reinforcement effect of bolts under cyclic shear loading,and showed that the shear effect of bolts is significantly affected by the number of cycles and cyclic displacement.Chen(2014),Chen and Li (2015) and Wu et al.(2019a) investigated the shear characteristics of D-bolts and TCC bolts,and showed that the shear resistance of these two types of energy-absorbing bolts is significantly better than that of ordinary bolts.In summary,previous studies have shown that the bolting angle,structural surface roughness,loading conditions,and other factors have significant effects on the shear resistance of bolts.However,these studies used bolts of ordinary PR material,and there have no studies on the shear properties of quasi-NPR steel.Therefore,it is urgent and important to study the shear properties of quasi-NPR steel bolted jointed rock masses.

In this study,to analyze the shear performance of quasi-NPR steel bolted rock joints,indoor shear tests of bolted rock joints were designed and carried out under different normal stresses.In addition,Q235 steel and#45 steel,two representative ordinary bolt steels,were set up as a control group to compare and analyze the shear strength,deformation and instability mode,shear energy absorption characteristics,and the bolting contribution of various bolts to serve as a reference for the practical engineering applications of quasi-NPR steel bolts.

Fig.3.Rock bolt specimens.

2.Testing program

2.1.Bolt preparation

To study the shear resistance of quasi-NPR steel bolted rock joints,the performance of quasi-NPR steel and ordinary PR steel was compared.The test bolt materials were made of three kinds of smooth steel bars with a diameter of 8 mm,i.e.quasi-NPR steel,Q235 steel,and #45 steel.Q235 steel is a commonly used bolt material in current engineering works.#45 steel is manufactured by the cold drawing process,which is commonly used in engineering to improve the yield strength of bolts.Therefore,these two types of steel are good representatives for comparison.First,these three kinds of steel bars were processed into a rod body with a length of 170 mm.Because the end of the bolt is usually installed with a base plate and a nut to lock the end of the bolt head to enhance the reinforcement effect,in this test,both ends of the steel bar were threaded with a thread length of 10 mm,and nuts and gaskets were provided for bolting at both ends of the samples(Fig.3).Fig.4 displays the typical stress-strain curves of these three steel bars under static tension conditions.The mechanical parameters of these 3 bars,as shown in Table 1,are obviously different.Q235 steel has an obvious yield platform when the strain is about 2%,the yield strength is about 340 MPa,the tensile strength is 531 MPa,and the elongation after fracturing is about 20%.#45 steel has no obvious yield platform after the cold drawing process,its tensile strength is 839 MPa,and its elongation after fracturing is only 10%.Quasi-NPR steel has no yield platform,its tensile strength can reach 987 MPa,the elongation after fracturing reaches 32%,and it has the characteristics of high strength and high elongation.

Table 1 Mechanical parameters of the test bolts.

2.2.Preparation of bolted joint sample

A sample model of the bolted rock joints used in the test is presented in Fig.5a.The test samples were processed from marble retrieved from the engineering site.In this test,the jointed rock samples consist of two cuboids and the size of each cuboid is 150 mm × 150 mm × 75 mm.Previous studies indicated that the roughness of the joint surface has a great influence on the shear performance of bolts.This paper only considers joints with a horizontal smooth surface.

The specific production process of the bolted rock joint samples is as follows.First,the marble retrieved on-site was cut into cuboids of 150 mm×150 mm×75 mm as the upper and lower plates of the jointed rock mass.Subsequently,a hole was drilled at the center of the cuboid rock blocks to facilitate subsequent bolt anchoring and grouting procedures.Professional drilling equipment was used,which mainly included a drilling power system,a water injection cooling device,and a drilling bit.By changing the diameter of the drilling bit,the hole diameter can be controlled (Fig.5b).Previous studies have shown that the borehole diameter should generally be 2-4 mm larger than the bolt diameter,and therefore the borehole diameter chosen in this study was 12 mm.Considering that there are viscous fillers such as fault gouge distributed between the structural surfaces like joints and faults at the engineering site,2-3 mm thick plain cement slurry was applied between the upper and lower cuboid rock blocks to form an unbolted jointed rock mass(Fig.5c).Both the plain cement paste applied and the grouting slurry in the boreholes were made up of ordinary Portland cement with a water-cement ratio of 0.42.After a standard indoor curing period of 7 d(Fig.5d),the cement slurry reached its initially preset strength,and subsequent operations such as anchoring and grouting were carried out.During the anchorage operation,the bolt was driven through the central hole of the rock blocks,with one end of the bolt being locked with a nut(Fig.5e),and then grouting was performed at the other end of the hole (Fig.5f).After the grouting was completed,gaskets and nuts were used to lock the bolts in place.The rock mass after anchoring and grouting was cured under indoor standard conditions for 28 d(Fig.5g).After the grouting strength reached its final preset strength,the anchoring of the jointed rock mass sample was completed.

Fig.4.Stress-strain relationship of different bolts.

2.3.Shear test procedure

To study the influence of quasi-NPR steel,Q235 steel,and 45#steel on the mechanical properties of bolted rock joints,direct shear tests with normal stresses(2 MPa,4 MPa,8 MPa,and 10 MPa)and 4 bolting types(unbolted,quasi-NPR steel,Q235 steel,and#45 steel)were carried out under the CNL condition.The test error was taken into account,and three rock samples were prepared for repeated tests under each working condition.A total of 48 samples were tested.The microcomputer-controlled direct shear equipment from China University of Mining and Technology (Beijing) was used in this experiment.The instrument is mainly composed of a normal and a tangential hydraulic control unit,a hydraulic servo control system,a control display system,and a pressure chamber(Fig.6a).The maximum normal and tangential forces that the equipment can apply are 500 kN,which is suitable for uniaxial compression tests or direct shear tests of rock,concrete,cement mortar,and other materials.The structural performance of the equipment also meets the requirements of relevant test specifications.Before the test,the sample was placed in the direct shear box.It should be noted that because the bolting ends of the sample in this study were higher than the surface of the rock mass sample,the conventional direct shear box could not be placed horizontally and stably.Therefore,the direct shear box needed to be improved.A small hole with a diameter of 15 mm was cut at the center of the top and bottom of the direct shear box.The test bolts could penetrate the cut holes to ensure that the direct shear box could be placed horizontally and meet the test loading requirements (Fig.6b).The stress control method was used to apply normal stress to the sample,and the normal loading rate was 0.1 kN/s.After the normal stress reached the preset value,it was stabilized for 10 s,and then the horizontal shear displacement was applied through the displacement control method.The shear displacement rate was 0.01 mm/s and this was applied until the bolt broke or the shear displacement reached 35 mm (the maximum range of the direct shear instrument).Then,the shear test was terminated.During the test,the shear force-shear displacement curve was monitored and recorded in real-time by the electro-hydraulic servo system.

3.Test results and analysis

3.1.Deformation and failure characteristics of the bolted rock joints

Fig.5.Schematic diagram and production process of the anchored jointed rock mass samples: (a) Sample model;and (b-g) Sample production process.

Fig.6.Testing setup: (a) Direct shear equipment;and (b) Shear test model of anchored jointed rock mass.

When bolts exert a lateral shear effect in a jointed rock mass,it inevitably produces a certain lateral deformation due to the comprehensive action of the external load and the surrounding rock’s compression(Pellet and Egger,1996;Li et al.,2015).Analysis of the deformation and instability characteristics of the jointed rock mass and the bolts after a shear test is important to understand the bolting mechanism.Fig.7 shows the deformation and instability of the bolted rock mass after the shear test.Fig.7a is a cut-away photo of the sample after the test.It can be seen that the bolt has local shear deformation near the joint surface,and the shape of the deformation is an anti-symmetric S-shape.In addition,a compression zone and a cracking zone were formed on the left and right sides of the bolt and the joint plane.In the cracking zone,the bolt was separated from the anchoring slurry,and in the compression zone,extrusion stress was produced at the interface between the bolt and the hole wall,causing the rock mass and the anchor slurry in the region to be crushed by compression.In the process of loading,stress concentration occurred at the orifice of some samples due to the extrusion of the bolt,and cracks appeared in the test blocks,which eventually led to the cracking of the sample (Fig.7b).However,because the sample was placed in the shear box,the fractured rock mass could continue to be loaded until the test termination conditions were met.When the upper plate of the rock mass sample was taken out after the test,it was observed that the ordinary PR bolts(Q235 steel and#45 steel)were directly cut off,and an obvious white elliptical wear area appeared near the walls of the joint face,that is,the damaged area occurred on the joint surface.The direction of the long axis of the ellipse was the shear direction.A compression zone formed on one side of the bolt,and the other side was debonded from the hole wall slurry to form a crack zone (Fig.7c).When the quasi-NPR steel was bolted,the jointed rock mass underwent large shear deformation until the test was terminated,and the quasi-NPR steel did not break(Fig.7d).

Fig.8 is a schematic diagram of the sample deformation before and after the direct shear test.During the shear loading process of the bolted jointed rock samples,the bolts are subjected to the combined effect of tension and shearing;therefore,in addition to axial tensile deformation,the bolt will also undergo bending deformation near the joint plane.When the bending moment reaches the maximum value,the bolt section at this point reaches completely plastic and causes a rotation effect.Finally,a pair of plastic hinges with oblique symmetric distribution is formed on both sides of the joint plane (Liu and Li,2017).To further analyze the deformation characteristics of the bolt,the bolt was taken out of the bolted rock mass after the test,and its geometric parameters were statistically analyzed,including the bolt deformation lengthAB,the vertical (AC) and the horizontal (BC) component lengths,and the plastic hinge angle θ.

Fig.7.Deformation and instability of anchor jointed rock masses after the shear tests:(a)Sectional view of the sample after shearing;(b)Fracture development in the bolted jointed rock mass;(c) Shear failure characteristics of the joint plane and shear failure of PR steel;and (d) Large deformation of quasi-NPR steel which does not fail.

Fig.8.Schematic diagram of the sample’s deformation (a) before and (b) after the direct shear test.

Fig.9 shows the deformation and failure images of the Q235 steel,#45 steel,and quasi-NPR steel under different normal stresses.Generally speaking,fracturing of the Q235 steel and #45 steel occurs when the deformation lengthABis 11.13-12.78 mm,that is,when the deformation of the bolt reaches 1.3-1.6 times its diameter when subjected to the combined action of tension and shearing.However,under the same test conditions,when the maximum deformation reaches 44.66 mm (shear displacement reaches the range of the testing machine,and the test is terminated),quasi-NPR steel does not fracture,and it can withstand a deformation of more than 5.5 times its diameter.Fig.10 shows the average lengths ofAB,AC,andBCof three samples under each test condition.Under different normal stress conditions,the deformation lengthABof all the bolts is relatively stable.However,the vertical componentACdecreases with the increase in the normal stress,and the horizontal componentBCincreases with the increase in the normal stress.In general,the deformation capacity of quasi-NPR steel is 3.5 times more than that of Q235 steel and #45 steel under the shear test conditions.In addition,Fig.10 shows that the plastic hinge angle θ of quasi-NPR steel is 34.22º,38.29º,46.04º,and 49.82ºunder the conditions of 2 MPa,4 MPa,8 MPa,and 10 MPa,respectively.As the normal stress increases,the plastic hinge angle increases.For further analysis,the plastic hinges of all the samples were counted,as shown in Fig.11.The plastic hinge angle θ was statistically calculated for the three samples under each test condition and the average value was used.The plastic hinge angle is the result of the combined action of many variables,and we try to explain the relationship between it and the normal stress as follows.The samples bolted by Q235 steel and#45 steel all show a phenomenon of the plastic hinge angle increasing with the increase in the normal stress.This is mainly because,as the normal stress increases,the compressive force between the upper and lower blocks of the bolted jointed rock mass sample becomes larger.This is equivalent to the bolt bearing a pair of larger bending momentMin the bending deformation area of the joint plane,which then leads to the increase in the plastic hinge angle θ.On the other hand,we found that in the previous analysis,the bolt undergoes S-shaped deformation under shear force.Therefore,the increase of the normal load increases the load applied to the S-shaped bending section of the bolt,which produces a larger bending deformation effect.

3.2.Shear stress-shear displacement

3.2.1.Unbolted rock joints

Fig.12a shows the shear force-shear displacement curve of the unbolted jointed rock mass under different normal stresses(2 MPa,4 MPa,8 MPa,and 10 MPa).These curves have the same development characteristics (Fig.12b) and can be divided into 4 stages:

Fig.9.Deformation and failure photos of the bolts: (a) Q235 steel;(b) #45 steel;and (c) Quasi-NPR steel.

Fig.10.Bolt deformation length AB,its vertical component AC, and horizontal component BC.

Fig.11.Relationship between the plastic hinge angle θ of the bolts and normal stress.

(1) Elastic rising stage (OA).In this stage,the relationship between the force and displacement is basically linear.A small displacement occurs in the shear direction,and the shear force increases rapidly.The jointed rock mass mainly depends on the bonding force between the rock surface and the cement grout to resist the horizontal shear force.

(2) Brittle fracture stage (AB).With the continuous increase in the shear force,which becomes greater than the cementing strength of the cement slurry,the cementation between the rock surface and the cement slurry is destroyed,and the shear force drops sharply in an instant.

(3) Residual compaction stage(BC).A penetrating failure surface is formed after the failure of the cementation of the joint surface,and it is gradually compacted.

(4) Residual deformation stage (CD).As the shear displacement increases,the shear force basically remains stable.In this stage,the jointed rock mass only relies on the friction between the joint surfaces to resist the horizontal shear force.

3.2.2.Bolted rock joints

Fig.13a shows the shear force-shear displacement curves of the bolted rock joints under four normal stresses,and the characteristic curve is shown in Fig.13d.The characteristics of each stage of the curves are analyzed as follows:

(1) Elastic rising stage (OE).Similar to the unanchored jointed rock mass,the shear force in this stage increases rapidly with the increase in the shear displacement,and the relationship between them is basically linear.

(2) Brittle fracture stage(EF).The cementation between the joint surface fails,the damage is brittle,and the shear force drops suddenly.

(3) Yield stage (FG).In this stage,the shear force shows an upward trend with the increase in the shear displacement,and the curve presents a nonlinear characteristic of a larger curvature.The anchor fully exerts its shear resistance and resists the relative deformation between the joint surfaces,i.e.it shows the‘dowel effect’.The friction between the joint surfaces still plays a certain role in resisting shear deformation in this stage.

(4) Plastic strengthening stage (GH).The jointed rock mass is strengthened by the bolt and can still maintain a high shear strength under a large shear displacement.Compared with the brittle failure characteristics of the unbolted jointed rock masses,the bolted jointed rock masses have significant ductile failure characteristics,which are of great significance to ensure the stability of deep rock masses.

(5) Fracture failure stage (HI).The shear force suddenly drops,and the sound of brittle fracturing of the steel bars was heard during the test.In this stage,the bolt breaks and the anchoring effect fails.

(6) Residual compaction stage (IJ).

(7) Residual deformation stage (JK).

A comparative analysis of the shear force-shear displacement curves of the quasi-NPR steel,the Q235 steel,and the #45 steel shows that the quasi-NPR steel does not undergo fracture failure at the end of the shear test,and it can provide stable shear resistance under the condition of a large transverse deformation,which effectively guarantees the safety and reliability of using quasi-NPR steel to bolt jointed rock masses under shear load.

3.3.Shear strength

Fig.12.Test results of the unbolted jointed rock mass: (a) The shear force-shear displacement curves;and (b) Characteristic curve of the unbolted jointed rock mass.

The shear strength of the bolted rock joints depends on the inherent shear strength of the unbolted jointed rock mass and the shear performance of the bolt.Shear strength refers to the peak strength when the rock samples fail during the shear test,and it represents the ultimate ability to resist shear failure.It is an important parameter to describe the shear characteristics.Table 2 shows the shear strength of the samples and the strength increment before and after bolting under different test conditions.Since the quasi-NPR steel did not break during the test,the shear strength is still increasing.For the convenience of comparative research,the shear stress at the end of the shear test is taken as the shear strength of the quasi-NPR steel bolted jointed rock mass.It can be seen in the table that the shear strength of the rock mass after anchoring has been improved to different degrees as compared with the unbolted jointed rock mass.The average strength increments of the Q235 steel,#45 steel,and quasi-NPR steel are 0.41 MPa,0.94 MPa,and 1.79 MPa,respectively.The quasi-NPR steel has the highest shear strength.

The shear strength of the bolted and unbolted jointed rock masses follows the Mohr-Coulomb strength criterion (Eq.(1)).To further analyze the data,the average shear strength of each test condition in Table 2 is fitted,and the results are shown in Fig.14.

wherecis the cohesion(MPa),σ is the normal stress(MPa),φ is the internal friction angle (º),and τ is the shear strength(MPa).

Table 3 shows the statistics of various parameters in the fitting results.Under different anchoring conditions,both the shear strength and the normal stress correlate well.The cohesion of the unbolted jointed rock mass is 0.562 MPa,and the internal friction angle is 32.54º.After anchoring,the slope and intercept of the fitting curve increase to different degrees,that is,the anchoring effect of the bolt increases the cohesion and the internal friction angle of the jointed rock mass,which are defined as the equivalent cohesion and equivalent internal friction angle,respectively.The equivalent cohesions of the Q235 steel,#45 steel,and quasi-NPR steel are 0.732 MPa,1.323 MPa,and 1.815 MPa,and the equivalent internal friction angles are 34.18º,33.74º,and 36.05º,respectively.These results show that the quasi-NPR steel bolt has the largest cohesion and internal friction angle in the jointed rock mass.Compared with the bolting effect of Q235 steel and#45 steel,the bolting effect of quasi-NPR steel is better.

3.4.Action length and shear energy absorption characteristics of the bolts

In support engineering at depth,the supporting structure should have certain strength to resist deformation and a certain flexibility to adapt to deformation.Therefore,for shear reinforcement of anchored jointed rock masses,the action length and shear energy absorption characteristics of the bolt are also important.These parameters were analyzed based on the shear force-shear displacement curves of the Q235 steel,#45 steel,and quasi-NPR steel bolted jointed rock masses.The point on the curve that represents the starting of the yielding stage is pointFin Fig.13d,and the corresponding displacement of this point is regarded as the shear displacementlswhen the bolt starts to exert its shear resistance.The point on the curve that denotes the end of the fracture failure stage is pointIin Fig.13d,and the displacement corresponding to this point is the shear displacementlfwhen the bolt fails.Since there is no fracture failure of the quasi-NPR bolt,to facilitate the overall analysis,the maximum shear displacement of 35 mm in the shear test is taken asls.The difference between the shear displacementlfandlsis defined as the bolt action length Δl.As shown in Table 3,under different normal stresses,the action length of Q235 steel is 7.45-8 mm,and it is 7.63-9.11 mm for#45 steel and 32.43-32.77 mm for quasi-NPR steel.The action length of the quasi-NPR steel is at least 3.5 times more than that of Q235 steel and#45 steel.It is worth noting that the quasi-NPR steel still does not undergo fracture failure under this action length,which means that the quasi-NPR steel can effectively be used to prevent engineering disasters caused by the deformation and dislocation of jointed rock masses exceeding the shear length of the bolt.To comprehensively evaluate the ability of different types of bolts to resist deformation and provide shear resistance during the shear process,the parameter of shear energy absorption is proposed.As shown in Fig.15,the area between the shear force-shear displacement curve and the horizontal coordinate axis within the range of the bolt action length is defined as the total energyEs,which mainly includes the energy absorbed by the bolt(Eb)and the energy absorbed by joint friction (Ef).Therefore,to compare the energy absorption characteristics of the bolt,we separately calculated the total energyEsand the joint friction absorption energyEf,and their difference was regarded as the bolt absorption energyEb:

The calculation results under different test conditions are listed in Table 4.Under the normal stresses of 2 MPa,4 MPa,8 MPa,and 10 MPa,the shear energy absorption of Q235 steel is 0.124 kJ,0.186 kJ,0.291 kJ,and 0.356 kJ,respectively,and the average is 0.239 kJ.For#45 steel,it is 0.199 kJ,0.266 kJ,0.495 kJ,and 0.396 kJ,respectively,and the average is 0.33 kJ.The shear energy absorption of the quasi-NPR steel is 1.311 kJ,1.342 kJ,1.164 kJ,and 1.045 kJ,respectively,and the average is 1.216 kJ.The results show that the quasi-NPR steel has significant energy-absorbing properties,which is at least 3.68 times that of Q235 steel and #45 steel.The quasi-NPR steel has obvious advantages when it comes to absorbing the energy released by the shear deformation of jointed rock masses.

Fig.13.Shear force-shear displacement curves of the bolted jointed rock masses:(a)Q235 steel;(b)#45 steel;(c)Quasi-NPR steel;and(d)Characteristic curve of the bolted jointed rock mass.

Table 2 Statistics of the shear strength and strength increment before and after anchorage.

Fig.14.Fitting curves of the shear strength of the jointed rocks before and after bolting.

3.5.Bolting contribution

The contribution of a bolt to the shear resistance of a jointed rock mass is one of the core issues in anchorage research of jointed rock masses.The contribution parameterRof the bolt is a key parameter used to evaluate the shear resistance increment of the bolt in a jointed rock mass.Grasselli (2005) and Jalalifar and Aziz(2010) put forward a formula for calculating the contributionRof a bolt as follows:

whereFsis the shear force of the anchored jointed rock mass(kN),andNis the normal force applied in the test(kN).

Table 5 shows the calculation results of the bolting contribution of the different bolt types.When the normal stresses of Q235 steel are 2 MPa,4 MPa,8 MPa,and 10 MPa,theRvalues are 19.07 kN,15.16 kN,17.31 kN,and 20.27 kN,respectively,and the average bolt contribution is 17.95 kN.The average bolt contributionRof #45 steel under the same test conditions is 31.22 kN,and it is 42.48 kN for the quasi-NPR steel.The contributionRof quasi-NPR steel is significantly higher than that of Q235 steel and #45 steel.Previous studies showed that the contribution of shear resistance of a bolt is mainly manifested in two aspects (Li and Liu,2019),that is,the transverse ‘dowel effect’ of the bolt directly contributes toRcand the axial ‘constraint effect’ indirectly contributes toRf.The direct contributionRcis also called the cohesion enhancement effect,and the indirect contributionRfis also called the internal friction angle enhancement effect.The bolt at the joint plane is subjected to a transverse shear force,resulting in bending deformation and the final failure,mainly due to the combined effect of the axial forceN0and the shear forceQ0produced by the bolt,as shown in Fig.16.The formulae for calculating the direct contributionRc,the indirect contributionRf,the axial forceN0,and the shear forceQ0of the bolt are as follows (Ferrero,1995;Pellet and Egger,1996;Li et al.,2016):

Table 3 Fitting results for shear strength by Mohr-Coulomb failure criterion.

Fig.15.Shear energy absorption diagram of the bolt.

where θ is the deflection angle of the bolt (º).

Dight(1983)proposed an analytical equation for predicting the failure of bolts that undergo shearing,that is,the axial forceN0and the shear forceQ0must satisfy the following equations:

whereNfandQfare the ultimate tensile and shear forces of the bolt(kN),respectively;σfand τfare the tensile and shear strengths of the bolt(MPa),respectively;andAbis the cross-sectional area of the bolt (mm2).

According to the Tresca criteria,we have

In Eqs.(4)-(9),the bolt contributionR,bolt deflection angle θ,internal friction angle φ,bolt tensile and shear strengths(σfand τf),and cross-sectional area of the boltAbwere all obtained by experiments.Accordingly,the axial forceN0and shear forceQ0of Q235 steel,#45 steel,and quasi-NPR steel under different normalstresses were calculated,as shown in Table 5.Since the shear strength of the bolt is much lower than its tensile strength,if a higher supporting resistance is required to achieve a better supporting effect in a bolted jointed rock mass,the bolt should exert axial resistance as far as possible instead of shear resistance.According to the axial forceN0and shear forceQ0,theQ0/N0ratios of Q235 steel,#45 steel,and quasi-NPR steel under different normal stresses are 1.05,1.02,and 0.63,respectively.This indicates that the shear force of Q235 steel and #45 steel plays a major role in their shear resistance,and therefore fracture failure occurs under small deformation of the bolts.However,the quasi-NPR steel can fully exert its axial force when resisting joint shear deformation,and therefore the bolt itself will not be sheared and fail when large deformation occurs.This effectively guarantees the supporting effect of a jointed rock mass bolted with quasi-NPR steel.

Table 4 Statistics of action length and shear energy absorption of different bolt types.

Table 5 Statistics of the bolt contribution and the axial and shear forces at failure.

Fig.16.Schematic diagram of bolting force of the bolted jointed rock mass.

4.Conclusions

In this study,indoor shear tests of quasi-NPR steel bolted rock joints under different normal stresses were performed and the shear performance of quasi-NPR steel was studied.Two representative ordinary steel bolts,Q235 steel and 45#steel,were set up as a control group for comparative tests.The main conclusions are as follows:

(1) Analysis of the deformation and failure of bolted rock joints shows that after the shear test,the bolt undergoes local shear deformation near the joint surface,and the deformation shape is an anti-symmetric S-shape.A compression zone and a cracking zone are formed on the left and right sides of the bolt and the joint plane.A pair of plastic hinges with oblique symmetric distribution is formed on both sides of the joint plane.When the normal stress increases,the plastic hinge angle increases.Fracturing of the Q235 steel and 45# steel bolts occurs when the deformation of the bolts reaches 1.3-1.6 times their diameter when subjected to the combined action of tension and shearing.Under the same test conditions,quasi-NPR steel has a significant advantage in terms of its deformation ability,which is more than 3.5 times that of Q235 steel and #45 steel.

(2) Analysis of the shear force-displacement curve shows that the shear process of the unbolted rock joint can be divided into four stages,and that of the bolted rock joints can be divided into seven stages.The bolted rock joints have significant ductile failure characteristics under shear load,which effectively improves the brittle failure performance of the bolted rock joints.

(3) Shear strength analysis shows that the average strength increments of Q235 steel,#45 steel,and quasi-NPR steel are 0.41 MPa,0.94 MPa,and 1.79 MPa,respectively;and the quasi-NPR provides the highest shear strength.The shear strengths of the bolted and unbolted jointed rock masses conform to the Mohr-Coulomb strength criterion.The results of linear fitting show that the cohesion and internal friction angle of the jointed rock mass increase the most when the jointed rock mass is anchored with quasi-NPR steel.

(4) Analysis of the bolt action length and shear energy absorption characteristics shows that the action length of quasi-NPR steel is at least 3.5 times more than that of Q235 steel and #45 steel.In addition,under the same conditions,the quasi-NPR steel has significant energy absorption characteristics,which is at least 3.68 times that of Q235 steel and#45 steel.The quasi-NPR steel has obvious advantages when it comes to absorbing the energy released by the shear deformation of a jointed rock mass.

(5) Analysis of the bolt contribution shows that the contribution of quasi-NPR steel is significantly higher than that of Q235 steel and #45 steel.The calculation results of the axial and shear forces show that the shear forces of Q235 steel and#45 steel play a major role in their shear resistance,and therefore fracture failure occurs under small deformations of the bolt.However,quasi-NPR steel can fully exert its axial force when resisting joint shear deformation,and therefore the bolt itself does not be sheared and fail when large deformation occurs.This effectively guarantees the supporting effect of quasi-NPR steel bolted rock joints.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This study has been funded by the National Natural Science Foundation of China (Grant No.41941018) and the Second Tibetan Plateau Scientific Expedition and Research Grant (Grant No.2019QZKK0708).