A novel energy-absorbing rock bolt with high constant working resistance and long elongation: Principle and static pull-out test

Construction and Building Materials 243 (2020) 118231

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A novel energy-absorbing rock bolt with high constant working resistance and long elongation: Principle and static pull-out test Yang Hao a,c, Yu Wu a,b,⇑, P.G. Ranjith c, Kai Zhang a,b, Guan Hao b, Yi Teng b a

State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China c Department of Civil Engineering, Monash University, Clayton Campus, Victoria 3800, Australia b

h i g h l i g h t s
A novel energy absorbing rock bolt with high constant working resistance and long elongation was proposed.
The mechanism on working resistance is the plastic flow of steel.
The structure and the installation process of the new bolt are simple with low-cost of material requirements.
Static pull-out experiments were conducted to test the static performance of the new bolt.

a r t i c l e

i n f o

Article history: Received 28 July 2019 Received in revised form 18 January 2020 Accepted 20 January 2020

Keywords: Energy-absorbing rock bolt High constant working resistance Long elongation Static pull-out test Numerical modeling

a b s t r a c t With mining at deep levels worldwide, surrounding rocks of roadways are prone to suffer from high stress fields, large deformation, and burst-potential. Therefore, it is critical to develop high performance energy-absorbing rock bolts to carry high load, accommodate large rock deformation, and energy absorbing. In this paper, a novel energy-absorbing rock bolt with high constant working resistance and long elongation is theoretically and experimentally investigated. The new bolt is composed of three main parts: a rebar, a sleeve tube with a partial slope in the inner surface, and a circle of steel balls. The working resistance is generated by plastic flow of the sleeve tube by contact force between the steel balls and the sleeve tube. A mechanical model is established based on Contact Mechanics to better understand the factors affecting the working resistance and to guide the static pull-out tests. Two batches of the new rock bolt with constant working resistances ranging from 60 kN to 145 kN were developed by changing the number and radius of the steel balls in static pull-out experiments. The load-displacement curves of the new rock bolt indicate the performance of the new rock bolt is characterized by high stiffness, high constant working resistance and adjustable supporting length. The constant working resistance corresponds positively to the gouging depth and the radial expansion of the sleeve tube, based on theoretical analysis verified by test results. A numerical simulation of deep soft roadway is applied to investigate the performance of new energy absorbing rock bolt. Ó 2020 Elsevier Ltd. All rights reserved.

1. Introduction Rock bolts have been applied in civil engineering, slope stability, and underground engineering (e.g. tunneling, subway excavation, roadway supporting) for many years [1–7]. With the mining depths for both metal ore and coal mines beyond 1000 m [8,9], the deformation capacity of conventional rock bolts, such as ⇑ Corresponding author at: State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China. E-mail address: [email protected] (Y. Wu). https://doi.org/10.1016/j.conbuildmat.2020.118231 0950-0618/Ó 2020 Elsevier Ltd. All rights reserved.

fully-grouted rock bolts, end-anchored mechanical rock bolts with pre-stress and frictional rock bolts is not capable of combating the large deformation of surrounding rock mass in weak and soft rocks induced by high field stress [10,11]. In addition, high stress may induce rock burst [12] in hard rocks, and the conventional rock bolts are too stiff to mitigate dynamic hazards. Therefore, a design philosophy for energy-absorbing bolts was given by McCreath and Kaiser [13], who proposed that the bolts must be allowed to yield and slide with ground movements and deform plastically over large displacements at high displacement rates to absorb a reasonable amount of kinetic energy in yielding up to 200–300 mm in deep underground engineering [14].

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Many studies have investigated energy-absorbing rock bolts based on theoretical analysis, numerical modelling, laboratory study and field application [9,15–20]. Energy-absorbing rock bolts can be categorized as structural component sliding types, and steel deformation types, based on their energy-absorbing mechanism [7]. Typical representatives of steel-deformation energyabsorbing rock bolts are those proposed by Ansell [14,21] and Li and colleagues [5,22–24]. Ansell (2005) proposed an energyabsorbing rock bolt composed of a smooth steel bar with impressions made over a section of its length to provide the required anchorage when fully grouted, in which the adhesive bond between the bar and surrounding grout is lost and the bolt is able to absorb energy by plastic lengthening when subjected to dynamic load. Laboratory tests were conducted with static test load velocity of 0.1 m/s and dynamic test load velocity of 10 m/s. The results indicated that the distribution of plastic strain along the length of a grouted rock bolt, as for a free steel bar, is not constant when dynamically loaded, whereas the plastic strain is constant under static load. Next, the effect of strain rates of 0.01 s1, 12.5 s1, 25 s1 on the yield stress of this rock bolt were experimentally investigated. The measured force–time relations can be divided into one part from impact and another from quasi-static tension. The impact from the retardation of the moving parts of the testing machine was plastic, initially large but decaying rapidly following an exponential curve [21]. An energy-absorbing rock bolt, called the D bolt, was proposed by Li et al. [5], which is a smooth steel bar with a number of anchors along its length. The bolt has large load-bearing and deformation capacities. The performance of D-bolts under static and dynamic loading was reported in detail in [23,24]. The static test results show that the smooth bolt section between anchors of 1000 mm may elongate by 110– 167 mm, indicating that the deformation capacity of this bolt is determined by the length and the number of anchors. An advantage of this bolt is that it avoids load peaks and premature bolt failure due to stress concentrations caused by fracture or joint opening. Dynamic test results were obtained for the relationship between the impact energy and the displacement of the D-bolt. Rock bolts with sliding structural components include cone bolts [22], the Roofex rock bolt [25], the cold drawing bolt [26], and the He bolt [16]. The cone bolt consists of a smooth steel bar with a flattened conical flaring, which is designed to plough through the grout when the pull load exceeds a pre-defined value. Wang et al. proposed an energy-absorbing rock bolt consisting of a yielding device named a draw die with a slope in the inner surface and a bolt rebar [26]. The mechanical mechanism is the draw die compressing the rebar, which is like the process of cold rolling. Static tests were conducted and the tests results showed that the new energy-absorbing rock bolt can elongate to a considerable length determined by the compressed length of the bolt rebar at a high load-bearing level [27]. He et al. introduced a novel energyabsorbing rock bolt with the negative Poisson’s ratio (NPR) effect, which has the capacity of both high constant resistance from 110 kN to 180 kN and large deformation up to 1000 mm [16]. The high constant resistance is generated by the stick–slip phenomenon between the energy-absorbing unit called the cone with a sleeve pipe. The dynamic tests are reported in detail in [28], in which the advanced split Hopkinson pressure bar (SHPB) dynamic loading system and a weight-falling system were employed to study the dynamic performance of NPR bolt. The dynamic test results indicate the NPR bolt can absorb impacting energy rapidly and it has a good ability to adapt to dynamic impact. In addition, a field application was applied to verify the actual anti-impact performance of the new NPR bolt, and the test results indicated the deformation of the NPR sections was less obvious and more controllable than that for traditional bolts, which means that the NPR bolt support has favorable protective and therapeutic effects

in deep rock burst disasters [9]. Based on the literature review, most of the current energy absorbing rock bolts have the limitation on the long elongation capacity at a high constant working resistance except for He bolt. However, the material of the sleeve tube of He bolt is titanium (Ti), which limits the large-scale field application of the bolt due to its high cost. In order to adapt to increasing demands for support systems and bolt devices in deep underground engineering with higher ground stresses and larger rock deformations, energy absorbing rock bolts should have the long elongation capacity at high working resistance level. In addition, the cost should be acceptable to apply in engineering application. In this paper proposes a novel energy-absorbing rock bolt mainly consisting of a steel tube with a partial slope in its inner face, a circle of steel balls, and a rebar. The structure and its working principles are introduced in Section 2. A mechanical analysis was studied to better understand the factors influencing the working resistance in order to guide the experimental study. The static experiments reported in Section 4 were employed to test the static performance of this new rock bolt and discusses its performance. In Section 5, a set of numerical modelling is employed to test the new energyabsorbing capacity in a deep soft roadway.

2. Structure and working principles The structure of the new energy-absorbing rock bolt is shown in Fig. 1, which mainly contains a rebar, a sleeve tube, and steel balls. It belongs to the type of structural components sliding. The sleeve tube is partially sculptured with a slope in the inner surface. The face plate with a void circular hole in the center is welded to the upper end of the sleeve tube. Steel balls are uniformly disposed on the inner surface on a plane. The rebar and sleeve tube are connected by the steel balls via contact behavior. Note that the inner diameter of the sleeve tube is larger than the diameter of the rebar. The location of the steel balls is determined by the radius of the steel balls, and the gap distance between the sleeve tube and the rebar. The gap distance refers to the distance between the inner surface of the sleeve tube and the outer surface of the rebar. In the outer end of the rebar, a length of thread is made. The connection is achieved by a nut as a function of screw-threading until the steel balls are tightly compressed to both the sleeve tube and bolt shank by the nut. Fig. 2 shows the vertical cross section view of new bolt installed in surrounding rock mass of roadways and its working principle. After the bolt shank is installed and then fixed in the borehole by resin or cement grout, radial dilation of surrounding rocks induces a pull load to the sleeve tube via the face plate, and the sleeve tube is displaced associated with the extension of the surface of surrounding rocks. During the dilation of surrounding rocks, the new bolt restrains the dilation by contact force generated by the steel balls gouging the sleeve tube in the dilation direction. The mechanism of the working resistance is the plastic flow of the sleeve tube induced by contact force. The movement process of new bolt associated with radial dilation of surrounding rocks can be divided into three stages. In Stage I, the contact stresses are quite small within the elastic limit of the sleeve tube in the contact area. Once the sleeve tube in the contact area enters the stage of plasticity in which deformation is permanent, the movement process enters Stage II. In this stage, working resistance rapidly increases with the decrease of gap distance. Note that the red part of enlarged contact area in Fig. 2 represents the embedded depth by steel balls gouging the sleeve tube. The embedded depth increases with the decrease on gap distance between rebar and sleeve tube, and at the end of the slope where the gap distance remains constant with further movement of the sleeve tube, the

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Front view

Void hole Tread

Face plate Sleeve tube

Nut Steel ball

Rebar Slope

(a)

Enlarge

(b) Fig. 1. Layout of proposed energy-absorbing rock bolt (a) schematic diagram (b) physical photos.

embedded depth keeps constant. This is the stage III, in which the working resistance keeps relatively stable due to the constant embedded depth. When the steel balls relatively move to the inner end of sleeve tube, the full elongation in restraining the rock radial deformation is done.

3. Mechanical analysis of new energy-absorbing rock bolt Before experimental static pull-out tests of the new bolt, a mechanical analysis was investigated to better understand the factors affecting its static performance. Theoretically, the contact pattern for steel balls with sleeve tube and rebar is spatial axisymmetric with the steel balls uniformly placed on the slope. It indicates the load-bearing capacity of each steel ball makes same contribution to the total working resistance. Therefore, the whole spatial contact modelling can be simplified as one steel ball interacting with sleeve tube and rebar. Then the working resistance of the structure can be estimated by the load bearing capacity of one steel ball multiplying the number of steel balls. The contact model of one steel ball with sleeve tube and rebar belongs to a point contact initially and gradually become the threedimensional (3D) spherical contact. In metallic contacts, there is

often plastic deformation, and hence, metallic contacts are often labeled by elastoplastic. The single peaks that applied in gears, rolling elements is employed to do theoretical analysis [29]. The mechanical contact models of gears and rolling are generally plane stress and plane strain, respectively. In this paper, the 3D spherical contact is similar to gears and rolling models while more complex. The contact stresses are spatial distribution and varied with yield stress of sleeve tube and deformation in contact area [29]. Therefore, the analytical solutions of contact stress are limited to 3D contact geometries. The aim on mechanical analysis is to better understand the factors affecting its static performance. Therefore, the 3D spherical contact model can be regarding as 2D version of single peak contact model with the maximum embedded depth cross section of steel ball shown in Fig. 3. Based on the acknowledgement on contact model of spherical indentation with flat, the assumptions with rigid steel balls and deformable sleeve tube and rebar in the mechanical analysis are adopted. After excavation, surrounding rocks deform towards the excavation space. The rock mass exerts an axial force on the plate (AF1) whereas a shear force (SF) between grout and the rebar occurs to prevent its outward movement. At the beginning of contact, as shown in Stage I, the contact type is point contact. A normal force (NF) vertically applied to the slope can be divided into the

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Fig. 2. Working principle of new energy-absorbing rock bolt.

With further movement of the surrounding rocks as well as the sleeve tube, the contact type changes to spherical contact. A set of normal stress p and tangential stress q is applied in the contact area. The relationship between p and q is as follows:

p ¼ ql

ð3Þ

where l denotes the friction coefficient between steel ball and slope. The value of 0.03 is referred to the contact modelling of rolling and strip [30]. The expression on AF2 and RF in spherical contact is formed as the integration of p and q:

8 RR 0 0 > < AF 2 ¼ ðpsinh þ qcosh ÞdA A RR 0 0 > : RF ¼ ðpcosh þ qsinh ÞdA

ð4Þ

A

Fig. 3. Simplified contact model of steel ball and sleeve tube.

axial force (AF2) and the radial force (RF). It is clear that the relationship among the AF1 and the AF2, the NF and the AF2, RF are as follows:

8 > < AF 1 ¼ n  AF 2 AF 2 ¼ NF  sinh > : RF ¼ NF  cosh

ð1Þ

where, n denotes the number of steel balls. Theoretically, the number of steel balls is at least 4. The location of the four steel balls should be at each quarter of the circle plane to make the whole structure stable and balanced. h is the angle of the slope, which is preferable of 10° or less to either avoid steel balls to bounce out or break in the slope under pull-out test. The working resistance (T) is supported by AF1, which means the relationship between T and AF2 is as follows:

T ¼ n  AF 2

ð2Þ

where h’ denotes the angle between the direction of q and the axial direction. The value of h’ increases from the initial contact location a to the end of contact location b shown in Fig. 3. A denotes the contact area between the steel balls and the inner surface of the sleeve tube. Note that the value of A increases with the gouging depth. The radial force makes the sleeve tube expand in the radial direction, including elastic and plastic expansion. The elastic expansion can be recovered after contact whereas the plastic expansion is permanent. This indicates that the radial expansion positively reflects the radial force. Consequently, the working resistance can be estimated by the radial expansion, considering the relationship between the radial and axial force. Substituting Eq. (3) into Eq. (4), it can be rearranged as:

8 RR 0 0 > < AF 2 ¼ ½pðsinh þ ucosh ÞdA A RR 0 0 > : RF ¼ ½pðcosh þ usinh ÞdA

ð5Þ

A

When the steel balls comparatively move to the end of the slope, the gouging depth keeps constant with the further movement of the sleeve tube, and the working resistance will keeps constant. The relationship between constant working resistance and axial force can be expressed combining Eqs. (2), (5) as follows:

ZZ

T¼n A

½pðsinh0 þ ucosh0 ÞdA

ð6Þ

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Based on Eq. (6), the constant working resistance is dependent on n, A, p, l and h’. The parameters of n, A, and h’ is depended on the radius of the steel balls, the gap distance between the sleeve tube and the rebar, the angle of slope. The normal stress distribution is dependent on yield strength Ys of sleeve tube, gouging depth P(in indentation models, it is termed as penetration depth), radius of real contact area L, and radius of the steel balls R [29] shown in Fig. 4. Analytical solutions of constant working resistance in this study are limited to the complex normal stress field and variation on h’ in contact area. The semi-analytical models that combining finite element method (FEM) [31]or irrelative methods with Elastoplastic [30] could be a potential to get the analytical outputs in the further. In conclusion, the constant working resistance is qualitatively affected by the gouging depth, yield stress of sleeve tube, radius and number of steel ball. This indicates that different constant working resistances can be obtained by just changing the radius and number of the steel balls while keeping the other parameters the same. In the next section, the results of static pull-out tests with variations in the radius and the number of steel balls while keeping other parameters the same are discussed in detail.

4. Static pull-out experimental tests 4.1. Experimental setup In this section, the testing machine, specimen preparation, and testing procedure are introduced. The static pull-out tests were conducted by Electro-mechanical Universal Testing Machine shown in Fig. 5 in the State Key Laboratory for Geomechanics and Deep Underground Engineering, at China University of Mining and Technology (CUMT), Xuzhou, China. This machine is controlled by electro servo system. As shown in Fig. 5(a), an adjustable crossbeam screwed in two cylinders can be lifted and downward between base and upper crossbeam. The pull-out tests of the new bolt were conducted by fixing the non-tread end of rebar in the lower griper and lifting the adjustable crossbeam to pull the sleeve tube. During pull-out tests, load and displacements are obtained from the load cell and displacement transducer, respectively. The pull-out capacities of this experiments are as follows: maximum tensile load: 300 kN; force-loading rate: 0.1–20 kN/min; displacement-loading rate: 0.1–200 mm/min. Noted that the stopping criteria of tensile tests are the two conditions: (1) The upper and lower compressive plate are contacting each other (shown in Fig. 5(b)), (2) or the load has a sharp drop to 50% of instantaneous load, which is a threshold set by microcomputer. Rebar 22 mm in diameter, which is commonly used in Chinese coal mines, was used as the bolt shank [10,15,32,33]. For the geometric matching of borehole drill bits 28–32 mm in diameter used in most Chinese coal mines, sleeve tubes 32/26 mm in outer and inner diameter, respectively were selected. The wall thickness, the height and angle of slope and the length of the sleeve tube were kept the same at 3 mm, 30 mm, 3.26°, and 300 mm, respectively. The geometric parameters of new bolt is shown in Fig. 1(a). The materials of the sleeve tube and rebar were from the same batch of 20# steel, which has good performance in both strength capacity and ductility. The elastic modulus and the Poisson’s ratio

Fig. 4. Diagram of contact model under constant working resistance.

Upper crossbeam

Compressive plate

Displacement transducer Adjustable crossbeam

300 mm

Cylinder Connector Screw Box

2000 mm

Lower griper Load cell

Base

Fig. 5. Diagram of Universal Testing Machine in CUMT.

1100 mm

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Fig. 6. Load versus displacement plot of 20# steel rebar 22 mm in diameter under static pull test and ideal constant working resistance of new energy-absorbing rock bolt.

of 20# steel are 210 GPa and 0.3, respectively. High load bearing balls with HRC 60 were selected, which are far harder than 20# steel. Before testing of the static performance of the bolts, the tensile strength of rebar with a diameter of 22 mm and a length of 700 mm were tested to predict the constant working resistance. The yield force, ultimate force and elongation were 145 kN, 252 kN, and, 91 mm respectively shown in Fig. 6. Therefore, the yield strength, ultimate strength, ultimate strain of 20# steel in this experiment were calculated as 380 MPa, 663 MPa, 12.8%, respectively. Note that the elastic limit and yield strength can be regarded as the same value from Fig. 6, in which the point A is the elastic limit and point B is the yield point. It is clear that the value is equal in the pull-out test of rebar. In order to achieve large elongation under a high constant working resistance, the load capacity was 80% of the elastic limit shown in Fig. 6 by the red dashed line. Therefore, the main task was to find a suitable match for the steel ball gouging sleeve tube to generate the constant working resistance. Based on our previous experimental results of one steel ball gouging a tube made of 27Simn steel (yield limit: 690 MPa, ultimate strength: 850 MPa), a gouging depth of 2 mm generates a contact force of 44.5 kN [34,35]. Therefore, the stiffness

Table 1 Geometric parameters of two batches of new energy-absorbing rock bolts. Batch 1

Diameter of steel balls /mm

Number of steel balls

Inner and outer diameter of tube/mm

Length of sleeve tube/mm

Diameter of rebar/mm

Gap distance max/ min(mm)

Height of slope/mm

No. No. No. No.

4 4 4 4

4 6 8 9

32/26 32/26 32/26 32/26

300 300 300 300

22 22 22 22

5/2 5/2 5/2 5/2

30 30 30 30

Diameter of steel balls /mm 3 3.5 4 4.5

Number of steel balls 9 9 9 9

Inner and outer diameter of tube/mm 32/26 32/26 32/26 32/26

Length of sleeve tube/mm 300 300 300 300

Diameter of rebar/mm 22 22 22 22

Gap distance max/ min (mm) 5/2 5/2 5/2 5/2

Height of slope/mm 30 30 30 30

1 2 3 4

Batch 2 No. 1 No. 2 No. 3 No. 4

Fig. 7. Movement process of new energy-absorbing rock bolt.

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140 120 100 Load (kN)

of 27Simn steel can be estimated to be 22.3 kN/mm. With the aim of a constant working resistance of 120 kN, it was roughly estimated that the goal could be achieved by of 4–10 steel balls digging into the 20# steel plate used in this experiment at depths ranging from 1 mm to 2 mm. To test the tensile property of the new bolt, the non-threaded end of the rebar is fixed on the lower griper. The face plate of the sleeve tube is placed on a self-designed box, which is linked to the connector merged with the adjustable crossbeam. A circle of steel balls is uniformly set in the slope to connect the rebar and sleeve tube. The location and maximum number of steel balls are determined by the geometric relationship between steel balls and gap between the rebar and the sleeve tube. Finally, the nut is rotated on the thread to compress the steel balls to tightly connect the rebar and the sleeve tube. Since the aim of the tests was to investigate the static performance of the new bolts, the constant displacement pull-out ratio was set at 10 mm/min [16]. More than 100 static pull-out tests were conducted on the new rock bolts. Two batches and typical geometric parameters of the new rock bolt are shown in Table 1.

80 60 Number of steel balls: 4 Number of steel balls: 6 Number of steel balls: 8 Number of steel balls: 9

40 20 0 0

50

100

150 200 Distance (mm) (a)

250

300

350

4.2. Test results The movement process of the new energy-absorbing rock bolt under static pull-out load is illustrated by four photographs presented in Fig. 7, namely the start of the test (point a), yielding point (a’), end of slope (point b), and final stage (point c). Moreover, three stages from Fig. 2 and load–displacement curve of steel ball of 4 mm in diameter and 9 numbers are employed to better realize the movement process. In the range of point a and a’, the contact stress are within elastic limit of sleeve tube. This range is corresponding to the Stage I. The displacement is too small to showing in load–displacement curves. When an obvious contact sound made by the steel balls gouging the sleeve tube occurs, it indicates the contact stress is over yielding point of sleeve tube and movement process enters to the stage II. When the working resistance increases to 115 kN at point b, the sharp increase of working resistance turns to slow down. It indicates the steel balls relatively move to the end of slope. The displacement between point a and b is about 27 mm, which is well corresponded to the length of height of slope minimize the radius of steel balls. With the further movement of sleeve tube, the working resistance increase from 115 kN to 120 kN with the displacement of 273 mm from point b to c. This range is corresponded to the stage III, in which the constant working resistance has been obtained with long elongation, thus to achieve the aim of energy-absorbing. The When the steel balls and nut were entirely pulled out from the sleeve tube, the full elongation ended. The physical movement was consistent with the theoretical analysis of the working principle in Section 2. Fig. 8 shows the load versus displacement curves and the gouging scratches of the sleeve tube in the first batch. The working resistance of the four specimens rapidly increases to the peak value at a small displacement within about 25 mm, which indicates the rock bolt can resist the deformation of rocks in a short elongation under static load. After the peak load, there was a slight drop for specimens No. 1 to No. 3. This phenomenon can be explained by the damping phase at the yielding stage of steel. The constant working resistance of specimen No. 1 was about 60 kN with a slight decrease until the test ended. It was largely induced by two small decreases in gouging depth observed in the sleeve tube shown in Fig. 8 for No. 1. The decrease of the gouging depth is regarded as the unbalanced contact force in the radial direction. For specimen No. 2, the constant working resistance was stable at 80 kN until the test finished. The six gouging scratches were uniform and stable. For specimen No. 3, although the eight gouging scratches were uniform and stable, the working resistance

Fig. 8. (a) Load-displacement curves (b) Gouging scratches in sleeve tube.

increased from 80 kN to about 100 kN with axial displacement from 30 mm to 285 mm. The load increase was caused by the strain hardening effect of steel. The green line of specimen No. 4 does not show a drop at the displacement of 30 mm. The working resistance remains at about 120 kN until the pull-out test finished. This phenomenon can be explained as the high contact stress concentration by each steel balls at a close distance, making the yield stage too short to show the damping phase. This indicates the greater the number of steel balls, the more stable the constant working resistance. Fig. 9 shows the load–displacement curves and the gouging scratches of the second batch. The constant working resistances of the four specimens are more stable than those of the first batch. There is no load drop range for the second batch. The nine gouging scratches of specimens No. 1 to No. 4 are stable and uniform based on physical pictures. Moreover, the gouging depths increase with the increase of the radius of steel balls from 3 mm to 4.5 mm shown in Fig. 9(b). As a result, the constant working resistance of the four specimens ranges from 82 kN to 145 kN. The rebar and

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140 120

Load (kN)

100 80 60 Diameter of steel balls : 3 Diameter of steel balls : 3.5 Diameter of steel balls : 4 Diameter of steel balls : 4.5

40 20 0 0

50

100

150 200 Distance (mm)

250

300

350

(a)

(b) Fig. 9. (a) Load-displacement curves of second batch (b) Gouging scratches in sleeve tube.

the sleeve tube of the two batches had the same geometric and material parameters. The different constant working resistances were obtained by changing the number and diameter of the steel balls. This is one merit of the new energy-absorbing rock bolt, which indicates that the constant working resistance can be adjusted by small changes in the steel balls. The aim for a constant working resistance of 120 kN was accomplished by specimen No. 4 of batch 1. Moreover, based on the test results of two batches of the new energy-absorbing rock bolt, two conclusions can be drawn: (1) The stability of constant working resistance can be enhanced by using more steel balls. (2) The constant working resistance corresponds positively to the gouging depth.

4.3. Static performance of new bolt In this section, the static performance of the new energyabsorbing rock bolt is discussed in detail, including the load capacity, the supporting length and the energy-absorbing ability. This section will help to better understand the mechanism and highlight the merits of the new rock bolt. Fig. 10 shows a comparison of the load–displacement curves of the new energy-absorbing rock bolt with those of other energyabsorbing rock bolts reported in the open literature [5,6,22– 24,27,36]. All the experimental results and the calculated parameters of the new energy-absorbing rock bolt are summarized in Table 2.

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Fig. 10. Load versus displacement plots of new energy-absorbing rock bolts with constant working resistance of 120 kN and other energy-absorbing rock bolts reported in open literature.

Table 2 Calculated and measured parameters of two batches of new energy-absorbing rock bolt. Batch 1

Constant working resistance /kN

Radial expansion /mm

Stiffness kN/mm

Supporting length /mm

Energy-absorbing capacity kJ/m

No. No. No. No.

60 78 90 120

0.24 0.36 0.46 0.68

2.72 3.56 3.56 2.58

292.58 295.34 296.09 298.11

58.57 78.66 90.36 110.37

Constant working resistance / kN 87 100 120 136

Radial expansion /mm 0.48 0.58 0.68 0.72

Stiffness kN/mm 1.51 3.15 4.00 2.88

Supporting length /mm 295.88 296.09 295.86 294.39

Energy-absorbing capacity kJ/m 66.68 82.04 107.53 123.28

1 2 3 4

Batch 2 No. 1 No. 2 No. 3 No. 4

4.3.1. Load capacity 4.3.1.1. Constant working resistance. The cone bolt was the first yield-supporting device developed to combat rock burst problems in deep mines and was invented in South Africa [22]. The cone bolt was later modified for resin grout in Canada, and a blade was added in the end of the cone for the purpose of resin mixing. The mechanism of the working resistance is so-called ‘‘ploughing”, which is dependent on the friction force between the cone and the grout. The displacement of a cone bolt can be considerable if it works in ploughing as intended. However, whether the ploughing occurs or not is dependent upon not only the shape and size of the cone, but also the strength of the hardened grout. Therefore, the load can vary versus the displacement, as shown by the blue line in Fig. 10. The D bolt invented in Norway [23] has a high load-bearing capacity and energy-absorbing capacity through plastic elongation of the steel. However, the supporting length determined by the deformation ability cannot combat the large deformation of soft rocks. The Roofex bolt consists of a steel bar 12.5 mm in diameter and can provide a load bearing level of 80 kN shown by the brown line in in Fig. 10. The energy absorber receives a total of six cemented carbide pins slightly engraved into the steel bar and performs a cold rolling process, deforming the original round shape to a hexagonal shape, whilst the steel bar travels along its sliding path. However, the energy-absorber unit makes the bolt inherently expensive due to its complex structure. As cemented carbide pins are slightly engraved into the steel bar, structural damage to the bar is inevitable. A modified energyabsorbing rock bolt with the maximum load capacity of 250 kN is proposed by Wang et al. (2013) in China. The high working resistance is based on the steel-steel interaction with a high quality steel ball traveling through a drawing die fixed with resin or cement grout inside the borehole. The structure is simple compared with that of the Roofex bolt. The deformation ability, how-

ever, is about 150 mm shown by the black line in Fig. 10. The working resistance of a maximum value of 180 kN with a supporting length of 1000 mm was proposed by He et al. (2014), as shown by the green line in Fig. 10. The structure of the He bolt is quite simple and installation is easy for o field application. However, the cost of the Ti sleeve tube is expensive. An axial splitting energy-absorbing component installed between the nut and plate is proposed by Dai et al. [36]. The cost is acceptable for the popularization and application of the new bolt for roadway support. However, as shown by the dark brown line in Fig. 10 of, the working resistance is about 120 kN with a supporting length of 110 mm. Compared with the other energy-absorbing rock bolts, the high constant working resistance of 120 kN generated by the plastic flow of the sleeve tube of the new energy-absorbing rock bolt is more stable in the load–displacement curve shown by the red line in Fig. 10. The materials of the sleeve tube and rebar are all 20# steel. This is cheap for field application.

4.3.1.2. Stiffness. Stiffness is a measurement of how quickly a support develops its load- carrying capacity, and is determined by measuring the change in support load as a function of the applied displacement. In this paper, the stiffness is calculated as the ratio of the peak load to the corresponding displacement. Based on the calculations, the new energy-absorbing rock bolt has the high stiffness, ranging from 1.69 kN/mm to 4.00 kN/mm, which means a quick support to resist deformation of the surrounding rocks in field applications. The ground response curve (GRC) are generally employed in interaction response between supporting and rocks. As shown in Fig. 11, there is a critical displacement to access the stability of roadways. When rock deformation exceeds the critical displacement, the rocks of roadway become unstable and major rocks failure occurs. A higher stiffness of energy absorbing rock

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Constant working resistance (kN)

160

140

120

100

80 Constant working resistance Fitting curve

60

0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 Fig. 11. Ground reaction curve relating convergence to support capacity [37,38].

Radial expansion (mm) Fig. 13. Relationship between constant working resistance and radial expansion.

bolt can rapidly resist rock deformation in a high load to prevent major rock failure more efficiently. 4.3.1.3. Radial expansion of sleeve tube. The sleeve tube undergoes internal radial tensile stress, which can cause the radial expansion of the sleeve tube, including both elastic and plastic expansion. Note that since elastic expansion can be recovered and is quite small compared to plastic expansion, the radial expansion here is equal to the plastic expansion to describe the degree of plastic deformation of the sleeve tube. Fig. 12 shows a set of photograph of the radial expansion of specimens after testing from batch 1 in Table 2. The outer diameter expanded from 32.24 mm to

32.68 mm, corresponding to the constant working resistance from about 60 kN to 120 kN. Statistical results of the relationship between plastic expansion and constant working resistance are shown in Fig. 13, from which the constant working resistance can be related to the radial expansion. 4.3.2. Supporting length The supporting length can be adjusted by the length of the sleeve tube, based on the requirement of the field application. It is determined by the length of the sleeve tube minus the distance between the steel balls and the upper end of the face plate. In case of support in weak or soft rocks, the length should be able to

Fig. 12. Radial expansion (unit: mm) of sleeve tube from batch 1 in Table 1.

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accommodate squeezing deformation. In hard or moderate rocks prone to bursting, the supporting length should be calculated to mitigate the dynamic hazards by absorbing the impact energy. 4.3.3. Energy-absorbing ability The energy-absorbing capacity refers to the area under load– displacement curve based on static pull-out tests. The total energy absorption therefore depends on the level of load capacity and the supporting length. Based on Fig. 10, the area of new rock bolt is larger than others apart from He bolt. Therefore, the new energyabsorbing rock bolt can have high energy-absorbing capacity. It should be noted that the energy-absorbing ability of the new yielding rock bolt is calculated in the static state. It is well known in material science that materials like steel are strain-rate sensitive. In the previous investigation by Ansell [21], the dynamic yield

stresses of soft steel with a yield stress of 300 MPa corresponding to the initial load velocities of 5 and 10 m/s were 400 and 450 MPa, respectively. In addition, the dynamic ultimate stress was probably higher than the statically-determined strength of 440 MPa. This implies that the new energy-absorbing rock bolt could take more energy under dynamic loading than under static loading. 5. Numerical simulation on energy absorbing performance of new bolt interaction with rocks In order to test the performance of new energy absorbing rock bolt, a numerical simulation is studied. Commercial numerical code FLAC3D is employed. A modeling of pull-out test is established to calibrate the load-distance curve with constant working resistance of 120 kN and supporting length of 300 mm. Then, a deep

Fig. 14. Mechanical representation of new energy-absorbing rock bolt interaction with rock mass.

Table 3 Parameters of rock bolt in laboratory experiments and numerical simulation. laboratory

Elastic modulus (N/m2)

tangent modulus (N/m2)

Tension force at yielding limit (N)

Maximum Tension force (N)

Rock bolt Stiffness N/m

Grout stiffness (N/m2)

grout cohesive strength (N/m)

Rebar New rock bolt

210 e9 78 e9

53 e9 ~

150 120

242 120

6 e3 4 e3

4.2 e9 4.2 e9

4.7 e5 4.7 e5

Numerical simulation Rebar New rock bolt

Elastic modulus (N/m2) 30 e9 10 e9

tangent modulus (N/m2) 5 e9 ~

Tension force at yielding limit (N) 150 120

Maximum Tension force (N) 242 120

Rock bolt Stiffness N/m 6 e3 4e3

Grout stiffness mm 4.2 e9 4.2 e9

grout cohesive strength (N/m) 4.7 e5 4.7 e5

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node, straight, finite elements with one axially oriented translational degree-of-freedom per node. Each cableSEL behaves as an elastic, perfectly plastic material can yield in tension or compression, but not a bending moment. Ft, Fc is the tensile and compressive yield strength of bolt rod in cableSEL. After yielding at yielding point, there is no loss of strength on bolt rod [39]. Therefore, the cableSELs can be employed to simulate the long-distance versus constant-load behavior on new energy absorbing rock bolt. The Mechanical representation of new energy-absorbing rock bolt interaction with rock mass is shown in Fig. 14. The anchorage sec-

soft roadway excavated in coal seam is employed, in which three modellings of no support, conventional rock bolt support, and new energy absorbing rock bolt support are established to highlight the performance on new energy absorbing rock bolt. 5.1. Implementation procedure on new energy absorbing rock bolt into cable structure elements (cableSELs) A conventional physical rock bolt can be modeled as a collection of cableSELs (rebar, grout) in FLAC3D. CableSELs are linked by two-

Rebar of 22 mm in diameter New rock bolt with elogation of 120 kN and 300 mm 250

Load (kN)

200

150

100

50

0 0

50

100

150

200

250

300

350

Distance (mm)

(a)

Fig. 15. Load-displacement curves of rebar and new energy absorbing rock bolt with constant working resistance of 120 kN and elongation of 1000 mm (a) laboratory tests (b) simulation results.

Y. Hao et al. / Construction and Building Materials 243 (2020) 118231

tion is composed of grout annulus, rebar in the grout range. The rock mass and grout are interlinked by spring and slider between node and grid point. The sleeve tube is simulated as zero value of grout shear stiffness and cohesion strength of grout. The face plate is simulated by rigid link between node to nearest zone. When rock mass deforms, the forces are corresponding transmitted to nodes through grout to generate mechanical response of the rock bolt, in return, the counterforces act to the rock mass for reinforcement. The new energy absorbing rock bolt with load of 120 kN and elongation of 300 mm is achieved through FISH language programming. The implementation procedures are as follows: (i) the elongation lengths of all anchor-free elements will be called from the main program, (2) the elongation length of the anchor-free part will be calculated, and (3) once the maximum elongation length Umax of a cableSELs elements reaches the displacement of yield

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point, the values of ultimate tensile force are set as 120 kN. Thus, the long elongation supporting with constant working resistance of the new bolt is realized. A set of pull-out tests simulation is employed to calibrate the 300 mm supporting length versus 120 kN load and the load–displacement curve of single rebar. A brick in 4 m  4 m  4 m (width  height  thickness) and 0.2 m of block size is established as rock mass simulation. Two cable elements with total length in 2.2 m and cableSEL length in 0.2 m are modeled into the rock. The block size and cableSEL length are set as same in order to increase the calculation precision based on the Explicit finite difference approximation in spatial derivatives. The face plate, free/ sleeve tube and anchorage lengths are set as 0.2 m, 0.8 m, and 1.2 m, respectively. The geometric parameters of physical and numerical study are the same with rebar diameter of 22 mm, cross

Fig. 16. (a) Modeling overview (b) Cross section view and deformation monitoring point of roadway with no supporting, conventional rock bolt, and new energy absorbing rock bolt.

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section area 3.84 * 104 m2, grout annulus diameter 32 mm, grout exposed perimeters of 0.07 m. The material, mechanical parameters are listed in Table 3. Note that the modified rock bolt modeling that being failure subjected to tensile load are achieved by a four stages constitutive model (as elastic stage, yielding stage, strain hardening stage, and failure stage)from Yan et al.[40]. The node of plate is applied a pull velocity of 1.0 * 106 m/step to decrease the influence of damping. The end of anchorage is fixed. The laboratory and calibration results are shown in Fig. 15(a) and (b). The simulation results are well corresponded to the laboratory results. 5.2. Simulation case study on a deep soft roadway excavated in coal seam 5.2.1. Model input A modeling of deep soft roadway excavated in coal seam are shown in Fig. 16. The model dimension is 50 m  50 m  50 m (x * y * z) and disassembled by hexahedron elements with a total of 267,508 units. The element size around roadway is 0.2 m * 1 m * 0.2 m (x * y * z). The vertical, horizontal stresses are 12 MPa, 20 MPa, and 15 MPa in z, x, y direction respectively. The bottom of modeling is fixed in x , y z; The upper boundary is free and horizontal boundary is fixed in their corresponding directions. The constitutive model of coal and all rocks are strain-softening model, and the strain softening parameters are from Zhang et al. [41]. In order to test the performance of new rock bolt, the roadway with height in 4 m and width in 6 m is along the y axial from 10 m to 40 m. Not that a vertical plane of symmetry through the center line of roadway excavation direction is employed, and only half of the roadway is modeled. The excavation is cut into 3 times: The first cut I is in the range of 10 m–20 m, there is no supporting, and in the range of second cut II from 20 m to 30 m and third cut III from 30 m to 40 m, the code of conventional rock bolts and new rock bolts of working resistance in 120 kN and elongation capacity of 1000 mm in Section 5.1 are implemented to compare the performance of new rock bolt. The roadway deformation and plastic zone range are monitored during the excavation. The monitoring points of roadway deformation are set from the surface center to a depth of 10 m in rib side and roof in the selected cross section of roadway at y axis of 15 m, 25 m, and 35 m, respectively. 5.2.2. Results and discussion Roadway deformation is shown in Fig. 17. The rib side deformation is larger than the roof deformation due to the excavation

Fig. 18. Plastic zone distribution of cross section at y axis 15 m, 25 m, and 35 m.

direction perpendicular to the direction of maximum principle stress. In Fig. 17(a), it can be seen the conventional rock bolt can resist rib deformation rapidly near surface (from 0 m to 1 m). This is due to the ultimate strength of 250 kN providing high working resistance. However, as the broken failure code of small elongation capacity (about 0.2 m) we implemented, the tensile strength and the elastic modulus are set as zero to resist roadway deformation with further deformation. Therefore, in the range of 1 m–10 m, the conventional rock bolt resists deformation as the same effect with no support. The new energy absorbing rock bolt can smoothly resist rib deformation and roof deformation at a constant working resistance with long elongation. The roof deformation and rib side deformation can be decreased by new energy absorbing rock bolt due to the long elongation capacity, thus to providing counterforces to rock. Fig. 18 shows the plastic zone of three cross section, in which no supporting, conventional rock bolt supporting, and new energy absorbing rock bolt are employed. It can be seen the smallest range of plastic zone in both rib side and roof is the new rock bolt employed. This is due to the long elongation capacity with constant working resistance strengthening the rock mass. Therefore, from the aspect of numerical modeling, the long elongation capacity with high constant working resistance of new rock bolt can resist large deformation of deep soft roadway and decrease the plastic zone around roadway.

(a)

(b) Fig. 17. Roadway deformation curves (a) rib side (b) roof.

Y. Hao et al. / Construction and Building Materials 243 (2020) 118231

6. Conclusion In this paper, a novel energy-absorbing rock bolt with high constant working resistance and long elongation is proposed. The structure of the new bolt has three main parts: a rebar, a sleeve tube with a partial slope in the inner face, and a circle of steel balls. The mechanism of high constant working resistance is the plastic flow of the sleeve tube by the contact force between the steel balls gouging the sleeve tube. The working resistance is positively related to the gouging depth, as illustrated by the mechanical model and verified by experimental tests. Two batches of the proposed new bolt with constant working resistances ranging from 60 kN to 145 kN and elongation of 300 mm were tested under static pull-out load at the loading rate of 10 mm/min. Different constant working resistances can be achieved by simply changing the radius and the number of steel balls. The stability of constant working resistance can be enhanced by using more steel balls and the constant working resistance corresponds positively to the gouging depth. The proposed rock bolt has high stiffness ranging from 1.69 kN/ mm to 4.00 kN/mm, which means it can provide rapid support to resist the deformation of surrounding rocks in field applications. The supporting length can be adjusted to accommodate the requirements of field applications, such as the long elongation support in soft rocks, and a suitable length for energy-absorbing ability in hard rocks. Energy-absorbing abilities ranging from 58.57 KJ/m to 123.28 KJ/m were calculated based on the area under the curve in the load–displacement diagram based on static pull-out tests. The dynamic performance for hard rocks will be investigated in the future. A numerical modeling of pull-out test is established to calibrate the load-distance curve with constant working resistance of 120 kN and supporting length of 1000 mm. A modeling of deep soft roadway excavated in coal seam with no support, conventional rock bolt support, and new energy absorbing rock bolt support are established to highlight the performance on new energy absorbing rock bolt. The results of roadway deformation and plastic range show that the long elongation capacity with high constant working resistance of new bolt can decrease the deformation and plastic range of deep roadway. CRediT authorship contribution statement Yang Hao: Conceptualization, Writing - original draft. Yu Wu: Conceptualization, Writing - review & editing, Supervision. P.G. Ranjith: Writing - review & editing, Project administration. Kai Zhang: Software, Investigation. Guan Hao: Investigation. Yi Teng: Investigation. 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 research was supported by the Fundamental Research Funds for the Central Universities (2018BSCXB23) and the Postgraduate Research and Practice Innovation Program of Jiangsu Province (KYCX18_1971). References [1] J. Chen, S. Saydam, P.C. Hagan, Numerical simulation of the pull-out behaviour of fully grouted cable bolts, Constr. Build. Mater. 191 (2018) 1148–1158.

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