Study on grout cracking and interface debonding of rockbolt grouted system

Construction and Building Materials 135 (2017) 665–673

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Study on grout cracking and interface debonding of rockbolt grouted system Xu Chang a,b,⇑, Guozhu Wang a,b, Zhengzhao Liang c, Jianhui Yang a, Chunan Tang c a

Henan Province Engineering Laboratory for Eco-architecture and the Built Environment, Henan Polytechnic University, Jiaozuo, China School of Civil Engineering, Henan Polytechnic University, Jiaozuo, China c Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian, China b

h i g h l i g h t s
A tri-linear cohesive zone model (CZM) is used to simulate interfacial behaviors.
The typical three failure modes are identified.
A critical bond strength which controls the failure modes is analyzed.

a r t i c l e

i n f o

Article history: Received 17 March 2016 Received in revised form 15 August 2016 Accepted 8 January 2017

Keywords: Rockbolt grouted system Pullout behavior Interfacial debonding Grout cracking

a b s t r a c t Tensile tests and numerical analysis of failure models of rockbolt grouted system were conducted in the contribution. The cohesive zone model (CZM) was employed to simulate the interfacial behavior of rockbolt-grout interface and the plastic damage model was adopted for the grout materials. The effects of the interface bond strength and grout compressive strength, etc., on the failure patterns and the load-displacement curves were investigated in detail. Three failure modes of the rockbolt grouted system, namely (1) rockbolt-grout interfacial debonding, (2) complete grout cracking, and (3) a combining pattern of interfacial debonding and grout cracking were identified. The results indicate that there exists a critical bond strength, which controls these failure modes. With the increasing of the bond strength, the failure patterns change from the interfacial debonding to the grout cracking. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Rockbolts have been widely adopted as permanent and temporary structure elements in the mining and tunnelling engineering to control slopes, support underground excavation and stabilize jointed rock mass [1–5]. Generally, the rockbolt support systems are classified into different types according to the interaction between the rockbolt and the surrounding rocks [6]. In the past several years, the Continuous Mechanically Coupled (CMC) system has become a popular support method in the practice due to its convenience, and consequently the lower costs compared to that of other support techniques. The rockbolt cementitious grout system (referred to as rockbolt grouted system hereafter) is the most common type of CMC one.

⇑ Corresponding author at: Henan Province Engineering Laboratory for Eco-architecture and the Built Environment, Henan Polytechnic University, Jiaozuo, China. E-mail address: [email protected] (X. Chang). http://dx.doi.org/10.1016/j.conbuildmat.2017.01.031 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved.

Considerable field tests and lab experiments have been carried out to investigate the pullout behavior of the rockbolt grouted system. Pells [7] investigated the behavior of the fully grouted system early. Freeman [8] monitored the stress distribution along the fully grouted rock bolts in the filed. Gambarova [9] and Li [10] indicated that under the pullout test the interfacial bond strength was basically consisted of adhesion, mechanical interlock and friction. Stillborg [11] conducted a series of tests on rockbolts embedded in high strength concrete to explore the interface failure process. Hyett et al. [12,13] conducted a number of laboratory and field pullout tests to study the dominant parameters controlling the bond strength. From the existing tests, it could be concluded that the properties related to the grout between the rockbolt and rock mass and the interfaces (grout/bolt interface or the rock/grout interface) play critical roles in the rockbolt grouted system by providing effective stress transferred from weaker rock zone to the stronger one and keeping integrity of rockbolt grouted system. Thus, the interfacial debonding and the cracking of the grout are two major failure modes for the rockbolt grouted system.

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interfacial debonding and cracking of the grout are two dominated failure patterns of the rockbolt grouted system. For the former, debonding at the rockbolt-grout interface is very common. Therefore, rockbolt-grout interfacial debonding and grout cracking are analysed in this paper and their relationship is discussed in detail. A parametric study, including the influence of grout strength and bond strength on the pullout behavior is also conducted.

Many analytical works have also been performed to study the pullout performance of the rockbolt grouted system. The interaction behavior between the rockbolts and the rock masses was earlier studied by the Shear-Lag Model (SLM) [14]. Abramento and Whittle [15] investigated the pullout behavior of planar geosynthetic reinforcement by the SLM. Farmer [16] proposed an analytical method for the behavior of the rockbolts under tensile forces. Benmokrane et al. proposed a tri-linear bond-slip model for the interfacial mechanism between the bolt and the grout [17]. More recently, Li and Stillborg [10] indicated that there was a progressive debonding front that attenuated at an increasing distance from load point. They then provided analytical method to investigate the distribution of axial load shear stresses along the anchored length under pull-out. Hyett et al. proposed a Frictional-Dilational Model (FDM) to investigate the failure of cable bolts [18]. Ren et al. [19] presented a full-range study on the pullout behavior of grouted rockbolts. The bolt-grout interaction was simplified as a tri-linear bond-slip model and satisfactory agreements between the analytical results and the field test are obtained. It should be noted that almost all these analytical approaches are focused on the interfacial debonding failure and the cracking of grout is not involved. As for the numerical approaches, Ghaboussi [20] conducted finite element simulations to study stress distribution and deformations in the rockbolt. Ana et al. [21] also investigated the rockbolt grouted system based on the Lumped Parameter Model (LPM). Recently, Chang et al. [22] study the interface behavior based on an assumption of heterogeneity. However, these numerical studies also solely concentrated on the interfacial debonding of the system. Zhu et al. [23] model the cracking of the grout materials; however, the interaction between cracking of grout and interface debonding is not discussed. The rockbolt grouted system is a composite material system comprising of three kinds of materials and two types of interfaces. This indicates that the mechanical performances of the system must be complicated. Thus, the stress distribution, load transfer and failure modes of the rockbolt grouted system should be clearly identified to optimally design properties of the grout material. The aforementioned analytical and numerical work is important and have led to a better understanding of the pullout behavior of the rockbolt grouted systems. However, few existing analytical and numerical work paid attention to the grout cracking failure. The absence of attention to grout cracking has limited the deeply and completely understand the pullout behavior of the rockbolt grouted system and the accuracy of prediction the pullout capacity by numerical approaches has been accordingly reduced. In this contribution, an axisymmetric finite element model is adopted to investigate the pullout behavior of the rockbolt grouted system by on the ABAQUS/standard solver. As mentioned above,

fc

2. Numerical model 2.1. Grout material In the bolt grouted system, the debonding failure and the grout cracking failure are determined by the grout material. And thus, modeling of the grout material is a basic task. The cementitious grout discussed in this study is a mixture of sand, water and cement, which is similar to the composition of the concrete. Therefore, the plastic damage model for concrete is adopted to simulate the grout material. The stress-strain relationship suggested by Park and Paulay [24] is adopted to describe the grout behavior under compression (indicated in Fig. 1a):

rc ¼ f c

2ec

eo


2  fc

ec eo

ð1Þ

where f c is the cylinder compressive strength of grout. Strain

eo ¼ 0:002, at which the peak compressive stress is obtained. The ultimate strain is adopted as 0.0038. The Poisson’s ratio lc , is 0.19 [25]. Under tension, the grout material behaves as a linear material before the initial cracking at

ecr ¼

ft Ec

ð2Þ

A linear softening relationship after peak strength (Fig. 1b) is adopted for grout material under tensile load. The tensile strength for the grout is determined by the compressive strength by CEB-FIP [26]:

qffiffiffiffi f t ¼ 0:33 f c

ð3Þ

And the fracture energy Gf is determined by Eq. (4) [26]


0:7 f 2 Gf ¼ ð0:0469da  0:5da þ 26Þ c 10

where da is the maximum aggregate size for concrete. In the paper, zero is adopted for the da since no coarse aggregate is used in the grout material.

σ

f′

ft

(1 − dc ) Ec Ec

Ec

0.1f ′

0.0038

0.002

ε

pl

ε

εc

(1 − dt ) Ec Gc εc

el

(a)

ð4Þ

(b)

Fig. 1. Constitutive models [24]: (a) grout in compression; (b) grout in tension.

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If the grout material is unloaded during the softening stage of the stress-strain curves, the stiffness of the material seems to be weakened. Therefore, a damage variable is adopted to describe the progressive degradation of grout. For grout under compression, the evolution of the compressive damage (dc ) is related to the plas-

τ τ max

tic strain (epl c ) and can be determined by the Eq. (5).

dc ¼ 1 

rc E1 c pl c ð1=bc

e

Critical shear stress in model with τ max limit

ð5Þ

 1Þ þ rc E1 c

Constant friction coefficient, μ

According to the tests by Sinha et al. [27], a value of 0.7 for bc is adopted. For grout under tension, unloading returns almost back to the origin and remains just a small residual strain [28]. Therefore, one simple way to define the damage variable under tension is to assume the unloading branch of the curve end at the origin of the coordinate system as indicated in Fig. 1b. Thus, the relationship between the stress (r), the strain (e) and the damage variable (dt ) can be described as: the cracking of the grout occurs, the slope of the unloading branch is

rt ¼ Ec ð1  dt Þ et

δ (a) Coulomb friction model for interface [30]

τ τ max

ð6Þ

Therefore, the relationship between damage variables and strain (or crack opening displacement) can be determined by Eqs. (1)–(6). The evolution for the damage variables are illustrated in Fig. 2, where f c ¼ 20 MPa.

Unloading and reloading paths

δ0

2.2. Grout-rockbolt interface

δ1

δ

(b) A tri-linear model for interface [17]

As mentioned above, the interfacial debonding is one of the dominated failure patterns of the rockbolt grouted system. Therefore, modeling of the interaction is the primary task of this paper. In the current literatures, three common approaches for modeling behavior of grout-rockbolt interface have been adopted, no bond, Coulomb friction model and spring slider model. The first approach is that the interaction between the rod and the grout is assumed to be frictionless during numerical analysis [29]. And for the Coulomb friction model, the shear stress is related to the contact pressure between the two materials [30], as indicated in Fig. 3(a). For the spring slider model, the shear behavior is determined by a shear spring which is characterized by the shear stiffness and the cohesive strength [31]. However, the test and analytical investigations indicated that the interfacial stress decrease after its peak value during the debonding process of rockbolt-grout interface. The first two approaches cannot capture the stress decrement along the interface. For the spring slider model, it is an exhausting work to model the interfacial behavior since the shear behavior by this method must be modeled between nodes. In recent years, the cohesive zone model (CZM) has been extensively adopted to describe the interaction between two materials, due to its simple formulation and convenience of application in numerical simulations [32–35]. In this paper, the CZM is introduced to model the

0.9 0.6 0.3 0.0 0.00

0.05

0.10

0.15

Cracking opening displacement/mm

fu fy

ε sy

ε su ε s

(c) A bin-linear model for rockbolt Fig. 3. Interfacial model and stress-strain response for rockbolt.

response of the rockbolt-grout interface to capture the debonding behavior. In the direction parallel to the rockbolt-grout interface, the behaviors of the CZM are defined by a traction model as presented in Fig. 3(b). This model has been extensively adopted and

Compressive damage variable

Tensile damage variable

1.2

σs

1.2 0.9 0.6 0.3 0.0

0

0.01

Compressive strain

Fig. 2. Examples for evolution of the damage variables.

0.02

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validated [17,19]. The shear stress (s) increases proportionally to the shear displacement (d) until the peak stress (smax ). And then a linear softening branch occurs. A horizontal stage with nonzero residual fractional strength (sf ¼ bsmax ) is assumed after debonding. For the pullout behavior, the external load is along the axis of rockbolt, and thus it can be assumed that the relative displacement normal to the interface is neglected.

3. Numerical simulation of rockbolt grouted system 3.1. Test validation The pullout tests were conducted to valid the proposed numerical model. The dimensions for the test specimens are indicated in Fig. 5. All test specimens have the same diameter (D1 ¼ 80 mm) and tube thickness (t ¼ 15 mm). The rockbolt was embedded in the center of the specimen with a length l ¼ 450 mm. Two types of rockbolt with different diameters (d ¼ 20 mm and d ¼ 15 mm) were used. The parameters for the test specimens were listed in Table 1. All tests were conducted under a universal testing machine with a capacity of 300 kN. Fig. 6 gave a general view of the test setups. The specimen was installed in a steel frame. To ensure that the test specimen was under tensile load, a spherical hinge was equipped between the specimen and the steel frame. The tensile load was controlled and measured by the electronic load transducer. The load increases by a small increment of 0.5 kN and each load interval is maintained for about 2–3 min, during which the displacement at the loaded end is also recorded. Fig. 7 presents numerical results compared with the tests results. It shows that the predicted load-displacement responses agree well with the test data.

2.3. Rockbolt The steel bolt is assumed to behave as an elastic-plastic material with strain hardening after yielding (Fig. 3c). The Mises yield surface is used to define the isotropic yielding of steel material with the associated flow rule of plasticity. The Young’s modulus, yield strength, ultimate strength and the corresponding strain of steel used in this work are listed in Table 2. 2.4. Model set-up The field tests can evaluate the accurate mechanical performance of the rockbolt grouted system. However, the field tests are destructive and it is hard to control the test conditions. Furthermore, the exact value of the thickness of the grout is unavailable from the existing in situ tests. Therefore, the laboratory pullout tests are conducted to evaluate the mechanical performance of rockbolt grouted system. Two common methods are often adopted in the laboratory tests. The first is that the bolt (bar) is grouted in a concrete block which is adopted to simulate the rock mass [36]. The other method is that the bolt (bar) is grouted into a stiff steel tube, which is used to represent the rock mass in field test. For the first method, the physical dimension of the concrete block is always much greater than that of the bolt. This means that more meshes are needed for the concrete block when a finite element (FE) model is set up. Therefore, in this paper, the method with a bolt grouted in steel tube is adopted. An axisymmetric model is employed for the rockbolt grouted system due to the symmetry of boundary condition and geometry, as shown in Fig. 4(a). The end of the steel tube is fixed in the direction parallel to the load. A mesh for the model is indicated in Fig. 4 (b). As mentioned above, the rockbolt/grout interfacial debonding and the grout cracking are concerned in this paper. Therefore, the fine mesh is adopted for the cohesive zone and grout material. The bilinear axisymmetric element is adopted for the grout (CAX4R). The cohesive zone is meshed by the axisymmetric cohesive element (COHAX4).

CZ

Steel tube

3.2. Failure modes In the following discussions, the geometrical dimensions and material parameters of the model are listed in Table 2. For a given strength level of the grout, the failure modes of the rockbolt grouted system seem to be determined by the interfacial bond strength. The typical three failure modes of the rockbolt grouted system are interfacial debonding, grout cracking and a combining failure of interface debonding and grout cracking. It is indicated that there exists a critical bond strength (sc ). When the bond strength is much smaller than the critical one, sc , full interface

l D2 Grout Material

Rockbolt

d Steel tube

Fig. 5. Details of test specimens.

Grout material

Rockbolt

Load

(a)

CZ

(b) Fig. 4. Mesh for the numerical model.

Symmetry axis

D1

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X. Chang et al. / Construction and Building Materials 135 (2017) 665–673 Table 1 Specimen parameters. Specimen ID

l (mm)

D1 (mm)

D2 (mm)

d (mm)

Concrete strength (MPa)

Yong’s modulus (GPa)

P1 P2

400 400

80 80

65 65

20 15

28.4 19.7

25 23

Table 2 Parameters for the numerical model. Specimen dimensions

Steel (tube and bolt)

Concrete

CZM

l (mm)

D1 (mm)

D2 (mm)

D (mm)

Yong’s modulus (GPa)

Possion’ ratio

Yield strength (MPa)

Ultimate strength (MPa)

Compressive strength (MPa)

Yong’s modulus (GPa)

Possion ratio

Bond strength (MPa)

Residual bond strength factor

400

80

65

20

210

0.25

245

340

28.4

25

0.19

2.0–14.5

0.1–0.3

4

6

3 1 2

1.Specimen 2.Spherical hinge 3.Steel frame

5

4.Fixed end 5.Loading end 6.Testing machine

(a)

(b) Fig. 6. (a) Sketch for the test setup; (b) Test arrangement.

200 P1

Load/kN

150

Predicted

100 50 0

0

10

20

30

Displacement/mm 150

Load/kN

P2 Predicted

100

50

0

0

10

20

30

Displacement/mm Fig. 7. Comparison between the predicated and the test.

debonding failure can be captured. If the bond strength is close to the critical value, a combining failure of the grout crack and the interfacial debonding occurs. When the bond strength is sufficiently greater than the critical one, the grout cracks before the interfacial debonding. The typical failure processes for these three types are indicated in Fig. 8. Case I is for the interfacial debonding failure; Case II is for the combining failure and case III is for the cracking of grout. For case I (Fig. 8a), the interfacial debonding is the dominated failure and the debonding initiates at the interface nearest to the load end and propagates to the free end. Clearly, the interfacial debonding process is similar to the existing studies [15,16]. For case II, the whole specimen can be divided into three sections based on the failure process, as shown in Fig. 8b. An inclined crack in the grout is firstly formed in the sectionⅠ. And then the crack propagates horizontally to free end in sectionⅡ. As the displacement increases, the failure mode transfers from the grout cracking to the interface debonding. Then the interfacial debonding propagates to the free end in section III until the full debonding occurs. It should be noted that the grout cracking in horizontal direction is quite different from the interfacial debonding. The interfacial debonding occurs in the cohesive zone while the horizontal cracking propagates in the thin zone nearest to the cohesive zone, as indicated in Fig. 8b.

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X. Chang et al. / Construction and Building Materials 135 (2017) 665–673

Debonding zone

Debonding zone

(a) case

Section ĉ

:Interfacial debonding failure

Section Ċ

Grout

Section ċ

Interface debonding

cracking

Cohesive zone

(b) case

: Combining failure of interface debonding and grout cracking

Section ĉ

Section Ċ

(c) case

: Grout cracking

Fig. 8. Typical failure modes for rockbolt grouted system. SDEG ranging from zero to one is used to describe the evolution of damage variable.

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X. Chang et al. / Construction and Building Materials 135 (2017) 665–673

0

Shear stress/MPa

For case III, the cracking of grout is the dominating failure and the failure process consists of two stages (shown in Fig. 8c). Similar to case II, an inclined crack in the grout is firstly formed. However, in the following stage, the failure is completely controlled by the grout cracking along the interface and no interfacial debonding can be observed.

3.3. Load-displacement responses and shear stress distributions

A

-3

B

-6

-9 0

The interface shear stresses for these three cases are indicated in Fig. 10(a)–(c), respectively. For case I, the shear stress near the load end reaches the bond strength at point ‘A’ (Fig. 9). After point ‘A’, interface debonding occurs and then propagates to the free end. When the full debonding occurs at point ‘B’, the load keeps as a constant with the increasing of the axial displacement. For case II, the combined failure of the grout crack and the interfacial debonding can be captured. The inclined crack in the grout nucleated in the section I (Fig. 8) as the load reaches point ‘C’ (Fig. 9). The inclined crack induces the drop of the shear stresses along interface in section I. With the propagation of the horizontal cracking of grout in sectionⅡ, the interfacial shear stresses also decrease to a lower level. As the displacement reaches point ‘E’, the shear stress reaches the bond strength and interfacial debonding occurs. The failure mode transfers from the grout cracking to the interfacial debonding. In the following section, the interfacial debonding propagates to the free end until full debonding occurs at points ‘F’. The shear stress distributions for case III are shown in Fig. 10c. The inclined crack and horizontal crack initiate point ‘C’ and point ‘G’, respectively. Both induce the drops of interfacial shear stresses. It is also indicated that the shear stresses never reach the bond strength, therefore no interfacial debonding occurs and the grout cracking spreads toward the free end along the interface. The interfacial debonding failure occurs when the bond strength is lower than the critical value. For this case the grout peak load is lower than other cases even with higher ductility. For case III, due to the brittle crack of the grout, the load abruptly

200

A

Load /kN

300

400

500

Section

Section

Section

Shear stress/MPa

0 C D E F

-3 -6 -9 -12

0

100

200

300

400

500

Distance from free end/mm

(b) case Section

Section

0 -3

C G H

-6 -9 -12

0

200

400

600

Distance from free end/mm

(c) case Fig. 10. Interfacial shear stress distributions for these three typical cases.

drops (from point ‘C’ to point ‘G’ in Fig. 9). Thus this failure mode was not a safe one. Due to the higher bond strength for case II, the peak load is higher than that of case I. There is also an obvious load drops due to the grout cracking, however, the final failure is controlled by the interfacial debonding, which seems to provide both higher residual load and higher ductility. Therefore, the combining failure of the interface debonding and the grout cracking is a desirable mode of failure.

C Case Case Case

150 100

3.4. Parametric study Factors possibly affecting the performance of the rockbolt grouted system are material parameters related to the interface and the grout. Therefore, parametric studies are carried out for clear understanding of the failure mechanism in this section. The default material properties are same as those mentioned above.

D

50 0

200

(a) case

Shear stress/MPa

‘A’ – Initiation of interfacial debonding for case I; ‘B’ – Full interfacial debonding for case I; ‘C’ – Onset of inclined cracking for case II or case III; ‘D’ – Onset of horizontal cracking for case II; ‘E’ – Onset of interfacial debonding for case II; ‘F’ – Complete interfacial debonding for case II; ‘G’ – Horizontal cracking for case III; ‘H’ – Complete cracking for case III.

100

Distance from free end/mm

The load-displacement responses for these three types are indicated in Fig. 9. The characteristic points are marked on the responses:

G

E H

0

10

F B 20

30

40

Displacement/mm Fig. 9. Load-displacement curves for these three typical cases.

3.4.1. Influences of bond strength on failure mode and peak load A series of numerical models with various bond strength is simulated. The influences of bond strength on the failure mode and

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X. Chang et al. / Construction and Building Materials 135 (2017) 665–673

200

200

150

150

Load /kN

Peak load /kN

β = 0.1

100 50 0

β = 0.2

β = 0.3

100 50

0

3

6

9

12

0

15

0

5

10

(a) cas

Fig. 11. Effect of bond strength on peak load.

200

β = 0.1

β = 0.2

150

Load /kN

peak load are presented in Fig. 11. It is indicated that the response behaves in two different manners. In the first stages, the bond strength increases from 2.0 MPa to 9.5 MPa, and the corresponding peak load increases from 90 kN to 179 kN. During the first stage, the interface debonding is the dominant failure mode. However, the peak load is almost constant when the bond strength is greater than 9.2 MPa and the system fails by grout cracking during this stage. This can be concluded that the critical bond strength plays a primary role on the load capacity of the rockbolt grouted system. For case of bond strength lower than its critical value, higher bond strength can lead to higher load capacity. For case of bond strength higher than its critical value, the bond strength cannot contribute more to the load capacity of the rockbolt grouted system because the dominant failure mode is grout cracking.

β = 0.3

100 50 0

0

5

10

15

20

3.4.3. Residual bond strength Fig. 13 gives the effect of residual bond strength factor (b) on the load-displacement curves. It is shown that the effect of the residual bond strength factor is closely related to the failure modes. For interfacial debonding failure, a larger b increases the loads in the descending and full debonding stages. For the combined failure mode, b only has a significant effect on full debonding stages that higher value of b always leads to higher loads in full debonding stages. For the grout cracking failure, b has no obvious effect on the load-displacement curves. It should be noted that 12

30

35

(b) cas 200

Load /kN

3.4.2. Effect of grout strength on critical bond strength The above discussions show the critical bond strength is the dominated factor for the failure mode of the rockbolt grouted system. The existing studies indicate that the interface bond strength is determined by the compressive grout strength. Thus, the effects of the compressive grout strength on the critical bond strength are firstly discussed in this section. In Fig. 12, with the compressive strength of the grout ranging from 30 MPa to 60 MPa, the critical bond strength increases from 3.8 MPa to 11.5 MPa.

25

Displacement/mm

160

β = 0.2

120

β = 0.3

80 40 0

0

5

10

15

20

Displacement/mm

(c) case Fig. 13. Effect of residual bond strength factor load-displacement curves.

the peak loads for these three failure modes are not influenced by the residual bond strength factor. 3.4.4. Influences of diameter of rockbolt Fig. 14 presents the relationship between critical bond strength and rockbolt diameter. The diameter increases from 15 mm to 30 mm and other geometrical and material parameters are unchanged. For each diameter, the bond strength is adjusted to obtain the critical value. It can be seen from the figure that the critical bond strength increases by increasing the rockbolt diameter. 12.0

8

4

0

0

20

40

60

80

Grout compressive strength/MPa

Critical bond strength/MPa

Critical bond strength /MPa

15

Displacement/mm

Bond strength/MPa

9.0 6.0 3.0 0.0 0

10

20

30

40

Diameter/mm Fig. 12. Relationship between critical bond strength and grout compressive strength.

Fig. 14. Influences of rockbolt diameter on critical bond strength.

X. Chang et al. / Construction and Building Materials 135 (2017) 665–673

4. Conclusions A numerical model for the rockbolt grouted system is developed. The rockbolt-grout interfacial debonding and grout cracking are concerned in this paper. The typical failure modes can be captured: interfacial debonding, grout cracking and a combining failure of interfacial debonding and grout cracking. For the rockbolt grouted system, there exists a critical value for the bond strength. If the bond strength is lower than the critical one, the system fails by interfacial debonding. For this case, the peak load is the lowest. When the bond strength is close to the critical value, a combining failure of interfacial debonding and grout cracking occurs. For this case, the final failure is controlled by the interfacial debonding. Therefore, the system seems to achieve both higher residual load and higher ductility. When the bond strength is greater than the critical value, only grout cracking occurs. For this case, highest peak load can be obtained. However, the ductility is lower because of brittle cracking of the grout. A parametric study indicates that the critical bond strength is closely related to the compressive strength of the grout. The bond strength and residual bond strength factor have significant influences on the mechanical performances of the rockbolt grout system. Acknowledgements This study is supported by Chinese National Natural Science Fund (Project No. 51304067, 41172244), the Distinguished Young Scholars of Henan Polytechnic University (No. J2015-1) and the Fundamental Research Funds for the Universities of Henan Province (No. NSFRF140206). References [1] B. Zhang, S.C. Li, X.Y. Yang, D.F. Zhang, C.L. Shao, W.M. Yang, Uniaxial compression tests on mechanical properties of rock mass similar material with cross-cracks, Rock Soil Mech. 33 (12) (2012) 3674–3679. [2] J. Chen, S. Saydam, P.C. Hagan, An analytical model of the load transfer behavior of fully grouted cable bolts, Constr. Build. Mater. 101 (2015) 1006– 1015. [3] C.H. Tan, Difference solution of passive bolts reinforcement around a circular opening in elastoplastic rock mass, Int. J. Rock Mech. Min. Sci. 81 (2016) 28–38. [4] H. Kang, Y. Wu, F. Gao, P. Jiang, P. Cheng, X. Meng, Z. Li, Mechanical performances and stress state of rock bolts under varying loading conditions, Tunn. Undergr. Space Technol. 52 (2016) 138–146. [5] T. Nguyen, K. Ghabraie, T. Tran-Cong, Applying bi-directional evolutionary structural optimisation method for tunnel reinforcement design considering nonlinear material behaviour, Comput. Geotech. 55 (2014) 57–66. [6] C.R. Windsor, A.G. Thompson, Rock reinforcement-technology, testing, design and evaluation, Compr. Rock Eng. Princ. Pract. Projects 4 (1993) 451–484. [7] Pells PJN. The behaviour of fully bonded rockbolt. 3rd ISRM Congress, Denver, USA, 1974, pp. 12127. [8] T.J. Freeman, The behaviour of fully-bonded rock bolts in the Kielder experimental tunnel, Tunnels Tunnelling 10 (1978) 37–40.

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