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Reinforcement of rock mass with cross-flaws using rock bolt
Tunnelling and Underground Space Technology 51 (2016) 346–353
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Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Reinforcement of rock mass with cross-flaws using rock bolt Bo Zhang a,b, Shucai Li a,c, Kaiwen Xia d,⇑, Xueying Yang e, Dunfu Zhang a, Shugang Wang f, Jianbo Zhu g a
School of Civil Engineering, Shandong University, Jinan, Shandong 250061, PR China State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei 430071, PR China c Research Center of Geotechnical and Structural Engineering, Shandong University, Jinan, Shandong 250061, PR China d Department of Civil Engineering and Lassonde Institute, University of Toronto, ON, Canada M5S 1A4 e Shandong Urban Construction Vocational College, Jinan, Shandong 250014, PR China f Department of Energy and Mineral Engineering, G3 Center and Energy Institute, The Pennsylvania State University, University Park, PA 16802, USA g Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong Special Administrative Region b
a r t i c l e
i n f o
Article history: Received 19 June 2014 Received in revised form 4 September 2015 Accepted 7 October 2015 Available online 24 October 2015 Keywords: Reinforcement Rock bolt Rock mass Cross-flaws
a b s t r a c t Rock bolting is one of the most effective and economical means of rock mass reinforcement. Existing studies of rock bolt reinforcement are mostly focused on rock masses without flaw, with a single flaw, or with parallel flaws. However in rock masses, cracks or flaws usually exist in the form of cross-flaws. In order to understand the impact of cross-flaws on rock bolt reinforcement and to further explore the differences of bolt reinforcement between rock mass with cross-flaws and rock mass with a single flaw, reinforced analog specimens with cross-flaws and with a single flaw were tested under uniaxial compressive condition. The experimental results show that the uniaxial compressive strength of the reinforced rock mass with cross-flaws in this research is higher than that of reinforced rock mass with a single flaw. This observation can be explained by the difference in the failure modes of reinforced specimens: the reinforced rock masses with a single flaw fail due to the formation of a shear crack while reinforced rock masses with cross-flaws fail as a result of a tensile fracture or interaction between tensile fracture and shear fracture. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Rock bolting is one of the most effective and economical means of supporting in rock engineering applications such as rock tunneling. Understanding of the bolt reinforcement effect is essential for an optimal usage of rock bolts and thus for safety of rock engineering infrastructures (Grasselli, 2005). Since the first application of rock bolt in 1913, researchers conducted a series of studies for a better understanding of the mechanics of rock bolting (Farmer, 1975; Littlejohn and Bruce, 1975; Aldorf and Exner, 1986; Endersbee, 1999; Kovári, 2003). Zou (2004) studied the in-situ rock bolt loading for a single crack in rock mass, and showed that the bolt tension may reach peak at any location. Aksoy and Onargan (2010) demonstrated that the ground settlements could be substantially decreased by limiting the tunnel face movement into the tunnel. Aksoy and Onragan’s face bolting system created an umbrella arch around the tunnel face, thus enhancing the stability of the tunnel face. However, Aksoy and Onargan (2010) did not consider any flaws that also impact on rock mass reinforcement. Kang et al. (2013) investigated ⇑ Corresponding author. E-mail address: [email protected] (K. Xia). http://dx.doi.org/10.1016/j.tust.2015.10.007 0886-7798/Ó 2015 Elsevier Ltd. All rights reserved.
the mechanisms and factors resulting in bolt fracture failure through a close examination of bolts obtained from underground roadways, but they did not consider rock cracks or flaws in their investigation. As a matter of fact, the rock flaw was ignored in most of the in-situ rock bolt studies. To carefully investigate the effect of flaws on rock bolting, researchers carried out bolt reinforcement tests with rock mass or rock analog material in laboratory. There was not a special term for the pre-existing crack in the beginning, and then gradually the term ‘‘flaw” has been used to describe an artificially created crack (Wong and Einstein, 2009). These pre-existing flaws can be either open or closed. Ge and Liu (1988) established a theory for rock bolt. They determined the optimal bolting angle based on shear tests of the rock mass with a single flaw. They found that the reinforced rock mass attains the highest shear strength when the bolt bar and the flaw was at an angle of aopt = 30° +u, where u is the frictional angle of flaw surface. Guo and Ye (1992) found that when the angle between the bolt bar and the flaw was at 30–50°, the reinforced rock mass achieved the highest shear and compressive strength. Ferrero (1995) carried out experiments on different types of rocks reinforced by various elements. His experimental and numerical simulation results on reinforced rock mass with a single flaw showed two failure modes: the first type of failure was caused
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by a combination of shear and tensile stresses at the joint intersection for hard rock, while the second was due to a combination of tensile stresses and bending moments for weaker rock. Jeng and Huang (1999) studied the holding mechanism of under-reamed rock bolts, their results showed that the under-reamed end was blocked by the surrounding rock mass, resulting in a larger holding capacity than conventional rock bolts. They used the pull-out experiments to examine the holding mechanisms of underreamed rock bolts. However, the influence of flaw in rock mass was not taken into consideration. Kılıc et al. (2002) studied the influence of grouting material on bolt reinforcement through pull-out test of rock bolt without considering the flaw. Their study showed that increasing the bolt diameter and length increased load bearing capacity of the bolt, and this increase was limited by the ultimate tensile strength of the bolt materials. Through large-scale shear tests on reinforced rock mass with two parallel flaws, Grasselli (2005) studied the different mechanical responses of the full steel bar and the frictional Swellex bar. Martín et al. (2013) presented a method to obtain the bolt-grout interface behavior of fully grouted rock bolts from laboratory experiments without considering the rock flaws. Researchers also studied the bolt reinforcement of rock mass through theoretical analysis (Li and Stillborg, 1999; Cai et al., 2004; Guan et al., 2007; Osgoui and Ünal, 2009). Li et al. (2012) proposed a method to back calculate the grout cohesive strength and the grout friction angle based on the measured field pull-out force of rock bolt without considering the rock flaws. Maghous et al. (2012) described a three-dimensional theoretical and numerical model for the behavior of tunnels with reinforced bolts, and the elastoplastic constitutive equations for the reinforced rock were derived in the framework of homogenization method. In rock mass, the pattern of cross-flaws is one of the most common flaw patterns. However the existing studies on the rock bolt reinforcement as discussed above focused on rock mass with no flaw/crack, a single flaw/crack or parallel flaws/cracks. It is thus the objective of this work to understand the rock bolt reinforcement of rock mass with cross-flaws. Using rock analog materials, specimens simulating rock mass with cross-flaws are fabricated. Bolted specimens are subjected to uniaxial compression with purpose to qualitatively demonstrate the bolt reinforcement effect. The angle between the main flaw and the loading direction, and the angle between the main flaw and the secondary flaw are considered. The strength of the bolted samples are measured and the failure modes are observed and discussed in the context of mechanism of reinforcement.
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The mold used to cast specimen is composed of steel plates. There is no a steel plate on the top of the mold for pouring the cement mixture. The procedure used for specimen preparation is as follows. First the sand is poured into a sieve with 0.9 mm mesh to remove particles bigger than 0.9 mm. Secondly the cement, sand and water are weighted and mixed in a blender for 5 min. Thirdly the plastic slices to simulate the flaws are glued into the steel mold with a direction parallel to the thickness, and the bolt bar is placed in the steel mold (Fig. 1). At the last step the cement, sand, and water mixture is poured into the steel mold. The mold with the fresh cement mixture is then vibrated at a room temperature for 3 min. The specimens are taken out of the mold 24 h afterwards, for curing in the water at a constant temperature of 20 °C for 7 days. The photo of cured specimen is shown in Fig. 2. The Loading is applied on specimens by displacement control at a rate of 0.02 mm/s with testing equipment (Fig. 3).
3. Experiments 3.1. The testing conditions The angle between the main flaw and the secondary flaw as well as the angle between the bolt bar and the loading direction are taken as testing parameters. The angle between the main flaw and the loading direction is fixed at 45°. The reason to choose 45° angle as the main flaw angle is that 45° is a representative angle of I–II type mixed mode fracture. The testing specimen configuration is schematically shown in Fig. 4, where a is the angle between the main flaw and the loading direction, b is the angel between the main flaw and the secondary flaw, and c is the angle between the bolt bar and the loading direction. The testing conditions are shown in Table 1, where the test specimen without b stands for the rock mass with a single flaw. The specimens are loaded in a uniaxial compression condition until failure. The loading direction is parallel to the longitudinal direction of the specimen.
3.2. Experimental results and discussions 3.2.1. Stress–strain relation of rock mass reinforced by bolt The stress–strain curve of testing condition c-0 without bolt and slice which represents the rock mass in-situ was plotted in Fig. 5. Stress–strain curves of reinforced rock masses are shown in Fig. 6, where c-1 to c-16 stand for the No. of the testing conditions.
2. Specimen preparation and testing equipment The rock analog specimens are made of cement mortar, with cement: sand: water = 1:3.58:0.73. The cement used in is #425 Portland cement, the diameter of sand is smaller than 0.9 mm, and the water used is tap water. The bolt bar is simulated with galvanized iron wires. Cross-flaws are made by cross plastic slices inserted in the mortar during casting. These flaws are thus between open and close flaws but can be considered as close flaws. The dimension of the testing specimens is 70 mm in width, 70 mm in thickness and 140 mm in height. The main flaw of the cross-flaws is 30 mm in length, and the secondary flaw of the cross-flaws is 20 mm long. The plastic slice for making the crossflaws is 0.2 mm thick. The cross-flaws are made through the thickness of the specimen, perpendicular to the 70 140 mm face. The bolt bar is 6.4 mm in diameter. The parameters of bolt bar material are as follows: the elastic modulus is 190 GPa, the yield strength is 190 MPa, and the ultimate strength is 420 MPa.
Fig. 1. The schematic diagram of steel mold with plastic slices and bolt bar.
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Fig. 2. The specimen for simulating reinforced rock mass. Fig. 4. The testing schematic diagram of reinforced rock mass.
Table 1 Testing conditions of rock mass analog material under uniaxial compression.
Fig. 3. The testing equipment.
Fig. 6 shows the stress–strain relation of rock mass reinforced with bolts. Taking the c-2 curve in Fig. 6a as an example, the stress–strain curve consists of a nonlinear stage at the initial loading period (OA), a linear loading stage (AB), a nonlinear stage
No.
a (°)
c-0 c-1 c-2 c-3 c-4
Unbolted specimen without flaws 45 – 30 45 90
b (°)
c (°) 32
c-5 c-6 c-7 c-8
– 30 45 90
42
c-9 c-10 c-11 c-12
– 30 45 90
118
c-13 c-14 c-15 c-16
– 30 45 90
138
before the peak value (BC), a stress decrease stage (CD), and a residual strength segment (DE). From the observation of crack propagation process, it is found that the crack propagation initiates between the linear loading stage and the nonlinear stage before the peak value. The nonlinear stage before the peak value is the stage that the crack is in a stable propagation situation, and the stress decrease stage is the stage that the crack is in a non-stable propagation situation. All testing results are summarized in Table 2, where E is the elastic modulus of specimen, Smax is the uniaxial compressive strength of specimen, R is the residual strength of specimen. From the results in Fig. 6 and Table 2, one can see that the angle between the main flaw and the secondary flaw influences
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Fig. 5. The uniaxial compression stress–strain curve of testing condition c-0.
the mechanical properties of rock mass reinforced with bolts. The uniaxial compressive strength of the reinforced rock mass with cross-flaws tested in this work is higher than that of the reinforced rock mass with a single flaw. The strength peak value of the reinforced rock mass with b = 30° (testing condition c-2) is nearly twice as that of the reinforced rock mass with a single flaw (testing condition c-1). Among the specimens with cross-flaws tested in this study, the specimen with b = 30° has the highest strength,
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the specimen with b = 45° has the lowest strength, the specimen with b = 90° has the intermediate strength. The unbolted specimens with same cross-flaws have been tested in literature (Zhang et al., 2012). The schematic diagram of specimen without bolt was shown in Fig. 7. The tested results were shown in Fig. 8. From Figs. 5–8 one can see whether the rock masses are bolted or not the rock masses with cross-flaws in the two studies have higher uniaxial compression strength than that of rock mass with a single flaw. The uniaxial compression strengths of bolted rock masses with a single flaw are almost same with that of unbolted rock mass without flaw(c-0). The uniaxial compression strengths of most bolted rock masses with cross-flaws are higher than that of unbolted rock mass without flaw(c-0). This shows that the cross-flaws influence the uniaxial compression strength of the rock mass. Comparing with Figs. 6–8 it can be seen that the bolted rock mass has higher uniaxial compression strength than that of unbolted rock mass. The specimens with b = 30° have the highest strength both in Figs. 6 and 8. The strength of specimen with b = 90° is higher than that of specimen with b = 45° in bolted specimens (Fig. 6). However, the strength of specimen with b = 45° is higher than that of specimen with b = 90° in unbolted specimens (Fig. 8). From Fig. 6 one can see that the c-2 with 77° angle between the bolt bar and the main flaw has the highest strength in the four testing conditions with the angle b = 30° (c-2, c-6, c-10 and c-14); the c-7 with 87° angle between the bolt bar and the main flaw has
Fig. 6. The uniaxial compression stress–strain curves of reinforced rock mass analog material specimens. (a) c = 32°; (b) c = 42°; (c) c = 118°; (d) c = 138°.
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Table 2 Uniaxial compression test results of rock mass analog material specimens. No.
E (MPa)
Smax (MPa)
R (MPa)
c-0 c- 1 c-2 c-3 c-4
569.53 471.11 1305.19 183.93 651.58
2.761 2.81 5.50 2.25 3.30
0.61 0.50 0.52 0.37 0.39
c-5 c-6 c-7 c-8
732.57 425.12 174.82 536.92
2.92 5.08 3.61 3.93
0.59 1.22 0.61 0.46
c-9 c-10 c-11 c-12
510.06 624.12 434.88 730.60
2.68 4.51 2.92 3.79
0.15 0.75 0.24 0.33
c-13 c-14 c-15 c-16
510.06 968.46 314.45 340.06
2.67 5.15 3.17 3.53
0.21 0.92 0.31 0.50
the highest strength in all the four testing conditions with the angle b = 45° (c-3, c-7, c-11 and c-15); the c-8 with 87° angle between the bolt bar and the main flaw has the highest strength in all the four testing conditions with the angle b = 90° (c-4, c-8, c-12 and c-16). These results show that the bolting position also influences the bolted rock mass uniaxial compression strength. 3.2.2. The failure process of rock mass reinforced by bolt The failure processes of testing conditions c-5, c-6, c-7 and c-8 are taken as examples to analyze the failure process of rock mass
Fig. 7. The testing schematic diagram of unbolted rock mass.
Fig. 8. The uniaxial compression stress–strain curves of unbolted rock mass analog material specimens (Zhang et al. (2012)).
reinforced by bolt. The testing failure processes are shown in Fig. 9, where T stands for the tensile crack, and S stands for the shear crack. The characteristics of tensile and shear cracks have been elaborated in the literature (Park and Bobet, 2010) The surface of tensile cracks is characterized by a plumose structure, and the crack is absent of pulverized powder. On the other hand, the surface of shear cracks is characterized by pulverized material and a very rough texture, and the crack contains crushed material. From the Fig. 9a it can be seen that the fracture of the reinforced rock mass specimen with a single flaw starts with a wing crack from its tip. As the load increases, a shear crack appears and the wing crack arrests. Eventually the specimen fails by the growth of the shear crack. Some researchers have already studied the failure process of unreinforced rock mass. For example Li et al. (2005) conducted uniaxial compression loading tests on unreinforced Marble specimens with a 45° single flaw. The tested results of Li et al. (2005) showed that both wing cracks and secondary cracks initiated from the flaw tips, the latter being the shear crack and leading to specimen failure (Fig. 10). These results show that the shear crack is the main cause of the failure of rock mass with a single flaw. From the Fig. 9b one can see that the fracture of the reinforced rock mass specimen with b = 30° starts with the wing crack from the tip of the main flaw. A tensile crack initiates from the tip of the secondary flaw until the former almost propagates to the edge of the specimen. For the reinforced rock mass specimen with a single flaw, the wing crack is arrested far away from the edge of the specimen, and the shear crack appears subsequently leading to the failure of the specimen. This implies the secondary flaw affects the formation of the shear crack. The reinforced rock mass specimens with b = 30° angle feature the highest uniaxial compressive strength in the specimens tested in this work. From the Fig. 9c one can find that the reinforced rock mass specimen with b = 45° fails along a shear crack that has almost the same failure mode as the reinforced specimen with a 45° single flaw. The uniaxial compressive strength of reinforced rock mass specimen with b = 45° is close to that of the reinforced specimen with a 45° single flaw. Fig. 9d shows that there are pulverized material and rough textures at the fracture initiated from the tip of the main flaw with b = 90°, which indicates that the fracture is shear in nature. After the fracture propagates to a certain distance, a tensile crack is initiated from the tip of the secondary flaw. The strength of the reinforced specimen with b = 90° is higher than that of reinforced specimen with b = 45°. From the discussions above, one can conclude that the strength of reinforced rock mass is greatly influenced by the angles between
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the flaws, which further control the nature of fractures initiated from the tips of the flaws. As far as the crack propagation patterns are concerned, there exist two types of fractures from the tips of the flaws: shear fractures and tensile fractures. When the failure is caused by the shear fractures under uniaxial compression, the reinforced rock mass has low strength and the failure is more brittle. The reinforced rock mass with a single flaw usually fails due to the shear fracture under uniaxial compression. When the failure of reinforced rock mass is mostly caused by the tensile fractures on the other hand, the reinforced rock mass would have higher strength. For some uniaxial tests of cross-flaws rock mass specimens, the fractures initiated from the tip of the main flaw and the
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secondary flaw are all tensile. These specimens exhibit the highest strength among the specimens tested in this work. For other uniaxial tests of cross-flaws rock mass specimens, the fracture initiated from the tip of the main flaw is shear while that from the tip of the secondary flaw is tensile, the tensile fracture interacts with the shear fracture, leading to a higher strength of the specimen. 4. Failure modes explained using sliding system The failure processes for c-5 to c-8 are schematically shown in Fig. 11, where T denotes tensile crack, S denotes shear crack, and
Fig. 9. The uniaxial compression failure processes of reinforced rock mass analog material specimens. (a) testing condition c-5; (b) testing condition c-6; (c) testing condition c-7; (d) testing condition c-8.
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B. Zhang et al. / Tunnelling and Underground Space Technology 51 (2016) 346–353 Table 3 The |s(hr)max| of main flaw tips. No.
|s(hr)max|/MPa
c-1 c-2 c-3 c-4
3.216 2.766 3.007 3.298
c-5 c-6 c-7 c-8
3.292 3.041 3.114 3.304
c-9 c-10 c-11 c-12
3.533 3.502 3.343 3.594
c-13 c-14 c-15 c-16
3.804 3.645 3.387 3.893
Note: s(hr)max is the maximum shear stress in polar coordinate, |s(hr)max| is the absolute value of s(hr)max.
Fig. 10. The failure mode schematic diagram of rock analog specimen without reinforcement (Li et al., 2005). T denotes tensile fracture and S denotes shear fracture.
dash line denotes the rock bolt. In this study we define the sliding or sliding tendency between the two faces of one flaw as sliding system. In the following, we use the interaction between the sliding system and the rock bolt to explain the observed failure modes of reinforced rock mass. In order to explain the failure modes with qualitative results in a certain extent, the stress field of testing conditions from c1 to c16 are computed with finite element method program ABAQUS in the linear-elastic range. The computing parameters of rock mass and bolt bar are same with the testing materials. The |s(hr)max| of main flaw tips are obtained and listed in Table 3. The computation models of c-5 to c-8 are shown in Fig. 12 as examples for testing conditions from c1 to c16. In the Fig. 11a, it can be seen that the shear sliding system goes through the single flaw ‘‘ab” and it is left-lateral. In the Fig. 11b, it can be seen that the main flaw ‘‘a1b1” and the secondary flaw ‘‘cd” both have the same shear sliding system of left-lateral. From Table 3 one can see the specimens with b = 30° have lower |s(hr)max| of main flaw tips than those of the reinforced rock mass
specimen with a single flaw under the same c. For example, the main flaw tip |s(hr)max| of c-6 is lower than that of c-5. From sliding system and numerical results one can see that these two same sliding systems interact and thus delay the formation of shear fracture, resulting in the highest strength of the specimen with b = 30° in all four cases shown in Fig. 11. From Table 3 one can see the specimens with b = 45° have lower |s(hr)max| of main flaw tips than those of the reinforced rock mass specimen with a single flaw under the same c. However in the Fig. 11c, it can be seen that the secondary flaw ‘‘ef” is vertical to the loading direction and thus there is no shear sliding system for this flaw. Therefore in this situation the secondary flaw has little influence on the fracture from the tip of the main flaw. The strength measured in the specimen with b = 45° is almost similar to that with a single flaw. From the Fig. 11d, it can be seen that the sliding system by the main flaw ‘‘a3b3” and that by the secondary flaw ‘‘gh” have opposite directions. The secondary flaw has no delaying effect on the fracture initiation from the main flaw. From Table 3 one can see that the specimens with b = 90° have higher |s(hr)max| of main flaw tips than those of the reinforced rock mass specimen with a single flaw under the same c. However after fracture initiation, the sliding from the fracture initiated from the tip of the secondary flaw increases the resistance of sliding of the fracture initiated from
Fig. 11. The failure modes schematic diagram of testing conditions c-5 to c-8. (a) testing condition c-5; (b) testing condition c-6; (c) testing condition c-7; (d) testing condition c-8.
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Fig. 12. The numerical computation models of testing conditions c-5 to c-8. (a) testing condition c-5; (b) testing condition c-6; (c) testing condition c-7; (d) testing condition c-8.
the tip of the main flaw, thus leading to a higher strength than that shown in Fig. 11a. From the Fig. 11d, one can see that the bolt is helpful to reduce the sliding/ sliding tendency of the main flaw ‘‘a3b3” and the secondary flaw ‘‘gh”. From the Fig. 11c, it can be seen that only the sliding/ sliding tendency of the main flaw ‘‘a2b2” can be reduced by the bolt. So the strength of specimen in Fig. 11d is higher than that in Fig. 11c.
5. Conclusions In this paper, the bolt reinforcement effect of rock mass with a single flaw and cross-flaws are studied with simulated rock mass and bolt bar. The reinforced rock mass with cross-flaws in this research exhibits higher uniaxial compressive strength than that of reinforced rock mass with a single flaw. This observation is interpreted using the interaction of the bolt bar and the factures initiated from the tips of the flaws. The reinforced rock mass with a single flaw fails due to a shear fracture. This mode of failure is highly brittle. Reinforced rock masses with cross-flaws on the other hand may fail by a tensile fracture or interaction between tensile fracture and shear fracture, thus leading to the higher uniaxial compressive strength. The failure modes of different b angles are explained using the interaction between the rock bar and the sliding systems associated with the flaws. Acknowledgements This paper is funded by National Natural Science Foundation of China (NO. 51379114, 51279095), Natural Science Foundation of Shandong Province, China (ZR2012EEQ007) and State Key Laboratory Open Fund of Geomechanics and Geotechnical Engineering (NO. Z013004). References Aksoy, C.O., Onargan, T., 2010. The role of umbrella arch and face bolt as deformation preventing support system in preventing building damages. Tunn. Undergr. Space Technol. 25 (5), 553–559. Aldorf, J., Exner, K., 1986. Mine Openings: Stability and Support. Elsevier, New York. Cai, Y., Esaki, T., Jiang, Y.J., 2004. A rock bolt and rock mass interaction model. Int. J. Rock Mech. Min. Sci. 41 (7), 1055–1067.
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Contents lists available at ScienceDirect
Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Reinforcement of rock mass with cross-flaws using rock bolt Bo Zhang a,b, Shucai Li a,c, Kaiwen Xia d,⇑, Xueying Yang e, Dunfu Zhang a, Shugang Wang f, Jianbo Zhu g a
School of Civil Engineering, Shandong University, Jinan, Shandong 250061, PR China State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei 430071, PR China c Research Center of Geotechnical and Structural Engineering, Shandong University, Jinan, Shandong 250061, PR China d Department of Civil Engineering and Lassonde Institute, University of Toronto, ON, Canada M5S 1A4 e Shandong Urban Construction Vocational College, Jinan, Shandong 250014, PR China f Department of Energy and Mineral Engineering, G3 Center and Energy Institute, The Pennsylvania State University, University Park, PA 16802, USA g Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong Special Administrative Region b
a r t i c l e
i n f o
Article history: Received 19 June 2014 Received in revised form 4 September 2015 Accepted 7 October 2015 Available online 24 October 2015 Keywords: Reinforcement Rock bolt Rock mass Cross-flaws
a b s t r a c t Rock bolting is one of the most effective and economical means of rock mass reinforcement. Existing studies of rock bolt reinforcement are mostly focused on rock masses without flaw, with a single flaw, or with parallel flaws. However in rock masses, cracks or flaws usually exist in the form of cross-flaws. In order to understand the impact of cross-flaws on rock bolt reinforcement and to further explore the differences of bolt reinforcement between rock mass with cross-flaws and rock mass with a single flaw, reinforced analog specimens with cross-flaws and with a single flaw were tested under uniaxial compressive condition. The experimental results show that the uniaxial compressive strength of the reinforced rock mass with cross-flaws in this research is higher than that of reinforced rock mass with a single flaw. This observation can be explained by the difference in the failure modes of reinforced specimens: the reinforced rock masses with a single flaw fail due to the formation of a shear crack while reinforced rock masses with cross-flaws fail as a result of a tensile fracture or interaction between tensile fracture and shear fracture. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Rock bolting is one of the most effective and economical means of supporting in rock engineering applications such as rock tunneling. Understanding of the bolt reinforcement effect is essential for an optimal usage of rock bolts and thus for safety of rock engineering infrastructures (Grasselli, 2005). Since the first application of rock bolt in 1913, researchers conducted a series of studies for a better understanding of the mechanics of rock bolting (Farmer, 1975; Littlejohn and Bruce, 1975; Aldorf and Exner, 1986; Endersbee, 1999; Kovári, 2003). Zou (2004) studied the in-situ rock bolt loading for a single crack in rock mass, and showed that the bolt tension may reach peak at any location. Aksoy and Onargan (2010) demonstrated that the ground settlements could be substantially decreased by limiting the tunnel face movement into the tunnel. Aksoy and Onragan’s face bolting system created an umbrella arch around the tunnel face, thus enhancing the stability of the tunnel face. However, Aksoy and Onargan (2010) did not consider any flaws that also impact on rock mass reinforcement. Kang et al. (2013) investigated ⇑ Corresponding author. E-mail address: [email protected] (K. Xia). http://dx.doi.org/10.1016/j.tust.2015.10.007 0886-7798/Ó 2015 Elsevier Ltd. All rights reserved.
the mechanisms and factors resulting in bolt fracture failure through a close examination of bolts obtained from underground roadways, but they did not consider rock cracks or flaws in their investigation. As a matter of fact, the rock flaw was ignored in most of the in-situ rock bolt studies. To carefully investigate the effect of flaws on rock bolting, researchers carried out bolt reinforcement tests with rock mass or rock analog material in laboratory. There was not a special term for the pre-existing crack in the beginning, and then gradually the term ‘‘flaw” has been used to describe an artificially created crack (Wong and Einstein, 2009). These pre-existing flaws can be either open or closed. Ge and Liu (1988) established a theory for rock bolt. They determined the optimal bolting angle based on shear tests of the rock mass with a single flaw. They found that the reinforced rock mass attains the highest shear strength when the bolt bar and the flaw was at an angle of aopt = 30° +u, where u is the frictional angle of flaw surface. Guo and Ye (1992) found that when the angle between the bolt bar and the flaw was at 30–50°, the reinforced rock mass achieved the highest shear and compressive strength. Ferrero (1995) carried out experiments on different types of rocks reinforced by various elements. His experimental and numerical simulation results on reinforced rock mass with a single flaw showed two failure modes: the first type of failure was caused
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by a combination of shear and tensile stresses at the joint intersection for hard rock, while the second was due to a combination of tensile stresses and bending moments for weaker rock. Jeng and Huang (1999) studied the holding mechanism of under-reamed rock bolts, their results showed that the under-reamed end was blocked by the surrounding rock mass, resulting in a larger holding capacity than conventional rock bolts. They used the pull-out experiments to examine the holding mechanisms of underreamed rock bolts. However, the influence of flaw in rock mass was not taken into consideration. Kılıc et al. (2002) studied the influence of grouting material on bolt reinforcement through pull-out test of rock bolt without considering the flaw. Their study showed that increasing the bolt diameter and length increased load bearing capacity of the bolt, and this increase was limited by the ultimate tensile strength of the bolt materials. Through large-scale shear tests on reinforced rock mass with two parallel flaws, Grasselli (2005) studied the different mechanical responses of the full steel bar and the frictional Swellex bar. Martín et al. (2013) presented a method to obtain the bolt-grout interface behavior of fully grouted rock bolts from laboratory experiments without considering the rock flaws. Researchers also studied the bolt reinforcement of rock mass through theoretical analysis (Li and Stillborg, 1999; Cai et al., 2004; Guan et al., 2007; Osgoui and Ünal, 2009). Li et al. (2012) proposed a method to back calculate the grout cohesive strength and the grout friction angle based on the measured field pull-out force of rock bolt without considering the rock flaws. Maghous et al. (2012) described a three-dimensional theoretical and numerical model for the behavior of tunnels with reinforced bolts, and the elastoplastic constitutive equations for the reinforced rock were derived in the framework of homogenization method. In rock mass, the pattern of cross-flaws is one of the most common flaw patterns. However the existing studies on the rock bolt reinforcement as discussed above focused on rock mass with no flaw/crack, a single flaw/crack or parallel flaws/cracks. It is thus the objective of this work to understand the rock bolt reinforcement of rock mass with cross-flaws. Using rock analog materials, specimens simulating rock mass with cross-flaws are fabricated. Bolted specimens are subjected to uniaxial compression with purpose to qualitatively demonstrate the bolt reinforcement effect. The angle between the main flaw and the loading direction, and the angle between the main flaw and the secondary flaw are considered. The strength of the bolted samples are measured and the failure modes are observed and discussed in the context of mechanism of reinforcement.
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The mold used to cast specimen is composed of steel plates. There is no a steel plate on the top of the mold for pouring the cement mixture. The procedure used for specimen preparation is as follows. First the sand is poured into a sieve with 0.9 mm mesh to remove particles bigger than 0.9 mm. Secondly the cement, sand and water are weighted and mixed in a blender for 5 min. Thirdly the plastic slices to simulate the flaws are glued into the steel mold with a direction parallel to the thickness, and the bolt bar is placed in the steel mold (Fig. 1). At the last step the cement, sand, and water mixture is poured into the steel mold. The mold with the fresh cement mixture is then vibrated at a room temperature for 3 min. The specimens are taken out of the mold 24 h afterwards, for curing in the water at a constant temperature of 20 °C for 7 days. The photo of cured specimen is shown in Fig. 2. The Loading is applied on specimens by displacement control at a rate of 0.02 mm/s with testing equipment (Fig. 3).
3. Experiments 3.1. The testing conditions The angle between the main flaw and the secondary flaw as well as the angle between the bolt bar and the loading direction are taken as testing parameters. The angle between the main flaw and the loading direction is fixed at 45°. The reason to choose 45° angle as the main flaw angle is that 45° is a representative angle of I–II type mixed mode fracture. The testing specimen configuration is schematically shown in Fig. 4, where a is the angle between the main flaw and the loading direction, b is the angel between the main flaw and the secondary flaw, and c is the angle between the bolt bar and the loading direction. The testing conditions are shown in Table 1, where the test specimen without b stands for the rock mass with a single flaw. The specimens are loaded in a uniaxial compression condition until failure. The loading direction is parallel to the longitudinal direction of the specimen.
3.2. Experimental results and discussions 3.2.1. Stress–strain relation of rock mass reinforced by bolt The stress–strain curve of testing condition c-0 without bolt and slice which represents the rock mass in-situ was plotted in Fig. 5. Stress–strain curves of reinforced rock masses are shown in Fig. 6, where c-1 to c-16 stand for the No. of the testing conditions.
2. Specimen preparation and testing equipment The rock analog specimens are made of cement mortar, with cement: sand: water = 1:3.58:0.73. The cement used in is #425 Portland cement, the diameter of sand is smaller than 0.9 mm, and the water used is tap water. The bolt bar is simulated with galvanized iron wires. Cross-flaws are made by cross plastic slices inserted in the mortar during casting. These flaws are thus between open and close flaws but can be considered as close flaws. The dimension of the testing specimens is 70 mm in width, 70 mm in thickness and 140 mm in height. The main flaw of the cross-flaws is 30 mm in length, and the secondary flaw of the cross-flaws is 20 mm long. The plastic slice for making the crossflaws is 0.2 mm thick. The cross-flaws are made through the thickness of the specimen, perpendicular to the 70 140 mm face. The bolt bar is 6.4 mm in diameter. The parameters of bolt bar material are as follows: the elastic modulus is 190 GPa, the yield strength is 190 MPa, and the ultimate strength is 420 MPa.
Fig. 1. The schematic diagram of steel mold with plastic slices and bolt bar.
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Fig. 2. The specimen for simulating reinforced rock mass. Fig. 4. The testing schematic diagram of reinforced rock mass.
Table 1 Testing conditions of rock mass analog material under uniaxial compression.
Fig. 3. The testing equipment.
Fig. 6 shows the stress–strain relation of rock mass reinforced with bolts. Taking the c-2 curve in Fig. 6a as an example, the stress–strain curve consists of a nonlinear stage at the initial loading period (OA), a linear loading stage (AB), a nonlinear stage
No.
a (°)
c-0 c-1 c-2 c-3 c-4
Unbolted specimen without flaws 45 – 30 45 90
b (°)
c (°) 32
c-5 c-6 c-7 c-8
– 30 45 90
42
c-9 c-10 c-11 c-12
– 30 45 90
118
c-13 c-14 c-15 c-16
– 30 45 90
138
before the peak value (BC), a stress decrease stage (CD), and a residual strength segment (DE). From the observation of crack propagation process, it is found that the crack propagation initiates between the linear loading stage and the nonlinear stage before the peak value. The nonlinear stage before the peak value is the stage that the crack is in a stable propagation situation, and the stress decrease stage is the stage that the crack is in a non-stable propagation situation. All testing results are summarized in Table 2, where E is the elastic modulus of specimen, Smax is the uniaxial compressive strength of specimen, R is the residual strength of specimen. From the results in Fig. 6 and Table 2, one can see that the angle between the main flaw and the secondary flaw influences
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Fig. 5. The uniaxial compression stress–strain curve of testing condition c-0.
the mechanical properties of rock mass reinforced with bolts. The uniaxial compressive strength of the reinforced rock mass with cross-flaws tested in this work is higher than that of the reinforced rock mass with a single flaw. The strength peak value of the reinforced rock mass with b = 30° (testing condition c-2) is nearly twice as that of the reinforced rock mass with a single flaw (testing condition c-1). Among the specimens with cross-flaws tested in this study, the specimen with b = 30° has the highest strength,
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the specimen with b = 45° has the lowest strength, the specimen with b = 90° has the intermediate strength. The unbolted specimens with same cross-flaws have been tested in literature (Zhang et al., 2012). The schematic diagram of specimen without bolt was shown in Fig. 7. The tested results were shown in Fig. 8. From Figs. 5–8 one can see whether the rock masses are bolted or not the rock masses with cross-flaws in the two studies have higher uniaxial compression strength than that of rock mass with a single flaw. The uniaxial compression strengths of bolted rock masses with a single flaw are almost same with that of unbolted rock mass without flaw(c-0). The uniaxial compression strengths of most bolted rock masses with cross-flaws are higher than that of unbolted rock mass without flaw(c-0). This shows that the cross-flaws influence the uniaxial compression strength of the rock mass. Comparing with Figs. 6–8 it can be seen that the bolted rock mass has higher uniaxial compression strength than that of unbolted rock mass. The specimens with b = 30° have the highest strength both in Figs. 6 and 8. The strength of specimen with b = 90° is higher than that of specimen with b = 45° in bolted specimens (Fig. 6). However, the strength of specimen with b = 45° is higher than that of specimen with b = 90° in unbolted specimens (Fig. 8). From Fig. 6 one can see that the c-2 with 77° angle between the bolt bar and the main flaw has the highest strength in the four testing conditions with the angle b = 30° (c-2, c-6, c-10 and c-14); the c-7 with 87° angle between the bolt bar and the main flaw has
Fig. 6. The uniaxial compression stress–strain curves of reinforced rock mass analog material specimens. (a) c = 32°; (b) c = 42°; (c) c = 118°; (d) c = 138°.
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Table 2 Uniaxial compression test results of rock mass analog material specimens. No.
E (MPa)
Smax (MPa)
R (MPa)
c-0 c- 1 c-2 c-3 c-4
569.53 471.11 1305.19 183.93 651.58
2.761 2.81 5.50 2.25 3.30
0.61 0.50 0.52 0.37 0.39
c-5 c-6 c-7 c-8
732.57 425.12 174.82 536.92
2.92 5.08 3.61 3.93
0.59 1.22 0.61 0.46
c-9 c-10 c-11 c-12
510.06 624.12 434.88 730.60
2.68 4.51 2.92 3.79
0.15 0.75 0.24 0.33
c-13 c-14 c-15 c-16
510.06 968.46 314.45 340.06
2.67 5.15 3.17 3.53
0.21 0.92 0.31 0.50
the highest strength in all the four testing conditions with the angle b = 45° (c-3, c-7, c-11 and c-15); the c-8 with 87° angle between the bolt bar and the main flaw has the highest strength in all the four testing conditions with the angle b = 90° (c-4, c-8, c-12 and c-16). These results show that the bolting position also influences the bolted rock mass uniaxial compression strength. 3.2.2. The failure process of rock mass reinforced by bolt The failure processes of testing conditions c-5, c-6, c-7 and c-8 are taken as examples to analyze the failure process of rock mass
Fig. 7. The testing schematic diagram of unbolted rock mass.
Fig. 8. The uniaxial compression stress–strain curves of unbolted rock mass analog material specimens (Zhang et al. (2012)).
reinforced by bolt. The testing failure processes are shown in Fig. 9, where T stands for the tensile crack, and S stands for the shear crack. The characteristics of tensile and shear cracks have been elaborated in the literature (Park and Bobet, 2010) The surface of tensile cracks is characterized by a plumose structure, and the crack is absent of pulverized powder. On the other hand, the surface of shear cracks is characterized by pulverized material and a very rough texture, and the crack contains crushed material. From the Fig. 9a it can be seen that the fracture of the reinforced rock mass specimen with a single flaw starts with a wing crack from its tip. As the load increases, a shear crack appears and the wing crack arrests. Eventually the specimen fails by the growth of the shear crack. Some researchers have already studied the failure process of unreinforced rock mass. For example Li et al. (2005) conducted uniaxial compression loading tests on unreinforced Marble specimens with a 45° single flaw. The tested results of Li et al. (2005) showed that both wing cracks and secondary cracks initiated from the flaw tips, the latter being the shear crack and leading to specimen failure (Fig. 10). These results show that the shear crack is the main cause of the failure of rock mass with a single flaw. From the Fig. 9b one can see that the fracture of the reinforced rock mass specimen with b = 30° starts with the wing crack from the tip of the main flaw. A tensile crack initiates from the tip of the secondary flaw until the former almost propagates to the edge of the specimen. For the reinforced rock mass specimen with a single flaw, the wing crack is arrested far away from the edge of the specimen, and the shear crack appears subsequently leading to the failure of the specimen. This implies the secondary flaw affects the formation of the shear crack. The reinforced rock mass specimens with b = 30° angle feature the highest uniaxial compressive strength in the specimens tested in this work. From the Fig. 9c one can find that the reinforced rock mass specimen with b = 45° fails along a shear crack that has almost the same failure mode as the reinforced specimen with a 45° single flaw. The uniaxial compressive strength of reinforced rock mass specimen with b = 45° is close to that of the reinforced specimen with a 45° single flaw. Fig. 9d shows that there are pulverized material and rough textures at the fracture initiated from the tip of the main flaw with b = 90°, which indicates that the fracture is shear in nature. After the fracture propagates to a certain distance, a tensile crack is initiated from the tip of the secondary flaw. The strength of the reinforced specimen with b = 90° is higher than that of reinforced specimen with b = 45°. From the discussions above, one can conclude that the strength of reinforced rock mass is greatly influenced by the angles between
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the flaws, which further control the nature of fractures initiated from the tips of the flaws. As far as the crack propagation patterns are concerned, there exist two types of fractures from the tips of the flaws: shear fractures and tensile fractures. When the failure is caused by the shear fractures under uniaxial compression, the reinforced rock mass has low strength and the failure is more brittle. The reinforced rock mass with a single flaw usually fails due to the shear fracture under uniaxial compression. When the failure of reinforced rock mass is mostly caused by the tensile fractures on the other hand, the reinforced rock mass would have higher strength. For some uniaxial tests of cross-flaws rock mass specimens, the fractures initiated from the tip of the main flaw and the
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secondary flaw are all tensile. These specimens exhibit the highest strength among the specimens tested in this work. For other uniaxial tests of cross-flaws rock mass specimens, the fracture initiated from the tip of the main flaw is shear while that from the tip of the secondary flaw is tensile, the tensile fracture interacts with the shear fracture, leading to a higher strength of the specimen. 4. Failure modes explained using sliding system The failure processes for c-5 to c-8 are schematically shown in Fig. 11, where T denotes tensile crack, S denotes shear crack, and
Fig. 9. The uniaxial compression failure processes of reinforced rock mass analog material specimens. (a) testing condition c-5; (b) testing condition c-6; (c) testing condition c-7; (d) testing condition c-8.
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B. Zhang et al. / Tunnelling and Underground Space Technology 51 (2016) 346–353 Table 3 The |s(hr)max| of main flaw tips. No.
|s(hr)max|/MPa
c-1 c-2 c-3 c-4
3.216 2.766 3.007 3.298
c-5 c-6 c-7 c-8
3.292 3.041 3.114 3.304
c-9 c-10 c-11 c-12
3.533 3.502 3.343 3.594
c-13 c-14 c-15 c-16
3.804 3.645 3.387 3.893
Note: s(hr)max is the maximum shear stress in polar coordinate, |s(hr)max| is the absolute value of s(hr)max.
Fig. 10. The failure mode schematic diagram of rock analog specimen without reinforcement (Li et al., 2005). T denotes tensile fracture and S denotes shear fracture.
dash line denotes the rock bolt. In this study we define the sliding or sliding tendency between the two faces of one flaw as sliding system. In the following, we use the interaction between the sliding system and the rock bolt to explain the observed failure modes of reinforced rock mass. In order to explain the failure modes with qualitative results in a certain extent, the stress field of testing conditions from c1 to c16 are computed with finite element method program ABAQUS in the linear-elastic range. The computing parameters of rock mass and bolt bar are same with the testing materials. The |s(hr)max| of main flaw tips are obtained and listed in Table 3. The computation models of c-5 to c-8 are shown in Fig. 12 as examples for testing conditions from c1 to c16. In the Fig. 11a, it can be seen that the shear sliding system goes through the single flaw ‘‘ab” and it is left-lateral. In the Fig. 11b, it can be seen that the main flaw ‘‘a1b1” and the secondary flaw ‘‘cd” both have the same shear sliding system of left-lateral. From Table 3 one can see the specimens with b = 30° have lower |s(hr)max| of main flaw tips than those of the reinforced rock mass
specimen with a single flaw under the same c. For example, the main flaw tip |s(hr)max| of c-6 is lower than that of c-5. From sliding system and numerical results one can see that these two same sliding systems interact and thus delay the formation of shear fracture, resulting in the highest strength of the specimen with b = 30° in all four cases shown in Fig. 11. From Table 3 one can see the specimens with b = 45° have lower |s(hr)max| of main flaw tips than those of the reinforced rock mass specimen with a single flaw under the same c. However in the Fig. 11c, it can be seen that the secondary flaw ‘‘ef” is vertical to the loading direction and thus there is no shear sliding system for this flaw. Therefore in this situation the secondary flaw has little influence on the fracture from the tip of the main flaw. The strength measured in the specimen with b = 45° is almost similar to that with a single flaw. From the Fig. 11d, it can be seen that the sliding system by the main flaw ‘‘a3b3” and that by the secondary flaw ‘‘gh” have opposite directions. The secondary flaw has no delaying effect on the fracture initiation from the main flaw. From Table 3 one can see that the specimens with b = 90° have higher |s(hr)max| of main flaw tips than those of the reinforced rock mass specimen with a single flaw under the same c. However after fracture initiation, the sliding from the fracture initiated from the tip of the secondary flaw increases the resistance of sliding of the fracture initiated from
Fig. 11. The failure modes schematic diagram of testing conditions c-5 to c-8. (a) testing condition c-5; (b) testing condition c-6; (c) testing condition c-7; (d) testing condition c-8.
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Fig. 12. The numerical computation models of testing conditions c-5 to c-8. (a) testing condition c-5; (b) testing condition c-6; (c) testing condition c-7; (d) testing condition c-8.
the tip of the main flaw, thus leading to a higher strength than that shown in Fig. 11a. From the Fig. 11d, one can see that the bolt is helpful to reduce the sliding/ sliding tendency of the main flaw ‘‘a3b3” and the secondary flaw ‘‘gh”. From the Fig. 11c, it can be seen that only the sliding/ sliding tendency of the main flaw ‘‘a2b2” can be reduced by the bolt. So the strength of specimen in Fig. 11d is higher than that in Fig. 11c.
5. Conclusions In this paper, the bolt reinforcement effect of rock mass with a single flaw and cross-flaws are studied with simulated rock mass and bolt bar. The reinforced rock mass with cross-flaws in this research exhibits higher uniaxial compressive strength than that of reinforced rock mass with a single flaw. This observation is interpreted using the interaction of the bolt bar and the factures initiated from the tips of the flaws. The reinforced rock mass with a single flaw fails due to a shear fracture. This mode of failure is highly brittle. Reinforced rock masses with cross-flaws on the other hand may fail by a tensile fracture or interaction between tensile fracture and shear fracture, thus leading to the higher uniaxial compressive strength. The failure modes of different b angles are explained using the interaction between the rock bar and the sliding systems associated with the flaws. Acknowledgements This paper is funded by National Natural Science Foundation of China (NO. 51379114, 51279095), Natural Science Foundation of Shandong Province, China (ZR2012EEQ007) and State Key Laboratory Open Fund of Geomechanics and Geotechnical Engineering (NO. Z013004). References Aksoy, C.O., Onargan, T., 2010. The role of umbrella arch and face bolt as deformation preventing support system in preventing building damages. Tunn. Undergr. Space Technol. 25 (5), 553–559. Aldorf, J., Exner, K., 1986. Mine Openings: Stability and Support. Elsevier, New York. Cai, Y., Esaki, T., Jiang, Y.J., 2004. A rock bolt and rock mass interaction model. Int. J. Rock Mech. Min. Sci. 41 (7), 1055–1067.
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