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2 International Journal of Mining Science and Technology 4 (14) Contents lists available at ScienceDirect International Journal of Mining Science and Technology journal homepage: Analysis profile of the fully grouted rock bolt in jointed rock using analytical and numerical methods Ghadimi Mostafa a,, Shahriar Kourosh b, Jalalifar Hossein c a Department of Mine, Science and Research Branch, Islamic Azad University, Tehran , Iran b Faculty of Mining, Metallurgy and Petroleum Engineering, Amir Kabir University of Technology, Tehran , Iran c Department of Petroleum and Mining Engineering, Environmental and Energy Research Center, Shahid Bahonar University of Kerman, , Iran article info abstract Article history: Received 1 December 13 Received in revised form 1 March 14 Accepted 5 April 14 Available online 18 August 14 Keywords: Fully grouted bolt Load transfer mechanism Jointed rocks Analytical and numerical methods The purpose of this study was to investigate the effect of bolt profile on load transfer mechanism of fully grouted bolts in jointed rocks using analytical and numerical methods. Based on the analytical method with development of methods, a new model is presented. To validate the analytical model, five different profiles modeled by ANSS software. The profile of rock bolts T 3 and T 4 with load transfer capacity, respectively 18 and 195 kn in the jointed rocks was selected as the optimum profiles. Finally, the selected profiles were examined in Tabas Coal Mine. FLAC analysis indicates that patterns 6+7 with NO flexi bolt 4 m better than other patterns within the faulted zone. Ó 14 Published by Elsevier B.V. on behalf of China University of Mining & Technology. 1. Introduction Steel bolts are an essential part of roadway support in coal mining roadways. The effectiveness of bolt reinforcement is a well known and well researched subject; however, little has been done in optimizing the bolt profile that directly contributes to the load transfer between the bolt and the surrounding grout. To improve bolt load transfer through the steel rebar design, it is essential to research the details of the bolt profile shape and configuration. Analytical studies, laboratory tests and numerical modeling provide the tools that enable a better understanding of the rebar profile role in increasing the shear resistance during the working life of bolts [1]. Investigations of load transfer between the bolt and grout indicate that the bolt profile shape and spacing play an important role in improving the shear strength between the bolt and the surrounding strata []. The short encapsulation pullout tests of rock bolt indicate significant variance of shear resistance for various bolt profile spacing, angle, shape and size [3,4]. Empirical studies can match the graphs of physical tests, however these methods cannot describe the exact reasoning why such behavior occurs [5]. Numerical modeling techniques are much better as they can mimic the physical tests in great detail, however, these methods depend on an accurate knowledge of the physical properties that must be incorporated or added into the model. The power of the Corresponding author. Tel.: address: m_yamchi@yahoo.com (M. Ghadimi). numerical model rests on its ability to compare several models and to establish the optimum solution to the problem. The laboratory testing has its challenges as fabrication of minute differences in bolt profile in the workshop is difficult. Nevertheless the laboratory tests are important to calibrate all the empirical work and the numerical models. At present mathematical description of the bolt profile and its behavior during the bolt pull out test is under development to provide better understanding of the physical process that influences the shear strength of the loaded bolt [6,7]. The in situ pullout tests are commonly used to examine the shear capacity of rock bolts. Only a few researchers have conducted laboratory tests to study various bolt profile parameters and their influence on the bolt anchorage [8 1]. A typical steel bolt profile configuration is shown in Fig. 1 [11]. This study develops a new analytical method to evaluate the effect of bolt profile on load transfer mechanism of fully grouted bolts in jointed rocks. The new analytical method validation was carried out by ANSS software and finally, the profiles of selected bolts from analytical and numerical methods were used for stability analysis in Tabas Coal Mine.. Load transfer capacity In a fully grouted rock bolt, the load transfer mechanism depends on the shear stress continued on the bolt to grout and grout to rock interfaces. Peak shear stress capability of the interfaces and the rate of shear stress generated determine the reaction /Ó 14 Published by Elsevier B.V. on behalf of China University of Mining & Technology.

3 61 M. Ghadimi et al. / International Journal of Mining Science and Technology 4 (14) Rib spacing a Rib width Rib height m Core diam Duter diam. Steel bolt Grout Rock c θ b p L Fig. 1. Steel bolt rib profile configuration [11]. F Weakness plane F Fig. 4. Single spacing between two bolt profiles showing geometry [7]. Rock It can be derived that: Load Grout r x þ r z ¼ a p p ð5þ Bolt r x r z ¼ sin a cosða þ dþ p p ð6þ of the bolt to the strata behavior. Load transfer is determined by measuring the peak shear stress capacity and system stiffness. Fig. shows the forces associated with load transfer [6,1]. 3. Stress distributions in infinite elastic media Derived mathematical equations enable the calculations of the stress tensor at any point within the grout encapsulating the loaded steel bolt. Such detail can make assessment of the bolt profile and its influence on the shear strength possible. Boussinesq derived the fundamental solutions for various loads on infinite or semi-infinite elastic media. While loading an infinite strip on the surface of a semi-infinite mass, the stress tensor anywhere within the media can be calculated as a function of the load, position and material properties (Fig. 3). For a uniform normal load as shown in Fig. 3, the stress tensor can be calculated using the Boussinesq equations while for the uniform shear load, the stress distribution can also be calculated via Cerutti s equations [13]. Applying the principle of superposition, the total stress r z at point A (X,Z) due to a strip load distributed over a width B =b may be written as: r z ¼ p½a þ sin a cosða þ dþš=p ð1þ Therefore r x, r y can be calculated. r x ¼ p½a sin a cosða þ dþš=p ðþ r y ¼ pma=p Fig.. Mechanism of load transfer [11]. where m is Poisson s ratio; and p the strip load per unit area. Shear stresses are as follows: s xz ¼ p½sin a sinða þ dþš=p ð4þ ð3þ 4. Normal and shear stress on a failure plane To draw a link between the load transfer system and the bolt profile configuration, a single spacing between two bolt ribs are examined (Fig. 4) [7]. In Fig. 4, F is the axial bolt pull out force, kn; c the rib spacing, mm; bsinh the rib height, mm; h the rib slope, ; a the profile width, mm; m the grout width, mm; and L the failure plane, mm. To investigate where the grout failure will occur, several potential planes of failure can be trailed. As an example a plane of failure that spans between the two rib tops is considered. The Mohr Coulomb criterion of failure was used to calculate the maximum pull out force needed for the assumed plane of failure. The equations to calculate the bolt pull out force are derived after linking the bolt geometry (Fig. 4), the sum of integrated normal and shear stresses along the failure plane. For static equilibrium, the sum of forces parallel to the bolt axis is zero: X Fy ¼! p ¼ F b sin h where P is the normal load on bolt boundary at the profile inclination b [7]. 5. Stress distributions in the grout To apply Bossiness s stress transformation equations in calculating the normal and shear stress along the studied plane of failure, the coordinate system must be rotated to match the geometry (Fig. 5). The distance PQ represents the failure plane and the angle h is the rib slope. Point A is any point on the plane of failure while variable h is the distance from Point P. Under normal conditions the grout elastic properties are similar to the ð7þ b p/unit area x z Q(Lcosθ, Lsinθ) Ah ( cos θ, m+ hsin θ) α δ h α δ z A (x, z) Fig. 3. Calculated stress tensor at any position given by x and z coordinates within the semi-infinite elastic medium loaded by a uniformly distributed load (p) [13]. θ B θ m b B p x x hcosθ b Fig. 5. Rotated axis of the loading diagram with the assumed plane of failure.

4 M. Ghadimi et al. / International Journal of Mining Science and Technology 4 (14) surrounding strata and the grout boundary can be extended to infinity [7]. The stress tensor transformation calculations using the Bossiness equations transform stress to shear and normal stress along the failure plane PQ (Fig. 5). To be able to calculate changes in normal and shear stress parallel to the failure plane when the bolt geometry changes, the bolt profile dimensions must be coupled with the stress within the equations. The angles a and d need to be substituted with bolt profile configuration parameters a, b, c and h (Fig. 5). To simplify derivation of the mathematical equations, this step is done after stress transformation. The normal and shear stress to the failure plane are determined after stress transformation, lengthy integrations, rearrangement and substitutions of each term [7]. r XX ¼ 1 ð r XX þ r Þþ 1 ð r XX r Þcos h s sin h ð8þ r zz ¼ 1 ð r XX þ r Þ 1 ð r XX r Þcos h þ s X sin h ð9þ s X ¼ 1 ð r XX r Þcos h þ s X sin h ð1þ Thus the normal and shear stress to the failure plane would be: r n ¼ 1 ð r X þ r Z Þþ 1 ð r z r x Þcos h s XZ sin h ð11þ s ¼ 1 ð r z r x Þsin h þ s XZ cos h ð1þ Calculations of R r n dh and R sdh caused by p on the supposed weakness plane: Z Z r n dh ¼ cos h s XZ sin h dh ð13þ r X þ r Z þ r Z r X Substituting the three expressions from Eqs. (4) (6) obtains: Z F hp r n dh ¼ pb sin h h ða þ b þ cþ ðaþbcos h þ cþ tan ða þ cþ cos h þ b cos h þðbcos h m sin hþ m þðaþcþsin h þ b sin h tan a þ b cos h þ c þ m sin h tan m sin h b cos h ð14þ And the sum of shear forces to the failure plane is: Z F sin h b þ m cot h F s ¼ sdh ¼ ð Þ pbðþ a þ b cos h þ c þ m sin h m sin h b cos h tan tan ð15þ In the following Eqs. (14) and (15) to calculate the rock bolt, grout and rock displacement will be used. 6. Analysis of fully grouted bolt A bolt installed in a deformable rock mass is subjected to an axial loading and it provides resistance to the movement of rock mass through shear stresses developed axially in the bolt grout interfaces. The bolt is represented by a one dimensional bar and hence the relationship between the shear force and the axial load can be established considering a small (differential) section of the bolt (Fig. 6). The force equilibrium in the axial direction leads to the following expression [14]. The new relationship to calculate the bolt, grout and jointed rocks displacement will be offered Rock mass displacement Displacement of the joint plane along rock bolts have been calculated by Deb and Das [14]. Therefore, in case of a circular tunnel with a joint plane as shown in Fig. 7, the distribution of rock displacement u r is represented by a continuous function that contains (i) elastic part of rock deformation, and (ii) displacement jump across the surface of the joint plane [14]. Thus U r ¼ U r e nx þ Xj i¼1 D i Hx L ji if ðx L j Þ!ðx L j Þ¼1 if ðx L j Þ!ðx L j Þ¼ U r ¼ ab f þ 1 r f þ1 e þðf 1Þ a ð16þ ð17þ ð18þ where H is the Heaviside function defined in Eq. (17); D the displacement of the joint plane (single); D i the displacement of the ith joint plane in case of multiple joint planes; n e (,1) the parameter controlling elastic part of rock deformation; a the tunnel radius; L j the length of the bolt up to at bolt intersect to the joint plane from the tunnel face; L ji the length of the bolt up to at bolt intersect to the ith joint plane; p the applied far field stress; v r the poison ration of the rock mass; E r the modulus of elasticity of the rock mass; and r e the elasto-plastic radius or radius of the boundary between the zone of plastic and elastic and expression of B. r re and f are defined in Eqs. (19) (1), respectively [14]. B ¼ 1 þ m r E r ðp r re Þ ð19þ r re ¼ ðð 1 þ h p þ bþ bþ ðþ tanð45 þ u=þ f ¼ tanð45 þ u= wþ ð1þ The parameters b and h can be found from the following expressions: b ¼ c tan u h ¼ tan 45 þ u ðþ ð3þ where c is the cohesion; and h the angle of internal friction [1]. Researchers calculate deformation elasto-plastic rock mass, during the bolt and joint; these studies are defined as Eq. (4). " U r ¼ L bb f þ 1 L # j þðf 1Þ ð4þ L b where L b is the rock bolt length. Displacement jump across the surface of the joint plane can be calculated through Eq. (5). D ¼ 1 E b Z x L J r n dx ¼ r n E b x L j ð5þ where r n is the normal stress in interface grout and rock; E b the modulus of elasticity of the bolt; and (x-l j ) the distance from the joint [15]. So rock displacement is

5 61 M. Ghadimi et al. / International Journal of Mining Science and Technology 4 (14) Joint plane Excavation face Lj Grout x ur+dur ur Rock bolt L Fs R dx σ n rb σ ub+dub xx σ xx + dx x ub Fig. 6. Proposed research model [14]. Rock displacement (ur) profile Table 1 Bolts characteristic [16]. a Initial tunnel face Deformed tunnel face Regular part Ur Jump part ( Δ) Joint plane Parameter T 1 T T 3 T 4 T 5 Bond length (mm) Rock bolt diameter (mm).... Grout diameter (mm) Rib height (mm) Rib spacing (mm) Profile top width (mm) Profile down width (mm) Max tensile load (MPa) Fig. 7. Distribution of rock displacement profile with a joint plane [14]. if L b L j! HLb L j ¼ 1! ur ¼ U r e nl J þ D B L b ¼ ðl b þ L j Þð1 þ f Þ þ r nðx L j Þ E b 6.. Rock bolt displacement L f þ1 j þðf 1Þ! L b ð6þ In the FLAC software, shear force developed along the interface bolt and rock is defined as Eq. (7). F s ¼ L K bond ðu b u r Þ ð7þ where F s is the shear force that develops in the grout, kn; K bond the grout shear stiffness, MPa; u b the axial displacement of the bolt, mm; u r the axial displacement of the medium soil or rock, mm; and L the contributing element length, mm [1]. Shear force developed along the interface bolt and jointed rock is defined by researcher as Eq. (8). Z F s ¼ sdh ¼ L K bond ðu b :8935u r Þ ð8þ By substituting Eqs. (15), (6) in (8), the rock bolt displacement based on profiles " as follows: BL b U b ¼ :9835 L f þ1 j þðf 1Þ! þ r # nðx L j Þ ðl b þ L j Þð1 þ f Þ L b E b " þ F sin hðb þ m cot hþ p LBK bond ðþ a þ b cos h þ c þ m sin h m sin h b cos h tan tan 6.3. Grout displacement ð9þ The elastic displacement of grout are obtained from division shear force on the shear stiffness system: Note: T 1, T, T 3, T 4 and T 5 are bolt types. " U g ¼ F sin hðb þ m cot hþ L:K bond pbðþ a þ b cos h þ c þ m sin h m sin h b cos h tan tan 7. Study of bolt profile by using analytical method ð3þ To select the optimum bolt profile and consider its effect on load transfer mechanism, it is necessary to examine the different profiles and check parameters, such as bolt, grout and jointed rocks displacement. The rock bolt characteristics and material properties are shown in respectively Tables 1 and. The results of the analytical method (tension 33 MPa) are shown in Table 3. According to Table 3, the following can be concluded: (1) rib height increase causes rock bolt, grout and rock displacement reduce; () rib spacing increase, causes bolt and grout displacement increase and rock displacement reduction; and (3) grout thickness increase causes rock bolt, grout and rock displacement reduce; rib widths increase causes rock bolt, grout and rock displacement reduce. 8. Numerical analysis A three dimensional finite element model of the reinforced structure subjected to the tension loading was used to examine the behavior of bolted jointed rocks and validate analytical results. Three governing materials (steel, grout, rock) with three interfaces (bolt grout, grout rock and joint joint) were considered for the 3D numerical simulation. A general purpose finite element program (ANSS, Version 1), specifically for advanced structural analysis, was used for 3D simulation of elasto-plastic materials and contact interfaces behavior. The model bolt core diameter D b of mm and the grouted cylinder D h of 7 mm had the same dimensions as those used in the laboratory test. Due to the symmetry of the problem, only one fourth of the system was considered here. Fig. 8 shows the three dimensional model.

6 M. Ghadimi et al. / International Journal of Mining Science and Technology 4 (14) Table Material properties [1]. Material Concrete ( MPa) Grout Steel E (GPa). 1.. Poisson s ratio.5..3 Table 3 Results of the analytical method (tension 33 MPa). Displacement T 1 T T 3 T 4 T 5 Bolt displacement (mm) Grout displacement (mm) Jointed rocks displacement (mm) File: bolt T Joined rock Bolt Grout Fig. 8. There dimensional image numerical model. The interface behavior of grout-concreted as a perfect contact was determined from the test results. However, the low value of cohesion (15 kpa) was adopted for grout steel contact. 3D solid elements (solid 65 and solid 95) that have 8 nodes nodes were used for concrete, grout and steel, respectively, with each node having there translation degrees of freedom. That tolerates shapes without significant loss in accuracy. 3D surface to surface contact elements (contact 174) were used to represent the contact between 3D target surface (steel grout and rock grout). This element is applicable to 3D structural contact analysis and is located on the surface of 3D solid elements with midsize nodes. The numerical modeling was carried out at several sub steps and the middle block of the model was gradually loaded in the direction of shear [17]. 9. Validation by using 3D numerical analysis In this section, the analytical method presented is verified by ANSS software. Bolt profile configuration is an important parameter in load transfer capacity of bolt. Maximum tensile stress in the bolt as load capacity is considered. So that load capacity bolts T 1 to T 5, respectively 16, 17, 18, 195 and 15 kn. The maximum tensile stress along the bolt is 33 MPa. This valve is in order of one half of the elastic yield point strength of 6 MPa. This means the bolt behaves elastically and is unlikely to reach the yield and situation. So the only bolt T 3 and T 4 that are the highest load capacity in this study is presented. Figs. 9-1 are shown in the displacement contours and change along bolt, grout and jointed rocks under tensile stress 33 MPa. The results of the tensile bolts under 33 MPa are shown in Table 4. From Table 4, it can be concluded that: rib height increase causes the load transfer capacity of the bolt increase; rib spacing increase causes load transfer capacity of the bolt increase; grout thickness increase causes load transfer capacity of the bolt increase; rib width reduction reduces load transfer capacity of the bolt; rib height increase causes rock bolt, grout and rock displacement reduce; rib spacing increase causes bolt and grout displacement and rock displacement increase; grout thickness increase causes rock bolt, grout and rock displacement reduce; Movement direction Movement direction X Z 33 MPa X X (a) Bolt (b) Grout (c) Jointed rocks Fig. 9. the bolt, grout and jointed rocks (mm) the bolt (mm) the grout (mm) the rock (mm) Joint Distance from end to top bolt (mm) Distance from end to top grout (mm) Distance from end to top rock (mm) (a) Bolt (b) Grout (c) Jointed rocks Fig. 1. the bolt, grout and jointed rocks and distance from end to top bolt, grout and jointed rocks.

7 614 M. Ghadimi et al. / International Journal of Mining Science and Technology 4 (14) Movement direction Movement direction 33 MPa Z X X (a) Bolt (b) Grout (c) Jointed rocks Fig. 11. the bolt, grout and jointed rocks (mm) the bolt (mm) the grout (mm) the rock (mm) Joint Distance from end to top bolt (mm) Distance from end to top grout (mm) Distance from end to top rock (mm) (a) Bolt (b) Grout (c) Jointed rocks Fig. 1. the bolt, grout and jointed rocks and distance from end to top bolt, grout and jointed rocks. Table 4 Results of the tensile bolts under 33 MPa by using numerical method. Displacement (mm) T 1 T T 3 T 4 T 5 Siltstone Fault Rock bolt Grout Jointed rock Load capacity (kn) Coal Sandstone rib widths increase causes rock bolt, grout and rock displacement reduce; the main utility of the grout is to supply a mechanism for the load transfer between the rock and the reinforcing element, rib spacing increase, and the shear stress increases in the grout and by increasing the grout thickness, the shear stress decreases; and models show that profile rock bolt T 3 and T 4 with load capacity 18 and 195 kn in the jointed rocks, are the optimum profiles. 1. A case study: Tabas Coal Mine Tabas underground coal mine is located some 85 km south of Tabas town, Birjand province, Iran. The E long wall panel had a face width of 18 m and panel length of 1 m [18]. The geometry of the area modeled was 4 m by 4 m with a roadway width of 4.5 m and height of 3.5 m. The coal seam was modeled as m thick Siltstone Fig. 13. Model roadway profile, layers and rock bolt pattern numerical modeling. and dipping at. The East tail gate immediate roof stratification sequence consisted of siltstone and sandstone above the roof. The vertical stress of 4 MPa and the ratio of horizontal to vertical stress k =.4 were determined for the site, according to the tectonic history of the region. The model roadway profile, layers and rock bolt pattern numerical modeling is shown in Fig. 13 [19]. Results of vertical and horizontal displacements around E TG are summarized in Table 5. Table 5 Horizontal and vertical displacements of around Eeast Tail Gate. Bolt type Load capacity (kn) Pattern Floor (mm) Roof (cm) Right hand rib (cm) Left hand rib (cm) T 18 9 bolt.4 m + flexi bolt 4 m. / bolt.4 m + flexi bolt 4 m.1 / T bolt.4 m + flexi bolt 4 m.8 / bolt.4 m + flexi bolt 4 m.7 / Critical displacement (cm)

8 M. Ghadimi et al. / International Journal of Mining Science and Technology 4 (14) To find the optimum rock bolts, four patterns have been proposed to model FLAC software. First and second patterns related rock bolt T 3 of load capacity 18 kn. Based on the results of Table 5, the first pattern (9 bolt.4 m + flexi bolt 4 m) to the second pattern (13 bolt.4 m + flexi bolt 4 m), less the wall displacement. The third and fourth patterns related rock bolt T 4 of load capacity 195 kn. Comparing the third pattern (9 bolt.4 m + flexi bolt 4 m) and fourth pattern (13 bolt.4 m + flexi bolt 4 m) is illustrated by the floor, walls and roof displacement of the third pattern, the pattern is less fourth. The results of analysis was determined that patterns 7+6 and NO flexi bolt 4 m are better than other patterns in the faulted zone. 11. Conclusions The important outcome of this study is to show that there is another way to examine grout failure around the bolt for different profile configurations that can be compared with numerical modeling. This method can provide better understanding of the bolt grout interaction with rock reinforcement. (1) Displacement caused by the bolt tension elements using analytical and numerical methods as follow: rib height increase causes rock bolt, grout and rock displacement reduce; rib spacing increase causes bolt and grout displacement increase and rock displacement reduce; grout thickness increase causes rock bolt, grout and rock displacement reduce; and rib widths increase causes rock bolt, grout and rock displacement reduce. () The effect of the rock bolt profiles on load transfer capacity as follow: rib height increase causes the load transfer capacity of the bolt increase; rib spacing increase causes load transfer capacity of the bolt increase; grout thickness increase causes load transfer capacity of the bolt increase; and rib width reduction reduces load transfer capacity of the bolt. (3) Profile bolt configuration is an important parameter in load transfer capacity of bolt. So that, load capacity of bolts T 1 to T 5 are 16, 17, 18, 195 and 15 kn, respectively. (4) According to this study, profile rock bolt T 3 and T 4 with load transfer capacity 18 and 195 kn in jointed rocks are the optimum profiles. (5) FLAC analysis indicates that patterns 6+7 with NO flexi bolt 4 m better than other patterns within the faulted zone. Acknowledgments The authors gratefully acknowledge Mr. Chen Cao of University of Wollongong. References [1] Jalalifar H, Aziz N, Hadi M. Modelling of sheared behaviour bolts across joints. In: Proceedings of the 5th underground coal operators conference, University of Wollongong & the Australasian Institute of Mining and Metallurgy, Wollongong; 4. p [] Aziz N, Webb B. Study of load transfer capacity of bolts using short encapsulation push test. In: Proceedings of 4th underground coal operators conference, University of Wollongong & the Australasian Institute of Mining and Metallurgy, Wollongong; 3. p [3] Martín LB. A new experimental and analytical study of fully grouted rock bolts subjected to pull-out tests. Constr Build Mater 11. [4] Li B, Qi T, Wang ZZ, ang LW. Back analysis of grouted rock bolt pullout strength parameters from field tests. Tunn Undergr Space Technol 1;8: [5] Aziz N, Jalalifar H, Concalves J. Bolt surface configurations and load transfer mechanism. In: Proceedings of the 7th underground coal operators conference, University of Wollongong & the Australasian Institute of Mining and Metallurgy, Wollongong; 6. p [6] Cao C, Nemcik JA, Aziz N. Advanced numerical modeling methods of rock bolt performance in underground mines. In: Proceedings of the 1th underground coal operators conference, University of Wollongong & the Australasian Institute of Mining and Metallurgy, Wollongong; 1. p [7] Cao C, Nemcik JA, Aziz N. Improvement of rock bolt profiles using analytical and numerical methods. In: Proceedings of the 11th underground coal operators conference, University of Wollongong & the Australasian Institute of Mining and Metallurgy, Wollongong; 11. p [8] Aziz N, Jalalifar H. Optimisation of the bolt profile configuration for load transfer enhancement. In: Proceedings of the 8th underground coal operators conference, University of Wollongong & the Australasian Institute of Mining and Metallurgy, Wollongong; 8. p [9] Blumel M, Schweger HF, Golser H. Effect of rib geometry on the mechanical behavior of grouted rock bolts. In: Proceedings of world tunneling congress 3rd general assembly of the international tunneling ass, Wien; p. 6. [1] Martín LB, Hadj-Hassen F, Tijani M. A new analytical solution to the mechanical behavior of fully grouted rock bolts subjected to pull-out tests. In: Proceedings of the 45th US rock mechanics/geomechanics symposium, San Francisco; 11. [11] Jalalifar H. A new approach determining the load transfer mechanism in fully grouted bolts. University of Wollongong; 6. [1] Jalalifar H. An analytical solution to predict axial load along fully grouted bolts in an elasto-plastic rock mass. J South Afr Inst of Min Metal 11;111: [13] Poulos H, Davis E. Elastic solutions for rock mechanics. New ork: Textbook by John Willey and Sons; TA71.P67, , [14] Das KC, Deb. Analytical model for fully grouted rock bolts considering movements of rock joints. In: Proceedings of the third indian rock conference by ISRMTT, Roorkee; 11. p [15] Cao C, Nemcik JA, Aziz N, Ren T. Failure modes of rock bolting. In: Proceedings of the 1th underground coal operators conference, University of Wollongong & the Australasian Institute of Mining and Metallurgy, Wollongong; 1. p [16] Aziz N, Jalalifar H. The role of profile configuration on load transfer mechanism of bolt for effective support. J Mines Metals Fuels 7: [17] Aminaipour F. The effect load transfer mechanism of fully grouted bolts. Bafgh: Department of mine, Islamic Azad University; 1. [18] Sahebi A, Jalalifar H, Ebrahimi M, Abdolrezaee. Stability analysis of Tabas coal mine roadway using empirical and numerical methods. In: Proceedings of the 1th underground coal operators conference, University of Wollongong & the Australasian Institute of Mining and Metallurgy, Wollongong; 1. p [19] Sahebi A, Jalalifar H, Ebrahimi M, Abdolrezaee. Stability analysis and optimum support design of a roadway in a faulted zone during long wall face retreatcase study: Tabas coal mine. In: Proceedings of 1th underground coal operators conference, University of Wollongong & the Australasian Institute of Mining and Metallurgy, Wollongong; 1. p