MINE ROOF SUPPORT DESIGN AND ANALYSIS Document no : 1806-2697-23 Revision no : 1.0
DOCUMENT TITLE : MINE ROOF SUPPORT DESIGN AND ANALYSIS DOCUMENT NUMBER : 1806-2697-23 ISSUE : Issue 1.0 DATE : 7 October 2003 ELECTRONIC MEDIA REF. : V2697.doc CLASSIFICATION : None PREPARED BY : MMS Technology CC 1017 Kruger Avenue Lyttelton Manor Centurion South Africa Tel. +27 12-6645696 Fax +27 12 664 2682 E-mail: mms@mmstechno.co.za POSTAL ADDRESS : P. O. Box 14057 Lyttelton 0140 South Africa PROPRIETARY NOTICE The information contained in this document is the property of MMS Technology CC and may not be distributed to any third party without the express written permission of MMS Technology CC. COPYRIGHT The copyright, manufacturing and patent rights stemming from this document in any form are vested in MMS Technolgy CC. 1806-2697-23 Issue 1 23/06/2005 Page 2 of 25
DISTRIBUTION : Copy number Designation Recipient 1 Master MMS Registry 2 MMS Mr. H. Bauermeister 3 MMS Mr. A. Newington 4 Research Enterprises Mr. D. Burger 5 6 APPROVAL : Signature Date Name Organisation Compiler Mr. H. Bauermeister MMS Technology Approved by Mr. L. D. More MMS Technology Approved by Approved by 1806-2697-23 Issue 1 23/06/2005 Page 3 of 25
CONTENTS. 1. INTRODUCTION... 5 2. GEOMETRIC DEFINITION... 6 3. FINITE ELEMENT MODELS.... 8 3.1 DYNAMIC ANALYSIS MODEL... 8 3.2 THREE DIMENSIONAL MODEL.... 9 4. MATERIAL PROPERTIES... 11 4.1 STEEL... 11 4.2 E-GLASS/VINYL-ESTER LAMINATE... 11 5. APPLIED LOADS... 12 5.1 DYNAMIC ANALYSIS... 12 5.2 STATIC ANALYSIS... 12 6. FINITE ELEMENT RESULTS.... 13 6.1 DYNAMIC ANALYSIS RESULTS.... 13 6.2 STATIC ANALYSIS RESULTS.... 18 7. CONCLUSIONS AND RECOMMENDATIONS.... 22 APPENDICES. Appendix A : Specification for mine roof support system. 1806-2697-23 Issue 1 23/06/2005 Page 4 of 25
1. Introduction. After failures experienced on the second generation of prototypes, it was decided to redesign the mine roof support system, taking the geometric, mass, stiffness, manufacturing constraints and cost into consideration. The following figure shows the geometric layout of the second generation mine roof support prototypes. Figure 1. Second generation mine roof support prototype geometry. Several reasons exist for this geometric layout, amongst others, the stope height, the hydraulic cylinder geometry and the maximum expected roof deflection during a seismic activity play a role in the determination of this geometry. As the hydraulic cylinder already existed, it was decided to maintain the interfaces as is. From an operational point of view the mass should be kept as low as possible. A target mass per leg of ±32kg was aimed for, as this was the approximate mass for each leg of the second generation of prototypes. Of all the specifications, stiffness of the mine roof support is the most important. During seismic activity, the displacement of the hanging wall occurs so fast that the valves in the hydraulic cylinder can not react quickly enough. This means the cylinder is equivalent to a solid beam between the two legs. To accommodate the hanging wall displacement, the beams then have to deflect to prevent the system from structurally failing. Perhaps one of the most widely discussed debates in the field of rock mechanics is what this actual displacement of the hanging wall is during a seismic activity. Some specialists claim 50mm, whilst others claim as 1806-2697-23 Issue 1 23/06/2005 Page 5 of 25
much as 150mm. From a structural point of view this makes the design of such a structure extremely difficult, as strength and stiffness start opposing each other in the design. If the structure is flexible enough, it is not strong enough. If the structure is strong enough, it is too stiff. Iteratively a point is reached where these two criteria are at their best values. During this design the aim was to maximise the maximum deflection of the structure to satisfy the conservative range of rock mechanic specialists. In order to achieve the best mechanical properties from a laminate, the manufacturing process plays a very important role. Achieving high fibre content is important to maximise the tensile, compressive and shear strength properties of the laminate. For this reason the vacuum infusion process was chosen. However, this process was also used for the first and second generation of mine roof support prototypes. The major difficulty with these prototypes was the packing of the fibres in the moulds, which was quite a laborious and difficult process. In mass production, this would have probably given problems with quality and cost. Optimal performance of laminates is normally obtained in the form of flat sheets. It was therefore decided to base the design of the third generation of mine roof support on a flat plate concept. Experience on other projects has also shown that water jet cutting of flat panels is a well established method of cutting these panels. Lastly cost is a very important factor. Here again the manufacturing process play a role, but also such factors as wastage of materials can become critical. In order to analyse the structure it was first decided to perform a dynamic analysis on a simplified beam model of the structure. This analysis was then followed up by a detailed solid model analysis of the mine roof support structure. This report summarises the results obtained from these analyses. A specification is included in appendix A. Note that this specification is for a roof support system consisting of two pairs of legs. 2. Geometric definition. After several iterations the following geometry for the third generation of mine roof support was designed. The gap dimensions at the hydraulic cylinder interfaces as well as the foot and headboard interfaces were kept similar to the second generation mine roof support. However, the problematic interface between the two legs were replaced by a link plate connecting the two beams, which alleviated the bearing and shear stress problem at this interface to a large extent. 1806-2697-23 Issue 1 23/06/2005 Page 6 of 25
Figure 2. Third generation mine roof support geometry. The following figure shows one of the concepts that were considered at this interface between the two beams. This interface however has the classic problem of shear capability discontinuity, which results in an un-optimised design. Several other concepts and geometric shapes were also considered. Figure 3. One discarded concept. 1806-2697-23 Issue 1 23/06/2005 Page 7 of 25
3. Finite element models. 3.1 Dynamic analysis model. At first dynamic analyses were performed on the mine roof support structure. For this a simple beam element, mass element and contact element model was generated. The following figure shows the model. Figure 4. Finite element model for dynamic analyses. This analysis was specifically tailored to simulate the Savuka test. In this test two mine roof supports are used. A 7 ton preload is placed on the two mine roof supports. In the finite element model only one structure is analysed, therefore 3.5ton is placed on the structure over a time period of 5 seconds and left to stabilise. Then a mass is dropped on the two mine roof support structures, with an impact energy value of approximately 40kJ. This is done by dropping a 10ton mass from a height of 400mm. E = mgh = 10000*9.81*0.4 = 39249 J Again, as we are only analysing one structure, only a 5ton mass is dropped by this height. The structure is then left to stabilise after impact and the peak displacement, reaction force and 1806-2697-23 Issue 1 23/06/2005 Page 8 of 25
stresses are extracted. Since it is easy to change the beam cross sectional properties, this model was used to do the initial sizing of the beams to comply with the stiffness and strength criteria. 3.2 Three dimensional model. After the initial sizing was performed with the dynamic analysis model, and the peak reaction forces extracted, a full three dimensional finite element model was generated to analyse the mine roof support structure in detail. The beams were modelled with 3D solid elements, making use of orthotropic material properties, with the element axes aligned with the lay-up angles of the laminates to account for the actual material characteristics in terms of stiffness and strength. Figure 5. Three dimensional finite element model of mine roof support structure. As shown in the following figure the hydraulic cylinder was modelled with beam elements. The interface to the beam was however modelled with links. Several analyses were performed on the structure, and after each analysis the links with tensile loading were unselected. This then resulted in a realistic application of the load to the beam. As shown in the next figure the link between the two beams was also modelled in detail. Again links were used to model the pin interfaces, with links experiencing tensile loads being unsellected. 1806-2697-23 Issue 1 23/06/2005 Page 9 of 25
Figure 6. Hydraulic cylinder interface to beam. Figure 7. Connection between two beams with link plates. 1806-2697-23 Issue 1 23/06/2005 Page 10 of 25
This procedure of unselecting links experiencing tensile loading is nothing other than another method of performing a nonlinear analysis. ANSYS has a nonlinear compression only link which does the same job, but takes slightly longer to converge. Hence the manual process was followed. 4. Material properties. In the analyses the following material properties were used. 4.1 Steel E = 207 GPa [Young s modulus] ν = 0.3 [Poisson s ratio] ρ = 7850 kg/m³ [Density] 4.2 E-glass/Vinyl-ester laminate Fibre : E-glass woven roving, 600g/m². Matrix : Derakane vinyl-ester, 411-350. Fibre content : ±70% by mass. Lay-up angle : (0º/90º) E x = 18.7 GPa [In plane longitudinal Young s modulus] E y = 18.7 GPa [In plane transverse Young s modulus] E z = 10.0 GPa [Transverse Young s modulus] G xy = 6.42 GPa [In plane shear modulus] G yz = 1.5 GPa [Transverse shear modulus] G zx = 1.5 GPa [Transverse shear modulus] ν xy = 0.18 [In plane Poisson s ratio] ν yz = 0.10 [Transverse Poisson s ratio] ν zx = 0.10 [Transverse Poisson s ratio] ρ = 1762.0 kg/m 3 [Density] σ xt 283 MPa [Longitudinal tensile strength] σ xc 352 MPa [Longitudinal compressive strength] σ yt 283 MPa [Transverse tensile strength] σ yc 352 MPa [Transverse compressive strength] τ xy 60 MPa [In plane shear strength] τ xz 24.5 MPa [Interlaminar shear strength] τ yz 147 MPa [Crosslaminar shear strength] Source : Dow Chemicals 1806-2697-23 Issue 1 23/06/2005 Page 11 of 25
5. Applied loads. As described earlier two types of analyses were performed. Firstly the dynamic analysis, and then a static analysis. 5.1 Dynamic analysis. In the dynamic analysis the following loads were applied to the finite element model. Load step Load Drop height Purpose 1 3500kg 0 To simulate the 3.5ton (7ton) preload at Savuka test. 2 5000kg 400mm To simulate 20 kj (40kJ) impact load at Savuka test. Table 1. Dynamic analysis loads. 5.2 Static analysis. In the static analysis a 27ton load was put on the structure. Figure 8. Loading and constraints on mine roof support structure. 1806-2697-23 Issue 1 23/06/2005 Page 12 of 25
6. Finite element results. 6.1 Dynamic analysis results. The following figures show the results from the dynamic analyses. This model was used to tailor the beam properties until a suitable design was achieved. Considering the following figure it can be seen that by placing the 3.5ton preload on the structure, a deflection in the order of 22mm is experienced. The structure then stabilises. At roughly 5s the falling 5ton mass makes contact with the beam. The maximum deflection of 167.7mm then occurs at a time of 5.371s. Figure 9. Displacement of headboard interface. Considering the next figure, which shows the reaction force at the bottom, the preload of 3.5ton can clearly be seen to be applied. Then on impact of the falling mass, the reaction force peaks to a value of 256200N, which equal 26tons, at a time of 5.357s. Interesting also is to note the peak axial force in the hydraulic cylinder, which reaches a value of roughly 480 000N, or 49ton, as shown in the next figure. The following figure also shows the axial force in the link between the two beams, which reaches a value of 280 000N, or 28.5ton, which should equal just over 14ton per side. 1806-2697-23 Issue 1 23/06/2005 Page 13 of 25
Figure 10. Reaction force at bottom. Figure 11. Axial force in hydraulic cylinder. 1806-2697-23 Issue 1 23/06/2005 Page 14 of 25
Figure 12. Axial force in link. At the time of maximum reaction the following forces, moments and stresses are experienced by the beams. Figure 13. Beam axial forces at time of maximum structure reaction. 1806-2697-23 Issue 1 23/06/2005 Page 15 of 25
Figure 14. Beam shear forces at time of maximum structure reaction. Figure 15. Beam bending moments at time of maximum structure reaction. 1806-2697-23 Issue 1 23/06/2005 Page 16 of 25
Figure 16. Axial stress in beams at time of maximum structure reaction. Figure 17. Bending stress at beam top at time of maximum structure reaction. 1806-2697-23 Issue 1 23/06/2005 Page 17 of 25
Figure 18. Maximum stress at time of maximum structure reaction. 6.2 Static analysis results. The following figures show the results obtained from the static analysis on the three dimensional finite element model. From the fist figure it can be seen that the vertical displacement of the structure due to a 27ton load is predicted to be 163mm. The next figure depicts the longitudinal stress in the beams. From this figure it is clear that the maximum longitudinal tensile stress at the top edge of the beam is in the order of 273 MPa. Maximum longitudinal compressive stress is in the order of 290 MPa, except for the region where the hydraulic cylinder interfaces with the beams. In this area the stress pattern is somewhat complex and difficult to predict due to very high contact stresses also being present in this area. The following figures depict the in-plane shear stress in the beams, showing a maximum value of 59 MPa on the top edge of the beams. Again in the region of hydraulic cylinder to beam interface the stress pattern is complex and difficult to predict due to the very high contact stresses also being present in this area. 1806-2697-23 Issue 1 23/06/2005 Page 18 of 25
Figure 19. Vertical displacement of mine roof support structure under 27 ton load. Figure 20. Longitudinal stress in beams. 1806-2697-23 Issue 1 23/06/2005 Page 19 of 25
Figure 21. Transverse stress in beams Figure 22. In-plane shear stress in beams. 1806-2697-23 Issue 1 23/06/2005 Page 20 of 25
Figure 23. In-plane shear stress in beams in link area. 1806-2697-23 Issue 1 23/06/2005 Page 21 of 25
7. Conclusions and recommendations. From the results of the analyses the following conclusions can be drawn: Dynamic analysis results: If the loading as used in this analysis represents the actual Savuka test loading: 1. The maximum deflection of the mine roof support system would be 167.7mm 2. The maximum reaction force due to this impact would be 26 tons. 3. The maximum axial compressive force in the hydraulic cylinder due to this impact would be 49 tons. 4. The maximum axial tensile force in the links would be 14 tons per link due to the impact. 5. The maximum shear force is 232 778 N and the maximum bending moment is 144 738 Nm in the beam due to this impact. 6. The maximum tensile bending stress in the beam is 281 MPa due to this impact. Static analysis results. The following table depicts the results obtained by the analysis. Stress type Location Stress value [MPa] Maximum allowable Stress [MPa] Reserve factor Tensile Top of beam 273 283 1.03 Compressive Bottom of beam 290 352 1.21 In-plane shear Top of beam 59 60 1.01 Table 2. Stresses and reserve factors in beams due to 27 ton load on mine roof support structure. 1. The stresses in the beams are within the material capabilities under a load of 27 tons, although the reserve factors are nearly equal to 1. 2. It is difficult to predict the stresses in the areas where the hydraulic cylinder interfaces with the beams, as the stress pattern is complex due to the very high contact stresses also being present in this area. From the above analysis results it is clear that the ultimate load capability of the beams are in the order of 27 tons. The predicted maximum load on the structure during a 40kJ impact load is 26 tons. This provides some margin of reserve, although not much. From the results of the analyses it is also clear that by increasing the reserve factor, two things are going to happen; the mass of the beams will increase unnecessarily, and the stiffness of the beams will increase. This again will cause the beams to be stiffer, with the resulting decrease in deflection which is undesirable. 1806-2697-23 Issue 1 23/06/2005 Page 22 of 25
From a testing point of view it is proposed to test the beams to a load where the total displacement does not exceed 140 mm. This is the maximum that is expected in the Savuka test, which in itself is a very conservative test. The following figure shows the prototype mine roof support. Figure 24. Prototype mine roof support. Figure 25. Mine roof support tests at Savuka. 1806-2697-23 Issue 1 23/06/2005 Page 23 of 25
Appendix A 1806-2697-23 Issue 1 23/06/2005 Page 24 of 25
1806-2697-23 Issue 1 23/06/2005 Page 25 of 25