1 INTRODUCTION

Wire mesh has been used as ground support in mining since the 1950s. The mesh may comprise welded wire, expanded metal or woven (chain link). The wire used in manufacturing the mesh may vary widely in its physical and mechanical properties. Experimental studies have been, and continue to be, conducted throughout the world, for example, South Africa (Ortlepp, 1983), Canada (Pakalnis and Ames, 1983, and Tannant et al, 1997), Australia (Thompson et al., 1999, Villaescusa, 1999, and Roth et al., 2004), Chile (Van Sint Jan and Cavieres, 2004) and USA (Dolinar, 2006). Each research group has applied different methods of testing and used different techniques to analyse and characterise the data. In practice, laboratory testing can only hope to investigate a limited range of configurations. Thompson (2001) demonstrated that more sophisticated analysis techniques that directly model the behaviour of the mesh and restraints have the potential to be used to simulate a wide range of loading configurations and boundary conditions.

A recent testing program has been undertaken at the new WASM static test facility. Two different modelling techniques have been used to attempt to simulate the force displacement characteristics of both welded wire and woven mesh using three dimensional deformations.

2 TEST FACILITY

2.1 Description In 2005, the Western Australian School of Mines designed and built a large scale static testing facility (Figure 1) to complement its existing dynamic test facility (Player et al., 2004). This new facility comprises a reaction beam and a frame to support the mesh sample. The mesh sample is assembled within a stiff frame that rests on the support frame. A screw feed jack is mounted on the reaction frame. The screw feed jack can be driven at a constant speed (4mm per minute) and allows large displacements to be imposed

on the mesh. Load is applied to the mesh through a spherical seat to a 300mm square hardened steel plate. The sample size is 1300mm x 1300mm and may be fully constrained on all sides or restrained at discrete locations.

2.2 Boundary Conditions The boundary restraint applied to the mesh sample is the most critical element in testing. Two different restraining systems have been used. The first system involved lacing 6mm wire rope through the sample and around a frame as shown in Figure 2. The rope was tensioned and then clamped using wire rope grips on each end of each side. This method provided reliable force-displacement response curves with consistent failure mechanisms. However the initial tensions applied to the mesh were not consistent and influenced the amount of displacement that occurred prior to the mesh responding and taking load.

Figure 1. WASM Static Test facility.

Testing and analysis of steel wire mesh for mining applications of rock surface support

E.C. Morton, A.G. Thompson & E. Villaescusa CRCMining / WA School of Mines, Kalgoorlie, Western Australia

A. Roth FATZER AG, Geobrugg Protection Systems, Romanshorn Switzerland

ABSTRACT: Steel wire mesh is widely used for rock surface support in mines. Experimental studies on mesh continue to be conducted throughout the world using different testing configurations and simple analysis techniques to characterise its performance. In practice, laboratory testing can only hope to investigate a limited range of configurations. The response of the mesh depends on the overall sample size, the restraints and the loading. A testing program using two different types of mesh has recently been completed at the WA School of Mines. The results of this testing are presented and the force-displacement responses highlight the deficiencies in previous analysis methods. More sophisticated analysis techniques incorporated into computer software are used to demonstrate the potential to predict the force-displacement response for any defined set of constraints and loading conditions.

Figure 2. Laced restraint system used as the first test arrangement.

Figure 3. Fixed restraint system used as final test arrangement.

In order to remove some of the inconsistencies of the lacing method, a new sample frame was designed to provide a fully fixed restraint system for the mesh. A system using high tensile bar, eye nuts and D shackles passing through the beam at regular positions (Figure 3) was selected as the most appropriate boundary system.

2.3 Mesh Types Testing has been undertaken on two different mesh types. The standard welded wire mesh (Mesh Type 1) used in Western Australian mines is 100mm x 100mm x 5.6mm galvanised weld mesh. The samples were donated by a local mine site. The second type of mesh (Mesh Type 2) was 4mm high tensile wire chain link mesh provided by sponsors Geobrugg.

3 MESH TESTING RESULTS AND ANALYSIS

Ten tests were conducted using the lacing boundary constraints. Eight of these tests were conducted on welded wire mesh (Type 1). Two tests were conducted on chain link mesh (Type 2). A summary of results is provided in Table 1.

A further 13 tests were conducted using the fixed boundary condition. Ten tests were conducted on weld mesh with the remaining 3 tests conducted on chain link mesh. The results from these tests are shown in Table 2.

There are significant differences between the two mesh types. The chain link mesh is less stiff and has been manufactured using high tensile wires to enable capacities over three times greater than that of standard welded wire mesh.

With few exceptions all the welded wire mesh samples first ruptured either through the weld or in the heat affected zone, on the boundary, where the wire was under direct loading. Failure then progressed along the boundary, alternating between two sides beginning with the directly loaded wires.

The chain link mesh failed on the edge of the plate either as a result of the plate cutting through the wires or as a result of the wires cutting each other. Generally only one or two strands broke. After the first rupture the load dropped completely as a result of plate movement and the test was stopped.

Figure 4 shows the difference in responses for the two mesh types and the differences between the different boundary conditions used. The lacing boundary condition was less stiff and thus more displacement occurred prior to the mesh taking load. The fixed boundary condition resulted in the mesh reacting immediately to the applied displacement.

The force-displacement responses of both mesh types showed significant displacements at low loads. Attempts to characterise the response for design purposes (as attempted previously and reported by Tannant et al., 1997 and Dolinar, 2006) have been largely unsuccessful as the maximum force or maximum displacement for a specific test configuration needs to be known. These analysis methods also cannot be applied to other restraint conditions.

Regression analyses of the force-displacement curves showed that the curves were nonlinear in nature and could be best represented by a cubic equation. Observations during the testing program suggest that the nonlinearities are associated with geometric distortion of the mesh and the mechanical properties of the wire; and the welds for Mesh Type 1.

Table 1. Summary of results from tests using the lacing boundary condition.

Test No

Mesh Type

Rupture Load (kN)

Displacement. at Rupture (mm)

Peak Load (kN)

Displacement at Peak (mm)

004 2 137.1 343 137.1 343 005 1 46.2 242 46.2 242 007 1 46.7 249 46.7 249 008 1 35.9 222 38.9 241 009 1 34.1 209 38.4 253 010 1 28.1 216 41.4 236 011 1 44.0 228 44.0 228 012 2 120.8 311 120.8 311 013 1 45.4 239 45.4 239 014 1 33.4 222 35.4 249 Mesh Type 1 Welded wire mesh Mesh Type 2 High tensile wire chain link mesh

Table 2. Summary of results from tests using the fixed boundary condition.

Test No

Mesh Type

Rupture Load (kN)

Displacement. at Rupture (mm)

Peak Load (kN)

Displacement at Peak (mm)

017 1 45.0 173 45.0 173 018 2 145.6 310 145.6 310 019 2 155.0 285 155.0 285 020 1 44.1 192 44.1 192 021 1 37.9 151 37.9 151 022 1 40.9 182 43.4 195 023 2 147.2 292 147.2 292.3 024 1 38.5 150 38.5 150 025 1 46.4 181 46.4 181 026 1 44.9 188 44.9 188 027 1 40.7 195 40.7 195 028 1 29.7 209 29.7 209 029 1 41.3 181 41.3 181 Mesh Type 1 Welded wire mesh Mesh Type 2 High tensile wire chain link mesh

020

40

60

80

100

120

140

160

0 50 100 150 200 250 300 350Displacement at Loading Point (mm)

Forc

e (k

N)

Fixed Weld Mesh Fixed Chain LinkLaced Chain Link Laced Weld Mesh

Figure 4. Force displacement responses for welded wire mesh and chain link mesh with fixed and laced boundary conditions.

4 MODELLING

Previous modelling attempts have simulated two-dimensional deformations. Based on the WASM test results the latest models have been modified to allow for three dimensional non linear modelling. The requirements for mesh analysis, based on testing program results and other considerations, are: Different mesh types. Variable wire diameters. Variable wire spacings. Non-linear stress-strain properties for the wire. Able to account for weld strength. Allow for slip of the mesh at the restraint. Allow for variable bolt tensions. Allow for variable bolt restraint spacings. Variable mesh orientation relative to bolt pattern. Allow for wire positions relative to the welds. Variable load types and areas. Allow for large mesh displacements.

Significant differences between welded wire mesh and chain link mesh required two different models to be used.

4.1 Modelling of welded wire mesh The basis of the method is to satisfy equilibrium of forces and moments and compatibility of displacements and rotations at every longitudinal wire and cross-wire intersection or node in the mesh. It is assumed the mesh is restrained at a number of nodes (representing plates and bolts) and subjected to either defined force or displacement loading at a variable number of nodes (representing rock loading). In the general case, there are 6 equations of

equilibrium associated with each node in the mesh. It is therefore necessary to find the solution to a large number of simultaneous equations. The resulting equations can be summarised in partitioned matrix notation as:

=

dd

KKKK

FF

ua

uuuaauaa

ua (1)

where: [Fa] = vector of applied forces [Fu] = vector of unknown forces [da] = vector of applied displacements [du] = vector of unknown displacements [Kij] = stiffness matrix relating forces and moments to

displacements and rotations at each node. Forces and displacements may be directed in any of the three coordinate directions. Applied displacement may be used to simulate either loading or restraint. A rigid restraint results from zero applied displacement. Non rigid restraints may be used to allow for modelling the effects of flexible boundary restraints or slip of the mesh relative to the plate as observed in previous testing (Thompson et al., 1999). Equation 1 may be partitioned into two separate matrix equations:

[ ] [ ] [ ] [ ] [ ]dKdKF uauaaaa += (2) [ ] [ ] [ ] [ ] [ ]dKdKF uuuauau += (3) These simultaneous matrix equations are solved in two parts. Firstly, Equation 2 is used to solve for the unknown displacements and, secondly, the unknown forces at the nodes may be calculated by substituting [du] into Equation 3. The results for two different arrangements of rigid restraint are shown in Figure 5.

Figure 5. Deformed mesh with higher forces shaded darker.

4.2 Modelling of high-tensile chain-link mesh For the modelling of the high-tensile chain-link mesh, the finite element software FARO was used. This software was developed by the Swiss Federal Institute of Technology, Zurich (Volkwein et al., 2002) and is based on an explicit time stepping approach. Equilibrium is treated separately for every node in the system. It is not therefore necessary to satisfy global equilibrium as in an implicit FE approach. The software was developed for dynamic impacts, but can also be used for the simulation of quasi-static loads by using constant velocities.

The software is based on Newtons Laws and involves the following steps. The acceleration of every node is calculated by considering external forces, gravity and the mass associated with each node. Then using a small time step interval, the velocity for the next time step is determined from the acceleration of every node. The translation vector for the location of every node in the next

time step can be calculated. The new location of every node is used to calculate the elongation of the elements between two nodes. From these elongations and the material laws, the forces in the single elements for the next time step are calculated. Finally, the resulting force on the node is determined, from which the node acceleration is calculated for the next time step.

Figure 6 shows the setup of the model and it is consistent with the tests executed in Australia in 2002/03 (Roth et al., 2004). The setup consists of the high-tensile chain-link mesh fixed at the boundaries, four bolts with plates and a square steel frame for applying load.

To calibrate the model, the parameters of the mesh (flexural stiffness, beginning of the tension behaviour, the tension resistance and the normal force) were adjusted in such a way that the model best fitted the results from the tests reported by Roth et al., (2004). Figure 7 shows the model with the applied load and Figure 8 the force-displacement charts of the test and the simulation.

Now that the model is calibrated, it is possible to simulate different setups with different static loads. The entire support scheme can be modelled by introducing the characteristics

Figure 6. Setup of the woven mesh model.

Figure 7. Numerical model with applied load.

Figure 8. Force displacement chart showing the results from the test and the simulation of the high-tensile chain-link mesh.

of the bolts. It is furthermore possible to simulate dynamic impacts (e.g. due to high stress and violent rock failure) and to predict the maximum deflection of the mesh, the loads in the bolts and the maximum energy absorption capacity.

5 CONCLUSION

The force-displacement response of different mesh types depends on many factors. Laboratory testing imposes boundary conditions which can have a significant effect on the force-displacement response. However, the boundary restraints and loading do not simulate the conditions in the field where large sheets or rolls of mesh are used and small areal restraint is provided at discrete locations associated with rock bolts. The only way to accurately predict the force displacement responses of various mesh types without testing is through three-dimensional, non-linear modelling.

ACKNOWLEDGEMENTS

The direct assistance of Barrick Gold and Geobrugg and the financial support and encouragement provided by the Australian mining industry for research at the WA School of Mines are gratefully acknowledged.

REFERENCES

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Pakalnis, V &. Ames, D. 1983. Load tests on mine screening. Underground support systems. Canadian Inst. of Min. Met. and Petroleum, Special Volume 35. Udd, J. (ed), 79 83.

Player, J.R., Villaescusa, E. & Thompson, A.G. 2004. Dynamic testing of rock reinforcement using the momentum transfer concept. Ground support in mining and underground construction, eds. Villaescusa and Potvin, 327-340, Leiden:Balkema.

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Thompson, A.G., Windsor, C.R. & Cadby, G.W. 1999. Performance assessment of mesh for ground control applications. Rock support and reinforcement practice in mining. E. Villaescusa, C. Windsor & A. Thompson (eds), 119-130. Leiden: Balkema.

Van Sint Jan, M. & P. Cavieres P. 2004. Large scale static laboratory test of different support systems. Ground support in mining and underground construction. E. Villaescusa and Y. Potvin (eds), 571-577, Leiden:Balkema

Volkwein A., Anderheggen E. & Grassl H. 2002, Numerical simulation of highly flexible rockfall protection systems, 5th World Congress on Computational Mechanics, Vienna, Austria.