3D core replacement method applied to support design on drift next to large excavation

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1 3D core replacement method applied to support design on drift next to large excavation J. Verdugo, A. Merino & V. Buscaglione Hatch Chile, Chuquicamata Underground Mine Project, Chile A. Russo CODELCO, Chuquicamata Underground Mine Project, Chile ABSTRACT: For reinforcement design of large excavations, explicit 3D models are commonly used and their results have been proven accurate and empirically validated. This design process usually requires several iterations for every excavation of the system, which in general consists of one large excavation and a number of secondary drifts. Numerical process takes time, it is common to run several models in order to reduce or increase the support design depending on its results. For this reason time reduction remains one of the major challenges of this kind of modeling. This paper describes the reinforcement design of a crusher cavern from Chuquicamata Mine Underground Project and the use and validation of a Core Replacement modeling on a secondary drift, in order to optimize its reinforcement simulation. Taking into account the quality shown by the rock mass, the analyzed method has given acceptable results and a significant save of time in the process. 1 INTRODUCTION The CODELCO Chuquicamata Underground Mine Project considers a block caving exploitation divided into 20 macro blocks. The crusher system assessed at the feasibility level is based on two Sizer crushers below each macro block, connected to the production level by four raise bored ore pass. Each Sizer crusher is located on a cavern with a section of 12.5 m 13 m. Several drifts are previously excavated next to the Sizer Room, so the geomechanical interaction between them and the main excavation have to be considered. The support design of the system is validated by a FLAC 3D (Itasca 2009) model, which is optimized by using a core replacement method for the drifts. 2 NUMERICAL MODELING 2.1 Geotechnical properties Considering the variability of the mine geology, two models of the excavations are achieved according to the rock mass quality. The first one is excavated on the Basic Geotechnical Unit (UGTB) called PES (Pórfido Este Sericítico), and it is representative of the North Sector of the mine. The second one is excavated on the UGTB Q=S (Cuarzo Igual Sericita) and it is representative of the Center Sector. The design obtained for the Center Sector will also be used for the South Sector which is considered of a better quality. These sectors and their geology can be observed in Figure 1. The rock mass is modeled as a continua Generalized Hoek & Brown material. Intact rock properties were obtained from Russo (2010) and the GSI values from Russo & Gajardo (2012). These parameters are presented in Table 1. Rock mass properties were scaled by using equations

2 described in Hoek, Carranza-Torres & Corkum (2002), and the Young s Modulus values were also scaled with the relation from Hoek & Diederichs (2006). ( ( ( Figure 1. Blocks model at meters above sea level for the three Sectors with their Geotechnical Units, the Sizer Room s location and the macro blocks. (a) Northern Sector (b) Center Sector (c) Southern Sector. Table 1. Hoek & Brown properties of the rock mass. Sector UGTB Domain γ GSI σci mi Em ν kn/m 3 MPa GPa North PES Americana Norte Center Q=S Americana Central South Q>S Americana Sur The field stress is obtained from a mine-scale 3D model that takes into account the mining stresses redistribution. These values were taken from Board & Poeck (2009) and are presented in Table 2.

3 Table 2. Field stress considered. Sector σ NS σ EW σ Z MPa MPa MPa North Center Geometrical description and excavation sequence In order to obtain results that considers the overall behavior of the excavations and their interaction, the model have been constructed including several drifts, which dimensions are presented in Table 3. The geometrical design of the Sizer Room and its associated drifts was completed using Maptek Vulcan software and exported as a DXF file. The meshing process was done using Gambit software. The result is a 200 m 200 m 200m mesh with seven million tetrahedral elements. The FLAC 3D mesh is presented in the Figure 2. Table 3. Excavations considered in the numerical modeling and their dimensions Level Excavation denomination Dimension (B H) Ore pass level Ore pass Station Access Drift 4 m 4 m Ore pass Level Access Drift 4 m 4 m Ore passes φ3.5 m Crusher level Ore pass Discharge Station Access 4 m 4 m Sizer Plant Access 5.5 m 5.0 m Plate feeder Room 7.0 m 13.0 m Sizer Room 12.5 m 13.0 m Haulage Level Intermediate Haulage Drift 6.5 m 5.0 m Figure 2. Overview of the model s mesh.

4 The excavation sequence is explicitly achieved into 172 steps using FLAC 3D. For each step the structural elements are defined. Drifts are excavated in 3 m steps. The Sizer Room is excavated starting with a roof pilot tunnel which is then laterally excavated to complete the roof arch. A slot is after achieved to start the benching of the room. Finally the Sizer Room is connected to the Intermediate Haulage Drift and the ore pass are excavated. Relevant steps of this sequence are presented in the Figure 3. Figure 3. Relevant steps of the excavation sequence. 2.3 Support design The support sections are defined based on empirical criteria: drifts are designed in accordance to the Barton & Grimstad (1993) chart, while the Plate Feeder Room and Sizer Room are designed considering the pattern recommended by these authors, but the bolts are replaced by minicaged cables which length is defined by the US Army Corps (1980) criteria. The support design obtained by this method is presented in Table 4.

5 Table 4. Support design obtained by empirical methods. Excavation Sector Pattern of bolt/cable Length Shotcrete thickness Drifts North 1.5 m x 1.5 m 2.5 m - Center 1.3 m x 1.3 m 2.5 m - Plate Feeder Room North 2.01 m x 2.1 m 6.0 m 10 cm Center 1.7 m x 1.7 m 8.0 m 10 cm Sizer Room North 2.1 m x 2.1 m 6.0 m 10 cm Center 1.7 m x 1.7 m 8.0 m 10 cm Several cables were also installed in different zones of confinement loss in order to prevent wide plastic behavior. Those support elements are explicitly modeled, bolt and cable are taken as cable elements which properties are define according to their strength and grout stiffness. The tension strength is 160 kn for the bolts and 350 kn for minicaged cable. Shotcrete is modeled as shell elements, the time hardening is considered changing stiffness property at each step of installation, according to the excavation sequence estimated at this feasibility level. The final compression strength of the shotcrete is assumed to be 30 MPa. Each model was run in a HP Workstation with an Intel Xeon CPU W3565@3.2 GHz processor and 30 Gb Ram, in approximately 5300 minutes. 2.4 Results In the Northern Sector, the rock mass around the Sizer Room shows stress concentration of about 40 MPa, and locally 60 MPa at the corners. The plastic zone has an extent of less than 1.0 m, greater displacement are 1.2 cm at the East wall of the room. Cables present a maximum force of 75 kn and the shotcrete shows a compression of about 800 kn per unit length. At the drifts, force in the bolts is variable depending on the distance from the tunnel front at which they are installed. Maximum forces are located at the nearest bolts from the front and are about 30 kn. In the Southern Sector, stress concentrations at the roof of the Sizer Room are about 20 to 30 MPa, and 60 at the corners. The plastic zone extent varies between 1.7 m to 2.0 m. Maximum displacement are located at the northern wall and are about 3.0 cm. Cables present a maximum force of 230 kn and shotcrete shows a compression of 1600 kn per unit length. At the drifts, maximum forces on the cable are about 75 kn. In Figure 4 graphical results of support for Southern Sector are presented. In Figure 5, the capacity plots of the shotcrete are shown for a factor of 1.5. Figure 4. Graphical results of the structural elements.

6 Figure 5. Capacity plots of the shotcrete. Factor of safety = MODELING OPTIMIZATION 3.1 Core Replacement method As said before, the explicit modeling used in the design takes a long time to be done. In fact, it is common to run several models in order to reduce or increase the support design depending on its results. For this reason time reduction remains one of the major challenges of this kind of numerical modeling. The Core Replacement method is chosen in order to find an improvement for this subject by simplifying the modeling. This method is described in Appendix 1 of the Kersten Lecture by Hoek et al. (2008) and involves determining the longitudinal closure profile for the excavation, and replacement of the core of the excavation by an elastic material that in equilibrium allows a closure similar to that which is generated at a certain distance from the front, where bolts are installed. This method allows solving an entire drift in only two steps, the first one generates the amount of deformation prior to support, and the second one solves the force on the support after completing drift excavation. 3.2 Core replacement applied to the Intermediate Haulage Drift The Core Replacement Method is applied to the Intermediate Haulage Drift at the Southern Sector. At a first stage, the relation between displacement at the edge of the excavation and the modulus of replacement material of the core is obtained by a 2D relaxing model, which is achieved reducing the Young modulus of the core from the rock mass modulus to zero. The mesh of this model is presented on Figure 6, and the results on Figure 7. The relation between the distance from the front and the closure of the excavation can be obtained by equations proposed by Vlachopoulos & Diederichs (2009) that involve the maximum tunnel wall displacement and the radius of the plastic zone far from the tunnel face. Nevertheless, in this case, the radius of the plastic zone is neglected due its value is less than twice the tunnel radius and the wall and face yield zones do not interact. Therefore the relationship for the longitudinal displacement profile derived by Panet (1995) in Equation 1, can be used: u u r max * d t where is the average radial displacement at a specified longitudinal position, is the maximum short term radial displacement distant from the face and corresponding to plane strain (1)

7 Displacement [m] analysis of a tunnel cross section, and is the quotient between a specified longitudinal position ( ) and the tunnel equivalent radius ( ). This relationship is based on elastic analysis. This relationship is applied for a distance of 70 cm which is the lowest distance between the bolt installation and the front of the drift in the explicit model. The average radial displacement obtained is 4.1 mm which in Figure 7 is equivalent to a Young s modulus of 3.44 GPa. Figure 6. Final view of the 2D relaxation model E E E+10 Young s Modulus [Pa] Figure 7. Results of the relaxation model as a relationship between Young s modulus and roof displacement. 3.3 Results of the Core Replacement method The 3D model shown in Figure 2 is solved by replacing the core of the Intermediate Haulage drift by an elastic material with a Young s modulus of 3.44 GPa. After the equilibrium is reached, support bolt are installed and the material excavated. The final displacement obtained by this method has a similar behavior compared to the one from the explicit modeling. The main difference between both of them is that the explicit modeling locally shows more displacement on the walls than the Core Replacement method. This can be explained by the fact that this displacements occur in a location far from the front, while the Core Replacement was applied to represent a closer section. This can be observed on Figure 8.

8 Force [kn] ( ( Figure 8. Total displacement by applying each method. (a) Core Replacement (b) Explicit modeling. The average force obtained at the overall length of the bolts of the roof is 41.6 kn while in the explicit model this value is of 41.2 kn. For both models, the results through the length of the bolts are presented in Figure 9, where segment 1 is the nearest from the excavation and segment 8 the farthest. For each segment, maximum and minimum values of the force are represented by the black lines for the explicit model. Despite the difference observed in the first segment of the rockbolt, the second and the third have very similar values, and between the fourth and the eighth the curves have a regular profile. It is presumed that the difference found between both behaviors is due to the in situ stress asymmetry, which is not considered in this method. This is significant because this asymmetry generates a different response at walls and the roof, and therefore the relationship between Young s modulus and closure of the drift should be analyzed differently for each direction. For that reason, future works may apply anysotropic material to the core replacement method in order to obtain more realistic results. The average forces obtained earlier for both methods are very similar, and it is important to notice that the Core Replacement method has given a slightly higher value, in addition the segment closest to the excavation (that in both cases is the maximum force) also presents higher values, which means that this method is more conservative, and can be applied for this types of drifts in this rockmass Rockbolt Segment Explicit Modeling Core Replacement (E=3.44) Figure 9. Average roof bolts forces obtained with explicit and core replacement models. For the first, maximum and minimum values can be seen for each segment of the bolts.

9 3.4 Time saving As said before, the overall model takes approximately 5300 minutes to run. The Intermediate Haulage Drift explicit model which is excavated into 24 steps, takes 745 minutes to run. The 2D relaxation model runs in less than one minute and the core replacement model takes only 205 minutes. In other words, the core replacement method applied to this Intermediate Haulage Drift saves 540 minutes which represents a 10% of improvement. By simple extrapolation, by applying this method to all secondary drifts, the overall time saving can be estimated in 2260 minutes which represent a 42% of the total time. Although it is difficult to estimate time taken in programming the explicit model, clearly core replacement model requires less time since excavations does not need to be discretized, and all structural elements are declared in the same excavation step. 4 CONCLUSIONS The reinforcement design for large excavations must be done cautiously due the importance these tunnels have in the main system. An explicit 3D modeling is very important in these cases, due the accuracy their results have shown, despite the time that it takes to provide results. Nevertheless, when a change is done in the first design and the modeling must be run again, the time that this process takes is not minor, and it is for that reason that it is interesting to search for another method that helps by saving time in the secondary drifts reinforcement design. In this case, the core replacement method has proven been acceptable while designing secondary drifts reinforcement, and shown an important save of time: The explicit modeling provided results in the order of 745 minutes, and if something is altered on the design it must be redone; on the other hand, the Core Replacement method took 205 on obtaining the rock bolt s forces. The core replacement results are considered acceptable at an engineering project feasibility level, but while the project studies requires more detailed analysis, it may be carefully used until this method is improved and its results are more accurate. REFERENCES Board M. & Poeck E Chuquicamata Underground Project 2009 Geotechnical Update. Itasca Denver, Inc. Grimstad, E. & Barton, N Updating the Q-System for NMT. In Proc. Int. Symp. On sprayed concrete - modern use of wet mix sprayed concrete for underground support, pp Oslo: Norwegian Concrete Assn. Hoek, E., Carranza-Torres, C., & Corkum B Hoek-Brown failure criterion 2002 Edition. In R. Hammah, W. Bawden, J. Curran, and M. Telesnicki (Eds.), Proceedings of NARMS-TAC 2002, Mining Innovation and Technology. Toronto, 10 July 2002, pp University of Toronto. Hoek, E., Carranza-Torres, C., Diederichs, MS. & Corkum, B Kersten Lecture: Integration of geotechnical and structural design in tunnelling. Proceedings University of Minnesota 56th Annual Geotechnical Engineering Conference. Minneapolis, 29 February 2008, pp Hoek, E. & Diederichs M.S Empirical estimation of rock mass modulus. International Journal of Rock Mechanics and Mining Sciences. 43: CrossRef, ISI. Itasca Consulting Group, Inc FLAC 3D Fast Lagrangian Analysis of Continua in 3 Dimensions, Ver Minneapolis: Itasca. Panet, M Le calcul des tunnels part la methode convergence-confinement. Paris: Presses de l ENPC. Russo, A Estimaciones propiedades geotécnicas de la roca intacta y del macizo rocoso en los dominios geotécnicos, Ingeniería básica PMCHS. CODELCO Proyecto mina Chuquicamata subterránea. Chile Russo, A. & Gajardo, D Calibración y validación del índice GSI, 1er nivel de explotación. CODELCO Proyecto mina Chuquicamata subterránea. Chile US Army Corps of Engineers Rock reinforcement. Washington, DC. Vlachopoulos,N. & Diederichs, M.S., Improved Longitudinal Displacement Profiles for Convergence Confinement Analysis of Deep Tunnels. Rock Mech.& Rock Eng.. Vol 42:2 Pgs