A Simple Method for Analysis of Point Anchored Rockbolts in Circular Tunnels in Elastic Ground

Summary.A simple analytical method for the analysis of point anchored rockbolts is presented in this paper. The solution has been derived for elastic ground and rockbolts, for plane strain conditions, and for tunnels with circular cross section. The method provides accurate results for the rockbolts’ loads and displacements and explicitly includes the connection of the rockbolts to the surrounding ground. The addition of such details to a Finite Element numerical model is critical; otherwise the solution obtained may be dependent on the discretization used and on the stiffness of rockbolts and ground. As an alternative to including details of the rockbolt head and anchor point in the numerical model, which could be computationally very expensive, an equivalent spring constant is proposed. The spring constant is obtained by matching numerical with analytical results for a simple case, but keeping the geometry, material properties, and discretization unchanged.

[1]  Herbert H. Einstein,et al.  Feasibility analysis for a radioactive waste repository tunnel , 1998 .

[2]  Erik Eberhardt,et al.  Numerical modelling of three-dimension stress rotation ahead of an advancing tunnel face , 2001 .

[3]  C. Hsueh,et al.  Interfacial debonding and fiber pull-out stresses of fiber-reinforced composites , 1990 .

[4]  Charles E. Augarde,et al.  Three‐dimensional finite element analysis of lined tunnels , 2001 .

[5]  Tetsuro Esaki,et al.  A rock bolt and rock mass interaction model , 2004 .

[6]  Weishen Zhu,et al.  Systematic numerical simulation of rock tunnel stability considering different rock conditions and construction effects , 2003 .

[7]  S. Timoshenko,et al.  Theory of Elasticity (3rd ed.) , 1970 .

[8]  R. S. Sinha.  Chapter 2 - Design Methods , 1989 .

[9]  Márcio Muniz de Farias,et al.  Displacement control in tunnels excavated by the NATM: 3-D numerical simulations , 2004 .

[10]  Giovanni Grasselli,et al.  3D Behaviour of bolted rock joints: experimental and numerical study , 2005 .

[11]  Leslie George Tham,et al.  Analytical design method for a truss-bolt system for reinforcement of fractured coal mine roofs¿illustrated with a case study , 2005 .

[12]  Andrew J. Whittle,et al.  Experimental Evaluation of Pullout Analyses for Planar Reinforcements , 1995 .

[13]  Yujing Jiang,et al.  An analytical model to predict axial load in grouted rock bolt for soft rock tunnelling , 2004 .

[14]  Faisal I. Shalabi.  FE analysis of time-dependent behavior of tunneling in squeezing ground using two different creep models , 2005 .

[15]  C. Hsueh,et al.  Elastic load transfer from partially embedded axially loaded fibre to matrix , 1988 .

[16]  H. Einstein,et al.  SIMPLIFIED ANALYSIS FOR TUNNEL SUPPORTS , 1979 .

[17]  Günther Meschke,et al.  A 3D finite element simulation model for TBM tunnelling in soft ground , 2004 .

[18]  Antonio Bobet,et al.  Analytical Solutions for Shallow Tunnels in Saturated Ground , 2001 .

[19]  C. Fairhurst,et al.  The elasto-plastic response of underground excavations in rock masses that satisfy the Hoek-Brown failure criterion , 1999 .

[20]  A. Serrano,et al.  Tensile resistance of rock anchors , 1999 .

[21]  Andrew J. Whittle,et al.  ANALYSIS OF PULLOUT TESTS FOR PLANAR REINFORCEMENTS IN SOIL , 1995 .

[22]  J. Nairn,et al.  On the use of planar shear-lag methods for stress-transfer analysis of multilayered composites , 2001 .

[23]  Bengt Stillborg,et al.  Analytical models for rock bolts , 1999 .

[24]  V Labiouse,et al.  Ground response curves for rock excavations supported by ungrouted tensioned rockbolts , 1996 .

[25]  Daniele Peila,et al.  RADIAL PASSIVE ROCKBOLTING IN TUNNELLING DESIGN WITH A NEW CONVERGENCE-CONFINEMENT MODEL , 1996 .

[26]  E. T. Brown,et al.  Underground excavations in rock , 1980 .

[27]  Håkan Stille,et al.  Support of weak rock with grouted bolts and shotcrete , 1989 .

[28]  John A. Nairn,et al.  On the Use of Shear-Lag Methods for Analysis of Stress Transfer in Unidirectional Composites , 1997 .

[29]  Ömer Aydan,et al.  A review of numerical analysis of tunnels in discontinuous rock masses , 1999 .

[30]  George V. Aristorenas.  Time-dependent behavior of tunnels excavated in shale , 1992 .

[31]  Andrew J. Whittle,et al.  Shear‐Lag Analysis of Planar Soil Reinforcement in Plane‐Strain Compression , 1993 .

[32]  G. Swoboda,et al.  Developments and applications of the numerical analysis of tunnels in continuous media , 1999 .

[33]  G. N. Pande,et al.  STABILITY OF ROCK MASSES REINFORCED BY PASSIVE, FULLY-GROUTED ROCK BOLTS , 1988 .

[34]  I. W. Farmer,et al.  Stress distribution along a resin grouted rock anchor , 1975 .

[35]  Antonio Bobet,et al.  EFFECT OF PORE WATER PRESSURE ON TUNNEL SUPPORT DURING STATIC AND SEISMIC LOADING , 2003 .

[36]  P. Cundall,et al.  A bonded-particle model for rock , 2004 .

[37]  P. Egger,et al.  Composite Element Model of the Fully Grouted Rock Bolt , 2004 .

[38]  C. Fairhurst,et al.  APPLICATION OF THE CONVERGENCE-CONFINEMENT METHOD OF TUNNEL DESIGN TO ROCK MASSES THAT SATISFY THE HOEK-BROWN FAILURE CRITERION , 2000 .

[39]  S. Nam,et al.  Effect of tunnel advance rate on seepage forces acting on the underwater tunnel face , 2004 .

[40]  R. S. Sinha.  Underground structures : design and instrumentation , 1989 .

[41]  C. Hsueh.  Effects of interfacial bonding on sliding phenomena during compressive loading of an embedded fibre , 1990 .

[42]  F. Varas,et al.  Ground response curves for rock masses exhibiting strain‐softening behaviour , 2003 .

[43]  Dwayne D. Tannant,et al.  Rockbolt behaviour under dynamic loading: Field tests and modelling , 1995 .

[44]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[45]  M. Hojo,et al.  Shear-lag simulation of the progress of interfacial debonding in unidirectional composites , 1999 .

[46]  C. R. Windsor.  Rock reinforcement systems , 1996 .