Stress field determination from local stress measurements by numerical modelling

Abstract A back analysis using a three-dimensional (3D) boundary element method (BEM) is used to calculate the far-field stress state from local stresses measured in situ. The far-field stresses are decomposed into tectonic and gravitational components and account for the influence of localized faulting and topography. Therefore, the far-field stresses are taken to consist of a constant term, a term that varies linearly with depth, and a hyperbolic term, with one of the principal stresses being vertical. A BEM for inhomogeneous bodies is introduced to calculate elastic gravitational stresses, which is necessary for determination of the far-field stresses. An application to the stress field determination for the Mizunami underground research laboratory (MIU) is carried out. Based upon the local stresses generally measured by conventional hydraulic fracturing (HF), the unknown stress state at MIU is estimated and compared with the measurements carried out recently by the improved HF method with flow rate measurements at the position of straddle packer. After calculating the far-field stress state by BEM back analysis, 3D-finite difference methods (FDM) forward analysis was carried to calculate the in situ stresses at certain locations. The 3D FDM results roughly coincide with the measured results.

[1]  W. Menke.  Geophysical data analysis : discrete inverse theory , 1984 .

[2]  Stephen J. Martel,et al.  A Two-dimensional Boundary Element Method for Calculating Elastic Gravitational Stresses in Slopes , 2000 .

[3]  R. J. Pine,et al.  In-situ stress measurement in the Carnmenellis granite—II. Hydrofracture tests at Rosemanowes quarry to depths of 2000 m , 1983 .

[4]  O. Sano,et al.  Review of Methods of Measuring Stress and its Variations , 2005 .

[5]  S. L. Crouch,et al.  Boundary element methods in solid mechanics , 1983 .

[6]  Brian P. Bonner,et al.  Self‐propping and fluid flow in slightly offset joints at high effective pressures , 1994 .

[7]  B. Valette,et al.  In situ stress determination from hydraulic injection test data , 1984 .

[8]  Jonny Rutqvist,et al.  Uncertainty in the maximum principal stress estimated from hydraulic fracturing measurements due to the presence of the induced fracture , 2000 .

[9]  Yoshiaki Mizuta,et al.  Three-dimensional elastic analysis by the boundary element method with analytical integrations over triangular leaf elements , 1995 .

[10]  Kazuo Hayashi,et al.  Analysis of crack reopening behavior for hydrofrac stress measurement , 1993 .

[11]  Takatoshi Ito,et al.  Hydraulic fracture reopening pressure and the estimation of maximum horizontal stress , 1999 .

[12]  G. Hocking,et al.  Three-dimensional elastic stress distribution around the flat end of a cylindrical cavity , 1976 .

[13]  Yoshiaki Mizuta,et al.  Three-dimensional elastic analysis by the displacement discontinuity method with boundary division into triangular leaf elements , 1993 .

[14]  F. Cornet,et al.  ISRM Suggested Methods for rock stress estimation; Part 3, Hydraulic fracturing (HF) and/ or hydraulic testing of pre-existing fractures (HTPF) , 2003 .

[15]  Satoshi Hibino,et al.  4. In situ stress measurements in the Japanese islands: Over-coring results from a multi-element gauge used at 23 sites , 1986 .

[16]  E. Hoek,et al.  Trends in relationships between measured in-situ stresses and depth , 1978 .

[17]  J. C. Jaeger,et al.  Fundamentals of rock mechanics , 1969 .

[18]  W. S. Keys,et al.  Hydraulic fracturing to determine the regional in situ stress field, Piceance Basin, Colorado , 1976 .

[19]  H. S. Swolfs,et al.  Gravitational stresses in long symmetric ridges and valleys , 1985 .

[20]  Mark D. Zoback,et al.  Laboratory hydraulic fracturing experiments in intact and pre-fractured rock , 1977 .

[21]  Gernot Beer,et al.  Introduction to Finite and Boundary Element Methods for Engineers , 1993 .

[22]  E. T. Brown,et al.  Rock Mechanics: For Underground Mining , 1985 .