13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- isolated defects on the fracture shape after re-fracturing are verified by large size true tri-axial experiments. 2. Basic model The basic model of stress distribution before re-fracturing in inclusion reservoir is shown as figure 1. The length of the inclusion is assumed far greater than its width, and the inclusion is seen as a line inclusion. For an elastic inclusion body, to better reflect the discontinuity of normal stress and tangential stress between the inclusion and rock matrix, the line inclusion is treaded as a thin bar. The Eshelby equivalent inclusion theory [11, 12] is used to solve the problem, only considering rock skeleton stress. 1θ 2θ θ r 1r 2r a a x y α z 2l min σ min σ max σ max σ o o' x' y' Figure 1. The stress distribution before re-fracturing in inclusion reservoir The stress field in the inclusion reservoir is composed of the following three parts: (1) The stress field induced by the artificial fracture; (2) The stress field induced by the line inclusion; (3) Far-field stress. The total stress state of elastic plane can be expressed as a, d, w, ( , ) ( , ) ( , ) (,) (,)(,) ij ij ij ij x y x y x y x y i j x y σ σ σ σ = + + = (1) where, ( , ) ij x y σ is the total stress field, MPa; a, ( , ) ij x y σ is the stress field induced by artificial fracture, MPa; d, ( , ) ij x y σ is the stress field induced by the line inclusion, MPa; w, ( , ) ij x y σ is the far-field stress, MPa. The boundary conditions are as follows, (1) Total stress at the edge of the line inclusions needs to meet the displacement compatibility relations. That can be written in the local coordinate ' ' ' x o y as follows,
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