刘建等：考虑端部摩擦的中心直裂纹巴西圆盘断裂参数解析解 5 0.7 12 [(a) This paper Dong et al. This paper Dong et al. (b) 0.6m 03 1.0 03 03 0% 0.8 0.4 0.3。 =0.6 0.2 0.4 0.1 0.2 0.0 0 J 10 15 0.0 20 25 30 5 10152025 30 Loading angle.) Loading angle,( 0.3@ -0.6 -0.9 -1.2 -1.5f This paper Li et al.Fr -1.81 -2.1 0 5 10 1520 25 30 Loading angle,6() 图3均布载荷加载下本文结果与Dong等及李一凡等四结果的对比.(a)Y:(b):(c)T* Fig.3 Comparison between the results of this study and the results of Dong et al.4 and Li et al under uniformly distributed pressure:(a)Y(b)Y and (c)T* 0.27 0.46 8名 (a) -1.14 (b) (c) 0.26 -1.18 -Parabolic 心有 0.44 0.254 -1.22 0.24 -1.26 0.42 0.23 -1.30 0.22 。一◆-Elliptical 0.40 +◆-Elliptical Parabolic -1.34 ◆苦 ---Parabolic --t,Quat山ep0yn0uma 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 030 0.2 0.40.60.8 0.56 a=5°a=15 d 0.90 -1.40 (e) -0.57 0.58 0.80 -1.80上。- -0.59 。--。-Uniform 0.70 2-2.20 062专转安 0.60 0.61 50 0.60 Elliptical -2.60 ◆-Elliptical -0.63 0.50L Parabolie -3.00 Parabolic polynomial 0.0 0.2 0.6 0.8 .00.2 0.40.60.8 0 0.20.4 0.60.8 1.55 Elliptical -0.30 h 1.50 a=15° -0.40 1.45 0.50 一一 1.40 0.60 -Elliptical 1.354 -0.70 Uniform ◆Parabolic 0.00.20.40.60.8 0.00.20.40.60.8 图4纯I型及纯Ⅱ型断裂的儿何参数随摩擦系数的变化特征.(a)-=0.2:纯I型Y:(b)=0.2:纯I型T*:(c)=02:纯Ⅱ型Ym:(d)=0.2:纯 Ⅱ型T*:(e)=0.8:纯1型Y:(f)=0.8:纯I型T*:(g)-0.8:纯Ⅱ型Y:(h)-0.8:纯Ⅱ型T* Fig.4 Variations in the Y,Yu and T of pure mode I and II fractures versus friction coefficient u:(a)B=0.2:pure mode-I Y;(b)B=0.2:pure mode-IT*; (c).2:pure mode-II Yn:(d)B-0.2:pure mode-II T(e)-.:pure mode-I Y(f)-0.8:pure mode-IT(g).8:pure mode-II Yu (h)-0.8:pure mode-II T*0 5 10 15 20 25 30 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 (a) YI Loading angle, θ/(°) 0 5 10 15 20 25 30 0.0 0.2 0.4 0.6 0.8 1.0 1.2 This paper Dong et al. (b) [4] β=0.3 β=0.4 β=0.5 β=0.6 β=0.3 β=0.4 β=0.5 β=0.6 This paper Dong et al.[4] β=0.3 β=0.4 β=0.5 β=0.6 β=0.3 β=0.4 β=0.5 β=0.6 This paper Li et al.[21] β=0.3 β=0.4 β=0.5 β=0.6 β=0.3 β=0.4 β=0.5 β=0.6 YII Loading angle, θ/(°) 0 5 10 15 20 25 30 −2.1 −1.8 −1.5 −1.2 −0.9 −0.6 −0.3 (c) T* Loading angle, θ/(°) 图 3    均布载荷加载下本文结果与 Dong 等[4] 及李一凡等[21] 结果的对比. （a）YI；（b） YII；（c） T* Fig.3    Comparison between the results of this study and the results of Dong et al.[4] and Li et al.[21] under uniformly distributed pressure: (a) YI ; (b) YII; and (c) T* 0.0 0.2 0.4 0.6 0.8 0.21 0.22 0.23 0.24 0.25 0.26 0.27 μ Uniform Elliptical Parabolic Quartic polynomial (a) YI α=5° α=15° 0.0 0.2 0.4 0.6 0.8 −1.34 −1.30 −1.26 −1.22 −1.18 −1.14 (b) μ Quartic polynomial Parabolic Elliptical Uniform T* α=5° α=15° 0.0 0.2 0.4 0.6 0.8 0.38 0.40 0.42 0.44 0.46 (c) μ Uniform Elliptical Parabolic Quartic polynomial YII α=5° α=15° μ 0.0 0.2 0.4 0.6 0.8 −0.63 −0.62 −0.61 −0.60 −0.59 −0.58 −0.57 −0.56 (d) Quartic polynomial Parabolic Elliptical Uniform T* α=5° α=15° 0.0 0.2 0.4 0.6 0.8 −3.00 −2.60 −2.20 −1.80 −1.40 (f) μ Uniform Elliptical Parabolic Quartic polynomial T* α=15° 0.0 0.2 0.4 0.6 0.8 0.50 0.60 0.70 0.80 0.90 (e) μ Uniform Parabolic YI Elliptical Quartic polynomial α=15° 0.0 0.2 0.4 0.6 0.8 1.35 1.40 1.45 1.50 1.55 (g) μ Uniform Elliptical Parabolic Quartic polynomial YII α=15° Elliptical Quartic polynomial α=15° 0.0 0.2 0.4 0.6 0.8 −0.70 −0.60 −0.50 −0.40 −0.30 (h) μ Uniform Parabolic T* 图 4    纯 I 型及纯 II 型断裂的几何参数随摩擦系数的变化特征. （a） β=0.2：纯 I 型 YI；（b）β=0.2：纯 I 型 T*；（c）β=0.2：纯 II 型 YII；（d） β=0.2：纯 II 型 T*；（e）β=0.8：纯 I 型 YI；（f）β=0.8：纯 I 型 T*；（g） β=0.8：纯 II 型 YII；（h）β=0.8：纯 II 型 T* Fig.4    Variations in the YI , YII and T* of pure mode I and II fractures versus friction coefficient μ: (a) β=0.2: pure mode-I YI ; (b) β=0.2: pure mode-I T*; (c) β=0.2: pure mode-II YII; (d) β=0.2: pure mode-II T*; (e) β=0.8: pure mode-I YI ; (f) β=0.8: pure mode-I T*; (g) β=0.8: pure mode-II YII; (h) β=0.8: pure mode-II T* 刘    建等： 考虑端部摩擦的中心直裂纹巴西圆盘断裂参数解析解 · 5 ·