13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- the crack position becomes large and the constraint of the crack opening becomes strong so that the KI values decrease. At the same time, the relative sliding of the crack surfaces along the x and y directions occurs so that the KII values are not equal to zero and increase with the crack distance d increasing. Referring to the results of the case 2=cα and / 0.5 = h c , the variations of the SIF values for the case 2 =− cα and / 0.5 = h c can be obtained easily from Figs. 3 and 4. For the case 2 =− cα and / 0.5 = h c , the crack position d should be calculated from the plane / 0.5 = z c , the KI values are positive and the KII values are negative, and the KI values and the absolute values of KII are the same as the case 2=cα and / 0.5 = h c . -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 KI/p(πc)1/2 x'/c d/c=0.05 0.15 0.25 0.35 0.45 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 KII/p(πc)1/2 x'/c d/c=0.05 0.15 0.25 0.35 0.45 Fig.3 Variation of KI with the crack distance Fig. 4 Variation of KII with the crack distance 5 A rectangular crack in layered rocks As shown in Fig. 5, an elastic layer is bonded to two semi-infinite domains and contains a rectangular crack parallel to its surfaces. The two elastic half-spaces are assumed to have the same elastic properties. Two types of rock, i.e., fine-grained sandstone and mudstone, are selected. The elastic parameters of fine-grained sandstone E1=56GPa and ν1=0.3, and the ones of mudstone E2=20GP and ν2=0.25. Thus, there are four types of layered rocks shown in Table 1. The thickness of the mid-layer h=2m. The side lengths of the square crack are 2m and 4m and the crack surface is parallel to the interface of the layered rocks. The crack surfaces are smooth and are subjected to a linear load shown in Fig. 6. The crack surface is discretized into 100 nine-node elements. In order to plot the values of the SIFs along crack front lines, a line coordinate L is used to measure the crack front lines from AB, BC to CD, shown in Fig. 6. The line coordinate L starts at the corner point A of the square crack (i.e. L=0). It increases along the line AB, BC to CD. Correspondingly, L increases from 0-2, from 2-6, and from 6-8, respectively. Fig.5 A rectangular crack in the interlayer of infinite domain h1 h A homogeneous half-space A homogeneous interlayer A homogeneous half-space 8M 8M y′ Fig. 6 A rectangular crack subject to linear load D C B A 4m 2m O′ x′
RkJQdWJsaXNoZXIy MjM0NDE=