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104 • Fourth International Symposium Salt-Northern Ohio Geological Society <br />trrTrf (n) OErTN (M) <br />t40 <br />J <br />6< <br />L <br />N <br />O~ <br />C <br />ut <br />4 I-- <br />i ~ <br />mN <br />C <br />U <br />J <br /><K <br />L <br />N <br />7 <br />K t <br />u r- <br />~_ a <br />a <br />~N <br />m <br />K <br />C) <br />SFMFT rz <br />(A) RELATIVE NORlZONTAI <br />DISPLACDENi IN A SiAFT <br />4E~ traG <br />[{BEAK <br />R[UTIVC ti0r11 ZOYTAL DI SI LwedEYT RC 4TIVC t30P IZ0YTwE Dls/uedEYr <br />(9) SEARING BREAKS IN TYO NE1(}gp(tING SFtAFTS <br />Figure 2. Field observations of horizontal movements of strata from shafts affected by mining operation (after Mohr, 1957, 195(3) <br />steps in the potential failure plane surface resulting from <br />the intersection of ta~o or more joint sets. The amount of <br />roughness may be measured by an average angle Qtr be- <br />t[veen the undulations on the joint surface and the direc- <br />tion of sliding along the joint (see Figure 3). The influence <br />ofjoint roughness on the shear strength of a rock surface <br />can be taken into account by increasing the friction angle <br />of the joint surface by fir. Consequently, [he effective fric- <br />tion angle ¢e of a rough joint surface is given by <br />The shear strength of a rough joint may be expressed by <br /> <br />Figure 3. Types of sliding surface roughness; taf surface roughness, <br />(b) veppetl foims. <br />in which r is the shear strength, and o• the normal stress <br />acting on the sliding plane. it should be noted that the <br />shear strength expressed by Eq. (4} may also be used as <br />a criterion for shear breaking along bedding planes. <br />On the basis of experience from other studies (Reyes <br />and Deere, 1966, and Nair, 1969b), it can be concluded <br />that the increased deformation that accompanies yielding <br />cxerts a minor influence on the subsidence pattern. It was <br />therefore concluded that the inclusion of the effect of <br />yielding would not lead to subsidence predictions that <br />differed significantly from the elastic analysis. Conse- <br />quen[ly, in this investigation, only the inability of rock to <br />withstand tension and [he phenomena of slippage along <br />bedding planes were studied. It should be recognized that <br />the me[hods of analysis used (or investigating slippage <br />(a) (6) <br />taro crow <br />