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Cu~iN METHODS IN ROCK MECHANIC' • <br />Two models of a natural cliff and a road cut <br />some 150 feet (45.70 m) high were studied simul- <br />taneously -- one using a classical 2-dimensional <br />plane strain, finite element model, and the other <br />incorporating "joint elements" (Goodman, et al., <br />1968), in order to simulate the vertical jointing <br />and the horizontal bedding of the rock. For the <br />model with the joint elements, both the bedding <br />planes and the joints were assumed to be continuous <br />The values of the normal and tangential stiffness <br />coefficients were taken from available literature <br />(Goodman, 7970; Goodman, et al., 1971). <br />Since the minor principal stresses are of <br />concern in determining the stability of the cut <br />slope, they are presented in Figures 2 and 3. Both <br />figures show the minor principal stresses within a <br />cliff before the excavation and after it. Figure 2 <br />depicts a plane strain, continuous-medium model <br />(without joint elements); and Figure 3 depicts a <br />model including both the bedding planes and joint <br />el err en ts. Both models show zones of tensile stresses <br />before and after the excavation. The location and <br />extent of tensile stress zones and the magnitude of <br />the stresses are different for the two models. As <br />can be expected, zones of tensile stresses are <br />larger and the stresses are higher in the rock mass <br />with joint elements. <br />Bo :n models show zones of tensile stresses <br />above ue crest of the cliff and inside the rock <br />mass. cones of tensile stresses inside the rock <br />mass are of particular interest, since they have <br />keen ca::s ing vertical fractures (stress relief <br />fractures) parallel with the cliff wall. As will <br />be show- later, open fractures of this type were <br />frequently encountered during the excavation of the <br />road cuts. <br />The excavation of a cut in both finite element <br />models favorably influences tensile stresses above <br />the cut crest. In the continuous model, tensile <br />stresses are eliminated completely, while the model <br />with joint elements shows a limited zone of tensile <br />stresses above the crest. <br />The cut excavation creates, however, zones of <br />tensile stresses behind individual benches. The <br />model with joints shows larger areas of tensile <br />stresses. The magnitude of these stresses is <br />fairly low. They reach the values of 1.2 ksf <br />(0.59 Kc/cm2) in the model without joints and 0.2 ksf <br />(0.10 Kc/cm2) in the model with joints. Tensile <br />stresses of this magnitude can be effectively handled <br />by ho ri:on tal rock bolts or possibly neglected. <br /> <br />0 IO b K mt <br />^ 3p1E OF iC MSi~C STM..ST~S <br />SipCS5E5 ip a5F <br />figure 2. Minor principal stress contours before and <br />after excavation, model without joints. <br />74 <br />