OCR Text |
Show 10 critical layer is intact at the moment of application of the force, then, if the angle of the slope is less than ft , the concentrated force can be increased arbitrarily without leading to failure. It is convenient to introduce a dimensionless force,"% , defined by "*•• = T & T ( 27) where i\^ is the applied force and H^ ft represents the weight of a cylinder whose height and radius are equal to the depth, < 4 . Since T| increases linearly with *** ( Fig- 9 ) , there is a value 91^ which corresponds to T"^ ( Point A). For a specific radius of fracture, lo , a curve can be constructed which passes through Point A. Consequently, the critical layer fails and the fracture is propagated up to a radius, Y" bi . For a very large fy , the influence of K disappears in relation to the weight of the cylinder of snow. Graphically, this is represented by a horizontal line which intersects the former straight line at B with abcissa fig and ordinate T|^> . If T ^ is greater than Tj^ o , and^ is large enough to initiate a fracture, then A is to the right of B and the fracture propagates. The abcissa of B, ft^ , is thus the maximum force that can be applied without inducing fracture propagation. As shown in Fig. 10, • L is a function of the slope angle j , the compressibility* , and the parameter U) . The angle ljJ , exists for 0 * M * ^ 1 M l r ( 1+ su* U>) ( 28) If j * Yi > n o fracture can be produced and hence PlQ does not exist; however, if T ^ rj , " H& exists and is greater than unity. For f^^ M *- s , 7f a. always exists and is less than unity for slopes less than 20°. Thus, * W is approximately ^ $ 3 for absolute stability. If the horizontal fracture line is considered, as for example produced by an elongated ski track, a similar analysis can be made, |