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Show Equation ( 22) is the basic one for the calculation of the final height of damming, while Equation ( 21) is to be applied in the calculation of dynamic pressure effects. For deposition of snow by sedimentation from powder avalanches smaller densities can occur than those given by Equation ( 22). C. Damming Effects With diminishing slope inclination the flow height hu of the avalanche increases according to Equation ( 8). It comes to a stop when, according to Equation ( 17), the flow height plus the pressure level reaches the energy level. Of great interest is the run out distance of the avalanche onto flat valley floors; all too often only the front of an avalanche has reached a few structures and swallowed up victims, which obviously would have been avoided if a small amount of the energy of the avalanche had been dissipated. If, m a broad avalanche, a longitudinal strip 1 meter wide is considered, which has a flow height h0 and a velocity v0 and pushes down below a slope of inclination ty0 onto the valley floor ( with a slope tyu , positive or negative), then, providing the slope of the valley floor is sufficiently small, the avalanche comes to rest after a run out distance s ( measured from the break in the gradient) During this time the snow increases approximately by the damming height v2 / 2g to a cone of maximum height hmax = h0 + Ah. Accordingly, the mass of the 1 meter wide strip pushed onto the flat terrain amounts to approximately: M = s [ ( h0 + h max)/ 2 ] y/ g = s ( y/ g) ( hQ - Ah/ 2> and its kinetic energy at the break in the gradient was: E= M v 2/ 2 k o This kinetic energy ER is transformed in the deposition of the snow: a) Into potential energy: Ep = Mg i\ where r\ = [ ( 3hQ + 2 Ah) /( 2hQ + A h) ] [ A h / 6 - ( s/ 3) tan ^ ] and signifies the elevation of the center of gravity of the wedge ( of snow). b) Into frictional work: The deposited mass M in flat terrain moves the center of gravity C against the frictional force Mg^ costu and and thereby performs the work: 38 |