. The Earth beneath the sea : History. Ocean bottom; Marine geophysics. 514 BAGNOLD [chap. 21 direction of flow), is small, the term tarijS can also be neglected. But when j3 is increased until P = (f> the stationary grain bed will move as an avalanche without any fluid stress being applied. It should be noted that relation (2) expresses a state of shear equilibrium between an a^^pliod and a resisting thrust, the thrusts being equal in value but different in kind. For this reason the externally applied fluid thrust is dis- tinguished for clarity by a special symbol ^—a capital script T, The
. The Earth beneath the sea : History. Ocean bottom; Marine geophysics. 514 BAGNOLD [chap. 21 direction of flow), is small, the term tarijS can also be neglected. But when j3 is increased until P = (f> the stationary grain bed will move as an avalanche without any fluid stress being applied. It should be noted that relation (2) expresses a state of shear equilibrium between an a^^pliod and a resisting thrust, the thrusts being equal in value but different in kind. For this reason the externally applied fluid thrust is dis- tinguished for clarity by a special symbol ^—a capital script T, The whole applied thrust, including the tangential gravity component, if any, on the solid phase, would be ^F + [{ps —p)lps\gnib sin jS. The distinctions between the four different stresses essentially involved in two-phase equihbrium are shown schematically in Fig. 3. FLUID STRESSES FLUID FLOW APPLIED STRESSES ^- RESISTING STRESSES iiiiiiiiiiniiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii MOVING SEDIMENT LOAD IIIIIIIIIIPIIIIIIIIII GRAIN STRESSES P gm sin /3 P'P T = -^-^ gm cos /3 tan <^ llilllllllllllllllllllllllllllll P- P r\ = ^^-^ am cosyS. Fig. 3. Sclieniatic diagram showing conditions of tw'O-phase stress eqviihbrium at base of a bed load. A part of the applied fivxid stress, ^p, is transferred to the bed-load grains above the bed boundary, and is transmitted to the bed as a grain stress. The overall equilibrium condition is expressed by ar_ . Ps-P Cy p Ps gmsin^ = tq + Ps-p ps gm cos jS tan (f>. The implications of the general equilibrium relation (2) as applied to trans- jjort over a homogeneous grain bed have been discussed in a further paper (Bagnold, 1956). It was there shown that the residual fluid element to cannot increase above its value rt = ^Pt at the threshold of grain motion over the bed when m\) is zero; and as ^p is increased to must, in fact, decrease progressively to a negligible value. Any increase in ^p must cause erosion of the bed grains, with a resulti
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