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11. Lateral Earth Pressure > 11.4 Rankine’s States of Plastic Equilibrium

11.4 RANKINE's STATES OF PLASTIC EQUILIBRIUM

Suppose every part of a semi-infinite mass (say, sand) at the K0-condition is brought on the verge of failure either by stretching or by compressing, then such a state is called the general state of plastic equilibrium. General states of plastic equilibrium are not possible in normal practical problems except when a geological process is involved. Normal practical problems of interest cause deformations only to a limited extent (for example, yielding of a retaining wall), and hence a local state of plastic equilibrium is produced.

Suppose a rigid, frictionless, infinite wall, backfilled with a dry non-cohesive soil, is allowed to move a slight distance away from the retained soil mass (Fig. 11.2a). The soil starts to expand or stretch in the direction following the movement of the wall, resulting in the decrease of horizontal stress from the initial at-rest condition. When adequate lateral movement has occurred, the horizontal stress is decreased to a certain magnitude such that the full shear strength of the soil is mobilized. There is no possibility for a further reduction in the horizontal stress, and such a stress condition is called the active stress, Image, and the ratio of horizontal to vertical stress is referred to as the coefficient of active stress or coefficient of active earth pressure, Ka.


  

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