The latter is caused by earth pressures reaching the limiting state on both side of a considered retaining structure, which thereafter moves towards the excavated area until the full-zone failure is reached. As movement can occur on the bottom part of the wall, the analysis of the structure will be taken as a free body. Thus there will be modified free earth support method (The free earth support revised method) and fixed earth support method. It is worth mentioning that both methods have assumed that active stress condition have been fully developed behind the retaining wall while the passive stress is right in front of the structure. This will allow for calculation using coulomb or Boussinesq theories that consider the actual stress distribution. 1. Modified free earth support method of analysis According to Clayton et al (1993, pp213-214), this method often gives the most economical design for retaining walls. For structure such as cantilever wall, the soil at the lower part of the pile should be strong enough to resist overturning moments. As shown in the above figure, the passive zone should be adequate in order to prevent lateral deflection and rotation at the lower end of the wall. However, the main principle behind the modified free earth support method of analysis is the assumption that the embedment of the wall is allowed to move and this will be to a certain distance under the action of the applied lateral earth pressure; this will cause the occurrence of negative bending moments at the considered location. This results in a statically determinate structure, only stable under certain conditions. Therefore, if a cantilever wall is to be designed based on this analysis, only the external passive and active forces will be considered. For the fact that the former will not be sufficient to cancel out the latter, in case of large and tall retaining structures no equilibrium will be meet. This will be because no fixity has been assumed at the bottom of the pile, as a consequence the structure will be under mechanism. When the structure has a height greater than 3m, this will not be the ideal design as the negative moment at the bottom of the file will increase with respect to height (increase of the active stress). As a consequence, to achieve equilibrium, strut or anchor must be added in the design. The addition will placed at the top of the structure, as shown in the picture below, to cancel out the negative moment at the base. Hence, the number of anchor will be directly proportional to the height of the wall. (Delattre, 2001,p3) When anchor or tie is added, the bending moment diagram of the wall will be as shown in the picture below. It can be seen that when moment is created by the anchorage at the top, at the bottom of the pile, the negative moment has been cancelled out; this will be only if both are equal or the former is greater than the overturning moment. As a consequence equilibrium has been satisfied; a moment created by the tie is balanced by the active earth pressure above it. Lancellotta (1995, pp305) explained: “the failure mechanism envisaged in this case involves a rotation about the anchor”. Here, the rotation of moment at C (shown in the above picture) will enable for calculating the depth by which the pile has to be embedded to satisfy equilibrium against rotation; in other words, the shear strength of the soil is mobilised with respect to the depth of embedment. The equilibrium of horizontal translation gives then the force of the anchor as a high anchorage force will result in movement of the pile ...
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