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## L.E.M. - Limit equilibrium method |

By selecting the L.E.M. icon, the limit equilibrium method will be used for the analysis of the bulkhead.

The limit equilibrium method is the usual one used for the design practice and is mainly used for the determination of the limit embedment depth. The L.E.M. method is used for works in which it is easily identified the failure mechanism, for example in the presence of cantilevered bulkheads or with a single row of anchors.

For the calculation we consider that the bulkhead is subject to the active thrust upstream and to the passive thrust downstream. The distribution of pressure on the structure is different for bulkheads in cohesionless soils and bulkheads in cohesive soils; also the distribution of thrusts in clayey soil varies in time. The calculation of the thrusts is performed using suitable values of the angle of shearing resistance, unit weight and cohesion, making reference to the thrust coefficients determined according to the classical theories present in the literature (Coulomb, Muller-Breslau, Caquot- Kerisel).

In plotting the pressures diagram are taken into account increases due to: earthquake, groundwater, loads on the embankment. In the computation of passive thrust is introduced a coefficient of safety on passive resistance. For the calculation of the embedment depths it must be proceeded as follows:

(a) Calculation of active and passive thrust coefficients

(b) Assume an initial embedment depth between 0.2H and 0.7H

(c) Calculation of the pressures acting on the work

(d) Equilibrium of moments at the foot (cantilever bulkhead)

The steps (a)-(b)-(c)-(d) will be repeated by increasing the embedment depth to obtain the equilibrium of moments, to which will correspond the sought embedment depth. To remedy the non-equilibrium of the horizontal forces, that depth will be increased by 20%. In case of anchoring, the following mechanisms can be present:

(I) The base of the bulkhead is free to rotate (free support method)

(II) The base of the bulkhead can not rotate (fixed support method)

Free support method (see. Anchors)

To perform the computation, proceed through the steps (a) - (b) - (d). The step (c) will be replaced by equilibrium of moments with respect to the anchors application point, in this case is not necessary to increase the embedment depth as the equilibrium of horizontal forces is verified.

Fixed support method - Equivalent beam method (see. Anchors)

It is hypothesized that the bulkhead is deformed with reversal of curvature, in this case the problem is not statically determined unless the position of the reversal point is known. If it is assumed that on the inversion point there is a hinge capable of transferring only shear stress (for the purposes of static support), it is possible to break the sheet pile into two equivalent beams. To fix the position of the inflection point, Blum recommends values as a function of flexibility, geotechnical characteristics, etc. Found the location of the inflection point, proceed as follows:

(a) From the equilibrium of moments with respect to the anchors, considering the upper beam at the center of rotation, is determined the reaction of the cart.

(b) From the equilibrium of moments with respect to the foot, considering the lower beam with respect to the center of rotation, is determined the embedment depth.

(c) That depth will be increased by 20%.

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