Keywords: cantilever retaining wall, concrete, reinforcing steel, optimisation, cutting plane, non linear programming.

This paper presents an application of cutting plane method to the non linear programming problem of the optimisation of a cantilever retaining wall. The application of this technique in optimising the cantilever beam design undertaken in this study is a new approach as compared to the conventional design being commonly practiced. In optimising the design of a cantilever retaining wall, the objective is to minimise the amount of materials used i.e. concrete and steel as well as to minimise the construction cost which eventually will minimise the overall cost of installing the retaining wall. The cutting plane method is applied to the non-linear equations to obtain linear ones by using an expanded Taylor series. Linear equations are solved using the conventional linear programming problem. The objective function of the cantilever retaining wall is formulated in mathematical programming form with constraints on the design variables. The solutions of the optimisation function represent the size of the retaining structure and the cross sectional area of the steel. The variables appear in the objective function are the dimensions of the area of toe steel, the area of the heel steel, the length of the toe wall plus the wall thickness, the length of the heel, and the thickness of the retaining wall's base, The requirements to prevent failures of the retaining wall as a result of overturning about the toe, sliding along the base as well as shear and tensile forces limitations become the main constraints in designing the retaining wall structure. There are five design variables and five failure modes (constraints) to be taken into consideration. The overall height of the wall is fixed at 6.0m. From this study, it has been shown that the optimal design for the cantilever retaining wall has been successful by applying the cutting plane technique. Moreover, by comparing the results obtained from the optimisation method with the values calculated using the conventional design technique, a reduction in cost of approximately 35% has been achieved. It has also been found in this study that the total costs for installing the cantilever retaining wall based upon the different overall stem height indicate that the percentage savings in cost increases as the stem height reduces. The percentage saving in cost obtained from the optimisation design process for the different overall stem heights of 3.5m, 4.0m, 4.5m, 5.0m, 5.5m and 6.0m is in the range of 35-40% compared with the results obtained by applying the conventional method of design.

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