Optimum Cross Section Design of Blockwork Gravity Quaywalls Using SQP Method

Gravity structures are used for waterfront quay walls where the seabed soil condition is appropriate. Some gravity walls are built behind a cofferdam on land but most walls are constructed in water by a method used only in maritime works, in which large pre-cast units are lifted or floated into position and installed on a prepared bed under the water. It is usual to use rubble or a free-draining granular fill immediately behind a quay wall so that the effects of tidal lag are minimized and earth pressure is reduced. Gravity quay walls can be classified into different types such as caissons, L-shaped blocks, rectangular concrete blocks, cellular concrete blocks and cast in-place concrete. Optimum design of block work gravity type quay walls with pre-cast concrete blocks are the object of the present investigation. The advantages of these quay walls are: simple construction technology, preferred costs and good durability.The external and environmental loads acting on these type structures are surcharge, deadweight of the wall, earth pressure, residual water pressure, buoyancy, seismic forces, dynamic water pressure during an earthquake and tractive forces of vessels. The principle modes of failure of this gravity structure are: sliding, overturning, deep slip and foundation failure, therefore in the stability calculations the following items should be examined in general: Settlement, Circular slip, Bearing capacity of the foundation, sliding and overturning at all horizontal surfaces between blocks. To study the behavior of a quay wall and to check the stability against probable different failure modes, a computer program has been developed. This program can easily consider the effects of different parameters such as section geometry of quay wall, material property and loading condition in design.In common designs, designers often select an accepted sketch with their experiences and cannot review different sketches and present the best one. Sometimes the final drawing may be uneconomical and also the transport and placing of blocks may be very difficult and probably impossible. Therefore, adopting an optimization procedure for design of these structures is needed. In this paper, a procedure for optimization of cross section of a block work gravity type quay wall has been introduced and a numerical program for this procedure has been developed. After reviewing design and construction considerations for such quay walls, available methods for optimum design of these structures are discussed and objective function, constraints, design variables are considered. The main constraints of the optimization problem in the present study is the safety factor in various modes of failures. As relation of safety factor with design variables is unknown, therefore, a proper method should be used for approximating the objective function and constrains according to design variables first. Then, an efficient method should be selected for formulation of mathematical optimization of the objective function under existing constrains. For this purpose, the optimization of the cross section is accomplished using Sequential Quadratic Programming (SQP) method in the present work. Results indicate that the cross section of a block work quay wall has an important role on stability of the structure and one can reduce costs of such structures by optimizing the cross section. Finally, some recommendations for optimum design of this type of quay wall are presented.