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    1.2    SCOPE  AND  OBJECTIVES
    This research is specifically concerned with the depth of cap requirement for the
    validity of the rigid cap assumption in the free-standing pile cap design. Although pile caps are usually located on or inside the soil layer, the soil underneath the pile caps is not considered and free-standing pile caps are used for the design in this research. It is because the soil layer underneath can be imagined as infinitely many springs, which restrict the maximum out-of-plane deflection of the pile caps. It means that for the pile caps in contact with the soil layer, the design chart concluded in this research will provide a design on the more conservative side.
    The difference between the flexible cap assumption and the rigid cap assumption is discussed, and a parametric study of the optimised depth of the cap for a free-standing rigid-pile cap is carried out. Finally, the concluded design curves for the required depth of a rigid-pile cap are compared with the existing design criteria of the pile cap thickness.

    The main objectives of the research in this thesis are as follows:
    1. The awareness of the discrepancies among the rigid cap and flexible cap assumptions in pile cap design and the conventional rigid method in mat foundation design are raised;
    2. Finite element modelling of reinforced concrete pile caps is introduced;
    3. Structural behaviours of a pile cap are analysed to provide a clear understanding of a rigid pile cap;
    4. Design curves for the depth of a pile cap for the validity of the rigid cap assumption are plotted and compared with conventional design methods as a standard of reference for practising engineers.

    1.3    THESIS  OVERVIEW
    An introduction to pile caps, the scope and objectives of the research and the overview of this thesis are presented in Chapter 1. Literature review on the current pile cap design in general and the cap thickness criteria is also discussed. Chapter 2 highlights the difference among the rigid cap assumption in pile cap design, the conventional rigid method of mat foundation design and the flexible cap assumption in pile cap design. Misconception of the torsional moments in rigid pile caps is also discussed in Chapter 2. Chapter 3 discusses the structural modelling by finite element method, with emphasis on the choice of three-dimensional finite elements, the geometric configuration, the boundary conditions, the critical loading case and the critical number of piles.

    Structural behaviours of a free-standing pile cap are analysed and parametric studies on the influence of the rigid pile cap design are conducted in Chapter 4. In Chapter 5, the design criterion for the depth of a rigid pile cap used in the research are presented. Design curves are then derived from the parametric studies discussed in Chapter 4, and finally compared with the conventional pile cap thickness design in general. Chapter 6 summarises the whole research study and draws conclusions on the depth of cap design for use of the rigid cap assumption.
    CHAPTER2 RIGID CAP VERSUS FLEXIBLE CAP ASSUMPTION

    2.1 INTRODUCTION
    The structural design of pile foundations can be carried out with the rigid cap assumption and the flexible cap assumption , the former of which is usually adopted in common practice. However, pile cap design involving these two assumptions is not well established and illustrated, and the conventional rigid method and the approximate flexible method of mat foundation design, illustrated in Das ,are often referred.

    2.2 CONSTRAINTS  IN  PILE  GROUP  DESIGN
    The pile cap design is mainly constrained by two major limitations - the minimum pile spacing and the allowable pile bearing capacity.

    ( I ) Minimum pile spacing
    Minimum pile spacing exists on the ground that when piles are placed close to each other, it is reasonable to assume that the stresses transmitted by the piles to the soil will overlap as shown in Fig. 2.5(a), reducing the load-bearing capacity of the piles. Das (2004) suggested that the minimum centre-to-centre pile spacing is 2.5 times the pile diameter in practice, and is about 3-3.5 times the pile diameter in ordinary situations. The Hong Kong Building (Construction)Regulations (1991) stipulates that the pile spacing should not be smaller than the perimeter of piles for driven piles, and lm for piles founded on rocks. Such a design requirement is commonly adopted by foundation designers in Hong Kong. The minimum pile spacing dictates the maximum number of piles that can be provided for a pile cap of a given plan area.
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