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(IV) Ignorance of pile stiffness
In Hong Kong, it is a common practice not to consider the pile stiffness when performing pile load analysis using the rigid cap assumption. The implicit assumption of such an analysis is that the piles are of equal stiffness. Designers can therefore avoid addressing the difficult problem of having to assess the stiffness of piles. If pile stiffness is ignored, re-analysis of pile load distribution is not necessary even if the actual pile lengths are unequal, sometimes by a very large amount. This concept is obviously incorrect, but provides designers with a great deal of convenience in foundation design.
Due to the above several advantages, the rigid cap assumption is usually preferred in tall building foundation design. Nevertheless, the rigid cap assumption is associated with the following drawbacks, and attention should be paid prior to design:
( I ) Higher cost
The thickness of the pile cap needs to be increased to resist the bending moment, thus increasing material costs of the pile cap and the cost for constructing deeper and/or more extension shoring works.
( II ) Increased amount of torsional reinforcements
A large amount of torsional reinforcements may be required in the reinforced concrete design of the pile cap in common practice. This is unfortunately due to a common misconception in the load transfer mechanism within a rigid cap, as will be discussed later. Torsional reinforcements are often not needed for a rigid cap.
2.5 TORSIONAL MOMENTS IN PILE CAPS BY BOTH ASSUMPTIONS
There is a deep-rooted misconception amongst local engineers that torsional moment is generated within a rigid cap in resisting the applied load.
Consider a simple four-pile cap supporting a wall subjected to pure bending moment as shown in Fig. 2.16. In transferring the load from the wall to the piles, it is generally thought that a torsional moment will be induced as shown in Fig. 2.17. For this reason, the regulatory authority often requires a substantial amount of torsional reinforcements to be provided in the pile cap to resist the shear stress induced by torsional moment.
The above concept is incorrect. For a torsional moment to develop in a rigid cap, the rigid cap must deform like a twisted plate as indicated in Fig. 2.4, like a flexible cap. This contradicts the assumption of a rigid cap that no bending and twisting are allowed in the rigid cap assumption. To help understand the true behaviour of a rigid cap, we can divide the rigid cap into a series of rigid strips as shown in Figure 2.16.
Consider a particular strip along the cross-section 1-1. The rigid strip, as shown in Fig. 2.18(a), acts like a beam resisting the loading induced by the loaded wall. Therefore, the shear stresses induced within the rigid cap near the pile positions are in fact due to “bending-induced” shear forces required to support the rigid beams. This will yield the distribution of shear stress as shown in Fig. 2.18(b). The variation of shear stress along the rigid cap in Fig. 2.18(b) will provide a net couple to balance the bending moment due to pile reaction.
To verify the difference between the shear stress distribution in a flexible pile cap and that in a rigid pile cap, finite element models of a four-pile cap supporting a wall subjected to pure bending moment, as shown in Fig. 2.16, are constructed and analysed by ABAQUS. The dimensions are listed below - span length L = 15m, pile spacing s = 10m, pile size D = 2.5m, wall thickness w = lm and depth of the cap d = lm. According to Zamana et al. (1993) and Selvadurai (1979), the rigidity of the pile cap is commonly compared by the flexural rigidity, R, expressed as follows:
where E is the Young’s modulus; d is the depth of the plate; and v is the Poisson’s ratio. Hence, finite element models with four different cases are considered:
Case 1: Flexible pile cap
Case 2: Rigid pile cap with E increased by 50 times