5.3 Geometry of pile caps: deep three-dimensional
5.3.3 Influence of confinement in three-dimensional structures
Confinement by inactive concrete is a feature of great interest in the model developed in this thesis project. Inactive concrete is defined as volumes of concrete that are subjected to low stresses. In well designed strut-and-tie models these volumes are the ones that are far from any strut or tie. It should be noticed that, due to the
d = 380mm
630mm 58,7%
41,3%
100%
100%
characteristic geometry of pile caps, a very important amount of concrete is inactive.
This feature is clearly pointed out in a strut-and-tie model, for example in Figure 4.1.
Important volumes of inactive concrete in a reinforced concrete structure give rise to important internal restraint when the element is loaded. These internal restraints can have a positive and a negative effect:
5.3.3.1 Deformation limitations due to internal restraint from inactive concrete Deformation limitations due to internal restraint from inactive concrete have some negative effects on pile caps. Indeed, even for rather little deformation or load levels, a highly internally restrained structure can develop wide cracks that would deteriorate the bearing capacity of the structure. As a result, important redistribution of forces cannot take place in a pile caps because they require large deformations to develop.
When the structure is loaded, the inactive concrete restrain For instance, steel reinforcement can hardly develop its ultimate strength because the need for deformation is not acceptable for the highly restrained structure. These facts are taken into account by drastic limitations on the choice of a strut-and-tie model for a pile cap:
Stress fields in pile caps cannot be chosen as antagonist as in flexural elements. As a result in the strut-and-tie model, the angle between two struts or a strut and a tie cannot be chosen as small in a pile cap as in a flexural element. For instance, in the model developed a very drastic choice was made to limit the admissible angle between the average strut inclination and the main horizontal tie to θ > 60 degrees at the concentrated nodal regions and to θ’ > 45 degrees at smeared nodal regions, as shown in Figure 5.15.
Figure 5.15 Limitations of angles between inclined compressive stress fields and the mean horizontal tie in the strut and tie model
Ftotal is the resultant of the forces transferred by arch action and truss action at the support; the vertical component of Ftotal is equal to the force F applied at the pile.
d
a 1-β
β θ
θ
Ftotal Ftotal
θ’
θ’
Farch Ftruss
F
F
It should be noticed that deformations in the service state are never critical for pile caps due to the high deformation limitation induced by internal restraint from inactive concrete. Indeed, it is likely that a pile cap fails before unacceptable deformations are reached. Therefore deformations in the serviceability limit state are normally not checked in pile caps. It is interesting to see that these explanations about the deformation limitation of highly restrained structures can somehow be applied to prestressed and post-tensionned elements as well. The high restraint by inactive concrete is also the reason why pile caps can be considered as very rigid in comparison to the piles, leading to the fact that the load distribution between the piles is mainly dependant on their relative stiffness and on the load case, but not on the distribution of forces in the pile cap.
5.3.3.2 Compressive stresses induced by internal restraint from inactive concrete
Compressive stresses induced due to internal restraint from inactive concrete have a positive effect on pile caps. In this thesis work, this effect is called “confinement by inactive concrete”; it can be defined as the radial compression that develops around the compressive struts far from nodal regions.
Confinement by inactive concrete reduces greatly the tendency of compressive struts to develop transverse tensile stresses within the strut, hence increasing the compressive capacity of these struts. However, confinement by inactive concrete does not have an important effect on the capacity of the nodal areas below the columns, which are already subjected to a triaxial state of stress due to the loading conditions.
The effect of confinement by plain concrete is also limited at the nodal areas above the piles where the support and incoming struts compressive pressures in the nodal region have an important magnitude.
Both triaxial compression due to the loading and to the confinement by plain inactive concrete lead to the choice of a failure criterion for concrete subjected to a multi-axial state of stress. In qualitative terms, the compressive capacity of a concrete strut is enhanced by compression in the other directions and decreased by tension in the other directions. A failure criterion depending on the triaxial state of stresses at the nodes is fundamental in a strut-and-tie model and is proposed in any design recommendation guide. A proposition for failure criterion of nodal zones is then presented in Section 3.6.3.3.
The procedure to evaluate the shear capacity of pile caps is not very relevant in design codes as pointed out in Chapter 7. The main reason is that the shear capacity of pile caps is evaluated in traditional sectional approaches as the lower value of the beam shear capacity and the punching shear capacity. However, stocky pile caps barely fail in a classic sliding failure mode as assumed by the equations of beam and punching shear. On the contrary shear failures in pile caps often have the form of a combination of splitting and crushing of the inclined struts in the web.
The shear capacity of a pile cap is better represented by the capacity of the inclined strut with regard to splitting and its ability to transmit compressive forces after cracking, than by traditional building code formulations for sectional design. The quality of the criterion for the strength with regard to splitting/crushing of the inclined struts going from the column to the pile is decisive for the reliability of the model.
However failure criteria for inclined struts surrounded by inactive plain concrete are seldom. This comes from the fact that wide elements distributing loads in three dimensions like pile caps are rather complicated and not that often studied. The model
developed in this thesis considers that the shear capacity in rather stocky pile caps without stirrups should be expressed as the load carrying capacity of a cracked inclined strut crossed by a tension field and surrounded by large volumes of inactive concrete. The shape of the strut is taken into account with great attention. A design method is proposed and presented in the Section 5.3.4 which follows.