Geotechnical Engineering Circular No. 9 Design, Analysis, and Testing of Laterally Loaded Deep Foundations that Support Transportation Facilities
Point of Fixity or Equivalent Depth of Fixity
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| 6.7.2 Point of Fixity or Equivalent Depth of Fixity The analysis of laterally loaded deep foundations has often included use of the term fixity in practice, sometimes also referred to as point of fixity or depth of fixity. Fixity is defined as the depth of a deep foundation element at which both lateral deflection and the slope of the deflected element are zero. For design, a practical depth to fixity can be initially estimated using procedures in AASHTO (2014), and verified using p-y analyses in final design. The depth to fixity is used for structural analysis of a foundation element. Equivalent depth to fixity can also be used to perform a preliminary analysis for buckling of unsupported pile lengths. However, for both applications, p-y analyses should be performed to verify the results for final debsign. Note that the final depth of embedment is typically below the depth to fixity, to achieve fixity for the foundation element. 84 Fixity herein refers to considerations relative to the embedded section of the pile. The fixity of the pile head i.e., the connection of the pile head into a cap, is a separate topic that is discussed in a subsequent section. 6.7.2.1 Fixity for Structural Analysis AASHTO (2014) Section 6.15.2 indicates that for structural analysis of piles subject to axial loads, the selection of resistance factors for structural analysis at the Strength Limit State should consider the depth to fixity as indicated in Figure 6-12. Above this depth, the pile is subject to compression and bending, and it will therefore need to be structurally analyzed for axial load, shear, and moment. Below this depth, the pile only needs to be analyzed for axial loads. Because of different load combinations, different values of resistance factors are applicable above and below the depth of fixity. The approach presented in AASHTO for selection of the resistance factor for axial compression, c, and the resistance factor for flexure, f, is presented in Figure 6-12. The depth of fixity is used for structural analysis at the strength limit state in order to determine over what depth the shear and moment will apply and therefore which resistance factors to use. For preliminary purposes, the depth to fixity below the ground, d f , can be calculated from procedures in AASHTO (2014) Section 10.7.3.13.4 as For clays: 𝑑𝑑 𝑓𝑓 = Equation 6-18) For sands 𝑑𝑑 𝑓𝑓 = Equation 6-19) Where E p = Elastic modulus of the pile/shaft (ksi). I w = Weak axis moment of inertia of the pile/shaft (ft. E s = Soil modulus for clays = 0.465 S u (ksi). n h = Rate of increase of soil modulus with depth for sands – refer to AASHTO (2014) Section 10.4.6.3. For foundation elements embedded in rock, a depth of fixity of half the foundation element diameter below the top of rock can be assumed. |