Bridge Design Soil-Structure Interaction Series Post#1: Pile Depth of Fixity

When designing bridge foundations on soft soils, deep foundation systems like pile-supported cap footings and cast-in-drilled-hole (CIDH) pile shafts are commonly employed to support bridge piers and abutments (Figure 1). These elements must be designed to resist and transfer vertical and lateral loads arising from both seismic and non-seismic events, including liquefaction.

Figure 1. Pile supported cap footing (left) and CIDH pile shaft (right)

In bridge engineering practice, the design of deep foundations necessitates close collaboration between structural and geotechnical engineers. The structural engineer is responsible for demand analysis and ensuring the adequacy of the foundation system. One simplified approach to analyzing pile system demands is the concept of "pile depth of fixity," which comprises an elastic frame-based analysis. This method estimates the unsupported cantilever length of the piles, enabling the analysis to approximate the response of a more rigorous soil-pile interaction model. Here, piles are modeled as cantilevered columns with a fixed base, capturing critical response parameters.

Key Objectives in Pile Depth of Fixity Analysis

Two critical outputs from this analysis are essential for the designer:

1. System Stiffness: Determining the stiffness of the soil-pile-foundation system is crucial for conducting a response spectrum analysis. Stiffness directly influences the structural period, which in turn determines the base shear attracted by the bridge substructure and foundation system.

   
   

2. Maximum Flexural Demand: Identifying the location of maximum flexural demand within the pile is essential for ensuring sufficient strength to resist applied loads.

   
   

Figure 2 illustrates how these outputs are derived.

Figure 2. Concept of stiffness and bending depths of fixity of piles

Stiffness Depth vs. Bending Depth

As depicted in Figure 2, it is important to note that the point of maximum in-ground flexural demand does not coincide with the point corresponding to the stiffness depth-of-fixity. The stiffness depth-of-fixity refers to the depth where the pile provides the same displacement as a fixed-base column, with no soil considered. In contrast, the bending depth-of-fixity, which reflects the maximum flexural demand, occurs closer to the ground surface. In pile caps with multiple piles, these depths may vary depending on the direction of loading —longitudinal versus transverse.

Common Misunderstandings

A frequent challenge arises when structural engineers request the "depth of fixity" from geotechnical engineers. First, it may not be clear if the structural engineer is asking for the stiffness or the bending depth of fixity. Additionally, geotechnical engineers often define this as the depth where either the bending moment or displacement in the pile reaches zero. However, this geotechnical depth of fixity is typically deeper than the depth required by structural engineers to capture either the correct system stiffness or the maximum in-ground bending moment for seismic analysis (Figure 3).

Figure 3. Geotechnical depth of fixity based on pile displacement

Recommendations and Best Practices

There is no universally accepted definition for "pile depth of fixity." Misunderstandings in how this term is defined can result in significant differences in the predicted pile response between structural and geotechnical analyses.

For preliminary sizing one could refer to the design standard and any local jurisdictional guidelines. For instance, as per commentary on this topic in the BC Ministry of Transportation and Infrastructure - Supplement to CHBDC S6-19:

"The depth-to-fixity may be used for determining the foundation input motion. The depth-to-fixity may be derived by equating the lateral stiffness of the cantilever to that of the elastic soil-pile system (Chai 2002). The depth-to-maximum-moment is different than the depth-to-fixity."

For final design, the pile depth of fixity should be obtained from the geotechnical engineering specialist on a case-by-case basis, as it depends on specific soil conditions and loading scenarios. Clear communication between structural and geotechnical engineers is essential to ensure both parties understand the purpose and application of the depth-of-fixity parameter. Properly defining and agreeing on this parameter helps prevent errors in design and ensures that the pile system performs as intended.

References:

• Priestley, M.J.N., Seible, F., and Calvi, G.M. (1998). Seismic Design and Retrofit of Bridges.

• BC Ministry of Transportation and Infrastructure (BC MoTI) Supplement to CSA S6:19

Authors:

Saqib Khan, P.Eng., SE, M.A.Sc., is Principal Engineer at Spannovation

Lalinda Weerasekara, Ph.D., P.Eng. is Principal Geotechnical Engineer at ECORA