### Tech Briefs

Study of Bearing Stiffness of Drilled Shafts Socketed in Heterogeneous Rock

The rock-socketed drilled-shaft system is widely used to support heavy structures such as high-rise buildings and bridges. New construction design practices, such as the Load and Resistance Factor Design (LRFD), require more rigorous design criteria taking into account the heterogeneous nature of the subsurface rock conditions. The reference given below discusses the development of such criteria by performing accurate finite element analyses using ADINA.

The rock-socketed drilled-shaft system consists of a shaft structure formed by excavation of a cylindrical borehole into the rock where reinforcing steel bars and concrete are cast. When the shaft is subjected to an axial loading, the shaft transfers the load as normal stress and shear stress to the rock. The normal stress develops at the tip of the shaft while the shear stress develops along the cylindrical interface between the shaft and the rock. The intuitive modeling approach is to model the shaft-rock interaction using contact. However, according to the reference, a better approach is to apply an interface bond on the shaft-rock interface. This approach is computationally more efficient and yields accurate
predictions of the pressure on the tip of the shaft and the shear
failure along the interface. Figure 1 shows the finite element model and Figure 2 shows the experimental set-up.

**Figure 1** Finite element model

**Figure 2** Experimental set-up: (a)12.5 G ton centrifuge at the University of Florida, (b) scale model of drilled-shaft casing (with strain gages) and (c) load frame of centrifuge

The results of the finite element analysis are compared to experimental results in Figure 3. The finite element results agree very well with the experimental data.

**Figure 3** Comparison of the finite element analysis results and the experimental data: (a) bearing response of the synthetic rock and (b) development of side resistance

This homogeneous model serves as the benchmark model for the subsequent heterogeneous rock condition studies. In the simulation of the heterogeneous rock conditions, the elastic modulus randomly varies per layer with unit thickness (i.e., every foot). A total of 18,000 simulations were required to statistically study the rock heterogeneity found at two bridge sites in north Florida. Figure 4 shows two typical cases of material assumptions solved. The movie at the top illustrates the load transfer.

It should be noted that the number of simulations performed (18,000)
is very large. However, using fewer samples in a method based on random
sampling may not be appropriate for this study because of the
fundamental assumptions then used. In fact, the large number of finite
element simulations used with ADINA presented no problem because of
the numerical efficiency of the analyses. The modeling approach used,
and the efficient and robust finite element procedures in ADINA make this
geostatistical analysis, with its high degree of precision, not only
realistic but also practical.

**Figure 4** Two typical cases of material assumptions solved

In Figure 5, the bearing stiffness of the homogeneous rock condition and heterogeneous rock conditions are compared. Clearly, heterogeneous conditions have a significant effect on the tip resistance.

**Figure 5** Comparison of homogeneous and heterogeneous conditions

Based on the above simulations, an easily implemented equation with an influence factor (to account for the stratum depth of the heterogeneous rock layer) was developed for bridge design.

This example demonstrates how the powerful modeling capabilities of ADINA can be used with experimental results in the advancement of engineering design practice.

**Reference**

- J.H. Chung, J. Ko, H. Klammler, M.C. McVay, P. Lai, "A Numerical and Experimental Study of Bearing Stiffness of Drilled Shafts Socketed in Heterogeneous Rock,"
*Computers and Structures*, Vol. 90-91, pp. 145-192, 2012.

*Keywords:*

Drilled-shaft, shaft-rock interaction, heterogeneous rock conditions, interface bond, statistic analysis, bridge design, Load and Resistance Factor Design, LRFD

*Courtesy of J.H. Chung, J. Ko, and M.C. McVay (University of Florida), H. Klammler (Federal University of Bahia, Brazil) and P. Lai (Florida Department of Transportation).*