# Development of Rock Embedded Drilled Shaft Resistance Factors in Korea based on Field Tests
## 2 Evaluation of Resistance for the Drilled Shaft
### Calibration for the Equivalent Load-Displacement Curve  
As described in the previous section, eight load tests were bi-directional and five were conventional. However, as the bi-directional drilled shaft load test relies upon a loading mechanism entirely different from that of the conventional pile load test, many investigators and practicing engineers have expressed concern that the bi-directional load test could produce inaccurate results, especially describing drilled shaft head settlement behavior. According to [PERSON] et al. [19], the top-down equivalent curve constructed from the bi-directional load test results predicted the drilled shaft head displacement to be about half that predicted by the conventional top-down load test. This is due to the difference in the load transferred to the soil layer. In the case of the bi-directional load test, the applied load is transferred to the rock layer, whose elastic modulus is larger than that of the soil layer, while in the case of the top-down load test, the load is transferred to the soil layer, which has a small elastic modulus and is much softer than the rock. The neglected elastic displacement is another reason for the potential inaccuracy of bi-directional load test results. In the procedure for obtaining the equivalent load-displacement curve, it is assumed that the drilled shaft is incompressible, so the elastic compression of the shaft is neglected during the construction of the equivalent load-displacement curve. As a result, many researchers including [PERSON] et al. [20] have insisted that the additional elastic compression of the shaft be considered in a complete analysis. Accordingly, [PERSON] et al. suggested the use of the newly developed plotting method for the equivalent load-displacement curve considering the load transferred to the soil layer and the elastic compression.  
To plot the equivalent load-displacement curves in this study, the axial load distributions were determined for each test drilled shaft and the load ratios quantifying the difference in load distribution between the top-down test and the bi-directional load test were calculated according to [PERSON] et al. The shaft displacement can be calculated from the end bearing load as follows:  
\[\Delta\mathrm{w_{P}}=\frac{\mathrm{Q_{pile}L_{pile}}}{\mathrm{E_{pile}A_{pile}}} \tag{3}\]  
where \(\mathrm{Q_{pile}}\) is the end bearing load for the downward movement of the pressure cell base w; \(\mathrm{A_{pile}}\) and \(\mathrm{L_{pile}}\) are the cross-sectional area and the length of the shaft, respectively; and \(\mathrm{E_{pile}}\) is the Young's modulus of the shaft. Taking as many random points as required, the top-down equivalent curve can be constructed by connecting the points described by the calculated load-displacement coordinates. For example, in the case of shaft TP 2, the load ratio (=\(\square\)ABCEA/\(\square\)ABCDA) was approximately 3.82, indicating that the shaft head settlement should be w + 3.82\(\mathrm{\Delta w_{s}}\) to induce the downward movement of w at the shaft toe when the shaft is loaded from the top (Figure 6). The calculated calibrated elastic moduli and load ratios for all test cases are summarized in Table 3.  
Figure 6: Estimation of the top-down load distribution from the bi-directional load test (TP 2).  
Using the resulting axial load distribution and appropriately reduced elastic modulus, the equivalent load-displacement curves for each test shaft were constructed and compared with the results of the conventional load testing method. In this study, the equivalent load-displacement curves used by [PERSON] et al. and the calibrated elastic modulus used by [PERSON] were selected to measure the resistance of the test drilled shafts. An example of the equivalent load-displacement curve is shown in Figure 7.