**4. Compression and displacement**

To a first-order approximation, the displacement of each zone of an axially-loaded deep foundation is the measurement *D* given by dial gages or displacement transducers at the head, or point of load application in bi-directional load tests. However, as discussed above the foundation element has a rigidity, which means it will compress or elongate elastically under applied stress. The degree of this compression or elongation can be estimated using the collected strain gage data.

For each zone, the zone strain is computed as the average of the measured strains at the top and bottom of the zone. Change in length (compression or elongation) *δ* is then computed as the average zone strain times the zone length *L*.

$$
\varepsilon\_{\text{zone}} = \frac{\varepsilon\_{\text{top}} + \varepsilon\_{\text{bottom}}}{2}, \delta\_{\text{zone}} = \varepsilon\_{\text{zone}} \cdot L\_{\text{zone}} \tag{14}
$$

Zones which do not have strain gage levels both at the top and bottom, but rather are located next to boundary changes (the zone(s) adjacent to the load-application device and/or the top and bottom of the foundation element) must be evaluated differently. Depending on the situation, the one available strain gage level may be assumed to be representative of strain throughout the zone, strain data from two or

*Perspective Chapter: Interpretation of Deep Foundation Load Test Data DOI: http://dx.doi.org/10.5772/intechopen.105142*

**Figure 12.** *Calculation of average strain, compression and displacement at top, mid-point and bottom of a zone.*

more levels may be extrapolated, or strain may be estimated by correlation to extensometer telltale rod data.

The total displacement of each zone *zj* is then computed at the midpoint of the zone. The calculation must include the displacement at the point of load application *D* as well as the change in length of all zones between the point of load application and the current zone:

$$z\_{j} = D + \sum\_{i=1}^{j-1} \delta\_{i} + \frac{1}{2}\delta\_{j} \tag{15}$$

This calculation will then result in the 'z' component of the t-z curve for every shear zone. **Figure 12** is a schematic of the zone displacement calculation.

In certain circumstances, the elastic compression of the test foundation may be a minor contributor to the total computed displacement. However, in situations with very stiff soils or rock, and/or with slender elements with a relatively small rigidity and large strains, the elastic deformation can be a significant if not major portion of the total displacement of each shear zone. While the interpretation of data described in this section is simpler than in the previous sections, it is no less critical to constructing the t-z and q-z curves from strain data correctly.
