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21 CHAPTER FIVE Data Analysis Once FWD data have been collected from the field, multiple Forward Calculation analysis tools are available to the SHA. These software pack- ages typically calculate pavement layer modulus, a mate- Forward calculation is a process of using the equations of rial parameter that is essential for pavement layer design. elastic layer theory to calculate stresses, strains, and deflec- According to survey data, 90% of SHAs use FWD data for tions caused by surface loads at any point in a pavement pavement layer modulus estimation (Appendix B, Question system. Computer programs such as BISAR, CHEVLAY2, 58). On JPC pavements, FWD data can be used to determine and ELSYM5 are used for forward calculation. The pro- LTE by placing one sensor on one slab and a second sensor cess is "forward" in the sense that it is closed form. By con- on a neighboring slab and determining how each slab moves trast, back-calculation uses forward calculation iteratively, when the weight is dropped. These data are analyzed with together with numerical methods to assist with convergence, the help of computer software. FWD data analysis software to "back out" the pavement layer moduli from measured sur- may be provided by FWD vendors, academic institutions, or face deflections. government bodies. This chapter briefly explores FWD data analysis methods and the software developed around them. Hogg and DELMAT Methods Data analysis tools are not necessarily compatible with Hogg (Stubstad et al. 2006) and DELMAT (Hossain 2006) data from FWD tests. Sources of incompatibility may be job methods have been used as checks and balances for backcal- type (e.g., parking lots vs. highways vs. airports), lack of culated data. As an example, Florida uses the Hogg model compatible file formats between FWD models, or differing and has shown reasonable agreement with backcalculated analysis software configurations. A 2001 study suggests fix- moduli for asphalt and subgrade layers. ing these issues by standardizing file formats among manu- facturers, allowing data analysis software to vary test site Load Transfer Efficiency stationing, and allowing quality controls such as the SLIC transform, nondecreasing deflections, and overflow checks Adjacent JPC slabs should move together when a load is (Schmalzer 2001). applied to one of them; faulting can result if they do not. The degree to which adjacent slabs move together is defined as LTE. LTE is calculated from FWD deflections by placing Data Analysis Methods the load cell on one PCC slab and then placing a sensor on an adjacent unloaded slab. When the weight is dropped, the Back-calculation measured deflections are used to calculate LTE with Eq. (1), The most common back-calculation method is an iterative Dunloaded LTE = 100% (1) mathematical process. The method assumes that a unique Dloaded set of layer moduli result in the deflections measured by the FWD. The data analyst, based on experience and judgment, where D unloaded represents the deflection of the unloaded selects seed moduli to calculate deflections. These calcu- PCC slab, and Dloaded represents the deflection of the loaded lated deflections are compared with the output from the PCC slab (Pierce et al. 2003). Bossinesq equations, or a two- or three-dimensional finite- element model. After the first calculation, the seed moduli The work done by Gawedzinski (2005) for IDOT pro- are adjusted and the calculation is repeated. The iteration vides a comprehensive example of load transfer analysis and stops once a predetermined level of tolerance has been contains a discussion of the state of the practice for LTE. reached between the measured and calculated deflections. From this iteration, layer moduli are estimated.