Statistical analysis and representation models of calendar-day liquidated damages

When projects suffer noncompletion, state highway agencies (SHAs) may trigger liquidated damage (LD) provisions, and at times, contractors may challenge their enforceability. Normally, to be compensated for the costs expected during the delay, states design the LD schedules by associating LD rates to specific contract sizes. A review of the literature found that states varied significantly in the LD schedule designs. However, no studies have explored the relationship between the LD rates and contract sizes (LDR-CS) across states. Exploring this relationship could lead to identifying the underlying model of the relationship, explaining how states vary the LD rates against contract sizes, running comparative analyses of the states' LD schedules, and designing optimal LD schedules, among other potential benefits. To realize these benefits, the objectives of this work were to (1) statistically explore and characterize the LDR-CS relationship, and (2) develop a representative model of the relationship. To achieve these objectives, descriptive, box-whisker, and cluster analyses were performed to characterize the relationship, and regression analysis was utilized to search for the best-fit representation model. The relationship was found to be challenging; it had a unique L-shape, and was modeled successfully only using transformed nonlinear regression. The research results could facilitate performing LD comparative analysis among states, help SHAs assess and build confidence in their LD rates, and help update and optimize LD schedule designs. This work contributes to the body of knowledge with new statistical dimensions to comprehend the LDR-CS relationship, providing tables, charts, and transformed nonlinear models.