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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. [ABSTRACT FROM AUTHOR]

Contractors tend to challenge the enforceability of liquidated damages (LDs), claiming they are unreasonable, excessive, penalty statements, or concurrently caused. States customarily assert that the LD rates are a genuine reflection of the expenses expected to be suffered when a project gets delayed due to noncompletion. While there are common practices among the states for articulating LD specifications, which generally follow the Federal Code of Regulations, there are no published studies that assist states in comparing their LD rates to those of other states so that the LD rates might be defended. Further, there are no studies that offer models that would uncover the relationship between the LD rates and the contract sizes so that the LD rates might be justified. This work addresses such gaps in the body of knowledge (BOK) in LDs. With emphasis on the working-days (WD) LD rate schedules, the objectives of this work are to characterize the LD rate schedules across the states and to model a formula(s) that would represent the relationship between the WD LD rates and the contract amounts. The data set for the work represents the LD schedules in the standard specifications of all departments of transportation in the United States. Descriptive and cluster statistical analyses were used for the LD rate characterization. For model development, several linear and nonlinear regression models were employed. The results highlighted considerable LDs variability in the smaller contract sizes and exceptional LD rates stability in the larger sizes. Despite the economic differences among the states, it is found that the LD rate is, on average, 0.02 ¢/$ for projects $20 million or above. Below that, the rate increases between 0.03 ¢/$ and 0.18 ¢/$ until the contracts reach $750,000. LD rates tend to decrease sharply with the increase in contract sizes, forming an L or reverse J shape. This pattern proved complex, and only nonlinear regression with transformed variables successfully modeled it. Credible models were obtained after satisfying the least-squares regression assumptions. The work contributes to the BOK by adding a new statistical dimension to understanding LDs and developing regression model(s) that explain the relationships between the LD rates and the contract sizes. The work should help SHAs create, evaluate, and justify their LD rates. [ABSTRACT FROM AUTHOR]