Freeze-thaw depth prediction with constrained optimization for spring load restriction

Document Type


Publication Date



Department of Civil, Environmental, and Geospatial Engineering


Spring Load Restriction (SLR) policies have been widely implemented in many countries to reduce the cost of road repair for freeze-thaw induced damages in cold regions occurring in the spring thawing season. In most SLR policies, accurate predictions of the Freezing Depth (FD) and Thawing Depth (TD) are very critical because both FD and TD directly determine the dates for the SLR initiation and removal. In this study, we propose a new constrained optimization approach to predict FD and TD and evaluate this approach for making SLR decisions with field measurements collected at four sites during two adjacent year cycles. The evaluation results showed that constrained optimization can not only accurately predict FD and TD with a determination coefficient of higher than 0.91 for most sites, but enable FD to meet TD in the thawing season for accurate SLR-decision making, which, however, cannot be achieved using non-constrained optimization widely adopted in the literature. We also discuss the accuracy of using a Thawing Index (TI)/Freezing Index (FI) ratio of 0.3 that still has been used by several agencies in the U.S. to determine the removal date of SLR. Our results indicated that on the true SLR removal dates, a TI/FI ratio is not equal even close to 0.3 for most sites. By comparison, a TI/FI ratio of 0.3 will be less accurate than the FD and TD prediction model for SLR decision-making. The methodology reported in this study is easy to use and implement for road engineers and the insights will help make accurate SLR decisions to prevent roads in cold regions from freeze-thaw induced damages.

Publisher's Statement

© 2020 Elsevier Ltd. Publisher’s version of record: https://doi.org/10.1016/j.trgeo.2020.100419

Publication Title

Transportation Geotechnics