Predictive Modeling of Freezing and Thawing of Frost-Susceptible Soils
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PREDICTIVE MODELING OF FREEZING AND THAWING OF FROST-SUSCEPTIBLE SOILS Final Report Report Number: RC-1619 Michigan Department of Transportation Office of Research Administration 8885 Ricks Road Lansing, MI 48909 By Gilbert Baladi and Pegah Rajaei Michigan State University Department of Civil & Environmental Engineering 3546 Engineering Building East Lansing, MI 48824 September 2015 Technical Report Documentation Page 1. Report No. 2. Government Accession No. 3. MDOT Project Manager RC-1619 N/A Richard Endres 4. Title and Subtitle 5. Report Date Predictive Modeling of Freezing and Thawing of Frost- September 2015 Susceptible Soils 6. Performing Organization Code N/A 7. Author(s) 8. Performing Org. Report No. Gilbert Baladi and Pegah Rajaei N/A Michigan State University Department of Civil and Environmental Engineering 9. Performing Organization Name and Address 10. Work Unit No. (TRAIS) Michigan State University N/A Department of Civil and Environmental Engineering 3546 Engineering 11. Contract No. East Lansing, Michigan 48824 2010-0294 11(a). Authorization No. Z9 12. Sponsoring Agency Name and Address 13. Type of Report & Period Covered Michigan Department of Transportation Final Report Research Administration 10/01/12 to 9/30/15 8885 Ricks Rd. P.O. Box 30049 14. Sponsoring Agency Code Lansing MI 48909 N/A 15. Supplementary Notes 16. Abstract Frost depth is an essential factor in design of various transportation infrastructures. In frost susceptible soils, as soils freezes, water migrates through the soil voids below the freezing line towards the freezing front and causes excessive heave. The excessive heave can cause instability issues in the structure, therefore predicting the frost depth and resulting frost heave accurately can play a major role in the design. The objectives of this study are to develop accurate and reliable models for predicting frost depths and frost heave and to estimate the resulting heave pressure. The frost depth model was developed and verified using data from MDOT and Minnesota DOT. The frost heave model was also developed and verified using the available MDOT data. 17. Key Words 18. Distribution Statement Heat Transfer, Thermal Conductivity, Cumulative No restrictions. This document is available Freezing Index, Frost Depth, Analytical Models, to the public through the Michigan Empirical Models, Frost Heave, , Heave Pressure, Frost Department of Transportation. Heave and Frost Depth Field Data 19. Security Classification - report 20. Security Classification - page 21. No. of Pages 22. Price Unclassified Unclassified N/A ii Acknowledgement The authors like to thank the Michigan Department of Transportation (MDOT) for the financial support and the MDOT staff for their cooperation and for providing soil samples and the soil temperature data. In addition the authors gratefully acknowledge the Minnesota Department of Transportation (MNDOT) for providing the soil temperature data and for its assistance. Research Report Disclaimer “This publication is disseminated in the interest of information exchange. The Michigan Department of Transportation (hereinafter referred to as MDOT) expressly disclaims any liability, of any kind, or for any reason, that might otherwise arise out of any use of this publication or the information or data provided in the publication. MDOT further disclaims any responsibility for typographical errors or accuracy of the information provided or contained within this information. MDOT makes no warranties or representations whatsoever regarding the quality, content, completeness, suitability, adequacy, sequence, accuracy or timeliness of the information and data provided, or that the contents represent standards, specifications, or regulations.” iii Table of Contents Chapter 1 - Introduction .................................................................................................................. 1 1.1 Problem Statement ........................................................................................................... 1 1.2 Study Objectives .............................................................................................................. 1 1.3 Research Plan ................................................................................................................... 2 1.4 Organization of this Report .............................................................................................. 3 Chapter 2 - Literature Review ......................................................................................................... 4 2.1 Frost Depth ....................................................................................................................... 4 2.1.1 Numerical Models .............................................................................................................. 4 2.1.2 Mechanistic Empirical Models ......................................................................................... 6 2.1.3 Empirical Models ............................................................................................................. 11 2.2 Frost Heave .................................................................................................................... 12 2.2.1 Capillary Theory ............................................................................................................... 13 2.2.2 Frozen Fringe Theory ...................................................................................................... 17 2.2.3 Frost Pressure .................................................................................................................... 32 2.3 Thaw Depth and Seasonal Load Restrictions ................................................................. 34 2.3.1 Thaw Depth ....................................................................................................................... 34 2.3.2 Seasonal Load Restriction ............................................................................................... 36 Chapter 3 - Data Mining ............................................................................................................... 40 3.1 Data Base........................................................................................................................ 40 3.2 Frost Depth Data ............................................................................................................ 40 3.2.1 The State of Michigan...................................................................................................... 40 3.2.2 The State of Minnesota .................................................................................................... 46 3.3 Soil Properties Data ........................................................................................................ 46 3.4 Frost Heave Data ............................................................................................................ 48 Chapter 4 - Analysis and Discussion of Frost Depth and Frost Heave ......................................... 51 4.1 Introduction .................................................................................................................... 51 4.2 UNSAT-H Model........................................................................................................... 51 4.3 Freezing Index and Freezing Degree Day Calculation .................................................. 53 4.3.1 Minnesota Cumulative Freezing Degree Day ......................................................... 53 4.3.2 Boyd Cumulative Freezing Degree Day .................................................................. 54 iv 4.4 Existing Frost Depth Prediction Models ........................................................................ 56 4.4.1 Stefan Equation..................................................................................................... 56 4.4.2 Modified Berggren Equation ................................................................................. 57 4.4.3 Chisholm and Phang Equation .............................................................................. 63 4.5 Empirical Models ........................................................................................................... 65 4.6 Thaw Depth .................................................................................................................... 79 4.6.1 Calculation of Cumulative Thawing Degree day (CTDD) .................................... 79 4.6.2 Nixon and McRoberts Equation ............................................................................ 79 4.7 Frost Heave .................................................................................................................... 79 4.7.1 Frost Heave Mitigation .......................................................................................... 86 4.7.2 Gilpin Frost Heave Model ..................................................................................... 92 4.7.3 Revised Frost Heave Model .................................................................................. 96 4.7.4 Discussion of the Results of the Revised Frost Heave Model ............................... 97 4.7.5 Heave Pressure .................................................................................................... 104 Chapter 5 - Conclusions .............................................................................................................. 108 5.1 Summary .....................................................................................................................