Form Approved
REPORT DOCUMENTATION PAGE
OMB No. 0704-0188
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1. AGENCY USE ONLY (Leave blank)
2. REPORT DATE
3. REPORT TYPE AND DATES COVERED
April 1999
4. TITLE AND SUBTITLE
5. FUNDING NUMBERS
Traveling Wave Solutions to the Problem of Soil Freezing
DA Project AT24-SC-F01
Described by a Model Called M1
6. AUTHORS
Yoshisuke Nakano
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
8. PERFORMING ORGANIZATION
REPORT NUMBER
U.S. Army Cold Regions Research and Engineering Laboratory
72 Lyme Road
CRREL Report 99-5
Hanover, New Hampshire 03755-1290
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)
10. SPONSORING/MONITORING
AGENCY REPORT NUMBER
Office of the Chief of Engineers
Washington, D.C. 20314-1000
For conversion of SI units to non-SI units of measurement consult Standard Practice for Use of the
11. SUPPLEMENTARY NOTES
International System of Units (SI), ASTM Standard E380-93, published by the American Society for Testing and Materials, 100 Barr
Harbor Drive, West Conshohocken, Pa. 19428-2959.
12a. DISTRIBUTION/AVAILABILITY STATEMENT
12b. DISTRIBUTION CODE
Approved for public release; distribution is unlimited.
Available from NTIS, Springfield, Virginia 22161.
13. ABSTRACT (Maximum 200 words)
The scientific study of soil freezing began in the early 1900s and an accurate mathematical description of the
freezing process has been sought for nearly 80 years. Despite numerous publications on the subject, there is as
yet no clear consensus on the mathematical model of soil freezing. In this report a mathematical model called
M1is presented. The existence of traveling wave solutions to the problem is shown. For a given fine-grained soil,
such solutions are shown to exhibit three distinct behaviors depending on given thermal and hydraulic condi-
tions. When a frost front (0C isotherm) advances, water is either attracted to the front or expelled from it. Under
certain conditions an ice layer containing hardly any soil particles grows. The report describes how the traveling
wave solutions have been used for the empirical verification of M1.
14. SUBJECT TERMS
15. NUMBER OF PAGES
41
Frost heave
Soil water expulsion
Ice segregation
Traveling wave solutions
16. PRICE CODE
Soil freezing
17. SECURITY CLASSIFICATION
18. SECURITY CLASSIFICATION
19. SECURITY CLASSIFICATION
20. LIMITATION OF ABSTRACT
OF REPORT
OF THIS PAGE
OF ABSTRACT
UNCLASSIFIED
UNCLASSIFIED
UNCLASSIFIED
UL
Standard Form 298 (Rev. 2-89)
NSN 7540-01-280-5500
Prescribed by ANSI Std. Z39-18
to Contents
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