There are two good sources for designing frost-protected shallow foundations (FPSFs): The National Association of Home Builders (NAHB) Research Center's Revised Builder's Guide to Frost Protected Shallow Foundations has basic information and offers a simplified FPSF design method for heated buildings that avoids crunching numbers, as well as a detailed design method for those who want to dig deeper. The American Society of Civil Engineers' publication, Design and Construction of Frost-Protected Shallow Foundations, offers greater detail. Both publications provide maps, tables, and charts necessary for the calculations.
The calculations below are for the sloped-site monolithic slab described in the article and follow the steps described in the NAHB's detailed method. The tables referenced are from NAHB's Builder's Guide (PDF).
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