A multi layer railway embankment consists of an upper ballast rock layer over the top of a sub-ballast layer. The foundation soil is a highly frost susceptible clay/silt which will cause frost heave problems if the freezing front is allowed to penetrate into it. Thermal properties of the three materials are given in the table below. The air freezing index is 1000C-days, the mean annual ground surface temperature is 5C, and the length of the freeze season is 120 days. Find the thickness of the sub-ballast layer, D, required in order to ensure that the freeze depth does not penetrate into the clay/silt layer. Use the Modified Berggren Equation. Note: you are already given all the thermal properties of these soils. For this solution, do not worry about using the average C and L for determination of the value for layer D (your welcome to if you would like for comparison, but it is an iterative process as outlined in TM-5-852-6). For your solution, for layer D, just use the Cavg and Lv given for layer D in the table below. This simplifies the process. You will use the partial index approach to solve for thickness D. (solution: ~1.17m (layer D))

Material Ballast Sub-ballast Clay/silt Thermal Conductivity, kavg 0.45 W/mC 1.4 W/mC 1.7 W/mc Specific Heat, Cavg 1675 kJ/m3c 2150 kJ/m3c 3250 kJ/m3C Latent Heat, Lv 4673 kJ/m3 14349 kJ/m 195000 kJ/m Jo.5m Ballast layer Sub-ballast layer Clay/silt foundation soil Material Ballast Sub-ballast Clay/silt Thermal Conductivity, kavg 0.45 W/mC 1.4 W/mC 1.7 W/mc Specific Heat, Cavg 1675 kJ/m3c 2150 kJ/m3c 3250 kJ/m3C Latent Heat, Lv 4673 kJ/m3 14349 kJ/m 195000 kJ/m Jo.5m Ballast layer Sub-ballast layer Clay/silt foundation soil