In laying water mains, utilities must be concerned with the possibility of freezing during cold periods. although the problem of determining the temperature in soil as a function of time is complicated by changing surface conditions, reasonable estimates can be based on the assumption of a constant surface temperature over a prolonged period of cold weather.

what minimum burial depth x would you recommend to avoid freezing under conditions for which soil, initially at uniform temperature of 20 oc, is subjected to a constant surface temperature of -15 oc for 60 days?