Samsul,

Ahhhh, buried pipelines. I was thinking of above ground piping systems in my mentions of "virtual anchors". Well, of course if you have a few changes in direction in a buried system it is a little easier to make "educated assumptions" about locating points of zero movement. In long lengths of straight pipe there are more uncertainties. Too many variables to be certain of very much. The friction of the piping interface with the soil is problematical at best (assumptions about soil compaction are no better). The best you can do is try to learn something about the mechanics of the soil-to-pipe interface by observation of the movements of existing systems at the same site. Then it becomes a matter of engineering judgment.

That answer does not please me but I must say if there is a better answer it has evaded me for 45 years. Sorry.

Regards, John