Mr. XU has a valid point.

Peng's 1978 paper provides formulations to calculate the soil spring function for the longitudinal-axial direction and tranverse-lateral directions only. In addition, Peng's formalations are outdated, and more recent and comprehensive formulations for soil restraint springs appear in the technical literiture regarding the soil-buried pipeline interaction.

The formulations for the vertical uplift and vertical bearing soil springs are not covered in Peng's 1978 paper. The reader will need to refer to subsequent more updated publications for these soil restraint functions (i.e. Nyman, Trautman, Luscher). The American Pipeline Alliance (ASCE) has a good paper summarizing this information.

Since CAESAR II does not have the capability to generate these vertical uplift and vertical bearing soil spring funtions properly, these need to be User specified in accordance with the criteria provided by the referenced authors.

CAESAR II does need to be upgraded with respect to this information.