How do you illustrate the various relationships that exist within a formal organizational structure of a medium construction company at site level on an organizational chart?

Try to use Social Network Analysis. It is a very useful tool to map relationships and flows between people, groups, organizations, etc. The nodes in the network are the people, groups or organizations. while the links show relationships or flows between the nodes. SNA provides both a visual and a mathematical analysis of human relationships. There are lots of software can do the analysis for you. If you need more information about SNA please check http://www.insna.org