A deep excavation application characterized by imprecise data and lack of adequate information is used to demonstrate the efficiency, applicability, and validity of the random set theory in combination with finite element method (RS-FEM). A case history of an anchored contiguous pile wall in overconsolidated fissured Ankara Clay constructed for supporting the 15 m deep basement excavation of a nursing house in Seyranbaglari district of Ankara is considered. Existing buildings around the excavation area necessitated a careful examination of the wall deformations and the reliability of the system as a whole. However, the geotechnical parameters of the soil had to be estimated combining the results of very limited in-situ and laboratory tests with those obtained through previous experience of finite element analyses under similar conditions, i.e., expert knowledge. Plane strain finite element analyses were then performed to predict the contiguous pile retaining wall behavior. The parameters in the random set finite element model were chosen according to sensitivity analyses. Most likely bounds of the wall horizontal deformations were compared with those obtained from inclinometer readings. As suggested by previous case histories, wall deformations were observed to fall within the lower third of the range predicted by RS-FEM.