Consolidation and restoration interventions on the Tower of Pisa: Interpretation and geotechnical analysis*
Few monuments have been studied as much by the engineers as the Leaning Tower of Pisa. Constructed over a period of roughly two hundred years (1173-1370), the tower was already perilously tilting even before it was fully built. In 1990, with a total southward tilt already in the order of about 5.5 degrees (or a deviation close to 5.5 meters at the top), the tower was declared dangerous and closed to the public. No fewer than 17 committees have been formed since the construction of the tower, and the latest one is still at work trying to find the best way to correct this dangerous tilt.
This project involving four geotechnical investigators has produced the first three-dimensional finite element model ever constructed for the tower of Pisa. Previous numerical models have utilized either plane strain or axisymmetric assumptions, which unavoidably introduced unknown geometrical errors into the analyses. The goal of this project is to use the three-dimensional model to study the time-dependent behavior of the foundation subsoil. Among the factors included in the investigation are hydrodynamic lag due to fluid flow (or consolidation), and creep effects arising from the viscous behavior of an underlying soft clay deposit known locally as Pancone clay.
The modeling procedure involves a process of sequential construction using the finite element method. With this procedure, the finite elements representing the tower body are placed sequentially using the element birth option of a nonlinear finite element code called SPIN. The accompanying figure shows the finite element mesh for the tower of Pisa at end of construction. The tilting of the tower is triggered by a soft silty layer located directly below the tower foundation block, which increases in thickness in the southward direction. This geological feature has been well documented from extensive geotechnical investigations, and serves as the "imperfection" required by the numerical model to make the tower tilt.
The numerical modeling requires consideration of both material and geometric nonlinearities. The foundation subsoils are modeled using critical state soil mechanics and theory of plasticity, in which the yield surface is represented by the ellipsoid of modified Cam-Clay theory. The parameters for this model were obtained from high-quality laboratory tests conducted in Rome. The geometric nonlinearity is included in the analysis using a methodology known in continuum mechanics literature as the multiplicative decomposition of the deformation gradient. More recently, a strain localization option has been added to the finite element code to investigate bearing capacity and other related stability problems as a possible cause of continued tilting.
In July 1993, about 600 tons of lead ingots were laid on the base of the tower as a temporary stabilization measure. In June 1995 engineers began installing a concrete ring around the monument. This ring will be anchored to a layer of sand 50 meters below the ground by means of steel cables, eventually replacing the lead ingots. The present committee is now studying other remedial measures that have longer-term impact, such as electro-osmosis to alter the compactness of the soil, and subsoil earth removal which has been used on a tilting cathedral in Mexico city. The goal is not to straighten the tower completely, but just bring it to a stable tilt. Once properly calibrated, the numerical model developed in this research may be used as a tool to study the consequences of such proposed remedial measures.