Curvature and Bending Moments from Inclinometer Data

Bending moments in excavation support walls and deep foundations are frequently estimated using curvature derived from inclinometer surveys. The basic idea involves fitting a curve or a series of curves to the inclinometer data. The curvature is then estimated as the second difference of the displacement profile. Although many methods are available to estimate curvature, there is a lack of a consistent standard in deducing curvature from inclinometer readings. Twelve methods for estimating curvature that lend themselves well to spreadsheet or programmable calculations are reviewed. They are then applied to 60 sets of inclinometer readings obtained from a variety of walls and drilled shafts. Included are six laterally load tested drilled shafts which were monitored using both inclinometers and strain gauges. A direct comparison of curvatures from inclinometers with those from strain gauges was performed. The comparisons show that a piecewise cubic polynomial curve fitting a moving window of five successive inclinometer data points provide curvature values that are in good agreement with those from strain gauges, and is proposed as a reasonable method for estimating bending moments from inclinometer data.