Inclinometer Chains: A Guide to Reconstructing Structural Deformation Profiles

An inclinometer chain is a set of sensors arranged at known distances along a common axis, each of which measures the local rotation of the segment of structure it is fixed to. By summing the contributions of the individual segments, software reconstructs the deformation profile, that is, the shape assumed by the structure over time.

Although the concept is straightforward, a chain provides information that a single inclinometer cannot deliver: where deformation concentrates along a pier, at what depth a sliding surface lies within a slope, how a retaining wall flexes during an excavation.

Why a single inclinometer is often not enough

An inclinometer installed on top of a 12-meter bridge pier that reads a rotation of 0.002° provides a correct but ambiguous datum. That rotation may originate from the formation of a plastic hinge at the base of the shaft, from bending distributed along the height, from a differential settlement of the foundation that tilts the entire pier as a rigid body, or from a combination of multiple mechanisms.

The three scenarios call for different interventions and have completely different implications for the residual life of the structure. A single sensor does not distinguish between them. A chain of sensors distributed along the height returns the shape of the deformation profile instead, and makes it possible to attribute the movement to the correct mechanism.

What a chain is made of

The data collected by a chain is a vector of angles, recorded with synchronized timestamps. The common axis along which the sensors are arranged can take three main geometries.

Vertical geometry

This is the most common configuration. The chain descends into a borehole along a slope, runs up the shaft of a bridge pier, or follows the column of a tall building. The direction being measured is orthogonal to the installation axis.

Horizontal geometry

In this case the chain runs along a substantially horizontal surface: the façade of a heritage building, the extrados of an arch, the deck of a bridge. The quantity reconstructed is the differential settlement between nodes.

Curved geometry

Rarer, but useful on flying buttresses or vault intrados. It only applies if the segment between two successive sensors can be considered straight, with the curved geometry reconstructed by discretization.

The distance between sensors, commonly between 0.5 and 10 meters, depends on the spatial scale of the expected deformation phenomenon. A pier where a plastic hinge is expected to form at the base requires higher density in that area. A retaining wall with an intermediate anchor requires sensors at the anchor levels. Uniform spacing is the simplest layout to design and rarely the most effective.

Where inclinometer chains are used

Inclinometer chains appear in all major areas of structural monitoring.

Bridge piers and pylons

A vertical chain along the shaft of a reinforced concrete pier distinguishes between flexural deformation, rigid foundation rotation and the formation of plastic hinges. On bridges classified as High Attention under the CSLP Bridge Guidelines, the chain is one of the most effective tools to capture the slow evolution of foundation settlements before damage becomes visible.

Retaining walls and deep excavations

During an excavation adjacent to existing buildings, a chain installed in the retaining wall makes it possible to follow the deformation of the support system in real time. The chain shows whether the wall is bending toward the excavation, rotating at the top or yielding as a rigid block. It is essential information for site safety and for managing claims with the adjacent stakeholders.

Slopes and unstable hillsides

A chain lowered into a borehole through an active slope makes it possible to locate the depth of the sliding surface. A single inclinometer reveals that the slope is moving but not at which depth. With a chain, the yielding layer can be identified and stabilization works can be designed accordingly.

Heritage and monumental buildings

A horizontal chain on the façade of a church, a historic palazzo or a tower makes it possible to monitor differential foundation settlements. On rigid and brittle structures, these settlements produce crack patterns that only become visible once the structural damage is already underway.

Tall buildings and vertical structures

On the columns of multi-story buildings, the vertical chain is used to monitor verticality during construction, post-seismic residual drift and seasonal thermal deformations.

Tunnels and underground works

In tunnels, shafts and chambers, chains measure lining convergence, the rotation of portal structures and the settlement of the buildings above during TBM advance.

How the deformation profile is reconstructed

The calculation principle is simple. Each sensor measures an angle. That angle, multiplied by the length of the structural segment the sensor is associated with, provides a relative horizontal displacement between the ends of the segment. By summing segment by segment, starting from a reference node, the position of every point along the chain is reconstructed.

The reference node is the point where integration starts and whose displacement is assumed known, typically zero. For a chain in a borehole, the reference is the bottom of the hole, assumed to be anchored in stable rock. For a chain on a bridge pier it can be the base, if the foundation is considered fixed, or the top, if the crown is considered stationary. The choice of reference is an engineering decision and changes the meaning of the reconstructed profile.

When the reference is not truly fixed, the reconstructed profile is relative, not absolute. To obtain absolute displacements, the chain must be paired with an independent external anchor, such as a GNSS station or a topographic benchmark.

The deformation profile chart and what it shows

The output of a chain is a two-dimensional chart. One axis carries the position along the structure, that is, the elevation of each sensor along the chain axis. The other axis carries the reconstructed horizontal displacement. For each time instant, one curve is obtained, and the animation of the curves over time returns the evolution of the deformation profile.

The shape of the curve describes the mechanism. A linear profile indicates a rigid rotation of the element. A curvilinear profile indicates distributed bending along the height. A sharp inflection point indicates a localized stress concentration, typically a plastic hinge in the structure or a sliding surface in the ground. A rigid offset between two portions of the profile indicates a structural or geotechnical discontinuity.

Comparing profiles at successive instants returns the incremental deformation, that is, how much the deformation profile has changed within a defined interval. Overlaying the deformation profile on environmental data (temperature, rainfall, seismic events, construction phases) separates the contribution of the different drivers, distinguishing for example a reversible thermal deformation from a progressive mechanical one. It is this passage, from local rotation to deformation profile and from deformation profile to mechanism, that turns the raw data into decision-grade information.

The MyMove Tiltmeter Chain Tool

Move Solutions has developed the Tiltmeter Chain Tool, a module of the MyMove platform that automates the deformation profile pipeline starting from the data of Move inclinometer chains. The module handles segmental integration from the configured reference node, timestamp synchronization across the sensors of the chain, the animated representation of the deformation profile over time and the segment-by-segment differential analysis used to identify anomalous concentrations of rotation.

The underlying logic is the same that manual in-hole inclinometers have applied for decades: discretize the structure into elements, associate the measured angle with each element, sum the displacements. What changes is that the reading happens continuously and remotely, instead of once a month with an operator in the field.

What a chain does not measure

A chain reconstructs the deformation profile along an axis. It does not capture rotation components outside that axis, unless biaxial inclinometers are used together with an adequate analysis. It does not capture uniform settlement of the entire structure: if everything lowers in the same way, the segments remain parallel to themselves and the sum of the rotations remains zero. It does not capture fast dynamic phenomena, such as the seismic response or the passage of a train, because the typical sampling rate of chains is in the minutes, not in the milliseconds.

In a complete monitoring campaign, an inclinometer chain works alongside accelerometers for the dynamic response, environmental sensors to separate thermal effects from mechanical ones and, where the nature of the phenomenon requires it, an external topographic reference to remove the ambiguity of the fixed point. The strength of the chain lies in its ability to return a spatial view of the deformation along an axis. Its weakness is that it remains a one-dimensional projection of a phenomenon that is three-dimensional in reality.

The ongoing developments on wireless MEMS sensors, from the extension of battery life to the improvement of thermal compensation, are gradually moving the applicability threshold of chains toward slower phenomena and larger structures. It is in this space that the next generation of structural monitoring campaigns will be decided.