Deformation Surveys and Analysis

Introduction
Measurements
Processing
Testing
Error Ellipses And Residuals
References

Introduction

Applications of deformation surveys include:
- Dam walls - earth and concrete
- Bridges
- Buildings
- Earth movements, for example continental drift, or subsidence as a result of mining
There can be considerable cost (human and $) for failing to detect deformations, and/or interpret them accordingly. Failure of the Teton dam in Idaho, 1977, killed 11, left 2500 homeless and resulted in $400 million in claims.
Besides the monitoring of engineering type structures other deformations to be aware of include (Krakivsky, 1986):
- Tidal effects - the earth's crust can deform by as much as 0.5m, although this happens uniformly over a large area.
- Crustal loading - caused by natural phenomena such as glacial advance and retreat, siltation in river basins, or with human intervention the draining/filling of lakes.
- Plate tectonics - tectonic plate drift is of the order of a few cm per annum, although violent earthquakes can cause deformation of metres
- Ground consolidation - especially due to the extraction of oil/gas or artesian water
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Measurements

High precision networks use survey equipment such as first order theodolites, precise levelling, Mekometer EDM and GPS translocation in order to detect the movement of survey stations or targets. Photogrammetry can be an effective tool for deformation monitoring depending on the scale of the object being measured.
Besides convention survey measurements other geotechnical measurements can be made (Chrzanowski, 1986):
- The physical properties of the structure
- Loads and internal stresses
- Dimensional changes
Instruments including extensometers, strainmeters, laser rangers, and tiltmeters are used. These intruments are extremely sensitive. Ideally all observations strutural/geotechnical/survey should be incorporated into the one adjustment model.
The gravity field may be considered in precise engineering surveys (integrated geodesy/least squares collocation). This is particularly important in large structural projects where newly introduced loads significantly distort the gravity field locally.
GPS is useful especially for long connections to stable ground. It has been successfully used in deformation monitoring of structures such as dams.
GPS also does not require a clear line of sight
In some cases, eg a steep dam wall, GPS may be unsuitable due to poor satellite visibility/geometry, and multi-pathing.

Processing

The adjustment of such survey networks require all the considerations with respect to elimination of errors and the correct estimation of measurement precisions.

Any deformation survey must pay particular attention to errors in the survey so that gross or systematic errors do not contaminate the detection of movements and produce false results (eg is the dam about to fail or did you forget to correct for the EDM index error?)

Certain field techniques and procedures can be applied:
- Forced centring - eliminates errors from multiple instrument/target setups, especially between epochs.
- Repeated measurements
- Simultaneous measurements
- Corrections for trunion axis tilt (in many cases small zenith distances will be encountered)
- Advancing theodolite circles, etc.
It is also important to determine in advance whether absolute or relative movement is important as the former will require an absolute datum to be defined outside the area of expected movement.

If only change in shape is important (eg bridge sag) then a minimal constraint or free network solution can be used to avoid any influence from external constraints. As in the diagram there is no survey connection to stable control.

If a block shift or rotation is important as well (eg dam deformation), then connections must be made to survey stations which are sited in stable areas to provide the required absolute datum. Often stable ground may be considerable distance away from the area being surveyed for deformation.

Surveys for deformation are generally repeated at certain time intervals (measurement epochs). The time interval depends on the expected movement / settlement of the structure and the risk to life.
Generally stations and targets are put in place and suitable field procedures established. The established procedure is repeated at each epoch to minimise systematic and gross errors
Each of these repeated network surveys is known as an epoch of measurement, so the comparison and analysis of the results of the repeated surveys is commonly known as epoch testing
Some structures deform at such a rate that the deformation must be modelled during the time taken to perform a measurement epoch.

Testing

The essence of epoch testing is to determine whether the differences between the coordinates from two different epochs are statistically significant
Epoch testing must take into account the precisions of the coordinates, as well as the correlations between both the coordinates of individual stations and coordinates of different stations hence the full weight coefficient matrices from each epoch contribute as follows :

Epoch 1:
x₁ station coordinates vector
Q₁ weight coefficient matrix

Epoch 2:
x₂ station coordinates vector
Q₂ weight coefficient matrix

and the differences in the coordinates and the associated weight coefficients are:

d = x₂ - x₁

Q_d = Q₁ + Q₂
If free networks are employed then there should be a 6 or 7 parameter transformation applied, to fit epoch 2 to epoch 1, using all points in the network
The first test conducted should always be the global congruency test : analogous to the global test for a single network
The quantity W = d^t Q_d^-1 d is tested against a Fisher statistic at an appropriate confidence level, if W passes then there has been no (statistically significant) movement and the networks are congruent
If W fails the global congruency test then each point must be assessed by a local test which compares the contribution to W of the point against a Fisher critical value : analogous to the local testing of residuals for a single network.

This test is done by recalculating W without each point in turn
The worst point (smallest W value) is rejected and the entire testing process repeated, including the transformation for free networks (without the rejected points, which are now considered to have moved) and the global congruency test
Once the global congruency test passes, all those points which have been rejected are considered to have moved whilst those that are still contributing to W are considered to be stable
It is not unusual to test groups of points (eg centre of the dam wall) and to amalgamate the survey data for stable points over two or more epochs
A good rule of thumb is that the point precisions from the survey should be at least six times (preferably ten times!) smaller than the expected magnitudes of the movement in order to confidently detect the unstable points
Where several epochs of data (usually > 3) are available a kinematic or dynamic model for the epochs can be formed. A kinematic model only considers the movements of the system without regard to their cause - a dynamic model also models the movement, but considers the forces causing the movement.

Error Ellipses and Residuals

Graphical representations of deformation analyses are often shown as error ellipses (95% or some other confidence interval - not the standard error ellipse) with vectors of movement - differences between measurement epochs. Example.
The visual representation is useful for empirical checking and for the identification of the characteristics of any movement. Examples with trends in residuals.
3D and multi-epoch representations are possible with CAD systems.

References

Chrzanowski, A., 1986. Geotechnical and other Non_Geodetic Methods in Deformation Measurements. Proceedings Deformation Measurements Workshop Modern Methodology in Precise Engineering and Deformation Surveys II. Bock, Y. (Ed.), Massachusetts, U.S.A., October 31 - November 1, 1986. Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Massachusetts, U.S.A., pp. 112 - 153.