Monitoring Deformations of Structures · 2017-09-10 · l J. P. ERLANDSON U. S. Army Corps ofEngineers Seattle, WA 98134 S. A. VERESS, D.Sc. University ofWashington Seattle, WA 98195

l J. P. ERLANDSON

U. S. Army Corps of EngineersSeattle, WA 98134S. A. VERESS, D.Sc.

University of WashingtonSeattle, WA 98195

Monitoring Deformations ofStructu res*

The procedures for determining deformations of structures,employing terrestrial cameras and analytical photogrammetry,are presented.

INTRODUCTION

I n 1970 the U. S. Army Corps of Engineers, Seattle District, realizing the practicaland economical potential ofanalytical photogrammetry as applied to monitoring structural

deformations, instituted several projects under the General Investigation Studies.The theoretical portions of these studies were formulated by S. A. Veress, D.Sc., as consul­

tant. J. P. Erlandson of the Engineering Division was responsible for the organization andpractical evaluation of this project. J. C. Peterson of the Automatic Data Processing Center,Seattle District Corps of Engineers, wrote the computer program and assumed generalresponsibility for the data processing (which will be the subject ofan additional presentation).

ABSTRACT: A mathematical model has been established for photo­grammetric measurement of structural deformations. The model ad­justs simultaneously ground-measured orientation elements andphotogrammetrically obtained plate coordinates by means of leastsquares. The computed variance and covariance matrices are used todetect errors as well as to show the interaction between variables. Acomputer-generated structure is used to establish standards forground and photogrammetric measurements. This generated struc­ture gives a guideline for the procedure offield measurements. Thesystem has achieved a high degree of accuracy and is capable ofaccepting five convergent photographs taken from terrestrial or aer­ial stations with 100 per cent overlap.

THE NEED FOR MONITORING

The general need for monitoring large structures is well known to the general public as wellas engineers due to the loss ofhuman lives in various countries when large structures fail. Thisneed further must be emphasized by the frequent danger of slide areas that cause extensiveproperty damage and disruption of general communications. Present methods of detectingand monitoring structural deformations and motions of slide areas can be divided into twobasic groups: internal and external.

Internal or subsurface methods generally utilize sophisticated instruments such as exten­someters, inclinometers, strain gauges, rock noise listening devices, settlement monuments

• Invited paper, International Symposium on Close Range Photogrammetric Systems, University ofIllinois, August 1975.

PHOTOGRAMMETRIC ENGINEERING AND REMOTE SENSING,

Vol. 41, No. 11, November 1975, pp. 1375-1384.1375

1376 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1975·1

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for monitoring movement, etc. The common characteristics of most of these devices are thatthey provide no more than one, or in some cases two, dimensional information and that they Imust be installed during construction. These instruments are reliable and relatively accurate; ~however, some of them are expensive to maintain and the large amount of data supplied by Ithem is difficult to interpret.

Because of these problems, the internal monitoring systems must be accompanied byexternal monitoring methods. External or surface methods utilize conventional field surveysfor obtaining measurements of movement. These external measurements, when combinedwith internal measurements, furnish the stress history ofthe structure. From knowledge ofthecomplete behavior of the structure, possible failure can be predicted in time and thus beprevented.

The external monitoring system consists of classical triangulation of monuments along thestructure, with accompanying measurements by conventional or electronic survey. There arelarge numbers of targets placed on the surface ofthe structure whose positions are determinedfrom the triangulation monuments. This survey is repeated in predetermined time intervals,and positions of the targets at each time are compared to quantify the deformations. Thissurvey is considerably time consuming because of individual observation required of eachtarget on the structure. Thus the system is point-dependent. A complete survey of a largerstructure may take more than two weeks. During this time deformation can occur, but wouldbe undetected.

METHODOLOGY

The photogrammetric system described is a surface monitoring method that basicallyeli minates some of the disadvantages of the classical field survey. It consists ofphotographingsuspect movement areas at regular intervals and measuring the coordinates of targets. Therelative displacement of these targets can then be determined by computational processes.

The photographs are made with a modified Wild BC-4 ballastic camera with a 305 mm focallength f 2.8 Astrotar lens. The modification of this ballastic camera to a phototheodolite hasbeen reported2 . The instrument used in the survey is shown by Figure 1. Convergentphotographs of the structure are taken from three to five camera stations depending on therequired accuracy and the geography of the terrain. These photographs are taken with 100 percent overlap.

The camera stations are connected with base lines which are permanently monumentedand precisely measured by means of electronic surveying. The standard error of these meas­urements is ±0.003 ft (1 mm) accomplished by repeated measurements. The BC-4 camera hasan adapter plate which replaces the photographic plate holder and houses an eye-piece. Thisenables the camera cone with its objective to be used as a telescope. The orientation angles ofthe photographs are 1> around the vertical axis and W around the horizontal axis. These anglesare measured employing the T-4 base, whose least reading is 1110 ofone second. The K angle ismeasured by striding level as shown in Figure 1. The photographs are made on Kodak 215 mmby 190 mm microflat spectroscopic type IVF glass plates which are 6 mm thick. The emulsionis high-contrast fine-grain with 200 lines-per-millimeter and ASA 20 sensitivity when de­veloped in Kodak D-76 developer for ten minutes. The photo-coordinates of the images of thetargets are at present measured in a Wild A-7 autograph used as a mono-comparator. Theaverage standard error of photo-coordinate measurement is ± 4.6 micrometers.

The general flow diagram of the mathematical data reduction is given in Figure 2.Due to the fact that the absolute position of points is not required for monitoring structural

deformations, the reduction of the plate coordinates is simplified. This simplification further isjustified by the fact that the exterior orientation elements of the camera at various stationsremains the same after subsequent photography. The reduction of the plate coordinatesconsists of a similarity transformation based on the collimation marks located at the corners ofthe photographs.

The computation of station coordinates consists in determining the ground coordinates ofthe front nodal point of the objective. The formulas accomplishing this task are

XOj

=XRi

+ EGh sin cP. cos Wi

YOi = YRj -- EGh

cos 1>, cos Wi

Zoo = Zp. + EGv sin WiI I

MONITORING DEFORMATIONS OF STRUCTURES 1377

FIG. 1. Modified BC-4 camera.

Reduction of PlateCoordinates

Computation ofStation Coordinates

I

Computation OrientationMatrix and Approximate

Coordinates

Formation of CombinedObservation &Condition

Equation

Solution of NormalEquations

I

Computation ofStandard Errors

Analysis

FIG. 2. Flow diagram of data reduction.

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where XRj , YRj, and ZPj are the coordinates of the rotational center of the camera at station "i"and EG is the eccentricity constant in the horizontal and vertical direction. For the BC-4cameraEG" and EGo are equal. The geometrical concept of these equations has been reported4 .

The final coordinates of the targeted points "i" on the structure are considered as

X j =Xo + t::.X

Yj = Yo + ~Y

In this equation Xo, Yo, and Zo are the approximate coordinates and t::.X, ~Y, and ~ are thedifferences which are determined by least-squares adjustments. To compute the Xo, Yo, and Zoapproximate coordinates, first the orientation matrix, M, for the camera stations can be ob­tained. The orientation matrix is formed from the <Pi Wi, and Kj orientations.

The M matrix is

(3)

This orientation matrix takes into account that the K angle is measured with the striding leveland thus is set equal to zero.

There are several possibilities for computing the approximate coordinates of points in theobject space. The method used here is a general one equally applicable to aerial and terrestrialphotographs, because this terrestrial photogrammetric method will be combined with aerialphotogrammetry at a later date.

The geometric outline of the problem is exhibited in Figure 3. The equation ofthe line fromcamera station OJ to point P in the object space in general notation is

Xo - X o;

cos XOjPYo - Yo; Zo - YOj

cos YOiP cos ZO;P (4)

1378 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1975

FIG. 3. General Geometry.

The direction cosines are defined as

( -Xi) G-Yj ) ( f )cos YOjP = m2I OiP + m22 OiP + m23 O-;P

where

Solving equation 4 for theXo• Yo. andZoapproximate coordinates from camera stations i andj,the working equations are

____1 (x _X + Y cos XOiP _ Y cos XOl)cos ZOjP cos XOjP OJ OJ OJ cos YOiP OJ cos YOjPcos YOjP cos YOjP

Xo = (Yo - YOj

) cos XO;P + XOjcos YOjP

(Y ) COSZOiP

Zo = Yo - °i cos YOiP + Zoi (5)

The general theory of the least-squares adjustment method of the formation of combinedobservation and condition equations is described in various publications together with thenomenclature9 • Here, therefore, only an outline of the theory will be given. The purpose ofthis least-squares adjustment is to determine the to(, .:lY, and .:lZ in equation 2 and thecorrections to the measured quantities; that is, the V Xj and V Yi of measured plate coordinates;Vw;, V<I>; and V K of exterior orientation elements; and the corrections to the "i" camera stationsvXp vYj> and vzi •

The combined observations in condition form are

-f MIX = 0Xi MsX

MONITORING DEFORMATIONS OF STRUCTURES

The orientation matrix is regarded as

and the X matrix is

1379

(6)

TheX o, Yo, andZo coordinates are the approximate coordinates ofpoints to be determined. TheXo;, YOi. and ZOi are measured coordinates of the camera station "('.

By using the conventional symbols equation 6 can be written in detailed form as

m ll (Xo - X o;)+ m l2()To - Yo)+ mla(Zo - Z,,;)Xi - f , ---= -W;l

mal(Xo - Xo)+ ma2(10 - Yo)+ maa(Zo - Zo)(7a)

Let the above equations be noted in function form as

X; - F 1 (X o. Yo, Zo) = Wil

(7b)y; - F 2 (X o, Yo, Zo) = W;2

where the Wi'S are the misclosures. These are the result of the small accidental errors in themeasurements oforientation angles, station coordinates, and photo coordinates. These condi­tion equations are not linear functions; a linearization process must be performed. Thelinearization in this case is obtained using the Taylor series, and the resulting formulas are

oFl oFl oFlvX ; - ow V w - a;j; v¢ - OK V K

oF l oF l of 1+ oX _Vx + aY':" Vy + tYZ: Vz

0, 01 0;

(8a)

1380 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1975

or in general matrix form:

BV + AX + W = O.

In this matrix equation the Vxj and Vyi are the corrections rendered to the measured platecoordinates; the v"" v</>, and V K are the corrections to the measured orientation elements; and thevx, Vy, and Vz are the corrections to the coordinates of the "i" camera stations. The rest of theterms are readily identifiable; further, the detailed mathematical terms in the B and Amatrices are omitted from these because they can be found in a number of references3 •

The normal equations can be obtained from the combined observation and condition. Thenormal equation in matrix form is

BP-l BTK + AX + W = 0

ATK = 0

or

j

(9a)

In these equations K is the correlate matrix and P is the weight matrix.In the case of monitoring structures, the P matrix can be assumed as unity because this

assumption will remain constant during the monitoring process and, therefore, has no effecton the structural deformations to be determined. It must be noted that, ifabsolute values oftheposition ofa target on a structure are required, the above assumption should not be permitted.

The P = I matrix simplifies the normal equation to

(9b)

The above normal equation can be solved by matrix inversion; that is,

or, by separating the unknown matrices,

x = -(ATM-lA)-lATM-1Wand K = -M-l(AX + Wjwhere M = BBl'·

The standard error of unit weight can be obtained from the formula

aD = JVTVr-u

(lOa)

(lOb)

(11)

where yTy=KTW and u is the number ofunknowns. The standard errors of the observed valuesand of the parameters are computed from the following general equation:

a o = a o VQ;;;;

(12)

where

and

Qxx = [ATM-tAfl.

Having theX matrix from equations lOa or lOb the most probable values ofthe coordinates areobtained from equation 2 and their standard errors from equation 12.

MONITORING DEFORMATIONS OF STRUCTURES 1381

The analysis ofthe results can be performed in several ways. First, the spatial coordinates ofobject points obtained at various times may be compared and examined for possible motion.The photogrammetric method is not point dependent to the extent ofthe classical field survey.This permits the statistical analysis ofthe points and their standard errors. The results furthercan be analyzed with respect to the prevailing geometry at each individual point. Using thestandard errors of coordinates, the eigen values for the error ellipsoid to the individual pointsmay be computed or plotted. Finally, if one analyzes the standard errors of observed quan­tities and their corrections and discrepancies in station coordinates, small blunders in themeasurements can be detected and erroneous measurements can be rejected.

MATHEMATICAL MODEL AND SPECIFICATIONS

A computer-generated structure, which will be called a mathematical structure, has beendeveloped. This mathematical structure was used to test the computer programs and toestablish specifications for practical measurements. This mathematical structure was gener­ated so that the X, Y, and Z coordinates of four camera stations were selected. The structurewas represented by 20 points whoseX, Y, andZ coordinates also were previously determined.The orientation matrix M for each camera station was obtained by assuming values for the wand ¢ angles (K=O) and by using equation 3. In this way a complete geometry between themathematical structure, the base lines (camera stations), and the photographs was defined.

The photo coordinates for camera station "i" were determined from the following equation:

= f muM + m12~Y + m13~Xi ~

m31M + m31~Y' + m33~Z

- f m21M + m22~Y + m23~Yi - m31 M + m32~Y + m33~ (13)

These photo coordinates are mathematically correct coordinates. A number of random acci­dental errors were generated and added to the correct values which were then regarded as"observations", that is, the base lines, the orientation angles, and the photo coordinates. Theobservations having accidental errors were used for computation. The computations wereperformed in two categories: first, only individual errors were studied which gave guidance todetection of possible mistakes. The second category was used to establish specifications. Allof these computations were performed by using two focallengths,fl = 150 mm andf2 = 300mm, due to the fact that the U. S. Corps ofEngineers, Seattle District, uses Wild P-30 and WildBC-4 cameras.

The following groups of errors were examined:Base errors: ::to.005, 0.01, 0.05, and 0.10 mAngular errors: 0 to 2", 2 to 5", and 5 to 10"Photo-coordinate errors: 0 to 5/Lm and 5 to 10/Lm

The conclusion drawn from these computations is that the desirable specifications for the fieldand photogrammetric measurements are that base errors should not exceed ::to.Ol m, angularerrors should be ::t5 seconds or less, and photo-coordinate errors should not exceed ::t6"m.

If the accidental errors are larger than three times these specifications they should beconsidered mistakes and be rejected. The rejection criterion therefore is base error;;;' 0.03 m =0.10 ft, an angular error;;;' 15 seconds of arc, and an observation error;;;' 20 micrometers.

If such specifications are maintained, then the achievable accuracy in coordinates oftargeted points will be 1/100,000 of the photographic distance.

The above specifications were examined in comparison with conventional ground survey,i.e., triangulation. Several such surveys have been reported5 •6 •8 • One of the most elaboratereports in this respect is given by Richardson concerning the measured deformation behaviorof Glen Canyon Dam. The angles were measured 16 times and the maximum deviation offourseconds was used as a rejection criterion. Closures in the triangles were 1.5 seconds, and thedistance variation between the triangulation points varied between 0.011 ft and 0.047 ft (0.003m and 0.014 m).

In view of the above, the specifications were regarded as realistic and practicable. Therejection criteria for mistakes, however, should be the same as the specifications in caseswhere maximum accuracy is desirable.

The accuracy of the various coordinates is different and depends on the geometry. It was

1382 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1975 ..found that the ideal geometry is a three-or four-sided pyramid composed ofthe camera stationsand their camera axis as they intersect at the surface of the structure. The parallatic angleshould be between 60 and 90 degrees. Such a geometry will provide equal accuracy in all thethree directions of the coordinate system.

The number of overlapping photographs should be three or four. The use of a fifth camerastation will not provide the amount of accuracy increase to justify it economically.

PRACTICAL EVALUATION

The practical evaluation of the method is in an interim stage basically due to the relativelyshort time available for such evalution and that substantial changes were executed in in­strumentation and observation techniques during the past year while the Corps of Engineers,Seattle District, practiced the method on a semi-routine basis. Consequently the followingshould be regarded as an indication of the potential of the method rather than the finalconclusion of its capability.

There are three different projects now in progress with the U. S. Army Corps of Engineers,Seattle District. The Lake Washington Ship Canal Project consists ofmonitoring an apartmentbuilding for possible motion due to nearby excavation and construction. Photographs aretaken from 760 feet and repeated bimonthly. There are four camera stations. This project hasbeen surveyed with Wild P-30 and modified Wild BC-4 ballastic cameras. The survey hasbeen checked against classical field measurement and compared with coordinate differencesof repeated measurement of targeted points.

The points are permanently targeted on the structure with metal plates on which a circular­shaped target is induced photographically. The size of these targets is determined individu­ally for each project in order to obtain the required accuracy. The target design is veryimportant in reduction of pointing error; therefore, the Seattle District is presently experi­menting with employment of spherical targets in order to replace the existing circular targetswhich are not ideal for convergent photography.

A recent slide area at the Mud Mountain Project is being monitored from a photographicdistance of 1300 feet. The area is photographed four times a year, concentrating in the fall andspring. Figure 4 shows the aerial photographs of the slide area and Figure 5 those made fromone of the five camera stations and taken by the BC-4 camera.

The largest area is at the Chief Joseph Project which is a potential slide area. It is approxi­mately one mile wide and four miles long and photographs from several camera stations aremade only once a year.

From these projects the following general analysis can be drawn:

The method as such is a flexible general method and is capable of monitoring structuraldeformations. The average residual coordinate errors are 1/50,000 of the photographicdistance. The best achieved on a routine basis is 1/94,000.

The Wild P-30 camera, after pedestal modification, is capable of performing photogram­metric structural surveys having a photographic distance of about 500 feet. If the photo­graphic distance is more than 800 feet, the BC-4 camera is recommended. This conclusionalso has been confirmed by computer simulation of the mathematical structure.

The measurement of orientation elements specified by the mathematical model for theP-30 phototheodolite can be performed with accuracy. The accuracy of the orientationelements using the BC-4 camera are less than those specified values. This is the main reasonwhich prevents achievement of higher accuracy. The major problem is the stability of thecamera and the accuracy ofthe observed angles. The camera is presently under modification,which will result in better stability and reduction ofweight. The accuracy ofobserved anglesalso will be increased partially by better stability. The problem with the stability occurswhen the observer changes the BC-4 camera from theodolite to photo-theodolite, that is,between the photographic activity and angle measurements.

One of the most important conclusions is that with the specifications presently adopted itis possible to achieve an accuracy of 1/100,000 of the photographic distance. A still betteraccuracy is possible by better field measurements; that is, to decrease the specifications.This is feasible considering the specifications for classical survey. The increase in accuracyof field measurements will increase the measuring time and expenses and consequently theaccuracy requirement and specifications with it. The measuring techniques must be care­fully balanced for each project. Such a balance cannot be determined from the three projectswhich are now in progress. There must be several years ofpractical experimentation to cometo a meaningful conclusion. .

The photogrammetric monitoring system needs nearly the same amount of field prepara­tion as the classical field survey. This preparation consists ofmonumentation and survey of

,

.'

MONITORING DEFORMATIONS OF STRUCTURES 1383

D

FIG,4, Mud Mountain Project,

FIG, 5, BC-4 photograph of Mud Mountain slide,

1384 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1975

camera stations and targeting of the structure. The basic advantage of the photogrammetricmethod is in the amount oftime required to complete the monitoring of the targeted points.If, for example, a project is considered where a large structure is covered from four to fivecamera stations and there are 50 targets on the structure, the conventional field measure­ments will take 8 to 14 days to complete the field survey and the monitoring, the datareduction not included. The same photogrammetric survey can be completed within fourdays. There is no major time difference in data reduction between the two systems.

During the two weeks of classical field measurements, certain deformation could takeplace, while in the photogrammetric method the photographs can be taken in a single day.The possibility of deformation during the field measurement is nearly zero.

r

CONCLUSIONS

The photogrammetric structural survey offers an economical alternative to the classicalfield survey. The main advantage is the short time lapse between the data acquisition and datareductions, thus providing an instantaneous descriptron of deformations or motions of struc­tures or slide areas.

The method as described is very flexible; however, as it is presented in this paper, it is to beused for terrestrial photogrammetry only. However, a careful analysis of equation 8 revealsthat ground-measured control points located and targeted on firm bedrock can also be used inthe mathematical model to determine camera stations by auxiliary computation. This meansthat a combination of aerial and terrestrial photogrammetric systems is possible. A completephotographic coverage from the ground as well as from the air of a large structure is feasible,making the system nearly independent of the topography around the structure. This form ofthe method is presently under investigation.

Finally, a combination of classical survey and photogrammetric survey can be used forprecise monitoring of a large area such as a whole valley several miles in length. The classicalsurvey, i.e., triangulation-trilateration, or a method such as developed by the U. S. ArmyEngineer Topographic Laboratories7 , can be used to control few but strategically locatedpoints. By using these control points, photogrammetric surveys can be used for detailedmeasurements of certain test areas. This type of measurement is not economically feasible atpresent.

In summary, it can be concluded that the analytical photogrammetric method is capable ofprecise structural survey. The full capability and potential has not been realized yet. This isdue partially to the short time of development and also to short semi-routine practice, andpartially due to the fact that there is no suitable photogrammetric instrument on the marketwhich would fulfill the specifications presented herein. As a consequence, the experimenta­tion of this project was twofold, instrumental and methodological. The instrumental ex­perimentation has been reported2 ,4 and it indicates that there is a need for such instruments tobe manufactured and calibrated for this purpose.

REFERENCES

1. A. J. Brandenberger and M, T. Erez, Photogrammetric Determination of Displacements and Defor­mations in Large Engineering Structures, Canadian Surveyor, Vol. 26, No.2, 1972.

2. J. P. Erlandson, J. C. Peterson, and S, A, Veress. The Modification and Use of the BC-4 Camera forMeasurements of Structural Deformations, Proceedings of A.S.P. Sept. 1974.

3. J. P. Erlandson, J. C. Peterson, and S. A. Veress. Performance Observations of Structural Deforma­tions by Photogrammetric Methods, Technical Reports Part I and II, U. S. Corps ofEngineers, SeattleDistrict.

4. J. P. Erlandson and S. A. Veress, Contemporary Problems in Terrestrial Photogrammetry, Photo­grammetric Engineering, Vol. XL, pp. 1079-1036, 1974.

5. J. D. Raynolds and J. A. Dearinger. Measuring Building Movement by Precise Survey,journal oftheSurveying and Mapping Divison, A.S.C.E., 1970.

6. J. T. Richardson Measured Deformation Behavior of Glen Canyon Dam, Journal of the Surveyingand Mapping Division, A,S.C.E., 1970.

7. K. D. Robertson. A Methodfor Reducing Refractive Index Errors in Length Measurements, Techni­cal Report, U. S. Army Engineer Topographic Laboratories.

8. L. H. Roehm. Deformation Measurements of Flaming George Dam, Journal of the Surveying andMapping Division, A.S,C.E., 1968.

9. S. A. Veress. Adjustment by Least-Squares, American Congress on Surveying and Mapping, 1974.

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