Analysis of Precision of Geodetic Instruments for Investigating Vertical Displacement of Structures

Available online at www.sciencedirect.com

ScienceDirect Procedia Engineering 165 (2016) 906 – 917

15th International scientific conference “Underground Urbanisation as a Prerequisite for Sustainable Development”

Analysis of precision of geodetic instruments for investigating vertical displacement of structures Boštjan Kovačič a, Rok Kamnik a, Andrey Pustovgar b, Nikolai Vatin c,* a University of Maribor, Smetanova 17, Maribor, SI 2000, Slovenia Moscow State University of Civil Engineering, Yaroslavskoye Shosse 26, Moscow, 12933, Russia c Peter the Great St. Petersburg Polytechnic University, Polytechnicheskaya 29, St. Petersburg, 195251, Russia b

Abstract This paper presents the analysis of preciseness and safety of different instruments for researching the vertical displacements of the objects in the space. In Slovenia researching the objects by the test of pressure is obligatory for all structures, which are longer than 15 meters (JUS U.M1.046). Among all the methods we choose geodetic as well as non-geodetic ones. There are many methods for researching the displacements, so we took limits to the instruments available to us. On the Faculty of Civil Engineering, University of Maribor, Slovenia, used the level, total station, and inductive transducer and laser level. The measures of displacements were made on the reinforced concrete plate, type PVP5. For the plate we calculated the foreseen displacements by the analytic as well as by the numeric method. For analytic calculation we used the national regulations (Euro code 2) and for numeric part we used the programme Ocean. For each instrument we calculated the standard deviation and the optimal accuracy, we checked the significance of results by the analysis of variances with one variable factor. In this paper we described all the instruments for following the displacements and the working principles of instruments by which the research was made and the measurement errors. The analysis of precise was made on the base of comparation between the results of foreseen displacements and the gained results of measurements. The results of this research are gathered in a conclusion and give us the answer to the goals. © 2016 2016The TheAuthors. Authors. Published by Elsevier © Published by Elsevier Ltd. Ltd. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the scientific committee of the 15th International scientific conference “Underground (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under scientific committee of the 15th International scientific conference “Underground Urbanisation as a Urbanisation as aresponsibility Prerequisite of forthe Sustainable Development. Prerequisite for Sustainable Development Keywords: innovative materials, accuracy of measurement results, analysis of preciseness, displacements;

* Corresponding author. Tel.: +7-921-964-37-62 E-mail address: [email protected]

1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 15th International scientific conference “Underground Urbanisation as a Prerequisite for Sustainable Development

doi:10.1016/j.proeng.2016.11.800

Boštjan Kovačič et al. / Procedia Engineering 165 (2016) 906 – 917

1. Introduction Experimental methods for investigating structures in their early phases were based on theoretic calculation that describes deformation growth and breakage under load. With the development of numerical sciences and the increased surge of information science in the last 30 years, numerous home and foreign experts have taken up the analysis of displacements and deformations and published their results in articles and books. Most of the authors analysed displacements and deformations, and fostered the upgrading of the compensation model for horizontal and vertical measurements [1-25]. Among home authors, Marjanovič [1] deserves to be mentioned who describes non-geodetic methods for measuring linear displacements. Methods for measuring displacements and deformations were presented also by Narobe in 1996 [2]. In his article, he presents measurements performed with inductive transducers, classic theodolite and precision level. All the results obtained were statistically processed, mathematical statistics thus forming a component part for the compensation of results. The statistical processing of data based on the growth of the nil or alternative hypotheses and on different tests for checking significance, as well as on the class of error values was presented by Pelzer [3]. An outstanding contribution to deformation measurement methods was made by Milev [4] in 1985. Welsch [5] made a schematic presentation of deformation analysis process of geodetic nets, which served as a basis for the creation of computer programs. The same topic was studied also by Kapović, Narobe and Mastelić [6] from the Geodetic Faculty in Zagreb, and Breznikar [7], Vodopivec and Stopar [8] from the Faculty of Civil Engineering and Geodesy of the University in Ljubljana. Their investigations focus on the calculation of precision measurements and errors in measuring structural displacements and deformations. As evident from this survey, numerous experts worked on the analysis of displacements and deformations. To repeat, the most notable contribution to the analysis of deformations was made by Welsch and Pelzer with coauthors. They set the bases of deformation analysis and solved key problems in the stability of geodetic nets. 2. Measuring instruments According to standards in Slovenia, all vertical displacements during statically loading test must not exceed calculated values. These values are calculated by static in statically calculation of constructions. Calculations are made for all critical points on constructions. These points are on structure typically: supporters and middle of the span (Figure 1). Vertical displacements are observed on these critical points. At observations of vertical displacement, three different geodetically and one physical measurement methods are used to get better uncertainty. Systematic errors can also be avoided when all methods are applied.

Fig.1. Measurement points on the bridge.

In geodetically measurements methods on traffic surface of a construction are used total station with precisely tripod, digital level with high accuracy and laser level with sensors. In physically measurement method are used

907

908

Boštjan Kovačič et al. / Procedia Engineering 165 (2016) 906 – 917

inductive transducers of displacement on the opposite surface of the traffic surface. Sensors must stand on reference to the grounding, so they can be used on structure not higher than 5 meters. Most of constructions don't make us possible to set up the inductive displacement transducers because of height or unapproachability of the area. In such cases the method of geodetic levelling and method of laser system are used, which enables us to determine vertical movements up to span of 300 meters. Laser system is made of sensors, laser level, communication terminal and the program "Laser", which notice the movements. Sensors and communication terminal are connected to coaxial cable RS-485, and the communication terminal is connected to the personal computer with the RS-232 cable. The reference station used with laser system and classical geodetic instruments must be set up on a stabile ground and at the appropriate distance from the construction, so, that vibrations caused by overloading aren't transmitted to instruments. To increase the accuracy of instruments, the reference station is set up to a pre-prepared massive tripod. With a tripod the error of subsiding the instrument, which we could expect with the use of classical geodetic tripod, is avoided. Geodetically prisms can also be set up to concrete squares (20x20x20 centimetres) to increase the accuracy of measurement. Sensors can be fastened to classical tripod or directly to construction, which is also more reliable (Figure 2a,2b).

Fig. 2. a) Position of geodetic instruments; b) The rotation level and sensors on the critical points

3. Calculated movements 3.1 Analytical methods To enhance the accuracy of measurements and to be able to verify the results, predicted displacements should be calculated before measurements have been taken. For an uncracked cross-section, with analytical methods, displacements can be computed with known methods of structural calculations. More problems are encountered at cracked cross-sections where cracks occur due to low tensile strength of concrete. This results in the reduction of inertial moment of average cross-section and thus in greater deformation. As the location and the height of cracks are difficult to determine, due to properties of concrete, they are stated in different national codes. Euro code 2 (EC2) [10] has lately been applied most frequently.

C3 C2

Boštjan Kovačič et al. / Procedia Engineering 165 (2016) 906 – 917

C1 P1=P/3 = 7.895/3 = 2.,632 kN

40 40 20 40 40 bp=1.60m ya

L=4.18m

yb Fig.3. Statically system.

3.2 Numerical methods It is often the case in practical applications that the required geometry of plates cannot be obtained by analytical methods. Therefore, different numerical methods are used which are based mainly on finite elements or finite differences. As the calculation procedure is a long one, different computer programs are used. One of them is Ocean [11]. It allows the computation of cracked cross-sections in accordance to EC2.

Fig.4. Simulation displacement in 4th step with program Ocean.

3.3 Calculated results The obtained results with both methods are similar. With analytically method we get in first three step linearly displacements while in the fourth step we observe a occurrence of steel cracked so because that the displacement in first step are greater and not linearly. With another method we get the dissimilar movements, which are not linearly in separate steps. This method are suitable to calculated a bigger constructions where is the expected displacements greater too.

909

910

Boštjan Kovačič et al. / Procedia Engineering 165 (2016) 906 – 917

3.4 Measuring results of experiments Considering mean values of individual instruments we obtain the following values in millimetres (Tabl. 1, Graph 1) Table 1. Measured and calculated values. Instruments/ displacement [mm]

Step 1

Step 2

Step 3

Step 4

Total station

0.4

0.9

1.3

1.8

Level

0.4

0.7

1.1

1.6

Inductive transducer

0.356

0.715

1.051

1.530

Rotation level

0.4

0.8

1.3

1.9

Calculated movements by EC2

0.3965

0.793

1.185

1.731

Calculated movements by Ocean

0.56

0.88

1.20

1.67

Graph. 1. Measured and calculated movements shown in graph.

It is evident from Graph 1, that correspondence with predicted displacements is the highest when measurements are performed with the level method, and the lowest when they are performed with the method of rotation level. It is also evident from the graph that the inductive transducer gives the most balanced results, while the least balanced are obtained with the rotation level.

911

Boštjan Kovačič et al. / Procedia Engineering 165 (2016) 906 – 917

4. Calculation of results adequacy, accuracy and safety 4.1 Mathematically calculation of results adequacy For this we use the mathematically method of interpolated polynom of 3rd. degree. For each instrument the equation system are combine. On the salvation of this system we execute an integrated comparison of results. We think that the prime results of integrated salvation are these that are fulfil expectations of hypothesis.

³ T x  f x dx b

a

1

n

min

(1)

Where is: Tn(x) – theoretically method function (EC2 and Ocean) fn(x) – estimation of 3rd degree polynom for each instrument The results integrated comparison to EC2 has a minimum hypothesis values at the rotations level. These results are similar like the obtained measurement results in Table 1. 4.2 Calculation of uncertainties and standard deviations of displacements For all methods calculations of uncertainties and standard deviations were made. Measured values were compared with calculated values of displacement [12].

s

>vv@

n 1

(2)

Uncertainties for each method are in mm: Table 2: Calculated standard deviations for step 1, 2, 3 and 4. Method

s – 1st step

s– 2nd step

s – 3rd step

s – 4th step

Total station

0.09

0.06

0.14

0.09

Level with micrometer

0.08

0.06

0.12

0.09

Rotating level

0.07

0.06

0.19

0.09

0.01

0.01

0.01

0.01

Inductive Transducer

Graph. 2. Uncertainties in 3D graph.

912

Boštjan Kovačič et al. / Procedia Engineering 165 (2016) 906 – 917

The standard deviations are calculated for each instrument. Results shown us that we measured in separate steps very precisely. Only in third steps the results are a little bit greater so we can this ascribe to appearance of cracks. All usage instruments are appropriate to measured micro displacement. If the constructions permitted the inductive transducer setting up (height) that is expedience to used it. 4.3 Calculated optimal measure accuracy of micro-displacement On the groundwork [6] the measurement procedure are determinate and optimal measurement accuracy are calculated for all used instruments. On the bases of measured results the means values and standard deviations are calculated. For this calculate we set two criterions: 1/20
5%

10%

20% 0.0793

Calculated displacement with EC2

0.3965mm

0.0198

0.0396

INSTRUMENT

Displacement [mm] - f

s

s/f

1/20< s/f<1/10

1/10
Level

0.4

0.08

0.20

NO

NO

Total station

0.4

0.09

0.225

NO

NO

Ind. transducer

0.36

0.01

0.028

NO

YES

Rotation level

0.4

0.07

0.175

NO

NO

CRITERION

Table 4. Optimal accuracy in step 2. STEP 2

5%

10%

20%

Calculated displacement with EC2

0.793mm

0.0396 0.0793

INSTRUMENT

Displacement [mm] - f

s

s/f

1/20< s/f<1/10

1/10
Level

0.7

0.06

0.086

YES

NO

Total station

0.9

0.06

0.067

NO

YES

Ind. transducer

0.719

0.01

0.014

NO

NO

Rotation level

0.8

0.06

0.075

NO

YES

5%

10%

20% 0.237

0.1586

CRITERION

Table 5. Optimal accuracy in step 3. STEP 3 Calculated displacement with EC2

1.1895mm

0.059

0.118

INSTRUMENT

Displacement [mm] – f

s

s/f

1/20< s/f<1/10

1/10
Level

1.1

0.12

0.109

NO

YES

CRITERION

913

Boštjan Kovačič et al. / Procedia Engineering 165 (2016) 906 – 917

Total station

1.3

0.14

0.108

NO

YES

Ind. transducer

1.091

0.01

0.009

NO

NO

Rotation level

1.3

0.19

0.146

YES

NO

5%

10%

20% 0.346

Table 6. Optimal accuracy in step 4. STEP 4 Calculated displacement with EC2

1.7307mm

0.086

0.173

INSTRUMENT

Displacement [mm] – f

s

s/f

1/20
1/10
Level

1.6

0.09

0.056

NO

NO

Total station

1.8

0.09

0.05

NO

NO

Ind. transducer

1.731

0.01

0.006

NO

NO

Rotation level

1.9

0.09

0.047

NO

NO

CRITERION

On the basis of this data we can extend the conclusion. Step 1 Criterion A: neither instrument not gives us the results that reply to ordered criterion. Criterion B: Only inductive transducers give us the replying results. Step 2 Criterion A: Only the levelling results replying to fixing criterion. Criterion B: The total station and rotation level results replying to this criterion. The inductive transducers results are absolutely accurate and replying to criterion between 1% and 5%. Step 3 Criterion A: All results replying in this interval. Criterion B: Only the total station and levelling results replying to this criterion. For inductive transducer holds same as step 2. Step 4 Criterion A and B: To settings criterions unsuitably none of results. The results are reply to criterion between 1% and 5%. 4.4 The analysis of variances This method is one of most effectiveness of mathematically statistics. With this method are answer received how any factors affected on stable symptom (this symptom is in own case deformations). These methods are definite on the variances addition base. For this analysis empirical data was needed. In own case the influence of loaded on a movement was investigated. For this purpose with first instrument was performed n1, with second n2, third n3 and fourth n4 reading. By this means we had N empirical data, which are grouping in k specimen. Table 7: Calculated estimation (Pavlić, 1971.) where is N number of all empirical data and k number of specimen. Variances Together

Least square of deviate

¦ ( xij  x0 ) 2  i, j

º 1 ª «¦ ( xij  x0 )» N ¬ i, j ¼

2

Step of freedom

Estimation of variances

N-1

s2

914

Boštjan Kovačič et al. / Procedia Engineering 165 (2016) 906 – 917

Between specimen

2

1 ª

¦ n «¦ ( x i

Inside specimen

i

¬

ij

j

º º 1ª  x0 )»  «¦ ( xij  x0 )» N ¬ i, j ¼ ¼

2

Difference upper sum

k–1

si2

N-k

su2

On the base of definite procedure of single changes factor variances analysis [14 and 15] in this title is onl y final equation and experiment results in the table 8 to 11. Step 1: Table 8: Calculated estimation for step 1. Variances

Least square

Step of freedom

Together

0.18

54

0.003

Between specimen

0.02

3

0.006

Inside specimen

0.16

51

0.003

Ftest=

1.86

P=

0.05

0,01

Fo=

2.79

4.2

Estimation of variances

F
Step 2: Table 9: Calculated estimation for step 2. Variances

Least square

Step of freedom

Together

0.462

58

0.008

Between specimen

0.048

3

0.016

Inside specimen

0.414

55

0.008

Ftest=

Estimation of variances

2.12 F
P=

0.05

0.01

Fo=

2.79

4.2

Step 3: Table 10: Calculated estimation for step 3 Variances

Least square

Step of freedom

Together

0.525

57

0.009

Between specimen

0.054

3

0.018

Inside specimen

0.471

54

0.009

Ftest=

Estimation of variances

2.05 F
Boštjan Kovačič et al. / Procedia Engineering 165 (2016) 906 – 917 P=

0.05

0.01

Fo=

2.78

4.16

Step 4: Table 11: Calculated estimation for step 4. Variances

Least square

Step of freedom

Together

1.479

58

0.026

Between specimen

3

0.065

Inside specimen

55

0.023

Ftest=

2.76

P=

0.05

0.01

Fo=

2.8

4.22

Estimation of variances

F
On the grounds of results quoted in the table we can give an opinion: In all steps the calculated F test is minor as Fo, which is taken from a statistic’s table. So the variances appreciation of separate test are not differentiate, Executed measurements are shown us that in the results are not significant distinction. For precisely measurements are appropriate all used instruments. 5. Analysis of methods based on the comparison of predicted and obtained results The method of classic levelling is the most frequently used method for determining displacements. Results show that measurements were performed continuously. In any case, the accuracy of the results depends on instruments and equipment used. For precise measurements of vertical displacements, it is suitable to use a digital level with the invar levelling rod, and take several readings in every measuring point. We can claim that this method is the most adequate of all geodetic methods for determining vertical displacements, although there is a certain time delay in taking readings with respect to other methods. The method of determining vertical displacements with the total station has shown itself the least accurate. The reason may be in the error when hitting reflexive targets. The method is suitable for determining displacements of the class bigger than 1 cm, where the required accuracy is 1/10 of the predicted displacement. The accuracy of the instrument is +/-0,3mm according to the producer. Thus, the results shorter than 1cm are not adequate for further processing. On the other hand, this method is suitable because it yields immediate results so that field measurements can be easily controlled. With better technology, this method will also become more accurate. The method of rotation level is a simple working method, although the results do not fulfil demands for accuracy. As with the method of total station, also this method is suitable for displacements larger than 1 cm, because the accuracy, according to the producer, is +-0.5 mm at the greatest distance, and +/-0.1 mm at the ideal distance of the sensor from the rotation level (up to 50 m). With this method, the problem lies in the communication link, because all sensors must be linked with a communication cable in sequence; each sensor demands the voltage of 110 V, which is not always available in the field. The method of inductive transducer has given the most accurate results. Surely, this method cannot be compared to geodetic methods, which produces far more readings in each series. On the average, we obtained approximately 15.000 readings for each loading step. In case that the structure enables the placement of inductive transducers, the method is very suitable for determining vertical displacements; in most cases, unfortunately, the correct placement of transducers cannot be assured. The reason is that with structures higher than 8 meters the access to central area is not possible. In practical applications, therefore, inductive transducers are placed at dilatation points, and possibly also in the first and last area of structure.

915

916

Boštjan Kovačič et al. / Procedia Engineering 165 (2016) 906 – 917

6. Conclusion The analysis of inspections allows not only to verify static calculations and the quality of the structure but also to make their corrections by influencing technology of production. The necessity of such analysis is justified also by the fact that static calculations were based on predictions, which did not represent real work of either building materials or structures. In the 30-is, works were started on verifying static calculations, especially calculations of limit conditions of structures, which required vast experimental work. We have been investigating and measuring vertical displacements and deformations for many years. During this time, we have performed about 50 experiments of loading structures and investigated them with different methods, either geodetic or others. We have tested bridges of different dimensions, prestressed concrete plates and beams of load-bearing walls. To identify displacements of this class, several methods and instruments exist. In our experiment, we confined ourselves to available instruments and performed measurements with 4 methods. The obtained results and their analysis provided us with the knowledge about the applicability of methods for determining the so-called micro-displacements. Determination of vertical displacements and deformations of different structures in space require high accuracy of measurements, which mostly depends on instruments used and on conditions at work. Vertical displacements were measured on a prestressed concrete plate of the type PVP with uniform loading in four steps. Loading was tested in the laboratory with constant temperature and pressure. In this way, we avoided errors that might influence the measurements. For the precise determination of vertical displacements and deformations, it is best to use several methods simultaneously. This, however, partly increases the costs and duration of measurements; these two factors, however, can be neglected in investigations of such sophistication. The advantages are the possibility of controlling measurements, comparing and analysing the results and presenting the results in a clearer way. References [1] R. Marjanović, Mjerenje deformacija ekstenzometrima i tiltmetrima, Geodetski list. 1-3 (1984)15-24. [2] Z. Narobe, Metode istraživanja pomaka i deformacija, Geodetski list. 1-3 (1986) 5-20. [3] H. Pelzer, Beurteilung der genauigkeit und der zuverlassigkeit geodatischer netze, Ingenieurvermessung. (1979) 273-304. [4] G. Milev, Geodatische methoden zur untersuchung von deformationen, Technische fakultet Stuttgart, 1985. [5] W. Welsch, Seminar Øber Deformationsanalysen, Hochschule der Bundeswehr, 1983, pp. 299-327. [6] Z. Kapović, Prilog određivanju i analizi pomaka i deformacija mostova s posebnim osvrtom na temperaturne utjecaje, Doctor disertation, Faculty for Geodesy, University of Zagreb, Zagreb, 1993. [7] A. Breznikar, Geodetsko inženirska dela pri gradnji objektov, Geodetski vestnik. 4 (1994). [8] B. Stopar, Relativne metode merjenja deformacij, Faculty for Geodesy, University of Ljubljana, Ljubljana, 1990. [9] S. Kontić, Geodezija, Faculty for Civil Engineering, University of Beograd, Beograd, 1995. [10] Eurocode 2: ENV 1992-1-1, 1991. [11] B. Bedenik, Statika konstrukcij, Faculty for Civil Engineering, University of Maribor, Maribo, 1997. [12] B. Kovacic, Analysis of precision of different instruments for investigating vertical micro-displacement of objects, Doctor disertation, Faculty for Geodesy, University of Zagreb Zagreb, 2001. [13] W.F. Caspary, Concepts of network and deformation analysis, School of survaying, University of New South Wales, Australia, 1987. [14] I. Pavlic, Statistic’s teory, Technical book, University of Zagreb, Zagreb, 1971. [15] G. Novakovic, Reasrching of function of geodetic instruments compensator, Doctor disertation, Faculty for Geodesy, University of Zagreb, Zagreb, 1996. [16] K. Krayushkina, O. Prentkovskis, A. Bieliatynskyi, R. Junevičius, Use of steel slags in automobile road construction, Transport. 27(2) (2012) 129-137. [17] O. Prentkovskis, J. Tretjakovas, A. Vedas, A. Bieliatynskyi, A. Daninas, K. Krayushkina, The analysis of the deformation state of the doublewave guardrail mounted on bridges and viaducts of the motor roads in Lithuania and Ukraine, Journal of Civil Engineering and Management. 18(5) (2012) 761-771. [18] A. Beljatynskij, O. Prentkovskis, J. Krivenko, The experimental study of shallow flows of liquid on the airport runways and automobile roads, Transport. 25(4) (2010) 394-402. [19] M. Starikov, A. Beljatynskij, O. Prentkovskis, I. Klimenko, The use of magnetic coercivity method to diagnose crane metalware, Transport. 26(3) (2011) 255-262. [20] N. Kuzhel, A. Bieliatynskyi, O. Prentkovskis, I. Klymenko, S. Mikaliunas, O. Kolganova, S. Kornienko, V. Shutko, Methods for numerical calculation of parameters pertaining to the microscopic following the leader model of traffic flow: Using the fast spline transformation, Transport. 28(4) (2013) 413-419.

Boštjan Kovačič et al. / Procedia Engineering 165 (2016) 906 – 917 [21] K. Krayushkina, O. Prentkovskis, A. Bieliatynskyi, J. Gigineishvili, A. Skrypchenko, A. Laurinavičius, K. Gopalakrishnan, J. Tretjakovas, Perspectives on using basalt fiber filaments in the construction and rehabilitation of highway pavements and airport runways, Baltic Journal of Road and Bridge Engineering. 11(1) (2016) 77-83. [22] B. Kovačič, R. Kamnikand A. Bieliatynskyi, The Different Methods of Displacement Monitoring at Loading Tests of Bridges or Different Structures, MATEC Web of Conferences. 53, art. no. 01048 (2016). [23] R. Usmanov, I. Mrdak, N. Vatin, V. Murgul, Reinforced soil beds on weak soils, Applied Mechanics and Materials, 633-634 (2014) 932935. [24] R. Usmanov, N. Vatin, V. Murgul, Experimental research of a highly compacted soil beds, Applied Mechanics and Materials, 633-634 (2014) 1082-1085. [25] R. Usmanov, M. Rakočević, V. Murgul, N. Vatin, Problems of sub-mountain area development associated with collapsing loess soils (Case of Tajikistan), Applied Mechanics and Materials, 633-634 (2014) 927-931.

917