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EXPERIMENTAL DETERMINATION OF HOMOGENEITY, COMPRESSIVE
STRENGTH AND MODULUS OF ELASTICITY OF CONCRETE IN REINFORCED
CONCRETE ELEMENTS BY NON-DESTRUCTIVE ULTRASONIC PULSE VE....
Conference Paper · October 2018
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Slovak University of Technology
in Bratislava
Faculty of Civil Engineering
and
Slovak Society for Mechanics SAS
16 t h International Conference
on
New Trends in Statics and Dynamics
of Buildings
Conference Proceedings
October 18 – 19, 2018 Bratislava, Slovakia
Proceedings of
16th International Conference on
New Trends in Statics and Dynamics of Buildings
Edited by
Norbert Jendželovský
Alžbeta Grmanová
Published by
Slovak University of Technology in Bratislava in
SPEKTRUM STU Publishers
Authors of contributions are responsible for the
statements or opinions expressed in the papers.
All papers have been reproduced from camera ready
manuscripts supplied by authors.
Papers were reviewed by members of the Scientific
Committee.
All rights reserved. No part of this publication may be
reproduced, stored in retrieval system or transmitted in
any form or by any means, without permission of the
publisher.
Copyright © Slovak University of Technology in
Bratislava
Edition 2018
ISBN 978-80-227-4845-2
Scientific committee:
Chairman:
Jendželovský Norbert
Slovak University of Technology Bratislava, Slovakia
Members:
Králik Juraj
Krejsa Martin
Máca Jiří
Melcer Jozef
Novák Drahomír
Partov Doncho
Paz Miguel Rodríguez
Ravinger Ján
Skrzypczyk Jerzy
Sokol Milan
Slovak University of Technology Bratislava, Slovakia
VŠB-Technical University of Ostrava, Czech Republic
Czech Technical University in Prague, Czech Republic
University of Žilina, Slovakia
Brno University of Technology, Czech Republic
Higher School of Civil Engineering (VSU) Sofia, Bulgaria
Tecnológico de Monterrey, Campus Puebla, Mexico
Slovak University of Technology Bratislava, Slovakia
Silesian University of Technology, Gliwice, Poland
Slovak University of Technology Bratislava, Slovakia
Conference organized by:
Slovak University of Technology in Bratislava
Faculty of Civil Engineering
Department of Structural Mechanics
Slovak Society for Mechanics SAS, Bratislava
Organizing committee:
Jendželovský Norbert
Grmanová Alžbeta
Ivánková Oľga
Chairman
Secretary
Reviewers of the papers published in the Proceedings:
Hubová Oľga, Ivánková Oľga, Jendželovský Norbert, Koleková Yvonna, Králik Juraj, Prekop Ľubomír,
Psotný Martin, Ravinger Ján, Sokol Milan, Tvrdá Katarína, Véghová Ivana.
Proceedings of the 16th International Conference on
New Trends in Statics and Dynamics of Buildings
October 18-19, 2018 Bratislava, Slovakia
Faculty of Civil Engineering STU Bratislava
Slovak Society of Mechanics SAS
LIST OF PAPERS
Niewiadomski, Lesław
THE INFLUENCE OF GEOMETRICAL IMPERFECTIONS OF COLUMNS ON THE FORCES IN THE
VERTICAL WALL BRACINGS OF A STEEL HALL
Partov, Doncho – Kantchev, Veselin – Stoyanov, Ch. – Křístek, Vladimír
NUMERICAL ANALYSIS OF THE RELAXATION OF A BENDING MOMENT, AROUSED OVER
THE SUPPORT DUE TO ITS SETTLEMENT IN A CONTINUOUS COMPOSITE STEELCONCRETE BEAM, USING INTEGRAL EQUATIONS OF VOLTERRA
Turis, Matúš – Ivánková, Oľga
VÝPOČET FAKTORU INTENZITY NAPÄTIA PRE CENTRÁLNU ŠIKMÚ TRHLINU
Rubint, Jakub
ČASOVO ZÁVISLÁ ANALÝZA DODATOČNE PREDPÄTEJ KONŠTRUKCIE MOSTA PRI SVRČINOVCI
Mahmud, Emin – Bonev, Zdravko – Abdulahad, Emad
NONLINEAR SEISMIC ANALYSIS OF MASONRY INFILLED RC FRAME STRUCTURES BY USING
THE N2-METHOD
Psotný, Martin
VPLYV POČTU UZLOVÝCH PARAMETROV NA RÝCHLOSŤ KONVERGENCIE RIEŠENIA
STABILITY STENY MKP
Antal, Roland – Jendželovský, Norbert
COMPARISON OF TWO CALCULATION METHODS USED FOR DETERMINATION OF
EXTERNAL PRESSURE COEFFICIENT FOR ATYPICALLY SHAPED STRUCTURE
Ivanchev, Ivan
EXPERIMENTAL DETERMINATION OF CRACK WIDTHS IN REINFORCED CONCRETE
ELEMENTS, SUBJECTED TO REPEATED LOADS
Véghová, Ivana – Sumec Jozef
STRESS-STRAIN RELATIONS OF PERIODICALLY LOADED VISCOELASTIC MATERIAL WITH
CONSTANT CIRCULAR FREQUENCY
Tsvetkov, Stanislav
R. C. TANKS FOR WATER STORAGE – SEISMIC ANALYSIS
Partov, Doncho – Petkov, Milen – Matuski, Vladimir – Zhelev, Dimo
PHILOSOPHY OF ROBUSTNESS DESIGN FOR TEMPORARY STEEL FRAME STRUCTURES, USED
FOR STRENGTHENING OF A GREAT EXCAVATIONS FOR NEW METRO IN SOFIA
I
th
16 International Conference on New Trends in Statics and Dynamics of Buildings
October 2018, Bratislava
Jivkov, Venelin et al.
POSITRON LIFETIME CALCULATION FOR THE INTERNATIONAL TERMONUCLEAR EXPERIMENTAL
REACTOR (ITER) FIRST WALL MATERIALS ASSESSMENT
Kowolik, Bernard – Kowolik, Marek
STATIC AND STRENGTH ANALYSIS OF THE TRUSS IN THE FIRE CONDITIONS
Kowolik, Bernard – Kowolik, Marek
ANALYSIS OF INFLUENCE OF COLUMNS STIFFNESS ON BEHAVIOUR OF THE SELECTED
MEMBERS IN THE STRUCTURE OF AN ARC-SHAPED ROOF WITH A TENSIONING CABLE
Jendželovský, Norbert
NUMERICKÉ MODELOVANIE PODLOŽIA POD ZÁKLADOVOU DOSKOU
Psotný, Martin
VOĽBA BÁZOVÝCH FUNKCIÍ V GEOMETRICKY NELINEÁRNYCH ÚLOHÁCH MKP PRÚTOV
Uhlířová, Lenka
VPLYV NAPLNENIA VODNEJ NÁDRŽE NA JEJ FREKVENCIU
Petkov, Velian – Partov, Doncho
SEISMIC ANALYSIS AND STRENGHTENING OF FRAMED MASONRY INFILLED BUILDINGS WITH
STEEL FRAMES
Chieffo, N. – Formisano, Antonio
FRAGILITY-BASED APPROACH FOR SEISMIC VULNERABILITY ASSESSMENT OF A MASONRY
BUILDING IN MUCCIA (ITALY)
Ivanchev, Ivan – Slavchev, Veselin
EXPERIMENTAL DETERMINATION OF HOMOGENEITY, COMPRESSIVE STRENGTH AND
MODULUS OF ELASTICITY OF CONCRETE IN REINFORCED CONCRETE ELEMENTS BY NONDESTRUCTIVE ULTRASONIC PULSE VELOCITY METHOD
Li, Zheng – Pasternak, Hartmut – Partov, Doncho
INFLUENCE OF STATISTICAL SIZE EFFECT IN STEEL ON STRUCTURAL SAFETY
Sucharda, Oldřich – Grmanová, Alžbeta – Ravinger, Ján
FEM AMENDED BY A TRANSFORMATION VIA EIGEN MODES FOR DYNAMIC POST-BUCKLING
BEHAVIOUR OF THIN-WALLED STRUCTURES
Ponchon, Alais
DETERMINING OF CRACK DEPTHS IN REINFORCED CONCRETE ELEMENTS WITH NONDESTRUCTIVE ULTRASONIC PULSE VELOCITY METHOD
II
Proceedings of the 16th International Conference on
New Trends in Statics and Dynamics of Buildings
October 18-19, 2018 Bratislava, Slovakia
Faculty of Civil Engineering STU Bratislava
Slovak Society of Mechanics SAS
EXPERIMENTAL DETERMINATION OF HOMOGENEITY,
COMPRESSIVE STRENGTH AND MODULUS OF ELASTICITY
OF CONCRETE IN REINFORCED CONCRETE ELEMENTS BY
NON-DESTRUCTIVE ULTRASONIC PULSE VELOCITY
METHOD
I.Y.Ivanchev 1 and V.S. Slavchev2
Abstract
In this paper are described the experimental researches for determining the homogeneity, compressive strength
and modulus of elasticity of concrete by the measured velocity of ultrasonic pulse, using the Non-Destructive
Ultrasonic Pulse Velocity Method. The researches were performed on 4 reinforced concrete beams. The
provided concrete grade is C25/30, fine fraction of course aggregate (dmax=12 mm), consistency S3. After
determining the probable concrete compressive strength and modulus of elasticity with portable ultrasonic
testing instrument type “Proceq – TICO”, using the Non-Destructive Ultrasonic Pulse Velocity Method
according to EN 12504-4:2004, the obtained results were compared to the theoretically calculated according
EN 1992-1-1:2004. The homogeneity and quality of the concrete is assessed.
Key Words
reinforced concrete, ultrasonic pulse velocity method, homogeneity, compressive strength, modulus of elasticity
1
INTRODUCTION
Traditional methods of diagnostics, for conditional assessment and analysis of building structures are
destructive, which are more costly and more labor-intensive. Methods that allow non-destructive control of the
properties of the used building materials, the quality of the elements and structures, both during their
construction and during different stages of their exploitation are being developed and implemented more and
more worldwide. This control is necessary for the safe exploitation of buildings and facilities.
One of the methods used for non-destructive control in structures is the ultrasonic pulse velocity method. The
time or velocity of propagation of an ultrasonic mechanical pulse in the material of the reinforced concrete
elements is measured. This velocity is very high and is proportional to the density of the material. The ultrasonic
property is used to pass through material and to reflect to boundary of two environments. In the devices based on
the ultrasonic method, two piezoelectric transducers are used, one generating ultrasonic waves and the other
receiving and recording them.
Depending on the way of receiving the ultrasonic pulse [2], [7], [8] there is (fig.1):
1
Chief Assist. Prof. Dr. I. Y. Ivanchev, USEA (VSU) "L. Karavelov", 175 Suhodolska Str., 1373 Sofia,
Bulgaria, iivanchev@mail.bg
2
Assos. Prof. Dr. V. S. Slavchev, USEA (VSU) "L. Karavelov", 175 Suhodolska Str., 1373 Sofia, Bulgaria,
slavchev@vsu.bg
16th International Conference on New Trends in Statics and Dynamics of Buildings



October 2018, Bratislava
direct (opposite) transition - transmitting transducer is located on one side of reinforced concrete
element, receiving transducer on the opposite one;
semi - direct transition;
indirect (surface) transition - transmitting and receiving transducer are located on one side of the
element.
Fig. 1. Position of transmitting and receiving transducer (personal archive of authors)
Semi – direct and indirect transition is performed for elements in existing buildings and facilities where access is
limited.
Ultrasonic pulse velocity method might be used for:
 Determination of concrete compressive strength according to EN 12504-4:2004
The concrete compressive strength based on the measured ultrasonic pulse velocity is most often determined by
[2]:
3,75
fc,UPV  cVUP
,
(1)
where:
VUP is the ultrasonic pulse velocity in km / s ;
f c ,UPV is in MPa ;
c is factor in the range of 0,158 to 0,231.
By this method, the concrete strength at different locations of a concrete or reinforced concrete element can be
determined without any damages. The accuracy of this method is not great, because the velocity of ultrasonic
signal depends on the type and age of concrete, on the degree of compaction of concrete, on its humidity, on
properties of the coarse aggregates, on temperature and other factors, but the ultrasonic pulse velocity method is
an easy and inexpensive way to determine the strength properties of concrete.
 Assessing the homogeneity and quality of the concrete.
This could be carried out by using statistical methods. Measurements (n by numbers) of the speed of the pulse
through the concrete have to be performed, the arithmetic mean of the pulse velocity Vbm [km/s] and mean
square deviation Sv have to be determined by the formulas [2]:
Vbm 
1 n
 Vbi ,
n i 1
n
Sv 
 (Vbi  Vbm )
(2)
2
i 1
n 1
,
(3)
where Vbi - ultrasonic pulse velocity at measurement i.
The homogeneity of the concrete is characterized by a factor khom, which is determined by:
k hom 
f c,UPV  3S v
f c,UPV
(4)
When khom > 0,9 the homogeneity is very good, if 0,7 ≤ khom ≤ 0,9 it is good, in case 0,5 ≤ khom ≤ 0,7 is
satisfactory and when khom < 0,5 is bad.
16th International Conference on New Trends in Statics and Dynamics of Buildings
October 2018, Bratislava
 Determination of modulus of elasticity of concrete according to EN 12504-4:2004
The dynamic modulus of elasticity Ec,din can be determined by the following formula [1],[2]:
2
,
Ec, din  kcVUP
(5)
where:
VUP is in [ m / s ];
k is factor that is assumed to be equal to 1  1  2  / 1   in case of longitudinal waves transition and
equal to 2 1   in case of transverse waves transition;
c is the acoustic density of the material in [ kNs 2 / m4 ]:
c 
c
g
,
(6)
where:
 c is the weight per unit volume of the concrete;
g is the gravity acceleration.
For the Poisson’s ratios  the following values can be accepted:
  0, 3 at age of concrete from 2 days to 14 days;
  0, 2 at age of concrete 28 days;
  0,15 at age of concrete equal to or greater than 90 days.
According to [5] the modulus of elasticity of concrete Ec could be determined by the following formula:
Ec  kl Ec, din ,
(7)
where kl is a factor, which is accepted 0.87 for low strength concrete and for a high-strength concrete is 0.954.
2
EXPERIMENTAL SETUP
Researches were carried out on four reinforced concrete beams. They are with span of 3m, cross section
15/30cm. For three of the beams (C1, C2 and C3) the longitudinal bottom reinforcement is 2N12 (steel B500B),
stirrups ф8/10(15)cm of steel B235. For one beam (D2) the longitudinal bottom reinforcement is 2N18 (steel
B500B), stirrups N8/10(15)cm of steel B500B. They were prepared of concrete grade C25/30, fine fraction of
coarse aggregate (dmax=12 mm), consistence S3. For two years, the reinforced concrete elements were in
confined spaces, and the next two years were left outdoors and subjected to the atmospheric impacts. The
measurements were performed at age 1430th day after the production.
Fig.2. Measurement with ultrasonic testing instrument Proceq-TICO (personal archive of authors)
16th International Conference on New Trends in Statics and Dynamics of Buildings
October 2018, Bratislava
The experimental non-destructive ultrasonic measurements were performed by using ultrasonic testing
instrument Proceq TICO [6] with measurement range from 15 to 6550 μsec (fig.2). For improving the contact
between the concrete surface and the transducers, a specialized coupling paste was used. Before each
measurement, the equipment was calibrated with calibration rod with known velocity of the ultrasonic pulse.
3
EXPERIMENTAL RESULTS
3.1 Determining the concrete compressive strength according to EN 12504-4:2004
For each of the four beams C1, C2, C3 and D2, 15 measurements for the ultrasonic pulse velocity were made. The
measurement points were uniformly distributed along the beam. The location of the longitudinal reinforcement
and the stirrups in the investigated regions were determined in advance with a rebar locator. Places with cracks
and reinforcement were avoided. The probable compressive strength of concrete (tab. 1) is determined by
formula (1). The concrete compressive strength, determined with ultrasonic pulse velocity method for beam C 1 is
40.9 MPa, for C2 is 40.8 MPa, for C3 is 40.4 MPa and for D2 is 40.4 MPa.
Number of
measurement
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Beam C1
Beam C2
Beam C3
Beam D2
VUP [km/s] fc,UPV [MPa] VUP [km/s] fc,UPV [MPa] VUP [km/s] fc,UPV [MPa] VUP [km/s] fc,UPV [MPa]
4.350
39.2
4.160
33.1
4.440
42.3
4.430
41.9
4.380
40.2
4.440
42.3
4.350
39.2
4.470
43.4
4.300
37.5
4.410
41.2
4.280
36.9
4.360
39.5
4.380
40.2
4.430
41.9
4.300
37.5
4.410
41.2
4.340
38.8
4.400
40.9
4.370
39.9
4.430
41.9
4.400
40.9
4.460
43.0
4.480
43.7
4.410
41.2
4.410
41.2
4.470
43.4
4.510
44.9
4.340
38.8
4.450
42.7
4.380
40.2
4.450
42.7
4.390
40.5
4.520
45.2
4.360
39.5
4.370
39.9
4.450
42.7
4.450
42.7
4.370
39.9
4.230
35.3
4.410
41.2
4.400
40.9
4.330
38.5
4.400
40.9
4.370
39.9
4.460
43.0
4.380
40.2
4.440
42.3
4.340
38.8
4.400
40.9
4.440
42.3
4.450
42.7
4.370
39.9
4.380
40.2
4.490
44.1
4.320
38.2
4.270
36.5
4.380
40.2
4.430
41.9
4.370
39.9
4.340
38.8
mean value:
mean value:
mean value:
mean value:
40.9
40.8
40.4
40.4
Tab. 1. Ultrasonic pulse velocities and concrete compressive strengths
3.2 Determining the homogeneity of concrete
For determining the homogeneity and quality of the concrete, at least 15 transitions at different points of the
reinforced concrete element must be performed. In this experiment these are places along the entire length of the
beam in which there are no cracks and no reinforcement. The transmitting and receiving transducer were located
opposite to each other on the side surfaces of the beam with maximum axial deviations of up to 1 cm.
Number of
measurement
VUP [km/s]
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
4.350 4.380 4.300 4.380 4.340 4.400 4.410 4.450 4.520 4.450 4.400 4.460 4.400 4.380 4.380
Vbm [km/s] =
4.400
Sv =
0.05398
fc,UPV [MPa] =
40.9
khom =
0.996
Tab. 2. Homogeneity factor khom for beam C1
Number of
measurement
VUP [km/s]
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
4.160 4.440 4.410 4.430 4.400 4.460 4.470 4.380 4.360 4.370 4.330 4.380 4.440 4.490 4.430
Vbm [km/s] =
4.397
Sv =
0.07898
fc,UPV [MPa] =
40.8
Tab. 3. Homogeneity factor khom for beam C2
khom =
0.994
16th International Conference on New Trends in Statics and Dynamics of Buildings
October 2018, Bratislava
By formulas (2), (3) and (4) were determined the arithmetic mean of the pulse velocity Vbm, mean square
deviation Sv and homogeneity factor of concrete khom for each of the four beams (tab. 2, tab. 3, tab. 4 and tab. 5).
The homogeneity factors of concrete khom for beam C1 is equal to 0.996, for C2 is 0.994, for C3 is 0.994 and for
D2 is 0.996, i.e. for all the beams the homogeneity is very good.
Number of
measurement
1
VUP [km/s]
2
3
4
5
6
7
8
9
10
11
12
13
14
15
4.440 4.350 4.280 4.300 4.370 4.480 4.510 4.450 4.370 4.230 4.400 4.440 4.450 4.320 4.370
Vbm [km/s] =
4.384
Sv =
0.07917
fc,UPV [MPa] =
40.3
khom =
0.994
Tab. 4. Homogeneity factor khom for beam C3
Number of
measurement
VUP [km/s]
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
4.430 4.470 4.360 4.410 4.430 4.410 4.340 4.390 4.450 4.410 4.370 4.340 4.370 4.270 4.340
Vbm [km/s] =
4.386
Sv =
0.05193
fc,UPV [MPa] =
40.4
khom =
0.996
Tab. 5. Homogeneity factor khom for beam D2
3.3 Determining the modulus of elasticity of concrete according to EN 12504-4:2004
Based on the 15 ultrasonic pulse velocity measurements for each of the beams by formulas (5), (6) and (7) were
determined acoustic density of the material c , dynamic modulus of elasticity Ec,din and modulus of elasticity
of concrete Ec (tab. 6, tab. 7, tab. 8 and tab. 9). The modulus of elasticity of concrete for beam C1 is 37403.6
MPa, for C2 is 37352.9 MPa, for C3 is 37138.1 MPa and for D2 is 37165.5 MPa.
Number of
measurement
1
VUP [m/s]
4350
2
3
4
5
6
7
8
9
4380 4300 4380 4340 4400 4410 4450
4520
10
11
12
4450 4400 4460
Vbm [m/s] =
4400
ν=
0.15
k=
0.947
Ec,din [MPa] =
42992.6
kl =
0.87
Ec [MPa] =
37403.6
13
14
4400
ρc [kNs2/m4] =
15
4380 4380
2.3445
Tab. 6. Modulus of elasticity of concrete determined with ultrasonic pulse velocity method for beam C 1
Number of
measurement
1
VUP [m/s]
4160
2
3
4
5
6
7
8
9
4440 4410 4430 4400 4460 4470 4380
4360
10
11
12
4370 4330 4380
Vbm [m/s] =
4397
ν=
0.15
k=
0.947
Ec,din [MPa] =
42934.4
kl =
0.87
Ec [MPa] =
37352.9
13
14
4440
2
4
ρc [kNs /m ] =
15
4490 4430
2.3445
Tab. 7. Modulus of elasticity of concrete determined with ultrasonic pulse velocity method for beam C2
Number of
measurement
1
VUP [m/s]
4440
2
3
4
5
6
7
8
9
4350 4280 4300 4370 4480 4510 4450
4370
10
11
12
4230 4400 4440
Vbm [m/s] =
4384
ν=
0.15
k=
0.947
Ec,din [MPa] =
42687.5
kl =
0.87
Ec [MPa] =
37138.1
13
14
4450
2
4
ρc [kNs /m ] =
15
4320 4370
2.3445
Tab. 8. Modulus of elasticity of concrete determined with ultrasonic pulse velocity method for beam C 3
16th International Conference on New Trends in Statics and Dynamics of Buildings
Number of
measurement
1
VUP [m/s]
4430
2
3
4
5
6
7
8
9
4470 4360 4410 4430 4410 4340 4390
4450
October 2018, Bratislava
10
11
12
4410 4370 4340
Vbm [m/s] =
4386
ν=
0.15
k=
0.947
Ec,din [MPa] =
42719.0
kl =
0.87
Ec [MPa] =
37165.5
13
14
4370
2
4
ρc [kNs /m ] =
15
4270 4340
2.3445
Tab. 9. Modulus of elasticity of concrete determined with ultrasonic pulse velocity method for beam D2
4
CONCLUSIONS
The paper presents an experimental study for the possibility to apply the non-destructive ultrasonic method for
assessing homogeneity, compressive strength and modulus of elasticity of concrete in reinforced concrete
elements. For concrete grade C25/30 with cement with strength class N the theoretically calculated cylindrical
compressive strength according to EC2 [3] at 1430th day of concrete is 32.92 N / mm2 , that is from 22.4% to
24.2% lower than the experimentally determined. Theoretically calculated modulus of elasticity of concrete
according EC2 [3] at 1430th day of concrete is 33066 MPa, that is from 12.3% to 13.1% lower than the
experimentally determined.
These measurements could be used for conditional assessment and quality of construction of reinforced concrete
elements. The presented study is preliminary. The authors intend to continue the research over time and to track
the changes in compressive strength and modulus of elasticity of concrete in the reinforced concrete elements
when they are subjected to severe service conditions and aggressive impacts. One of the main scientific methods,
empirical, will be used for achieving the goal.
ACKNOWLEDGEMENT
The researches were carried out under a research project funded by University of Structural Engineering and
Architecture (VSU) "Lyuben Karavelov", Sofia - “Experimental determination of compressive strength, modulus
of elasticity, homogeneity, internal defects and cracks in the concrete of Reinforced Concrete elements with nondestructive methods”, 2018.
REFERENCES
[1]
Bogas, J. A. – Gomes, M. G. – Gomes, A.: Compressive strength evaluation of structural lightweight
concrete by non-destructive ultrasonic pulse velocity method, Elsevier, Ultrasonics, vol. 53, pp. 962-972,
2013.
[2]
Dimov, D.: Non-destructive testing of Building Structures, Direct Services, Sofia, Bulgaria, 2011.
[3]
EN 1992-1-1:2004 Eurocode 2: Design of Concrete Structures – Part 1-1: General Rules and Rules for
Buildings
[4]
EN 12504-4:2004 Testing Concrete – Part 4: Determination of Ultrasonic Pulse Velocity.
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