New predictive models to evaluate concrete compressive strength using the SonReb method

Journal Pre-proof New predictive models to evaluate concrete compressive strength using the sonreb method M.T. Cristofaro, S. Viti, M. Tanganelli PII:

S2352-7102(19)30821-6

DOI:

https://doi.org/10.1016/j.jobe.2019.100962

Reference:

JOBE 100962

To appear in:

Journal of Building Engineering

Received Date: 22 May 2019 Revised Date:

17 September 2019

Accepted Date: 19 September 2019

Please cite this article as: M.T. Cristofaro, S. Viti, M. Tanganelli, New predictive models to evaluate concrete compressive strength using the sonreb method, Journal of Building Engineering (2019), doi: https://doi.org/10.1016/j.jobe.2019.100962. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.

NEW PREDICTIVE MODELS TO EVALUATE CONCRETE COMPRESSIVE STRENGTH USING THE SONREB METHOD M.T. Cristofaro, S. Viti and M. Tanganelli Department of Architecture (DiDA), University of Florence, Italy

Keywords: Existing RC buildings; concrete compressive strength; non-destructive methods; SonReb method; on-site assessment; experimental database.

Abstract An accurate assessment of the concrete compressive strength is a fundamental step towards evaluation of existing reinforced concrete structures under gravity and seismic loads. It can be conducted using destructive and non-destructive methods. Data obtained with destructive methods (core sampling) and non-destructive methods (sclerometric, ultrasonic and combined sonic rebound) have been collected by the Regional Seismic Department of Tuscany from a large number of RC structures, built between the 50s and 80s. The database, which includes crushing strength, ultrasounds velocity and rebound index, has been adopted to check the predictive effectiveness of the currently available analytical models. On the basis of the same database, new models have also been calibrated and proposed herein. They have been validated on a further database, not included in the one used for models calibration. The paper takes advantage of a large database to check the effectiveness of the available prediction models, and to propose new relationships, which are very effective for predicting the concrete strength of Italian RC buildings made in the latter decades of the XX century. The paper faces important issues of concrete characterization, beyond simply providing an original set of data.

1

1. INTRODUCTION In Italy more than half of the existing buildings are made of Reinforced Concrete (RC) and it is about buildings designed in most cases only for gravity loads, lacking any specific seismic guidelines. In the last decades many disasters took place, either on the account of incompetent design or old age of the involved buildings; owing to this, the need to update the national code regulations has turned out to be urgent, so as to grant a better structural safety of both new and existing buildings. The latest Italian seismic code regulations [1,2] have classified almost the entire Italian territory as seismic, thus bringing forth the need to evaluate the existing buildings’ safety through static and seismic verification methods. In performing the seismic analysis, one of the most crucial issues is the assessment of the mechanical properties of materials. A comprehensive analysis of the mechanical properties of concrete is essential both for the correct assumption of the strength to assume in the analysis [3-6] and for the evaluation of possible vulnerabilities of the structure, due to weak components or to strength irregularities within the building [7], which can induce torsional effects [8-15]. The most important Technical Codes [16-19] assume that the concrete strength is defined on the basis of destructive compressive tests, which can be integrated by further data provided by nondestructive methods. As to non-destructive methods, the most widespread ones are the Schmidt rebound hammer, the ultrasonic pulse velocity and the sonic rebound (SonReb), which combine Schmidt rebound hammer and ultrasonic pulse velocity. These methods, though being favorably less invasive and easy to be extended to a larger number of elements, are affected by many contingency factors arising during the test execution such as carbonation, porosity, cracks or aggregate outcropping and environmental circumstances (like humidity and temperature). The combined SonReb method is the most widespread non-destructive method suitable to determine the concrete’s mechanical features. It allows the offsetting of some limits and margins for uncertainty inherent in both the Schmidt rebound hammer and ultrasonic pulse velocity methods, whenever individually considered. The first use of Schmidt rebound hammer results combined with those obtained by ultrasonic pulses goes back to the mid of the sixties and yet the first important scientific paper has to be attributed to Facaoaru [20]. In particular, the author proposes a procedure to evaluate the concrete’s strength, based on some correction factors reliant upon the cement type and dosage, as well as on the nature and granulometry of the aggregates. Later on, during the seventies, Samarin and Smorchevsky [21] began to use the combined SonReb method, where the only known variables before the test are the aggregate type and the approximate concrete’s age. Since the end of the seventies several scientific papers have been published and have focused on formulations being calibrated ad hoc to define the concrete’s mechanical strength by using the SonReb method [22,23]. In 1993 also RILEM NDT4 [24] suggested the use of this combined method and provided ISO-based resistance curves where the concrete compressive strength is defined by knowing both the rebound index and the ultrasonic velocity. In Italy many researchers have been faced this issue since 70s, due to the high number of interventions on existing RC buildings. In 1979 Cianfrone and Facaoaru [25] have presented their results related to the application of the SonReb method in Italy according to the Romanian recommendations. In 1980 Giacchetti and Laquaniti [26] have proposed a formulation to define the concrete mechanical features, which was grounded on the results of compressive tests carried out on samples extracted from existing buildings. However, such kinds of formulation have increased and spread over the country since today [27-33].

2

Since the nineties, the Regional Seismic Department of Tuscany operating in the framework of national and regional programmes on seismic prevention [34], has started campaigns of destructive (coring) and non-destructive (Schmidt rebound hammer test, ultrasonic pulse velocity test and combined SonReb test) investigations on RC existing buildings built in Tuscany between the 50’s and the 80’s. Such experimental campaign involved 263 RC buildings, consisted in over 2000 data; namely, 860 samples have been checked through crushing strength, ultrasounds velocity and rebound index, leading a significant calibration program. The data provided by the experimental campaign have been organized into a database [35,36] which has been adopted to check the effectiveness of many available correlation methods. Such study has evidenced on the one hand the extreme variability of the concrete compressive strength, even within a single structural system and, on the other hand, the poor correlation between the data obtained by destructive and non-destructive tests performed on the same structural element by implementing formulations available in literature. In this work, after presenting an essential state-of-art on the mechanical characterization of concrete (Section 2), the database collecting the results of the Seismic Department of Tuscany [34] experience has been presented and compared to the predictions provided by the correlation models available in the technical literature (Section 3). Furthermore, some new models, differing from each other for their structure, have been calibrated on the database by performing a regression analysis (Section 4). Finally (Section 5), the proposed models, together with the ones presented in the Section 2, have been validated on a case-study which does not belong to the considered database, consisting of 78 samples. The work shows a wide state-of-art of the methods for the characterization of the concrete strength, and offers some original contributions which take advantage from the large databased produced by the Regione Toscana within four decades of research.

CURRENT APPROACHES FOR THE CONCRETE STRENGTH ASSESSMENT

2. 2.1

Destructive methods

The methods which can be called 'destructive' are the ones involving the removal of a localized portion of material from an existing structure. As concerns RC buildings, the mechanical characterization of material is made through the coring, which consists in the extraction of cylindrical samples to use for compression test in laboratory, so as to obtain the compressive strength value fcore. This value cannot represent the actual quality of the composite construction material when in place, but it is modified to take into account the specific conditions which can affect the sample strength [37], such as the slenderness and the diameter of the sample, the presence of steel bars and the disturbance due to extraction modes. In the technical literature there are many formulas which return the cubic (Rcub) or the cylindrical strength (fcyl) as a function of the compressive strength provided by the crushing test (fcore) [27]. Table 1. Formulations to switch from fcore to Rcub or fcyl. Author Concrete Society [38]

Year 1976

Formulation

Cestelli Guidi and Morelli [39]

1981

=

British Standard Institution 1881 [40]

1983

=

=

∙ ∙ ∙

.

1.5 + 1.5 +

ℎ ℎ

∙

Units [MPa]

(1)

[MPa]

(2)

[MPa]

(3)

3

Braga et al. [41]

1992

ACI [42]

2003

Augenti [43]

2003

Masi [4]

2005

=

=(

=#

= %&

∙

∙

∙ ℎ ! ∙

1.5 + ∙ ∙ ∙

∙

∙

$ ℎ ∙& ∙& '∙

)

1.5 +

∙&

[MPa]

(4)

[MPa]

(5)

[MPa]

(6)

[MPa]

(7)

More specifically, in the analysis carried out herein, the Rcub is calculated as the average R’cub of values obtained by the formulations proposed by Concrete Society [38], Cestelli Guidi and Morelli [39], British Standard Institution [40], Braga et al. [41], ACI [42], Augenti [43] and Masi [4]. The formulations (1), (2), (3) e (4), as shown in Table 1, define the concrete compressive strength of cubic specimens Rcub, whereas the formulations (5), (6) and (7) define the compressive strength of cylindrical specimens fcyl, namely the equivalent strength of an undisturbed cylindrical specimen. The formulations shown in Table 1 allow the transformation of the fcore into cubic or cylindrical (through the 0.83 factor) strength to be used during the design or verification steps.

2.2

The combined SonReb method

The SonReb method is the most common non-destructive approach for concrete strength assessment. In the technical literature there are many empiric formulations to determine concrete compressive strength with the SonReb method [35]; in this paper seventeen formulations are taken into account. The considered studies do not exhaust all the existing contributions [44-47] focused on the SonReb thecnique; however, they represent an important sample of the predictive models proposed so far. In Table 2 the considered formulations are listed, and the type of sample used for the calibration has been specified. Many of them have been calibrated upon data related to compressive tests of cubic concrete samples (A) or cylindrical concrete samples (B) as prepared in laboratory, while other ones have been calibrated on data related to compressive tests of cores, as extracted from existing buildings (C). As to formulations (13), (16) and (17) what cannot be taken for certain is the type of sample (D) as used by the authors to calibrate their proposed expression. Another relevant criterion for classifying the prediction relationships regards their “structure”, i.e. the type of correlation between the concrete strength and the independent variables; depending on their “structure”, the relationships have been classified as: linear (LN), polynomial (PL), power (PW), exponential (EXP) and logarithmic (LN). Table 2. Formulations to define the Rcub with the SonReb method Author

Year

Bellander [22]

1979

Meynink, Samarin [23]

1979

Giacchetti, Lacquaniti [26]

1980

Bocca, Cianfrone [48]

1983

Samarin, Dhir [49]

1984

Gašparik [50]

1992

RILEM [24]

1993

Di Leo, Pascale [51]

1994

Arioğlu, Köylüoğlu [52]

1996

Ramyar Kol [53]

1996

Kheder [54]

1999

Beconcini, Formichi [55]

2003

Formulation

Units

= 0.00082 ∙ +, + 11.03 ∙ . / − 32.7

= −24.1 + 1.24 ∙ + + 0.058 ∙ . 3/ = 7.695 ∙ 10

6

∙

= 2.765 ∙ 10

∙

= 0.0286 ∙ +

.738

69

. 7.8 /

∙+

. 7.3:; /

∙+

.3

.,

= −12 + 0.1 ∙ . 3/ + 0.76 ∙ + = 9.27 ∙ 10

6

3

∙ . /.:

∙+

.3

∙

. 7.8 /

= 1.2 ∙ 1069 ∙ . 7.338 ∙+ /

.< :

= 0.00153 ∙ (+, ∙ . 3/ )<.8

= −39.57 + 1.532 ∙ + + 5.0614 ∙ . / = 0.0158 ∙ +

.

;

∙ . <.37 /

= 5.9 + 2.712 ∙ 106

3

∙ + ∙ . 3/

MPa, km/s

Sample Correlation type type A PL (8)

[MPa, km/s

B

PL

(9)

MPa, m/s

C

PW

(10)

2

kg/cm , m/s

A

PW

(11)

MPa, km/s

B

PL

(12)

MPa, km/s

D

PW

(13)

MPa, m/s

A

PW

(14)

MPa, m/s

B

PW

(15)

MPa, km/s

D

PW

(16)

MPa, km/s

D

LN

(17)

MPa, m/s

A

PW

(18)

MPa, m/s

C

PL

(19)

4

Caiaro et al. [56]

2003

Del Monte et al. [57]

2004

Menditto et al. [58]

2004

Faella et al. (a) [59]

2009

Faella et al. (b) [59]

2009

= 1.74 ∙ 106; ∙ +6<.<8;3 ∙ . 7.,8 /

MPa, m/s

= 0.00004 ∙ +

MPa, m/s

∙ (+7 ∙ . ,/ )<.

= 4.40 ∙ 10

6;

= 2.6199 ∙ 10

.:: 3:

6:

∙+

8,3

∙ . <.:<:3< /

<. ,3

∙

. 7.7:;: /

A

PW

(20)

MPa, m/s

C

PW

(21)

MPa, m/s

A

PW

(22)

C

PW

(23)

C

LN

(24)

= 0.26511 ∙ + + 0.01385 ∙ . / − 34.51583 MPa, m/s

THE CONSIDERED DATA COLLECTION

3.

3.1. The sample Defining an investigation campaign to be carried out in situ is a very important step. The concrete sample extracted from a structural system can be considered as a part of an infinite dimension population whose mechanical proprieties are the subject matter we want to define. Since it is not possible to perform an unlimited number of experimental observations, the analysis has to be done on a population made of samples in a finished list whose characteristics can statistically stand for the entire population under observation. The data shown in this paper are related to 263 RC public buildings located in Tuscan areas having high seismicity, such as: Lunigiana, Garfagnana, Mugello, Casentino, Valtiberina and Amiata [60]. The buildings have undergone both non-destructive tests (Schmidt rebound hammer and ultrasonic velocity) and destructive (coring) tests. The ultrasonic test is marked out by the propagation speed of ultrasound Vus measured on the structural elements under analysis, while the sclerometric test is characterized by the rebound index Ir. The actual database consists of 860 values of Vus, Ir, fcore e R’cub. In Table 3 the main data of each parameter, such as the number of considered values, the average value, the standard deviation and the Coefficient of Variation (CoV), are listed. The value related to the COV of fcore, which is equal to 51%, highlights that the sampled data set is heterogeneous, as it includes data concerning good quality concrete as well as concrete having poor mechanical properties. In Table 4 the statistical parameters of the database are shown for each considered decade of construction. Table 3. Statistical parameters related to the database under investigation. Statistical parameters Number of values Mean value Stand. Dev. CoV

Vus [m/s] 860 3084 582 0.19

Ir [-] 860 39.3 7.0 0.18

fcore [MPa] 860 17.80 9.2 0.51

R’cub [MPa] 860 23.6 11.9 0.51

Table 4. Statistical parameters of the database divided into the constructions decades of the buildings Decade

50’s

60’s

Statistical parameters Number of values mean stand.dev. CoV Number of values mean stand.dev.

Vus [m/s] 55 2731 594 0.22 275 2882 601

Ir [-] 55 34.0 7.0 0.21 275 36.8 7.0

fcore [MPa] 55 10.6 4.7 0.44 275 14.7 6.7

R’cub [MPa] 55 14.2 6.6 0.47 275 19.5 8.9

5

CoV Number of values mean stand.dev. CoV Number of values mean stand.dev. CoV

70’s

80’s

0.21 332 3096 528 0.17 198 3442 433 0.13

0.19 332 40.5 5.8 0.14 198 42.0 6.8 0.16

0.46 332 18.64 8.9 0.48 198 25.9 10.1 0.39

0.45 332 24.7 11.8 0.48 198 34.4 13.2 0.38

40

fcore

35

80

R'cub

70 60

30

R'cub [MPa]

Compressive strength [MPa]

The R’cub average value related to concrete samples belonging to buildings made in the 50’s is approximately 14 MPa, while the same average value for buildings made in the 80’s is over 30 MPa, as reported in Figure 1. When considering the entire database, the correlation between the compressive strength of core, fcore, and the corresponding cubic compressive strength R'cub has been evaluated. In particular, the reliability of the expressions used to determine Rcub has been questioned and assessed. As reported in Figure 2, results point out that there is a good correlation in the examined samples, which has been confirmed as well by the value of the determination coefficient r, equal to 0.99.

25 20 15

50 40 30 20

10

10

5

0 0

0 50's

60's

70's

10 20 30 40 50 60 70 80

80's

’

Figure 1. Values of fcore and R cub for each decade of the buildings construction..

fcore [MPa]

Figure 2. Correlation between fcore and R’cub for the database under investigation.

3.2. Validation of the considered SonReb predictive methods In this Section the relationships listed in Table 2 have been applied to the assumed database. Figure 3 reports, for each single formulation, the average value of the estimated strength, Rcub, obtained as the average of values related to estimated cubic compressive strength concerning the entire database and the mean value of R’cub, equal to 23.6 MPa (Table 3).

Ramyar, Kol

Gašparik

Arioğlu, Köylüoğlu

Faella et al. (a)

Faella et al. (b)

Del Monte et al.

Di Leo, Pascale

Beconcini, Formichi

Samarin, Dhir

Giacchetti, Lacquaniti

Meynink, Samarin

Caiaro et al

Ramyar, Kol

Gašparik

Arioğlu, Köylüoğlu

Faella et al. (a)

Faella et al. (b)

Del Monte et al.

Di Leo, Pascale

Beconcini, Formichi

Samarin, Dhir

Giacchetti, Lacquaniti

Meynink, Samarin

Caiaro et al

Menditto et al.

RILEM

Kheder

0

Bellander

10

Menditto et al.

20

RILEM

30

Coefficient of Variation

Kheder

CoV

40

Bocca, Cianfrone

Rcub [MPa]

50

100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Bocca, Cianfrone

mean

Bellander

60

6

60s

50s Rcub [MPa]

Rcub [MPa]

Rcub [MPa]

Di Leo, Pascale Beconcini, Formichi

Del Monte et al.

Del Monte et al.

Faella et al. (a)

Faella et al. (a)

Faella et al. (a)

Faella et al. (b)

Faella et al. (b)

Faella et al. (b)

Ramyar, Kol

Gašparik

Gašparik Arioğlu, Köylüoğlu Ramyar, Kol

CoV

Arioğlu, Köylüoğlu Ramyar, Kol

CoV

CoV

100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%

100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%

100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Bellander

Bellander

Bellander

Bocca, Cianfrone

Bocca, Cianfrone

Bocca, Cianfrone

RILEM

RILE M

RILEM Kheder

Kheder

Kheder Caiaro et al

Caiaro et al

Caiaro et al

Menditto et al.

Menditto et al.

Menditto et al. Meynink, Samarin

Giacchetti, Lacquaniti Di Leo, Pascale Beconcini, Formichi

Ramyar, Kol

Percentage difference

Percentage difference

Percentage difference

RILE M

RILEM

Kheder

Kheder

Kheder

Caiaro et al

Caiaro et al

Caiaro et al

Menditto et al.

Menditto et al.

Menditto et al.

Meynink, Samarin

Meynink, Samarin

Meynink, Samarin

Samarin, Dhir

Samarin, Dhir

Giacchetti, Lacquaniti

Giacchetti, Lacquaniti

Gašparik Arioğlu, Köylüoğlu

7

Ramyar, Kol

Del Monte et al. Faella et al. (a) Faella et al. (b) Gašparik Arioğlu, Köylüoğlu Ramyar, Kol

Beconcini, Formichi Del Monte et al. Faella et al. (a) Faella et al. (b) Gašparik Arioğlu, Köylüoğlu Ramyar, Kol

Gašparik Arioğlu, Köylüoğlu Ramyar, Kol

Squared Mean Error

Bellander Bocca, Cianfrone RILEM Kheder Caiaro et al Menditto et al. Meynink, Samarin Samarin, Dhir Giacchetti,… Di Leo, Pascale Beconcini, Formichi Del Monte et al. Faella et al. (a) Faella et al. (b) Gašparik Arioğlu, Köylüoğlu Ramyar, Kol

SME

Faella et al. (a) Faella et al. (b)

Beconcini, Formichi

Di Leo, Pascale

% DIFFERENCE

Del Monte et al.

% DIFFERENCE

Beconcini, Formichi

% DIFFERENCE

Samarin, Dhir Giacchetti, Lacquaniti

Di Leo, Pascale

150%

RILE M

100%

Bellander Bocca, Cianfrone

50%

Bellander Bocca, Cianfrone

0%

-50%

150%

100%

50%

0%

-50%

150%

100%

50%

0%

-50% Bellander Bocca, Cianfrone

Faella et al. (a) Faella et al. (b)

300

Ramyar, Kol

Gašparik Arioğlu, Köylüoğlu

Del Monte et al.

250

Arioğlu, Köylüoğlu

Faella et al. (a) Faella et al. (b)

Di Leo, Pascale Beconcini, Formichi

200

Gašparik

Del Monte et al.

Samarin, Dhir Giacchetti, Lacquaniti

150

Ramyar, Kol

Faella et al. (a) Faella et al. (b)

Di Leo, Pascale Beconcini, Formichi

Meynink, Samarin

50

Gašparik Arioğlu, Köylüoğlu

Del Monte et al.

Caiaro et al Menditto et al.

100

Faella et al. (a) Faella et al. (b)

Di Leo, Pascale Beconcini, Formichi

Samarin, Dhir Giacchetti, L acquaniti

RILEM Kheder

0

Del Monte et al.

Samarin, Dhir Giacchetti, Lacquaniti

Coefficient of Variation

Coefficient of Variation

Samarin, Dhir

Coefficient of Variation

Meynink, Samarin

Meynink, Samarin

Di Leo, Pascale

mean

Arioğlu, Köylüoğlu

Del Monte et al.

mean

mean

Gašparik

Beconcini, Formichi

Bellander Bocca, Cianfrone

% DIFFERENCE

Di Leo, Pascale Beconcini, Formichi

150%

Di Leo, Pascale

100%

Samarin, Dhir Giacchetti, Lacquaniti

50%

Meynink, Samarin

0%

Samarin, Dhir Giacchetti, Lacquaniti

Caiaro et al Menditto et al.

-50%

Samarin, Dhir Giacchetti, Lacquaniti

RILEM Kheder

Percentage difference

Figure 3. Concrete strength provided by the considered formulations.

Meynink, Samarin

80

Meynink, Samarin

70

Caiaro et al Menditto et al.

60

Caiaro et al Menditto et al.

50

Kheder

40

Kheder

30

Bellander Bocca, Cianfrone

RILEM

20

0

Bellander Bocca, Cianfrone

RILEM

10

80

70

60

50

40

30

20

0

10

80

70

60

50

40

30

20

0

10

Bellander Bocca, Cianfrone

The quality of the results has been checked in terms of difference from numerical prediction and experimental strength. The best results have been considered the ones most approaching the experimental values, without exceeding them. As to each type of sample (A), (B), (C) and (D) it should be noted that some formulations tend to underestimate the cubic compressive strength R’cub, while others tend to overestimate it significantly. Particularly, all the formulations calibrated on samples (C) underestimate R’cub, with values varying between 17.42 MPa in the Giacchetti and Laquaniti [26] formulation and 22.75 MPa in the formulation by Del Monte et al. [57]. The results obtained according to these formulations have values of Coefficients of Variation ranging from 41% [57] to 57% [26] as shown in the second image of Figure 3. Among the formulations belonging to the A group, the one proposed by Caiaro et al. [56] results to be the most effective, with a predicted strength close and lower than the experimental one. Even the models proposed by Gašparik [50] and Arioğlu &Köylüoğlu [52], belonging to the group D, provided very good predictions.

70s

A

C

D

100%

50%

Ramyar, Kol

Gašparik

Arioğlu, Köylüoğlu

Faella et al. (a)

Faella et al. (b)

Di Leo, Pascale

Del Monte et al.

Beconcini, Formichi

Samarin, Dhir

Giacchetti, L acquaniti

Menditto et al.

Meynink, Samarin

RILEM

Kheder

Bellander

-50%

Caiaro et al

0%

Bocca, Cianfrone

Ramyar, Kol

Gašparik

Arioğlu, Köylüoğlu

Faella et al. (a)

Faella et al. (b)

Del Monte et al.

Beconcini, Formichi

Samarin, Dhir

Di Leo, Pascale

Giacchetti, Lacquaniti

Caiaro et al

Percentage difference

B

Menditto et al.

Gašparik

Ramyar, Kol

Arioğlu, Köylüoğlu

Faella et al. (a)

Faella et al. (b)

Del Monte et al.

Beconcini, Formichi

Samarin, Dhir

Di Leo, Pascale

Giacchetti, Lacquaniti

Menditto et al.

Meynink, Samarin

RILEM

Kheder

Caiaro et al

Bellander

0

Bocca, Cianfrone

10

Meynink, Samarin

20

RILEM

30

% DIFFERENCE

Coefficient of Variation

Kheder

CoV

Rcub [MPa]

80s

40

150%

100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Bellander

mean

Bocca, Cianfrone

60 50

experimental data

Figure 4. Concrete strength provided by the considered formulations for each decade

To better check the quality of prediction of the considered models, the strength values (Rcub) provided by the models have been compared to the corresponding experimental value (R’cub) in terms of percentage difference and Mean Squared Error (MSE). The most satisfactory models provide low values of percentage difference, with a negative sign, which indicates a safe prediction (i.e. a predicted strength lower than the experimental one). As can be seen in Figure 3, the percentage difference ranges from 136% in the formulation by Bellander [22] and -25% in the one by Bocca and Cianfrone [48]; the model of Del Monte [57] provided the better result, with a percentage difference equal to -4%. The SME, defined as the squared value of the difference between the experimental and the predicted strength, presents a scatter even larger than the percentage difference. The minimum values of SME are around 60 MPa2 (Beconcini and Formichi [55], Del Monte [57]), whilst the maximum values exceed the upperbound limit of the diagram, achieving 536 MPa2 with the model proposed by Ramyar and Kol [53] and 1693 MPa2 with the model proposed by Bellander [22]. It should be noted that the considered database consists of samples “C” according to the assumed classification; the models belonging to the C-group, therefore, result to be more consistent to the database. As a matter of facts, they provide the best results, with strength values close to the experimental ones and “safe” approximations, i.e. with predictions lower than the experimental values. The same comparative analysis has been performed by dividing the database into the four decades related to the construction period under consideration (Figure 4). In all the occurrences, the formulations calibrated on samples C underestimate or provide values very close to R’cub. In particular, in the formulation (24) by Faella et al. [59], the CoV has different values ranging from 29% as to the buildings built in the 80’s and 74% as to the buildings built in the 50’s. There were also high values of percentage difference for samples of buildings built all along the four decades time span in the formulations by Bellander [22] (100% and over) and Ramyar and Kol [53] (48% and over), characterized by strength values much higher than the R’cub.

4. 4.1

PROPOSED PREDICTIVE MODEL(S) The proposed predictive models

The results presented in the Section 3 show that the existing predictive models provide results very different from each other; some of them should not be considered trustworthy, since they can largely overestimate the mechanical features of the construction material (see Figure 3). In this section some new models are proposed, taking advantage from the large available data collection. The proposed models, differing from each other for their mathematical structure, have been set by performing a nonlinear regression analysis. The regression analysis allows to find out a mathematical relationship

8

between a dependent variable and one or more independent variables [61, 62]. In the non-linear approach, each model is previously generalized, thus changing into its logarithmic form and, then, retransformed. The independent variables have been considered to be both the propagation speed of ultrasound Vus and the average rebound index Ir, while the quantity R’cub has been considered as a dependent variable. As to the entire sample of experimental data, the following types of expressions have been calibrated, by minimizing the error between numerical prediction and experimental data through the software Essential Regression and Experimental Design [63]. In Table 5 the equations, having respectively a linear (25), polynomial (26), power (27), exponential (28) and logarithmic (29) structure, are shown. Other similar expressions, not reported for the sake of brevity, have been calibrated on the experimental data obtained subdividing the entire sample under investigation into the construction decade of the buildings and, hence, referring to a range of strength being much more limited. Table 5. Proposed predictive models. Formulation

Units MPa, m/s

Type linear

Code L

(25)

MPa, m/s

polynomial

PL

(26)

Rcub,PL = 10−4,251 ⋅Vus1,281 ⋅ I r0,686

MPa, m/s

power

PW

(27)

Rcub,EXP = 1,974⋅ e0,000542⋅Vus ⋅ e0,01605⋅Ir

MPa, m/s

exponential

EXP

(28)

Rcub , LOG = 26,74 ⋅ Ln (Vus ) + 15,67 ⋅ Ln ( I r ) − 249,21

MPa, m/s

logaritmic

LOG

(29)

Rcub , L = −28,44 + 0,01174 ⋅ Vus + 0,370 ⋅ I r −6

Rcub,PL = 41,59 − 0,02181⋅Vus − 0,859⋅ I r + 5,808⋅10 ⋅ V + 0,01539⋅ I 2 us

2 r

4.2 Analysis of the predictions provided by the proposed models In this section the proposed predictive models have been applied to the available database, and the obtained strength predictions have been compered in terms of mean, CoV, percentage difference, and Mean Squared Error (MSE). Figure 5 reports the main information regarding the models predictions for the entire database under investigation. As can be noted, all the proposed models provide a strength prediction very close to the experimental one, with a percentage difference ranging between -5% (models L, PL and LOG) and -11% (PW model). Moreover, it should be noted that all the models provided Rcub values lower than the experimental one. The CoV ranges from 30% to 40%, resulting therefore lower than the CoV of the experimental data. The PL model has the higher value of CoV (40%), that is the closest to the one of the sample. In Figure 6 the trend of the provided strength has been related to the two independent variables, in order to check the stability of the prediction. mean

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Figure 6. Values of Rcub provided by the proposed formulations

Namely, the predicted strength has been found by considering ultrasonic velocity values ranging from 1000 to 4000 m/s, by assuming a constant amount of index rebound (Ir equal to 15, 20, 25, 30, 35, 40 and 45, respectively). As can be noted, whilst the PW and the EXP models exhibit a monotonic trend and positive values of Rcub for all the possible combination of Ir and Vus, the effectiveness of the trend of the other models is related to the consistency of the data. The linear and the logarithmic models, indeed, for some combination of Ir and Vus can return negative values of the concrete strength, which would result not consistent with the physical evidence. The polynomial model, in turn, for some range of ultrasound velocity, provides a concrete strength which decreases at the increase of Vus. However, such restrictions in the application of the linear, polynomial and logarithmic relationships, which occur even in the models used in the literature having the same structure, do not affect the effectiveness of prediction for application of engineering consistence, i.e. for combination of data likely to occur. A further calibration of the proposed models has been performed on the basis of the databases referred to each construction decade. Figure 7 shows the results provided by the proposed models both from the general and the decade-specific formulations. As can be noted, in all cases the more specific calibration induces a decrease of the CoV.

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Figure 7. Prediction provided by the proposed models.

The sensitivity of the strength prevision to the specific calibration is different for the considered decades: for the data referred to the 60s and 70s the mean strength is almost the same for the two cases; for the 80s sample, instead, the prediction of the specific calibration is much better than the general one, since it reduces very much the underestimation of the strength. Even in the 50s samples, the decade-specific formulations provide a better prevision, with a numerical strength lower (i.e. safer) than the experimental one. All the five proposed models provide a strength prediction similar to each other; the CoV, instead, results to be more sensitive to the considered model, with lower values for the PW models in all the considered decades, both in the general and in the decade-specific formulations. The difference from prediction and experimental values (% DIFF) is similar for all the considered models. It should be noted that the general formulations provide satisfactory results even when compared to sample collecting specimens of specific decades.

5.

VALIDATION OF THE PROPOSED MODEL

The proposed model has been validated on the experimental data acquired on a case-study which does not belong to the presented database. The building complex has been object of accurate investigations [64,65], which include both destructive and SonReb tests. In this section such data are presented and the results provided by the adoption of the proposed models have been compared to those found through destructive tests. The considered case-study consists of different RC buildings, which have been made in different years, ranging between 1960 and 1980. In this research all the data have been considered to belong to the same sample, and the distinction between different buildings has not been kept. In Table 6 the data referring to the experimental campaign of the case-study are listed. The campaign consisted of 78 samples; each of them has been checked both by SonReb and core crushing analysis. The samples used for the core crushing were cylindrical, with a diameter ranging between 44 and 104 mm, and height having a double length than the diameter. The values of fcyl, Masi listed in Table 6 refer to the compressive strength found through the crushing test and normalized through the Masi [4]

11

formulation. The comparison with the considered models has been made by using the cubic strength, Rcub, masi, defined as fcyl, Masi /0.83. Figure 8 shows the comparison between the main statistical data of the tested sample and the results provided by the models presented in the Section 2.2 and the proposed models. As can be observed, all the proposed models provide a mean strength very close to that of the sample, with a percentage difference between 5% and 15%; the CoV ranges between 18% and 28%, resulting, in all the cases, much lower than the one of the experimental sample. The diagrams representing the percentage difference and the squared mean error have been cut at -100% and 500, respectively, in order to show the values of the models which better approach the tested sample. From the plots shown in Figure 8, all the five proposed models result to be effective in predicting the compressive strength of the sample; the large size of the database leads to perform an effective calibration no matter which structure is chosen for the relationship. As regards the effectiveness of the existing relationships, all the models belonging to the group C provide strength previsions lower than the experimental one, with contained (26%-39%) differences with the experimental sample. The models which provide a better prevision result to be the ones by Caiaro et al. [56] for the group A, the ones by Di Leo & Pascale [51] and Del Monte et al. [57] for the group C, and those by Gasparik [50] and Arioğlu & Köylüoğlu [52] for the group D.

Table 6. Data provided by the experimental campaign in the case-study. No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Diameter [mm] 84 84 84 84 84 84 84 84 84 84 84 84 84 104 84 84 84 84 84 84 84 84 84 104 84 84 84 84 84 84

fcore [MPa] 24.96 21.37 22.27 28.68 23.94 28.10 19.17 17.09 21.23 17.56 23.52 25.09 29.89 26.12 14.21 18.77 23.28 27.29 15.75 12.92 16.42 14.69 18.66 16.82 11.64 14.72 14.57 12.89 15.77 14.91

fcyl,Masi [MPa] 27,98 23,95 24,97 32,16 26,84 31,50 23,45 20,90 23,80 21,48 26,37 28,13 33,51 28,68 17,38 22,96 26,10 30,60 19,26 15,81 20,08 17,96 22,83 20,15 14,23 18,00 17,82 15,76 19,29 18,23

Iv 44,0 43,9 45,2 45,9 42,6 44,9 48,1 47,5 44,2 45,4 47,8 52,8 50,5 48,0 40,6 44,7 50,9 46,1 42,8 42,4 43,4 40,4 45,9 40,2 38,9 42,0 39,8 38,6 39,5 39,6

Vus [m/s] 3608,7 3218,9 3271,9 3607,4 3359,5 3337,0 3173,2 3021,1 3235,1 3316,4 3448,3 2983,1 3615,0 3521,5 3011,0 3416,9 3614,5 3504,4 3230,3 3099,2 2848,1 2765,8 2993,0 2882,8 3088,5 2990,0 3275,8 2947,0 3134,6 3116,5

No 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69

Diameter [mm] 84 84 84 104 84 84 84 84 44 44 44 44 84 44 44 84 84 84 54 54 54 54 84 84 84 84 84 104 104 83

fcore [MPa] 17.94 22.98 20.30 29.16 12.75 20.96 21.70 23.78 25.39 11.87 11.12 13.59 8.01 14.79 16.86 11.51 6.42 7.61 9.66 8.43 8.36 20.16 22.05 12.40 13.41 9.21 19.49 15.66 17.99 17.08

fcyl,Masi [MPa] 21,95 25,76 22,76 32,02 15,60 23,50 24,32 26,66 31,99 14,96 14,01 17,13 9,80 18,63 21,25 14,10 7,86 7,46 11,83 10,32 10,24 22,60 24,72 15,17 16,42 11,28 23,56 18,93 22,00 20,88

Iv 41,1 42,3 40,6 41,2 36,3 44,7 45,6 44,1 42,5 34,1 24,1 38,6 32,6 37,5 40,7 39,1 33,5 36,7 40,8 36,8 42,5 39,6 40,3 37,0 39,9 38,2 34,2 36,1 44,8 43,3

Vus [m/s] 3201,7 3473,6 3115,3 3229,3 2913,6 3178,0 3264,4 3169,0 3062,2 2770,9 2770,9 2945,0 2538,8 2974,2 3082,2 3012,0 2852,6 2207,5 3194,9 2754,0 3207,4 3364,5 3584,2 3323,5 3062,3 3000,0 3218,9 3133,7 2874,5 3530,8

12

31 32 33 34 35 36 37 38 39

84 84 84 84 84 84 84 84 84

18.73 11.47 11.90 9.94 9.03 12.91 14.41 16.84 21.73

22,90 14,03 14,55 12,16 11,04 15,79 17,62 20,60 24,37

42,7 36,3 33,4 29,1 32,6 37,5 35,5 39,2 47,8

3222,3 3775,2 2964,4 2691,4 2816,9 2969,3 2892,0 2969,3 3521,1

70 71 72 73 74 75 76 77 78

83 83 83 83 83 83 83 94 94

24.04 28.98 30.69 44.49 40.68 23.60 22.32 20.21 18.16

26,95 32,49 34,40 48,86 44,68 27,38 25,89 23,45 22,88

49,6 50,8 48,8 51,9 51,4 43,3 43,3 41,2 41,2

3543,3 4135,3 3291,8 3765,3 3685,5 3434,5 3434,5 3239,7 3239,7

In Figure 9 the correlation between numerical prediction and measured compressive strength Rcub, Masi has been shown for all the considered models. Since the two models proposed by Faella et al. [59], expressed by the equations (23) and (24) provide almost identical results, only one of the model (eq. 23) has been shown, for sake of brevity. As can be noted in Figure 9, some of the models provide a strength prevision much higher than the experimental values (Bellander [22], Menditto et al. [58], Ramyar & Kol [53]). Even the models belonging to the group B, set on samples prepared in laboratory, (Meynink, Samarin [23] Samarin, Dhir [49]) do not provide satisfactory predictions, with numerical values much higher than the experimental ones. The good results provided by the models by Gasparik [50] and Arioğlu & Köylüoğlu [52] is confirmed by the plots in Figure 9; as can be seen, indeed, the numerical prediction seems to be very effective at least in the low-average range of strength values, whilst they can hardly predict the high values of strength, like all the other considered models. 70

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Figure 8. Predictions of the considered model applied to the case-study

The proposed models provide strength predictions very similar to each other. They evidence a good effectiveness especially for the samples in the low-average range, whilst they slightly underestimate

13

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those with high strength (over 40 MPa). The PL model is the one which better represents the experimental distribution, whist the other models, especially PW and EXP ones, tend to gather the values around the mean value, as confirmed by the lower value of the CoV, shown in Figure 8.

6. CONCLUSIONS The paper faces the problem of characterizing the concrete’s compressive strength in existing RC buildings by exploiting the combined SonReb method. A large database has been used for checking the reliability of the most common prediction models available in the technical literature, and new semiempirical formulations have been proposed as well, by adopting the regression approach. The sample of experimental data to deal with is of high relevance from the statistical point of view, because it is based on a high number of data related to concrete types which differ from each other both for strength values and construction periods; indeed, the database consists of 860 “triple” data, including the results of the SonReb (Iv and Vus) and crushing test (fcore), which refer to 263 buildings. In particular, the data are related to concrete types with strengths ranging from 14 MPa to 34 MPa and belonging to buildings built in Tuscany between the fifties and the eighties. 60

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Seventeen models, selected form the most common available in the technical literature, have been checked on the basis of the considered database. The obtained results have shown that some formulations should not be always considered trustworthy, since they can largely overestimate the mechanic features of the construction material. Five different models, differing from each other for their mathematical structure (i.e.: linear, polynomial, power, exponential and logarithmic) have been calibrated on the assumed database by applying a regression analysis. The proposed models have been analyzed in terms of their prediction, dispersion and application field, evidencing the trend of the provided concrete strength in a wide range of Ir (from 15 and 45) and Vus (from 1000 m/s to 4000 m/s), to check the applicability conditions of each model. The proposed models have been validated on a further experimental campaign, whose data, published in this paper for the first time, are not included in the databased used for the calibration. They provided with a good and safe approximation the concrete compressive strength of the sample, especially for the samples in the low-average range, with strength below 40 MPa. The proposed models proved to be very effective in predicting the strength of concrete of buildings made in Italy in the second half of the XX century. Despite presenting some differences related to the assumed structures, the consistency of the calibration provides a good effectiveness to all the five proposed models, whichever their structure is. This work provides a contribution on the adoption of predictive methods based on the SonReb test, proposing new and effective formulations, and shows unpublished experimental data which can be used for further validation analyses.

ACKNOWLEDGMENTS The authors thank the Regional Seismic Department of Tuscany for making available the data of experimental data.

REFERENCES [1] OPCM 3274 (2003). Ordinanza del Presidente del Consiglio dei Ministri nr. 3274 del 20 marzo 2003 “Primi elementi in materia di criteri generali per la classificazione sismica del territorio nazionale e di normative tecniche per le costruzioni in gzona sismica”, Italia (in Italian). [2] NTC (2018). Decreto del Ministro delle Infrastrutture del 17 gennaio 2018. “Nuove norme tecniche per le costruzioni”, Italia (in Italian). [3] Bisch, P., Carvalho, E., Degee, H., Fajfar, P., Fardis, M., Franchin, P., Kreslin, M., Pecker, A., Pinto, P,. Plumier, A., Somja, H., Tsionis, G. (2012). Eurocode 8: Seismic Design of Buildings Worked examples. Editors: B. Acun, A. Athanasopoulou, A. Pinto E. Carvalho, M. Fardis. [4] Masi, A., (2005). “La stima della resistenza del calcestruzzo in situ mediante prove distruttive e non distruttive”, Il Giornale delle Prove Non Distruttive, Monitoraggio, Diagnostica, nr 1, pp. 23-32 (in Italian).

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State-of-art on predictive models of concrete strength through non-destructive tests Comparison between the results provided by the existing methods and a wide database Calibration of new predictive models on the database though regression analysis Validation of proposed and existing models on a different and unpublished database

I declare, even on behalf of my co-authors, that I have no conflict of interest which can influence the results of my research and the content of the paper titled “NEW PREDICTIVE MODELS TO EVALUATE CONCRETE COMPRESSIVE STRENGTH USING THE SONREB METHOD”.

Firenze, 17/09/2019

Stefania Viti