Alternative Method for Determining the Elastic Modulus of Concrete

A. H. A. Santos et al. Int. Journal of Engineering Research and Applications www.ijera.com
ISSN: 2248-9622, Vol. 5, Issue 9, (Part - 3) September 2015, pp.63-68
www.ijera.com 63 | P a g e
Alternative Method for Determining the Elastic Modulus of
Concrete
A. H. A. Santos*
, G. O. Ribeiro**
, R. L. S. Pitangueira**
, E. V. M. Carrasco**
* (Departamento de Engenharia Civil - Instituto Politécnico - Pontifícia Universidade Católica de Minas Gerais)
** (Departamento de Engenharia de Estruturas - Escola de Engenharia - Universidade Federal de Minas Gerais)
ABSTRACT
This paper presents the use of the technique of digital image correlation for obtaining the elasticity modulus of
concrete. The proposed system uses a USB microscope that captures images at a rate of five frames per second.
The stored data are correlated with the applied loads, and a stress-strain curve is generated to determine the
concrete compressive modulus of elasticity. Two different concretes were produced and tested using the
proposed system. The results were compared with the results obtained using a traditional strain gauge. It was
observed a difference in the range of 4% between the two methods, wherein this difference depends of a lot of
parameter in the case of the DIC results, as focal length and a video capture resolution, indicating that DIC
technique can be used to obtain mechanical properties of concrete.
Keywords - Experimental testing, Concrete strain, Concrete Structures
I. INTRODUCTION
An evaluation of the concrete compressive
modulus of elasticity is obtained directly from the
stress-strain curve experimentally. Normal
techniques, such as the Brazilian standard [1] and the
American standard [2], suggest methods for concrete
strain determination using an electrical resistance
strain gauge, a demec mechanical strain gauge and a
compressometer. An electrical strain gauge is the
most widely used method for concrete strain
determination [3]. However, the adhesion of the
strain gauge in a concrete sample requires time and
attention from the workers, and the adhesion is not
reused and results in a technique that is
unsustainable. Additionally, the use of a strain gauge
determines the size of the concrete samples for this
application. Consequently, a strain gauge cannot be
attached to smaller or larger parts unless the size is
specified by the strain gauge producers.
In recent decades, new technologies, such as
acoustic emission [4, 5], digital image correlation [6-
11] and shearography [12,13], have been used for
certain mechanical parameters of concrete, including
the elasticity modulus.
Among these techniques, digital image
correlation (DIC) has gained rapid recognition. The
DIC technique has several advantages, including
accuracy, dynamics and the rapid analysis of data.
This technique uses speckle patterns (natural or
artificial) as information carriers. By matching the
surface speckles captured before and after a
deformation or displacement using a correlation
function, adequate speckle displacement can be easily
obtained [14].
The use of the DIC technique has been widely
accepted in structures engineering because it is an
important method for characterizing the mechanical
response of homogenous [15-19] and heterogeneous
materials [20-24] undergoing nominally planar
deformation, especially when evaluating the fracture
behavior [25-28]. When using the DIC technique for
an evaluation of the elasticity modulus of concrete,
the work of Robert et al [29] was the first to
demonstrate excellent correlation between the results
obtained for the DIC technique with the results
obtained by the traditional method. Other work
which also made this comparison was to Huang [3].
In this study, Huang [3] used two high-resolution
CCD cameras equipped with long working distance
lens. The proposed system that is presented in this
paper uses a single USB microscope.
Using the principle of DIC, the motion estimated
for each point is obtained from the expansion of the
imaging system (correlation in mm/pixel). According
to Pan [22] and Sutton [30], this estimate only depicts
the real point of movement if two requirements are
met: (a) the sample surface must be at an angle of 90
degrees to the sensor pickup and remain in this
position during loading; (b) the image should not
suffer from geometric distortion.
Fig. 1 shows images of a random pattern of a
surface captured before and after deformation. To
determine the displacement of point A, a region near
this point is chosen in the reference image (Fig. 1a)
and in the combined deformed image (Fig. 1b). The
centroid of the selected rectangular area is used as a
reference point for measuring the relative
displacements. Additionally, the vertices of the
RESEARCH ARTICLE OPEN ACCESS

rectangle are used by the image processing software
to check the rotation and/or translation of the point.
Figure 1 - Object deformed texture pattern and
"overall dimensions"
After capturing the images and the definition of
the reference points, subroutines are processed using
specific software to store the displacements as
rotations (image by image) or as generating
coordinates (x, y) (point by point), which are
converted using the ratio of pixels per unit length and
are adopted as "overall dimensions" as shown in Fig.
1.
This article aims to evaluate the DIC technique
for obtaining the elasticity modulus of concrete.
Next, samples of concrete, which were prepared for
two different compositions, were used for the test of
uniform axial compression. The DIC technique
results were compared with the results obtained using
the strain gauge methods.
The DIC technique was applied using the USB
microscope (800x) and specific software. The
elasticity modulus of the concrete was determined
using the stress-strain diagram.
II. MATERIAL AND METHODS
According to Pan [22], the DIC technique
consists of three consecutive steps: (a) The
preparation of the sample surface and the experiment,
(b) The recording images from the planar surface of
the sample before and after the application of the
load, (c) The processing of images acquired using
appropriate algorithms to obtain the desired
displacements and deformations.
Fig. 2 shows the schematic setup of the proposed
system for monitoring the deformation of the
concrete. A single high-resolution USB microscope
was used to capture images in a region (2.0 cm x 1.5
cm). The USB digital microscope (800x) has an
image sensor of 1.2 megapixels and a video capture
resolution of 1280 x 960 pixels. The rate of capture
of the images is five frames per second and is
recorded in an AVI video format no compression.
The lighting is generated by an LED lamps’
microscope.
For image processing, software was developed
using the LabVIEW platform, which analyzes the
movements of translation and rotation of the
monitoring points and determines the relative
displacements. The respective software implemented
two techniques that are specific to image processing:
shift invariant and rotation invariant. The first
technique considers that during loading, monitoring
points can rotate up to four degrees. Values higher
than four degrees should be analyzed based on the
second technique. The PhD dissertation of Guetti
[31] developed the program and validated. In Annex
A, this PhD dissertation is shown the steps and
routines of digital image correlation software. The
proposed set (Microscope and software) is used to
measure the deformation.
Ten standard cylindrical concrete samples that
have a 100-mm diameter and a 200-mm length were
produced.
The specimen is under uniform axial
compression, which is calculated using the ratio
between the load and the initial cross-sectional area
of the specimen (Fig. 2). The longitudinal strain of
the concrete cylinder is obtained from the relative
displacement (d) in the axial direction of two points,
is used as the basis of measurement (DL) and is
located on the surface of the specimen near the
generatrix of the cylinder. Using the stress-strain
diagram, the elasticity modulus of the concrete is
determined.
Figure 2 - System that Captures Digital Images
The studied region was prepared prior to testing
by sanding the surface and was sprayed with black
and white speckles to provide a good contrast image.
A template with points spaced at 0.5 mm is
generated. The test can be performed without any
surface preparation, but the assurance of the
monitoring points will be dependent on the
randomness of the medium. The focal length of the
microscope was 5 cm with an optical zoom of 200
times (200x). Next, the obtained digital scale was
approximately 2 mm/pixel in both image directions.
This ratio is suitable for determining deformations
that are uniform and constant, when the precision of
the deformation attainable is from 153 me.
The proposed method uses samples that were
created with a concrete mixture. Both were produced

by coarse aggregate limestone, river sand and cement
(CP II - E32). No additives were included in the
mixture. Fig. 3 shows the grading curves of the
coarse and fine aggregates, which have a maximum
diameter (fmax) of 2.4 mm and 12.5 mm,
respectively.
The two types of concrete are denoted by L1 and
L2. The mix proportions are listed in Table 1. The
compressive strength test was performed, and the
samples were healed outdoors for 28 days and were
protected from direct sunlight.
Figure 3 - Grading curve for (a) fine aggregate,
(b) coarse aggregate limestone
The average compressive strength that was
determined at 28 days (fc 28) was 40 MPa (for L1
concrete) to 33 MPa (for L2 concrete).
Table 1 - Concrete mix proportions and
compressive strength for 28 days
Concrete
Cement
(kg/m³)
Coarse
aggregate
(kg/m³)
Fine
aggregate
(kg/m³)
Water
(kg/m³)
Water/ceme
ntratioA/C
Fc28(MPa)
L1 400 1200 600 220 0,50 40
L2 400 1200 600 220 0,55 33
Following a standard concrete testing method
indicated by technical standards [1,2], specimens
were prepared with a surface flatness of contact using
sulfur-based capping. The axial compression tests
were performed using a servo-hydraulic machine
EMIC, Model PC 200. When the cylinder sample
was compressed, a series of images was captured and
analyzed. To determine the elastic modulus, the
elastic section of the stress-strain curve was
considered in the narrow range between 0.5 MPa and
was 30% of the ultimate concrete strength. The data
of the compressive strength were previously
estimated using the uniaxial compression test, and the
strength data were used to determine the ultimate
loading for the cylinder specimens and to determine
the static modulus of elasticity in compression. The
value of 0.5 MPa is used to ensure a uniform contact
between the specimen and the machine, which leads
to an approximate initial deformation of 0.0001 mm /
mm
Charging and discharging cycles were performed
to stabilize the test at a rate of 0.45 MPa/s for
intervals of 30 seconds between loading and
discharge.
Using the system of data capture called SPIDER
8, the displacements’ information and the applied
loads were stored in time. The images captured by
the microscope were simultaneously stored on a hard
disk in parallel. Once, the data capture system and the
microscope are decoupled the variable "time" was
adopted as the parameter compatibility information.
The compatibility was performed using an
electronic spreadsheet, where, before performing the
assay, the simultaneity of the system clocks data
capture and the USB microscope was done.
Additionally, an equivalent definition for the
sampling frequency of the numerical data (5 Hz) and
for the rate of image capture (5 fps) was performed
before the test.
Fig. 4 shows a photograph of the experiment
assembly.
Figura 4 - Real setup of the experiment using a
servo-hydraulic machine EMIC, Model PC 200
and an USB microscope (800x). The sample is also
affixed with traditional strain gauges (mechanical
extensometer).
In addition to the USB microscope (800x),
traditional strain gauges (Clip Gauges) were installed
diametrically (i.e., opposite the surface of the
specimen) to obtain the deformation, and the results
were used for comparison with the proposed method.

III. RESULTS AND DISCUSSION
Fig. 5 shows the deformation versus the time
curves for the fourth specimen of concrete L1
obtained from the USB microscope and the
traditional strain gauges. The charging and
discharging cycles are very evident in the curves
(Fig. 5). This variation was captured by the DIC
technique even though the reference length (DL = 13
mm) of the image was different from the reference
length of the traditional strain gauges (DL = 100
mm). The difference between the two curves can be
attributed to the non-homogeneity of the composite
material as well the difference between the reference
length adopted for each of the methods for
calculating the deformation.
Figura 5 - Curve deformation versus time for
specimen CP4 - L1
The DIC technique has always presented a
greater deformation than the traditional strain gauges
(Fig. 5). For the highest stress levels, this difference
is reduced. The percentage difference between the
curves at points A and B is 6.5% and 47.8%,
respectively.
An improved fitting in the curves for the highest
stress may demonstrate that the DIC technique
enhances their sensitivity as the deformation
increases.
Figura 6 - Stress-strain curve for a 28-day
cylindrical concrete sample CP4 –L1
Fig. 6 shows typical stress-strain curves for the
cylindrical concrete sample CP4 - L1 that is obtained
from the USB microscope and the traditional strain
gauges. The resulting curves are very similar to each
other. The horizontal shift in the axis of the
deformation is a direct consequence of the difference
observed and discussed in Fig. 5.
The dispersion of the data (Fig. 6) that occurred
in the loading and unloading cycles could be related
to the fact that the test is held at the same stress level
for 30 seconds to stabilize. The cycles may vary
because of the apparatus oscillation in the load,
which occurs to maintain the stress. For this sample,
the difference between the values of the elasticity
modulus for the DIC technique and the traditional
strain gauges was approximately 3%.
For the other samples, similar curves were
obtained, and the average of the elasticity modulus
and the standard deviation was calculated (Table 2).
For concrete L1, the average elasticity modulus
that was obtained using the DIC technique was 30.56
GPa, and the average elasticity modulus that was
obtained using the traditional strain gauges was 29.49
GPa. For concrete L2, the average elasticity modulus
obtained using the DIC technique was 28.75 GPa,
and the average elasticity modulus that was obtained
using the traditional strain gauges was 27.97 GPa.
The values obtained for the two types of gauges are
similar. The difference between these values for the
L1 concrete was 3.63%, and the difference between
these values for the L2 concrete was 2.8%. This
divergence can be attributed to the differences of the
analysis points, the difference between the reference
lengths (DL) used to compute the strain for each
method and the very characteristic of the
inhomogeneous concrete.
Table 2 - Comparative data between the results
obtained using the DIC technique and the
traditional strain gauges (MPa)
The results obtained for the specimens are shown
in Fig. 7 and Fig. 8. It is noticed that to DIC strain
values using a microscope, thus with a small

"optical" strain gauge size (13 mm, of same order of
the mean size of the coarse aggregates), has very
similar results with a large strain gauge size (100
mm). The test was performed using DIC repeatedly
changing the position of the microscope. The values
found for the same specimen were different, but
within the range of the standard deviation shown in
Tab.2. This result shows that the response DIC, even
though localized, representing the macroscopic
behavior of the axial compression test.
Figura 7 - Elasticity Modulus versus Reference
Length - Trace L1
Figura 8 - Elasticity Modulus versus Reference
Length - Trace L2
The results showed that the DIC technique
provides values equivalent to the values obtained
using traditional strain gauges as well as significant
advantages. The first major advantage is that the DIC
technique can be used without surface preparation or
for the preparation of only a small region. Currently,
no dependence exists for the randomness of the
medium for this technique. The second major
advantage is that the dynamics and flexibility of the
DIC technique can be applied for studies in which the
electrical strain gauge or mechanical strain gauge are
not possible, including samples of various sizes. The
third advantage includes the accuracy of the system,
which can be improved in accordance with the
situation by changing both the focal length and the
focus area to achieve greater precision. Finally, the
proposed system offers low-cost, easy use and
sustainability because the hardware can be reused
indefinitely.
IV. CONCLUSIONS
A method for obtaining the concrete strain and
displacements using a USB microscope (800x) and
for determining the concrete elasticity modulus of
compression has been proposed and validated in this
paper. The values obtained by the proposed system
was of the same order of magnitude of the values
generated using the traditional strain gauge. A
difference of up to 4% was found for the values of
the modulus of elasticity.
New tests will be performed to improve this
analysis. For example, a system will be developed for
coupling the load to the images without the need for
human intervention. In addition, the installation of
other microscopes simultaneously will enable the
identification of strains in the longitudinal and
transverse plane as well as the outside shooting plane.
Generally, the digital image correlation
technique is a technology with a wide range of
applications in structures engineering and can be used
with any type of material, such as wood and steel.
Acknowledgements
The authors acknowledge the support received
from Pró-Reitoria de Pesquisa da Universidade
Federal de Minas Gerais - UFMG.
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