Nghiên cứu ứng dụng sóng siêu âm dự đoán cường độ chịu nén và vết nứt của bê tông sử dụng tro bay và bột đá TT TIENG ANH

THE UNIVERSITY OF DA NANG

UNIVERSITY OF SCIENCE AND TECHNOLOGY

VUONG LE Thang

APPLICATION OF ULTRASONIC PULSE VELOCITY
FOR PREDICTION OF COMPRESSIVE STRENGTH
AND CRACKS OF CONCRETE MADE OF FLY ASH
AND STONE POWDER
Major: Engineering Mechanics
Major Code: 9520101

SUMMARY OF DOCTORAL THESIS

Danang 2021


This work was finished at:
THE UNIVERSITY OF DANANG
UNIVERSITY OF SCIENCE AND TECHNOLOGY

Supervisors:
1. Assoc. Prof. LE Cung
2. PhD. NGUYEN DINH Son

Reviewer 1:
Reviewer 2:

The thesis will be defended in front of the Doctoral Thesis Defend
Committee at the University of Science and Technology, the

University of Danang at ……hour, on ……. month …… in 2021
The thesis can be found at:
- Vietnam National Library
- Information Center and Library of University of Science and
Technology, The University of Danang.


INTRODUCTION
1. Motivation and problem statement
Concrete is a commonly used material in construction works in
Vietnam, so the concrete quality needs to be taken care of to ensure the
load-bearing capacity of buildings. According to Vietnamese standard
TCVN 4453:1995, the concrete quality is expressed through many
parameters such as compressive strength, flexural strength,
waterproofing, abrasion resistance, slump,... Among them, compressive
strength is the most important one and is regularly controlled in
constructions.
Traditional materials for making concrete are sand, gravel, Portland
cement, and water. The excessive exploitation of these materials,
especially sand mining in rivers, has caused adverse effects on nature.
Therefore, it is urgent to seek alternative sources of materials for these
traditional ones. In the Central region, according to the report of Vung
Ang Thermal Power Plant in Ha Tinh province, each year, the plant
generates about one million tons of ash and slag, and in quarries, there is
a large amount of waste stone powder from the mining (Fig. 1). These
two materials can partially substitute for concrete components, and this
substitution will affect the compressive strength, a key parameter of
concrete quality.

Fig. 1. Thermal Power Plant in Vung Ang, Ha Tinh Province and

Phuoc Tuong Quarry, Danang City
Nowadays, there are two methods for evaluating the concrete
compressive strength: destructive and non-destructive tests. The former
gives direct results; however, it will destroy the test specimen. The latter
can predict the compressive strength without affecting the sample.
However, both can only evaluate the compressive strength of finished
1


concrete, not expect the concrete mixtures and the proportion of
substitute materials to ensure the concrete compressive strength.
Many studies with new materials use regression (linear, nonlinear,
univariate, multivariable) and artificial neural network (ANN) models to
predict concrete compressive strength based on different input
parameters. In our country, some recent works have used ANN
networks for predicting concrete compressive strength. However, no
studies predict the compressive strength of the concrete containing
substitute materials fly ash and stone powder. That is why elaborating a
model for predicting the compressive strength for this type of concrete
is a crucial issue.
During the concrete operation using substitute materials, cracks also
need to be studied besides compressive strength. A problem arises: how
to predict the size of the concrete cracks, particularly their depths,
especially with concrete made of the substitute materials mentioned
above. Many studies currently use ultrasonic methods to determine the
crack depth, such as the Impact-Echo Method, Time of Flight
Diffraction Method (TOFD), Surface Wave Transmission Method, and
Diffusion Method. Therefore, to evaluate the crack, it is necessary to
investigate and simulate the wave propagation in concrete; it aimed to
study the propagation characteristics of ultrasonic waves in cracked

concrete, finding out experimental methods to estimate their depths.
From the above analysis, the study and application of ultrasonic
waves to predict compressive strength and cracks of concrete containing
waste products of fly ash and stone powder in the Central region are
very urgent and highly applicable.
2. Research objectives
• Elaborating a program to simulate the ultrasonic wave propagation
in concrete containing fly ash and stone powder, taking into account the
attenuation of wave amplitudes in different concrete mixtures, thereby
studying the propagation characteristics of ultrasonic waves in concrete
with and without defects (cracks, holes, etc.).
• Building regression and ANN models to predict the compressive
strength of concrete made of fly ash and stone powder, reaching
2


compressive strength from grades B10 to B45, based on ultrasonic pulse
velocity (UPV), attenuation ratio of ultrasonic wave amplitudes, and
concrete mixtures.
• Determining the method to predict the open-crack depth in
concrete using substitute materials like fly ash and stone powder,
implementing numerical simulation and experiments to predict open
crack depth in the concrete mentioned above.
3. Object and scope of research
• Research object: Concrete compressive strength, Rayleigh
damping coefficients of concrete, and crack depths in concrete.
• Research scope of the topic:
o Concrete components are materials in Central Vietnam: sand,
gravel, Portland cement, stone powder (substituting 20% sand), fly
ash (replacing 20% cement), and water.

o In the wave propagation simulation, concrete is supposed to be
a homogeneous and elastic material, and a two-dimensional
problem model is considered.
o Open cracks perpendicular to the concrete surface.
4. Research content
• Theoretical research:
o Investigate the mathematical model of wave propagation in
concrete and methods for solving wave propagation equations.
o Investigate the Rayleigh damping model to determine the
attenuation of ultrasonic waves when transferring through concrete.
o Elaborate the program to simulate the ultrasonic wave
propagation in concrete using fly ash and stone powder, taking into
account the attenuation of wave amplitude when propagating
through concrete with different mixtures.
o Investigate models to predict concrete compressive strength
based on ultrasonic pulse velocity, wave amplitude attenuation
ratio, and concrete mixtures.
o Investigate the method to predict the depth of open cracks
perpendicular to the concrete surface by evaluating of diffraction
time of ultrasonic wave propagation.
3


o Numerically simulate ultrasonic wave propagation for
investigation of the propagation characteristics of ultrasonic waves
in concrete with and without defects (cracks, voids, etc.), and at the
same time to verify the prediction method of the depth of open
crack perpendicular to the surface of concrete using fly ash and
stone powder.
•

Experimental study:
o Elaborating a set of experimental data based on concrete cubic
specimen 15x15x15cm3: Physical and mechanical properties of
concrete components, concrete mixtures (72 mixtures), density,
Young modulus, ultrasonic pulse velocity at the age of 28 days,
ultrasonic amplitude attenuation ratio and concrete compressive
strength at the age of 28 days.
o Elaborating multivariable models to predict the concrete
compressive strength based on linear regression and ANN models.
o Elaborating the experimental setup to determine the Rayleigh
damping coefficients of concrete (corresponding to 72 mixtures)
when ultrasonic waves of 54kHz frequency propagate through a
concrete cubic specimen each edge of 15cm.
o Implementing the experimental setup to estimate the depth of
open cracks perpendicular to the surface of concrete using fly ash
and stone powder by the TOFD method, thereby verifying the
simulation results and the method for evaluating crack depth.
5. New contributions of the thesis
• Elaborating a two-dimensional simulation program of ultrasonic
wave propagation in the concrete environment, taking into account the
damping matrix using the Rayleigh damping model through damping
coefficients α and β of concrete estimated by experiments.
• Building an experimental data set based on 72 concrete mixtures
containing by-products, namely, fly ash and stone powder as substitute
materials for partial replacement of cement and sand. The concrete
compressive strength of testing specimens achieved grades from B10 to
B45. This data set consists of the following information: concrete
mixture, ultrasonic pulse velocity at the ages of 28 days, density and
4

Young modulus of concrete, ultrasonic wave amplitude attenuation ratio
at 28 days, and 28-day concrete compressive strength.
• Setting up models to predict the compressive strength of concrete
by both linear regression and ANN networks based on the experimental
data set. The models contribute to concrete manufacturers to determine
the pertinent range of concrete ingredient contents to ensure the required
value of compressive strength by designers.
• Estimating Rayleigh damping coefficients for 72 concrete mixtures
containing by-products of fly ash and stone powder. Building an ANN
model to predict the Rayleigh damping coefficients α and β of concrete
at any mixture based on experimental data set.

Chapter 1:

STATE-OF-ARTS

The analysis and synthesis in the state-of-arts of worldwide and
national works have shown that two main methods to simulate the wave
propagation in concrete exist: finite difference method (FDM) and finite
element method (FEM). Regarding the advantages and disadvantages of
the two approaches, the FEM is suitable for one of the requirements of
the research topic, which is to simulate the propagation of ultrasonic
waves in concrete.
However, the damping matrix is the main difficulty confronted with
the current research when using the FEM method to simulate wave
propagation. Among the many theories of damping, the Rayleigh model
is suitable for determining the damping matrix. Rayleigh coefficients are
determined experimentally for specific cases of investigated concrete.
For predicting the concrete compressive strength, most national

studies often create the relationships between compressive strength (R)
and two parameters of ultrasonic pulse velocity (UPV) and bouncing
gun value (n). Meanwhile, compressive strength depends on many other
factors, so these prediction models are inaccurate compared to
multivariable ones with several inputs.
Currently, two multivariable models are used to predict compressive
strength: multivariable regression (linear and nonlinear) and ANN
models. Many worldwide and domestic studies are performed according
to this research axe. The analysis of the state-of-arts shows that the
5


ANN has high accuracy. However, when using these models, the
selection of input parameters is crucial and affects the prediction
accuracy.
There are different methods for predicting crack depth using
ultrasonic waves with their advantages and disadvantages. For the
Impact-Echo Method, the peak frequency fT for each crack is different
and does not follow a specific rule. The Surface Wave Transmission
Method is required to satisfy the condition that the ratio of crack depth h
to wavelength λ is greater than or equal to 1.5 (h/λ  1.5), and the
concrete surface must have enough space to set up the measurement. In
addition, since surface waves do not penetrate too deeply into the
concrete, this method is usually only suitable for cracks located near the
concrete surface.
The Diffusion Method and the Time of Flight Diffraction Method
(TOFD) have appreciated as with higher accuracy. These two methods
are used to create the approach to predict the crack depth in different
concrete objects. The numerical simulation aims to verify the proposed
method, and experiments are implemented for validating the proposed

approach and numerical simulation results. Among these two methods,
the TOFD is suitable for the research content of the topic. The wave
propagation time (time-of-flight) will be estimated by experiments and
by the simulation program using the FEM method, and Rayleigh
damping coefficients are determined experimentally presented in
Chapter 3 of the thesis.
From the overview analysis of the modelling and simulating
ultrasonic propagation problems, of the prediction of compressive
strength and crack depths, the following conclusions are derived:
1. With the simulation of the ultrasonic wave propagation in concrete,
the FEM method is suitable, even if the concrete specimen has defects
(cracks, holes...). The difficulty confronted with the FEM method is to
determine the damping matrix when the ultrasonic wave propagates in
concrete. For this purpose, the Rayleigh damping model is suitable. The
Rayleigh damping coefficients of the investigated concrete materials
will be determined experimentally in Chapter 3.
2. A multivariable model should be used to predict the compressive
6


strength of concrete containing fly ash and stone powder. In this
situation, two models with linear regression and ANN network are
implemented, and their performances are compared, thereby selecting
the most suitable one to solve the mentioned task.
3. With the prediction of crack depth of this new concrete using fly
ash and stone powder, the TOFD method is suitable. This method
possessed high accuracy. The time-of-flight can be determined from
numerical simulation using the FEM method (considering the damping
matrix using the Rayleigh damping model) and verified by experiments.

Chapter 2: SIMULATION OF ULTRASONIC WAVE
PROPAGATION AND PREDICTION OF CRACK DEPTH
IN CONCRETE
2.1. Numerical simulation of ultrasonic wave propagation using
finite element method
2.1.1. Determining characteristic matrices of the FEM method
At time t, let consider volume V bounded by the surface S of the
moving medium. The volume, with velocity field 𝐯, is subjected to a
volume load 𝐊. Each element on its boundary S is acted upon by the
stress vector 𝐓n. The motion equation of one particle in the medium
reads as:
σij
2 u j
(2.1)
+ ρK j = ρ 2
x i
t
When taking into account damping effects of the medium, Hook’s law
is written as follows:
σij = cijmn ε mn + ηijmn ε mn
(2.2)
By substituting Eq. (2.2) into Eq. (2.1) and ignoring the influence of
the volume load, we have:
cijmn u m,nj + ηijmn u m,nj = ρu i
(2.3)
Using the FEM method, Eq. (2.3) can be re-written as follows:
MQ(t) + CQ(t) + KQ(t) = F(t)

(2.4)
Where: M, C, K, F are global mass matrix, damping matrix, stiffness

matrix, and load vector.
The global stiffness matrix K and mass matrix M of the whole
7


structure are assembled from the stiffness and mass matrix of all
elements:
K =  TeT K e Τe với K e =  BT DBdV
e

(2.5)

Ve

M =  TeT M e Te với M e =  N T ρNdV
e

(2.6)

Ve

Rayleigh damping model is used to determine the damping matrix C
according to the following expression:
(2.7)
C = αM + βK
Where: , β are the Rayleigh damping coefficients according to mass
and stiffness matrices.
2.1.2. Solution of motion equation using Newmark’s numerical
integration method
Based on the mathematical model of ultrasonic wave propagation in

concrete, using the FEM method and Newmark algorithm, we elaborate
the algorithm and a Matlab program for the simulation of twodimensional (2D) ultrasonic wave propagation in concrete. Concrete
(cement and aggregates), voids, reinforcements each are assumed to be a
homogeneous, elastic solid medium. The attenuation of ultrasonic wave
amplitude when propagating is taken into account using the Rayleigh
damping matrix, with the coefficients α and β determined for each
concrete mixture based on the experimental data set (Chapter 3).
The ultrasonic wave generated by the transmitter is simulated by
displacement excitation as follows:
q = q 0 sin ( t ) ;
dq / dt = q = v = .q 0 cos ( t ) ;

(2.8)

dv / dt = q =  .q 0 sin ( t )
2

Where, q: displacement at the transmitting point of ultrasonic wave.
2.2. Numerical results of ultrasonic wave propagation in specimens
2.2.1. Investigated specimens
The investigated specimens are cubic blocks, each edge of 15cm, as
shown in Fig. 2.1. The images of wave propagation through the
specimens are shown in Fig. 2.2 and the displacements at the receiving
8


points (point 1, point 2, point 3) of specimen 1 in Fig. 2.3. The simulation
results give us the visual look of the ultrasonic wave propagation in the
concrete specimens and the agreement with the wave propagation
characteristics. They show that the hole (in specimen 2) and the crack (in

specimen 4) significantly prevent the propagation of ultrasonic waves to
the receiving point.

Fig. 2.1. Configurations of investigated specimens

Fig. 2.2. Ultrasonic wave propagation in specimens 2 and 4
9


Fig. 2.3. Displacements at points 1, 2, and 3 of specimen 1
2.2.2. Validation of simulation results by experiments
The simulation program using Matlab is verified by comparing the
ultrasonic wave amplitude attenuation ratio obtained from simulation
results and experimental measurements after propagating through
specimen 1 at point 3. The displacements uy from the Matlab simulation
program at the transmitting point 1 and at receiving point 3 in specimen 1
are shown in Fig. 2.4a and Fig. 2.4b, respectively. The signal waveforms
received from experimental measurements at point 1 (transmitter) and
point 3 (receiver) are shown in Fig. 2.5.

a) Transmitting signal
b) Received signal
Fig. 2.4. Displacements at points 1 and 3 in specimen 1 (Matlab)

a) Transmitting signal
b) Received signal
Fig. 2.5. Waveforms at points 1 and 3 in specimen 1 (experiment)
10

The wave amplitude attenuation ratio based on simulation program:
A2/A1=0.1225, and on measurements: A2/A1=2.557/20=0.1279. The
results show a high agreement between the numerical simulation results
and the experimental ones, the relative error of this attenuation ratio when
propagating through the specimen is 4.2%.
2.3. Numerical simulation for evaluating concrete crack depth
The investigated specimen for evaluating the open crack depth in
concrete is shown in Fig. 2.6a. The simulation image shows that the
signals emitted by the transmitter will propagate in concrete and reaches
the top of the crack, and this position, in turn, becomes a secondary
transmitter that continues to emit signals that propagate to the receiving
point (Fig. 2.6b).
a)

b)

Fig. 2.6. a) Investigated model, b) Image of wave propagation
through the crack
The formula to evaluate the depth of open crack perpendicular to the
concrete surface:
D = (C p .t / 2) 2 − H 2

(2.9)

Where Cp is the propagation velocity of the longitudinal wave
(determined by experiment), H is the distance from the transducer to the
crack, t is the time-of-flight from the transmitter to the receiver. As a
result, the crack depth from the simulation is 7.5cm.
2.4. Conclusions of Chapter 2
The program for simulating the two-dimensional propagation of

ultrasonic waves in concrete using fly ash and stone powder is
implemented assuming that the concrete is homogeneous, elastic, and
isotropic. Numerical simulations were performed for four investigated
specimens: pure concrete specimen, specimens with defects (hole and
crack), and specimen with steel reinforcement. The properties of concrete
11


introduced in the simulation are measured experimentally. The numerical
simulation results have good agreements with those of the experiment.
The simulation program is used to evaluate the depth of open crack
perpendicular to the concrete surface, and the relative error is 7.1%
compared to actual crack depth. This error is acceptable. The difference
between the simulation result and actual depth crack value may be due to
the assumption that the concrete (cement and aggregates) is considered a
homogeneous medium.
The difficulty in the simulation problem is to know the Rayleigh
damping coefficients of concrete using fly ash and stone powder. These
coefficients will be determined by the experimental method proposed and
detailed in Chapter 3 of the thesis.

Chapter 3: EXPERIMENTS FOR PREDICTION OF
COMPRESSIVE STRENGTH, RAYLEIGH DAMPING
COEFFICIENTS, AND CRACK DEPTHS OF CONCRETE
3.1. Experimental materials
Table 3.1. Selection of test materials
Materials
Fine aggregate
Coarse aggregate
Binder

Sand
Stone powder
Gravel
Cement
Fly ash

Percentage (%)
80%
20%
100%
80%
20%

Based on literature reviews and the actual data of concrete mixtures
at concrete making plants in Central Vietnam, the test materials for
specimen manufacturing are shown in Table 3.1. The physical and
mechanical characteristics of the materials fully satisfy the requirements
in concrete production.
3.2. Experiments for concrete compressive strength prediction
3.2.1. Analyzing factors affecting compressive strength
Many factors shown in Fig. 3.1 affect the concrete compressive
strength, but the problem will be highly complicated if all these factors
are investigated in the same model. Therefore, the thesis only considers
the concrete mixture factors, and the other conditions are assumed to
comply with usual ones.
12


Fig. 3.1. Leading factors affecting concrete compressive strength

3.2.2. Experimental procedure and data sets
3.2.2.1. Experimental procedure
Referring to the instructions of the Ministry of Construction on the
concrete components selection, the ingredient contents to obtain the
compressive strength from grades B10 to B45 are designed. Based on
the variation of ingredient content, thember of variation levels of
ingredients is shown in Table 3.2.
Table 3.2. Ingredients and variation levels of ingredient contents
Variation levels
Designation

A
B
C
D

Ingredients

1

Fine aggregate (kg)
640
Coarse aggregate (kg) 1100
Binder (kg)
216
Water (liter)
190

2

3

792
1200
319
210

944
422
230

4

No. of
variation
levels

525

3
2
4
3

The required number of concrete mixtures for the experiment was
determined by the multifactor design of experiment method:
21×32×41=72
From the above analysis, the experimental procedure to determine the
concrete compressive strength is as follows (Fig. 3.2).

Fig. 3.2. Procedure for elaborating experimental data sets
13


3.2.2.2. Elaborating experimental data set
1. Ultrasonic pulse velocity measurement: Using a Tico ultrasound
machine of Proceq, Switzerland, pulse frequency 54 kHz, with two
transducers placed on opposite sides of the specimen (direct
transmission). The UPV is measured at the age of 28 days of concrete
and for all 72 concrete mixtures.
2. Determination of the ultrasonic amplitude attenuation ratio:
Recording the signal waveform from the transmitter of the Tico
ultrasonic instrument (pulse frequency 54kHz), and receiving the signal
waveform, using SYSAM-SP5 digital signal acquisition and Latis-Pro
software of Eurosmart, France. The amplitude attenuation ratio of the
ultrasonic wave through the specimen: A2/A1, where A2, A1 are the
amplitudes of the receiving signal after propagating through the
specimen and of the transmitting signal, respectively. The ratio A2/A1 is
measured for all 72 concrete mixtures.
3. Determination of the densities of concrete specimens: At 28 days,
weigh the specimens and determine the densities of 72 concrete
mixtures.
4. Determination of the Young modulus of concrete
specimens: Based on the instructions of TCVN 9357:2012, the Young
modulus is interpolated based on ultrasonic pulse velocity.
5. Determination of the concrete compressive strength: Using a
hydraulic compressor SYE-2000A, whose maximum load is 200 tons.
3.2.3. Elaborating models for predicting concrete compressive
strength
Three prediction models for each method (linear regression and

ANN) with different input parameters were elaborated to compare their
performances and aim for an optimal one.
• Model 1: 05 input parameters including fine aggregate A[kg],
coarse aggregate B[kg], binder C[kg], water D[liter] and 28-day
UPV [m/s]; The output is the 28-day compressive strength
R[daN/cm2].
• Model 2: 05 input parameters including fine aggregate A[kg],
coarse aggregate B[kg], binder C[kg], water D[liter] and amplitude
14


attenuation ratio A2/A1; The output is the 28-day compressive
strength R[daN/cm2].
• Model 3: 06 input parameters including fine aggregate A[kg],
coarse aggregate B[kg], binder C[kg], water D[liter], UPV 28
days[m/s] and amplitude attenuation ratio A2/A1; The output is the
28-day compressive strength R[daN/cm2].
3.2.3.1 Multivariable linear regression model
a. Predicted results of regression models
The regression equations of the three models (models 1, 2, and 3) to
predict the compressive strength of concrete using alternative materials
are given by Expressions (3.1), (3.2), and (3.3).
R1 = −150 + 0,094.A − 0,047.B + 1,096.C − 1,328.D + 0,0718.UPV
R 2 = 132 + 0,0912.A + 0,012.B + 1,1768.C − 1,675.D + 91,9(A 2 / A1 )
R 3 = −506 + 0,1723.A + 0,041.B + 0,967.C − 1,07.D + 0,1099.UPV

+ 132,8(A 2 / A1 )

(3.1)
(3.2)

(3.3)

The residual plots can be analyzed to evaluate the fitting of the
regression equation (Fig. 3.3). The analysis shows a high fitting of all
three models, and it is entirely possible to use the above regression
equations to predict the concrete compressive strength.

Fig. 3.3. Residual plot of compressive strength (Model 1)
15


b. Evaluation of prediction models
The results show that model 3 is the best one. Therefore, model 3 is
chosen to predict the compressive strength of concrete. However, if only
one of the two parameters UPV or A2/A1, can not be measured, model
1 or 2 is used.
Table 3.3. Performance coefficients of different multivariable linear
regression model
Performance coefficients
Deviation S, daN/cm2
Determination coefficient R2, %
R adjacent square Radj2, %

Model 1
49,08
90,32
89,59

Model 2

48,90
90,40
89,67

Model 3
47,80
90,96
90,13

c. Prediction of concrete mixtures
Contour plots are used to predict the concrete mixture range required
to ensure a given compressive strength (Fig. 3.4). The optimal analysis
is used to find the most suitable concrete mixture among 72 ones for a
required concrete compressive strength ( Fig. 3.5).

Fig. 3.4. Contour plot for predicting concrete mixtures

Fig. 3.5. Optimum mixture for compressive strength of 300daN/cm2
16


3.2.3.2 ANN models
The ANN network is implemented for models 1, 2, and 3 to compare
the compressive strength prediction accuracy with the regression
method.
a. ANN structure
The number of neurons in the input layer corresponds to the number
of input parameters of the three models (Section 3.2.3), and the output
layer has one neuron, which is the compressive strength of concrete.
Trials and errors determine the suitable number of hidden layers and

neurons in the hidden layers. The ANN structures suitable for the
predictive models are Model 1: 5x10x1, Model 2: 5x10x1, and Model 3:
6x10x1 (Fig. 3.6).
A total of 72 specimens are used for training, validation, and testing.
Data for training: 70% (50 specimens), for validation: 15% (11
specimens), for testing: 15% (11 specimens). The allocation of 72 data
sets for the three subsets mentioned above is done randomly by the
nntool in Matlab software.

Fig. 3.6. ANN structure

Fig. 3.7. Training procedure and predicted results by ANN
17


b. Analysis of results of different models
The above analysis results show that model 3 is the most accurate and
suitable model to predict the compressive strength of concrete using fly
ash and stone powder by ANN network (Fig. 3.7).
3.2.3.3 Comparison of compressive strength prediction models
The performance parameters of three models, 1, 2, and 3 (using linear
regression and ANN), are shown in Table 3.4. The ANN model gives
more accurate results than the regression one. Among the three
proposed ANN models, model 3 has the highest accuracy, so it is the
most suitable one to predict the compressive strength of concrete using
substituting materials like fly ash and stone powder. However, when it
is impossible to determine one of the two input parameters UPV or
A2/A1 ratio, model 1 or 2 can also predict with high accuracy.
The performance parameters of three models, 1, 2, and 3 (using linear
regression and ANN), are shown in Table 3.4. The ANN model gives

more accurate results than the regression one. Among the three
proposed ANN models, model 3 has the highest accuracy, so it is the
most suitable one to predict the compressive strength of concrete using
substituting materials like fly ash and stone powder. However, when it
is impossible to determine one of the two input parameters UPV or
A2/A1 ratio, model 1 or 2 can also predict with high accuracy.
Table 3.4. Performance parameters of models 1, 2, and 3
Performance
parameters
Deviation (S)
R square (R2)
R adjacent square (Radj2)

Regression models
Model
Model
Model
1
2
3
49,08
48,90
47,80
90,32
90,40
90,96
89,59
89,67
90,13

Model
1
38,05
93,63
93,54

ANN models
Model
Model
2
3
38,89
35,26
93,38
94,55
93,29
94,48

3.3. Rayleigh damping coefficients of concrete
3.3.1. Experimental procedure for determining Rayleigh damping
coefficients
The relationship between the wave attenuation coefficient kw and the
Rayleigh damping coefficients  and β is written by Equation (3.4).
α
β
kw =
+ ω2
(3.4)
2c 2c
18

Based on this expression, a method to determine the two damping
coefficients  and β was proposed as follows:
• Transmitting signals with a frequency of 54kHz through a cubic
concrete specimen of 15x15x15cm3, determining the amplitude of the
transmitting and receiving signal waveform, thereby determining the
wave attenuation coefficient kw. The ultrasonic pulse velocity is
measured by experiment.
• In Eq. (3.4), taking =0, β can be determined and denoted β0:
β 0 = 2ck w / ω2 (3.5). Continuing to take β=0, calculate  and denote it
0: α0 = 2ck w (3.6).
• Based on the calculated values of 0 and β0, find two coefficients
k and kβ, such that: α = α 0 / k α ,β = β 0 / k β (3.7), provided that the
simulated ultrasonic wave attenuation coefficient k MP
is equal to the
w
one from the experiment k TN
.
In
Eq.
(3.5),
because
the angular
w
frequency ω is very high, the value of β0 tends to zero, so the coefficient
kβ in Equation (3.7) does not have much influence on the coefficient β.
To simplify the calculation, instead of having to find two coefficients k
and kβ, just find a common factor kR for both  and β values. Then the
Eq. (3.7) becomes α = α0 / k R ,β = β 0 / k R (3.8).

• After having determined the kR coefficient, the Rayleigh damping
coefficients  and β are calculated from Eq. (3.8).
The procedure for determining the Rayleigh damping coefficients 
and β is shown in Fig. 3.8. Based on this procedure, the Rayleigh
damping coefficients of 72 concrete mixtures are evaluated.

Fig. 3.8. Procedure for determining Rayleigh damping coefficients
3.3.2. Elaborating model for prediction of Rayleigh damping
coefficients in concrete
In practical situations, where the concrete mixture is not one of the
72 designed mixtures, it is necessary to determine the Rayleigh damping
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coefficients for this concrete mixture. Therefore, the ANN network
model is proposed to predict two Rayleigh damping coefficients  and
β, for any concrete mixture (Fig. 3.9).

Fig. 3.9. ANN structure for predicting Rayleigh damping coefficients

Fig. 3.10. Predicted results of Rayleigh damping coefficient using ANN
Using the proposed ANN, we can determine the Rayleigh damping
coefficients  and β for any concrete mixture (Table 3.5).
Table 3.5. Predicting Rayleigh damping coefficients of concrete by ANN
Rayleigh damping
coefficients

Ingredient content
Concrete
grade

Grd. 200
Grd. 300
Grd. 400

Fine agrregate
Stone
powder
(20%)
kg

Sand
(80%)

515
489
482

129
122
120

Gravel
kg

1200
1150
1100

Binder

CiFly
ment
ash
(80%)
(20%)
kg

224
304
360

56
76
90

Water



β

liter

rad/s

s/rad

195
195
195

52747.05
9579.14
4644.47

4.59E-07
8.34E-08
4.04E-08

This result is highly significant because these damping coefficients
are used to determine the damping matrix C in the simulation problem
in Chapter 2. Since then, the simulation of ultrasonic propagation in
concrete using fly ash and stone powder can be calculated for any
concrete mixtures.
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3.4. Experimental prediction of depth of open cracks perpendicular
to the concrete surface
An experimental procedure was set up to determine the crack depth
(Fig. 3.11) to verify the simulation results for the crack depth in Section
2.4. The photos of the specimen making and the measurement of
propagation time from transmitter to receiver as shown in Fig. 3.12.

Fig. 3.11. Experimental procedure for determining crack depths
The predicted values of the crack depth from simulation (Section
2.3) and the experiment are shown in Table 3.6. The results show that
the predicted crack depth value based on experimental measurements by
ultrasonic pulses is larger than the value predicted by numerical
simulation. This matter is appropriate. Because in numerical simulation,

the concrete material is assumed to be a homogeneous environment. As
for experimental measurements on concrete specimens, the material
structure is heterogeneous, there may be voids inside the specimen due
to the manufacturing process, from which the propagating waves will be
scattered with coarse aggregates and with these voids, and the wave
propagation, when measured experimentally, will be different from that
of numerical simulation.

Fig. 3.12. Specimen manufacturing and time-of-flight measuring
Table 3.6. Predicted results of crack depth
Methods
Simulation
Experiment

Predicted
crack depth
7.5cm
7.92cm
21

Actual crack
depth
7cm
7cm

Error
(%)
7.1%
13.1%

3.5. Conclusions of chapter 3
The objective of chapter 3 is to implement experiments on concrete
made of fly ash and stone powder to perform the following tasks:
Predicting concrete compressive strength by multivariate regression and
ANN network, determining the Rayleigh damping coefficients of
concrete to evaluate the damping matrix in the simulation problem in
Chapter 2, and estimating the crack depth experimentally to verify the
simulation results in Chapter 2.
The thesis proposes three models with various input parameters for
each method (multivariable linear regression and ANN network) to
predict the concrete compressive strength. The results show that the
ANN network model (Model 3) is the most accurate. In Model 3, the
input consists of six parameters: four material parameters (fine
aggregate, coarse aggregate, binder, and water) and two parameters on
ultrasonic properties (UPV and wave amplitude attenuation ratio
A2/A1). The output is concrete compressive strength. The model allows
high accuracy to predict the compressive strength of concrete made of
substituting materials (fly ash and stone powder).
An experimental procedure is proposed to determine the Rayleigh
damping coefficients α and β, thereby determining the Rayleigh
damping coefficients for 72 concrete mixtures using fly ash and stone
powder. In addition, an ANN network is proposed to predict Rayleigh
damping coefficients for any concrete mixture with reasonable
accuracy. In the model, the input is four material parameters (fine
aggregate, coarse aggregate, binder, and water), the output is the
Rayleigh damping coefficients α and β.
The concrete crack depth results evaluated by experiments have
deviations from numerical simulation but with acceptable errors. Those
can be improved by adding the assumption that the concrete is

heterogeneous when simulating wave propagation.

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CONCLUSIONS AND PERSPECTIVES
Thesis results:
1. Elaborating the algorithm and a program by finite element
method to simulate two-dimensional ultrasonic wave propagation in
concrete containing by-products, namely fly ash and stone powder. The
new feature of the program is that the damping matrix of the concrete is
considered and determined by the Rayleigh damping model through the
Rayleigh damping coefficients α and β determined experimentally.
2. Elaborating an experimental data set including 72 concrete
mixtures, achieving compressive strength from the level of B10 to B45.
These concrete mixtures use ingredient materials in the Central region:
Sand, gravel, Portland cement, and especially two by-product materials
which are fly ash and stone powder. This data set includes information
about concrete mixture, ultrasonic pulse velocity at the ages of 28 days,
density, Young modulus of concrete, ultrasonic amplitude attenuation
ratio at 28 days, and 28-day concrete compressive strength.
3. Proposing method and elaborating models to predict the
compressive strength of concrete containing fly ash and stone powder
by linear regression and artificial neural network. This model allows to
accurately predict the compressive strength of concrete corresponding to
the given mixtures. Thereby helping the concrete manufacturers
estimate the range of concrete ingredient contents and determine the
optimal mixture, ensuring designers’ required compressive strength.
4. Proposing an experimental method to determine Rayleigh
damping coefficients for 72 concrete mixtures containing by-product

materials such as fly ash and stone powder, building an artificial neural
network model allowing predicting the Rayleigh damping coefficients
of concrete using substitute materials at any mixture.
5. Determining an appropriate method to predict the depth of open
cracks perpendicular to the surface of concrete specimen containing byproduct materials such as fly ash and stone powder. This method is
based on the time-of-flight diffraction method (TOFD) to estimate the
23