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Transcript of Lab4_combined_final
University of Waterloo Department of Civil and Environmental Engineering
Making and Testing of Concrete
Labs 2 & 4
CIVE 265
November 7, 2014
Prepared for: Prof. S. Walbridge
Department of Civil and Environmental Engineering University of Waterloo
Prepared by:
Group No. 16
Heidi Vanheule 20505468
Mena Shamshoom 20519304 Michelle Liu 20457298
Salika Gnanasampanthan 20521680
i
Abstract
It is essential for all civil engineers to understand the properties and characteristics of one of the
most common engineered construction materials: concrete. Various applications of concrete exist
in the world today such as buildings, foundations, bridges, dams and many more. In order to
investigate the behaviour of this material, various mixtures of general use concrete were casted
and later tested for compressive and splitting tensile strengths. All concrete specimens were
made and tested according to CSA guidelines. Water-cement ratios and slump test results were
obtained prior to casting and strength properties including compressive and split tensile strengths
and compressive elastic moduli were successfully determined. A power-operated destructive
testing machine was used to determine maximum loads necessary to compute compressive and
tensile strengths. The compressive strength of concrete linearly decreases as the water cement
ratio increases. The split-tensile strength of concrete also decreases linearly as the water cement
ratio increases. However, the decrease in strength occurs at a much faster rate in comparison to
compressive strength.
ii
Table of Contents List of Figures ……………………………………………………………………………….. iv List of Tables ………………………………………………………………………………... iv 1.0 Introduction ……………………………………………………………………………… 1 1.1 Purpose of Study …………………………………………………………………….. 1 1.2 Objective …………………………………………………………………………….. 1 1.3 Scope ………………………………………………………………………………… 1 2.0 Data Analysis …………………………………………………………………………..... 2 2.1 Hand-mixing and Casting …………………………………………………………… 2 2.2 Destructive Testing ………………………………………………………………….. 3 3.0 Data Interpretation ………………………………………………………………………. 9 3.1 Sources of Error …………………………………………………………………………. 22 4.0 Conclusion ………………………………………………………………………………. 23 5.0 References ……………………………………………………………………………….. 23 6.0 Appendices ………………………………………………………………………………. 25 Appendix A: MATLAB Codes ………………………………………………………….. 26 Appendix B: Spreadsheet Calculations ………………………………………………….. 30
iii
List of Figures
Figure 1. Compression Test Apparatus 4 Figure 2. Concrete specimen placed in splitting tensile test apparatus 7 Figure 3. Slump vs. Water Cement Ratio for Machine Mixed Concrete 9 Figure 4. Slump vs. Water Cement Ratio for Hand Mixed Concrete 9 Figure 5. Non-Vibrated Compressive Strength vs. Water Cement Ratio 11 Figure 6. Compressive Strength vs. Water Cement Ratio (Vibrated) 12 Figure 7. Compressive Elastic Modulus vs. Water Cement Ratio (Non-vibrated) 13 Figure 8. Compressive Elastic Modulus vs. Water Cement Ratio (Vibrated) 14 Figure 9. Split Tensile Strength vs. Water Cement (Non-Vibrated) 15 Figure 10. Split Tensile Strength vs. Water Cement Ratio (Vibrated) 15 Figure 11. Ratio of Mean Split Tensile to Compressive Strength vs. Water Cement Ratio (Non-Vibrated) 16 Figure 12. Ratio of Mean Split Tensile Strength to Compressive Strength vs. Water Cement Ratio (Vibrated) 17 Figure 13. Coefficient of Variation for f'c, Ec, and fst vs. Water Cement Ratio (Non-vibrated) 18 Figure 14. Coefficient of Variation for f'c, Ec, and fst vs. Water Cement Ratio (Vibrated) 19 Figure 15. Split Tensile Testing Aggregate Failure 21 Figure 16. Type One Failure from Compression Test. 21
List of Tables
Table 1. Summary of Hand Mixed Designs. 2 Table 2. Summary of Machine Mixed Designs. 3 Table 3. Compressive Strength of Concrete Samples in Compression Test. 5 Table 4. Compressive Elastic Modulus of Concrete Samples in Compression Test. 5 Table 5. Split Tensile Strength of Concrete Samples in Splitting Cylinder Test. 7
1
1.0 Introduction
1.1 Purpose of Study
The purpose of conducting this experiment was to collect data pertaining to concrete strength
properties of three different types of concrete mixtures: dry mix, normal mix and wet mix
concrete. The variability in concrete strength as a result of batch variation and water-cement
ratios was tested and results have been analyzed and discussed.
1.2 Objective
Raw data obtained during this lab includes water-cement ratios, slump measurements and
maximum load values for compressive and split tensile strength tests. The maximum load values
were then used to compute compressive strength and elastic modulus, and split tensile strength of
concrete specimens. In addition, mean values, standard deviations and coefficients of variations
for the aforementioned strength properties had been established.
1.3 Scope
The experiments were governed by CSA guidelines. However, data is limited to the concrete
specimens prepared and tested. Standard tools and devices were available, and experimental data
was collected in a professional laboratory setting.
2
2.0 Data Analysis
2.1 Hand Mixing and Casting
Three different concrete mixes that were produced in this lab were a dry mix, a normal mix, and
a wet mix. The dry mix had a water cement ratio (w/c) of 0.38, the normal mix had a w/c of 0.46
and the wet mix had a w/c of 0.49. The following table includes the mixture design for the hand
mixes that were prepared in this lab.
Table 1. Summary of Hand Mixed Designs
Batch Water (g) Cement (g) w/c Ratio Slump (mm) Dry 2300 6085.4 0.38 0
Normal 2800 6085.4 0.46 100 Wet 3000 6085.4 0.49 195
As the water cement (w/c) ratio increases, the workability of the concrete mix and the slump also
increases. Workability is defined as the ability of the concrete to be shaped, moulded, or worked.
The dry mix has the least amount of workability and slump while the wet mix has the greatest
amount.
The advantage of utilizing dry concrete mix in comparison to normal or wet mix is that the dry
mix is stronger and more robust. However, dry concrete lacks the higher degree of workability
possessed by normal and wet mix concrete. Dry mix concrete would be used for simple shapes
such as pillars which require a great amount of strength, but little workability. In comparison to a
dry mix, the wet mix has a great amount of workability, but decreased strength. This mixture
would be used for projects that require a lighter more workable concrete. An application would
be concrete used for intricate mouldings, such as arched bridges. Normal concrete is in between
dry and wet mix with respect to strength and workability. This type of mixture would be used for
projects that require strong, yet workable concrete. Normal concrete may be used for simple
projects such as flooring.
3
In addition to hand-mixed concrete, machine-mixed concrete was prepared. A summary of the
machine-mixed concrete design is summarized below in Table 2.
Table 2. Summary of Machine Mixed Designs
Water (kg) Cement (kg) Water
Cement Ratio
Coarse Aggregate
(kg)
Fine Aggregate
(kg)
Slump (mm)
2.10 7.00 0.30 25.00 18.00 0 2.45 7.00 0.35 25.00 18.00 0 2.80 7.00 0.40 25.00 18.00 25 3.15 7.00 0.45 25.00 18.00 40 3.50 7.00 0.50 25.00 18.00 150 3.85 7.00 0.55 25.00 18.00 190 4.20 7.00 0.60 25.00 18.00 245 4.55 7.00 0.65 25.00 18.00 275
The concrete casting procedure used in this lab was according to CSA A23.2-3C. The method of
consolidation used was the rodding method. This method consisted of adding three equal layers
of concrete to a cylinder with a diameter of 100mm and a height of 200mm. With the addition of
each new layer of the mixture, a tamping rod of diameter 10mm, was used to penetrate the
underlying layer 20 times at a depth of 25mm. Strokes were initially applied to the outer
diameter of the cylinder, gradually working inward. The rodding method was used in the slump
test procedures as well.
2.2 Destructive Testing
Cylindrical concrete specimens were created following CSA A23.2-3C. The concrete mixtures
were moulded into non-absorbent cylindrical moulds (CSA-A23.2-3C, 2009) and cured for 28
days at 23˚C ± 2˚C. In accordance to CSA standards, the length of each test sample was twice its
diameter (CSA-A23.2-3C, 2009). Two tests were performed on the concrete samples:
compression and split cylinder tests. In total, 39 specimens were tested for compressive strength
and 32 for split tensile strength. Samples with water content 0.30 to 0.40 included both rodded
and vibrated samples; these were examined separately.
4
Compressive Test
The compression test was used to determine the compressive strength of the cylindrical concrete
specimens. The testing apparatus was power-operated, with two steel bearing blocks on the top
and bottom (CSA-A23.2-9C, 2009). The top plate is spherically-indented to seat the sample. The
concrete samples were placed between the two steel blocks, as shown in Figure 1, and a
continuous load was applied until specimen failure. The applied load was held at constant rate of
0.15MPa/s to 0.35 MPa/s until the maximum load was achieved; this was evident when the
specimen showed visible cracks (CSA-A23.2-9C, 2009). The maximum load was recorded.
Figure 1. Compression Test Apparatus.
5
The maximum/peak load (P) and cross-sectional area (A) were used to calculate the compressive
strength (f'c) of the first 39 specimens using Equation 2.1 (CEE, 2014). The diameter
measurement used to find the area was an average of the two measured values.
𝑓`! =𝑃𝐴 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 2.1
Specimens were grouped by water content, and the mean and standard deviation was calculated
for each group. Vibrated samples demonstrated significantly different behaviours, and were
listed separately. The abbreviated data of compressive strength computations are summarized in
Table 3.
Table 3. Compressive Strength of Concrete Samples in Compression Test
Water Content (w/c)
Mean f'c (MPa)
Standard Deviation of f'c (MPa)
Coefficient of Variance [-]
0.30 28.019 3.061 0.109 0.30 (vibrated) 61.878 2.235 0.036
0.35 29.328 1.696 0.058 0.35 (vibrated) 53.190 0.612 0.011
0.40 48.051 1.945 0.040 0.40 (vibrated) 58.822 3.449 0.059
0.45 45.318 0.492 0.011 0.50 40.479 1.514 0.037 0.55 34.253 0.786 0.023 0.60 30.122 1.051 0.035 0.65 23.453 1.439 0.061
The computed values for compressive strength were further used to estimate the compressive
elastic modulus of concrete (EC), following Equation 2.2 (CEE, 2014). The mean values EC
samples and the corresponding water content are summarized in Table 4.
𝐸! ≈ 4500 ∙ 𝑓`! 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 2.2
6
Table 4. Compressive Elastic Modulus of Concrete Samples in Compression Test
Water Content (w/c)
Mean Ec (MPa)
Standard Deviation of Ec (MPa)
Coefficient of Variance [-]
0.30 23793.504 1288.256 0.054 0.30 (vibrated) 35395.276 639.441 0.018
0.35 24364.821 704.816 0.029 0.35 (vibrated) 32818.670 188.364 0.006
0.40 31188.737 637.222 0.020 0.40 (vibrated) 34502.896 1020.928 0.030
0.45 30292.904 164.061 0.005 0.50 28626.589 531.806 0.019 0.55 26335.345 300.725 0.011 0.60 24694.598 433.094 0.018 0.65 21785.199 668.582 0.031
Split Cylinder Test
Split cylinder tests were conducted in order to determine the splitting tensile strength of the
concrete specimens. Firstly, the diametric lines of each specimen were marked. Furthermore, the
diameter and length were measured to the nearest millimetre. The specimens were placed
horizontally on the testing apparatus, with each bearing plate running parallel to the diametric
lines. Plywood bearing strips were placed along the upper and lower bearing plates in order to
provide an even distribution of force along the curved surface (CSA-A23.2-13C, 2009), as
shown in Figure 2. The load was applied at a constant rate of 700 kPa/min to 1400 kPa/min, until
failure. The maximum load at failure was recorded.
7
Figure 2. Concrete specimen placed in splitting tensile test apparatus.
In order to determine the split tensile strength (fst) the other 32 specimens, Equation 2.3 (CEE,
2014) was used where P represents the maximum load recorded in the test, l is the length of the
cylinder and d is the diameter. The values for length and diameter are the average of the two
measured values.
𝑓!" = 2 ∙ 𝑃𝜋 ∙ 𝑙 ∙ 𝑑 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 2.3
The mean split tensile strength was determined for every corresponding water content value, and
summarized in Table 5. The values of f'c, Ec, and fst for every specimen can be found in
Appendix B, along with the diameter and length values.
8
Table 5. Split Tensile Strength of Concrete Samples in Splitting Cylinder Test
Water Content (w/c) Mean fst (MPa)
Standard Deviation of fst (MPa)
Coefficient of Variance [-]
0.30 3.863 0.739 0.191 0.30 (vibrated) 5.811 0.351 0.060
0.35 4.215 0.523 0.124 0.35 (vibrated) 4.834 N/A N/A
0.40 5.045 0.114 0.023 0.40 (vibrated) 4.893 0.164 0.034
0.45 4.542 0.371 0.082 0.50 4.271 0.420 0.098 0.55 3.594 0.513 0.143 0.60 3.541 0.047 0.013 0.65 2.961 0.446 0.151
9
3.0 Data Interpretation The slump versus water cement ratio is shown in Figure 3 pertaining to machine mixed concrete
and Figure 4, pertaining to hand mixed concrete. The trend of both plots demonstrates a positive
correlation between the water cement ratio and the slump. The slump, and hence workability of
concrete increases as the w/c ratio increases. Theory and published results support the positive
correlation between slump and w/c ratio which was seen in this lab. The curve of this correlation
is non-linear relationship.
Figure 3. Slump vs. Water Cement Ratio for Machine Mixed Concrete
10
Figure 4. Slump vs. Water Cement Ratio for Hand Mixed Concrete
Curing is the process through which the concrete gains strength while retaining moisture. The
strength which is obtained during the curing process is dependent on the humidity and
temperature of the curing environment. The curing process for the concrete cylinders mixed in
the lab is as follows: when the concrete is placed in the cylinder mould and the rodding process
is applied, a lid is placed on the mould to prevent water evaporation. The cylinder moulds are
placed in a disturbance free environment at 23˚C ± 2˚C for approximately 20 hours ± 4 hours to
complete the initial curing process. The cylinders are then removed from the moulds and stored
in a humid environment for the duration of the time until testing can be completed.
If the curing temperature is decreased from the specified temperature, the rate at which the
specimen hardens will decrease as well, but the strength of the cylinder will be increased with
respect to the long term. Much in the same way, if the specimen is cured in a moist environment,
the strength of the cylinder also increases. The strength of the concrete cylinder may be
11
negatively impacted if the curing temperature is higher than thirty degrees Celsius or less than 0
degrees because the water in the concrete mixes will either evaporate causing a great amount of
voids, or freeze and expand which created internal stresses. If water evaporates from the sample
very quickly, this may lead to shrinkage and cracking at the surface of the concrete which will
decrease the durability of the specimen.
Normal strength concrete has an expected elastic modulus of approximately 25.4-36.6 GPa, a
split tensile testing strength of approximately 2-5MPa, and a compressive strength of 37.3-
41.3MPa (Callister, 2014).
Figure 5. Non-Vibrated Compressive Strength vs. Water Cement Ratio
12
Figure 6. Compressive Strength vs. Water Cement Ratio (Vibrated)
The data collected throughout the lab for the compressive strength versus the w/c demonstrated
expected results for a majority of the data points. The mean value of all the tested compressive
strengths established was 41.17MPa, which lies within the expected range for compressive
strength of concrete. Although metals such as steel act similarly in compression as they do in
tension, the compressive strength for concrete is greater than compressive strength for steel.
Concrete can withstand enormous amounts of compressive forces.
Within the compressive strength plot in Figure 5 for the non-vibrated specimens, it is observed
that specimens with water cement ratios of 0.3 and 0.35 exhibit a compressive strength ranging
between 25-30MPa. At a w/c ratio of 0.4, the compressive strength jumps to approximately 45-
50MPa, and decreases linearly until the last specimen of a w/c ratio of 0.65. Published results
show the compressive strength linearly decreasing as the w/c ratio increases. The jump in the
compressive strength in the data collected was due to the specimens with the low w/c ratio not
13
being properly consolidated. The water in the mix aids with consolidation, and through use of the
rodding method opposed to the vibrated method, the specimen is less likely to be properly
consolidated, leading to a decreased compressive strength.
Figure 7. Compressive Elastic Modulus vs. Water Cement Ratio (Non-Vibrated).
The elastic moduli of the specimens were approximately around the expected range of 25.4-
36.6GPa, although the specimens with low and high w/c ratios displayed elastic moduli slightly
below the expected value. The mean elastic modulus of all specimens tested is 28.53GPa, which
lies between the expected range. The elastic modulus for concrete is much lower than the elastic
modulus for metals such as steel and aluminum alloys which have a modulus of elasticity of
approximately 200GPa and 70GPa respectively (Callister, 2014). This displays that concrete is
not as ductile as metal and cannot elastically deform as well.
14
Figure 8. Compressive Elastic Modulus vs. Water Cement Ratio (Vibrated)
The compressive elastic modulus graph for non-vibrated samples follow the same trend as the
compressive strength.
The split tensile strength for all the specimens tested were within the predicted range of 2-5MPa,
as shown in Figure 9 and Figure 10, with the mean of all data collected being 4.32MPa. Much in
the same way as the elastic modulus, the tensile strength of metals is much greater than that of
concrete. The tensile strength for steel alloys are approximately 400-1000MPa, and the tensile
strength for aluminum alloys are 200-500MPa (Callister, 2014). This proves that concrete is not
a reliable material to use in tension.
15
Figure 9. Split Tensile Strength vs. Water Cement Ratio (Non-vibrated)
Figure 10. Split Tensile Strength vs. Water Cement Ratio (Vibrated)
16
Much in the same way, the split tensile strength versus water cement ratio for non-vibrated
specimens shown in Figure 9 follow the same trend as the compressive strength, with a spike in
the tensile strength at a w/c ratio of 0.4 and a linear decrease in the strength succeeding. Again,
the published trend for the tensile strength is a linear decline in strength as the w/c increases. The
lack of proper consolidation in the specimens of low w/c ratio affects the tensile strength of
concrete in the same way as compressive strength.
Figure 11. Ratio of Mean Split Tensile Strength to Compressive
Strength vs. Water Cement Ratio (Non-vibrated)
17
Figure 12. Ratio of Mean Split Tensile to Compressive Strengths vs. Water Cement Ratio (Vibrated)
The ratio of compressive and tensile strength is approximately 0.14-0.145 for w/c ratios of 0.3-
0.35, and then decreases until it reaches a minimum ratio of 0.1 at a w/c ratio of 0.45. It then
begins to again increase as the w/c ratio increases for the remainder of the specimens. This trend
shows that throughout every test, the specimens are much weaker in tension than they are in
compression. Published results state that as the amount of water is increased, the concrete
becomes weaker in compression. As the w/c ratio increases, both the compressive and tensile
strengths decrease as well, but the tensile strength decreases at a more impressive rate than the
compressive strength. The data points at a w/c ratio of 0.3 and 0.35 can be considered as outliers
as they do not follow the increasing trend that is expected. This may be due to the poor
consolidation of the concrete at a lower w/c ratio.
18
The trend found in this lab correlates to published results. The strength of concrete is partially
depended on the reaction between cement and water known as “hydration”. A w/c ratio of 0.25 is
the minimum amount of water required to complete the hydration reaction for Portland concrete
(Wikipedia, 2014). Although this ratio is the strongest concrete, it leads to very little workability.
Therefore the w/c ratio is increased in most concrete mixes to increase workability, although the
water not used in the hydration reaction evaporates during the curing process and creates pores in
the concrete which reduce the final strength. Therefore it is expected that as the w/c ratio is
increased, the tensile and compressive strength is decreased as well.
Figure 13. Coefficient of Variation for f'c, Ec, and fst vs. Water Cement Ratio (Non-vibrated)
19
Figure 14. Coefficient of Variation for f'c, Ec, and fst vs. Water Cement Ratio (Vibrated)
For the variation of the compressive strength (f’c), the compressive elastic modulus (Ec), and the
split tensile strength (fst), all parameters have the greatest variation among the lowest w/c ratio
(0.3) and the largest w/c ratio (0.65). The graphs of variation for compressive elastic modulus
and the compressive strength follow the same curve, with the greatest variation being among the
least and greatest w/c ratios. The remaining specimens follow a quadratic like curve, with the
minimum variation being at a w/c ratio of 0.45. Although they follow the same shape curve, the
compressive strength has a greater variation than the compressive elastic modulus. The shapes of
the curves are similar because the compressive elastic modulus is determined by Equation 2.2:
𝐸! ≈ 4500√𝑓′! 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 2.2
20
The compressive elastic modulus is determined by using the compressive strength, so as the
variability of the compressive strength changes, so does the variability of its modulus. The
variability of the split tensile strength has the greatest amount of variation at a w/c ratio of 0.3,
0.55, and 0.65, and a minimum variation at a w/c ratio of 0.4 and 0.6. This variation is
determined by the standard variation divided by the mean of the specimen at each w/c ratio.
During compression testing of the cylinders, the cylinders typically failed with a type one failure.
This failure can be determined by the well-formed ends of the cylinder, which remain intact after
the testing has completed. Types two and three failures were observed in few of the poorly
consolidated cylinders. During the split tension testing, the failure usually occurred along the
centre length of the cylinder. When tensile testing occurs, there are shear forces acting on the
cylinder above and below the centre axis, in the direction of the centre axis. These shear forces
create the failure along the centre of the cylinder.
During failure, the stresses at the grain boundaries get so large that the bonds begin to break
apart. In concrete, there are many grain boundaries of different sizes due to the different
materials used to create the concrete, such as large aggregate, small aggregate, cement, and
water.
During the lab, there was evidence of aggregate failure in the specimens, mainly seen in the
specimens that were used for the split tension test. Aggregate failure is expected during testing
due to the different strengths of course aggregate found in the specimen. If a specimen is well
consolidated and has coarse aggregate with small fractures present, the fractures in the aggregate
will fail as the tensile forces increase.
21
Figure 15. Split Tensile Testing Aggregate Failure
Aggregate failure can be seen in Figure 15 which exhibited split tensile testing. A type one
fracture can be seen in Figure 16 in the sample that underwent the compression test. The fracture
occurs around the aggregate.
Figure 16. Type One Fraction from Compression Test.
22
The failure type seen with throughout all w/c ratios was primarily failure type one. There was
very little variation among the failure types. There was no change of failure type as the w/c ratio
was changed, although there were type two and three failures observed for the poorly
consolidated samples.
3.1 Sources of Error
Throughout the course of preparing concrete cylinder specimens, various sources of error may
have occurred. When placing the concrete in the cylindrical moulds, the concrete may not have
been symmetrically distributed, causing segregation of course aggregates within the mixture.
Specimens that were subject to vibration may have also experienced segregation due to
excessive-vibration with respect to the specimen workability. Following the addition of each new
layer of concrete mixture within the mould, the concrete may not have been evenly penetrated
along the cross-section, causing variability in consolidation of the cylindrical specimens. The
sides of the mould cylinder was not tapped in order to close any holes resulting from the rodding
process, as mentioned in clause 8.2.1.1 of the CSA standards (CSA_A23_2-3C, 2009).
Throughout the duration of curing, the specimens were not kept in a moist environment at all
times as per CSA standards. During split-tensile testing, bearing strips were re-used for each
specimen tested which was not recommended in clause 4.3 of CSA Standards (CSA_A23_2-
13C, 2009). Also, during testing, the application of loads onto the cylindrical specimen, accurate
loads applied may not have been applied, as mentioned by Lab Technicians. Hence, this may
have resulted in the variation between the expected compressive and split tensile strength values
and the experimental values obtained.
23
4.0 Conclusion
Three types of concrete specimens, a dry mix, normal mix and wet mix were prepared and tested
for concrete strength properties.
Through conducting this experiment, it is established that both hand mixed and machine mixed
concrete, as the water cement ratio increases, the slump, and as a result, the workability of the
mixture increases.
The mean of all the tested compressive strengths established were within the expected range for
compressive strength for concrete. The mean value of the tested compressive strengths was 41.17
MPa. Hence, it is evident that concrete can withstand large amounts of compression. The
compressive strength of concrete linearly decreases as the w/c ratio increases. The mean elastic
modulus of all specimens tested is 28.53 GPa which was between the expected range and
indicated that concrete is not very ductile.
The mean value of split tensile strength of concrete was 4.32 MPa, indicating that concrete is not
a suitable material to withstand large amounts of tension. As the w/c ratio increases, the tensile
strength decreases linearly.
Both the compressive and tensile strengths decrease with increasing w/c ratios. However the
tensile strength decreases at a much faster rate than the compressive strength.
5.0 References Civil and Environmental Engineering (CEE) Department, Lab Manual, “Lab #2 – Making
Concrete”, 2014. CSA-A23.2-3C, “Making and Curing Concrete Test Specimens in the Field”, Canadian
Standards Association, 2009. CSA-A23.2-9C, “Making and Curing Concrete Test Specimens in the Field”, Canadian
Standards Association, 2009.
24
CSA-A23.2-13C, “Splitting Tensile Strength of Cylindrical Concrete Specimens”, Canadian Standards Association, 2009.
University of Waterloo: Civil and Environmental Engineering (CEE) Department, Lab Manual, “Lab #4 – Concrete Testing”, 2014. Wikipedia, (2014 August 16), “Water Cement Ratio”. Retrieved from
http://en.wikipedia.org/wiki/Water%E2%80%93cement_ratio William D. Callister Jr. and David G. Rethwisch, “Materials Science and Engineering an
Introduction: 9th Edition”, John Wiley Sons and Inc., 2014.
25
6.0 Appendices
26
Appendix A: MATLAB Codes
close all, clear, clear all, clc, format short, format compact % 3.0 Data Interpretation (Plots) % ------------------------------------------------------------------------ % Plot slump versus w/c for % Machine mixed figure(1) m_wc = [0.3,0.35,0.4,0.45,0.5,0.55,0.6,0.65]; m_slump = [0,0,25,40,150,190,245,275]; scatter(m_wc,m_slump), hold on m_fit = polyfit(m_wc,m_slump,2); m_slump_fit = polyval(m_fit,m_wc); plot(m_wc,m_slump_fit), hold off title('Slump vs. Water Cement Ratio for Machine Mixed Concrete') xlabel('Water Cement Ratio'), ylabel('Slump (mm)') % Hand Mixed figure(2) h_wc = [0.383358891,0.483365558,0.533368891]; h_slump = [10,125,215]; scatter(h_wc,h_slump), hold on h_fit = polyfit(h_wc,h_slump,2); h_slump_fit = polyval(h_fit,h_wc); plot(h_wc,h_slump_fit), hold off title('Slump vs. Water Cement Ratio for Hand Mixed Concrete') xlabel('Water Cement Ratio'), ylabel('Slump (mm)') % ------------------------------------------------------------------------ % Plot of compressive strength versus w/c % non-vibrated figure(3) csnv_wc = [0.30,0.30,0.30,0.30,0.35,0.35,0.40,0.40,0.40,0.40,0.45,0.45.... 0.45,0.45,0.50,0.50,0.50,0.50,0.50,0.55,0.55,0.55,0.55,0.60,... 0.60,0.60,0.60,0.65,0.65,0.65,0.65]; csnv = [25.19,28.64,32.06,26.19,28.13,30.53,49.23,48.51,49.28,45.18,... 45.10,46.05,45.12,45.00,38.83,40.19,42.95,40.45,39.97,35.39,34.13... 33.65,33.83,30.61,30.07,31.12,28.68,24.60,22.31,24.79,22.11]; scatter(csnv_wc,csnv), hold on mean_csnv_wc = [0.3,0.35,0.4,0.45,0.5,0.55,0.6,0.65]; mean_csnv = [28.02,29.33,48.05,45.32,40.48,34.25,30.12,23.45]; plot(mean_csnv_wc,mean_csnv), hold off title('Compressive Strength vs. Water Cement Ratio (Non-Vibrated)') xlabel('Water Cement Ratio'), ylabel('Compressive Strength (MPa)') legend('All data','Mean for each W/C')
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% vibrated figure(4) csv_wc = [0.30,0.30,0.35,0.35,0.35,0.40,0.40,0.40]; csv = [63.46,60.30,53.89,52.79,52.88,60.92,54.84,60.71]; scatter(csv_wc,csv), hold on mean_csv_wc = [0.3,0.35,0.4]; mean_csv = [61.88,53.19,58.82]; plot(mean_csv_wc,mean_csv), hold off title('Compressive Strength vs. Water Cement Ratio (Vibrated)') xlabel('Water Cement Ratio'), ylabel('Compressive Strength (MPa)') legend('All data','Mean for each W/C') % ------------------------------------------------------------------------ % Plot of compressive elastic modulus versus w/c % non-vibrated figure(5) cemnv_wc = [0.30,0.30,0.30,0.30,0.35,0.35,0.40,0.40,0.40,0.40,0.45,0.45.... 0.45,0.45,0.50,0.50,0.50,0.50,0.50,0.55,0.55,0.55,0.55,0.60,... 0.60,0.60,0.60,0.65,0.65,0.65,0.65]; cemnv = [22583.86,24080.45,25481.14,23028.57,23866.44,24863.20,31574.36... 31340.75,31591.42,30248.42,30219.51,30537.47,30228.56,30186.08... 28042.86,28527.34,29492.19,28621.14,28449.43,26771.86,26289.41... 26105.60,26174.50,24898.00,24675.90,25104.21,24100.29,22317.63... 21257.21,22406.97,21158.98]; scatter(cemnv_wc,cemnv), hold on mean_cemnv_wc = [0.3,0.35,0.4,0.45,0.5,0.55,0.6,0.65]; mean_cemnv = [23793.50,24364.82,31188.74,30292.90,28626.59,26335.35... 24694.60,21785.20]; plot(mean_cemnv_wc,mean_cemnv), hold off title('Compressive Elastic Modulus vs. Water Cement Ratio (Non-Vibrated)') xlabel('Water Cement Ratio'), ylabel('Compressive Elastic Modulus (MPa)') legend('All data','Mean for each W/C') % vibrated figure(6) cemv_wc = [0.30,0.30,0.35,0.35,0.35,0.40,0.40,0.40]; cemv = [35847.43,34943.12,33035.53,32695.80,32724.68,35122.61... 33324.56,35061.52]; scatter(cemv_wc,cemv), hold on mean_cemv_wc = [0.3,0.35,0.4]; mean_cemv = [35395.28,32818.67,34502.90]; plot(mean_cemv_wc,mean_cemv), hold off title('Compressive Elastic Modulus vs. Water Cement Ratio (Vibrated)') xlabel('Water Cement Ratio'), ylabel('Compressive Elastic Modulus (MPa)') legend('All data','Mean for each W/C') % ------------------------------------------------------------------------ % Plot of split tensile strength versus w/c % non-vibrated figure(7)
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stsnv_wc = [0.30,0.30,0.35,0.35,0.40,0.40,0.45,0.45,0.45,0.45,0.50,... 0.50,0.50,0.50,0.50,0.55,0.55,0.55,0.55,0.60,0.60,0.60,0.60,0.65,... 0.65,0.65,0.65]; stsnv = [4.385080843,3.340069488,4.584746376,3.845454077,4.965112013,... 5.125753136,4.826870306,4.086149859,4.862176021,4.394524664,... 4.306545519,3.816958631,4.776092363,4.57510688,3.881979737,... 3.001232013,4.160630278,3.366188499,3.847228214,3.524198273,... 3.518146345,3.611465384,3.511108184,2.455894601,2.812357469,... 3.517800678,3.056227682]; scatter(stsnv_wc,stsnv), hold on mean_stsnv_wc = [0.3,0.35,0.4,0.45,0.5,0.55,0.6,0.65]; mean_stsnv = [3.862575165,4.215100227,5.045432574,4.542430212,... 4.271336626,3.593819751,3.541229546,2.960570107]; plot(mean_stsnv_wc,mean_stsnv), hold off title('Split Tensile Strength vs. Water Cement Ratio (Non-Vibrated)') xlabel('Water Cement Ratio'), ylabel('Split Tensile Strength (MPa)') legend('All data','Mean for each W/C') % vibrated figure(8) stsv_wc = [0.30,0.30,0.35,0.40,0.40]; stsv = [5.562553489,6.058841610,4.834491468,5.009362249,4.777158928]; scatter(stsv_wc,stsv), hold on mean_stsv_wc = [0.30,0.35,0.40]; mean_stsv = [5.810697549,4.834491468,4.893260588]; plot(mean_stsv_wc,mean_stsv), hold off title('Split Tensile Strength vs. Water Cement Ratio (Vibrated)') xlabel('Water Cement Ratio'), ylabel('Split Tensile Strength (MPa)') legend('All data','Mean for each W/C') % ------------------------------------------------------------------------ % Plot of the ratio of the average split tensile strength to % compressive strength versus w/c % non-vibrated figure(9) rationv_wc = [0.3,0.35,0.4,0.45,0.5,0.55,0.6,0.65]; mean_csnv = [28.02,29.33,48.05,45.32,40.48,34.25,30.12,23.45]; mean_stsnv = [3.862575165,4.215100227,5.045432574,4.542430212,... 4.271336626,3.593819751,3.541229546,2.960570107]; rationv = mean_stsnv./mean_csnv; scatter(rationv_wc,rationv), hold on plot(rationv_wc,rationv), hold off title('Ratio of Mean Split Tensile Strength to Compressive Strength vs. Water Cement Ratio (Non-Vibrated)') xlabel('Water Cement Ratio'), ylabel('Mean Split Tensile Strength to Compressive Strength') % vibrated figure(10) ratiov_wc = [0.3,0.35,0.4]; mean_csv = [61.88,53.19,58.82]; mean_stsv = [5.810697549,4.834491468,4.893260588]; ratiov = mean_stsv./mean_csv; scatter(ratiov_wc,ratiov), hold on
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plot(ratiov_wc,ratiov), hold off title('Ratio of Mean Split Tensile Strength to Compressive Strength vs. Water Cement Ratio (Vibrated)') xlabel('Water Cement Ratio'), ylabel('Mean Split Tensile Strength to Compressive Strength') % ------------------------------------------------------------------------ % Plot of coefficient of variation for f?c, Ec, and fst versus w/c % non-vibrated figure(11) cvnv_wc = [0.3,0.35,0.4,0.45,0.5,0.55,0.6,0.65]; cvnv_cs = [0.109,0.058,0.040,0.011,0.037,0.023,0.035,0.061]; cvnv_cem = [0.054,0.029,0.020,0.005,0.019,0.011,0.018,0.031]; cvnv_sts = [0.191,0.124,0.023,0.082,0.098,0.143,0.013,0.151]; plot(cvnv_wc,cvnv_cs,'-o',cvnv_wc,cvnv_cem,'-s',cvnv_wc,cvnv_sts,'-v') title('Coefficient of Variation for f''c, Ec, and fst vs. Water Cement Ratio (Non-Vibrated)') xlabel('Water Cement Ratio'), ylabel('Coefficient of Variation for f''c, Ec, and fst') legend('Compressive Strength','Compressive Elastic Modulus','Split Tensile Strength') % non-vibrated figure(12) cvv_wc = [0.3,0.35,0.4]; cvv_cs = [0.036,0.011,0.059]; cvv_cem = [0.018,0.006,0.030]; cvv_sts = [0.060,0,0.034]; plot(cvv_wc,cvv_cs,'-o',cvv_wc,cvv_cem,'-s',cvv_wc,cvv_sts,'-v') title('Coefficient of Variation for f''c, Ec, and fst vs. Water Cement Ratio (Vibrated)') xlabel('Water Cement Ratio'), ylabel('Coefficient of Variation for f''c, Ec, and fst') legend('Compressive Strength','Compressive Elastic Modulus','Split Tensile Strength')
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Appendix B: Spreadsheet Calculations
Compressive Strength of Concrete Samples in Compression Test
Water Content (w/c)
Specimen Average Diameter (mm)
Compressive Strength f'c
(MPa)
Mean f'c (MPa)
Standard Deviation of f'c
(MPa)
Coefficient of Variance
0.30 S14-‐1 50.88 25.19 28.02 3.06 0.11 S14-‐2 50.75 28.64 S14-‐5 50.69 32.06 S14-‐6 50.75 26.19 S14-‐V1 50.88 63.46 61.88 2.24 0.04 S14-‐V2 50.94 60.30
0.35 S16-‐1 50.75 28.13 29.33 1.70 0.06 S16-‐2 50.69 30.53 S16-‐V1 50.69 53.89 53.19 0.61 0.01 S16-‐V2 50.56 52.79 S16-‐V4 50.63 52.88
0.40 S11-‐1 50.94 49.23 48.05 1.94 0.04 S11-‐2 51.13 48.51 S11-‐5 50.69 49.28
S11-‐6 50.88 45.18
S11-‐V1 50.69 60.92 58.82 3.45 0.06 S11-‐V2 50.73 54.84 S11-‐V3 50.75 60.71
0.45 S10-‐1 50.69 45.10 45.32 0.49 0.01 S10-‐2 50.69 46.05 S10-‐6 50.64 45.12 S10-‐7 50.63 45.00
0.50 S1-‐1 50.81 38.83 40.48 1.51 0.04 S1-‐2 51.13 40.19 S1-‐5 51.13 42.95 S1-‐6 51.25 40.45 S1-‐9 50.81 39.97
0.55 S2-‐1 50.88 35.39 34.25 0.79 0.02 S2-‐2 50.63 34.13
S2-‐5 51.00 33.65
S2-‐6 50.88 33.83 0.60 S13-‐1 50.75 30.61 30.12 1.05 0.03
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Compressive Strength of Concrete Samples in Compression Test Continuation S13-‐2 50.81 30.07 S13-‐5 50.69 31.12 S13-‐6 50.94 28.68
0.65 S4-‐1 50.88 24.60 23.45 1.44 0.06 S4-‐2 50.81 22.31 S4-‐5 50.94 24.79 S4-‐6 51.06 22.11
Compressive Elastic Modulus of Concrete Samples in Compression Test
Water Content (w/c)
Specimen Average Diameter (mm)
Compressive Elastic
Modulus Ec (MPa)
Mean Ec (MPa)
Standard Deviation of Ec
(MPa)
Coefficient of Variance
0.30 S14-‐1 50.88 22583.86 23793.50 1288.26 0.05 S14-‐2 50.75 24080.45 S14-‐5 50.69 25481.14 S14-‐6 50.75 23028.57 S14-‐V1 50.88 35847.43 35395.28 639.44 0.02 S14-‐V2 50.94 34943.12
0.35 S16-‐1 50.75 23866.44 24364.82 704.82 0.03 S16-‐2 50.69 24863.20 S16-‐V1 50.69 33035.53 32818.67 188.36 0.01 S16-‐V2 50.56 32695.80 S16-‐V4 50.63 32724.68
0.40 S11-‐1 50.94 31574.36 31188.74 637.22 0.02 S11-‐2 51.13 31340.75 S11-‐5 50.69 31591.42 S11-‐6 50.88 30248.42 S11-‐V1 50.69 35122.61 34502.90 1020.93 0.03 S11-‐V2 50.73 33324.56 S11-‐V3 50.75 35061.52
0.45 S10-‐1 50.69 30219.51 30292.90 164.06 0.01 S10-‐2 50.69 30537.47 S10-‐6 50.64 30228.56 S10-‐7 50.63 30186.08
0.50 S1-‐1 50.81 28042.86 28626.59 531.81 0.02 S1-‐2 51.13 28527.34 S1-‐5 51.13 29492.19 S1-‐6 51.25 28621.14 S1-‐9 50.81 28449.43
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Compressive Elastic Modulus of Concrete Samples in Compression Test Continuation 0.55 S2-‐1 50.88 26771.86 26335.35 300.72 0.01 S2-‐2 50.63 26289.41 S2-‐5 51.00 26105.60 S2-‐6 50.88 26174.50
0.60 S13-‐1 50.75 24898.00 24694.60 433.09 0.02 S13-‐2 50.81 24675.90 S13-‐5 50.69 25104.21 S13-‐6 50.94 24100.29
0.65 S4-‐1 50.88 22317.63 21785.20 668.58 0.03 S4-‐2 50.81 21257.21 S4-‐5 50.94 22406.97 S4-‐6 51.06 21158.98
Split Tensile Strength of Concrete Samples in Splitting Tensile Test
Water Content (w/c)
Specimen Average Diameter (mm)
Average Length (mm)
Compressive Elastic
Modulus Ec (MPa)
Mean fst (MPa)
Standard Deviation of fst (MPa)
Coefficient of Variance
0.3 S14-‐4 101.625 191 4.385 3.863 0.739 0.191
S14-‐3 101.75 198 3.340
S14-‐V4 101.75 201 5.563 5.811 0.351 0.060
S14-‐V3 102.25 201 6.059
0.35 S16-‐3 101.88 196.00 4.585 4.215 0.523 0.124
S16-‐4 102.50 198.50 3.845
S16-‐V3 102.38 195.00 4.834 4.834 N/A N/A
0.4 S11-‐3 102.13 199.50 4.965 5.045 0.114 0.023
S11-‐4 102.25 202.00 5.126
S11-‐V5 102.13 195.00 5.009 4.893 0.164 0.034
S11-‐V4 102.50 201.00 4.777
0.45 S10-‐3 101.50 200.5 4.827 4.542 0.371 0.082
S10-‐4 101.25 198.5 4.086
S10-‐8 101.75 201 4.862
S10-‐9 101.63 199 4.395
0.5 S1-‐3 102.00 200 4.307 4.271 0.420 0.098
S1-‐4 102.00 199 3.817
S1-‐7 102.13 201 4.776
S1-‐8 102.25 201 4.575
S1-‐10 102.25 200 3.882
0.55 S2-‐3 101.63 198.5 3.001 3.594 0.513 0.143 S2-‐4 101.75 198.5 4.161
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Split Tensile Strength of Concrete Samples in Splitting Tensile Test Continuation S2-‐7 102.63 197 3.366 S2-‐8 101.63 198 3.847
0.6 S13-‐3 101.88 197 3.524 3.541 0.047 0.013 S13-‐4 102.25 197.5 3.518 S13-‐7 101.75 197.5 3.611 S13-‐8 101.50 196.5 3.511
0.65 S4-‐3 101.63 201 2.456 2.961 0.446 0.151 S4-‐4 101.75 198 2.812 S4-‐7 101.75 196 3.518 S4-‐8 102.00 198.5 3.056