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')

27

% 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)

28

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

29

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')

30

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  

31

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              

32

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              

33

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