Research Proposal: The recognition the compressive strength of weak concretes by using of Ultrasonic method (NDT)

Introduction

Once concrete has hardened it can be subjected to a wide range of tests to prove its ability to perform as planned or to discover its characteristics if its history is unknown. For new concrete this usually involves casting specimens from fresh concrete and testing them for various properties as the concrete matures. The ‘concrete cube test' is the most familiar test and is used as the standard method of measuring compressive strength for quality control purposes. Concrete beam specimens are cast to test for flexural strength and cast cylinders can be used for tensile strength. Specimens for many other tests can be made at the same time to assess other properties (For example: Drying shrinkage, thermal coefficient, modulus of elasticity).

For existing concrete samples will need to be taken from the structure (smaller precast units can be tested as found). Non destructive testing (NDT) methods are useful in some instances and can help identify areas from which samples should be taken. The normal method of concrete sampling is by coring although some chemical analysis techniques can be carried out on drilling dust samples. Once back in the laboratory many techniques can be used to examine and test hardened concrete to assess a wide variety of properties. Due to the large expansion in concrete projects and due to the importance of time and its direct impact on project cost, an essential need to estimate the hardened concrete strength.

Problem Statement

Concrete is unique in that it is the only engineering material in which strength determination is attempted from ultrasonic measurements. The reason for this unusual attempt is the need created by the acute infrastructure problem. If the concrete is not strong enough (for instance, it has deteriorated) the consequence can be excessive repair, shortened service life and, in extreme cases, collapse of the structure causing property loss, injuries and even loss of life. Once a reliable conclusion as to the condition of a structure has been reached, then, and only then, it can a technically and economically sound selection be made among alternative repair strategies.

Nowadays, the quality control of hardened concretes as a structure into buildings (beams, columns, footings etc) is the problem. Perhaps, it could be considered that there is an easy way to control the quality of hardened concretes and this way is the coring by using of rotary machinery. But when we utilize from coring method, as the matter of fact, we are destroying the structure by cutting some steel bars replaced into concrete. On the other hands, there is notably limitation to check the quality of the concrete by this way. Assume there are 200 concrete columns at the site that should be controlled. Can we test all of 200 columns by using of the coring method? This method is very expensive and takes too much time. In fact, we have to proceed to test hardened concretes by using of coring method randomly. The seriousness of the infrastructure problem is well known. According to the "ASCE 1998 Report Card for America's Infrastructure,” 59 percent of our roadways are in poor, mediocre or fair condition.

It will cost a total of $357 billion to eliminate the backlog of needs and produce modest improvement. In addition, 31.4 percent of our bridges are rated structurally deficient or functionally obsolete. It will require $80 billion to eliminate the current backlog of bridge deficiencies and maintain repair levels”. Yet there is unanimous agreement among engineers that the presently available test methods for non-destructive determination of concrete strength are, without exception, inadequate. Fifty years of research in this area could produce no better solution to the problem than empirical formulas obtained by elementary curve fitting for the calculation of the strength. In view of the complexities of the problem, discussed in the article, it would appear to be overly optimistic to attempt to formulate an ultrasonic test method for the determination of concrete strength. However, considering the seriousness of the infrastructure problem and the magnitude of the cost of rehabilitation, major advancement is desperately needed to improve the current situation. There is no acceptable method at present for the non-destructive determination of concrete strength.

Goals and Objective

The objective of this research is to contribute to the development of a pragmatic method for the improved non-destructive determination of concrete strength in structures. One novel Strategy is discussed that seem promising for such development. In this new idea the velocity of ultrasonic waves in concrete is used. This feature is called pulse velocity in this research. The purpose of this research is to develop rapid, reliable, low-cost experimental techniques for evaluating the compressive strength of weak concretes. 

The objective is to determine whether nonlinear ultrasonic methods can be used in combination with the commonly used expansion tests to provide an earlier indication of aggregate, the rocks (especially sedimentary rocks) in which we are able to utilize the concepts of Rock Mechanics accompanied by Concrete Technology.

The goals of this research are:

-To determine the compressive strength of weak hardened concretes

-To examine the compatibility Rock Mechanics science and Concrete Technology in order to use of Ultrasonic method

-To recognize low strength concretes from high strength concretes at the site

- To control the quality of hardened concretes clearly

-To find out Non-uniformity of hardened concretes at the site

Scope of Study

One of the research goals was to identify a strategy on how to proceed in the testing so to get the best possible outcome out of each technique and what each one could actually achieve compatibly with the limited time resources, given also the number of specimens to undergo investigation. Furthermore, from the combined use of the various techniques it was hoped that not only the results from one could be confirmed by other techniques, where possible, but that they could complement each other in carrying out a thorough investigation and in refining the information regarding the presence of defects, their location, depth and possible size. Therefore, at the first, we have to define the period of time and maximum cost for this research. In the case of this study, we consider minimum 12 months of work included in all of Lab. tests and analysis of data. We should make at least 500 samples of fresh standard cubic concrete accompanied by specimens of aggregate and tin-section study by microscope. In the meanwhile, we should consider all of made fresh concretes will be low compressive strength that this target also is our limitation. 

Literature Review

The non-destructive testing (NDT) of concrete is of great scientific and practical importance. The subject has received growing attention during recent years, especially the need for quality characterisation of damaged constructions made of concrete, using NDT methods. Malhotra (1976) presented a comprehensive literature survey for the non-destructive methods normally used for concrete testing and evaluation. Leshchinsky (1991) summarized the advantages of non-destructive tests as reduction in the labour consumption of testing, a decrease in labour consumption of preparatory work, a smaller amount of structural damage, a possibility of testing concrete strength in structures where cores cannot be drilled and application of less expensive testing equipment, as compared to core testing. These advantages are of no value if the results are not reliable, representative, and as close as possible to the actual strength of the tested part of the structure.

Longitudinal ultrasonic waves are an attractive tool for investigating concrete. Such waves have the highest velocity so it is simple to separate them from the other wave modes

The equipment is portable, usable in the field for in situ testing, is truly non-destructive and has been successful for testing materials other than concrete. In addition, none of the available non-destructive methods for testing concrete strength is better. Nevertheless, there are intrinsic and practical factors that may interfere with the determination of concrete strength by ultrasonic means. Concrete is a mixture of four materials: Portland cement, mineral aggregate, water and air. This complexity makes the behaviour of ultrasonic waves in concrete highly irregular, which, in turn hinders non-destructive testing. In the view of the complexities of the problem it would appear to be overly optimistic to attempt to formulate an ultrasonic test method for the determination of concrete strength. However, considering the seriousness of the infrastructure problem and the magnitude of the cost of rehabilitation, major advancement is desperately needed to improve the current situation. For instance, Popovics (1998) stated that it has been demonstrated repeatedly that the standard ultrasonic method using longitudinal waves for testing concrete can estimate the concrete strength only with ± 20 percent accuracy under laboratory conditions.

Earlier researchers such as Prassianakis (2003) and Arioglu (1998) on finding the correlation between concrete strengths and UPV were generally limited to the specimens prepared in laboratory conditions. In these researches different correlation formulas were found for different concrete mixture ratios.

Furthermore, a general expression of a concrete strength and UPV correlation by not taking the ratio of concrete mixture and its age into consideration does not exist in these earlier researches (Prassianakis and Arioglu). Beside, the concrete mixture ratios were variable and the ages of the specimens were generally 28 days. Only Prassianakis (2003) used a restricted amount of specimens with 28 years old. In this research, the ages of existing reinforced concrete structures taken cores ranges between 28 days to 36 years and their concrete mixture ratios are not known. Unknown concrete mixture ratios in existing reinforced concrete structures are one of the most common issues that cause difficulties so as to determinate the strength-UPV relationship. In this respect, because of variability in the concrete mixture ratio findings obtained from laboratory researches (Prassianakis and Arioglu) do not have a general pattern, the strength of concrete cannot be determined appropriately. Thus, these findings cannot represent a general way of analysis as well.

Research Methodology

The methodology of this research will be in accordance with below procedure.

 At the first time, we should make Index Tables by using of following steps:

Step1) To do Ultrasonic test on mix of aggregate (coarse and fine) with variable ratios and compactions. Of course, the appropriate (qualified) material of mould should be selected.

Step2) To do Ultrasonic test on rocks which are the source of aggregate (ASTM D2845).

Step3) To do Ultrasonic test on cement paste (Portland type1) with various types of water to cement (W/C) ratios and degree of hydration equal to %100 (ASTM C597).

Step4) To do Ultrasonic test on concrete with maximum compaction (entrapped air=%1) and different water to cement (W/C) ratios and h=%100 and cement type1 (ASTM C597).

Step5) To do Ultrasonic test on concrete with W/C=0.7 and with various types of compactions (vice versa of Step 4).

Step6) Calibration of experimental formulas of Fourmaintraux (1976) in Rock Mechanic to use of steps 1,2,3,4 and 5.

All of above steps have been included in below chart:

 Significant of Research

The outgoing of this research will establish a logical connection between Rock Mechanic and Concrete Technology and so it is a new idea of research to develop concrete technology. On the other hand, we will be able to control the qualification of low strength concretes easily. Where we have so many research materials on correlation between high strength concretes and the velocity of pulse generated from Ultrasonic test but we cannot find any research on low strength concretes while we need to have second one.

Data collection and analysis of discussion

After above steps and to obtain index tables, we can test ultrasonic method on hardened concrete at working place to measure the actual velocity of longitudinal waves (Correct reinforcement according to B.S 1881:part203).

Then we should take samples of hardened concrete particles for utilization of particles thin sections, which will be illustrated by microscope (polarized). Of course, particles (tin sections of concrete) should be saturated. By studying of saturated tin sections, we are able to determine the rate of water absorption for calculating the volume percentage of aggregate (coarse + fine), cement paste and finally total voids in concrete.
According to experimental formulas by Fourmaintraux (1976), we have:

Iq =100-1.6Np%

Where,

Iq: quality index

Np: total voids

On the other hand, we have:

Iq =V/V'*100%

Where,

V: actual velocity of longitudinal waves (at working place)

V': calculated longitudinal wave velocity according to volume percent and longitudinal wave velocity in aggregate (Coarse + fine) and cement paste (step1 to 6)

In addition, V' is equal to:

1/V'=SUM (Ci / Vi)

Where,

Ci: volume percent of materials constituent i

Vi: longitudinal wave velocity in materials constituent i

According to above mentioned, we can obtain longitudinal wave velocity into cement paste and regarding to step3, we will get proportion of water to cement (W/C) to compare the strength of concrete and to define relationship between them.

In the meanwhile, we can control the total void of proportion water to cement obtained (W/C) by using of maximum aggregate size (entrapped air percent) into concrete particles by following formula:

 P = (W/C-0.17+a/C) / (0.317+1/Pf*Af/C+1/Pc*Ac/C+W/C+ a/C)

Where,

P: total void in concrete
a: entrapped air percent
Ac: mass percent of coarse aggregate
Af: mass percent of fine aggregate
C: mass percent of cement
Pc: specific gravity of coarse aggregate
Pf: specific gravity of fine aggregate

Recommendation

Before the start of the test at Libratory, I suggest that we utilize from simulation method by using of some software or design a software for simulation in which we should introduce all reactions among paste, aggregates and Ultrasonic waves.

References

Ø  -Malhotra V. M. (Ed.), Testing Hardened Concrete: Non-destructive Methods, ACI, monograph No. 9, Detroit, US, 1976.

Ø  -Leshchinsky A., Non-destructive methods instead of specimens and cores, quality control of concrete structures, In: Proceedings of the International Symposium Held by RILEM. Belgium, E FN SPON, U.K., 1991, pp.377-386.

Ø  -Popovics S., Strength and related properties of concrete: a quantitative approach, New York: John Wiley Sons Inc., 1998.

Ø  -Prassianakis I.N., Giokas P., Mechanical properties of old concrete using destructive and ultrasonic non-destructive testing methods, Magazine of Concrete Research, 55 (2003) 171-176.

Ø  -Bungey J.H., The validity of ultrasonic pulse velocity testing of in-place concrete for strength, N.D.T. International 13(6) (1980) 296-300.

Ø  -Elvery R.H, Ibrahim LAM., Ultrasonic assessment of concrete strength at early ages, Magazine of Concrete Research (1976) 181-190.

Ø  -Teodoru, G.V., The use of simultaneous nondestructive tests to predict the compressive strength of concrete, ACI SP-112 ,1998,137-152.

Ø  -Arioglu, E., Arioglu, N., Testing of concrete core samples and evaluations, Evrim Publisher, Istanbul, 1998.

Ø  -ASTM C 597-83, Test for pulse velocity through concrete, ASTM, U.S.A., 1991.

Ø  -BS 1881-203, Recommendations for measurement of velocity of ultrasonic pulses in concrete, BSI, U.K., 1986.

Ø  -ACI 318-95, Building Code Requirements for structural concrete, (ACI 318-95) and commentary-ACI 318R-95, ACI, U.S., 1995.

Ø  -BS 1881: Part 120: 1983, Method for Determination of Compressive Strength of Concrete Cores, BSI, U.K., 1983.

Ø  -ASTM C 42-90, Standard test method for obtaining and testing drilled cores and sawed beams of concrete, ASTM, U.S.A., 1992.

Ø  -Popovics, S., Effect of curing method and final moisture condition on compressive strength of concrete, ACI Journal 83 (4) (1986) 650-657.

Ø  -A. Nilsen, P. Aitcin, Static modulus of elasticity of high strength concrete from pulse velocity tests, Cem Concr Aggr 14 (1) (1992) 64-66.

Case Analysis of Nike, Inc.: Cost of Capital (CON)

Cost of Equity

The cost of equity is comprised the cost of preferred stock and common stock. In this case, I am willing to focus on the cost of common stock because Nike did not pay any dividend after June 30, 2001(see Exhibit 4).

The cost of common stock is the return needed on the stock by shareholders in which investors discount the expected dividends of the firm to ascertain its share price. To perceive this definition, let me bring you an example:

Assume you want to invest on the stock of Nike, Inc. Your expected return is 12% for one year. The current share price is $42. Your benefit of the investment to purchase one share will be $5.04. If the company pay the dividend of $2.04 per share annually, the share value should increase to $45 in the next year to secure your benefit ($5.04). Therefore, the cost of equity is to cope with the risk of share price’s changes and the dividends paid by the company. There are two techniques to obtain the cost of equity as follows:

1) Capital Asset Pricing Model (CAPM)

As you know, the Capital Asset Pricing Model (CAMP) establishes a rational relationship between Non-Diversifiable risk and return of all assets due to all companies can eliminate or decrease Diversifiable risk by playing on the type and return of assets.

Here is the formula of CAPM:

Rs = Rf  + [ b * (Rm – Rf)]

Where:

Rs: Cost of equity

Rf: Risk – free rate of return (commonly measured by the return on a U.S. Treasury bill)

Rm: market returns (return on the market portfolio of assets)

b: beta coefficient or index of non- diversifiable risk for all assets of company

(Rm – Rf): market risk premium

Referring to above formula, we should find true data and assumptions for Rf, Rm, and beta (B).

At the first, we should consider FRICTO analysis (Flexibility, Risk, Income, Control, Timing and Others).

In this case, the timing is very important factor. We have to recognize what is NorthPoint’s timing. Would it be ok a short term investment or long term?  What will be the period of investment?

Let me remind you about previous article mentioned as follows:

“   "She should use current yields on US Treasuries 3 to 12 months at 3.59% because the yield curve is upward sloping.  Upward sloping yield curve means that North Point Group should rely to short-term financing instead of long term financing.  In fact, by short term financing, the manager can use cheaper cost of equity. It means that North Point Group should sell the purchased shares of Nike during the period of one year.”

    Therefore, my suggestion to NorthPoint is a short – term investment for the period of one year. Consequently, we should consider Rf = 3.59%

    Regarding to Exhibit (4), we have Nike Historic Betas.

    What is our choice for beta? Do we focus on the average (0.8)?

    Let me tell you my analysis as follows:

According to the short term investment and the graph of Nike share price performance relative to S & P 500 presented in Exhibit (4), we can see the interaction between beta (B) and share price of Nike / S &P500 index. In early 2000 (Feb & Mar), Nike / S&P500 = 0.55 that it presents us more risky shares of Nike so that beta is also high (0.83). Higher beta (B) indicates that its return is more responsive to the changes of market returns. Therefore, higher beta is more risky.

But after July 2000, we can see a significant increase of Nike / S&P500 until July 2001 (the time of this case) in which it shows lesser risk of investment for Nike’s share price and we have beta (B) equal to 0.69

In the result, I assumed beta equal to 0.69 (B = 0.69) for a short term investment.

According to Exhibit (4), we have two types of Historical Equity Risk Premiums (Rm – Rf), Geometric mean and Arithmetic mean.

Which one should we consider?

In finance, we usually choose geometric mean because it is a better estimate for longer life valuation while the arithmetic mean is better for a one-year estimated expected return. For longer life valuation, we can find stable valuation. But I would like to refer you to the paper submitted by www.mit.edu that citation is as follows:

Jacquier, E., Kane, A., & Marcus, A. (2002, Dec 18). Geometric or Arithmetic Mean: A Reconsideration. Forthcoming: Financial Analysts Journal. Retrieved May 20, 2003, from http://web.mit.edu/~jacquier/www/papers/geom.faj0312.pdf

According to this paper, the proper compounding rate is in – between these two values. Therefore, I consider 6.7% as market risk premium.

(5.9% + 7.5 %) / 2 = 6.7%

Now, we can calculate the cost of equity as follows:

Rs = 3.59% + [0.69 * (6.7%)] = 8.21%

I also analyzed a long term investment (please see my spreadsheet) in which I used the adjusted beta in the reference with Blume's technique; it is assumed that all of beta in the future will reach to 1. I chose this technique because it presents us the sense of the future for beta instead of historic beta. (Adjusted Beta = 0.343 + 0.677 Bh)

In the case of long term investment, the cost of equity is equal to 10.61% where I considered Bh = 0.8

You can compare the cost of equity for long term and short term investment.

2) The Constant-Growth Valuation (Gordon) Model

We as well as know that the value of a share of stock is equal to the present value (PV) of all future dividends, which in one model were assumed to grow at a constant annual rate over an infinite time horizon (Gordon Model) in which we have below formula:

Po = D1 / (Rs – g)

Where:

Po: Value of common stock

D1: Per – share dividend expected at the end of year 1

Rs: Required return on common stock

g: Constant rate of growth in dividends

According to my spreadsheet and Exhibit (4), Rs is calculated as follows:

Rs =  D1/P0 + g

= 0.24 / (42.09+0.063)        

= 6.87%

Since Nike did not pay any dividend after June 30, 2001(see Exhibit 4), I rejected this model because it does not reflect the true cost of capital.

Weighted Average Cost of Capital (WACC)

CAPM was found to be more superior to other methods of calculating cost of equity, hence the cost of equity used in the WACC is one derived by CAPM. At this point, I calculated the WACC of Nike Inc. using the weights and costs of debt and equity. The formula used is as follows:

WACC = wd*kd (1-T) + we*ke

= [10.2%*8.59 ( 1-38%)] + [89.8%*8.21%]

= 0.54% + 7.38%

= 7.92%

The weighted average cost of capital for Nike Inc. is equal to 8.27 percent.

EVALUATION

Kimi Ford used a discount rate of 11 percent to find a share price of $43.22. This makes Nike Inc. share price undervalued as Nike is currently trading at $42.09. I already told you this discount rate does not reflect the true market value and solved for a discount rate that would be more accurate.

I found the weighted average cost of capital by using CAPM that presented a discount rate of 7.92 percent. This discount rate results in a share price of $75.8*, meaning that Nike Inc. is undervalued by $33.71 per share ($75.8 - $42.09).

(Refer to sensitivity analysis table in exhibit 2).

DECISION

Using this data, I found that Nike Inc. should be added to the NorthPoint Large-Cap Fund at this time because the stock is undervalued and I can say to you that the safety factor is equal to 1.8 (Fs = 75.8 / 42.09). Whereas I have still doubt on projection analysis done by Kimi Ford.

Appendix  

Now, let me bring you my detail calculations to explain my spreadsheet about the cost of debt (Method (2): Based on calculating the IRR) as follows:

Calculation of cost of debt by using IRR method:

Note:  “All spreadsheets and calculation notes are available. The people, who are interested in having my spreadsheets of this case analysis as a template for further practice, do not hesitate to ask me by sending an email to: soleimani_gh@hotmail.com or call me on my cellphone: +989109250225. Please be informed these spreadsheets are not free of charge.”




To be continued .......

Double Discounting Method to Analyze Financial Case of Euroland Foods S.A.

Following to article of "Case Analysis of Euroland Foods S.A. plus a new implement strategy", I received the emails which presented the concern about Sensitivity analysis and Double discounting methods.

Let me explain you the details each one of this methods as follows:

1) Sensitivity Analysis Method

The common question was: “Why did I choose IRR = 17% for all of projects?

First step, I chose the range of IRR more than WACC = 10.6%. For instance, IRR = 11% to IRR = 14%. Then I ranked all of projects by high NPV and high Equivalent Annuity.

Second step, I increased the range of IRR to 16%. Then I ranked again all of projects.

Third step, I continued to increase of the range IRR and control the rank of all projects in which I obtained the constant ranking for all projects, in this case was IRR = 17%

2) Double Discounting method

In this method, we should compare all projects in minimum time period of cash flows.

The index time period is 3 years that is referred to the project of Inventory-Control System. At the first, we should exchange and discount all cash flows of the projects on three years. Then we will able to calculate NPV and IRR for all projects in the same period (three years).

How can we exchange and discount all cash flows to three years?

There are two ways as follows:

-To subtract present value of total time period from present value for three years

Delta (PV) = PV (t=n) – PV (t=3)

PV (t=n) = SUM [Ct / (1+WACC) ^n]   where: t = 0 to t = n

PV (t=n) = SUM [Ct / (1+WACC) ^n]   where: t = 0 to t = 3

After that, we should replace C3 of each project by Delta (PV) + C3

-In this way, we should calculate present value in which it will be the time equal to zero (t =0) for cash flow of third year. Then all cash flows before third year accompanied by third year will be considered equal to zero. Please see the example of project (1):

Year            0     1          2          3       4       5        6        7

Cash flow    -   -11.85   4.5      5.25     6      6.75    7.5     10.5

The present value should be calculated for below state:

Year           0    1     2       3      4      5         6        7

Cash flow   -    0     0       0      6      6.75    7.5      10.5

After that, we should replace C3 of each project by (New present value) + C3

If you calculate the present value by two ways, the result will be the same.

Finally, we should calculate NPV and IRR for all projects in the same period (three years).

Note:  “All spreadsheets are available. The people, who are interested in having my spreadsheets (two Excel files included six sheets) of this case analysis as a template for further practice, do not hesitate to ask me by sending an email to: soleimani_gh@hotmail.com or call me on my cellphone: +98 9109250225. Please be informed these spreadsheets are not free of charge.”