Statistical Analysis Concrete

APPROVED QUALITY PROGRAM

Mix Design Statistical Analysis Program

Guidelines

A Publication of

READY MIXED CONCRETE ASSOCIATION OF ONTARIO 365 Brunel Road, Unit #3

Mississauga, Ontario L4Z 1Z5

Phone #: (905) 507-1122 Fax #: (905) 890-8122 Email: [email protected]

2009 Property of Ready Mixed Concrete Association of Ontario

TABLE OF CONTENTS

1.0 Introduction .................................................................................................... 1 1.1 Background ................................................................................................ 1

2.0 Definitions ...................................................................................................... 2 3.0 Statistical Analysis ......................................................................................... 3

3.1 Modification Factor for Less than 30 Samples ........................................... 4 3.2 CSA Suggested Average Design Strength ................................................. 4 3.3 Minimum Number of Mixes to be Analyzed ................................................ 5

4.0 Recommended Procedure ............................................................................. 6 4.1 The Adverse Effects of Inaccurate Test Data ............................................. 7 4.2 Sample Reports ......................................................................................... 7

LIST OF APPENDIX

APPENDIX A: Increased Assurance in Obtaining Specified Strength ................... 8 APPENDIX B: Category 1 Samples ...................................................................... 9 APPENDIX C: Category 2 Samples .................................................................... 10

LIST OF TABLES

Table 1: Standard Deviation Modification Factors ................................................ 4 Table 2: Required Average Strength ..................................................................... 8 Table 3: Category 1 Sample ................................................................................. 9 Table 4: Category 2 Sample ............................................................................... 10

RMCAO Mix Design Statistical Analysis Program Guidelines 1

1.0 Introduction The RMCAO Technical Committee has developed a Mix Design Statistical Analysis Program to be implemented as a Standard Practice requirement for all producing Members. Included as a key component of this plan is the need for Members to provide documented evidence that concrete mix designs used for production have been developed in accordance with a standard, statistical based method and meet the technical requirements of CSA A23.1. The purpose of this document is to describe, in detail, the requirements of the proposed RMCAO methodology to be used. Elements of CSA A23.1, “Concrete Materials and Methods of Concrete Construction”, and ACI 214 “Standard Practice for the Evaluation of Strength Test Results for Concrete”, have been used to develop this guideline. The intent of this guideline is to offer assurance to specifying Engineers that all members of the Association are committed to producing concrete of a consistent and dependable quality. Furthermore, it will provide the member companies with the tools necessary to develop a Quality Assurance Plan that will enable them to have confidence in their daily concrete production methods. 1.1 Background Although not an absolute indicator of concrete quality, the 28 day Compressive Strength test is a generally accepted method of specifying, controlling and evaluating the quality of concrete placed on a project. Portland Cement Concrete (PCC) is subject to numerous factors that influence its plastic and hardened properties. Included among these are:

1. Raw Material Variations. 2. Concrete Production, Delivery, Placement and Consolidation

Techniques. 3. Curing Method and Duration. 4. Preparation, Handling and Testing of Cylinder Strength Specimens.

Ideally, the design of a concrete mix should consider the variability introduced by all of the above factors. Currently, concrete mixes are generally over-designed, for fear of producing results that do not satisfy minimum specified strength criteria of the Engineer. The following methodology will provide a simplified discussion on compressive strength variance analysis, and it will also provide criteria to follow in order to properly design concrete mixes.


2.0 Definitions Strength Test: The average of two cylinder specimens cast from a single

load of concrete and tested at the same age. For example, the 28 day strength of a load is calculated as the average of two cylinders cast from the same load of concrete, tested at 28 days.

Average Strength: The average of all individual strength tests cast on a specific

class of concrete from a given plant using similar materials. For example, the average of fifteen, 28 day Compressive Strength test results for 30 MPa, MTO concrete is 36.3 MPa.

Range: The difference between the highest and lowest values in a

data group. For example, the 28 day range for 2 Compressive Strength cylinders tested at 37.6 MPa and 39.2 MPa is 1.6 MPa.

Standard Deviation (s): The root mean square deviation of the measured strengths

from their average. Essentially, Standard Deviation measures the degree to which an individual strength test may be expected to vary from the average. For example, an average strength of 36.3 MPa with a standard deviation of 1.5 MPa will be expected to vary from 31.8 MPa (average strength minus 3 standard deviations) to 40.8 MPa (average strength plus 3 standard deviations) with a 99.9% confidence level.

Coefficient of Variation (C.V.): The standard deviation expressed as a percentage of the

average strength. For example, concrete with an average strength of 36.3 MPa and a standard deviation of 1.5 MPa will have a Coefficient of Variation of 4.1% (1.5 ÷36.3 x 100).

Cement Efficiency: The average amount of cementitious material, in kg, required

to produce 1 MPa of compressive strength per m3 of concrete. For example, a concrete of average strength 36.3 MPa designed with 335 kg of cementitious material will have an efficiency of 9.23 kg/MPa per m3 (335 kg ÷36.3 MPa).


3.0 Statistical Analysis Concrete compressive strengths have a natural tendency to vary around a central value commonly described as the Average or Mean. The distribution of results follows a symmetrical pattern represented by the Normal Distribution or the Bell Shaped Curve. An in-depth presentation of statistical calculations will not be presented here, however, the calculations are easily performed by means of a statistical calculator or in a typical computer spreadsheet program (such as Excel or Lotus 123). To analyze concrete cylinder compressive strength data, the following values need to be calculated: 1. Average: The sum of all individual test results divided by the number of tests. 2. Standard Deviation: The sum of the root mean squared differences between

each test result and the sample average divided by the number of samples less 1.

3. Coefficient of Variation: The Standard Deviation divided by the Average Strength and expressed as a percentage.

4. Cement Efficiency: The total mass of cementitious material per m3 divided by the Average Strength.

Important Note: All strength tests used in any evaluation of concrete performance must be conducted in strict compliance with CSA A23.2, and be performed either by a CSA certified laboratory, or be stamped by a PEO licensed Engineer as being accurate. In theory, the analysis is most accurate when a minimum of 30 consecutive, representative test results are used. It is important that a “Rational or Random Sampling Technique” be followed, which ensures that no bias is evident in the results through selective sampling or choice of the sampler. What should be avoided is a situation where the sample is taken every Monday at 8:00 am. All tests incorporated in the analysis must be taken within the previous twelve (12) months of operation, with at least fifteen (15) 28 Day Compressive Strength Tests performed on each class of concrete during the twelve month testing period.


3.1 Modification Factor for Less than 30 Samples When a production facility has less than 30 samples, but has a record based on 15-29 tests, the calculated Standard Deviation must be modified by multiplying by the appropriate factor from the following table (ACI –318 Clause 5.3.1.2): Table 1: Standard Deviation Modification Factors

Number of Compressive Strength Test*

Modification Factor For The Standard Deviation

15 1.16 20 1.08 25 1.03

30 + 1.00 * = Interpolate for an intermediate number of tests. (ACI-318 Table 5.3.1.2) 3.2 CSA Suggested Average Design Strength CSA A23.1, Clause 4.4.6.6.1 indicates that the strength level of each class of concrete shall be considered satisfactory if the averages of all sets of three (3) consecutive strength tests for that class at one age equal or exceed the specified strength (f’c) and no individual strength test is more than 3.5 MPa below the specified strength. This criterion can be met with 99% confidence when the concrete mix is proportioned to produce the following Average Design Strength:

1. = f’c + (1.4 x Standard Deviation) [When the Standard Deviation is not more than 3.5 MPa] 2. = f’c + ((2.4 x Standard Deviation) - 3.5))

[When the Standard Deviation is more than 3.5 MPa] CSA states that individual strength tests from concrete meeting these requirements can be expected to be below specified strength approximately 10% of the time. Appendix A provides a detailed list of formulas for determining the Average Design Strength based upon the maximum percentage of tests the design Engineer would like to see below the specified strength. An important qualification in CSA A23.1 is that a Standard Deviation may be used to design mixes whose strength is within 7 MPa of the mix analyzed, provided that they are made with similar materials and under similar conditions to those expected. As such, a 20 MPa, non air-entrained mix analysis can be used to design 13 to 27 MPa, non air-entrained concretes. Similarly, a 30 MPa, air-entrained mix may be used to design 23 to 37 MPa, air-entrained concretes.


3.3 Minimum Number of Mixes to be Analyzed For the purpose of this program, each producing Member must analyze the following two categories of concrete: 1) Category 1: Under 30 MPa with or without Air Entrainment. 2) Category 2: 30 MPa or higher with Air Entraining Admixture (A.E.A.). It is recommended that the analysis be conducted on as many mixes as practical for each specific plant. Low Production Facility Allowance: Low Production Facilities are defined as ready mixed concrete production facilities (permanent or portable) that have produced less than 20,000 cubic metres (m3) of concrete during the previous calendar year. If a plant meets this criteria, they are exempted from monitoring Category 1 concrete. All concrete plants shall at a minimum conduct testing on Category 2 concrete.


4.0 Recommended Procedure The recommended RMCAO Mix Design Statistical Analysis Program procedure is as follows:

1. For each plant, select the mix design that will be used the most for each category of concrete to be tested.

2. Obtain the 28 day Compressive Strength test results during the 12 month moving window. At a minimum, 15 tests must conducted for each class of concrete (Note: Additional test results will reduce the Standard Deviation Modification Factor and limit the effects of extreme test results).

3. Members are required to keep on file the Compressive Strength Test Reports (completed by a CSA certified laboratory or stamped by a PEO Engineer) for each category of concrete.

4. Review the data as it is collected to confirm that no one individual test is lower than 3.5 MPa below the specified strength and that the running average of the last three compressive strength tests are greater than the specified strength.

5. Input the data in a summary table to allow for quick inspection by the Engineer during the Plant Audit and Certification Program (See samples in Appendix 2 & 3).

6. Calculate the Average Strength and Standard Deviation for a given class of concrete at a given plant for the current testing period.

7. Modify the Standard Deviation value as required based upon the number of 28 Day Compressive Strength Tests used in program (Table 5.3.1.2).

8. Determine CSA’s recommended Average Design Strength based upon your specific data.

9. Adjust the design mixes in accordance with the statistical analysis data. One possible method is to determine the cement efficiency, as described previously, for the mix design in question.


4.1 The Adverse Effects of Inaccurate Test Data When determining the Standard Deviation of a given category of concrete, it is important to remember that testing inaccuracies cause a significant portion of the variability in a mix design. It is recommended that the Within Test Variability, which is a measure of testing consistency and performance, be determined as follows:

1. Determine the range in each set of cylinders comprising a single strength test.

2. Determine the average range as the sum of the ranges divided by the number of strength tests.

3. Calculate the within test coefficient of determination as the average range divided by the average strength, expressed as a percentage.

As per ACI 214 guidelines, if the within test Coefficient of Variation exceeds 6.0%, it is likely that testing error is influencing the accuracy of test results. It is important that test results influenced by testing not be used in designing concrete mixes. 4.2 Sample Reports Enclosed are two sample reports for the two categories of concrete included in the Mix Design Statistical Analysis Program. The purpose of these samples is to indicate the information that is required to complete the statistical analysis and provide Members with a sample layout. Copies of these Excel spreadsheets are available from the Association. Note: In order to highlight the main objectives of the program, both samples

contain data that fails to meet the requirement of CSA A23.1 Clause4.4.6.6.1. These failures do not indicate that the Member has failed to meet the requirements of Mix Design Statistical Analysis Program. The only requirement of the Program is that the Member modify its mix designs to address these issues and continue the monitoring program to determine the effectiveness of the modifications.


APPENDIX A: Increased Assurance in Obtaining Specified Strength If specifying Engineers require greater assurance that the specified strengths will be achieved, the factor by which the standard deviation is multiplied may be increased. ACI-214 provides the following guide: Table 2: Required Average Strength

Required Average Strength Percentage of Low Tests (%) f’c + 0.00 x S.D. 50.0 f’c + 0.10 x S.D. 46.0 f’c + 0.20 x S.D. 42.1 f’c + 0.30 x S.D. 38.2 f’c + 0.40 x S.D. 34.5 f’c + 0.50 x S.D. 30.9 f’c + 0.60 x S.D. 27.4 f’c + 0.70 x S.D. 24.2 f’c + 0.80 x S.D. 21.2 f’c + 0.90 x S.D. 18.2 f’c + 1.00 x S.D. 15.9 f’c + 1.10 x S.D. 13.6 f’c + 1.20 x S.D. 11.5 f’c + 1.30 x S.D. 9.7 f’c + 1.40 x S.D. 8.1 f’c + 1.50 x S.D. 6.7 f’c + 1.60 x S.D. 5.5 f’c + 1.70 x S.D. 4.5 f’c + 1.80 x S.D. 3.6 f’c + 1.90 x S.D. 2.9 f’c + 2.00 x S.D. 2.3 f’c + 2.10 x S.D. 1.8 f’c + 2.20 x S.D. 1.4 f’c + 2.30 x S.D. 1.1 f’c + 2.40 x S.D. 0.8 f’c + 2.50 x S.D. 0.6 f’c + 2.60 x S.D. 0.45 f’c + 2.70 x S.D. 0.35 f’c + 2.80 x S.D. 0.25 f’c + 2.90 x S.D. 0.19 f’c + 3.00 x S.D. 0.13

Any Engineer who, unrealistically, refuses to recognize the variability that exists and demands that no test falls below the specified strength, must realize that the required average strength is 3.0 standard deviations above the specified strength, resulting in over-designed and uneconomical mixes.


APPENDIX B: Category 1 Samples

Table 3: Category 1 Sample


APPENDIX C: Category 2 Samples

Table 4: Category 2 Sample

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Statistical Analysis Concrete