混凝土强度试验结果评定推荐规程

The batch-to-batch and within-test sources of variation are related to the overall variation [Eq. (3-3)] by the following expression:

σ² = σ₁² + σ₂² (3-6)

where

σ = overall standard deviation

σ₁ = within-test standard deviation

σ₂ = batch-to-batch standard deviation

Once these parameters have been computed, and with the assumption that the results follow a normal frequency distribution curve, a large amount of information about the test results becomes known. Fig. 3.4.2 (a) indicates an approximate division of the area under the normal frequency distribution curve. For example, approximately 68 percent of the area (equivalent to 68 percent of the test results) lies within ±1σ of the average, 95 percent within ±2σ, etc. This permits an estimate to be made of the portion of

Fig. 3.4.2(b)-Cumulative distribution curves for different coefficients of variation

Fig. 3.4.2(c)-Cumulative distribution curves for different standard deviations

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CHAPTER 1-INTRODUCTION

The purposes of strength tests of concrete are to determine compliance with a strength specification and to measure the variability of concrete. Concrete, being a hardened mass of heterogeneous materials, is subject to the influence of numerous variables. Characteristics of each of the ingredients of concrete, depending on their variability, may cause variations in strength of concrete. Variations may also be introduced by practices used in proportioning, mixing, transporting, placing, and curing. In addition to the variations which exist in concrete itself, test strength variations will also be introduced by the fabrication, testing, and treatment of test specimens. Variations in the strength of concrete must be accepted, but concrete of adequate quality can be produced with confidence if proper control is maintained, test results are properly interpreted, and their limitations are considered.

Proper control is achieved by the use of satisfactory materials, correct batching and mixing of these materials, correct batching and mixing of sired quality, and good practices in transporting, placing, curing, and testing. Although the complex nature of concrete precludes complete homogeneity, excessive variation of concrete strength signifies inadequate concrete control. Improvement in control may permit a reduction in the cost of concrete since the average strength can be brought closer to specification requirements.

Strength is not necessarily the most critical factor in proportioning concrete mixes since other factors, such as durability, may impose lower water-cement ratios than are required to meet strength requirements. In such cases, strength will of necessity be in excess of structural demands. Nevertheless, strength tests are valuable in such circumstances since, with established mix proportions, variations in strength are indicative of variations in other properties.

Test specimens indicate the potential rather than the actual strength of the concrete in a structure. To be meaningful, conclusions on strength of concrete must be derived from a pattern of tests from which the characteristics of the concrete can be estimated with reasonable accuracy. Insufficient tests will result in unreliable conclusions.

Statistical procedures provide tools of considerable value in evaluating results of strength tests and information derived from such procedures is also of value in refining design criteria and specifications. This report briefly discusses variations that occur in the strength of concrete, and presents statistical procedures that are useful in the interpretation of these variations with respect to required criteria and specifications. For these statistical procedures to be valid, the data must be derived from samples obtained by means of a random sampling plan designed to reduce the possibility that choice will be exercised by the sampler. "Random sampling" means that each possible sample has an equal chance of being selected. To insure this condition, the choice must be made by some objective mechanism such as a table of random numbers. If sample batches are selected by the sampler on the basis of his own judgment, biases are likely to be introduced that will invalidate results analyzed by the procedures presented here. Reference 1 contains a discussion of random sampling and a useful short table of random numbers.

Additional information on the meaning and use of this recommended practice is given in Realism in the Application of ACI Standard 214-65.³ This volume is a compilation of information on ACI 214-65 that was presented at a symposium held at Buffalo, N. Y., in 1971. In addition to the papers from the symposium, it includes reprints of some pertinent papers that were published earlier in the ACI JOURNAL, and of discussion that resulted from them. Although the information given was based on ACI 214-65, most of it is still relevant. An additional source of material on evaluation of strength tests is ACI Bibliography No. 2, published in 1960.³

CHAPTER 2-VARIATIONS IN STRENGTH

2.1-General

The magnitude of variations in the strength of concrete test specimens depends on how well the materials, concrete manufacture, and testing are controlled. Differences in strength can be traced to two fundamentally different sources as shown in Table 2.1: (a) differences in strength-producing properties of the concrete mixture and ingredients, and (b) apparent differences in strength caused by variations inherent in the testing.

2.2-Properties of concrete

It is well established that strength is governed to a large extent by the water-cement ratio. The

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first criterion for producing concrete of constant strength, therefore, is a constant water-cement ratio. Since the quantity of cement and added water can be measured accurately, the problem of maintaining a constant water-cement ratio is primarily one of correcting for the variable quantity of free moisture in aggregates.

The homogeneity of concrete is influenced by the variability of the aggregates, cement, and admixtures used, since each will contribute to variations in the concrete strength. The temperature of fresh concrete influences the amount of water needed to achieve the proper consistency and consequently contributes to strength variation. Construction practices may cause variations in strength due to inadequate mixing, poor compaction, delays, and improper curing. Not all of these are reflected in specimens fabricated and stored under standard conditions.

The use of admixtures adds another factor since each admixture adds another variable to concrete. The batching of accelerators, retarders, pozzolans, and air-entraining agents must be carefully controlled.

2.3-Testing methods

Concrete tests may or may not include all the variations in strength of concrete in place depending on what variables have been introduced after test specimens were made. On the other hand, discrepancies in sampling, fabrication curing, and testing of specimens may cause indications of variations in strength which do not exist in the concrete in the structure. The project is unnecessarily penalized when variations from this source are excessive. Good testing methods will reduce these variations, and standard testing procedures such as those described in ASTM standards should be followed without deviation.

The importance of using accurate testing machines and producing thin, high-strength, plane, parallel caps should need no emphasis since test results can be no more accurate than the equipment and procedures used. Uniform test results are not necessarily accurate test results. Laboratory equipment and procedures should be calibrated and checked periodically.

CHAPTER 3-ANALYSIS OF STRENGTH DATA

3.1-Notation

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Fig. 3.3(a)-Frequency distribution of strength data and corresponding normal distribution

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The batch-to-batch and within-test sources of variation are related to the overall variation [Eq. (3-3)] by the following expression:

σ² = σ₁² + σ₂² (3-6)

where

σ = overall standard deviation

σ₁ = within-test standard deviation

σ₂ = batch-to-batch standard deviation

Once these parameters have been computed, and with the assumption that the results follow a normal frequency distribution curve, a large amount of information about the test results becomes known. Fig. 3.4.2 (a) indicates an approximate division of the area under the normal frequency distribution curve. For example, approximately 68 percent of the area (equivalent to 68 percent of the test results) lies within ±1σ of the average, 95 percent within ±2σ, etc. This permits an estimate to be made of the portion of

Fig. 3.4.2(b)-Cumulative distribution curves for different coefficients of variation

Fig. 3.4.2(c)-Cumulative distribution curves for different standard deviations

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