TRANSPORT and ROAD RESEARCH LABORATORY

Department of the Environment

TRRL REPORT LR 547

EFFECTS OF RATE OF LOADING ON FLEXURAL STRENGTH AND FATIGUE PERFORMANCE OF CONCRETE

by

J W Galloway, CEng, MIMechE

and

K D Raithby, BSc, CEng, AFRAeS

Structural Properties Division Structures Department

Transport and Road Research Laboratory Crowthorne, Berkshire

1973

CONTENTS

Abstract

1. Introduction

2. Design and preparation of concrete specimens

2.1 Materials and mix design 2.2 Preparation of specimens 2.3 Variability of control cylinder strengths

3. Experimental equipment

4. Test procedure

4.1 Preparation of specimens and test conditions 4.2 Modulus of rupture tests 4.3 Fatigue tests

5. Results

5.1 Dynamic modulus of elasticity tests 5.2 Modulus of rupture tests 5.3 Fatigue tests

6. Discussion and comparison of results

7. Conclusions

8. Acknowledgements

9. References

Page

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( • ) CROWN COPYRIGHT 1973

Extracts f r o m the text may be reproduced provided the source is acknowledged

Ownership of the Transport Research Laboratory was transferred from the Department of Transport to a subsidiary of the Transport Research Foundation on 1 st April 1996.

This report has been reproduced by permission of the Controller of HMSO. Extracts from the text may be reproduced, except for commercial purposes, provided the source is acknowledged.

EFFECTS OF RATE OF LOADING ON FLEXURAL STRENGTH AND FATIGUE PERFORMANCE OF CONCRETE

ABSTRACT

Results are given of an investigation into the relationship between the flexural strength and the rate of increase of extreme fibre stress of small beam specimens of two concretes. In addition, a limited investigation was made to determine the effect of rate of loading upon the fatigue performance, and the latter was related to the flexural strength at comparable stressing rates.

The flexural strength was shown to be highly dependent upon rate of loading. At rates of loading approximating to the rates at which stress is applied in fatigue tests at 20Hz, flexural strengths were about 50 per cent higher than those obtained under loading rates specified in the current British Standard flexural test.

No significant difference in fatigue performance was found in repeated loading tests on one concrete at loading frequencies of 4Hz and 20Hz.

1. INTRODUCTION

The Transport and Road Research Laboratory is studying the characteristics of plain concrete, when subjected to repetitive loading, as part of a broad research programme I aimed at characterising material properties for use in a structural method of pavement design. Among the factors being studied in relation to the fatigue performance of concrete are the effects of moisture condition, age and rate of loading. This Report, the first of a series describing these studies, deals with the effects of rate of loading on flexural strength and, in a more limited investigation, the effects of variation in frequency of loading upon fatigue performance.

Fatigue performance data for concrete are frequently expressed in terms of the nominal "stat ic" strength determined from tests carried out at a standard rate of loading which is much less than the rate at which load is applied in the fatigue tests. The rate of loading has been shown to have an appreciable effect on the maximum

• load achieved in flexural strength tests on concrete and mortar beams 2 ,3,a over the range 0.0006 to 3.6 MN/ma/sec. The tests reported here covered somewhat higher rates of loading and were performed to provide a more realistic basis for assessing the fatigue performance of concrete beams.

Because the modulus of rupture is so dependent upon the rate of loading it might be expected that fatigue performance would depend upon the frequency of loading. Previous investigators 5 ,6 have shown, however, that for cyclic frequencies between 0.5Hz and 7.5Hz there was little difference in fatigue life.

The objects of the work described in this Report were to extend the study of the effects o f stressing rate on flexural strength to rates comparable to those applied in fatigue tests at 20Hz, and to conduct a limited investigation into the effects of cyclic frequency on fatigue performance from 4Hz to 20Hz. The rate of loading tests (molulus of rupture) were carried out on small beam specimens of two types of plain concrete, one having an uncrushed flint gravel aggregate, the other a crushed limestone; only the former concrete was used for the frequency of loading (flexural fatigue) investigation.

2. DESIGN AND PREPARATION OF CONCRETE SPECIMENS

2.1 Materials and mix design

All the blended Portland cement used in this work came from one batch and was stored in a heated cement store in sealed metal 50kg drums. The sands and coarse aggregates came from separate stockpiles and were oven-dried before being stored, the coarse aggregates having been graded into separate sizes (19-9.5 mm and 9.5-4.8 mm).

A great deal of information is available on concrete having an uncrushed flint gravel aggregate and a mix (PQ1) containing this type of material has been used for much of the current fatigue work. To investigate the effect of changing the type of aggregate a second mix (PQ2) was made with a crushed limestone aggregate and designed to have the same 28-day indirect-tensile strength as mix PQ1. Table 1 gives, for both concretes, details of the aggregates, mix design and trial mix strengths.

2.2 Preparation of specimens

In order to obtain a continuous supply of concrete specimens for this work and other work in the overall research programme one or two batches were made, under carefully controlled conditions, every week for over two years.

The mixes were prepared and mixed in a 50-1itre open-pan mixer using the standard method 7 adopted by the TRRL. From each batch of concrete six 508 mm x 102 mm x 102 mm beams and five 152 m m x 102 mm diameter control cylinders were cast. These specimens were compacted on a vibrating table in layers approximately 50 mm deep, each layer being vibrated for 90 secs. They were thela stored under damp matting covered with polyethylene for 24 hours before being demoulded and cured under water in accordance with BS 1881 " 1970.

2.3 Variability of control cylinder strengths

As a means of checking the quality of the concretes throughout the whole mixing programme, indirect- tensile splitting tests were made on four cylinders from each batch at an age of 28 days. The coefficients of variation of the mean batch strengths were, for concretes PQ1 and PQ2 respectively, 3.8 per cent (152 batches) and 5.4 per cent (34 batches). The coefficients of variation of all the individual results were, respectively, 5.4 per cent (608 results) and 6.7 per cent (136 results).

3. EXPERIMENTAL EQUIPMENT

A pair of servo-controlled electro-hydraulic actuators, mounted in a stiff frame, formed the basis of two testing machines which were used to apply third-point loading to the beam specimens. Each actuator was controlled from a common function generator capable of providing a controlled rate of loading as well as various cyclic wave shapes over a practical frequency range of 0.001 to 50Hz.

Each beam was supported (see Hate 1) on a pair of steel rollers and the load was applied through two similar rollers mounted at the third points of the supporting span. All rollers were self-aligning to ensure that no local restraint was imposed on the test specimen. The loading frame and control equipment are shown in Hate 2, and Fig. l shows a schematic layout of the closed-loop testing system. The load applied to the specimen was sensed by a load cell, connected to the end of the actuator, and the load cell output used as a feedback signal to control the load applied by the actuator.

2

For the flexural strength tests the load cell signal was recorded on an ultra violet light oscillograph recorder having a range of paper speeds. The recorder was used to check the rate of loading applied to the specimens and to determine the load at failure.

4. TEST PROCEDURE

4.1 Preparation of specimens and test conditions

All beams were removed from the curing tanks 26 weeks after manufacture. After removing surface water they were measured, weighed and their dynamic moduli of elasticity determined by means of a non- destructive electrodynamic method s. Flexural tests, see 4.2 and 4.3 below, were then carried out under two nominal moisture conditions:

(i) Saturated: beams, whilst still moist, were sealed in polyethylene bags with some free water.

(ii) Surface-dry: beams were allowed to partially dry out in a laboratory atmosphere for 7 days before being tested.

To allow for the effect of the strength variability of the concrete, flexural tests were arranged so that there was not more than one beam from any given batch in any group of tests at a particular test condition. Each specimen was carefully aligned between the rollers on the testing frame with the top surface (as cast) uppermost. An initial load of approximately 25N was applied to this surface in order to maintain the loading system in a closed servo loop.

4.2 Modulus of rupture tests

Flexural strength tests were carried out on saturated beams of both concretes at various stressing rates, using the function generator in the constant rate of loading mode and with the output of the load cell coupled to the UV recorder.

The lowest stressing rate (0.0172MN/m2/sec) was the lowest practical rate that could be applied to the particular concrete specimens and was approximately midway between that laid down in BS 1881 : 19529 and BS 1881 : 1970 l° as the rate of stressing to be applied in standard flexural strength tests on concrete beams. The highest rate (172MN/m2/sec) was approximately the average rate at which stress was applied in fatigue tests, on these concretes, at 20Hz. The surface-dry beams were tested at the lowest stressing rate only.

4.3 Fatigue tests

All fatigue tests were carried out under constant amplitude sinusoidal loading in which the minimum load was approximately zero, thus subjecting the lower surface of the specimen to wholly tensile cyclic stresses.

Concrete PQ1 was tested in both moisture conditions at loading frequencies of 4 and 20Hz, and concrete PQ2 was tested only in a saturated condition at 20Hz.

5. RESULTS

5.1 Dynamic modulus of elasticity tests

The dynamic modulus of elasticity was measured as a check on the quality of each specimen before it was tested in flexure. The mean values obtained on the saturated specimens immediately after removal f rom the curing tanks were, for concretes PQ 1 and PQ2 respectively, 45,500MN/m 2 (191 specimens) and 39,500MN/m z (65 specimens); the coefficients of variation of results were less than 2 per cent for each concrete.

3

5.2 Modulus of rupture tests

Fig. 2 shows examples of load-time records obtained from the UV recorder at some of the higher loading rates. As soon as a specimen fractured the oil supply to the actuator was cut off; the rise in load after failure of the specimen was caused by the broken portions falling and coming into contact with a wooden block before the loading system was fully de-energised.

For each beam the load at failure was determined from the records and the modulus of rupture calculated from the formula:

WL fr = . m BD 2

where

W =

L =

B =

D =

modulus of rupture in MN/m 2

maximum applied load in newtons

distance between axes of lower rollers in millimetres

width of beam in millimetres

depth of beam in millimetres

The values of the modulus of rupture at the various stressing rates are given in Table 2 for both concretes and are plotted in Fig. 3 which also shows, for comparison, curves published by other researchers 2'3'4 on various types and ages of mortar and concrete.

5.3 Fatigue tests

The results of the fatigue tests are summarised in Tables 3A and 3B and are plotted in Fig. 4, the points plotted at ½ cycle being the modulus of rupture at a stressing rate of 0.0172MN/m2/sec. Some tests were terminated before failure occurred; in such cases the maximum number of loading cycles obtained was taken as a conservative estimate of the life of the beam.

The fatigue results include some comparative tests on concrete PQ1 at 4Hz and 20Hz to see whether there was any measurable frequency effect on fatigue performance. These tests were carried out mainly on surface-dry specimens but tests were also made at one stress level on saturated specimens of concrete PQ1. Regression line data were calculated for the results at each frequency and for both frequencies combined. There was no significant difference between the regression lines for each loading frequency. It was concluded that frequency of loading had no effect on fatigue performance over the range 4 to 20Hz. For all subsequent tests in the current research programme of the Structural Properties Division 20Hz has been adopted as a standard test frequency for the fatigue testing o f cement bound materials.

6. DISCUSSION A N D COMPARISON OF RESULTS

Earlier studies 2 ,3,4 on the effect of rate of stressing on flexural strength carried out on a variety of types and ages of mortar and concrete beams (summarised in Fig. 3) suggest that up to about 2MN/m2/sec there is a linear relationship between the modulus of rupture and the logarithm of the rate of application of flexural stress, although in fact most of these tests were carried out at stressing rates of less than 0.1MN[m2/sec. The results of the current series of tests also showed a linear relationship up to 2MN/m2/sec, with a slope similar to the mean slope of the earlier curves. At rates higher than 2MN/m2/sec, however, there was a marked departure from linearity, indicating that the rate of increase of strength was becoming even greater at the higher rates of loading. At rates o f loading corresponding to fatigue tests at 20Hz (i.e. about 170MN/m2/sec) the modulus of rupture was between 40 and 60 per cent greater than that obtained from the current BS 1881 flexural test conditions.

4

Fatigue tests were carried out on both saturated and surface dry specimens of concrete PQ1 at loading frequencies of 4Hz and 20Hz. Flexural strength tests on saturated beams at loading rates corresponding to these two frequencies indicate that a difference in modulus of rupture of nearly 15 per cent might be expected. If fatigue strength were related directly to quasi-static flexural strength, a 15 per cent difference in modulus of rupture might be expected to cause the mean fatigue life at particular stress levels to differ by an order of +magnitude. In fact comparative tests showed no significant.difference in fatigue performance between 4Hz and 20Hz, either for the saturated beams or for the surface-dry beams. This result is in agreement with conclusions reached by Kesler et al 4, based on flexural fatigue tests over the range 1.2 to 7.3Hz. The explanation for the apparent discrepancy between flexural strength and fatigue behaviour may lie in differences in stress- strain relationships in the pre-cracking and post-cracking stages of loading. Kesler and others have pointed out that as long as the stress-strain curves are linear (usually up to about 40 to 60 per cent of the static strength) variations in rate of loading have little effect but that above this level, when microcracks are developing, rate of loading has a substantial effect on the strain response. It may be inferred therefore that, since the load levels in the fatigue tests are usually largely within the linear range of response, then little difference in fatigue performance would be expected. There is insufficient evidence from the present test results to substantiate this but any future research on this topic should include a more detailed examination of the stress-strain relationships for all the different loading conditions. A further factor which might have some influence is the extent to which the achieved strength may be affected by creep at high loads.

The results of fatigue tests on concrete are commonly expressed as endurance curves having as ordinates the ratio of the maximum applied stress to the "static ult imate" strength and it is frequently stated that the fatigue strength or endurance limit of concrete is of the order of 55 per cent of the static strength. The "static ultimate" strength is usually derived from tests at very much slower rates of loading than in the fatigue tests. As the modulus of rupture is sensitive to the rate of stressing, it would be more logical to relate fatigue strength to the flexural strength at a rate of loading approximating to the rate at which load is applied in the fatigue tests. This has been done in Fig. 5 for the two concretes PQ1 and PQ2. For the low.er curve in each case, the o,,,~1+°~ ~+,o~ i~ expressed +~ + . . . . e +~o ¢-,, +,,- . . . . . . . . . s . . . . . . modulus o, , ~ , p ~ u , e corresponding to the aver;age o~,ess,,,~°*" ~ . . . . . . ,,,~e~ m" the fatigue tests, (i.e. the maximum Cyclic stress multiplied by twice the frequency) appropriate values being read off from Fig. 3. For the upper curves, the conventional definition of flexural strength has been used. In the case of PQ2, some extrapolation was necessary since the increased loads at the higher frequencies were beyond the capacity of the testing equipment.

It will be seen from Fig. 5 that correcting the fatigue curves for the effects of rate of loading on modulus of rupture has an appreciable effect on the shape of the curves, resulting in fatigue strengths which are a much lower proportion of the true flexural strength. Such differences must be taken into account in any at tempt to explain or interpret the relationship between fatigue performance and flexural strength. The fact that the replotted curves show an effective fatigue limit of around 40 per cent may well have some significance in relation to the shape of the corresponding stress-strain curves, but this will require further study.

7. CONCLUSIONS

A considerable increase in the modulus of rupture was obtained by increasing the rate of application of extreme fibre stress on beam specimens of two saturated concretes. Increasing this rate by a factor of 10,000 (corresponding roughly to the difference between the standard flexural strength test and a fatigue test at 20Hz) resulted in an increase in modulus of rupture of the order of 50 per cent for each of the two types of concrete tested in a saturated condition. The rate of increase at the higher stressing rates was greater than that predicted from earlier investigations made at slower testing rates.

Repeated loading tests carried out at frequencies of 4Hz and 20Hz on one type o f concrete in a surface- dry condition, showed no significant effect of rate of loading on fatigue performance for each of the three stress levels used. Similar, but more limited, tests at 4Hz on the same concrete in a saturated condition gave results which were almost identical to those obtained at 20Hz. The lack of effect of rate of loading on fatigue

performance, noted also by other research workers, seems at first sight inconsistent with the very marked effect on flexural strength. The explanation may lie in likely differences in stress-strain relationships over difference stress ranges for the various rates of loading but there is insufficient evidence from these tests to establish whether this is so. Further work is needed to clarify this point.

8. ACKNOWLEDGEMENTS

The work described was carried out in the Repeated Loading of Materials Section of the Structural Properties Division (Divisional Head Mr D F Cornelius). The authors wish to express their appreciation to Mr H M Harding for his assistance in making and testing the specimens.

9. REFERENCES

1.

2.

3.

4.

.

.

7.

.

9.

10.

BURT, M E. Progress in pavement design. Department of the Environment, TRRL Report No. LR508, Crowthorne, 1972.

McHENRY, D, and J J SHIDELER. Review of data on effect of speed in mechanical testing Of concrete. American Society for Testing Materials. T~chnical Publication No. 185, June 1955.

WRIGHT, P J F. The flexural strength of plain concrete - its measurement and use in designing concrete mixes. DSIR, RRL Technical Paper No. 67, Harmondsworth, 1964. (Road Research Laboratory).

LLOYD, J P, J L LOTT, and C E KESLER. Fatigue of concrete. Engineering Experimental Station Bulletin No. 499, University of Illinois, Urbana, Illinois, 1968.

RAITHBY, K D, and A C WHIFFIN. Failure of plain concrete under fatigue loading - a review of current knowledge. Ministry of Transport, RRL Report LR 231, Crowthorne, 1968. (Road Research Laboratory.

KESLER, C E. Effect o f speed of testing on flexural fatigue strength of plain concrete. Proceedings, Highway Research Board, 32, 1953.

CORNELIUS, D F, R E FRANKLIN, and T M J KING. The effect of test method on the indirect tensile strength of concrete. Ministry of Transport, RRL Report No. LR 260, Crowthorne, 1969, (Road Research Laboratory).

BRITISH STANDARDS INSTITUTION. Methods of testing concrete. London, BS 1881 : Part 5: 1970.

BRITISH STANDARDS INSTITUTION. Methods of testing concrete. London, BS 1881 • 1952.

BRITISH STANDARDS INSTITUTION. Methods of testing concrete. London, BS 1881 : Part 4 " 1970.

6

TABLE 1

Details of concretes and trial mixes

Aggregate and strength details

Aggregate

Mix • proportions

Cement

Trial mix details

Concrete

PQ1 PQ2

Source Chertsey Whatley

I Classification Flint Limestone

Type Uncrushed gravel Fully crushed rock

Particle shape

Surface texture

Water 19 - 9.5 mm absorption % 9.5 - 4.8 mm and mix passing

• proportions % 4.8 mm

Grading of fines

' Aggregate/cement ratio

Free water/cement ratio

Type

Workability

28 day indirect-tensile strength on 152 mm x 102 mm diameter cylinders

28 day compression test on 102 mm cubes

Irregular Angular

Smooth Fairly rough

1.9 41 3.3 20 1.1 39

Zone 2

6.7

0.5

0.8 17 0.7 39 0 . 5 44

Zone 1

5.2

0.62

"Typical" blended ordinary Portland

Compacting factor 0.84 "V-B" test 7 secs

3.50MN/m 2 3.48MN/m 2

44.80MN/m 2 33.30MN/m 2

7

TABLE 2

Modulus of rupture results

Concrete

Rate of increase of

extreme fibre stress

MN/m2/sec

Number of

results

Mean modulus

of rupture MN/m 2

Standard deviation

MN/m 2

Coefficient of

variation %

PQ1 surface 0.0172 5 3.31 0.158 4.8

dry*

0.0172 10 4.21 0.329 7.8

0.172 11 4.64 0.377 7.3

0.86 11 5.19 0.409 7.9

PQ1 1.72 12 5.17 0.344 6.7 saturated

m .

17.2 10 5.86 0.461 7.9

68.9 10 6.32 0.157 2.5

172.0 10 6.97 0.507 7.3

0.0172 10 5.67 0.453 8.0

PQ2 saturated 1.72 5 6.54 0.377 5.8

68.9 5 7.66 0.187 2.4

All specimens were cured under water for 26 weeks.

* Surface-dry specimens were allowed to partially dry out in laboratory atmosphere for 1 week after curing.

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Fatigue test results : Concrete PQ2

Moisture state

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Maximum stress

MN/m 2

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4.60

4.27

3.90

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10

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502,800

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P R I N T E D IN E N G L A N D

ABSTRACT

Effects of rate of loading on flexural strength and fatigue performance of concrete: J W GALLOWAY, CEng, MIMechE and K D RAITHBY, BSc, CEng, AFRAeS: Depart- ment of the Environment, TRRL Report LR 547: Crowthorne, 1973 (Transport and Road Research Laboratory). Results are given of an investigation into the relationship between the flexural strength and the rate of increase of extreme fibre stress of small beam specimens of two concretes. In addition, a limited investigation was made to deter- mine the effect of rate of loading upon the fatigue performance, and the latter was related to the flexural strength at comparable stressing rates.

The flexural strength was shown to be h igh lydependent upon rate of loading. At rates of loading approximating to the rates at which stress is applied in fatigue tests at 20Hz, flexural strengths were about 50 per cent higher than those obtained under loading rates specified in the current British Standard flexural test.

No significant difference in fatigue performance was found in repeated loading tests on one concrete at loading frequencies of 4Hz and 20Hz.

ABSTRACT

Effects of rate of loading on flexural strength and fatigue performance of concrete: J W GALLOWAY, CEng, MIMechE and K D RAITHBY, BSc, CEng, AFRAeS: Depart- ment of the Environment, TRRL Report LR 547: Crowthorne, 1973 (Transport and Road Research Laboratory). Results are given of an investigation into the relationship between the flexural strength and the rate of increase of ext reme fibre stress of small beam specimens of two concretes. In addition, a limited investigation was made to deter- mine the effect of rate of loading upon the fatigue performance, and the latter was related to the flexural strength at comparable stressing rates.

The flexural strength was shown to be highly dependent upon rate of loading. At rates of loading approximating to the rates at which stress is applied in fatigue tests at 20Hz, flexural strengths were about 50 per cent higher than those obtained under loading rates specified in the current British Standard flexural test.

No significant difference in fatigue performance was found in repeated loading tests on one concrete at loading frequencies of 4Hz and 20Hz.