QUANTITATIVE DAMAGE ANALYSIS OF CONCRETE

Proc. Int. Sytnp. ((BrittleMatrix Composites 7" A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003

QUANTITATIVE DAMAGE ANALYSIS OF CONCRETE Piet STROEVEN Faculty of Civil Engineering and Geosciences Delft University of Technology Stevinweg 1,2628 CN Delft, The Netherlands, e-mail: [email protected]

ABSTRACT The load-induced damage structure in concrete can be conceived as a spatial structure of dispersed surfaces of which the connectivity increases during load increase. Quantitative image analysis by line scanning in 'vertical sections' allows determination of crack surface area per unit of volume and degree of crack orientation. This paper presents the methodology, and demonstrates its applicability for assessing damage evolution characteristics in low-cycle compression fatigue domain and in direct tension. The associated tests have been conducted earlier.

Keywords Compression, cracking, damage, modelling, stereology, tension.

INTRODUCTION The damage evolution process can be considered uniquely reflecting certain loading regimes operative under specified circumstances. Vile [l] was probably the first to propose a model for meso-cracking underlying global damage evolution in direct compression. The topic also received attention by Stroeven [2], Newman & Newman [3], and Perry and Gillott [4], providing experimental evidence in support of the model. Analytical support comes from elastic solutions of single inclusions in an infinite matrix the oldest of which dates back some seventy years [5-81. The first systematic experimental investigation into damage evolution of concrete, using different techniques, was performed by the 'Cornell group' [8,9]. Images of sections were analysed two-dimensionally, however. It was concluded, among other things, that 50% of the damage at ultimate loading was already present in the virgin state [8], so not typical of the loading regime. To complicate matters further, the fractal concept has revealed such ratios to be sensitivity-dependent [lo]. Quantitative microscopy is the more common way to quantify local features of damage in concrete [ I 1,121; specimens are easy to handle and grinding and polishing operations can be automated. Applications of quantitative image analysis (stereology) for assessment of three-dimensional global damage parameters are extremely scarce [2,13-161. Yet, results can offer insight into cracking mechanisms underlying mechanical phenomena, or allow structural interpretation of macro-mechanical models.

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QUANTITATIVE IMAGE ANALYSIS Apartially linear system, as a close approximation for the damage structure induced by uniform compression in a cylindrical specimen, can be emphasized as a mixture of 3-D and I-D systems. The cracks are in both systems randomly distributed as to location. In the first case, the cracks are also randomly distributed as to orientation, whereas in the second one all cracks are parallel to a line, the axis of the specimen. In a vertical secfion, the 3-D system yields a random pattern of traces, while the I-D system leads to traces parallel to the axis of the specimen. The number of intersections with a parallel line probe is indicated by P , and its density by P / L = PL. Perpendicular to the orientation axis of the traces the intersection density will have a maximum value, while a minimum is found in an orthogonal direction. It is well known that the intersection density in a certain direction, & ( O ) , is an unbiased estimator of the total projected length of the traces, per unit of area, on a line perpendicular to the grid direction, L;(O + x / 2 ) . Hence, P'(0) =.Li(O + n / 2 ) [2,16]. For the axial and transverse direction it is readily found that

in which LA, and LA, are the areal trace densities in the 1-D and 3-D system, respectively. Obviously, LA = LAI+ LA,, so that

The degree of orientation in the trace pattern can be defined by

The 3-D interpretation of a similar set of observations is equally simple! The same probabilistic principle holds. Hence 1 I F 1 2 PL(0)=-Sv3 and PL(-)=-Sv3 +-S VI IF 2 2 2

In analogy with the 2-D case:

(4)

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In case of unifbrm tension, the actual damage structure can be conceived composed of a mixture of 3-D and 2-D systems. Again, cracks in both systems are supposed to be randomly distributed as to location, and in the 3-D set also as to orientation. In the 2-D system, all cracks are developed, however, perpendicular to the loading direction, so parallel to the socalled orientation plane. This is referred to as partially planar crack orientation. The vertical section reveals a mixture of these systems, the pattern of which is equivalent to the one obtained for the partially planar case but rotated in the plane over 90'. In analogy with eqs. (4) and (9,we have 1 R 1 2 PL(0)=-Sv3 and P L ( - ) = - S v 3 + - S v z R 2 2 2

(6)

A comparison between the two- and three-dimensional expressions for w and crack density will reveal the bias of the seemingly (but not really) simpler two-dimensional approach. The partially planar model has been used for evaluation of direct tensile tests on two-sided notched prisms, and the partially linear model for doing so for low-cycle compression fatigue tests on prismatic specimens. EXPERIMENTAL: COMPRESSION CASE Testing was performed in low-cycle compression fatigue to evaluate the effects of average stress level, stress amplitude and frequency on the number of cycles to fracture, N. The frequencies covered were 17.5 Hz and 0.175 Hz. The upper stress level,o,', was taken for all tests at 87.5% of the 28-days short-term compressive strength,o;,, , of prismatic specimens with similar composition. Hence, this is well above the so-called endurance limit. A relative stress amplitude, S, is defined by S = (0,' - o b ' ) / o ) z 8 in,which ob' is the lower stress level. S varied in the investigations between zero and 0.475. Out of the eight stress amplitude cases encompassed in the experiments, three were included in the quantitative image analysis. The selected cases, S O , S0.075 and S=0.35, represent the mechanical states of permanent loading, and of low-cycle fatigue loading with small, respectively, with large load amplitude. A total number of 72 prismatic specimens (100x100~345mm3) were cast from concrete with a maximum grain size of 8 mm and a water to cement ratio of 0.46. Average 28-days compressive strength of reference prisms amounted to 56.2 MPa. The prisms were stored 10 days under water, followed by 7 days under controlled conditions (22' C, 50%RH), whereupon the specimens were placed until the day of testing at about 1 month in the test room. Sieve curves were between the As and Bs curves of DIN 1045. A single specimen whose deformational behaviour was as close as possible to that of the group average was selected for quantitative damage analysis. Deformations were recorded by clip gauges in longitudinal and in transverse direction. Specimens were subjected to sinusoidal load variations in a servohydraulic testing machine. The loading process was automatically stopped when the transverse deformation attained a certain threshold value [ 171. This rendered possible to study the

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internal damage structure of the specimens without introducing a significant bias in the number of cycles to fracture. Each selected specimen was axially sliced to yield three equally spaced sections at a distance of 27 mm [18]. Specimens were cast, compacted and stored in vertical position. Since the loading was applied also in the same direction, the longitudinal axis of the specimen can be considered an axis of symmetry of the damage structure (excluding boundary zones). Fields of 51x102 mm2 were selected at the centre of each section image. Hence, a sample encompassed three independent so-called 'vertical' fields, which were subjected to intersection counting in the two main directions. The distance between the grid lines was optimised to yield a number of intersections roughly equal to the number of cracks in a field. In doing so, a total test line length of 1734 mm was obtained. Contrast was improved by employing the filtered particle method [2,16]. Mechanical properties were generally found in agreement with published data. They were supported by the stereological outcomes [ 17-19]. Additional information is offered on underlying damage evolution mechanisms, however. Table 1 presents some illustrative data. Note that N A is the number of cracks in the section per unit of area. We will focus on a peculiar phenomenon [ 181, i.e. a prevailing direction of damage evolution perpendicular to the compression direction! This occurred under maximum amplitude (S=0.35) and maximum frequency conditions (17.5 Hz). Average loading was in that case 17.5% lower than under permanent loading (S=O). Nevertheless, these conditions proved very destructive (T is time to fracture). The proposed model by Vile [l] for damage evolution on meso-level, elaborated earlier for general use by this author [2], was applied to the present case [17,18]. The wellknown column-like structure of concrete that is subjected to a uniform state of relatively high compression is effectively broken down by debonding (thus: cracking) at aggregate-matrix interfaces perpendicular to the compression direction. This is the result of secondary tensile stresses initiated under stress release to below the so-called discontinuity point. Table 1:Low cycle fatigue data at 17.5 Hz S

S"

0 0.075 0.350

[mm-'] 0.561 0.601 0.678

NA

0 3

~ m m - ~ ] [%I 0.127 8 0.113 11 0.151 -3

N 42.800 1361300 4,600

T [set 1 2.446 81246 263

EXPERIMENTAL: TENSION CASE Two-sided notched fine-grained concrete prisms (60x50~250mm3) were subjected to a shortterm direct tensile loading in a servo-controlled system with a maximum capacity of 100 kN. The notches reduced the cross sectional dimensions to 50x50 mm2. Concrete was composed of 375 kg/m3 Portland cement and 905, 363 and 540 kg/m3 aggregate of the size ranges 0-2 mm, 2-4 mm and 4-8 mm, respectively. The specimens were cut from larger 50 mm thick panels that were cast vertically to avoid boundary effects. Average compressive and tensile strength values at 28-days were 47.1 and 3.20 N/mm2, respectively. Specimens were glued between steel platens to promote the fracture process zone to undergo uniform deformations. Deformation measurements were executed by a series of extensometers with a gauge length of 35 mm positioned on both surfaces over the notches.

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From this study six specimens were selected which had been subjected to different postpeak deformational states. The damage state was 'frozen' by gluing aluminium strips to the longitudinal sides of the prisms. Thereupon, four equidistant and parallel 'vertical' sections were prepared of the central portion of the specimens. Spacing between the vertical sections was larger than maximum grain size (8 mm) to obtain statistically independent structural information. The surfaces of the sections were treated with a fluorescent spray [2]. Crack patterns were recorded on slide under illumination by UV light. An area of 48x35 mm2 and a smaller portion of 48x13 mm', located symmetrically with respect to the notch section, were analysed for crack extension. For that purpose Saltikov's method of directed secants was applied to about 7 to 10 times magnified pictures of the designated areas. This was accomplished by projecting a slide on a semi-transparent glass plate. All cracks visible with the unaided eye were taken into consideration, so that the sensitivity will be about a quarter of a millimetre. Rotating the grid allows assessment of the crack orientation distribution. The mechanical experiments revealed the development of a non-uniform distribution of axial deformations over the notch section at yielding (see, e.g. Fig. 4 in [20]). Hence, due to inhomogeneity-induced eccentricity the specimen was subjected to bending. This phenomenon was already known, of course, from experiments using photo-elastic coatings. In [21] this phenomenon was later studied in more detail. Yielding reduced the bending stiffness in the fracture process zone, so that locally a rotation could be accommodated. At larger global deformations, this degree of rotation was maintained. Measurements at front and backside over the notches of the specimens revealed completely different post-peak deformational behaviour even involving compaction [22]. The experimental observations were confirmed by a finite element (FE) simulation based on the smeared out crack approach using the DIANA package. For more details on the mechanical aspects one is referred to [21], and for the FE simulation to [23]. Slides of four vertical sections of the six specimens have been elaborated. Since only single specimens could be selected from the mechanical experiments, scatter between samples (as an average of four images) proved to be too large to draw quantitative conclusions on changes in damage evolution rates during yielding. The scatter was dramatic among the serial sections. For section images, see [16,22]. Table 2 gives some of the damage evolution parameters pertaining to the post-peak range; C-7 and C-5, respectively, C-4 are specimens with a residual load-bearing capacity of 75% and 50% of ultimate. Added are data on a section (C5-4) of a specimen subjected to the same loading history as in case of specimen C-7, but both specimens were unloaded in a different way [ 161. It should be noted that this table reports on data pertaining to the 13 mm wide central zone as well as to the two 11 mm wide boundary zones encompassed in the wider area of 35x48 mm2around the notched section. Table 2: Stereological damage estimates Area location notched zone boundary zone notched zone boundary zone

Damage parameter

S, in mm-l w3 in%

C-7-2 0.333 0.181 18.7 7.6

Specimen number C-7-3 C-5-4 0.543 0.218 0.366 0.146 21.3 9.3 17.5 15.9

C-4-4 0.257 0.193 13.3 3.0

Finally, images were analysed on deviations from symmetry in the damage structure of the so-called Fracture Process Zone (FPZ). Since major cracking will be perpendicular to the

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Piet STROE VEN

e,(O)

global tensile loading direction, the data (in the axial direction) for the more significant cracks (after eliminating the small and widely scattered cracks) are determined separately for the two sides of the specimen [16]. Representative data on C-7-2 and C-5-4 are presented in Table 3. For a selected set of sections also N A was determined. Data obtained in this way for average 2-D crack size (=LA/ N A )fall between 0.5 and 0.7 mm. As an example, [22] gives N A4 . 4 17 mm-' for C-7-2. WithS~4.333mm-' (Table 2), the average crack size in the 13 mm central portion will be 0.65 mm. In [16] the average crack length at DP (assuming completed bond 5 avcracking) was estimated by n d o / 4 , in which do is the sensitivity level. For do~ 0 . mm, erage crack size at DP will be 0.4 mm. Hence, damage evolution between DP and the investigated post-ultimate loading situation is only moderate. The ensemble of 4x6 images reveals a very large amount of structural scatter, as illustrated by presented data (and by earlier published images). Shuffling these images like playing cards would make it impossible to restore their original position in a particular specimen! Systematic features dealing with macro-crack formation only appear in the post-peak range. But a definite delineation of the macro-crack is only found after a considerable amount of yielding has taken place, as can be concluded from a comparison of C-7 and C-4 images. The macro-crack is obviously the final result of a hazardous process of crack coalescence, initially driven by high residual stresses and later primarily by structural stress raisers. The probability of having crack coalescence in the neighbourhood of the notched section is somewhat increased by a 20% higher average stress. The latter leads to a gradually increasing crack density toward the notched section (Table 2), hence to crack concentration, a phenomenon becoming more pronounced during yielding of the specimen. Because the distances between cracks are as a consequence reduced, their interaction will promote further coalescence. The hazardous process of growth and coalescence of the widely scattered cracks on structural level that are only weakly affected by the presence of a notch is alien to the engineering concept of a single crack initiated at a notch and propagating along the notch section. Also, the concept of a fracture process zone symmetric around the notched section is an engineering concept not reflected by the damage structure that, indeed, was found a 'zone spaced without sharp boundaries' [24]. Table 3: Eccentricity in damage evolution Area location

Damage parameter

Specimen number C-7-2 c-5-4 left side right side left side right side

Notched zone

P,(O) in mm-'

0.15

0.06

0.17

0.17

Boundary zone

P,(O) in mm-'

0.12

0.06

0.10

0.14

CONCLUSIONS The interpretation of engineering mechanical behaviour in terms of cracking mechanisms and features of damage evolution by the methodology outlined in this paper allows a structural interpretation of relevant research, and renders possible at least qualitatively estimating mechanical characteristics on the basis of structural modifications. Damage is a fractal-like phenomenon. Hence, observations on damage evolution are resolution-dependent. This also holds

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for the present experiments. Extent of damage and characteristics of the crack orientation distribution are functions of the sensitivity level set by the researcher (here, 0.2 mm). The data presented herein, though of illustrative nature, nevertheless reveal significant structural differences implied by different loading regimes, which allows gaining a clear insight into the operative damage evolution mechanisms.

REFERENCES 1. Vile, G.W.D., Behaviour of concrete under simple and combined stresses, PhD Thesis, Univ. London, UK 1965 2. Stroeven, P., Some aspects of the micromechanics of concrete, PhD Thesis, Delft Univ. Technology, Delft, The Netherlands 1973 3. Newman, K., Newman, J.B., Failure theories and design criteria for plain concrete. In: “Structure, Solid Mechanics and Engineering Design”, M. Te’eni ed. Wiley, New York 1969, pp 963-995 4. Perry, C., Gillott, J.E., The influence of mortar-aggregate bond strength on the behaviour of concrete in uniaxial compression. Cem. Concr. Res., 5, 1977, pp 553-564 5. Goodier, J.N., Concentration of stress around spherical and cylindrical inclusions and flaws, J. Appl. Mech. ASME, 55, 7, 1933, pp 39-44 6. Sezawa, K., Nishimura, G., Stresses under tension in a plate with a heterogeneous insertion. Rep. Aeron. Res. Inst., Tokyo Imp. Univ., 6, 25, 1931, pp 25-43 7. Muskhelishvili, N.I., Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen 1953 8. Hsu, T.C., Slate, F.O., Sturman, G., Winter, G., Microcracking of plain concrete and the shape of the stress-strain curve. J. ACI, 60, 2, 1963, pp 209-224 9. Slate, F.O., Olsefski, S., X-ray for the study of internal structure and microcracking of concrete. J. ACI, 60, 5, 1963, pp 575-588 10. Stroeven, P., Fractals and fractography in concrete technology. In: “Brittle Matrix Composites 3”, A.M. Brandt, Marshall I H. eds. Elsevier, London 1991, pp 1-10 1 1 . Ringot, E., Automatic quantification of microcracks network by stereological methods of total projections in mortars and concretes. Cem. Concr. Res., 18, 1988, pp 35-53 12. Saito, M., Characteristics of microcracking in concrete under static and repeated tensile loading. Cem. Concr. Res., 17, 1987, pp 2 11-2 18 13. Stang, H., Shah, S.P., Damage evolution in FRC materials modelling and experimental observations. In: “Fibre Reinforced Cements and Concretes”. Recent Developments, R.N Swamy, B. Barreds. Elsevier, London 1989, pp 378-387 14. Stroeven, P., Application of various stereological methods to the study of the grain and the crack structure of concrete. Journ. Microsc., 107, pt 3, Aug. 1976, pp 3 13-321 15. Stroeven, P., Geometric probability approach to the examination of microcracking in plain concrete. Journ. Mat. Sc., 14, 1979, pp 1141-1 151 16. Stroeven, P., Some observations on microcracking in concrete subjected to various loading regimes. Engr. Fract. Mech., 35,415, 1990, pp 775-782 17. Reinhardt, H.W., Stroeven, P., den Uijl, J.A., Kooistra, T.R., Vrencken, J.H.A.M., Einfluuss von Schwingbreite, Belastungshohe und Frequenz auf die Schwingfestigkeit von Beton bei niedrigen Brucklastweckselzahlen. Betonw. und Fertigteiltechnik, 44, 9, 1978, pp 498503. 18. Stroeven, P., A case of compression failure in concrete due to stress release. In: “Fracture Mechanics of Concrete Structures I”, F.H. Wittmann ed. AEDIFICATIO Publ., Freiburg 1995, pp 461-470

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19. Stroeven, P., Mechanics of microcracking in concrete subjected to fatigue loading. In: “Mechanical Behaviour of Materials 3”, K.J. Miller, R.F. Smith eds. Pergamon Press, Toronto 1979, pp 141-150 20. Cornelissen, H.A.W., Hordijk, D.A., Reinhardt, H.W., Experimental determination of crack softening characteristics of normal weight and lightweight concrete, Heron, 3 1,2, 1986, pp 45-56 21. Hordijk, D.A., Local approach to fatigue of concrete. PhD Thesis, Delft University of Technology, Delft 1991 22. Stroeven, P., Quantitative image analysis of damage in concrete subjected to direct tension. In: “Quantitative Description of Materials Microstructure”, L.J. Wojnar, K. Rozniatowski, K. Kurzydlowski eds. Jagielian Univ. Press, Krak6w 1997, pp 515-522 23. Rots, J.G., Hordijk, D.A., De Borst, R., Numerical simulation of concrete fracture in ‘direct’ tension. In: “Numerical Methods in Fracture Mechanics”, A.R. Luxmore et al eds. Pineridge Press, Swansea 1987, pp 457- 471 24. Buresch, F.E., A structure sensitive Klc-value and its dependence on grain size distribution, density and microcrack formation. In: “Fracture Mechanics of Ceramics 4”, R.C. Bradt, D.P.H. Hasselman, F.F. Lange eds. Plenum Press, New York 1978, pp 835-847