Fracture of cold jointed concrete interfaces

Engineering Fracture Mechanics 74 (2007) 122–131

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Fracture of cold jointed concrete interfaces

J.M. Chandra Kishen *, P. Subba Rao

Department of Civil Engineering, Indian Institute of Science, Bangalore 560 012, India

Available online 3 March 2006

Abstract

The behavior of concrete–concrete, transversely cold jointed interface beams is experimentally investigated to determinetheir fracture properties. Simply supported beams under three-point bending with different compressive strengths of con-crete on either side of the interface are considered. It is found that the fracture energy decreases as the difference betweenthe compressive strength of the material on either side of the interface increases. In addition, three different sizes of geo-metrically similar cold jointed interface specimens are tested to study the size effect using the Bazant’s size effect model ofconcrete. It is found that the interface specimens exhibit size effect similar to intact concrete specimens and the slope of thenominal strength versus size on a logarithmic plot is �1/2, indicating the applicability of linear elastic fracture mechanics.LEFM analyses are carried out on damaged concrete beams strengthened by external application of new concrete over theparent substrate, thus producing a cold jointed interface. It is found that the elastic properties of the repair material shouldbe as close as possible to those of the parent one in order to get an efficient repair configuration.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Bi-material interface; Cold jointed interface; Fracture energy

1. Introduction

Repair and rehabilitation of concrete members is a common requirement in present day maintenance ofinfrastructures. Many concrete infrastructures have been rehabilitated in order to extend the service life orrestore the original strength of the structures. An interface appears whenever a repair material is applied toan infrastructure system after rehabilitation. Usually the interface is relatively weaker than the material oneither side of it in a repaired system. The performance of the repaired system is strongly dependent on theperformance of the interface. In a repaired system, the chances of failure by cracking along the interface ishigher because of the stress concentration and rapid change of stress levels along the interface [1]. Thus,the improvement of mechanical behavior of interface is an important issue in the rehabilitation of concretestructures as well as the selection of a repair material.

Compatibility between repair material and substrate concrete is important for prevention of cracking butreliable quantification of the required parameters is lacking [2]. Restrained contraction of repair materials with

0013-7944/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.engfracmech.2006.01.017

* Corresponding author. Tel.: +91 80 2293 3117; fax: +91 80 2360 0404.E-mail address: [email protected] (J.M. Chandra Kishen).

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J.M. Chandra Kishen, P.S. Rao / Engineering Fracture Mechanics 74 (2007) 122–131 123

the restraint being provided through the bond to the existing concrete substrate, significantly increases thecomplexity of repair projects compared to new construction. Volume changes are the causes of contractionthat often result in cracking and debonding of the repaired section.

The weak transition zone between new and old concrete controls many properties of repaired concrete. Ithas been shown [3] that the interface between new and old concrete is the weakest link in repaired concrete.Reinhardt [4] tested specimens consisting of two pieces of pre-fabricated concrete adhered together using mor-tars of different compressive strengths. He treated the joint as a discontinuity and its strength was assumed tobe due to cohesion between the joined parts. He reported that specimens adhered by mortars with higher com-pressive strengths followed LEFM solutions. Buyukozturk et al. [5,6] have studied fracture of interfacesbetween dissimilar materials by including a thin layer of aggregate sandwiches in a mortar matrix. They foundthat the experimental results were in agreement with LEFM mixed mode analysis on the aggregate mortarsandwich specimens. The fracture toughness of cement paste–aggregate interface was studied by Mitsuiet al. [7] by developing a pushout test. They used backscattered electron imaging and energy dispersion analysisof X-rays to characterize the microstructure of the interface. They reported that the interfacial properties likefracture toughness, stiffness and frictional stress are related to the microstructure of the interface. Wang andMaji [8] conducted uniaxial tension tests on mortar–limestone interface specimens to obtain the bridging stressversus crack opening displacement curve. They reported that both mechanical interlock and chemical interac-tion contribute to the interface bonding between mortar and limestone whereas only mechanical interlockingis likely responsible for the bond between mortar and rock salt. Chandra Kishen [9] conducted tests on lime-stone–concrete interface compact tension specimens to obtain the fracture parameters. The author reportedthat the difference in the behavior between intact and interface specimens lies in their post-peak load defor-mation behavior.

In most of the work reported, the interface between different materials is considered. However, there is verylittle information about the cracking and fracture process at the interfaces between new and old concrete. Thisinformation is required in order to study the cracking behavior of patch-repaired systems that are commonlyencountered in the rehabilitation of damaged concrete structures. Furthermore, in large concrete structuressuch as dams, cold joints between successive lifts are inevitable. Therefore, in this paper, fracture parametersof the interface between different concrete mixes are obtained by conducting tests on beams with concrete-to-concrete cold joints. In addition, beams of different depths are used, in order to study the size effect on thefailure stress. Furthermore, finite element analyses are carried out on concrete beams that are damaged inthe flexural zone and strengthened by external application of new concrete over the parent substrate, thus pro-ducing a cold jointed interface. The cold jointed interface in this study is considered as a zero-thickness inter-face with two different materials on either side.

2. Experimental program

In the present work, beams having a transverse cold joint between two different strengths of concrete areprepared and tested under three-point bending. Geometrically similar notched beams of three different depths,with span to depth ratio of 2.5, notch to depth ratio of 0.1 and notch width of 2 mm are used. Fig. 1 shows thegeometry of the beam. The cross-sectional dimensions and span of the beams are shown in Table 1. The thick-ness of all the beams is kept constant at 50 mm. Four different concrete mixes A, B, C and D with mix

Fig. 1. Geometrical parameters of notched interface beam.

Table 1Dimensions of beams used in the test

No. Beam designation Depth b (mm) Span s (mm) Length L (mm)

1 Small 76 190 2412 Medium 152 380 4313 Big 304 760 810

Table 2Compressive strength of different mixes

No. Mix designation Mix proportion Compressive strength (N/mm2)

1 A 1.0:1.67:3.13:0.5 282 B 1.0:1.34:2.52:0.4 393 C 1.0:1.26:2.36:0.33 514 D 1.0:1.24:2.31:0.3 58

Table 3Designation of beams

Specimen designation Description

A No interface. Intact beam of mix AAA Cold joint between mixes A and AAB Cold joint between mixes A and BAC Cold joint between mixes A and CAD Cold joint between mixes A and D

124 J.M. Chandra Kishen, P.S. Rao / Engineering Fracture Mechanics 74 (2007) 122–131

proportions and compressive strengths as shown in Table 2 are used for preparing the beams. In this table, themix proportions shown are in the order cement:fine aggregate:coarse aggregate:water cement ratio. The dif-ferent combinations of material/concrete mix on either side of the interface used for preparing the specimensare shown in Table 3 along with their designation. The specimens are prepared by casting the first half of beamwith concrete of mix A (Table 2). The surface of the first half which comes in contact with the second half wasfinished smooth with a trowel. The second half of the beam with concrete mix A, B, C or D (Table 2) is castafter two days. This creates a cold joint between the two mixes of concrete. A notch is introduced at the inter-

Fig. 2. Load versus CMOD plot of interface notched small beam AD.

Fig. 3. Load versus CMOD plot of intact notched small beam A.

Table 4Average peak load, P 0

j ðkNÞNo. Beam size A AA AB AC AD

1 Small 5.5 3.7 3.1 2.8 2.42 Medium 8.1 5.4 4.6 4.1 3.63 Big 11.4 7.6 6.4 5.9 5.1


face during the casting process itself. An intact beam (without an interface) with concrete mix A is also pre-pared. The specimens are demoulded after two days of casting the second mix and placed in water for curing.A total of 45 beams were prepared.

The beams were tested in a closed-loop servo-hydraulic testing machine under CMOD control. The CMODwas monitored using a clip gage. Typical load–CMOD plots obtained for interface small beam AD and intactsmall beam A are shown in Figs. 2 and 3, respectively. The average peak loads of the beams for various inter-faces and that of intact beams are shown in Table 4. It is seen that the maximum load carrying capacity ofinterface beams decreases when the difference in the strengths on either side of the interface increases. Further,as the size of the specimen increases the maximum load carrying capacity also increases.

3. Determination of fracture energy

The fracture energy of interface specimens is determined using the RILEM [10] method which is based onthe size effect model by Bazant et al. [11,12] for concrete. It may be mentioned here that the direct tension testis the only test which gives the true fracture energy. Unfortunately, it is difficult to perform a stable tension testwith the facilities available here. Since it is much easier to perform stable bending tests on notched specimens,the RILEM committee has chosen the three point bend test on a notched beam. The general idea of this typeof test is to measure the amount of energy which is absorbed when the specimen is broken into two halves [13].One of the requirements for the test specimen is that the relative influence of the energy absorption outside thefracture zone should be limited. Since, this requirement is satisfied for the interface specimens the samemethod is adopted here. In this method only the maximum loads P1, P2, . . . ,Pn, for specimens of various sizesb1, b2, . . . ,bn and the modulus of elasticity E are needed to determine the value of fracture energy Gf. Theweight of the specimen is taken into account by correcting the maximum loads as P 0

1; P02; and P 0

3 using

P 0j ¼ P j þ

2Sj � Lj

2Sjgmj ð1Þ

Fig. 4. Linear regression plot.


where j = 1, 2, 3, mj is mass of the specimen j, g = 9.81 m/s2, Sj and Lj are as shown in Fig. 1. By introducing

Y j ¼bjt

P 0j

!2

and X j ¼ bj ð2Þ

for j = 1, 2, 3, a linear regression

Y ¼ AX þ C ð3Þ
is plotted as shown in Fig. 4, where A is the value of the slope and C is the intercept on the Y-axis. Since thespecimens used in the tests have a ratio of S/b = 2.5, a geometric factor g(a0) is calculated with a0 = a0/b using[14],
gða0Þ ¼Sb

� �2

pa0½1:5g1ða0Þ�2 ð4Þ

where

g1ða0Þ ¼1:0� 2:5a0 þ 4:49a2

0 � 3:98a30 þ 1:33a4

0

ð1� a0Þ3=2ð5Þ

The fracture energy is determined using

Gf ¼gða0ÞEA

ð6Þ

The length of the fracture process zone for an infinitely large specimen cf is obtained using

cf ¼gða0Þg0ða0Þ

CA

� �ð7Þ

where g 0(a0) is the first derivative of g(a0).The modulus of elasticity of the interface specimens are obtained from a typical load–CMOD curve shown

in Figs. 2 and 3 using the relationship [14]

E ¼ 6Sa0g2ða0ÞCib

2tð8Þ

where Ci is the initial compliance and g2(a0) is a geometric factor calculated using

g2ða0Þ ¼ 0:76� 2:28a0 þ 3:87a20 � 2:04a3

0 þ0:66

ð1� a0Þ2ð9Þ

Table 5Computed material properties of different interfaces

Specimen designation E (GPa) Gf (N/m) Cf (mm)

A 20.91 31.92 10.70AA 12.91 23.13 0.61AB 10.65 19.89 0.66AC 9.76 18.50 0.66AD 7.54 17.77 0.66


Equivalent Young’s modulus of various interfaces and material properties of the interfaces namely fractureenergy (Gf) and size of process zone (cf) computed using the above relations are shown in Table 5. It is seenthat the fracture energy decreases as the difference in specimen strength between the mixes on either side of theinterface increases. It is well known that concrete compressive strength is directly related to its elastic moduli.Hence, when the difference in compressive strength increases, the elastic moduli mismatch increases and it canbe concluded that the interface fracture toughness decreases as the elastic moduli mismatch between the twomaterials on either side of the interface increases. This implies that greater the difference in compressivestrength or elastic moduli mismatch between the parent and repair material in patch repair systems, greateris the vulnerability to cracking for the same loading configuration. The fracture energy of interface specimendesignated AA is 27% less than that of intact specimen designated A although the mix proportion of both arethe same. This is due to the absence of aggregate interlock mechanism in an interface specimen when com-pared to the intact ones. Further, it is seen that the size of the process zone remains constant at cf = 0.66for all the mix ratio combinations considered. It may be mentioned here that Bazant and Pfeiffer [11] havereported cf = 13.5 mm for a concrete of maximum aggregate size 13 mm and cf of 1.90 mm for a mortar withmaximum aggregate size of 5 mm. Once again this is due to the fact that there is no aggregate interlock mech-anism in the case of interface specimens as observed in intact concrete or mortar specimens. Hence, the processzone, which is formed due to the cohesive forces only, remains constant having a very small magnitude forinterface between different mixes of concrete.

4. Size effect in fracture of interface

It is well known that the size effect is the most compelling reason for adopting fracture mechanics in designof concrete members. In conventional plastic limit analysis, the load capacity or the fracture criterionexpressed in terms of stress remain constant for any size of structure and for any given geometry. By contrast,failures governed by linear elastic fracture mechanics exhibit a rather strong size effect. For concrete struc-tures, the curve obtained by plotting strength versus size on log–log plot approaches a horizontal line forthe strength criterion if the structure is very small and an inclined straight line of slope �1/2 if the structureis very large [15].

In this work, interface specimens of three different sizes are considered for verifying whether size effect isseen to be similar to that observed in intact concrete specimens. Bazant’s size effect law proposed for concretemembers is used in this study for interfaces. Fig. 5 shows a plot of nominal strength versus the size (depth) ofthe interface specimen on log–log scale. In this figure, the nominal strength is computed using

rNC ¼C2

nEGf

g0ða0ÞCf þ gða0ÞD

� �1=2

ð10Þ

where D is depth of the specimen, E is the equivalent elastic modulus of the interface (Table 5), Gf the fractureenergy (Table 5), g 0(a0), Cf and g(a0) are as explained earlier. Cn is test specimen constant which is equal to 1.5times span to depth ratio of the geometrically similar beam specimens. In this figure, it is seen that the slope ofthe inclined straight lines are equal to �1/2 for all the interface specimens considered and these lines coincideswith that of LEFM. This implies that the failure of interface specimens is governed by linear elastic fracturemechanics.

0 0.5 1 1.5 2–1

–0.9

–0.8

–0.7

–0.6

–0.5

–0.4

–0.3

–0.2

–0.1

0

Log(b/b0)

Log(

σ NC/B

f t)

AAAABACADLEFM

Fig. 5. Size effect plot for the interface and intact specimens.


5. Fracture analysis of concrete–concrete patch repaired beam

Linear elastic fracture mechanics (LEFM) based numerical analysis is carried out on a simply supportedbeam that is repaired in the tension zone by a patch of concrete with different strengths. It is assumed thatthe patch repaired system fails in Mode I similar to delamination type of failure. Due to bending deforma-tions, the tensile strength at the mid-span is reached in the repair and hence a crack perpendicular to the lon-gitudinal axis develops. Horizontal interface cracks between the parent and repair concrete are assumed todevelop from the tip of the flexural crack and they extend horizontally at the interface outwards towardsthe supports, a kind of delamination or tearing that occurs predominantly in Mode I due to the curvatureof the member during bending.

The geometry together with the cross-sectional dimensions of the beam is shown in Fig. 6. The beam is sym-metrically loaded with two concentrated equal loads each having a magnitude of 1.35 N. The uniaxial com-pressive strength of the parent material is kept constant at 28 MPa while that of the repair concrete isvaried as 28 MPa, 39 MPa, 51 MPa and 58 MPa. It may be recalled that these values correspond to the com-pressive strengths of the materials used in the tests as shown in Table 2. Further, the effect of the thickness ofthe repair concrete on the critical crack length is studied by varying the thickness of the repair patch.

The finite element analysis was conducted using INterface FrActure MEchanics (INFAME code developedlocally [16]). This code has the capabilities of evaluating the stress intensity factor’s of cracks present inbetween the interface of bi-material systems. An oscillatory type of singularity is present at the bi-materialinterface crack [17] as compared to the inverse square type singularity in a homogeneous single material. This

Fig. 6. Geometry of the patch repaired configuration.

100 200 300 400 500 600 700 800 900 10000

5

10

15

20

25

30

35

40

45

Crack length (mm)

KI(M

Pa

mm

1/2 )

40 mm60 mm80 mm100 mm120 mmKIc

KIc=17.3

Fig. 7. Variation of Mode I SIF with crack length for different repair thickness.


is accounted for in the present analysis while computing the bi-material stress intensity factors. The finite ele-ment formulation is based on the traditional displacement method. The stress intensity factors are obtainedusing the contour integral method [18] based on Betti’s reciprocal work theorem. As the stress intensity factorsare extracted in terms of integral involving tractions and displacements on contour remote from the crack tip,eight noded elements are used for all the problems considered and no special elements are used. Contours aretaken along the Gaussian stations. Contours could also be taken along the element edges, but this is purposelyavoided as it will necessitate the extrapolation of stresses thereby inducing more approximation. Also closelyspaced contours can be taken if the contour paths are allowed to pass through the Gauss points.

Due to symmetry, only one half of the beam is analysed. A small initial crack is introduced at the mid-spanregion between the parent and repair concrete. The crack is propagated incrementally along the interface andthe corresponding bi-material stress intensity factors (which account for the oscillatory type of singularity) arecomputed. Fig. 7 shows the plot of Mode I stress intensity factor versus crack length for different thickness ofrepair material for the case of parent–repair combination AA. The critical crack lengths computed for differ-ent repair concrete strengths and for different thicknesses are shown in Table 6. The critical crack length isobtained using the LEFM criterion when the Mode I stress intensity factor reaches the respective criticalvalue. The critical values of the Mode I stress intensity factor shown in Table 6 for different interface combi-nations are obtained from the computed Gf and E values listed in Table 5. It is seen that the critical crack

Table 6Critical Mode I SIF and critical crack lengths for different repair combinations

Repair configuration KIc ðMPaffiffiffiffiffiffiffiffimmp

Þ Critical crack length for different thickness of repair patch (mm)

40 60 80 100 120

AA 17.3 900 850 750 700 700AB 14.6 800 750 700 650 650AC 13.5 725 700 650 600 600AD 11.6 675 650 600 575 550


length decreases as the difference in compressive strengths of the parent and the repair material increases. Thisimplies that for an effective repair configuration the difference in compressive strength of the parent and repairmaterial should be close to each other assuming that failure of the patch repair system takes place by crackpropagation along the interface. Further, from Table 6 it is seen that as the thickness of the repair materialincreases, the critical crack length decreases. Although this decrease is not quite considerable, it indicates thatthe thickness of the repair patch should be kept as small as possible to avoid brittle crack propagation at theinterface at lower loads.

6. Conclusions

In this work, beams having cold jointed interface between concrete–concrete with different mixes on eitherside are subjected to three-point bending test in order to obtain the fracture parameters such as the fractureenergy and the size of the process zone. In addition, the size effect in these specimens is studied by testing geo-metrically similar specimens of three different sizes. Furthermore, numerical analysis is carried out using linearelastic fracture mechanics concepts to study the efficiency of a patch repaired system. The following conclu-sions are made from this study:

• The fracture energy of interface decreases as the difference in the compressive strengths of the material oneither side of the interface increases. This implies that the compressive strength of a patch-repaired concreteshould not be very much different from that of the parent concrete in patch repair systems.

• The size of the process zone formed near an interface crack is found to be constant for all combination ofconcrete mixes on either side of the interface. This implies that the process zone size depends strongly on theaggregate interlock mechanism as observed in the case of intact concrete specimens. This mechanism isabsent for interface specimens.

• In the case of interface specimens, the slope of the nominal strength versus size on a logarithmic plot is�1/2,indicating that the failure stress is governed by linear elastic fracture mechanics concepts.

• The critical crack length gets smaller as the difference between the compressive strengths of the parent andrepair materials gets larger. This implies that for an efficient repair configuration the difference in compres-sive strength of the parent and repair material should be close to each other.

• The thickness of the repair patch should be kept as small as possible to avoid brittle crack propagation atthe interface at lower loads.

References

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[3] Li G, Xie H, Xiong G. Transition zone studies of new-to-old concrete with different binders. Cem Concr Compos 2001;23:381–7.[4] Reinhardt HW. Length influence on bond strength in composites precast concrete slabs. Int J Cem Compos Light Weight Concr 1982;

4:139–43.[5] Buyukozturk O, Lee K. Interfacial fracture mechanics of concrete composites. In: Bazant ZP, editor. Proceedings of first international

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[13] Hillerborg A. The theoretical basis of a method to determine the fracture energy GF of concrete. RILEM Mater Struct 1985;18(106):291–6.

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[15] Bazant Z, Planas J. Fracture and size effect in concrete and other quasibrittle materials. CRC Press; 1997.[16] Darunkumar Singh K. Crack propagation at bimaterial interface: application to safety of gravity dams. M.Sc. (Engg.) thesis,

Department of Civil Engineering, Indian Institute of Science, Bangalore, India, Department of Civil Engineering, 1999.[17] Rice J, Sih G. Plane problems of cracks in dissimilar media. J Appl Mech 1965:418–23.[18] Hong CC, Stern M. The computation of stress intensity factors in dissimilar materials. J Elast 1978;8(1):21–34.

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Fracture of cold jointed concrete interfaces