Influence of different sizes of concrete and roller compacted concrete on double-K fracture parameters

Affected by physical properties of various components, characteristics and stress states of junction surface and other multiple factors, concrete, as a kind of multi-phase composite material, has complicated failure mechanism, thus making its fracture mechanism research difficult. But concrete has been widely used in engineering construction, so research on concrete fracture theory is of important realistic significance and construction value. This study discusses influence rule of specimen size and crack-depth ratio (α0/h) on doubleK fracture parameters (initial fracture toughness ini IC K and unstable fracture toughness un IC K ) and its size effects by using fracture test. Different sizes of concretes and roller compacted concrete (RCC) specimens are adopted to explore influence of specimen size on concrete double-K fracture parameters. Results reveal that initial fracture toughness ini IC K and unstable fracture toughness un IC K increase as specimen size enlarges, showing a size effect; besides, subcritical crack extends with the increase of specimen size. With regard to specimens with different crack-depth ratios, its unstable fracture toughness un IC K is unrelated to initial crack-depth ratio when crack-depth ratio is more than or equal to 0.4, while initial fracture toughness ini IC K is correlated with initial crack-depth ratio, which indicate that double-K fracture parameters can be considered as material constants describing concrete initial fracture, stable expansion and whole process of stability failure.


INTRODUCTION
o date, fracture mechanics is applied in concrete structure from three aspects [1]: first is research on fracture mechanism of concrete; second is decision of endanger degree of some serious cracks in concrete structure, for example, stability analysis of crack in pier, upstream face crack in massive-head dam and pressure vessel crack of prestressed concrete (PC) in atomic power station; third is improvement of design method of concrete structure, for T instance, decision of stability of various thorough cracks in concrete pouring blocks and calculation of cracking load of reinforced concrete (RC) in diagonal direction, etc.People are expected to improve design methods of gravity dam and arch dam using fracture mechanics [2].Two-parameter model considers actual crack in combination with micro-crack zone as an effective crack, then obtains results using theory of linear elastic fracture mechanics and combines it with numerical computation method.Its essence lies in using valid crack tip opening displacement (CTOD) to reach critical valid CTOD, i.e., fracture criterion.Xu Shilang [3], a scholar from China, put forward a simple and applicable fracture criterion in 1999, namely, double-K fracture criterion.This criterion, belonging to the first type, not only corrects linear elastic fracture mechanics model based on a complete theory, but also decides its fracture parameters with the help of simple test methods, which is expected to be popularized and applied in practical engineering.Two fracture parameters are introduced into this criterion, initial fracture toughness ini IC K and unstable fracture toughness un IC K .Test indicates that those two parameters without size effect under a certain size, as fracture parameters, can be well applied in the analysis of concrete structure crack extension, and have drawn much attention [4][5][6][7].A relevant trial [8] reveals that maximum seam strain is 10 times of average value of ordinary bending ultimate strain, which is exactly a ratio of theoretical strength and breaking stress of a point of concrete material.This thesis aims to explore characteristics of double-K fracture parameters (initial fracture toughness ini IC K and unstable fracture toughness un IC K ) of concrete using data obtained from test.

Material Selection and Mix Proportion
aterials include tap water for life, 32.5 ordinary Portland cement, fly ash (level II), natural medium sand with particle size of over 5mm, macadam with maximum particle size of 20 mm (level I), high efficiency slushing agent suitable for mass concrete, and mix proportion is shown in Tab. 1. Wedge splitting specimen [14,15] is adopted in this test (Fig. 1) and Tab. 2 displays specimen parameters.All specimens are divided into two categories containing 12 kinds of working conditions, the quantity of specimen in each working condition is presented in Tab. 2 and testing devices are in Fig. 2.

Testing Devices
Testing devices are shown in Fig. 2.

Clip-on extensometer
Wedge holder

Load sensor
Top board

Test Results
Specimen over 150×150×150 mm 3 is calculated with following formula, and specimen (150×l50×l50 mm 3 ) uses regular computing method [9][10][11].Unilateral opening specimen is affected by axial tension, and stress intensity factor (SIF) can be calculated with formula below: where, where, 1/ 2 1/ 2 Overlapping formula ( 1) and ( 2), SIF expression of crack tip in any load time with wedge splitting geometry is obtained: As some problems may exist in part of specimen making and maintenance, here, the quantity of several effective specimens with good surface, basically complete trial curve, small deviation and calculative in double-K fracture parameter is listed in Tab. 3. Arithmetic mean value of initial fracture of 4~6 specimens from each group is taken as trial results.When the difference between single value and average value is over 15% of the average value, this value is excluded, and mean value of the rest of values is considered as trial result.
Trial result is:

INFLUENCE OF CRACK-DEPTH RATIO ON CONCRETE FRACTURE STIFFNESS
edge splitting specimens (crack-depth ratio: 0.3:0.4:0.5:0.6 and size: 150 mm × 150 mm × 150 mm) are selected for studying influence of a/h on double-K fracture parameter and crack mouth opening displacement (CMODc) and influence rule of crack-depth ratio in concrete fracture process and fracture strength.

Test Design
Tap water, 32.5 ordinary Portland cement, fly ash (level II), natural medium sand with particle size of over 5mm, macadam with maximum particle size of 20 mm (level I) and high efficiency slushing agent suitable for mass concrete are used in the test and their mix proportions are shown in Tab. 4.

Phenomenological Analysis of Wedge Splitting Test
This test is carried out on a 200kN compression-testing machine and adopts formula to calculate valid crack growth quantity.From cracks in damaged trial (Figs. 3, 4), effective subcritical growth quantity can be obviously found in figures, and direction of crack growth is not smooth, which is mainly caused by reasons of concrete itself, as well as various construction aggregates.Cracks will bypass and keep on growing when encountering construction aggregates with large particle size.K based on initial crack-depth ratio not only has size effect, but also changes with the changes of initial crack-depth ratio.That indicates that subcritical growth quantity of wedge splitting specimen changes with size, related to initial crack-depth ratio as well, which is different from three-point bending beam.Thus, it is obvious that small specimen has to take stable growth of crack into consideration.Flexibility coefficient applied in calculating valid subcritical crack growth length ( c a ) with double-K fracture criterion is diverse, thereby leading to different c a .After obtaining c a , fracture toughness S IC K and CMODc can be figured out, so valid subcritical crack growth length ( c a ) is believed to be an important parameter [12][13].In two-parameter model, because unloading point in test is hard to be controlled in a specified point, valid subcritical crack growth length ( c a ) obtained by computer is biased compared with theoretical value.However, double-K fracture criterion is with no need for unloading process and controlling unloading point in test, simply works out valid subcritical crack growth length ( c a ) with P max and its corresponding CMODc, and the test results are relatively close to theoretical value.Ordinary concrete has the same change rule of unstable fracture toughness with RCC.Crack-depth ratio has an effect on the fracture toughness of ordinary concrete and RCC, but there are also differences.The fracture toughness of ordinary concrete decreases as crack-depth ratio increases, and this principle is basically suitable for CRR.

DISCUSSION
t is summarized from analysis of fracture test results of RCC and ordinary concrete wedge-splitting specimens that double-K fracture criterion may have some differences although it is simple, practical and without human distractions.Concrete fracture toughness has size effect, that is to say, concrete fracture toughness increases as size of specimen increases; besides, crack-depth ratio affects concrete fracture toughness to some extent, but the influences are not all consistent.Change rules of unstable fracture toughness of ordinary concrete and RCC are basically the same, and crack-depth ratio plays a role in fracture toughness of ordinary concrete and RCC, but not identical.The rule to ordinary concrete is that concrete fracture toughness is reduced with the increase of crack-depth ratio, and the rule to RCC partially conforms to ordinary concrete rule.In addition, crack-depth ratio of specimen also has a great influence on fracture toughness, and varies non-uniformly; when 0 / 0.4 a h  , S IC K increases as 0 / a h rises; it decreases as 0 / a h rises when 0 / 0.4 a h  , and reaches maximum when 0 / 0.4 a h  , i.e., unstable value.

Figure 2 :
Figure 2: Acquisition of test data with wedge splitting method

Table 1 :
Mix proportion of roller compacted concrete (RCC) and common concrete.

Table 2 :
Working conditions of specimen.
Unilateral opening specimen is affected by bending moments only, and SIF is:

Table 3 :
Trial results of various working conditions.

Table 4 :
Mix proportions of RCC and ordinary concrete.Wedge splitting specimen is applied in the trial, containing two categories (12 kinds of working conditions), and quantity of specimen in each working condition is shown in Tab. 5.

Table 5 :
Working conditions of specimen.

W
Analysis of Calculation ResultsP-MOD curve character parameters of wedge splitting specimen are figured out based on test results (Tab.6).

Table 6 :
Basic test results.Tab.7 makes a list of unstable fracture toughness calculated by initial crack-depth ratio and maximum load Pmax,