Influence of chlorides on the fracture toughness and fracture resistance under the mixed mode I/II of high-performance concrete

Influence of chlorides on the fracture toughness and fracture resistance under the mixed mode I/II of high-performance concrete MIARKA, P.; SEITL, S.; HORŇÁKOVÁ, M.; LEHNER, P.; KONEČNÝ, P.; SUCHARDA, O.; BÍLEK, V. Theoretical and Applied Fracture Mechanics 2020, vol. 110, December 2020, pp. 1−15 ISSN: 0167-8442 DOI: https://doi.org/10.1016/j.tafmec.2020.102812 Accepted manuscript © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ dspace.vutbr.cz 1 Influence of Chlorides on the Fracture Toughness and Fracture Resistance Under the Mixed Mode I/II of High-Performance Concrete Authors Name and Affiliations Petr Miarkaa,b, Stanislav Seitla,b, c, Petr Lehnerc, c, c, Vlastimil Bílekc. a Institute of Physics of Materials, Czech bBrno University of Technology, Faculty of Civil Republic cV B Technical University of Ostrava, Faculty of Civil Engineering, Ludvíka Pod 1875/17, 708 00 Ostrava-Poruba, Czech Republic Corresponding Author Petr Miarka ([email protected]) Abstract This experimental study shows the conjunction of fracture mechanics with the ability of highperformance concrete (HPC) to resist an aggressive chloride environment. Moreover, the influence of a chloride-contaminated environment on the fracture toughness and fracture resistance under the mixed mode I/II is presented. The experimental study was performed considering different aggressivity levels of the environment, water, and fully saturated sodium chloride solution (NaCl-). The experimental tests were performed on a Brazilian disc specimens to test the indirect tensile strength ft and on a Brazilian disc with a central notch to evaluate the fracture toughness KIC and the fracture resistance under the mixed mode I/II. The mixed mode I/II fracture resistance was evaluated by the generalised maximum tangential stress (GMTS) criterion . The level of chloride contamination present and its boundary in the concrete was estimated by the colorimetric method using silver nitrate (AgNO3). Keywords: Brazilian disc, HPC, Mixed mode I/II, Fracture toughness, Chloride ingress, Diffusion. Abbreviations/nomenclature 2D two-dimensional BD Brazilian disc BDCN Brazilian disc with a central notch FEM finite element analysis FMP fracture mechanical properties GMTS generalised maximum tangential stress HO higher order terms HPC high performance concrete HSC high-strength concrete LEFM linear elastic fracture mechanics MTS maximum tangential stress RCPT rapid chloride penetration test SCM supplementary cementitious materials SIF stress intensity factor WE s expansion notch inclination angle (°) 2 r, polar coordinates tangential stress ahead of crack tip (MPa) ,C critical tangential stress ahead of crack tip (MPa) t tensile stress (MPa) 0 crack initiation direction (°) a initial notch length (mm) An, Bm -) B Beff,Cl effective based on chloride penetration depth (mm) Beff,KIC effective based on fracture toughness(mm) E known shape functions for mode I (-) ft indirect tensile strength (MPa) indirect tensile strength for chloride saturated specimen (MPa) Gf fracture energy (N/mm) hClchloride penetration depth (mm) KI, KII stress intensity factor for mode I and mode II (MPam1/2) KIC fracture toughness for mode I (MPam1/2) fracture toughness for mode I for chloride saturated specimen (MPam1/2) P load (kN) R rC critical distance (mm) T-stress in crack plane T-stress (MPa) 1. Introduction The last two decades have witnessed a considerable progress towards the design, construction and maintenance of concrete structures which concerned both economic and environmental impacts of these structures on the environment to be built in. These two primary demands can be met by the development and eventual use of a material which exhibits higher mechanical performance and simultaneously has a lower environmental impact. The use of high-strength concrete (HSC) [1] allows for a material reduction in the cross-sectional dimensions, while high-performance concrete (HPC) [2, 3] exhibits higher long-term performance and durability of the structure. The structures (e.g. bridges or beams) to be built from such materials can benefit from a greater span length, a shallow beam cross-section and an extended service lifetime. The modern HPC mixtures used in the construction consume less natural resources, i.e. raw materials for cement production, aggregates, water, and their mixture typically contains less cement (lower CO2 emission) [4, 5], while the mechanical and/or durability performance is enhanced. This results in a reduction of the production cost (subtle structural element) and CO2 emissions (lower cement content). This reduction of natural resources is done by composing an HPC mixture which contains mineral admixtures, i.e. supplementary cementitious materials (SCM) like silica fume [6], ground granulated blast furnace slag [7], fly ash, or it can include natural pozzolans, e.g. pumice [8], metakaolin or zeolite [9] etc. 3 On the other hand, subtle structures made of the new materials drew attention to a comprehensive structural analysis, which resulted in the use of advanced material models as implemented in the finite element method (FEM) software. This overcame a traditional, sometimes empirical design methods mentioned in the standards [10, 11] or in recommendations [12], due to the lack of knowledge of the Subsequently, these advanced material models often use input parameters directly related to the crack initiation and crack propagation usually referred to as fracture mechanical parameters (FMP). These FMPs, e.g. fracture toughness KIC and fracture energy Gf, are usually identified during a complex material testing. A verification of such a set of input data is usually conducted with the inverse analysis [13], with an example of such application to the fracture energy to be found in [14]. The most problematic concrete property, which attracts the most attention, is its response to the tensile load as the tensile strength is approximately ten times lower than the compressive strength. Thus, the mode I - tensile crack opening and propagation is mostly studied, whereas the mode II shear cracks are often omitted in the aim of a given research. For instance, even a simply supported beam with a distributed load exhibits a combination of tensile and shear loading modes (See Figure 1(a)). If the to this distributed load is plotted in principal stresses, one can find the location of the highest tensile stress (mid span) and the highest shear stress (above the support), which produce two main failure mechanisms of the concrete structure. However, there is a location with a combination of tensile and shear stress which cause the mixed mode I/II crack initiation due to transverse tension. These mixed mode I/II loading conditions and crack initiation are often neglected in the research studies. On the other hand, in practical design, this weakest material point is being supressed by using shear reinforcement stirrups [10] (See Figure 1(b)). (a) (b) Figure 1: Principal stress 1 and 2 trajectories on the simply supported beam with a distributed load (a) and designed steel reinforcement (b). Despite the improved strength and performance, the HPC concrete is prone to forming microcracks, which propagate and increase in size throughout the cover layer. This leads to a significant durability issue as the steel reinforcement is exposed to weather conditions [15-20]. Moreover, these weather conditions are often highly aggressive (de-icing salts or a marine environment) and assist to accelerate the steel reinforcement corrosion which results in the premature degradation [21, 22]. Typically, an aggressive environment exhibits the presence of chloride ions [22-24]. A large number of studies from multiple research fields have been devoted to this phenomenon, e.g. modelling of damage induced by chloride penetration [25-29], long-term concrete penetration resistance [30-33], or evaluation of the chloride penetration depth based on colorimetric methods [34-37]. Consequently, these studies resulted in the formulation of standards and proposed the methodology of assessing the level of chloride contamination in a concrete structure, e.g. Nordtest [38, 39], American Association of State and Highway Transportation [40, 41] or ASTM standard [42]. The above-mentioned research objectives and standards focus on the effect of chlorides with respect to the level of resistance. Moreover, knowing the relationship between the level of fracture and the rate of chloride penetration can significantly improve the accuracy and reliability of life estimation models [43]. Also, other studies investigate the dependence of crack growth with respect to the ability 4 of concrete to resist chloride ingress [44, 45]. However, the research of the actual effect of soluble chlorides on the crack development is unique, especially considering HPC concrete mixtures. Therefore, the relationship between the FMPs of the cement-based composite/concrete and its resistance to chloride penetration is a very interesting problem to investigate. The aim of this pilot experimental study is to investigate the influence of the aggressive chloride environment on the fracture toughness KIC and fracture resistance under the mixed mode I/II loading conditions of HPC mixture. For this, a series of experimental tests, including chloride-free and chloridesaturated specimens, was performed on the concrete Brazilian disc (BD) and on the concrete Brazilian disc with central notch (BDCN) samples. 2. Theoretical Background Firstly, the Williams s expansion for the description of stress fields in the cracked body under the mixed mode I/II conditions is presented. Then we describe the used fracture criterion for the mixed mode I/II fracture resistance. Afterwards, the Brazilian disc specimen with central notch geometry is introduced together with analytical formulas used for the stress intensity factor and for the T-stress calculation. Finally, we briefly discuss the critical distance and various options used in obtaining its proper value. 2.1 Stress Fields and Crack Initiation Criteria This experimental study is based on the linear elastic fracture mechanics (LEFM) concept. The LEFM uses the WE) [46] for the description of the stress fields in a close vicinity of the crack tip of a homogeneous isotropic cracked material. This expansion is an infinite power series, which describes the stress field as follows: (1) where i,j is the stress tensor, r and are the polar coordinates, n and m is the order of term in the WE and the coefficients An correspond to the mode I and coefficients Bn correspond to mode II. The and are known geometry functions for mode I and for mode II in polar coordinates. The coefficient of the first singular term for n = 1, i.e. A1, is related to the stress intensity factor (SIF) for mode I, and the second coefficient A2 corresponds to the distance-independent term called T-stress. Similarly, for mode II, the first singular term for m = 1, i.e. B1, is related to SIF for mode II. These engineering quantities can be expressed as follows: . (2) Usually, the mixed mode I/II fracture analysis is done by employing various fracture criteria. Traditional criteria are, for example, the maximum tangential stress (MTS) criterion [47-49] and the strain energy density (SED) criterion [50, 51], or the recently postulated advanced fracture criteria, e.g. the generalized strain energy density (GSED) criterion [52, 53], the averaged strain energy density (ASED) criterion [54-57], the extended maximum tangential strain (EMTSN) criterion [58-61], and the generalized maximum tangential stress (GMTS) criterion [62-64]. The traditional criteria for the mixed mode I/II fracture analysis are only using SIFs for mode I and mode II, while the advanced criteria use SIFs, T-stress (or more WE terms) and the critical distance rC. In order to evaluate the fracture resistance under the mixed mode I/II, the GMTS criterion will be used. The GMTS criterion was selected over the other criteria as the tangential stress steadily opens the crack in mode I (in tension) even when the pure mode II is present (See Figure 2). Another reason is that the calculation and evaluation is relatively simple as the inputs are values of the SIFs, T-stress, fracture toughness KIC and critical distance rC, which are determined from the analytical formulas. In addition to this, it provides reliable results on the concrete material, see [65-68]. 5 The tangential stress from Eq. (1) is expressed by using the first two engineering terms presented in Eq. (2): (3) where HO are the higher order terms, and it is assumed that they can be neglected near the crack tip. According to the GMTS criterion for mixed mode I/II, the brittle fracture occurs radially from the crack in the direction of the maximum tangential stress 0. The crack initiates along the 0 and critical distance rC, when the maximum tangential stress reaches its critical value ,C. The brittle fracture occurs when KI = KIC, KII = 0. and 0 = 0°; this assumption simplifies Eq. (3) to: where KIC is the fracture toughness for mode I. The crack initiation direction 0 can be obtained from the conditions when: and (5) This leads to a modification of Eq. (3) to the following form: (6) Eq. (6) shows that the angle 0 of maximum tangential stress for any combination of modes I and II depends on KI, KII, T and rC. The angle 0 determined form Eq. (6) is then used to predict the beginning of the mixed mode I/II fracture. The critical tangential stress expressed as ,c in Eq. (4) can be drawn with another stress tensor component. The critical tangential stress ,C, together with critical distance rC and the onset of fracture 0 (crack initiation direction), are shown in Figure 2. Figure 2: Stress tensor in polar coordinates with a critical distance rC, onset of fracture 0 and critical tangential stress ,C. Such Eq. (7) can be used for the calculation of fracture initiation for pure mode I, pure mode II and mixed mode I/II. 2.2 Stress Intensity Factor for Mixed Mode I/II and T-stress A BDCN specimen was used in this study due to its simple specimen preparation, straightforward experimental set-up, and due to possible mixed mode I/II loading. The mixed mode I/II loading conditions can be studied on a semi-circular bend (SCB) specimen [69-73] or on the edge notched disc bend (ENDB) specimen [74], which can be used to test the mixed mode I/III load conditions [75, 76]. The mixed mode I/II in the BDCN geometry is produced by inclining the initial notch by an angle against the loading position (see Figure 3). The BDCN geometry allows for testing the mode I ( = 0°), mode II ( = 25.25° for a/R ratio of 0.4), and mixed mode I/II (0°; 25.2) . Another (4) (7) 6 advantage of this specimen is that it can be used on both the existing structure to study the FMPs prior to renovation, or on the new material as it is prepared in a demanded thickness from cylindrical samples. Figure 3: Brazilian disc test with central notch geometry dimensions and the loading conditions. The SIF for the BDCN geometry for mode I and mode II are analytically calculated by using Eqs. (8)and (9) according to the handbook by Tada & Paris [77]. (8) (9) where P is the applied compressive load, R is the specimen s radius, a is the crack length, is the notch inclination angle, B is t thickness, and YI and YII are the shape function for mode I and mode II, respectively. The values of the analytical shape functions for mode I, mode II, and the T-stress can be found in the literature, e.g Ayatollahi Aliha [63] or [78], Seitl [66], and Fett [79]. The experimental verification of such functions by the digital image correlation (DIC) method was done in [80] and [81]. The values used in this study, i.e. for relative notch length of a/R of 0.4, are shown in Figure 4. (a) (b) Figure 4: Geometry function for mode I and II - (a) and (b) - T-stress values for the BDCN geometry. Fracture resistance for both modes is expressed by the ratios KI/KIC and KII/KIC. To obtain these ratios from Eq. (7), the whole expression has to be divided by KI, KII respectively. Then the fracture resistance for mode I can be expressed as: 7 , (10) and for mode II: (11) Both Eqs. (10) and (11) show noticeable dependency of the whole GMTS criterion on the second term of the WE and on the critical distance rC. Thus, the estimation of the proper value of the critical distance rC in this case is crucial and the literature offers various options for the calculation of rC. The basic method to obtain critical distance rC is to consider various boundary conditions, i.e. plane stress or plane strain boundary condition [32]. Assuming these boundary conditions, the critical distance rC can be calculated by Eqs. (12) and (13). plane stress, (12) plane strain. (13) where KIC is the fracture toughness for mode I, and t is the tensile strength. It is assumede that the plane strain boundary conditions are present in the middle of the specimen, while the plane stresses are present on its surface. The literature a offers calculation of the critical distance by using the third term of the WE A3 [82-84], which provides the size-independent results. Nonetheless, the prediction by the GMTS criterion showed reliable results by using the critical distance calculated from Eqs. (12) and (13); see [66]. 3. Experimental Details Firstly, the studied material is introduced together with the measured material properties according to European standards. Then, the dimensions used in the evaluation of the indirect tensile test and for mixed mode I/II fracture resistance are presented. Afterwards, the technique of measuring the chloride penetration depth is described. Lastly, the experimental set-up for the BD and BDCN specimens are introduced. 3.1 Material In this experimental study, a HPC was designed in close cooperation with a concrete precast plant, in order to improve mechanical performance of C 50/60 as presented in [66], and to reduce the production costs. For this, a binder, Portland cement CEM I 42.5 R, was used together with one mineral admixture. Moreover, the binder consisted of 88 % of CEM I 42.5 R and 12 % ofmetakaolin Metaver. The water/binder ratio was 0.25. The aggregates were composed of natural 0/4 mm sand and crushed highquality granite with a size of 4/8 mm and 8/16 mm (minimum/maximum aggregate size of used sieve). A polycarboxylate-based superplasticizer was selected based on its compatibility with cement, and to reach good workability of the mixture. The concrete was mixed in a 1 m3 volume, and poured immediately into moulds. The material composition per m3 is showed in Table 1. Table 1: Material composition of studied High-performance concrete per m3. CEM I 42.5R Metakaolin Metaver Superplasticizer Water Sand 0/4 Crushed aggregates 4/8 Crushed aggregates 8/16 575 80 20 165 680 200 810 The prepared samples were carefully covered with a PE-foil, which helped to prevent excessive moisture exchange with the environment, as the specimens were stored outside of the laboratory environment (precast concrete plant), with a - 25oC for a period of 28 days. The measured mechanical properties of the studied HPC presented in Table 2 below were in accordance with the European standards at the 28 days age. Table 2: Mechanical properties of studied HPC mixture. 8 Compressive strength at 1 day fc,cube [MPa] 30.2 Compressive strength at 28 days fc,cube [MPa] 102.0 Indirect tensile strength - cube fct [MPa] 5.8 Young's modulus - cube Ecube [GPa] 42.1 Young's modulus - cylinder Ecyl [GPa] 39.5 The cubes were tested in the age of 1 and 28 days to see the strength development over time. As it can be seen from Table 2, the intent to design the mixture with higher mechanical performance compared to the C 50/60 concrete was fully met. 3.2 Geometry In this experimental study, the BD specimens were used in order to obtain the strength ft and the BDCN specimens were tested to get the s under the mixed mode I/II loading conditions. Such discs were manufactured from standardized cylinders with a diameter D = 150 mm and thickness B of approximately 28 mm. Afterwards, the discs were stored in two different environments with different levels of aggressivity conditions. The first set of discs was stored in a chloride-free environment, i.e. in a water tank placed in laboratory-controlled conditions. The other samples/disc were stored in a chloride-contaminated environment, i.e. in a fully saturated sodium chloride NaClsolution. The measured dimensions of the BD specimens were diameter D and thickness B. The measured discs dimensions are presented in Table 3 for both studied cases of different environmental conditions. Table 3: Dimension of Brazilian discs specimens used in the indirect tensile strength ft test for both studied environmental conditions. D [mm] B [mm] Clfree samples HPC_50_K16 149.26 27.78 HPC_51_K16 149.27 27.88 HPC_52_K16 149.22 27.75 HPC_53_K16 149.29 27.89 HPC_54_K16 149.15 28.04 Clsaturated samples HPC_45_K16_CL 149.28 28.03 HPC_46_K16_CL 149.18 27.64 HPC_48_K16_CL 149.15 28.16 HPC_49_K16_CL 149.21 29.68 The initial notches of the BDCN specimens were made by a water jet cutter in order to provide a straightthrough notch; the literature provides studies with a chevron notch type on BDCN [85]. The notch length 2a was 60 mm, which gives a relative notch length ratio a/R of 0.4 with thickness of approximately of 2 mm. The specimens prepared in such process have been used in the measurement of the FMPs of the studied material. To have complete information about the mixed mode I/II loading conditions and the related fracture process, the BDCN specimens were tested for pure mode I ( = 0°), for pure mode II ( = 25.2°), and for mixed mode I/II ( = < 5°; 10°; 15°; 20°>). Three specimens were tested for each notch inclination angle in order to cover the , which in total makes 18 samples for both studied cases of the various levels of environment aggressivity. The measured dimensions of each tested specimen are presented in Table 4. Table 4: Measured dimensions of the BDCN specimens. [°] R [mm] a [mm] B [mm] Clfree samples HPC_30_K16 0.00 74.57 30.03 28.16 HPC_31_K16 0.00 74.62 30.01 29.46 HPC_32_K16 0.00 74.67 30.01 27.77 HPC_40_K16 5.00 74.57 29.79 28.19 HPC_41_K16 5.00 74.42 29.98 27.75 HPC_42_K16 5.00 74.66 29.62 27.50 HPC_14_K16 10.00 74.66 29.98 27.65 HPC_15_K16 10.00 74.65 29.87 27.66 15 Figure 10: Comparison of measured fracture loads PC under various mixed mode I/II load conditions for chloride-free and chloride-saturated discs. This difference in the measured fracture forces PC is more noticeable for the cases where mode I load prevails. For the case of pure mode II, i.e. for the case of = 25°, where the measured fracture forces PC show a similar value for both investigated cases of Clenvironment. In Figure 11(a) the recorded forces P over the normalized time ti/tmax (time over the total duration of the test), and in Figure 11(b) the recorded forces P over the vertical deformation are presented to illustrate the experimental measurement in more detail. Except for the difference in the measured fracture force Pc, another observation can be made, which is related to the stiffness and total deformation. This confirms the observation made in Figure 10, as, with the increasing mode II load, the fracture force increases in size, while the maximum deformation has a similar value of 0.2 mm. Similarly, a difference in the (a) (b) Figure 11: Comparison of the measured P-t diagram and Pdiagrams for the various notch inclination angles . Similarly to the values of indirect tensile strength ft, it is necessary to distinguish between the values of fracture toughness KIC measured for the different Clenvironments. Thus, KIC is used for the values of fracture toughness experimentally measured on the Cl--free samples, and is used for the values of fracture toughness experimentally measured on the specimens saturated with Cl-. Both values KIC and can be calculated as an average value for the cases with the angle = 0° as shown in Table 7 and Table 8. The measured values of the fracture toughness of the HPC concrete mixture exposed to different environments are KIC of 0.926 MPam1/2 and of 0.788 MPam1/2, respectively. This difference seems 16 to be linked to the assumption made in Figure 7(b), as the Cl-ions penetrate the disc s body not only from both the top and the bottom surface, as in the case of the samples used for the indirect tensile strength measurement, but also Clions can penetrate from the notch, which creates another surface exposed to the Clenvironment. This leads to a lower value of fracture toughness , as the crack initiates from the notch end. A comparison of the calculated SIF values for various notch inclination angles with marked values of evaluated KIC for both cases are presented in Figure 12. (a) (b) Figure 12: Comparison of the evaluated SIF values for various environmental conditions with highlighted values of fracture toughness KIC and , respectively - (a) Cl--free samples and (b) Cl--saturated samples. The experimental results presented in Figure 12(b) for the case of the Cl--saturated samples show overall lower values of KI and KII, as they are directly related to the measured fracture forces PC shown in Figure 10. Putting both values of fracture toughness KIC and and both values of indirect tensile strength ft and into Eqs. (12) and (13), a critical distance rC can be calculated. The calculated values of critical distance rC for both studied cases of environment aggressivity are presented in Table 9. Table 9: Calculated values of critical distance rC for both studied cases of Cl--free and Cl--saturated environment aggressivity, respectively. Fracture toughness [MPam 1/2 ] rC [mm] - plane strain rC [mm] - plane stress KIC = 0.926 1.344 4.033 = 0.788 0.972 2.917 Similar values of critical distance rC of 1.5 mm for fine grain cement mortar with a similar value of fracture toughness KIC [90] and of 1.45 mm for sandstone with a similar value of tensile strength ft [91] can be found in the literature. The calculated critical distances for the case of the Cl--saturated specimens show again a lower value by approx. 30%, which results in an earlier crack initiation and a lower value of fracture toughness KIC. According to the GMTS criterion, the onset of a fracture begins when the critical value of tangential stress ,C is reached. In the case of the Cl--saturated samples, the value of ,C is reached in the closer distance from the crack tip, which results in an earlier failure. This assumption is again supported by the measured values of the fracture loads PC and fracture toughness KIC, for which the Cl--saturated discs show an overall lower value of fracture load PC, while keeping a B of approx. 28 mm. The reduction of the critical distance rC and reducing the load-bearing capacity can be caused by various reasons, e.g. chloride binding to the concrete matrix and crystallization in pores. However, in this case, the notch preparation by the water jet could also disrupt the concrete structure (bound between the aggregate and cement paste) with microcracks. These microcracks act as a stress concentrator and, more importantly, they created another free surface, where the chloride ions could penetrate the concrete body. 17 In addition to this, chlorides can transform themselves into Friedel , which extends in its volume and damages the pores. Recently, it has been showed that metakaolin in Portland cement blends increases the formation [92], which is used in the studied HPC mixture. Using the calculated critical distances rC from Table 9 in the Eq. (6), one can derive the fracture resistance curves for the mixed mode I/II loading conditions. Please note that if the critical distance rC is equal to 0, the Eq. (6) simplifies itself to the traditional MTS criterion. The evaluated fracture resistance curves of the BDCN geometry for both studied cases of various environment aggressivity levels are showed in Figure 13. (a) (b) Figure 13: Comparison of evaluated fracture resistance curve under the mixed mode I/II loading conditions - (a) chloride Cl- -free samples and (b) chloride Cl--saturated samples. From the fracture resistance curves presented in Figure 13,a similar observation to the previous statements can be made, i.e. the chloride saturated BDCN specimens show a better fracture resistance to the mixed mode I/II conditions. The GMTS fracture criterion predicts the fracture resistance with a relatively good agreement for both cases of the Clenvironment. However, for the cases of pure mode II, the fracture resistance shows a relatively high dispersion for the cases of Cl--saturated BDCN specimens. A visible discrepancy between the experimental results and the prediction of fracture criteria (MTS and GMTS) was evaluated by using the root mean squared error (RMSE). The calculated values of RMSE for both studied cases and various critical distances rC are presented in Table 10. Table 10: Evaluated root mean square error for given fracture resistance curves for both studied cases of environment aggressivity and various boundary conditions. MTS GMTS plane stress GMTS plane strain RSME for Cl - free 0.7735 0.8814 0.9477 RSME for Cl - saturated 0.7451 0.9353 0.9299 From the values of RSME presented in Table 9, a notable difference in the accuracy of the MTS and the GMTS criterion can be seen. Although the MTS criterion predicts the failure with a good agreement only for the cases of mode I, the GMTS criterion can predict the fracture in the whole range of various mode mixite conditions with a relatively good agreement with a difference limited to 22%. Another observation from Table 10 can be made, that the GMTS criterion for the Cl--free samples predicts the failure more accurately for the plane stress conditions, the samples saturated with Clshows a better agreement for the plane stress boundary conditions. This phenomenon is due to the fact that the Clions can The differences caused by chloride penetration in the calculated values of critical distances rC influence the calculated crack initiation directions 0 from Eq. (6) used in the evaluation of the GMTS fracture resistance curves. The-chloride saturated case showed higher values of the angle 0 compared to the 18 chloride-free cases, while the values of 0 are the same for both cases. This difference in the values of 0 increases with an increasing mixed mode I/II load. This leads to a lower fracture resistance to the applied load. The calculated crack initiation directions 0 are showed in Figure 14. Figure 14: Crack initiation angle 0 calculated by MTS and GMTS for various boundary conditions and for various environmental conditions. This influence of various levels of the environment aggressivity is more observable, if the fracture resistance curves are plotted in absolute values, i.e. plotted as KII against KI instead of the ratio of KI/KIC and KII/KIC, respectively. The mixed mode I/II fracture resistance curves with various levels of environment aggressivity are shown for plane stress in Figure 15(a) and for plane strain in Figure 15(b). (a) (b) Figure 15: Fracture resistance under mixed mode I/II expressed in absolute values of stress intensity factors for mode I and mode II (a) plane stress and (b) plane strain. The fracture resistance curves presented in Figure 15 again show a clear influence of the chloride aggressivity on the fracture resistance under the mixed mode I/II load. This difference for both studied cases of the aggressive environment is again about 15%. Consequently, this influence of the chloride penetration on the fracture resistance under mixed mode I/II should be taken into account, as it can lower the fracture load, for which a crack can initiate in a real structure. Moreover, this result has a major influence as it was experimentally proven before, that if HPC has some content of metakaolin, it improves the mixture resistance to chloride penetration [93-95]. 19 4.3.1 Influence of the Thickness The above-presented results of the fracture toughness, SIFs, and related fracture resistance were evaluated on the specimens with a similar thickness B of 28 mm. This was done to provide a direct and clear comparison for both studied environmental conditions. However, if there is introduced an effective thickness Beff, which is reduced by a fracture toughness ratio /KIC as follows: (16) or by reducing hClas: . (17) Both Eqs. (16) and (17) assume statement presented in Figure 7(b). This effective thickness is used in Eqs. (8) and (9) for each measured fracture force PC of the chloride-saturated case. A clear increase of KI values can be seen. The evaluated KI values using only load-bearing thickness, i.e. by using effective thickness Beff are presented in Figure 16(a). (a) (b) Figure 16: Influence of effective thickness of the specimens on the values of KI (a) fracture toughness ratio /KIC and (b) chloride penetration depth hCl-. (a) (b) Figure 17: Influence of effective thickness of the specimen on the values of KII (a) based on fracture toughness ratio /KIC and (b) based on chloride penetration depth hCl-. 20 From the both results presented in Figure 16 and in Figure 17, a clear influence of the chloride penetration of the concrete body can be seen. The transformation of the effective thickness Beff by the fracture toughness ratio /KIC by using Eq. (16), shows more accurate results than by the transformation done by the actual chloride penetration depth hClusing Eq. (17). This difference is caused, due to overestimation of the chloride penetration depth, as it is not very clear where the boundary of the chloride ingress is. Beff evaluated by the fracture toughness ratio, to provide the same SIF values as the chloride free samples, is approximately 23.7 mm. This, again, agrees with the assumption made in Figure 7(b), i.e. the thickness is reduced due to the higher surface area exposed to the chloride ions. 5. Conclusion This pilot experimental study showed a conjunction of the fracture mechanics with the ability of highperformance concrete (HPC) to resist an aggressive chloride environment. Moreover, the influence of a chloride-contaminated environment on the fracture toughness and fracture resistance under mixed mode I/II was presented. The experimental study was performed considering different aggressivity levels of the environment, water, and a fully saturated sodium chloride solution. The experimental tests were performed on Brazilian disc specimens to determine the indirect tensile strength ft and on a Brazilian disc with a central notch to evaluate the fracture toughness KIC and the fracture resistance under mixed mode I/II. Mixed mode I/II fracture resistance was evaluated by the generalised maximum tangential stress (GMTS) criterion. The level of chloride contamination present and its boundary in the concrete was estimated by the colorimetric method using silver nitrate. The experimental results of the BD test showed virtually no influence of the chloride-contaminated environment on the indirect tensile strength ft. However, a clear influence of the chloride environment on the fracture toughness and fracture resistance to the mixed mode I/II load was observed. The chloride environment showed a 15% reduction of the experimentally measured fracture toughness KIC. 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