3.     Results and their analysis

3.1. Evaluation of the mechanical properties using in-situ tests

This section evaluates the relationship between the results obtained from in-situ tests and the mechanical properties of the mortars using linear and exponential regression analysis. The linear regression curve passes through the origin of the coordinates to measure the coefficient of determination between the compressive strength of the mortars and the in-situ test results. Moreover, since the relationship between the compressive and flexural strengths is exponential, the relationship between the in-situ tests and the flexural strengths of the mortars was evaluated using exponential regression analysis.

3.1.1.         Results of the friction-transfer Test

Fig. 8 depicts the relationship between the compressive strength of the mortars and the results of the friction-transfer test.

According to Fig. 8, the coefficient of determination in the linear mode is 0.9518; however, when the curve passes through the origin, the coefficient is 0.9517. As can be seen, a slight difference exists between the coefficients of determination. Therefore, the compressive strength of the PMM can be determined using friction-transfer tests and the equation y=0.113x.

In a study on the relationship between the compressive strength of the concrete and the friction-transfer test results, coefficients of determination of more than 90% were observed [28]. This study also showed that the coefficient of determination between the compressive strength of the mortars and the friction-transfer test results was 95%.

Fig. 8. Correlation between compressive strength and results of “friction-transfer” test

Fig. 9 depicts the relationship between the flexural strength of the mortars and the results of the friction-transfer test.

According to Fig. 9, it is observed that the coefficients of determination equal to 0.77. Therefore, the flexural strength of the PMM can be determined using friction-transfer tests and the equation .

3.1.2.         Results of the “Pull-off” test

Fig. 10 depicts the relationship between the compressive strength of the mortars and the results of the pull-off test.

According to Fig. 10, the coefficient of determination in the linear mode is 0.9473; however, when the curve passes through the origin, the coefficient is 0.9449. As can be seen, a slight difference exists between the coefficients of determination. Therefore, the compressive strength of the PMM can be determined using pull-off tests and the equation y=0.063x.

Fig. 11 depicts the relationship between the flexural strength of the mortars and the results of the pull-off test.

Fig. 9. Correlation between flexural strength and results of “friction-transfer” test

Fig. 10. Correlation between compressive strength and results of “Pull-off” test

Fig. 11. Correlation between flexural strength and results of “Pull-off” test

According to Fig. 11, it is observed that the coefficients of determination equal to 0.725. Therefore, the flexural strength of the PMM can be determined using pull-off tests and the equation .

3.2. Shrinkage of polymer-modified repair mortars

This section evaluates the shrinkage of repair mortars at different ages. The effects of different percentages of polymer on the PMM are also discussed. Fig. 12 presents the shrinkage curve of the mortars. As can be seen from Fig. 12, higher volumes of polymer in the mortars reduced the shrinkage. The shrinkage of ordinary mortars at the age of 90 days was 0.082%, while the shrinkage of the PMM with 10%, 15%, and 20% polymer was 0.056%, 0.051%, and 0.047%, showing 31%, 37%, and 43% reduction in shrinkage, respectively. Moreover, the shrinkage reduced significantly as the percentage of the polymer increased. Similar results have been reported in other studies.

Fig. 12. The mortars’ shrinkage

Different study on the effect of SBR latex had also concluded that adding polymer reduces the dry shrinkage [38]. One of the main reasons in the shrinkage decrement of the polymer-modified mortars is the sealing property of latex that prevents the humidity output from the inside of the cement matrix [39-40].

3.3. Bond strength

3.3.1.         Bond shear strength obtained from the “friction-transfer” test

Fig. 13 demonstrates the bond shear strength between repair mortars and the concrete substrate obtained from the “friction-transfer” test.

Fig. 13 shows that adding 10% of SBR latex to the mortar increased the bond shear strength within the ages of 7, 42, and 90 days by 35.9, 141.7 and 209.7%, respectively. Also, by adding 15% of SBR latex, the adhesion increment in the mentioned ages was equal to 58.7, 184.8 and 269.9%, respectively. The bond shear strength increment is also observed by adding 20% of SBR latex so that the bond strength increment within the ages of 7, 42, and 90 days was equal to 49.1, 167.5 and 250.3%, compared to the polymer-free mortar, respectively.

However, as can be seen, adding 20% polymer had a smaller effect compared to adding 15% polymer since the SBR latex created air bubbles inside the cementitious material’s structure, creating porosity in the mortar [41]. Therefore, larger increases in the amount of polymer can have adverse effects.

Similar results have been observed in other studies, where the addition of SBR latex increased the bond strength between the mortar and the substrate [42]. The rise in the adhesion in such mortars is due to the formation of polymer films. When a polymer has contact with the cement paste, the strong covalent or ionic bonds give more cohesion to the entire matrix, improving adhesion [43].

3.3.2.         Bond tensile strength obtained from the “Pull-off” test

Fig. 14 shows the bond strength between the concrete and the polymer-modified mortars based on the pull-off tests.

As can be seen from Fig. 14, at the age of 90 days, the rise in the adhesion of the mortars containing 10%, 15%, and 20% polymer was equal to 170.2%, 220.3%, and 201.3%, respectively. The corresponding values were 94.8%, 125.7%, and 113.2% at the age of 42 days, and 31.4%, 56.7%, and 44.8% at the age of 7 days, respectively.

However, as can be seen, adding 20% polymer had a smaller effect compared to adding 15% polymer since the SBR latex created air bubbles inside the cementitious material’s structure, creating porosity in the mortar [41]. Therefore, larger increases in the amount of polymer can have adverse effects. Fig. 15 shows the correlation between bond shear strength obtained from the “friction-transfer” test and bond tensile strength obtained from the “pull-off” test.

Fig. 13. Bond shear strength

Fig. 14. Bond tensile strength

Fig. 15. The correlation between the results of “friction-transfer” and “pull-off” tests

According to the Figure. 15, the determination factor of “pull-off” and “friction-transfer” tests is 91%.  Considering the high correlation factor of the results of “pull-off” and “friction-transfer” tests, it is possible to obtain the results of one test and consider it for the other test. Also, it is worth noting that the damages of two methods are negligible. However, unlike the “pull-off” test, in which we have to use of chemical adhesives for attaching the metal cylinder to the mortar surface, all the employed instruments are mechanical in the “friction-transfer” test  therefore, it has the unique application for each type of laboratory and environmental conditions. Also, it can be used without any humidity and thermal constraint. Therefore, the simple and cheap machine of the “friction-transfer” test can be used instead of the expensive machine of the “pull-off” test for determining the bond strength between the concrete substrate and the polymer-modified mortars.

Other studies have obtained similar results. A study has mentioned that the correlation coefficients of more than 93% exist between the friction-transfer and the pull-off test results for ordinary mortars [28].

3.4. Evaluating the effect of polymers on flexural and compressive strengths

This section discusses the effect of styrene-butadiene polymers on the compressive and flexural strengths of repair mortars. As stated previously, the 28-day compressive strength of the concrete substrate was 57 MPa. Table 4 provides the compressive and flexural strengths of the mortars.

As can be seen, the compressive and flexural strengths of the mortars have been increased by the completion of the hydration process due to the rise in the age of the specimens. Adding the styrene-butadiene rubber increased the flexural strength of the mortars. Therefore, in comparison with ordinary mortars, the 7-day flexural strengths of the mortars modified with 10%, 15%, and 20% polymers have been increased by 18.1%, 38.6%, and 44.9%, respectively. Similar rises were observed at other ages as well. However, the addition of the polymer reduced the compressive strength of the mortars. In specific, the 7-day compressive strengths of those modified with 10%, 15%, and 20% polymers were decreased by 24.9%, 30.2%, and 33.1%, respectively. Similar observations were also witnessed for other ages. Also, in other studies have obtained similar results. As reported in [41], the styrene-butadiene rubber delayed the hydration process and reduced the compressive strength. Furthermore, the addition of the SBR to the mortar increased the air bubbles and porosity in the mortars, which directly reduced their compressive strengths. Another article reported an increased adhesion between the cement paste and aggregates by adding the styrene-butadiene rubber, which consequently yielded higher flexural strengths [44].

The SEM images of the specimens were obtained to evaluate their microscopic structures. Fig. 16 illustrates the microscopic image of the mortar containing SBR. As can be seen, the added SBR polymer in the mortar structure filled the cracks and prevented widening. As shown in Fig. 17, to make a better assessment, the diameter distribution of the SBR polymers in the mortar, along with their distribution histograms, were plotted using the Image J and Origin software programs. As can be seen, the most frequent diameter of the polymers was approximately 0.1 μm. Table 5 lists the statistical parameters of the measurement.

Table 4. The compressive strength of the mortars (MPa)

Fig. 16. Microscopic image of the mortar containing SBR

Fig. 17. The diameter distribution histogram of the SBR polymer in the mortar

Table 5. Statistical parameters obtained from the diameter distribution of SBR fibers in the mortar

As shown in Table 5, the mean diameter of the polymers was approximately 98nm. Therefore, they could be considered nanoparticles due to having diameters lower than 100nm. Moreover, the smallest and largest measured diameters were 53nm and 201nm, respectively. Nanoparticles of the material have unique properties, which cannot be observed in larger particles of the same material. Thus, the reduced nanometric diameter of the polymers has improved the properties of the bond between the mortar and the substrate.

3.5. Modeling the “friction-transfer” and “pull-off” tests

ABAQUS provides brittle cracking, smeared cracking, and concrete damage plasticity models to consider the nonlinear behavior of brittle materials. The concrete damage plasticity model supports static and dynamic analyses with tensile cracking and compressive crushing mechanisms. Since by imposing a torsional moment in a friction-transfer test, the core is subjected to compressive and tensile forces, this study used the concrete damage plasticity model for modeling.

In order to model the friction-transfer and pull-off tests, the cubic mortar piece was meshed using a combination of C3D8R and C3D4 elements. The main part of the model, which was under compression or tension, was meshed using C3D8R 8-node cubic elements with reduced integration. The convergence of meshes with sizes of 0.5, 1, and 2 mm was evaluated, among which 1-mm meshes were chosen to be used in the modeling.

The important point in the meshing of the specimens is convergence. The results obtained from solving a problem in the FEM are always dependent on the size of the meshes and the size of the elements used. The problem-solving converges to a single solution by reducing the dimensions of the elements. However, the meshing size improvement should be done so as not to cause a sharp increase in computational volume. Since finite element solutions are dependent on the meshing size, the meshing convergence must always be checked in areas of the model where the values of stress, strain, or any other parameter must be accurately calculated. The meshing size can be considered large enough in areas far from stress concentration points.

As it can be seen in Figure 18, the modeling is performed with different kinds of meshing. The results were highly changed by decreasing the elements from 2 to 1 mm. Although, it can be observed that the value of maximal responses will be very close together by changing the size of the element from 1 to 0.5 mm. It was therefore decided to use meshing with the size of 1 mm.

Moreover, the edges were meshed using tetrahedral 4-node continuous elements with a minimum element size of 1 mm in the areas connected to the major elements, and a maximum element size of 15 mm on the edges. In the pull-off test, the adhesive was meshed with 2-mm C3D8R elements, and the mesh size of the steel piece was also 2 mm. along the axial direction, 10-mm meshes were used for the steel piece (Fig. 19).

Fig. 18. Mesh sizing sensitivity

a) Friction-transfer

b) Pull-off

Fig. 19. The meshing of the specimens

The specimens were braced inside a steel frame to perform the friction-transfer tests. The bracing section had a height of 30 mm from the bottom of the specimen. As shown in Fig. 20.a, the bottom part of the specimen was defined as a support in the modeling. In the pull-off test, since the apparatus was placed on the top surface of the specimen in the laboratory, the top part of the specimen was defined with boundary conditions in the modeling (Fig. 20.b).

In order to define the behavior of the concrete after cracking under tension, with respect to the default mode of the program, the compressive hardening recovery, w_c, was considered “one” to completely recover the compressive hardening while the cracks were getting closed (after cracking under tension). On the other hand, w_t was considered “zero” to ignore the tensile hardening recovery.

The default values of the program were also considered for the plasticity properties of the concrete (Table 6). The dilation angle is a parameter in degrees, which depends on the materials’ density and angle of internal friction. The eccentricity is a small positive value indicating the closeness rate of a hyperboloid to its asymptote. The third item in the Table 6 is the performance ratio of the biaxial initial stress to the uniaxial initial stress, and K denotes the ratio of the second tensile stress to the compressive stress.

In order to build the model and introduce the materials’ properties, the specimen parts were created at first using the “Create part” command. In order to model the concrete part using the “Create line” command, the rectangle of the concrete’s cross-section was plotted, and its depth was defined as 150 mm. The “Create circle” command was used to plot the steel part and the adhesive. The “Property” module was used to define the materials’ properties. Table 7 lists the properties of the used materials.

Afterward, the materials were assigned to the parts by using the commands “Create section” and “Assign section”. In the “Plasticity” item, the “Concrete damaged plasticity” option was selected to define the plasticity properties. The compressive and tensile behaviors were then defined in the “Compressive behavior” and “Tensile behavior” sections. Afterward, the parts were assembled using the “Assembly” command.

As shown in previous sections, in the friction-transfer test, a metal piece was placed around the mortar core, which was fixed with the surrounding bolts, and enclosed the core. In order to evaluate the effects of lateral pressures applied by the metal piece on the core on the results, various lateral pressures were imposed on the core. As shown in Fig. 21, by clicking on the “Pressure” option in the “Load” item, the core’s edges were selected, subjected to various pressures, and then analyzed.

a) Friction-transfer

b) Pull-off

Fig. 20. Boundary conditions

Table 6. The plasticity properties of the concrete

Table 7. The properties of the adhesive and the steel

Fig. 21. The pressure of the metal piece on the core

Applying various pressures did not lead to a significant change in the results. Therefore, in order to model the interaction between the metal piece and the core in the friction-transfer test, a torsional moment was applied to the core perimeter in the form of a rotational displacement around the core axis using the coupling constraint, as shown in Fig. 22. To do so, a reference point was created on top of the core using the item “Tools” and choosing the option “Reference point”. Then, a coupling constraint was imposed in the “Interaction” section, and the areas around the core interacting with the metal core were chosen as the controllable part.

A mortar with a compressive strength of 47.6 MPa was used to model the specimens. The results of the friction-transfer and pull-off tests on the abovementioned specimen in the laboratory were 115 Nm and 4500 N, respectively.

Fig. 22. Modeling the interaction between the metal piece and the mortar

When modeling the friction-transfer test, the cracks appeared on the edges and corners of the specimen, subjected to the largest stress, at the moment of 54 Nm. Then, at the moment of 107 Nm, the cracks reached each other, and the specimen failed (Fig. 23). By comparing the results of modeling and the experimental results it is obvious that the sample fracture in the “friction-transfer” test occurs in both cases as 45 degrees. Since, based on the Mohr circle the main compressive and tensile stresses make a 45 degrees angle with the horizon. Considering that the brittle materials such as mortar have the tensile fracture, therefore, in this case, the fracture planes appear to be vertical to the tensile stress. Therefore, in the “friction-transfer” test, the core fracture has an angle of about 45 degrees with the horizon.

When modeling the pull-off test, the first cracks appeared on the edges of the connection between the steel cylinder and the specimen at the force of 2448 N. Then, the cracks reached each other, and the specimen failed at the force of 1555 N (Fig. 24).

In order to verification the modeling results obtained from ABAQUS and to make a detailed comparison between the numerical and experimental results, they are provided in the following. Table 8 presents the results obtained from the modeling, the friction-transfer test, and the pull-off test.

Fig. 23. The moment of failure in the friction-transfer test

Fig. 24. The moment of failure in the pull-off test

Table 8. The numerical and experimental results of the friction-transfer test

As can be seen, the differences between the modeling results and those obtained from the friction-transfer and pull-off tests in the laboratory were smaller than 7% and 2%, respectively.

4.     Conclusions

In this paper, regression analysis was used to determine the correlation between the measurements of the semi-destructive tests and the results obtained for the compressive and flexural strength of the mortars. Furthermore, calibration curves were developed to obtain the mechanical properties of the mortars. The effects of the polymer on the shrinkage and the bond strength between the mortars and the concrete substrate were also investigated. Eventually, the stresses and cracks formed in the friction-transfer and pull-off tests were obtained through finite element analysis in ABAQUS. The results are as follows:

• The styrene-butadiene rubber increased the shear and bond tensile strength between the repair mortars and the concrete substrate. The largest rise in the shear and bond tensile strength (i.e., 269.9% and 220.3%, respectively) belonged to the mortar containing 15% polymer.
• The styrene-butadiene rubber reduced the shrinkage of the mortars, which is an important factor in increasing the adhesion between the mortar and the concrete. At the age of 14 days, the addition of 10%, 15%, and 20% SBR reduced the shrinkage by 32.8%, 36.1%, and 42.1%, respectively.
• Given the high correlation between the friction-transfer and pull-off tests, the low-cost and simple friction-transfer apparatus can be used instead of the imported pull-off apparatus to measure the adhesion between the mortar and the concrete.
• Due to the high correlation between the results of the in-situ tests and the compressive and flexural strengths of the mortars, the abovementioned tests can be used for evaluating the strength of the polymer-modified mortars.
• The styrene-butadiene rubber latex had a positive effect on the flexural strength of the mortars, i.e., adding 20% polymer increased the 90-day flexural strength by 50.3%.
• The results obtained from the finite element analysis in ABAQUS had a good agreement with those obtained in the laboratory, confirming the high accuracy of the semi-destructive tests for evaluating the strength of the mortars.

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