Roughness quantification

Roughness quantification was performed using interval mechanical probing, consisting of three measurement intervals, each 250 mm in length, with one measurement every 0,5 mm. The resulting 2D roughness profile is an approximation of the measured surface. One of the resulting 2D roughness profiles is illustrated in fig. 3.17. The 2D roughness profile describes the height of every

measurement point in respect to the mean of the profile, and distance to measurement interval starting point. The global slope is corrected to ensure the measured surface is parallel to the CNC x-axis. From the resulting 2D roughness profiles, roughness parameters and their distributions can be derived.

Figure 3.17: 2D roughness profile (series 3, measurement path 1) 3.3.3 Concrete strength

The cube compressive strength of the concretes used was determined at time of testing. For every series, 3 to 9 cubes were tested for both the precast floor plate, and the compression layer.

Table 3.3: Average cube compressive strengths

Series Number of

cubes per concrete

Precast floor plate Compression layer 𝒇𝒄𝒌,𝒄𝒖𝒃𝒆

(𝑵/𝒎𝒎^𝟐)

St.Dev.

(𝑵/𝒎𝒎^𝟐)

𝒇𝒄𝒌,𝒄𝒖𝒃𝒆 (𝑵/𝒎𝒎^𝟐)

St.Dev.

(𝑵/𝒎𝒎^𝟐)

Series 1 – SCC untreated 3 86,20 1,96 44,30 1,03

Series 2 – SCC lightly smoothed 9 56,29 5,49 59,85 2,58

Series 3 – TC untreated 9 40,00 3,74 17,50 0,71

Series 4 – TC untreated 6 70,22 1,15 44,91 2,34

Series 5 – TC roughened, raked 9 56,67 1,79 42,13 2,80

Series 6 – SCC extremely smoothed 9 88,20 1,87 42,86 3,52

Series 7 – SCC roughened, raked 9 93,80 2,99 37,59 1,31

Series 8 – TC roughened, raked 9 66,21 0,63 40,23 3,74

-0,8 -0,6 -0,4 -0,2 0 0,2 0,4 0,6 0,8 1

0 25 50 75 100 125 150 175 200 225

Position Y-axis (mm)

Position x-axis (mm)

Figure 3.18: Average cube compressive strength of precast floor plate for every series

Figure 3.19: Average cube compressive strength of compression layer for every series 0

20 40 60 80 100

120 Series 1 - SCC untreated

Series 2 - SCC lightly smoothed Series 3 - TC untreated Series 4 - TC untreated Series 5 - TC roughened, raked Series 6 - SCC extremely smoothed Series 7 - SCC roughened, raked Series 8 - TC roughened, raked N/mm2

0 20 40 60

80 Series 1 - SCC untreated

Series 2 - SCC lightly smoothed Series 3 - TC untreated Series 4 - TC untreated Series 5 - TC roughened, raked Series 6 - SCC extremely smoothed Series 7 - SCC roughened, raked Series 8 - TC roughened, raked N/mm2

4 A NALYSIS

4.1 A

NALYSIS OF SHEAR EXPERIMENT DATA

To further interpret the test results plotted in fig. 3.16, test series can be grouped with series that are alike in concrete type and roughness (fig 4.1). Test results and linear regression plots of the separate specimen groupings can be found in Appendix 3 – Experimental results.

Figure 4.1: Test results grouped by specimen characteristics

Assuming the average cube compressive strength of the weakest concrete as the interface compressive stress, the concrete-to-concrete interface Mohr-Coulomb failure envelope can be constructed for these experimental results. However, this resulting failure envelope is based on a series average, and is neither a lower nor upper bound. This failure envelope should only be used for inter-series comparison.

Figure 4.2: Construction of the Mohr-Coulomb failure envelope for the concrete-to-concrete interface 0

0,5 1 1,5 2 2,5 3 3,5

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

τ(N/mm2)

σ_n(N/mm²)

SCC very smooth SCC untreated SCC raked TC untreated TC raked

Table 4.1: Parameters of Mohr-Coulomb failure envelopes constructed for every grouping

Experimentally found Derived

Specimen group 𝝉_𝟎

(𝑵/𝒎𝒎^𝟐)

Slope coeff.

𝒇_{𝒄𝒌,𝒊} (𝑵/𝒎𝒎^𝟐)

𝒇_{𝒄𝒕𝒌,𝒊} (𝑵/𝒎𝒎^𝟐)

𝝉_𝒎𝒂𝒙 (𝑵/𝒎𝒎^𝟐)

𝝈_𝒎𝒂𝒙 (𝑵/𝒎𝒎^𝟐)

SCC very smooth 0,57 2,25 42,86 0,24 20,59 22,28

SCC untreated 1,63 1,66 44,30 0,91 20,88 23,40

SCC raked 1,87 1,32 37,59 1,26 17,30 20,29

TC untreated 1,08 1,31 17,50 0,73 8,21 9,39

TC raked 1,10 1,88 40,23 0,55 19,13 21,10

4.2 A

NALYSIS OF ROUGHNESS QUANTIFICATION DATA

From the obtained 2D roughness profiles, roughness parameters and their distributions can be derived. Since there is no consensus on which roughness parameter is most suitable, a multitude of parameters are derived and will be analyzed. The distribution of one of the roughness parameters, Ra, is illustrated in fig. 4.3. The distributions of other roughness parameters can be found in

Appendix 4 – specimen roughness, and are presented in table 4.2. No reference precast floor plates are available for series 5 and 6, however series 5 is produced similarly to series 8, and series 5 was smoothed until the surface was perfectly flat.

Figure 4.3: Distribution of average roughness deviation (Ra) 0

1 2 3 4 5 6 7 8 9

0 0,5 1 1,5 2

Average roughness deviation Ra (mm)

Series 1 - SCC untreated Series 2 - SCC lightly smoothed Series 3 - TC untreated Series 4 - TC untreated Series 7 - SCC roughened, raked Series 8 - TC roughened, raked

Table 4.2: Roughness parameters and their distribution for every series Roughness

parameter

Series Average (mm) St.Dev. (mm) COV (%)

𝑅_𝑎 1 – SCC untreated 0.162 0.064 39.6

2 – SCC lightly smoothed 0.127 0.050 39.3

3 – TC untreated 0.159 0.066 41.8

4 – TC untreated 0.196 0.103 52.4

7 – SCC roughened, raked 0.478 0.164 34.3

8 – TC roughened, raked 1.003 0.525 52.3

𝑅_{𝑧(𝐷𝐼𝑁)} 1 – SCC untreated 0.973 0.419 43.1

2 – SCC lightly smoothed 0.732 0.395 54.0

3 – TC untreated 0.876 0.319 36.4

4 – TC untreated 1.254 0.573 45.7

7 – SCC roughened, raked 2.829 0.936 33.1

8 – TC roughened, raked 5.701 2.644 46.4

𝑅_𝑝𝑚 1 – SCC untreated 0.443 0.234 52.8

2 – SCC lightly smoothed 0.405 0.309 76.4

3 – TC untreated 0.449 0.210 46.9

4 – TC untreated 0.556 0.254 45.6

7 – SCC roughened, raked 1.159 0.579 50.0

8 – TC roughened, raked 1.849 0.636 34.4

𝑅_𝑣𝑚 1 – SCC untreated 0.530 0.384 72.5

2 – SCC lightly smoothed 0.327 0.177 54.2

3 – TC untreated 0.428 0.216 50.4

4 – TC untreated 0.698 0.425 60.9

7 – SCC roughened, raked 1.671 0.549 32.9

8 – TC roughened, raked 3.852 2.430 63.1

𝑅𝑞 1 – SCC untreated 0.241 0.090 37.3

2 – SCC lightly smoothed 0.201 0.104 52.0

3 – TC untreated 0.223 0.081 36.2

4 – TC untreated 0.288 0.130 45.2

7 – SCC roughened, raked 0.683 0.271 39.6

8 – TC roughened, raked 1.547 0.890 57.5

To investigate whether the chosen probing tip dimensions are correct, a check is performed to determine if the probing tip has been deflected off of its course by a steep cliff. If the inclination of the measured 2D roughness profile exceeds the angle of the tip, the tip has been deflected off of its course, and has measured a spot not intended. This was the case a total of 32 times in 9000

measurements, 25 times in series 8, 5 times in series 7, and 2 times in series 4. This however is a lower bound. For a surface with a high roughness, a probing tip with a higher degree of sharpness is recommended.

4.3 N

UMERICAL MODELING

To interpret the experimental results, a constant distribution of shear stress over the interface is presumed. This however, is not the case. To investigate the stress distribution over the concrete-to-concrete interface characteristic for this test setup, a linear elastic Finite Element Analysis model of the test specimen is used.

A FEM software suite, Abaqus FEA, is adopted. Two models are considered, one model with a similar concrete strength class for the precast floor plate and the compression layer, and one with a precast floor plate concrete strength class that is 1,5 times higher than the compression layer. The coefficient of Poisson is considered equal to 0.2 and a mesh size of 5 mm, with quadrilateral plane strain

elements, is used at the interface. The two equal loads are applied to the nodes that are situated in the load introduction area and the support area (width of 15 mm adjacent to interface, 3 nodes).

A 2D model of the specimen is adopted, with a symmetry axis (fig. 6.14 dotted line) at the specimen centerline. At this symmetry axis, rotations and horizontal translations are constrained. The stress distributions shown are characteristic for the midline of the test specimen interface, shown as the red line in fig. 5.14. The precast floor plate thickness used is 70mm, compression layer thickness used is 90mm, specimen height used is 300mm.

Figure 6.14: Abaqus FEA model geometry

The stress distribution of the interface midline in the cardinal directions is illustrated in fig. 6.15 (element centroids). Note that the interface is in a state of triaxial compression near the load introduction, and near the support. Splitting tensile stresses in the x-direction are also found in the interface. The situation plotted in fig. 6.15 and fig 6.16 is a situation without external compression perpendicular to the interface, subject to a loading of F = 100 kN. The addition of a 𝜎_𝑛 does not affect the distribution of these stresses, and the resulting stress can simply be added to the found stresses in the x-direction. The addition of an external compression perpendicular to the interface will thus decrease the splitting tensile stresses.

The interface shear stress distribution is plotted in fig. 6.16. The shear stress distributions for a model with two materials with the same modulus of elasticity, and a model with a precast floor plate of 1.5 times the modulus of elasticity of the compression layer. A difference in modulus of elasticity does influence the stress distribution at the concrete-to-concrete interface, and may cause higher peak stresses. The stress concentrations found near the load introduction sites suggest that actual interface shear resistance may be larger than the average shear stress that was assumed.

The principal stress distribution over the interface midline is plotted in fig. 6.17, maximum tensile stresses occur at 32,5 mm from the bottom edge. Specimen failure will most likely initiate in this location. The small flexural stresses occurring in the specimen slightly increase the tensile stresses at the bottom of the specimen.

Figure 6.15: Stress distribution (𝜎𝑥, 𝜎_𝑦, 𝜎_𝑧) in the cardinal directions at the interface midline (at F = 100 kN) 0

50 100 150 200 250 300

-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4

Position (mm from bottom edge)

stress (N/mm2)

x-direction y-direction z-direction E-mod ratio 1:1

Figure 6.16: Shear stress (𝜏𝑥𝑦) distribution at the interface midline with different modulus of elasticity ratios (at F = 100 kN)

Figure 6.17: Principal stress distributions at the interface midline (at F = 100 kN) 0

50 100 150 200 250 300

0 2 4 6 8

Position (mm from bottom edge)

shear stress N/mm2

E-mod. ratio 1:1

E-mod. Ratio 1:1.5

Averaged shear stress

0 50 100 150 200 250 300

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4

Position (mm from bottom edge)

Principal stress (N/mm2)

Maximum principal stress Minimum principal stress

4.4 C

ORRELATION ANALYSIS OF EXPERIMENTAL RESULTS

The research goal is to investigate which parameters of a concrete-to-concrete interface influence the shear behavior. To examine the relationship between the experimental results and the

corresponding material parameters, statistical analysis is used. For each test specimen, the following variables are entered into the statistical analysis:

- Average shear stress at failure (N/mm²) - Average 𝜎𝑛 (N/mm²)

- 𝑓_{𝑐𝑘,𝑐𝑢𝑏𝑒} of the strongest concrete - 𝑓𝑐𝑘,𝑐𝑢𝑏𝑒 of the weakest concrete

- Ratio between 𝑓_{𝑐𝑘,𝑐𝑢𝑏𝑒} of the strongest concrete and the weakest concrete - Roughness parameters (^𝑅𝑎, 𝑅_{𝑧(𝐷𝐼𝑁)}, 𝑅_𝑝𝑚, 𝑅_𝑣𝑚 𝑎𝑛𝑑 𝑅_𝑞)

- Average horizontal displacement at failure - Average vertical displacement at failure

- Linear regression components of test results (𝜏0 and slope coefficient) - Eurocode 2 cohesion and friction components

- FIB Model Code 2010 adhesion and friction components - Shear resistance prediction of Eurocode 2

- Shear resistance prediction of FIB Model Code 2010 - Whether or not the precast floor plate is SCC

For every hypothesis, the Pearson correlation coefficient is computed to provide a measure of the linear correlation between the investigated variables. Statistical significance is studied by computing the p-value for the investigated variables, a two-tailed test is used because hypothesis direction is not always specified. This p-value is compared to an adopted 𝛼 of 0.05 as the threshold to reject the null hypothesis in the investigated relationship, additionally an 𝛼 of 0.01 is adopted to signify very significant relationships. The software suite SPSS Statistics is used to construct a correlation matrix for the entered variables. From this matrix, the correlations corresponding to the hypotheses can be extracted (fig 7.1). This correlation matrix describes whether or not the null-hypothesis could be rejected, the correlation, and the significance of this correlation. Both the full correlation matrix and the correlation matrix for the hypotheses can be found in appendix 5 – correlation matrices.

Figure 7.1: Correlation matrix of investigated variables

Average shear stress at failure

The averaged shear stress at failure has no direct one-on-one correlation with concrete strength, or roughness. This was expected, since the shear resistance is a linear function consisting of multiple components. Correlation with one of these components does not imply correlation with their sum.

These three components, 𝜏0, slope coefficient, and 𝜎𝑛 are also investigated.

The maximum shear resistance found in experimental testing, does have a significant, medium-size, positive correlation with the Eurocode 2 and FIB Model Code 2010 expression for shear resistance.

The FIB Model Code 2010 expression describes the found experimental results more accurately than the Eurocode 2 expression.

Compression perpendicular to the interface

The compression perpendicular to the interface has a very significant, large, positive correlation with the maximum shear resistance of an interface.

The compression perpendicular to the interface has no significant correlation with the interface displacements.

𝝉_𝟎 regression constant

The found shear strength in the absence of normal loading, 𝜏0 , has no significant correlation with any of the cube compressive strengths. However, the ratio between the two concrete strengths (presumably caused by difference in modulus of elasticity) does have a significant, medium-size, positive correlation with 𝜏0. Meaning that 𝜏0 increases when there is a large difference between the concrete strengths of the precast floor plate and the compression layer.

The found shear strength in the absence of normal loading, 𝜏₀ , has no significant correlation with any of the measured surface roughness parameters. This is contrary to the expressions found in codes.

The found shear strength in the absence of normal loading, 𝜏0 , has a very significant, large, negative correlation with the found regression slope coefficient. This suggests that specimens with a larger shear strength 𝜏₀ are less sensitive to compression perpendicular to the interface.

The found shear strength in the absence of normal loading, 𝜏0 , has no significant correlation with the cohesion described in both Eurocode 2 and FIB Model code 2010.

Regression slope coefficient

The regression slope coefficient has no significant correlation with the cube compressive strength of the strongest concrete. But does have a very significant, large, positive correlation with the concrete strength of the weakest concrete. This is contrary to the expressions found in codes, where the friction coefficient is not attributed to concrete strength.

The regression slope coefficient has a very significant, large, negative correlation with the ratio between the two concrete strengths. Meaning that when the two concretes have a more similar cube compressive strength, the found regression slope is steeper, and the shear resistance is more sensitive to compression perpendicular to the interface. This may be caused by differences in modulus of elasticity.

The regression slope coefficient has no significant correlation with any of the measured surface roughness parameters. This is contrary to the expressions found in codes.

The regression slope coefficient has a very significant, large, negative correlation with the slope coefficient described in Eurocode 2. This suggests that the coefficients of friction found in Eurocode 2 are inversely related to the found regression slope coefficients.

The regression slope coefficient has a significant, small, negative correlation with the slope

coefficient described in FIB Model Code 2010. This suggests that the coefficients of friction found in FIB Model Code 2010 are inversely related to the found regression slope coefficients.

Roughness parameters

The measured surface roughness parameters have no significant correlation with any of the other investigated variables. The roughness parameters have no correlation with either horizontal- or vertical displacements measured up until specimen failure.

5 C ONCLUSIONS AND RECOMMENDATIONS

5.1 C

ONCLUSIONS Interface shear resistance

The shear resistance of an unreinforced concrete-to-concrete interface is currently attributed to the concrete strength of the weakest concrete, the compressive stress perpendicular to the interface, and coefficients of cohesion and friction. In an uncracked unreinforced concrete-to-concrete interface, adhesion shear transfer occurs.

These coefficients proposed by EC2 and fib MC 2010 are based on previous experimental results. EC2 relies on qualitative visual inspection, whilst fib MC 2010 proposes these coefficients to be based on roughness parameter Ra. This roughness parameter is derived from a 2D roughness profile.

Three different shear transfer mechanisms can be identified: adhesion-, friction- and reinforcement shear transfer. In an unreinforced concrete-to-concrete interface, adhesion- and friction shear transfer determine shear resistance.

Direct shear experiments

To re-evaluate expressions for this shear resistance, direct shear tests under compression

perpendicular to the interface were performed. The test setup used, satisfied the requirements. The independent control over shear loading and loading perpendicular to the interface was as intended.

The test setup also allowed for a realistic production method, reduced flexural stresses, and provided opportunity to minimize and check eccentricities. No unexpected specimen behavior occurred during testing.

The found shear strength in the absence of normal loading, 𝜏0 , ranged from 0,57 𝑁/𝑚𝑚² to 1,87 𝑁/𝑚𝑚², the found slope coefficient ranged from 0,50 to 2,94. No apparent relationship between interface roughness and shear resistance was found. The test series can be grouped with series that are alike in concrete type and roughness (table 5.1).

Table 5.1: Parameters of linear part in the Mohr-Coulomb interface failure envelope

Specimen group 𝝉_𝟎

(𝑵/𝒎𝒎^𝟐)

Slope coefficient

𝒇_{𝒄𝒌,𝒊} (𝑵/𝒎𝒎^𝟐)

SCC very smooth 0,57 2,25 42,86

SCC untreated 1,63 1,66 44,30

SCC raked 1,87 1,32 37,59

TC untreated 1,08 1,31 17,50

TC raked 1,10 1,88 40,23

Roughness quantification

The adopted method, interval mechanical probing, was found suitable to describe a 2D roughness profile of a given surface. 2D roughness profile interpretation using roughness parameters is sensitive to changes in assessment length. Roughness parameters Ra and Rz(DIN) were found to be least susceptible to changes in measurement technique. Using specialized roughness quantification equipment may improve accuracy of the derived roughness profile.

Material properties testing

The cube compressive strength of the concrete was measured. However, measurement of the splitting tensile strength and the modulus of elasticity of the materials used may be valuable in the

interpretation of the experimental data. In this research, additional pull-off tests were performed according to fig. 2.9. Lack of rest results proved these tests inconclusive, but the testing method performed well.

Numerical modeling

Near the load introduction, a tri-axial state of compression occurs. The specimen also experiences some splitting tensile stresses perpendicular to the interface. Peak shear stresses occur that are higher than the assumed interface average, actual shear stress capacity might be larger. A large difference in modulus of elasticity between the two concretes further increases peak stresses, which may reduce interface shear resistance. Shrinkage stresses might further influence the stress

distribution, but this was not studied due to lack of temperature- and relative humidity data for the manufacturer production locations.

Correlation analysis

The fib Model Code 2010 expression is a better predictor of the experimentally found shear resistance than the Eurocode 2 expression. The Pearson correlation coefficient between the fib Model Code 2010 expressions and test results is 0.4133, whilst the Pearson correlation coefficient between Eurocode 2 expressions and test results is 0.3420.

The found shear strength in the absence of normal loading, 𝜏₀ , was found to have no correlation with concrete strength parameters, unlike assumed in codes. Neither has 𝜏0 any correlation with the shear resistance at 𝜎𝑛= 0 described by both Eurocode 2 and fib Model Code 2010.

The regression slope coefficient has a large positive correlation with the strength of the weakest concrete. The regression slope coefficient has a large negative correlation with the ratio of concrete strengths, suggesting that a large difference in modulus of elasticity between the two concretes may lower interface shear resistance. The regression slope coefficient has no correlation with surface roughness, contrary to code suggestion. The regression slope coefficient has negative correlations with the Eurocode 2 and fib Model Code 2010 predictions, suggesting codes do not describe this behavior correctly.

Surface roughness has no correlation with interface adhesion shear transfer, however, it will

influence the shear transfer when the interface has debonded (appendix 8). A rough interface might increase the probability that the cast concrete adheres better to the old concrete, but this was not the topic of research, since pre-cracked specimens rejected. A rough interface might increase the robustness of the cast joint.

Code expression safety

The code expressions for shear resistance of an unreinforced concrete-to-concrete interface are compared to test result characteristic values (Appendix 9). This demonstrates that the Eurocode 2 and fib Model Code 2010 expressions are conservative and are sufficiently safe.

5.2 R

ECOMMENDATIONS

The test setup used is the cause of peak stresses, additional studies utilizing a different test setup may be done to evaluate found relationships. The limited size of the test specimens might influence the found shear resistance, further experimental research might include larger scale direct shear tests to minimize the influence of the peak stresses at the load introduction sites.

To investigate the influence of differential elasticity moduli on shear behavior, further experimental research may be done. Material tests to determine the modulus of elasticity of each concrete are advised.

In this research, macroscopic roughness characteristics were quantified. However, microscopic roughness and porosity might have a large influence on interface shear behavior. These

characteristics are highly sensitive to production methods and environmental parameters. In future research this aspect could be investigated.

The influence of differential shrinkage stresses was not studied due to lack of temperature- and relative humidity data for the manufacturer production locations. These stresses may however influence the interface stress distribution. In future research, this aspect could be analyzed.

During post-test inspections, it was noted that the roughness characteristics of the cracked surface

During post-test inspections, it was noted that the roughness characteristics of the cracked surface

In document Eindhoven University of Technology MASTER Behavior of unreinforced concrete-to-concrete interfaces under shear loading Croes, L. (pagina 33-0)