Variation in Compressive Strength of Concrete aross Thickness of Placed Layer

Is the variation in the compressive strength of concrete across the thickness of horizontally cast elements negligibly small or rather needs to be taken into account at the design stage? There are conflicting answers to this question. In order to determine if the compressive strength of concrete varies across the thickness of horizontally cast elements, ultrasonic tests and destructive tests were carried out on core samples taken from a 350 mm thick slab made of class C25/30 concrete. Special point-contact probes were used to measure the time taken for the longitudinal ultrasonic wave to pass through the tested sample. The correlation between the velocity of the longitudinal ultrasonic wave and the compressive strength of the concrete in the slab was determined. The structure of the concrete across the thickness of the slab was evaluated using GIMP 2.10.4. It was found that the destructively determined compressive strength varied only slightly (by 3%) across the thickness of the placed layer of concrete. Whereas the averaged ultrasonically determined strength of the concrete in the same samples does not vary across the thickness of the analyzed slab. Therefore, it was concluded that the slight increase in concrete compressive strength with depth below the top surface is a natural thing and need not be taken into account in the assessment of the strength of concrete in the structure.


Introduction
The view that the compressive strength of concrete varies across the thickness of horizontally cast elements (concrete slabs, floorings, etc.) is seldom expressed in the literature on the subject. Opinions as to the significance of this variation are widely divided, as the following survey of literature indicates.
The research published by Stawiski [1][2][3] provided the direct incentive for this study of the distribution of concrete compressive strength along the height of horizontally cast elements. On the basis of ultrasonic tests of core samples taken from concrete, Stawiski found the compressive strength of the concrete to be lower in the top zone than in the bottom zone by as much as 40-50% [1][2][3]. The variation in compressive strength along the height of the cross section was approximately linear. The fall in ultrasonic wave velocity at the sample's top surface is ascribed by Stawiski [1] to the surface weakening effect connected with concrete consolidation resulting in the segregation of concrete components. The main factor responsible for the decrease in concrete compressive strength is considered to be porosity, which very strongly affects ultrasonic wave velocity. Also the inadequate curing of fresh concrete, damage to the structure of concrete caused by corrosion, and mechanical damage to the top surface of the concrete which can arise in the course of the service life of the element are also possible factors.
Stawiski [3] proposed to introduce (besides the grade of concrete) strength gradient ∇fc into the evaluation of concrete in horizontally cast elements (e.g., floor toppings). On the basis of his research [3] Stawiski pointed out that in, e.g., an approximately 15 cm thick element the strength gradient of the concrete at the depth of 10 cm from the bottom amounted to 0.7 MPa/cm, whereas in the layers situated

Ultrasonic Tests of Concrete
In order to verify the phenomenon of concrete compressive strength variation across the thickness of horizontally cast elements, samples with diameter d = 100 mm height h = 350 mm (Table 1), taken from a specially cast slab made of concrete C25/30 (the grade of the concrete was determined using concrete cubes cast when casting the slab) were subjected to ultrasonic tests. CEMII/BS-32.5 cement (270 kg/m 3 ), fly ash additive (60 kg/m 3 ), plasticizer (2.43 kg/m 3 ), water (170 kg/m 3 ) and 1879 kg/m 3 of natural aggregate (sand 0/2 mm −40%, gravel 2/8 mm −26%, gravel 8/16 mm −34%) were used in the concrete mix for the slab construction. The latter had been compacted by means of an immersion vibrator and cured for 28 in the laboratory conditions defined in standard [14]. The slab had been exposed to variable weather conditions for two years. Samples (01−06 in Figure 1) were drilled out of the slab perpendicularly to its top surface. For reference purposes specimens (07−12) were drilled out of the slab parallel with its top surface. Prior to the tests, the actual dimensions of the samples and their weight were determined (Table 1). kg/m 3 of natural aggregate (sand 0/2 mm −40%, gravel 2/8 mm −26%, gravel 8/16 mm −34%) were used in the concrete mix for the slab construction. The latter had been compacted by means of an immersion vibrator and cured for 28 in the laboratory conditions defined in standard [14]. The slab had been exposed to variable weather conditions for two years. Samples (01−06 in Figure 1) were drilled out of the slab perpendicularly to its top surface. For reference purposes specimens (07−12) were drilled out of the slab parallel with its top surface. Prior to the tests, the actual dimensions of the samples and their weight were determined (Table.1).  (Figures 1 and 2) were marked on the sides of the core samples. Velocity CL of ultrasonic wave passage through concrete was measured in two perpendicular directions. No concrete/probe coupling material was used. The probes were set perpendicularly to the tested side surface of the sample ( Figure 2). The distributions of velocity CL of longitudinal ultrasonic wave passage through the concrete were obtained from the tests (Tables 2 and  3, and Figures 3   A Unipan Materials Tester Type 543 with point-contact exponential probes [15] and a frequency of 40 kHz ( Figure 2) was used to measure the time taken for the longitudinal ultrasonic wave to pass through the tested sample. Prior to the tests, the instrument had been calibrated to determine the time taken for the ultrasonic wave to pass through the probes alone (t0 = 36.6 s). The details of the operation of exponential heads with point-to-point contact with the examined surface are described in detail in the paper [15]. The measuring points spaced at every 1 cm (Figures 1 and 2) were marked on the sides of the core samples. Velocity C L of ultrasonic wave passage through concrete was measured in two perpendicular directions. No concrete/probe coupling material was used. The probes were set perpendicularly to the tested side surface of the sample (Figure 2). The distributions of velocity C L of longitudinal ultrasonic wave passage through the concrete were obtained from the tests (Tables 2 and 3, and Figures 3 and 4).      A Unipan Materials Tester Type 543 with point-contact exponential probes [15] and a frequency of 40 kHz ( Figure 2) was used to measure the time taken for the longitudinal ultrasonic wave to pass through the tested sample. Prior to the tests, the instrument had been calibrated to determine the time taken for the ultrasonic wave to pass through the probes alone (t 0 = 36.6 µs). The details of the operation of exponential heads with point-to-point contact with the examined surface are described in detail in the paper [15].        Tables 2 and 3 and Figures 3 and 4 showed that the distributions of velocity C L of the longitudinal ultrasonic wave along the height of the core samples with d 100 mm were quite constant (except for the top layers). The mean velocity C L of ultrasonic wave propagation in the samples (01-06) taken perpendicularly to the top surface of the slab was C L1 = 3.54 km/s, a standard deviation s CL1 = 0.13 km/s and a variation coefficient ν CL1 = 3.67%. In the case of the samples (07-12) taken parallel with the top of the slab, the following were obtained: C L2 = 3.45 km/s, s CL2 = 0.072 km/s and ν CL2 = 2.09%. On the basis of the obtained velocities C L of the longitudinal ultrasonic wave in the range: C L = 3.5-4.5 km/s, it can be assessed [16] whether the quality of the concrete as good, whereas the velocities in the range of 3.0-3.5 km/s indicated dubious quality.
The observed slight fluctuations of velocity C L of the longitudinal ultrasonic wave in the inner layers of the concrete are due to local concrete defects (e.g., air voids) or local strengthening with larger aggregate grains. Lower velocities C L of the longitudinal ultrasonic wave were registered in the samples (01-06) taken perpendicularly to the top surface of the slab (Figures 3 and 5). In the samples (07-12) taken parallel with the top of the slab, a decline in velocity CL of the longitudinal ultrasonic wave was observed only at the edge constituting the side edge of the slab (Figures 4 and 6). the range of 3.0-3.5 km/s indicated dubious quality.
The observed slight fluctuations of velocity CL of the longitudinal ultrasonic wave in the inner layers of the concrete are due to local concrete defects (e.g., air voids) or local strengthening with larger aggregate grains. Lower velocities CL of the longitudinal ultrasonic wave were registered in the samples (01-06) taken perpendicularly to the top surface of the slab (Figures 3 and 5). In the samples (07-12) taken parallel with the top of the slab, a decline in velocity CL of the longitudinal ultrasonic wave was observed only at the edge constituting the side edge of the slab (Figures 4 and  6).
Initially, it was though that the falls in velocity CL of the longitudinal ultrasonic wave were due to the sample end effect. Ultimately, it was decided that this phenomenon in samples 01-06 was caused from the top by bleeding [17] and concrete sedimentation, and from the bottom by the improper vibration of the concrete by means of the immersion vibrator (the vibrator was not fully immersed in the freshly placed concrete). In samples 07-12, the fall in velocity CL of the longitudinal ultrasonic wave can be caused by the wall effect [9,10]. Figures 5 and 6 show the structure of the concrete along the height of the samples taken perpendicularly to and parallel with the top surface of the slab. The image of the structure of the samples in Figures 5 and 6 was prepared in GIMP 2.10.4 using the filter: LCHH(ab) component with a contrast of 50%. In Figure 5 the altered structure of the concrete is visible in the sample's upper part (an approximately 30-40 mm thick layer) and lower part (an approximately 30-50 mm thick layer). In these places, reduced velocities of the longitudinal wave velocity were observed. In Figure 6, the altered structure of the concrete can be seen in an approximately 20-80 mm thick layer located at the side wall of the slab. Also in this layer, falls in the velocity of the longitudinal ultrasonic wave were recorded.  the range of 3.0-3.5 km/s indicated dubious quality.
The observed slight fluctuations of velocity CL of the longitudinal ultrasonic wave in the inner layers of the concrete are due to local concrete defects (e.g., air voids) or local strengthening with larger aggregate grains. Lower velocities CL of the longitudinal ultrasonic wave were registered in the samples (01-06) taken perpendicularly to the top surface of the slab (Figures 3 and 5). In the samples (07-12) taken parallel with the top of the slab, a decline in velocity CL of the longitudinal ultrasonic wave was observed only at the edge constituting the side edge of the slab (Figures 4 and  6).
Initially, it was though that the falls in velocity CL of the longitudinal ultrasonic wave were due to the sample end effect. Ultimately, it was decided that this phenomenon in samples 01-06 was caused from the top by bleeding [17] and concrete sedimentation, and from the bottom by the improper vibration of the concrete by means of the immersion vibrator (the vibrator was not fully immersed in the freshly placed concrete). In samples 07-12, the fall in velocity CL of the longitudinal ultrasonic wave can be caused by the wall effect [9,10]. Figures 5 and 6 show the structure of the concrete along the height of the samples taken perpendicularly to and parallel with the top surface of the slab. The image of the structure of the samples in Figures 5 and 6 was prepared in GIMP 2.10.4 using the filter: LCHH(ab) component with a contrast of 50%. In Figure 5 the altered structure of the concrete is visible in the sample's upper part (an approximately 30-40 mm thick layer) and lower part (an approximately 30-50 mm thick layer). In these places, reduced velocities of the longitudinal wave velocity were observed. In Figure 6, the altered structure of the concrete can be seen in an approximately 20-80 mm thick layer located at the side wall of the slab. Also in this layer, falls in the velocity of the longitudinal ultrasonic wave were recorded.  Initially, it was though that the falls in velocity C L of the longitudinal ultrasonic wave were due to the sample end effect. Ultimately, it was decided that this phenomenon in samples 01-06 was caused from the top by bleeding [17] and concrete sedimentation, and from the bottom by the improper vibration of the concrete by means of the immersion vibrator (the vibrator was not fully immersed in the freshly placed concrete). In samples 07-12, the fall in velocity C L of the longitudinal ultrasonic wave can be caused by the wall effect [9,10]. Figures 5 and 6 show the structure of the concrete along the height of the samples taken perpendicularly to and parallel with the top surface of the slab. The image of the structure of the samples in Figures 5 and 6 was prepared in GIMP 2.10.4 using the filter: LCHH(ab) component with a contrast of 50%. In Figure 5 the altered structure of the concrete is visible in the sample's upper part (an approximately 30-40 mm thick layer) and lower part (an approximately 30-50 mm thick layer). In these places, reduced velocities of the longitudinal wave velocity were observed. In Figure 6, the altered structure of the concrete can be seen in an approximately 20-80 mm thick layer located at the side wall of the slab. Also in this layer, falls in the velocity of the longitudinal ultrasonic wave were recorded.

Ultrasonic Tests of Concrete
For further investigations the core samples (Table 1) were cut into smaller samples (Figure 7) with height h = 100 mm (h/d = 1). In the terminal samples (e.g., 01/1-the top of the sample, 01/3-the bottom of the sample) the actual end faces were left unchanged (or were slightly trimmed to make them level). The middle sample (e.g., 01/2) was cut to the required size of 100 mm. Then, the end faces were prepared by grinding for compressive strength tests (Figure 8).

Ultrasonic Tests of Concrete
For further investigations the core samples (Table 1) were cut into smaller samples (Figure 7) with height h = 100 mm (h/d = 1). In the terminal samples (e.g. 01/1 -the top of the sample, 01/3 -the bottom of the sample) the actual end faces were left unchanged (or were slightly trimmed to make them level). The middle sample (e.g. 01/2) was cut to the required size of 100 mm. Then, the end faces were prepared by grinding for compressive strength tests (Figure 8).  The compressive strength tests were carried out in conformance with standard [13] in the ZD100 strength testing machine (Figure 9a) satisfying the requirements of standard [18]. All the samples showed the same type of failure (Figure 9b). The parameters of the samples and the test results are presented in Table 2.

Ultrasonic Tests of Concrete
For further investigations the core samples (Table 1) were cut into smaller samples (Figure 7) with height h = 100 mm (h/d = 1). In the terminal samples (e.g. 01/1 -the top of the sample, 01/3 -the bottom of the sample) the actual end faces were left unchanged (or were slightly trimmed to make them level). The middle sample (e.g. 01/2) was cut to the required size of 100 mm. Then, the end faces were prepared by grinding for compressive strength tests (Figure 8).  The compressive strength tests were carried out in conformance with standard [13] in the ZD100 strength testing machine (Figure 9a) satisfying the requirements of standard [18]. All the samples showed the same type of failure (Figure 9b). The parameters of the samples and the test results are presented in Table 2. The compressive strength tests were carried out in conformance with standard [13] in the ZD100 strength testing machine (Figure 9a) satisfying the requirements of standard [18]. All the samples showed the same type of failure (Figure 9b). The parameters of the samples and the test results are presented in Table 2. The compressive strength tests were carried out in conformance with standard [13] in the ZD100 strength testing machine (Figure 9a) satisfying the requirements of standard [18]. All the samples showed the same type of failure (Figure 9b). The parameters of the samples and the test results are presented in Table 2.
(a) (b) Figure 9. The sample in strength testing machine: a) during loading, b) after failure. The concrete strength values (Table 4) yielded by the tests carried out on the100 mm high samples were used to evaluate the class of the concrete and the variation of strength along the core sample height (h = 350 mm) and were correlated with the results obtained using the ultrasonic method. According to standard [19], the result of concrete compressive strength tests carried out on cylindrical specimens with diameter d = 100 mm and height h = 100 mm, cut out of a structure directly corresponded to the strength of concrete determined on 150 × 150 × 150 mm standard cubes (f ck,is = f ck,is,cube ). Standard [19] states that due to drilling, which undoubtedly can slightly damage the core's material, the strengths of core samples determined in-situ are usually lower than the strengths of the standard samples. For this reason, it is allowed to use a correction factor of 0.85, understood as a ratio of the in-situ characteristic compressive strength to the characteristic compressive strength determined on the standard samples. As a result, the concrete compressive strength values coming directly from strength tests are increased.
The mean compressive strength of the concrete, determined on the 18 samples taken perpendicularly to the top surface of the slab, amounted to f m (18),is = 31.45 MPa (the minimum value f is,lowest = 30.58 MPa). The mean standard deviation amounted to s = 0.49 MPa. The coefficient k 1 = 1.48 was assumed. The characteristic compressive strength of the concrete in the structure (f ck,is ) was determined on the basis of standard [13], from the condition: f ck,is = min(f m (18) This confirms the observation that the strength of core samples drilled out horizontally is lower (on average by 8% [12,13]) than that of core samples drilled out vertically.
On the basis of the obtained f ck,is,cube values, the actual strength class of the concrete in the structure is estimated to be f ck,is,cube = 30.72 MPa and 29.91 MPa, respectively. When the correction factor of 0.85 is applied, this gives the concrete strength class respectively f ck,is,cube = 36.1 MPa and 35.2 MPa, which corresponds to at least concrete class C25/30.

Scaling of Correlation Curve
On the basis of the measurements, the mean longitudinal ultrasonic wave passage velocities C L were correlated with the mean compressive concrete strengths f is . When calculating the mean longitudinal ultrasonic wave passage velocity C L , the values from the areas of disturbances near the ends of the samples were rejected. The correlation curve was scaled according to the procedure described in standard [13] (version 2). In accordance with [16], a hypothetical base regression curve for ordinary concrete, i.e., f CL,b = 2.39C L 2 − 7.06C L + 4.2 for C L = 2.4-5.0 km/s, was adopted. Then, the differences δf between experimental compressive strength f is and the strength obtained from base curve f CL , as well as the mean value δf m(n) of the differences and standard deviation s were determined. The shift of the base correlation curve was calculated from the relation ∆f = δf m(n) − k 1 ·s for coefficient k 1 = 1.48 [13]. Ultimately, the corrected correlation curve f CL = f CL,b + ∆f has the form f CL = 2.39C L 2 − 7.06C L + 25.09. The obtained curve only slightly differs from the curves determined separately for samples 01 ÷ 06 and 07-12.
The obtained correlation was evaluated using two accuracy characteristics, i.e., the correlation coefficient η > 0.75 and the mean square relative deviation ν k ≤ 12 ≤ %. The correlation coefficient amounted to:  (1) and the mean square relative deviation to: Thus, it can be said that a good correlation between the mean longitudinal ultrasonic wave passage velocities C L and the mean concrete compressive strengths f is was obtained. The

Analysis of Test Results
With the corrected correlation curve: f CL = 2.39·C L 2 − 7.06·C L + 25.09, it was possible to trace the variation of the compressive strength of the concrete along the height of the analyzed samples. Figures 10 and 11 show the variations of concrete compressive strength along the height of the core samples respectively, and perpendicular to ( Figure 10) and parallel with ( Figure 11) the top surface of the slab. Further, the results of the destructive tests and the averaged results of the ultrasonic tests for the particular samples with a height h = 100 mm are included in the diagrams.  An analysis of the concrete compressive strength values for the particular samples 01-06 ( Figure 10) taken perpendicularly to the top plane of the slab indeed showed a slight increase (by 3%) in this strength in the sample's lower part relative to its upper part. A similar phenomenon (also an increase by approximately 2.6%) was observed for samples 07-12 ( Figure 11) taken parallel with the top plane of the slab. However, it should be noted that the compressive strength values were strongly averaged for the samples and included the effect of various factors connected with the destructive test itself.  The averaged compressive strength results obtained from the ultrasonic measurements showed (Figures 10 and 11), however, that there was no increase in the compressive strength of the concrete along the height of the sample. This applies to the samples taken both perpendicularly to and parallel with the top plane of the slab.
The ultrasonic tests indicate that the variation in the compressive strength of concrete along the height of the sample is minimal and random. It can even be considered as negligible. The obtained results do not corroborate Stawiski's theses [1][2][3], but confirm the results reported in [7][8][9][10].
The decreases in the compressive strength of the concrete occurring at the ends of the samples taken perpendicularly to the top plane of the slab (samples 01-06) and at the edge constituting the side edge of the slab for the samples taken parallel with the top plane of the slab (samples 07-12) were found to be interesting.

Conclusions
The following conclusions emerge from the investigations of the compressive strength of concrete carried out on core samples taken perpendicularly to and parallel with the top surface of the approximately 35 cm thick element, using different testing methods (the ultrasonic method and the destructive method): The concrete compressive strength destructively determined along the height of the placed layer of concrete changed slightly (by 3%-samples 01-06) with a depth below the top surface of the element. The averaged concrete strength determined on the basis of the ultrasonic tests of the same samples did not vary across the thickness of the analyzed slab.

1.
The obtained compressive strength increments across the thickness of the placed layer of concrete do not corroborate Stawiski's theses [1][2][3], but confirm the results reported in, [7][8][9]. Therefore, there can be agreement with Neville's statement [10] that the slight increase in concrete compressive strength with depth below the top surface is a natural thing and need not to be taken into account in the evaluation of the strength of concrete in the structure.

2.
The concrete compressive strength determined on core samples only slightly depends on the depth of where the sample came from (provided the ingredients of the concrete do not segregate as it is being placed and compacted). 3.
The use of the ultrasonic method for testing concrete with point-contact exponential probes showed the variation in concrete strength along the height of the core sample could be quite accurately evaluated and areas of lower quality concrete could be indicated. This was mainly from the thick layer (approximately 30-40 mm) extending from the top edge and the thick layer (approximately 30-50 mm) extending from the bottom edge of the samples 01-06 taken perpendicularly to the upper plane of the element. Further, from the thick layer (approximately 20-80 mm) extending from the edge constituting the side plane of the slab for the samples taken parallel with the top plane of the element (samples 07-12). The decline in the strength of the concrete in the upper part of samples 01-06 is caused by the bleeding of water from the concrete mixture (the bleeding phenomenon [17]) and the sedimentation of the latter. While in the lower part of the samples, it is due to the improper vibration of the placed layer of concrete mixture. The decrease in concrete strength at the side edge of the slab in the case of samples 07-12 can be due to the wall effect [9,10].

4.
From the point of view of the assessment of the concrete structure, supplementary tests on the slab in the future should be carried out using ultrasonic tomography [20,21]. 5.
The ultrasonic method of testing concrete by means of point-contact exponential probes enables the accurate assessment of the quality of concrete (the segregation of concrete components, porosity, density, strength, etc.) along the height of a core sample drilled out perpendicularly to the placed layer.