# Validation of Selected Non-Destructive Methods for Determining the Compressive Strength of Masonry Units Made of Autoclaved Aerated Concrete

^{*}

## Abstract

**:**

^{3}), at various moisture levels. Empirical data including the shape and size of specimens, were established from tests on 494 cylindrical and cuboid specimens, and standard cube specimens 100 mm × 100 mm × 100 mm using the general relationship for ordinary concrete (Neville’s curve). The effect of moisture on AAC was taken into account while determining the strength f

_{Bw}for 127 standard specimens tested at different levels of water content (w = 100%, 67%, 33%, 23%, and 10%). Defined empirical relations were suitable to correct the compressive strength of dry specimens. For 91 specimens 100 mm × 100 mm × 100 mm, the P-wave velocity c

_{p}was tested with the transmission method using the ultrasonic pulse velocity method with exponential transducers. The curve (f

_{Bw}–c

_{p}) for determining the compressive strength of AAC elements with any moisture level (f

_{Bw}) was established. The developed methods turned out to be statistically significant and can be successfully applied during in-situ tests. Semi-non-destructive testing can be used independently, whereas the non-destructive technique can be only applied when the developed curve f

_{bw}–c

_{p}is scaled.

## 1. Introduction

_{k}. These methods cause quite a significant damage to the wall. Consequently, the number of tests to be performed becomes sharply limited.

_{b}into f

_{m}), and using standard equations in their exponential form f

_{k}= Kf

_{b}

^{α}f

_{m}

^{β}(K—coefficient specified in EC-6). There are not many tests in this field, and the performed ones are rather single cases [14,15,16] and usually refer to solid brick and traditional mortar. Non-destructive and semi-non-destructive tests are indirect techniques because they do not determine compressive strength of the wall, but the strength of its component (masonry unit or mortar). Neither NDT nor MDT techniques can be used to determine compressive strength of the wall without performing destructive tests to scale the suitable correlation curve to convert obtained strength values into the requested value f

_{k}[17].

_{B}and calculated (with empirical factors η

_{w}and δ expressing the specimen moisture and shape) an average normalized compressive strength. This procedure involves the relationship according to Eurocode 6 [18], and is used to calculate the specific compressive strength of the masonry wall:

_{b}—average normalized compressive strength of masonry unit determined for specimens 100 mm × 100 mm × 100 mm, f

_{B}—average compressive strength of the whole masonry unit or a specimen with moisture content w = 0, f

_{Bw}—compressive strength of the specimen from the masonry with real moisture content.

^{3}, and its compressive strength varies from 1.5 to 10 N/mm

^{2}. Taking into account all construction materials, AAC is characterized by the highest thermal insulation power (thermal conductivity coefficient λ is 8–10 times lower compared to brick or reinforced concrete). AAC has been commonly used since the middle of the 1950s. This material (>40% of the construction segment in Europe) is used for masonry structures, precast wall or floor elements, and lintels [24]. The open-pore structure explains why AAC is sensitive to direct exposure to moisture, which results in worse insulating and strength properties. The available articles, apart from general relations specified in standards, do not contain detailed references expressed as empirical relations.

_{b}on the basis of tests performed on specimens of any shape and real moisture content, and to develop the universal curve representing ultrasound velocity c

_{p}and compressive strength, taking into account moisture content.

_{Bw}using semi-non-destructive techniques. Neville’s curve [20], in the commonly known form from diagnosing ordinary concrete, was used and calibrated to nominal density classes of AAC (400, 500, 600, and 700). Knowing that, apart from the effect of rising and hardening [25,26], also moisture content in AAC influences the compressive strength, tests were performed and additional empirical relations were defined. The analysis included test results [27] from 494 + 127 cylindrical and cuboid specimens used to develop empirical curves. Results obtained from destructive tests on standard cube specimens 100 mm × 100 mm × 100 mm at different moisture content were correlated with results from testing velocity of P-wave generated by point transducers with the transmission method. Developed curves and the test procedure can be employed in a widely understood diagnostic of masonry structures to evaluate the safety of AAC structures.

## 2. Minor-Destructive Testing

#### 2.1. Specimens, Technique of Tests, and Analysis

_{B}(in accordance with Appendix B to the standard EN 771-4 [16]). Drilled core and cube specimens are illustrated in Figure 1. All specimens drilled from blocks were dried until constant weight at a temperature of 105 °C ± 5 °C (for at least 36 h).

_{B}was determined for cube specimens 100 mm × 100 mm × 100 mm (dried until constant weight). The summary of our test results for core and cube specimens is shown in Table 1 and Table 2. Tables show dimensions and strength of each tested specimen, average strength and coefficient of variation for each tested series. Arrows indicate the direction of AAC growth. When dried until constant weight, each cuboid specimen was weighed and its apparent density was calculated (Table 3).

#### 2.2. Determining an Empirical Curve in Air-Dry Conditions

_{1}and σ

_{2}are failure stresses for specimens with volume V

_{1}and V

_{2}, respectively; m is constant.

_{c,cube150}obtained from standard specimens 150 mm × 150 mm × 150 mm with strength f

_{B}for specimens 100 mm × 100 mm × 100 mm drilled from masonry units, and the ratio 152hd with volume of the standard specimen 100hd, the relationship (3) can be expressed as:

_{B}is the compressive strength of normalised specimen 100 mm × 100 mm × 100 mm with moisture content w = 0, f

_{c}is the compressive strength of a specimen with any shape and dimensions, and moisture content w = 0, a and b are constant coefficients for the curve, $y={f}_{\mathrm{c}}/{f}_{\mathrm{B}}$ is the ratio of compressive strength, and $x=V/(100hd)+h/d$ is the dimensionless coefficient representing the effect of specimen volume and slenderness.

_{c}/f

_{B}≠ 1. To obtain the ratio f

_{c}/f

_{B}= 1 from normalized specimens, curves needed to be translated in parallel to the intercept axis using the additive correction factor Δb for the common curve:

_{2}= n − k − 1 and f

_{1}= k (k = 1), and the assumed statistical significance α = 5%. The obtained statistical values were compared to critical values from the Fisher–Snedecor tables (F

_{α,f1,f2}). Statistical results are presented in Table 4. Analyses demonstrated that correlations were significant at the assumed statistical significance equal to 5%, thus the proposed model based on the general Neville relation was statistically significant. Besides, descriptive statistics based on the Guillford scale [32] was applied. It describes the correlation degree of individual curves. For concrete with the lowest density, obtained values R were sufficient for evaluating the relationship as poor, and for other classes of density R > 0.5, correlations could be regarded as moderate and the value of correlation factor as real. For the common curve, the obtained coefficient was R = 0.512. Thus, the relationship was moderate and real.

#### 2.3. Calibrating a Curve in Air-Dry Conditions

_{w}and b

_{w}of the common curve were used to develop correlations illustrated in Figure 5.

_{w}= 0.321, and b

_{w}= 0.730 (see Table 4).

#### 2.4. Calibrating an Empirical Curve in Moisture Conditions

_{w}is the mass of wet specimen, and m

_{s}is the mass of specimen dried until constant weight.

_{max}in AAC corresponded to the level of water, at which no further increase in mass m

_{w}was observed as the effect of passage of (capillary) water. Relative moisture was calculated as the ratio of current and maximum moisture w/w

_{max}.

_{max}= 100%, 67%, 33%, 23%, 10%, and 0%. Average test results for individual series of specimens are shown in Table 5.

^{3}to 674 kg/m

^{3}, the maximum moisture content was varying within w

_{max}= 53.3–89.9%, which made it possible to determine a straight line of the least square in the following form:

_{Bw}, and the results are illustrated in Figure 6a as a function of moisture w. Figure 6b presents the obtained strength values with respect to the strength f

_{B}of dry (w = 0) AAC as a function of relative moisture w/w

_{max}.

_{Bw}calculated from Equations (18) and (19) included the moisture effect, so it did not require conversion to average normalized compressive strength f

_{b}.

_{w}= 0.8 recommended by the standard EN 772-1 [19], and used to take into consideration the effect of moisture level. The standard recommendation provides the safe reduction of compressive strength only for the moisture level w/w

_{max}= 0.2. Tests on walls with higher moisture content showed that compressive strength could be even reduced by 40%, that is, over twice more than the provisions recommend.

_{k}required at first, taking into account varying shape and moisture, in-situ estimation of moisture content, specimen drilling, estimation of density, and compressive strength, and then the conversion relevant to moisture. Compressive strength calculated from the Equations (18) or (19) could be substituted to the Equation (1).

## 3. Ultrasonic Non-Destructive Method

^{3}should not exceed 25 cm, and at both-side access—15 cm [37].

#### 3.1. Testing Technique of Specimens

_{max}= 100%, 67%, 33%, 23%, and 10%, and specimens dried until constant weight w/w

_{max}= 0% were used in tests. Each series of elements included at least > 20 specimens, and 91 specimens in total were tested.

_{1}= 4.2 mm and ø

_{2}= 50 mm, and frequency 54 kHz were employed. The applied research methodology and equipment was also used for testing also for ultrasonic tomography for concrete [40,41] or masonry [42,43].

^{3}to 2379 m/s in concrete of class 700 kg/m

^{3}. An increase in P-wave velocity c

_{p}was also proportional to density increase in wet specimens.

#### 3.2. Calibrating a Curve in Air-Dry Conditions

_{B}. At the beginning, the curve representing the relationship between the average measured ultrasound velocity as a function of compressive strength f

_{Bw}of wet AAC, grouping results by AAC density (Figure 8a). Higher sound velocity was found in concrete with greater density and compressive strength. Linear dependence, equations of which are illustrated in Figure 8a, are adequately precise approximations. Figure 8b illustrates results for compressive strength and corresponding ultrasound velocity of dry AAC (w/w

_{max}= 0%), selected from each density class of AAC. Then, the relationship c

_{p}–f

_{B}was calculated with the least square method. For example, Figure 8b also shows the relationship of concrete with maximum moisture content (w/w

_{max}= 100%), obtained similarly.

_{max}= 0%, the following empirical relationship was obtained:

^{2}= 0.98.

#### 3.3. Calibrating a Curve in Moisture Conditions

_{max}and densities, was found with the least square method (Figure 9a). The equation of the common curve was:

_{w}, b

_{w}, and c

_{w}for the common curve, and then plotted to the graph Figure 9b.

_{bw}–c

_{p}illustrated in Figure 9a was the same as for ordinary concrete [1]. Linear and parabolic relations were obtained for solid brick [21,44]. Generally, the result was similar to predictions. Taking into account that ultrasound velocity depends on the modulus of elasticity E, Poisson’s ratio ν, and density ρ, and connected with the relationship ${c}_{\mathrm{p}}=\sqrt{E\left(1-\nu \right)/\rho \left(1+\nu \right)\left(1-2\nu \right)}$, it was easily demonstrated that greater density caused by moisture content resulted in an increase in the modulus of elasticity. Obtained curves shown in Figure 9b are statistic. High R

^{2}values represent non-linear correlations. All curves had the minimum at moisture content in the range of w/w

_{max}= 0.4–0.5. As a consequence, a difference in results with reference to the common curve will be the biggest. The curve obtained at this moisture content f

_{bw}–c

_{p}was likely to be shifted downwards. Further studies require additional tests at moisture content in the range of w/w

_{max}= 0.4–0.5.

_{Bw}–c

_{p}for AAC with any moisture level and density:

## 4. Procedure Algorithm for Determining Characteristic Compressive Strength of Masonry

## 5. Conclusions

_{w}= 0.8 recommended by the standard PN-EN 772-1 may give dangerously overestimated strength of masonry with moisture content w > 20%.

^{3}, minimum velocity was 1847 m/s in concrete with density of 400 kg/m

^{3}). Increasing density of AAC caused a significant reduction of the velocity.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Testing compressive strength of AAC specimens [27]: (

**a**) tests on cores using a strength testing machine with an operating range of 100 kN, and (

**b**) tests on cuboid specimens using a strength testing machine with an operating range of 3000 kN.

**Figure 3.**Destruction of specimens with varying slenderness ratio [27]: (

**a**) specimen 143 mm × 143 mm × 143 mm, (

**b**) specimen 100 mm × 100 mm × 200 mm, and (

**c**) specimen 80 mm × 80 mm × 158 mm.

**Figure 6.**Test results for AAC strength, taking into account moisture level: (

**a**) strength f

_{Bw}as a function of moisture w, and (

**b**) relative strength of AAC f

_{Bw}/f

_{B}as a function w/w

_{max}.

**Figure 7.**A test stand for measuring ultrasound velocity: (

**a**) specimen geometry and elements of the stand (given in millimeters), (

**b**) geometry of exponential transducer, and (

**c**) a test stand; 1, tested AAC specimen 100 mm × 100 mm × 100 mm; 2, exponential transducers; 3, cables connecting transducers with recording equipment; 4, recording equipment; and 5, an insulating pad.

**Figure 8.**Results from P-waves velocity testing: (

**a**) compressive strength of AAC including density classes, and (

**b**) AAC strength in wet concrete (f

_{Bw}) and totally dry concrete (f

_{B}).

**Figure 9.**Results from ultrasound velocity testing: (

**a**) common curve f

_{Bw}–c

_{p}for all AAC densities and moisture levels, and (

**b**) equations for curve coefficients at varying moisture content in AAC f

_{Bw}.

No. | Class of Density kg/m^{3} | Specimen Type | Dimensions, mm | No. of Specimens n | Average Compressive Strength f_{ci}, N/mm^{2} | Standard Deviation $\mathit{s}=\sqrt{\frac{{\left({\mathit{f}}_{\mathbf{i}}-{\mathit{f}}_{\mathbf{ci}}\right)}^{2}}{\mathit{n}-1}},\mathbf{N}/{\mathbf{mm}}^{2}$ | C.O.V $\frac{\mathit{s}}{{\mathit{f}}_{\mathbf{ci}}},$ % | |
---|---|---|---|---|---|---|---|---|

Diameter, ø | Height, h | |||||||

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

1 | 400 | 150 | 150 | 6 | 2.84 | 0.40 | 14 | |

2 | 301 | 3 | 2.33 | 0.13 | 6 | |||

3 | 76 | 3 | 2.70 | 0.06 | 2 | |||

4 | 97.6 | 97.8 | 4 | 2.61 | 0.29 | 11 | ||

5 | 195 | 3 | 2.16 | 0.21 | 10 | |||

6 | 49 | 4 | 2.81 | 0.39 | 14 | |||

7 | 79.4 | 79.2 | 3 | 2.53 | 0.25 | 10 | ||

8 | 159 | 3 | 2.26 | 0.26 | 12 | |||

9 | 40.6 | 3 | 2.85 | 0.17 | 6 | |||

10 | 61 | 61 | 4 | 2.77 | 0.17 | 6 | ||

11 | 121.8 | 3 | 2.65 | 0.12 | 5 | |||

12 | 31.8 | 5 | 2.51 | 0.39 | 15 | |||

13 | 39.5 | 40 | 5 | 2.82 | 0.42 | 15 | ||

14 | 79 | 4 | 2.28 | 0.34 | 15 | |||

15 | 20.5 | 4 | 2.60 | 0.35 | 14 | |||

16 | 25 | 24.4 | 3 | 2.33 | 0.30 | 13 | ||

17 | 49.2 | 3 | 2.69 | 0.42 | 16 | |||

18 | 12.5 | 3 | 3.56 | 0.33 | 9 | |||

1 | 500 | 150 | 150 | 6 | 2.94 | 0.25 | 9 | |

2 | 301 | 3 | 3.28 | 0.18 | 6 | |||

3 | 76 | 3 | 3.01 | 0.12 | 4 | |||

4 | 97.6 | 97.8 | 4 | 2.88 | 0.16 | 6 | ||

5 | 195 | 3 | 3.09 | 0.06 | 2 | |||

6 | 49 | 4 | 3.15 | 0.29 | 9 | |||

7 | 79.4 | 79.2 | 3 | 3.30 | 0.12 | 4 | ||

8 | 159 | 3 | 2.90 | 0.21 | 7 | |||

9 | 40.6 | 4 | 3.27 | 0.45 | 14 | |||

10 | 61 | 61 | 4 | 3.21 | 0.23 | 7 | ||

11 | 121.8 | 3 | 3.17 | 0.26 | 8 | |||

12 | 31.8 | 5 | 3.19 | 0.18 | 6 | |||

13 | 39.5 | 40 | 4 | 2.94 | 0.30 | 10 | ||

14 | 79 | 4 | 2.89 | 0.32 | 11 | |||

15 | 20.5 | 4 | 3.63 | 0.36 | 10 | |||

16 | 25 | 24.4 | 4 | 2.91 | 0.27 | 9 | ||

17 | 49.2 | 3 | 3.16 | 0.18 | 6 | |||

18 | 12.5 | 4 | 4.06 | 0.25 | 6 | |||

1 | 600 | 150 | 150 | 5 | 5.06 | 0.36 | 7 | |

2 | 301 | 3 | 4.23 | 0.21 | 5 | |||

3 | 76 | 3 | 5.11 | 0.68 | 13 | |||

4 | 97.6 | 97.8 | 4 | 4.49 | 0.22 | 5 | ||

5 | 195 | 3 | 4.26 | 0.18 | 4 | |||

6 | 49 | 4 | 5.01 | 0.61 | 12 | |||

7 | 79.4 | 79.2 | 4 | 4.43 | 0.09 | 2 | ||

8 | 159 | 3 | 4.73 | 0.25 | 5 | |||

9 | 40.6 | 4 | 5.14 | 0.52 | 10 | |||

10 | 61 | 61 | 4 | 4.65 | 0.47 | 10 | ||

11 | 121.8 | 3 | 4.54 | 0.16 | 3 | |||

12 | 31.8 | 5 | 5.19 | 0.66 | 13 | |||

13 | 39.5 | 40 | 4 | 4.87 | 0.53 | 11 | ||

14 | 79 | 3 | 4.18 | 0.31 | 8 | |||

15 | 20.5 | 4 | 6.00 | 0.81 | 14 | |||

16 | 25 | 24.4 | 4 | 5.17 | 0.27 | 5 | ||

17 | 49.2 | 3 | 4.79 | 0.64 | 13 | |||

18 | 12.5 | 4 | 6.88 | 0.76 | 11 | |||

1 | 700 | 150 | 150 | 5 | 7.12 | 0.96 | 14 | |

2 | 301 | 3 | 7.25 | 0.56 | 8 | |||

3 | 76 | 4 | 7.69 | 0.63 | 8 | |||

4 | 97.6 | 97.8 | 4 | 7.37 | 0.76 | 10 | ||

5 | 195 | 3 | 7.22 | 0.42 | 6 | |||

6 | 49 | 4 | 7.93 | 0.28 | 4 | |||

7 | 79.4 | 79.2 | 3 | 6.77 | 0.35 | 5 | ||

8 | 159 | 3 | 7.25 | 0.57 | 8 | |||

9 | 40.6 | 4 | 8.87 | 0.36 | 4 | |||

10 | 61 | 61 | 4 | 7.25 | 1.04 | 14 | ||

11 | 121.8 | 3 | 7.05 | 0.51 | 7 | |||

12 | 31.8 | 5 | 8.57 | 0.35 | 4 | |||

13 | 39.5 | 40 | 3 | 7.55 | 0.32 | 4 | ||

14 | 79 | 3 | 7.21 | 1.08 | 15 | |||

15 | 20.5 | 4 | 9.18 | 0.77 | 8 | |||

16 | 25 | 24.4 | 3 | 7.66 | 0.77 | 10 | ||

17 | 49.2 | 3 | 7.73 | 0.40 | 5 | |||

18 | 12.5 | 4 | 13.42 | 0.95 | 7 |

No. | Class of Density kg/m^{3} | Specimen Type | Dimensions, mm | No. of Specimens n | Average Compressive Strength f_{ci}, N/mm^{2} | Standard Deviation $\mathit{s}=\sqrt{\frac{{\left({\mathit{f}}_{\mathbf{i}}-{\mathit{f}}_{\mathbf{ci}}\right)}^{2}}{\mathit{n}-1}},$ N/mm ^{2} | C.O.V $\frac{\mathit{s}}{{\mathit{f}}_{\mathbf{ci}}},$ % | ||
---|---|---|---|---|---|---|---|---|---|

Width, d | Thickness, b | Height, h | |||||||

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

1 | 400 | 143 | 143 | 143 | 3 | 2.80 | 0.18 | 6 | |

2 | 72 | 3 | 2.91 | 0.14 | 5 | ||||

3 | 285 | 3 | 2.47 | 0.05 | 2 | ||||

4 | 100 | 100 | 100 * | 6 | 2.88 | 0.36 | 12 | ||

5 | 50 | 3 | 2.59 | 0.24 | 9 | ||||

6 | 200 | 3 | 3.16 | 0.13 | 4 | ||||

7 | 80 | 80 | 80 | 3 | 3.12 | 0.23 | 7 | ||

8 | 39 | 3 | 3.60 | 0.44 | 12 | ||||

9 | 158 | 3 | 2.71 | 0.15 | 5 | ||||

10 | 59 | 59 | 59 | 3 | 2.99 | 0.11 | 4 | ||

11 | 30 | 3 | 3.16 | 0.17 | 5 | ||||

12 | 121 | 3 | 2.98 | 0.08 | 3 | ||||

13 | 40 | 40 | 40 | 3 | 2.85 | 0.07 | 3 | ||

14 | 19.6 | 3 | 3.02 | 0.07 | 2 | ||||

15 | 78.5 | 3 | 2.77 | 0.41 | 15 | ||||

16 | 24 | 24 | 24 | 3 | 2.80 | 0.20 | 7 | ||

17 | 12.5 | 3 | 3.23 | 0.56 | 17 | ||||

18 | 49 | 3 | 2.43 | 0.26 | 11 | ||||

1 | 500 | 143 | 143 | 143 | 3 | 2.33 | 0.28 | 12 | |

2 | 72 | 3 | 3.74 | 0.06 | 2 | ||||

3 | 285 | 3 | 2.16 | 0.11 | 5 | ||||

4 | 100 | 100 | 100 * | 6 | 3.59 | 0.13 | 4 | ||

5 | 50 | 3 | 3.29 | 0.13 | 4 | ||||

6 | 200 | 3 | 3.40 | 0.06 | 2 | ||||

7 | 80 | 80 | 80 | 3 | 3.31 | 0.15 | 5 | ||

8 | 39 | 3 | 3.67 | 0.11 | 3 | ||||

9 | 158 | 3 | 2.48 | 0.22 | 9 | ||||

10 | 59 | 59 | 59 | 3 | 2.83 | 0.09 | 3 | ||

11 | 30 | 3 | 3.20 | 0.55 | 17 | ||||

12 | 121 | 3 | 2.94 | 0.17 | 6 | ||||

13 | 40 | 40 | 40 | 3 | 2.90 | 0.04 | 1 | ||

14 | 19.6 | 3 | 3.28 | 0.21 | 6 | ||||

15 | 78.5 | 3 | 2.77 | 0.44 | 16 | ||||

16 | 24 | 24 | 24 | 3 | 4.78 | 0.39 | 8 | ||

17 | 12.5 | 3 | 4.92 | 0.90 | 18 | ||||

18 | 49 | 3 | 1.79 | 0.10 | 6 | ||||

1 | 600 | 143 | 143 | 143 | 3 | 3.97 | 0.10 | 2 | |

2 | 72 | 3 | 5.69 | 0.10 | 2 | ||||

3 | 285 | 3 | 3.58 | 0.25 | 7 | ||||

4 | 100 | 100 | 100 * | 6 | 4.95 | 0.35 | 7 | ||

5 | 50 | 3 | 5.80 | 0.35 | 6 | ||||

6 | 200 | 3 | 5.34 | 0.61 | 11 | ||||

7 | 80 | 80 | 80 | 3 | 6.01 | 0.75 | 12% | ||

8 | 39 | 3 | 6.60 | 0.12 | 2 | ||||

9 | 158 | 3 | 4.45 | 0.19 | 4 | ||||

10 | 59 | 59 | 59 | 3 | 4.58 | 0.08 | 2 | ||

11 | 30 | 3 | 5.85 | 0.04 | 1 | ||||

12 | 121 | 3 | 4.84 | 0.09 | 2 | ||||

13 | 40 | 40 | 40 | 3 | 5.81 | 0.41 | 7 | ||

14 | 19.6 | 3 | 5.06 | 0.17 | 3 | ||||

15 | 78.5 | 3 | 5.65 | 0.20 | 4 | ||||

16 | 24 | 24 | 24 | 3 | 6.02 | 0.74 | 12 | ||

17 | 12.5 | 3 | 6.30 | 0.19 | 3 | ||||

18 | 49 | 3 | 4.19 | 0.91 | 22 | ||||

1 | 700 | 143 | 143 | 143 | 3 | 4.88 | 1.03 | 21 | |

2 | 72 | 3 | 7.21 | 0.27 | 4 | ||||

3 | 285 | 3 | 5.28 | 0.44 | 8 | ||||

4 | 100 | 100 | 100 * | 6 | 8.11 | 0.58 | 7 | ||

5 | 50 | 3 | 7.02 | 1.07 | 15 | ||||

6 | 200 | 3 | 7.56 | 0.25 | 3 | ||||

7 | 80 | 80 | 80 | 3 | 6.31 | 0.27 | 4 | ||

8 | 39 | 3 | 8.79 | 0.89 | 10 | ||||

9 | 158 | 3 | 6.50 | 0.98 | 15 | ||||

10 | 59 | 59 | 59 | 3 | 5.76 | 0.34 | 6 | ||

11 | 30 | 3 | 6.31 | 1.10 | 17 | ||||

12 | 121 | 3 | 4.65 | 0.95 | 20 | ||||

13 | 40 | 40 | 40 | 3 | 5.48 | 0.52 | 10 | ||

14 | 19.6 | 3 | 7.00 | 0.22 | 3 | ||||

15 | 78.5 | 3 | 6.71 | 0.29 | 4 | ||||

16 | 24 | 24 | 24 | 3 | 5.38 | 1.98 | 37 | ||

17 | 12.5 | 3 | 9.37 | 1.96 | 21 | ||||

18 | 49 | 3 | 4.89 | 1.66 | 34 |

_{B}.

No. | Nominal Class of Density, kg/m^{3} | No. of Cuboid Specimens (see Table 2) | Average Density, kg/m^{3} | Standard Deviation s, kg/m^{3} | C.O.V., % |
---|---|---|---|---|---|

1 | 400 | 57 | 397 | 22.01 | 6 |

2 | 500 | 57 | 492 | 15.86 | 3 |

3 | 600 | 57 | 599 | 13.39 | 2 |

4 | 700 | 57 | 674 | 19.83 | 3 |

Density Range of AAC, Average Density ρ, (Nominal Class of Density) kg/m ^{3} | Coefficient for Curve | R | Additive Correction Factor Δb | Corrected Coefficient for Curve b _{kor} | Curve Equation | n | $\begin{array}{c}{\mathit{F}}_{\mathbf{exp}}\\ {\mathit{F}}_{\mathsf{\alpha},{\mathbf{f}}_{1},{\mathbf{f}}_{2}}\end{array}$ | |
---|---|---|---|---|---|---|---|---|

a | b | |||||||

from 375 to 446 397, (400) | 0.159 | 0.857 | 0.324 | 0.06 | 0.921 | $\frac{{f}_{\mathrm{c}}}{{f}_{\mathrm{B}}}=0.921+\frac{0.159}{\frac{V}{100hd}+\frac{h}{d}}$ | 123 | $\begin{array}{c}14.19\\ 3.919\end{array}$ |

from 462 to 532 492, (500) | 0.312 | 0.682 | 0.533 | 0.16 | 0.844 | $\frac{{f}_{\mathrm{c}}}{{f}_{\mathrm{B}}}=0.844+\frac{0.312}{\frac{V}{100hd}+\frac{h}{d}}$ | 125 | $\begin{array}{c}48.81\\ 3.918\end{array}$ |

from 562 to 619 599, (600) | 0.349 | 0.779 | 0.612 | 0.05 | 0.826 | $\frac{{f}_{\mathrm{c}}}{{f}_{\mathrm{B}}}=0.826+\frac{0.349}{\frac{V}{100hd}+\frac{h}{d}}$ | 124 | $\begin{array}{c}73.06\\ 3.919\end{array}$ |

from 655 to 725 674, (700) | 0.454 | 0.608 | 0.614 | 0.16 | 0.773 | $\frac{{f}_{\mathrm{c}}}{{f}_{\mathrm{B}}}=0.773+\frac{0.454}{\frac{V}{100hd}+\frac{h}{d}}$ | 122 | $\begin{array}{c}72.62\\ 3.920\end{array}$ |

common curve | a_{w} = 0.321 | b_{w} = 0.730 | 0.512 | 0.11 | 0.840 | $\frac{{f}_{\mathrm{c}}}{{f}_{\mathrm{B}}}=0.840+\frac{0.321}{\frac{V}{100hd}+\frac{h}{d}}$ | 494 | $\begin{array}{c}174.8\\ 3.860\end{array}$ |

No. | Density Range of AAC, Average Density ρ, (nominal class of density) kg/m ^{3} | Average Moisture Content w, % | Average Relative Moisture w/w _{max} | Average Compressive Strength f_{Bw}, N/mm^{2} | Standard Deviation, s, N/mm ^{2} | COV, % | Average Relative Compressive Strength f _{Bw}/f_{B} |
---|---|---|---|---|---|---|---|

1 | from 375 to 446 397, (400) | 0 | 0 | 2.88 * | 0.36 | 12 | 1.0 |

2 | 8.3 | 0.10 | 2.64 | 0.21 | 8 | 0.92 | |

3 | 20.1 | 0.23 | 2.09 | 0.11 | 5 | 0.72 | |

4 | 29.1 | 0.33 | 2.18 | 0.16 | 8 | 0.76 | |

5 | 58.3 | 0.67 | 1.96 | 0.14 | 7 | 0.68 | |

6 | 89.9 | 1.00 | 1.78 | 0.13 | 7 | 0.62 | |

7 | from 462 to 532 492, (500) | 0 | 0 | 3.59 * | 0.13 | 4 | 1.0 |

8 | 6.2 | 0.10 | 3.00 | 0.22 | 7 | 0.84 | |

9 | 16.2 | 0.23 | 2.44 | 0.49 | 20 | 0.68 | |

10 | 22.8 | 0.33 | 2.12 | 0.21 | 10 | 0.59 | |

11 | 46.1 | 0.67 | 2.06 | 0.29 | 14 | 0.57 | |

12 | 66.0 | 1.00 | 2.24 | 0.23 | 10 | 0.62 | |

13 | from 562 to 619 599, (600) | 0 | 0 | 4.95 * | 0.35 | 7 | 1.0 |

14 | 5.40 | 0.10 | 4.71 | 0.49 | 10 | 0.95 | |

15 | 12.6 | 0.23 | 4.21 | 0.38 | 9 | 0.85 | |

16 | 18.2 | 0.34 | 3.88 | 0.52 | 13 | 0.78 | |

17 | 58.3 | 0.67 | 1.96 | 0.33 | 9 | 0.68 | |

18 | 61.1 | 1.00 | 2.82 | 0.28 | 10 | 0.57 | |

19 | from 655 to 725 674, (700) | 0 | 0 | 8.11 * | 0.58 | 7 | 1.0 |

20 | 5.30 | 0.10 | 6.86 | 0.63 | 9 | 0.85 | |

21 | 11.7 | 0.22 | 5.96 | 0.71 | 12 | 0.74 | |

22 | 16.8 | 0.34 | 5.56 | 0.58 | 10 | 0.69 | |

23 | 46.1 | 0.67 | 2.06 | 0.70 | 13 | 0.57 | |

24 | 53.3 | 1.00 | 4.95 | 0.41 | 8 | 0.61 |

_{B}—compressive strength of dry AAC, when w = 0.

No. | Density Range of AAC, Average Density ρ, (nominal class of density) kg/m ^{3} | w/w_{max} | Average Path Length L, mm | Average Passing Time of Wave t, µs | Average P-Wave Velocity c _{p} = L/t, m/s | N | Standard Deviation, $\mathit{s}=\sqrt{\frac{{\left({\mathit{c}}_{\mathbf{pi}}-{\mathit{c}}_{\mathbf{p}}\right)}^{2}}{\mathit{n}-1}}\text{}\mathit{s},\text{}\mathbf{m}/\mathbf{s}$ | C.O.V., $\frac{\mathit{s}}{{\mathit{f}}_{\mathbf{ci}}}\text{}\%$ |
---|---|---|---|---|---|---|---|---|

1 | from 375 to 446 397, (400), | 0 | 100.2 | 54.3 | 1847 | 21 | 35.9 | 1.9 |

2 | 0.10 | 57.4 | 1746 | 21 | 24.0 | 1.4 | ||

3 | 0.23 | 67.0 | 1501 | 21 | 37.7 | 2.5 | ||

4 | 0.33 | 67.6 | 1483 | 21 | 32.8 | 2.2 | ||

5 | 0.67 | 76.5 | 1315 | 21 | 25.6 | 1.9 | ||

6 | 1.00 | 72.7 | 1384 | 21 | 44.5 | 3.2 | ||

7 | from 462 to 532 492, (500), | 0 | 100.4 | 52.4 | 1917 | 23 | 51.4 | 2.7 |

8 | 0.10 | 56.3 | 1671 | 23 | 28.3 | 1.7 | ||

9 | 0.23 | 62.3 | 1614 | 23 | 33.6 | 2.1 | ||

10 | 0.33 | 63.0 | 1595 | 23 | 34.7 | 2.2 | ||

11 | 0.67 | 64.4 | 1562 | 23 | 70.2 | 4.5 | ||

12 | 1.00 | 62.0 | 1520 | 23 | 43.9 | 2.9 | ||

13 | from 562 to 619 599, (600), | 0 | 100.2 | 47.7 | 2101 | 24 | 49.7 | 2.4 |

14 | 0.10 | 50.5 | 1985 | 24 | 41.7 | 2.1 | ||

15 | 0.23 | 52.5 | 1910 | 24 | 59.6 | 3.1 | ||

16 | 0.34 | 54.7 | 1832 | 24 | 52.7 | 2.9 | ||

17 | 0.67 | 58.0 | 1738 | 24 | 69.1 | 4.0 | ||

18 | 1.00 | 55.6 | 1812 | 24 | 58.3 | 3.2 | ||

19 | from 655 to 725 674, (700), | 0 | 100.5 | 42.2 | 2379 | 23 | 46.2 | 1.9 |

20 | 0.10 | 44.3 | 2269 | 23 | 43.1 | 1.9 | ||

21 | 0.22 | 47.0 | 2139 | 23 | 52.4 | 2.4 | ||

22 | 0.34 | 47.6 | 2111 | 23 | 51.5 | 2.4 | ||

23 | 0.67 | 48.4 | 2085 | 23 | 56.1 | 2.7 | ||

24 | 1.00 | 48.2 | 2094 | 23 | 28.3 | 1.4 |

w/w_{max} | Curve Coefficient | R^{2} | Curve Equation | ||
---|---|---|---|---|---|

a | b | c | |||

0 | 5.73 × 10^{−6} | −1.46 × 10^{−2} | 10.30 | 0.99 | ${f}_{\mathrm{Bw}}=5.73\times {10}^{-6}{\left({c}_{\mathrm{p}}\right)}^{2}-1.46\times {10}^{-2}{c}_{\mathrm{p}}+10.3$ |

0.1 | 4.37 × 10^{−6} | −1.02 × 10^{−2} | 7.56 | 0.97 | ${f}_{\mathrm{Bw}}=4.37\times {10}^{-6}{\left({c}_{\mathrm{p}}\right)}^{2}-1.02\times {10}^{-2}{c}_{\mathrm{p}}+7.56$ |

0.23 | 4.22 × 10^{−6} | −9.19 × 10^{−3} | 6.35 | 0.99 | ${f}_{\mathrm{Bw}}=4.22\times {10}^{-6}{\left({c}_{\mathrm{p}}\right)}^{2}-9.19\times {10}^{-3}{c}_{\mathrm{p}}+6.35$ |

0.33 | 3.33 × 10^{−6} | −6.21 × 10^{−3} | 3.88 | 0.98 | ${f}_{\mathrm{Bw}}=3.33\times {10}^{-6}{\left({c}_{\mathrm{p}}\right)}^{2}-6.21\times {10}^{-3}{c}_{\mathrm{p}}+3.88$ |

0.67 | 3.59 × 10^{−6} | −7.75 × 10^{−3} | 5.84 | 0.95 | ${f}_{\mathrm{Bw}}=3.59\times {10}^{-6}{\left({c}_{\mathrm{p}}\right)}^{2}-7.75\times {10}^{-3}{c}_{\mathrm{p}}+5.84$ |

1 | 6.15 × 10^{−6} | −1.72 × 10^{−2} | 13.90 | 0.98 | ${f}_{\mathrm{Bw}}=6.15\times {10}^{-6}{\left({c}_{\mathrm{p}}\right)}^{2}-1.72\times {10}^{-3}{c}_{\mathrm{p}}+13.90$ |

common curve | a_{w} = 5.33 × 10^{−6} | b_{w} = −1.39 × 10^{−2} | c_{w} = 10.90 | 0.97 | ${f}_{\mathrm{Bw}}=5.33\times {10}^{-6}{\left({c}_{\mathrm{p}}\right)}^{2}-1.39\times {10}^{-2}{c}_{\mathrm{p}}+10.9$ |

**Table 8.**Procedure algorithm for determining characteristic compressive strength of masonry with semi-NDT and NDT techniques.

Step | Description | |||
---|---|---|---|---|

Semi-Non-Destructive Testing | Reference | Non-Destructive (ultrasonic) Testing | Reference | |

1 | Determining moisture content by weight w in AAC at the tested (in-situ) point | Equation (16) | Determining moisture content by weight w in AAC at the tested point | Equation (16) |

2 | Calculating maximum moisture content w_{max} in AAC | Equation (17) | Calculating maximum moisture content w_{max} in AAC | Equation (17) |

3 | Drilling specimens from AAC, drying them until constant weight and calculating density ρ | - | Determining P-waves velocity (c_{p} = L/t,) using the transmission method after measuring the path length L and time t. | - |

4 | Calculating coefficients a and b of the empirical curve | Equations (14) and (15) | Calculating coefficients a and b of the empirical curve | Equations (22)–(24) |

5 | Calculating the correction factor Δb | Equation (13) | Calculating compressive strength of AAC f_{Bw} acc. to the curve | Equation (25) |

6 | Performing destructive tests and determining compressive strength of dry AAC f_{c} | - | Graduating the curve according to the standard EN 13791:2008 | - |

7 | Calculating compressive strength f_{B} acc. to the corrected curve | Equation (13) | Calculating compressive strength of AAC f_{Bw} acc. to the graduated curve | - |

8 | Calculating compressive strength f_{Bw} depending on moisture content in AAC | Equations (18) and (19) | Calculating characteristic compressive strength of AAC masonry | Equation (1) |

9 | Calculating characteristic compressive strength f_{k} of AAC masonry | Equation (1) |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Jasiński, R.; Drobiec, Ł.; Mazur, W. Validation of Selected Non-Destructive Methods for Determining the Compressive Strength of Masonry Units Made of Autoclaved Aerated Concrete. *Materials* **2019**, *12*, 389.
https://doi.org/10.3390/ma12030389

**AMA Style**

Jasiński R, Drobiec Ł, Mazur W. Validation of Selected Non-Destructive Methods for Determining the Compressive Strength of Masonry Units Made of Autoclaved Aerated Concrete. *Materials*. 2019; 12(3):389.
https://doi.org/10.3390/ma12030389

**Chicago/Turabian Style**

Jasiński, Radosław, Łukasz Drobiec, and Wojciech Mazur. 2019. "Validation of Selected Non-Destructive Methods for Determining the Compressive Strength of Masonry Units Made of Autoclaved Aerated Concrete" *Materials* 12, no. 3: 389.
https://doi.org/10.3390/ma12030389