Design of mock-ups for ultrasonic testing in civil engineering using numerical simulations

doi:10.21203/rs.3.rs-3437967/v1

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Design of mock-ups for ultrasonic testing in civil engineering using numerical simulations

https://doi.org/10.21203/rs.3.rs-3437967/v1

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published 06 May, 2024

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The major objective when applying non-destructive testing (NDT) in civil engineering is the detection of defects such as honeycombs. Defects can impair the service life of structures and could lead in the worst case to fatal failures. All structures such as bridges, tunnels, locks etc. are unique objects with variation in geometry, dimensions, materials, environmental condition, load scenarios etc. Thus, the interpretation of NDT data is challenging and the validation of the NDT method, the training of inspectors and the reliability analysis of NDT rely on mock-ups with known defect situations mimicking the type of defect as realistic as possible. The considered defect sizes should cover the transition zone between detectable and non-detectable to properly evaluate the capability of the inspection system. However, knowledge about the limits of an inspection system is mostly non-existent. To overcome this limitation, this study applies numerical simulations for ultrasonic testing in reinforced concrete performed with the elastodynamic finite integration technique (EFIT) to identify this transition zone. First, the study shows the development and the validation of a numerical representation of concrete considering the implementation of a qualitatively realistic noise level. Additionally, the accurate representation of the sources during ultrasonic testing is confirmed by an investigation of the radiation characteristic for dry point contact ultrasonic transducers. The simulation outcome enabled the design of a mock-up for the detection of honeycombs applying ultrasonic testing considering major influencing factors. A case study completes the study demonstrating the applicability of the design scheme based on numerical simulation. In the real specimen, \(68\text{\%}\) of the implemented defects are detectable proving the effectiveness of the design method.

simulation

ultrasonic testing

reliability

EFIT

reference specimen

concrete

Non-destructive testing (NDT) methods, such as ultrasonic (UT) or impact echo testing play an important role for the remaining service life assessment of civil infrastructures. Failures, such as the Ponte Morandi bridge in Genoa (Italy), can have fatal consequences [1]. Thus, the service life assessment requires high reliability which is only achievable with the knowledge about the reliability of the applied inspection methods. However, reliability assessments of NDT methods are very rare in the field of civil engineering until today [2–4]. Typically, they are performed on mock-ups specifically designed for this purpose [5]. These mock-ups should contain artificially produced defects, whose size covers the entire transition zone between detectable and non-detectable. For example, POD analysis requires \(80\text{\%}\) of the data points to have a detectability between \(10\text{\%}\) and \(90\text{\%}\) [6]. Thus, it is evident that a priori information on defect detectability is required for the design of such mock-ups.

In addition to reliability assessments, such mock-ups can also be used for the training of inspectors [7]. To test the inspector’s expertise during training it is also important that it is possible to detect defects without it being trivial. Furthermore, capability studies that test the effectiveness of an NDT method for a given problem also require mock-ups that are specifically designed for this purpose [8].

This study presents an approach to estimate defect detectability for ultrasonic testing in concrete with numerical simulations. In order to do so, the simulations need to be validated beforehand to ensure the realism of the results. For the simulations to be realistic, they need to incorporate noise, which is the most limiting factor for defect detection. In concrete, most of the noise during ultrasonic testing comes from elastic wave scattering at the interior boundaries between aggregates, pores, and cement matrix [9]. Therefore, a numerical representation of the concrete is presented and validated first. Afterwards, it is tested whether the sources for UT are simulated correctly by investigating radiation characteristics of dry point contact transducers for homogeneous and concrete-like media. With this validation of the code, it is possible to conduct simulations of different defect scenarios. The results are then processed using the total focusing method [10] and evaluated visually just like real inspection data. This evaluation provides the base for the design of mock-ups with honeycombs that are difficult to detect. In the end of this study, the inspection results are presented, evaluated, and discussed.

The simulation code used for this study is the elastodynamic finite integration technique (EFIT) [11]. EFIT is a staggered-grid finite differences code for the time-explicit simulation of elastic wave propagation, which is very robust for strongly heterogeneous media [12] and has been used in the past for the simulation of UT [13] inspections in concrete. The simulation code was implemented in fortran and parallelized using the message passing interface MPI. Different versions of this code allow for simulations in 2D as well as 3D. The parallelized fortran implementation allows for fast computations especially using the high-performance computers of the Helmut Schmidt University.

2.1 Numerical concrete model

To perform NDT simulations for the described purpose, a suitable numerical model for concrete is mandatory. Here, the concrete model described by Schubert & Köhler (2004) [9] is used, in which aggregates and pores are represented as ellipsoids. The maximum aspect ratio for each ellipsoid is two. In the model the aggregate size follows a given grading curve, while the pore size remains adaptable. Both, pores, and aggregates, are distributed randomly with a random spatial orientation inside the simulation domain. To fill the simulation domain with the ellipsoids the largest objects are placed first. The sizes then gradually decrease until a given share of the medium is occupied. In the end, the cement matrix fills the rest of the medium. Material parameters are assigned to each grid cell separately, allowing each aggregate to have different mechanical properties. Pores are simulated as voids, so that no elastic waves can propagate inside of them.

A control sequence to identify and avoid overlapping aggregates and pores must be implemented effectively as the generation of the numerical concrete can take a lot of time, especially in 3D [14]. In the implemented algorithm, the maximum half axis size is determined for each ellipsoid and the overlap check is then performed within a cube with twice the maximum half axis as the side lengths around the designated center of the aggregate/pore. Additionally, EFIT only allows for rectangular grid cells. As all materials are treated as isotropic, cubic grid cells are used for all simulations. With such a mesh, all geometries inside the simulation domain are generated using a staircase approximation. Therefore, aggregates and pores are not perfectly ellipsoidal.

2.2 Validation of simulation results

Using this numerical concrete model, validation of the code is mandatory before designing the mock-up. As the mock-up shall be designed for UT, it must be ensured that the sources as well as the noise are simulated correctly. Therefore, a recreation of a real UT inspection from a reference specimen is performed to validate the used concrete model. Afterwards, radiation characteristics for ultrasound transducers are simulated and compared to analytical solutions.

2.2.1 Recreation of ultrasound data

The first validation experiment is the recreation of an UT inspection on a reference specimen with an embedded cladding pipe. The specimen was produced by the Fraunhofer Institute for Nondestructive Testing IZFP and has dimensions of \(80 50 38 \text{c}{\text{m}}^{3}\) [15]. The pipe has a diameter of \(5 \text{c}\text{m}\). For the inspection, two longitudinal ultrasound transducers with a center frequency of \(100 \text{k}\text{H}\text{z}\) were used in a source-receiver configuration. Both source and receiver were placed alongside a line circling the specimen at \(x = 40 \text{c}\text{m}\). For a visualization of the specimen and the measurement positions see Fig. 1.

Simulations are performed in two ways: once using a homogeneous concrete model and once using the heterogeneous concrete model as described in section 2.1. In both models the P-wave velocity is set at \({c}_{P} = 3700 \text{m}/\text{s}\), while the shear wave velocity is \({c}_{S} = 2300 \text{m}/\text{s}\). For the homogeneous model, a constant density of \(\rho = 2400 \text{k}\text{g}/{\text{m}}^{3}\) is used. In the heterogenous model this density is used for the cement matrix only, whereas aggregates have varying densities between \({\rho }_{agg} = 1400 – 3400 \text{k}\text{g}/{\text{m}}^{3}\) to allow for scattering at the interface. The porosity is \(2 \text{v}\text{o}\text{l}.-\text{\%}\) and pore sizes vary equally between \(1.2 \text{m}\text{m}\) and \(2.4 \text{m}\text{m}\). In these simulations the grid cell size is fixed at \(0.6 \text{m}\text{m}\).

The results for the two different simulations can be compared to the measurement result in Fig. 2. Here, the source position is kept constant (Position 8), while the receiver moves around the specimen. From the comparison between the three results, it is evident, that both simulations can reproduce the correct onsets for P- and S-waves. However, both simulations show that the Rayleigh wave would propagate around the entire specimen, but this cannot be observed in the measurement data. Apart from that, the heterogeneous simulation is also able to reproduce the noise, which is present in the measurement data with realistic amplitudes. In Fig. 2d) the amplitudes from the first P-wave arrival can be directly compared to one another. Here, the overall distribution of amplitudes is relatively similar for all three scenarios. However, near the edges between the side walls and the surface, where the source is applied, the small P-wave amplitudes predicted by the simulations cannot be observed in the measurement data (receivers 15–20 and 50–54). Since the radiation characteristic for P-wave transducer shows amplitudes close to zero at these angles (\(\approx 90^\circ\)) [16], it is likely that the high amplitudes observed in the measurement data are caused by noise or surface waves. Also, some amplitude variations occur in the measurement data due to different coupling of the sensors at each position. Overall, it can be concluded that the EFIT code can recreate the actual measurement well in all facets except for the surface wave propagation, which differs strongly from the measurement data.

2.2.2 Radiation characteristics of ultrasound transducers

In the past, dry point contact transducers have proven to be very efficient tools for UT in civil engineering [17]. Theoretically, the radiation characteristics of such transducers should equal those of single force point sources [16]. However, in a validation experiment, large deviations from the analytical solutions were measured for S-waves, while the measured radiation characteristics for P-waves agreed with the theory [18]. To test the radiation characteristics numerically, wave propagation is simulated in 2D and 3D at different distances from the source. Also, it is investigated how the heterogeneous mesostructure of concrete influences radiation characteristics through scattering.

Using 2D simulations in a homogeneous, concrete-like medium, the behavior of relative wave amplitudes at different distances from the source shall be studied. For this, P- and S-wave amplitudes are measured at different azimuth angles relative to the source at during different stages of the wave propagation [19]. Here, it is evident that P-wave amplitudes converge quickly towards the analytical solution, while S-waves do not reach a convergence at 43 wavelengths from the source (see Fig. 3). However, the results suggest that the radiation characteristic for S-waves could eventually converge at even greater distances. Note that the plots depicted in Fig. 3 vary from those found in [19]. This is due to a previous error in the calculation of the theoretical radiation characteristic. The obtained amplitudes from the simulations remain unchanged.

The S-wave radiation characteristic obtained at a distance of 6.25 wavelengths away from the source also matches well with the experimentally obtained radiation characteristic [18] when neglecting the high amplitudes caused by superposition with Rayleigh waves at angles close to \(\pm 90 ^\circ\). This leads to the conclusion, that the radiation characteristic does indeed change over the traveled distance. From the obtained waveforms (see Fig. 4), it is observed that the complex radiation characteristics for S-waves are generated by interference between the S-wave and the head wave, which approaches the S-wavefront at the critical angle \(\phi = {\text{s}\text{i}\text{n}}^{-1}({c}_{s}/{c}_{P})\) [20].

Using 3D simulations, it was possible to obtain radiation characteristics for homogeneous as well as for heterogeneous concrete-like media. Here, a comparison with analytical representations of radiation characteristics was not possible as the analytical solutions are only valid in 2D. From the EFIT simulations, it was found that the complex radiation characteristics for S-wave can also be found in 3D for homogeneous media. However, for heterogeneous media, these effects get widely eliminated due to wave scattering. Graphical representations of the 3D radiation characteristics can be found in [19].

Overall, EFIT simulations can recreate 2D radiation characteristics well. A convergence towards the analytical solution could not only be confirmed for P-waves due to a lack of computational power and precision. When simulating S-waves even with double precision at large distances, the wavefront tends to differ from a perfect half-circle, which is the reason why radiation characteristics at larger distances were not evaluated.

As the simulation code is now validated for UT simulation in concrete, it can be used to design a mock-up with defect sizes and depths in the transition of detectability. According to Berens (2000) [6], at least \(80\%\) of the data points used for a POD analysis, which is the most common form of reliability analysis, require a detectability between \(10\%\) and \(90\%\). This condition just proves the necessity to being able of estimating defect detectability from simulations, which supports the design of complex defect scenarios.

To design the mock-up for this study UT pre-simulations on a numerical model of the mock-up are carried out beforehand. The approximate defect sizes and depths, in which a detection is difficult, are then estimated from the simulation results. In this study the simulation data is processed using the total focusing method (TFM) [10], which is also used for measurement data to generate the images, that would be manually interpreted in a real inspection. In a feasibility study, it was shown that this design approach works for a specimen with honeycombs by estimating their impact solely from raw simulation data [21]. However, the specimen produced in the feasibility study is quite small (\(50 \times 50 \times 17 \text{c}{\text{m}}^{3}\)) and only contained three honeycombs of one size and in one depth meaning that a full capability demonstration of UT could not be performed with these results. Therefore, a larger specimen is needed.

3.1 Design of the reference specimen

Similar to the mock-up produced in the feasibility study [21], this mock-up also contains honeycombs, all of which are spherical to reduce the degrees of freedom. However, as the number of honeycombs shall be larger, this necessarily implies a larger thickness. Here, a thickness of \(30 \text{c}\text{m}\) is chosen. As the lateral dimensions of the mock-up need to be large enough to fit all defects, they were chosen to be \(1.5 \text{m}\) in x- and y-direction. This way, also a good transportability of the mock-up within the lab can be guaranteed as the total weight is kept under \(2000 \text{k}\text{g}\). Additionally, the aspect ratio is more favorable for other NDT methods like Impact Echo [22], which might also be applied on this mock-up in the future.

To estimate honeycomb detectability many test simulations with differently sized defects in different depths are carried out. The simulations use a testing frequency of \(65 \text{k}\text{H}\text{z}\), which is the same frequency that is be used for the measurements. Honeycombs are assumed to be regions with a low-density cement matrix (\({\rho }_{cem} = 400 \text{k}\text{g}/{\text{m}}^{3}\)) [23–24], which shall resemble the large pore clusters found in a real honeycomb. To simulate different noise levels and testing conditions, some simulations have rebars (12mm diameter) placed directly above the honeycombs with a concrete cover of 44 mm. For the decision, which honeycomb sizes shall be placed in which depths, three different depth regions are considered separately: \(5-10 \text{c}\text{m}\), \(10-15 \text{c}\text{m}\), and \(15-20 \text{c}\text{m}\). Numerical simulations are carried out using different honeycomb sizes at depths of \(8 \text{c}\text{m}\), \(12 \text{c}\text{m}\), and \(17 \text{c}\text{m}\), which correspond to the centers of each region. The decision process is exemplary visualized for a depth of \(12 \text{c}\text{m}\) in Fig. 5. To estimate the lower detection limit, the less noisy setup without steel reinforcement is used. During a real inspection, honeycombs can either be detected by a decreased backwall echo amplitude, by a shifted backwall echo, or by a direct reflection from the honeycomb itself [8]. In the comparison between a simulation without defect and a honeycomb size of \(6 \text{c}\text{m}\), it can be observed that the honeycomb only causes a slight reduction in backwall echo amplitude, while no direct reflection is visible. As the backwall echo is clearly reduced, a detection of this honeycomb under favorable conditions, in which noise amplitudes are low so that the backwall echo has stable amplitudes in the undamaged regions, could be possible. For the upper detection limit, the setup with a rebar directly above the honeycomb is used. For a honeycomb with a diameter of \(12 \text{c}\text{m}\) a clear direct reflection is identifiable. However, the amplitude of this reflection is similar to the reflection of the rebar. The backwall echo again shows clearly reduced amplitudes, but the echo is still continuous, which should result in a small chance that this defect might be overlooked.

The abovementioned decision process Is also applied to the other depth regions. There it is found that honeycombs with diameters of \(4-8 \text{c}\text{m}\) should be placed in a depth between \(5-10 \text{c}\text{m}\), and honeycombs with diameters between \(6 \text{c}\text{m}\) and \(9 \text{c}\text{m}\) in a depth of \(15-20 \text{c}\text{m}\). With this knowledge a total of 36 honeycombs are produced using pervious concrete. These honeycombs have diameters between \(4 \text{c}\text{m}\) and \(12 \text{c}\text{m}\) with an increment of \(1 \text{c}\text{m}\), so that four honeycombs of each size exist.

For the steel reinforcement, rebars with a diameter of \(12 \text{m}\text{m}\) and an irregular mesh with sizes varying from \(120 \text{m}\text{m}\) to \(300 \text{m}\text{m}\) is used. This way, different reinforcement levels can be incorporated into the measurement by placing honeycombs at different lateral positions in the mock-up. Additionally, the steel reinforcement mesh at the bottom mirrored the one at the top, so that the reinforcement level would be different for each honeycomb when the measurement was performed at the front or back side. A 3D model of the mock-up without honeycombs as well as a honeycomb map can be found in Fig. 6.

3.2 Measurement results

On this specimen a total of 52 Ultrasonic line scans are carried out every \(10 \text{c}\text{m}\) while always leaving \(15 \text{c}\text{m}\) to each edge to avoid unwanted reflections from the sides. All signals are recorded using the same settings and processing methods. The center frequency is \(65 \text{k}\text{H}\text{z}\) in all measurements, which is also the highest possible frequency that the device can generate. This allows to assess the maximum capability of the used device. At the start of the inspection, the shear wave velocity is measured to obtain the correct velocity, which is then used for the TFM. In the end all line scan TFM results are exported as images, which are then analyzed manually to detect the honeycombs in a hit/miss fashion. For honeycomb detection, either the back wall echo amplitude must be significantly reduced, or a direct honeycomb reflection must be identifiable. Shifted backwall echoes are not found in the data.

Overall, each of the 36 honeycombs are measured four times (measurements in x- and y-direction on both sides of the mock-up). In total about \(68\%\) (99/144) of all honeycombs can be detected this way. Examples for detected and undetected honeycombs can be seen in Fig. 7. Here, also the complexity of the signals becomes visible. Of the four honeycombs present in this image, only three exhibit a weakened backwall echo, while only two show a clear direct reflection signal. Therefore, it is likely that at least one honeycomb (especially the one at \(x= 1.35 \text{m}\)) would be overlooked in a real inspection. In general, the back wall echo as well as the top rebar layer are clearly identifiable in all measurements. However, the amplitude of the backwall echo is highly variable even in the undamaged areas of the specimen. Such an effect can also be observed in Fig. 7 at a position of about \(1.0 \text{m}\). This variability could be mistaken as a defect indication. Additionally, noise is present in all sections of the data. In some cases, this noise also appears as an additional reflection (false alarm), which might be caused by a strong local heterogeneity of the concrete. An example for such a signal can be seen in at a lateral position of about \(0.25 \text{m}\) shortly before the backwall echo (marked red in Fig. 7).

The obtained measurement results suggest that the design method was successful in finding defect scenarios that are difficult to detect. However, a direct comparison between a simulated defect scenario and a measured one is yet to be evaluated. Such a scenario can be seen in Fig. 8. Here, the honeycomb has a diameter of \(8 \text{c}\text{m}\) at a depth of \(13 \text{c}\text{m}\). It is located (almost) directly underneath a rebar. In the measurement, the honeycomb is shifted slightly to the side of the rebar. Overall, there are many similar features in the two results: the rebar echo and the backwall echo are clearly visible. A direct reflection of the honeycombs is visible on both occasions, but their amplitude is much smaller than the rebar echo. Also, the backwall echo is weakened to some degree in the areas affected by the honeycomb. However, the focused rebar echo is much smaller in the simulation than in the measurement. This might be a sign for local, unplanned honeycombing near the rebar. In the measurement results, the rebar echo is not clearly separated from the honeycomb echo, while there is a gap of about \(6 \text{c}\text{m}\) in the simulation result. Since the main honeycomb echo is at the correct depth for the measurement result, an uplift of the honeycomb during concreting is unlikely. The fact, that all defect properties are simulated correctly, also indicates that the chosen numerical model for the honeycombs behaves like a real honeycomb. For future studies, the numerical model ideally should be validated beforehand. Here the feasibility study [21], in which a smaller specimen was produced using the same approach and the same numerical model, was already seen as a validation of the model, as it was successful. However, the comparison between measurement and simulation results confirms this as well.

Apart from the previously discussed differences, the simulation captures the main features of the defect scenario well and produces a realistic noise level. Therefore, the detectability of real defects should generally be estimated well with the simulations. The importance of simulating noise for this purpose can be seen by comparing the same defect scenario using a homogeneous and heterogeneous concrete model (see Fig. 9). Here, it is evident that even the smallest direct reflection will be identifiable if a homogeneous concrete mode is used. Therefore, an estimation of defect detectability would be impossible.

Another aspect that affects defect detection, that has not been considered here, is the choice of migration velocity. To transform the time-signals into depths, the correct velocity must be chosen for the TFM method. If the chosen velocity is incorrect, then the obtained signals will not focus as well, and defects might get overlooked. Choosing a suitable velocity for TFM also means that the overall wave velocity inside the reconstructed volume needs to be homogeneous or at least should not contain any gradients. However, due to heterogeneous hydration conditions and compaction effects, this might not always be the case for concrete. Other processing methods like the full-waveform inversion allow for heterogeneous models, but they are usually too computationally expensive to be applied for a wide range of data.

This study demonstrates a possible approach for the design of mock-ups for capability assessments of UT in civil engineering using numerical simulations. The EFIT simulations can qualitatively predict UT measurement results including noise and reproduce the same radiation characteristics needed to simulate ultrasound dry point contact transducers. After the validation, the code was used for defect detectability estimation to find scenarios, in which honeycombs of different sizes and depths are not trivially detectable. The simulation results are then directly used to design a mock-up. Overall, about \(68\text{\%}\) of the defects inside this specimen could be detected using UT, which implies that the design approach was successful and is recommendable for future studies as well. In the future, also other NDT methods can be tested on this mock-up to allow for a performance comparison in different testing scenarios.

This investigation paves the way for future reliability analysis of UT measurements in reinforced concrete, which shall be carried out in the near future.

Acknowledgements

We would like to acknowledge Andrea Castro, Svetlana Heger, and the rest of the laboratory team for the help in constructing the mold for the specimen and their overall expertise in concrete technology. This work was part of the project “Normung für die probabilistische Bewertung der Zuverlässigkeit für zerstörungsfreie Prüfung”, which was funded by the German Federal Ministry for Economic Affairs and Climate Action under the signature 03TN0006. All numerical simulations were carried out on the “HSUper” high performance computer of the Helmut Schmidt University. The HPC cluster HSUper has been provided by the project hpc.bw, funded by dtec.bw–- Digitalization and Technology Research Center of the Bundeswehr. dtec.bw is funded by the European Union–- NextGenerationEU.

Ethical Approval: not applicable

Funding: This work was part of the project “Normung für die probabilistische Bewertung der Zuverlässigkeit für zerstörungsfreie Prüfung”, which was funded by the German Federal Ministry for Economic Affairs and Climate Action under the signature 03TN0006.

Availability of data and materials: All data and self-written evaluation programs can be accessed upon request by sending an e-mail to the corresponding author.

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No competing interests reported.

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Design of mock-ups for ultrasonic testing in civil engineering using numerical simulations

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Abstract

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1 Introduction

2 Elastodynamic Finite Integration Technique

2.1 Numerical concrete model

2.2 Validation of simulation results

2.2.1 Recreation of ultrasound data

2.2.2 Radiation characteristics of ultrasound transducers

3 Design of experiment for UT capability demonstration

3.1 Design of the reference specimen

3.2 Measurement results

4 Discussion

5 Conclusions and outlook

Declarations

References

Additional Declarations

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