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22nd International Conference on Modelling in Mechanics 2024

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Procedia Structural Integrity 63 (2024) 51–57

22nd International Conference on Modelling in Mechanics 2024 Elastic modulus of Cement Bound Granular Material (CBGM) Stanis ł aw Majer a, *, Bartosz Budzi ń ski a ,Petr Lehner b a Department of Construction and Road Engineering, Faculty of Civil and Environmental Engineering, West Pomeranian University of Technology in Szczecin, Piastów Street 50a, Szczecin, Poland b Department of Structural Mechanics, Faculty of Civil Engineering, VSB-Technical University of Ostrava, Ludvika Podeste 1875/17, 708 00 Ostrava-Poruba, Czech Republic Abstract The modulus of elasticity of Cement Bound Granules Materials (CBGM) is a key parameter used in the design of road infrastructure as well as other construction projects. This article presents the results of research on cement bound materials. The research was conducted for an investment in Poland. Three mixtures differing in grain size distribution and cement content were tested. For this purpose, a research method suitable for concrete was adapted. The result of the analyses was the selection of one of the mixtures, which was used in the implementation of the project. © 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of 22nd International Conference on Modelling in Mechanics 2024 organizers

Keywords: Elastic modulus; cement bound granular material; case study

1. Introduction 1.1. Background of the conducted research

Elastic modulus (E) is one of the parameters defining elastic behaviour of a material under analysis (Zvonari ć et al., 2024). It represents the resistance of a given material to elongation or contraction in the elastic or Hooke’s law

* Corresponding author. Tel.: +48914494146 E-mail address: Stanislaw.Majer@zut.edu.pl

2452-3216 © 2024 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of 22nd International Conference on Modelling in Mechanics 2024 organizers 10.1016/j.prostr.2024.09.008

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region of its behaviour. Elastic modulus or Young's modulus is highly relevant to structural design by influencing, together with the thickness of components, the structural rigidity of the system. In the case of cement bound granular materials (CBGM) its value depends on the content of cement in the mix, and thus their compressive strength (Katsakou & Kolias, 2007; Zvonari ć et al., 2024). This material, which is used as a primary and secondary road base, potentially offers the possibility of utilizing many waste materials. (Crucho et al., 2022; Farhan et al., 2018; Stehlik et al., 2015; Yuan et al., 2011). Concrete and cement bound granular material is not an isotropic material having tensile strength in the range of 6 9% of its compressive strength. With decreasing strength, the linear expansion coefficient also decreases. This property is used to characterise bottom layers of road pavements, which are considered flexible when their compressive strength is lower than 5 MPa. Table 1 summarizes the selected schemes for performing the modulus of elasticity tests for cement-bound mixtures.

Table 1. Selected methods for determining the elastic modulus.

Standard/ References

Method

Equipment

Type of loading

Comments

(EN 13286-43, 2003; Zvonari ć et al., 2024)

The static compressive modulus, (E c )

Compression testing machine

Tests conducted to destroy the sample

(EN 12504-4:2021, 2021; Pasetto & Baldo, 2016)

Ultrasonic Test Equipment

The dynamic modulus (E D )

non-destructive test

2PB-TR 2BP-PR

Testing machine with strain control

(EN 12697-26, 2018)

(Buczy ń ski et al., 2020; EN 12697-26, 2018; Farhan et al., 2016)

Testing machine with strain control

IT-CY

1.2. Case study The research was conducted, on one of the investments being carried out in Poland (large-scale industrial tanks). During one of the implemented projects, the possibility of changing the designed structural solution emerged. The first option considered in the project was deep foundation on piles. However, FEM calculations showed that it was actually possible to use foundation slabs instead which significantly reduced the costs of constructing the foundations. These should be made of cement-bound mixes of Elastic modulus 400 MPa or higher. Thus, 0.55 m thick prestressed concrete slabs were designed for the planned structures. The slab was placed on 1.75 m thick concrete base layer. Considering the critical nature of the project, extensive preliminary site examinations and tests were carried out to specify a concrete mix of appropriate Elastic modulus value. In addition, it should not pose construction problems during placement. The cement-stabilized layer should be made from on-site materials. Before starting the mixture design, input data was

Stanisław Majer et al. / Procedia Structural Integrity 63 (2024) 51–57

obtained, with the most important being the parameters of the native soil. This was fine sand. Basic parameters of the sand are summarized in Table 2. Figure 1 shows the flowchart for the case study.

Table 2. Basic soil parameters. Parameter Optimum moisture content

Unit

Results

Standard

16.3 1.58

EN 13286-2 EN 13286-2 EN 13286-47

Maximum dry density

Mg/m 3

CBR

% M

Soil capillarity

0.42 1.35 82.3

Uniformity Coefficient d 60 /d 10

mm/mm

EN 933-1 EN 933-8

Sand equivalent

Coefficient of permeability

m/d

7.6

USBSC equation

Fig. 1 Flowchart for the case study.

Stanisław Majer et al. / Procedia Structural Integrity 63 (2024) 51–57

2. Materials and methods Based on the analysed properties of cement-bound mixes, a mix specified in the Polish guide for design of flexible and semi-rigid pavements was chosen of 28 day (Judycki et al., 2014) compressive strength in the range of 2.5-5.0 MPa. It should have Elastic modulus value of 4.500 MPa before cracking, dropping to 300 MPa after cracking. This is a consequence of the decrease in modulus due to repetitive loads (Judycki, 1991). The following three mixes were chosen for preliminary tests (Table 3). The road requirements were the most suitable for the project being implemented.

Table 3. Composition of tested mixtures. Mix No. [-] Sand [%]

Gravel [%]

Cem III/A 32.5 N [%]

Fly ash [%]

1 2 3

62.2 91.6 92.6

29.7

4.9 4.7 4.2

3.7 3.7 3.2

0 0

The Elastic modulus and compressive strength values were determined experimentally on  =150 mm and h =300 mm cylindrical samples made in 3-gang split design concrete cylinder moulds with top and bottom pieces. The compaction effort was 0.6 J/cm 3 ±10%. During the moulding process, samples for CBR and Proctor tests were taken. In the Elastic modulus and compressive strength test the compressive stress increased at a rate of 0.6±0.4 MPa/m 2 ꞏ s. On the cylinder side walls lines were marked to measure strain. Three measurements were carried out on these vertical lines spaced at 120° intervals around the side wall. (Fig. 2).

Fig. 2. Elastic modulus tester.

The method of loading the sample was adapted from the measurement of the modulus of elasticity of cement concretes, while simultaneously appropriately reducing the forces acting on the test samples. The gauge length centre

Stanisław Majer et al. / Procedia Structural Integrity 63 (2024) 51–57

was located at half the height of the sample. The following procedure was applied in the Elastic modulus test (Fig. 3, Fig. 4):  the sample was loaded up to compressive stress of  b = 0.05 MPa and the resulting strain  b0 was measured  the test load was increased up to  a =1/3 f c , maintained for 60 s at that level, and after the next 30 s  a0 was measured  the sample was unloaded to stress level  b , which was maintained for 60 s and after the value of  b1 was measured (Fig 3),  this procedure was repeated at least 2 times,  when all the required values had been determined, load was increased up to failure of the sample (Fig 4). The elastic modulus of CBM materials was investigated using the stress-strain relationship of the mixture from the test. The elastic modulus (E) is calculated by equation below: ܧ ൌ ఙ ఢ (1)

Fig. 3. Load increase over time during the E-modulus test.

Fig. 4. Stress-strain plot of one of the tested mixes.

Stanisław Majer et al. / Procedia Structural Integrity 63 (2024) 51–57

3. Results Mixes No. 1 and No. 2 were chosen for field testing based on the results of the preliminary laboratory tests (Table 4). The trial construction sites were located at the planned tanks location. They were removed after the test. The compaction equipment used in the test was the same as in the future construction. The slabs were cast in 3 three lifts and 150/300 mm cylinders were cored after 7 days of curing (see construction site in Fig. 5).

Table 4. Gives the results obtained on the tested mixes after seven days of curing. Mix No. E s 7 days [MPa]   f c 7 days [MPa]

f c 28 days [MPa]

1 2 3

7,594 2,882 2,123

23.2 17.1 18.1

2.54 0.85 0.77

3.86 1.76 1.52

Fig. 5. Trial construction site and coring of cylinders for E-modulus test.

Finally, the construction supervision team and lead designers approved the Contractor’s proposal to use Mix 2 as a material for construction of the designed foundation slabs for the tanks in question. The research results clearly indicate that each of the three prepared mixtures exhibits a significantly higher modulus of elasticity than required by the designers in the analysed case. The average results obtained ranged from 2100 MPa to 7500 MPa (Table 2), suggesting that it is not possible to design a mixture with such a low modulus as required. The addition of cement and the binding of the layer, achieving very low strength at the level of 0.77 MPa (after 7 days), allows achieving a modulus of at least 2000 MPa. 4. Conclusions The modulus of elasticity of cement bonded granular materials (CBGM) is a key parameter used in the design of road infrastructure and other construction projects. This paper presents the results of our research on cement-bonded materials. Three mixtures varying in grain size composition and cement content were tested. Therefore, a research method suitable for concrete was adapted for this purpose. Mix 2 was selected as the most suitable, despite the fact

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that all the mixes analysed showed sufficient values of modulus of elasticity. This is due to the addition of cement. Further research in a similar area should prove the above conclusions. Acknowledgements The authors express their gratitude for the financial assistance provided by the VŠB-Technical University of Ostrava, which was made possible through the Czech Ministry of Education, Youth, and Sports. This support was provided as institutional aid to facilitate the conceptual development of science, research, and innovation. References Buczy ń ski, P., Iwa ń ski, M., Mazurek, G., Krasowski, J., & Krasowski, M. (2020). Effects of Portland Cement and Polymer Powder on the Properties of Cement-Bound Road Base Mixtures. Materials, 13(19), 4253. https://doi.org/10.3390/ma13194253 Crucho, J., Picado-Santos, L., & Neves, J. (2022). Mechanical Performance of Cement Bound Granular Mixtures Using Recycled Aggregate and Coconut Fiber. Applied Sciences, 12(4), 1936. https://doi.org/10.3390/app12041936 EN 12504-4:2021. (2021). Testing concrete in structures—Part 4: Determination of ultrasonic pulse velocity. European Committee for Standardization. EN 12697-26. (2018). Bituminous mixtures -Test methods—Part 26: Stiffness,. European Committee for Standardization. EN 13286-43. (2003). Unbound and hydraulically bound mixtures—Part 43: Test method for the determination of the modulus of elasticity of hydraulically bound mixtures. European Committee for Standardization. Farhan, A. H., Dawson, A. R., & Thom, N. H. (2016). Characterization of rubberized cement bound aggregate mixtures using indirect tensile testing and fractal analysis. Construction and Building Materials, 105, 94–102. https://doi.org/10.1016/j.conbuildmat.2015.12.018 Farhan, A. H., Dawson, A. R., & Thom, N. H. (2018). Damage propagation rate and mechanical properties of recycled steel fiber-reinforced and cement-bound granular materials used in pavement structure. Construction and Building Materials, 172, 112–124. https://doi.org/10.1016/j.conbuildmat.2018.03.239 Judycki, J. (1991). Structural characterization of road base materials treaated with hydraulic binders. University of Oulu. Judycki, J., Jaskula, P., Pszczola, M., Alenowicz, J., Do łż ycki, B., Jaczewski, M., Rys, D., & Stiness, M. (2014). Katalog typowych konstrukcji nawierzchni podatnych i pó ł sztywnych [Catalogue of typical flexible and semi-rigid pavement constructions]. Politechnika Gda ń ska. Katsakou, M., & Kolias, S. (2007). Mechanical properties of cement-bound recycled pavements. Proceedings of the Institution of Civil Engineers - Construction Materials, 160(4), 171–179. https://doi.org/10.1680/coma.2007.160.4.171 Pasetto, M., & Baldo, N. (2016). Recycling of waste aggregate in cement bound mixtures for road pavement bases and sub-bases. Construction and Building Materials, 108, 112–118. https://doi.org/10.1016/j.conbuildmat.2016.01.023 Stehlik, D., Dasek, O., Hyzl, P., Coufalik, P., Krcmova, I., & Varaus, M. (2015). Pavement construction using road waste building material – from a model to reality. Road Materials and Pavement Design, 16(sup1), 314–329. https://doi.org/10.1080/14680629.2015.1029680 Yuan, D., Nazarian, S., Hoyos, L. R., & Puppala, A. J. (2011). Evaluation and Mix Design of Cement-Treated Base Materials with High Content of Reclaimed Asphalt Pavement. Transportation Research Record: Journal of the Transportation Research Board, 2212(1), 110–119. https://doi.org/10.3141/2212-12 Zvonari ć , M., Benši ć , M., Bariši ć , I., & Dokšanovi ć , T. (2024). Prediction Models for Mechanical Properties of Cement-Bound Aggregate with Waste Rubber. Applied Sciences, 14(1), 470. https://doi.org/10.3390/app14010470

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Procedia Structural Integrity 63 (2024) 13–20

22nd International Conference on Modelling in Mechanics 2024 Numerical Modelling of Water Mist Dispersion Due to Traffic Ivan Kolos a, * , Lenka Lausova a , Vladimira Michalcova a a Department of Structural Mechanics, Faculty of Civil Engineering, VSB-Technical University of Ostrava, Ludvika Podeste 1875/17, 708 00 Ostrava-Poruba, Czech Republic Abstract In winter, de-icing salt causes degradation of traffic structures in the vicinity of the road. The article deals with the numerical analysis in Ansys Fluent software of the transport of water mist from passing cars in order to solve the microclimatic situation around the road. As part of the numerical analysis, a domain was created based on a specific road cut, where measurements of deposition chloride ions will be taking place. The content of the article was an evaluation of the distribution and quantity of salt fog droplets injected from the tires of a passing vehicle falling into the near and far surroundings of the road. Four wind direction variants were evaluated, two from the front and two from the back, all with the wind entering at 60-degree angle. Droplets on three sampling zones at distances of 5, 9 and 13 m from the vehicle axis were monitored. A strong influence of the wind on the behavior of the swirling particles behind the vehicle was confirmed. © 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of 22nd International Conference on Modelling in Mechanics 2024 organizers

Keywords: natural frequency; mode shape; stiffness matrix; mass matrix; bisection method

1. Introduction Sprinkled de-icing salts are used for safe driving on roads in winter. On the other hand, however, they cause corrosion of steel and steel-concrete road bridges and degradation of other transport structures. Monitoring the microclimate in the vicinity of roads can be of great importance for the design of these structures sufficiently resistant to this negative phenomenon.

* Corresponding author. Tel.: +420 596 991 340. E-mail address: ivan.kolos@vsb.cz

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Some articles published in previous years have been devoted to this topic. A study Vacek et al. (2022) deals with the same issue in a similar location. The result of their work is an experimental research on the measurement of the amount of salt in the vicinity of the road and the evaluation of average corrosion loss and average concentration of SO 2 . Numerical analysis of truck generated salt spray transport near bridges is processed in a study Lottes and Bojanowski (2013). This report documents work using CFD analysis to study the conditions and mechanisms that lead from the salt spray thrown from truck tires to salt water droplets reaching bridge girders. Computer simulations to study the transport, dispersion, and deposition of pollutant particles near the bridge are published in the Liu and Ahmadi (2005), where k- ε models of the Fluent software were used to simulate mean airflow conditions. A Lagrangian particle tracking model was used and the dispersion and deposition of particulate emissions from motor vehicle exhaust on the bridge was analyzed. The corresponding deposition rates on different surfaces were studied and the importance of wind turbulence and gravity on particle deposition was evaluated. In the paper Suto et al. (2017), a method combining a computational fluid dynamics model and a statistical procedure is proposed for the efficient estimation of the area-wide distributions of the cumulative amount of sea salt in the air, taking into account the local topography. The result was that the predicted amount of sea salt in the air decreases with increasing distance from the coast and varies with topography and onshore winds. In the article Hu et al. (2015) there was an investigation of the numerical simulation of spray induced by a simplified wheel model and a modified square-back model. In the simulation process, the phenomenon of breakup and coalescence of drops were considered. The relationship between the vehicle external flow structure and body soiling was discussed. The study Joung and Buie (2015) highlights new phenomena associated with droplets on porous media that could have implications for environmental aerosol formation research. Prevention of bridge degradation due to sea salt and the comparisons between the numerical and observed results are made in the article Obata et al. (2014). The paper Vargas Rivero et al. (2022) presents a real-time simulation of the effect of sprayed water on an automotive sensor. The simulation is based on physically measurable quantities, the sensor and the environment are simulated using the Blender and Cycles software tools. 2. Solution procedure The aim of this paper is numerical analysis of the transport of water mist sprayed from the road to the near and far surroundings by passing one truck in different wind directions. The possibility of comparing the numerical model with the ongoing real measurement in the road cut is used here. The passage of the car through the road cut is solved, see Fig. 1, the slope of the ground body is approximately 25°. The sensors are located at three distances from the axis of the communication, and in these places a numerical analysis was also evaluated for comparison.

Fig. 1. Cross-section of the road cut with the positions of the measuring points.

Ivan Kolos et al. / Procedia Structural Integrity 63 (2024) 13–20

This road cut is used for the creation of the domain in the ANSYS Fluent 2023 R2 software for a model of a moving truck of which the flow field is solved.

3. Numerical analysis 3.1. Numerical model

Dimensions of the domain are based on the real geometry of the nearby road, on which probes are installed to measure the amount of chloride deposits. The computing domain is 240 m long, 60 m wide and 15.85 m high and it is divided into 3 zones (Fig. 2): preparation zone (120 m long), analytic zone (90 m long), exit zone (30 m long).

Fig. 2. Computational domain divided into zones.

The truck was placed in a separate subdomain in a 410 m long box, which allows simulation of the movement of the vehicle using the sliding mesh technique. The vehicle was located at a distance of 60 m from the analytical domain. This distance is assumed to be sufficient for the flow around the vehicle to fully develop before entering the analytic zone. The domain mesh consists of 800 thousand polyhedral cells. Cells in close vicinity of vehicle have diameter within range 0.05 and 0.2 m, maximum size of all other cells is 0.5 m. The vehicle was modeled in a simplified geometry based on Ardian (2018). It represents a general, most commonly used, truck with a length of 16 m, a width of 2.7 m and a height of 4 m. Preliminary study calculations have shown that the detailed modelling of droplet spraying by the entry of a rotating wheel into the liquid layer is inefficient due to the scale of the task, with excessively high demands on computing power. Therefore, a simplifying model was considered, where particles are injected from sidewalls of tires. Inert particles of constant diameter 2.5e-5 m, total flow rate 4.5 kg/s (based on Lottes and Bojanowski (2013)), initial particles velocity magnitude is 25 m/s, material of particles is simplified to liquid water with density 998.2 kg/m 3 . Total run time of the vehicle is 7.2 s. After 2.4 s, the vehicle enters the analytic zone and after 4.8 s reaches end face of the exit zone. Particles are evenly injected from the vehicle's wheels throughout the entire travel. Four directions of the wind are simulated in the model, two from the front and two from the back, all with the wind entering at 60-degree angle. Wind direction is shown schematically in Fig. 3. The angle is measured in the xz plane relative to the x-axis. The directional vector of the wind is horizontal, i.e. it lies in the xz plane.

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3.2. Boundary conditions Bottom faces of the domain and walls of the truck have wall boundary condition. Top face of domain is zero shear wall. Front, back, left and right sides of domain are velocity inlets or pressure outlets depending on direction of the wind flow according Fig. 3. There are also interfaces between moving subdomain and surrounding domain allowing smooth fluid and particles transport. Inlet wind velocity magnitude is 20 m/s. The vehicle moves with constant speed 25 m/s.

Fig. 3. Variants of wind flow.

3.3. Solutions and results The aim of the analysis is to evaluate the amount of droplets falling from a passing truck on the created sampling zones in the analytic zone of the domain. Standard k- ε turbulent model including wall functions was used to model wind flow. Discrete phase is modeled by Euler-Lagrange approach. Three sampling zones are defined in the analytic part of domain at distances of 5, 9 and 13 m, they are 1.5 m high (sampling zone 5, sampling zone 9 and sampling zone 13). During the vehicle's travel, the sampling zones are used to monitor the particles that fly through them. As already mentioned above, four variants of the wind flow are solved in the simulations. A detailed description of these variants and how they differ can be seen from Table 1.

Table 1. Variants of the wind flow in the simulations.

Variants of the wind flow

Wind flow side

Orientation of the flow relative to the position and movement of the vehicle

Variant 1 Variant 2 Variant 3 Variant 4

the right side the right side the left side the left side

In the front against the vehicle

In the back in the direction of the vehicle

In the front against the vehicle

In the back in the direction of the vehicle

The results of the performed simulations are shown in the following Fig. 4 to Fig. 8. Aerosol wake behind and passing truck for all wind direction are shown in Fig. 4. The figures clearly show how the different wind direction affects the resulting particle trajectory in the wake behind the vehicle.

Ivan Kolos et al. / Procedia Structural Integrity 63 (2024) 13–20

(a)

(b)

(c)

(d)

Fig. 4. Aerosol wake behind a passing truck. Wind 20 m/s. (a) Variant 1, (b) Variant 2, (c) Variant 3, (d) Variant 4.

Distribution and relative quantity of droplets in kg/m 2 are recorded in Fig. 5. There are shown the local extremes of the amount of captured droplets in all variants on the sampling zone 5. The highest local extremes of the number of captured droplets were recorded in the right-side variants. Specifically, in the front against the vehicle (variant 1) 0.275 kg/m 2 and in the back in the direction of the vehicle (variant 2) 0.124 kg/m 2 . In the case of the left wind flow side, the extremes would be an order of magnitude lower, specifically: in the front against the vehicle (variant 3) 0.0492 kg/m 2 and in the direction of the vehicle (variant 4) 0.0492 kg/m 2 .

Fig. 5. Sampling zone 5 – distribution and quantity of droplets in kg/m 2 . Variants 1 to 4, order top to bottom.

Ivan Kolos et al. / Procedia Structural Integrity 63 (2024) 13–20

The values of the local extremes on the other two sampling zones are in Fig. 6-7.

Fig. 6. Sampling zone 9 – distribution and quantity of droplets in kg/m 2 . Variants 1 to 4, order top to bottom.

Fig. 7. Sampling zone 13 – distribution and quantity of droplets in kg/m 2 . Variants 1 to 4, order top to bottom.

The distribution of droplets on the sampling zone 5 m from the road axis is also shown in a 3D graph for the calculated wind directions in Fig. 8. This graphical representation may allow to better imagine in which places and with what intensity the drops fell on the marked sampling zone.

Ivan Kolos et al. / Procedia Structural Integrity 63 (2024) 13–20

(a)

(b)

(c)

(d)

Fig. 8. Sampling zone 5 in 3D diagram – distribution of droplets. (a) Variant 1, (b) Variant 2, (c) Variant 3, (d) Variant 4.

The total amount of captured droplets in the entire length of the 90 m analytical zone are presented in Table 2, which shows the number of droplets in kg captured on individual sampling zones in the analytic zone for the solved wind direction variants.

Table 2. Amount of droplets in kg on sampling zones at distances of 5, 9 and 13 m from the road axis. Amount of droplets [kg] Sampling zone 5 Sampling zone 9 Sampling zone 13 Variant 1 2.713 0.189 0 Variant 2 2.629 0 0 Variant 3 0.224 0.019 0 Variant 4 0.004 0.006 0.012

The values displayed in the Table 2 show a trend that the number of droplets decreases with the increasing distance of the sampling zones from the roadway axis, except for the last variant 4 (the left wind flow, in the direction of the vehicle). In this variant, the fewest droplets were captured in the nearest sampling zone 5, but the particles tended to rise upwards and therefore also reached the most distant sampling zone 13. 4. Conclusions The article dealt with simulations of a moving vehicle, when sliding mesh approach was used for modelling the movement of the vehicle. The goal was to evaluate the distribution and total amount of droplets that are sprayed from a moving truck to different distances in a road cut. Four variants of the wind flow were solved. Modeling was done in ANSYS Fluent software and standard k- ε turbulent model was used to model wind flow. Discrete phase was modeled by Euler-Lagrange approach. As expected, the most droplets landed on the nearest monitored sampling zone at a distance of 5 m from the axes of the road, when the wind flowed from the side of the sampling zone (variants 1 and 2). An order of magnitude fewer

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droplets landed in the calculated variant 3, when the wind flowed from the opposite side, from the front side and against the movement of the vehicle. In addition to variant 4, the trend that the number of droplets decreases with increasing distance of the sampling zones from the roadway axis was confirmed. It is clear that the wind direction strongly influences the behavior of the swirling particles behind the vehicle. The results of this analysis will be used for comparison with the ongoing experimental measurement in the road cut. The experience gained from this analysis can be used in further research to solve the microclimate around the road, e.g. under the bridge. Knowledge of this issue could be used in the design of transport objects to prevent increased deposition of aerosols or impurities blown by traffic on the structure. In the future, it is possible to simulate a model of two cars, different combination of cars, or to evaluate numerical simulations using other turbulent models. Acknowledgements This contribution has been developed as a part of the research project GACR 22-19812S ‘‘Effect of gaseous and traffic induced pollutants on the durability of selected construction materials” supported by the Czech Science Foundation. This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic through the e INFRA CZ (ID:90254). References Ardian, Jaka, 2018. “Truck DAF Free 3D Model - .Blend .Obj .Fbx - Free3D.” Retrieved June 19, 2024 (https://free3d.com/3d-model/truck-daf-99043.html). Hu, Xingjun, Lei Liao, Yulong Lei, Hanbo Yang, Qingyin Fan, Bo Yang, Jing Chang, and Jingyu Wang, 2015. “A Numerical Simulation of Wheel Spray for Simplified Vehicle Model Based on Discrete Phase Method.” Advances in Mechanical Engineering 7(7):1–8. doi: 10.1177/1687814015597190/FORMAT/EPUB. Joung, Young Soo, and Cullen R. Buie, 2015. “Aerosol Generation by Raindrop Impact on Soil.” Nature Communications 2015 6:1 6(1):1–9. doi: 10.1038/ncomms7083. Liu, Chaosheng, and Goodarz Ahmadi, 2005. “Computer Simulation of Pollutant Transport and Deposition Near Peace Bridge.” Particulate Science and Technology 23(2):109–27. doi: 10.1080/02726350590922288. Lottes, S. A., and C. Bojanowski, 2013. Computer Modeling and Analysis of Truck Generated Salt Spray Transport Near Bridges. Argonne National Laboratory . Argonne, IL (United States). doi: 10.2172/1087817. Obata, Makoto, Li Guotai, Yasunari Watanabe, and Yoshiaki Goto, 2014. “Numerical Simulation of Adhesion of Sea-Salt Particles on Bridge Girders.” Structure and Infrastructure Engineering 10(3):398–408. doi: 10.1080/15732479.2012.757328. Suto, Hitoshi, Yasuo Hattori, Hiromaru Hirakuchi, Naoto Kihara, and Yasumasa Nakashiki, 2017. “Computational Fluid Dynamics Simulation and Statistical Procedure for Estimating Wide-Area Distributions of Airborne Sea Salt Considering Local Ground Conditions.” Structure and Infrastructure Engineering 13(10):1359–71. doi: 10.1080/15732479.2016.1268173. Vacek, Miroslav, Vít K ř ivý, Kate ř ina Kreislová, Markéta Vlachová, and Monika Kubzová, 2022. “Experimental Measurement of Deposition Chloride Ions in the Vicinity of Road Cut.” Materials 2023, Vol. 16, Page 88 16(1):88. doi: 10.3390/MA16010088. Vargas Rivero, Jose, Thiemo Gerbich, Boris Buschardt, and Jia Chen, 2022. “The Effect of Spray Water on an Automotive LIDAR Sensor: A Real-Time Simulation Study.” IEEE Transactions on Intelligent Vehicles 7(1):57–72. doi: 10.1109/TIV.2021.3067892.

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Procedia Structural Integrity 63 (2024) 43–50

22nd International Conference on Modelling in Mechanics 2024 Numerical Model of 3D Printed Joint of Wooden Frame Petr Lehner a, *, David Jura č ka a , Dominik G ř ešica a , Martin Krejsa a a Department of Structural Mechanics, Faculty of Civil Engineering, VSB-Technical University of Ostrava, Ludvika Podeste 1875/17, 708 00 Ostrava-Poruba, Czech Republic

Abstract Regardless of the type of material, 3D printing seems to be an interesting alternative to conventional construction methods. Leaving aside the use of 3D printing systems for concrete or cement composites, the more conventional 3D printing of plastic, metal or other separated materials may also have its hypothetical benefits in the creation of structural joints. For truss structures, such as arch bridges, certain types of joints can be expected that do not always have the same angle between the single-plane load-bearing elements of the structure. In such a case, the use of 3D printing technology for joint fabrication is defensible. In the case of a standard scale and using experience from timber bridges, one would assume that an embedded plate and pin connection would be the appropriate connection form. In contrast, from the point of view of producing smaller physical models, mainly for a deeper understanding of the comparability issues of numerical modelling and experimental testing, it is advantageous to use so-called enveloping timber element connections. The present paper describes the basic process of numerical analysis of a detail of a wooden arch bridge connection made from 3D printed polycarbonate joints. © 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of 22nd International Conference on Modelling in Mechanics 2024 organizers

Keywords: 3D printing; structural joint; FEM analysis; ANSYS

1. Introduction 3D printing or additive manufacturing (AM) is used in all sectors of human activity (Nguyen et al., 2023; Su and Al’Aref, 2018). Similarly, 3D printing has found its way into the construction industry over the past decade. An example is concrete printing (Cuevas et al., 2021), which is a separate industry and there are many research groups

* Corresponding author. E-mail address: petr.lehner@vsb.cz

Petr Lehner et al. / Procedia Structural Integrity 63 (2024) 43–50

and applications around the world. On the other hand, a separate chapter is 3D printing using plastics, metals, and wooden materials (Nicolau et al., 2022). This possibility of applicability in construction is not publicly known because there are many unresolved research questions (Arrêteau et al., 2023). For example, inaccuracies in 3D printing that need to be investigated and new techniques and procedures are being developed for this (Kozior et al., 2024). While we find some practical applications, there is a lack of in-depth logical integration of standard construction practices and needs with the benefits of 3D printing. The first step in such a deeper understanding is to find the goal. In this case, the goal is to create a numerical model of a scaled-down physical model of a truss arch bridge that combines wooden elements and 3D printed joints. This goal is based on the idea that the shape of the arch bridge can be generated by nonrepeating angles of the member connections and, moreover, that there is great potential for design variability. The reduced physical model was chosen so that the results could be experimentally verified with the numerical model in the future. When a goal is chosen, the path to that goal must be clearly defined. The path to the mentioned goal is set out by not simply understanding the behaviour of the base material used in the 3D printer, but through the correct definition of the numerical model of the joint, the numerical model of the whole structure, and the linking of the results into the most realistic output. This paper focusses on one of these steps, namely, the modelling of a truss connection example. The aim is not to present or evaluate a specific case, but to highlight the actual process of creating a detailed numerical model (based on finite element method (FEM) software) (Bathe, 2008), to demonstrate the differences when using two different sources of material information and to highlight some interesting points. It is worth noting here that the presented study focusses purely on numerical modelling and does not include information on future real-world printing of samples and their testing. 2. Materials characteristics The material and its properties are very important for models. In the case presented, three variants were analysed. The first material model adopted information on the behaviour of the material printed by the 3D printer from the manufacturer and supplier (Hu, 2021). In the second variant, tensile tests were performed on test specimens in the lab, and material properties were derivated on the basis of these tests. In the first two cases, it was a classically supplied (see also (Dedek et al., 2024)) polycarbonate (PC) blend, and in the third case, it is a polycarbonate blend carbon fiber (PCCF), which is also supplied by the printer manufacturer (Hu, 2021). In the first material model, the following material properties are set for the 3D printed element: the modulus of elasticity in tension is 1.9 GPa, the tensile strength is 63 MPa, the Poisson constant is 0.4 and the density is 1220 kg/m 3 (Hu, 2021). This model is marked as PC01. In the second model, the first phase consisted of the analysis of test results for 5 pieces of samples for the tensile strength test dog-bone specimen. The samples were 170 mm long and the cross-section at the neck was 10 x 4 mm. The resulting tension and deformation diagram was converted to a stress and strain diagram. From these data, a tensile strength of 50 MPa and a modulus of elasticity at tension of 1.5 GPa were determined. This model is marked as PC02. It should be noted here that the manufacturer himself states that the values are guaranteed due to the nature of 3D printing based on the specific size of the printed layers and precisely defined conditions. From that point of view, it is interesting that in this case the differences are around 20%. As a complement to these two models of the same material, but with parameters from different sources, a model where the material was different was added. PCCF have this material property: the modulus of elasticity in tension is 3.5 GPa, the tensile strength is 64 MPa, the Poisson constant is 0.4 and the density is 1220 kg/m 3 (Hu, 2021). This model is marked as PC03. For all models, the C24 wood class was used as the material for connected beams.

Table 1. Material characteristics Model No.

Fly ash [%]

Modulus of elasticity [GPa]

Poisson constant [-]

Density [kg/m 3 ]

PC01 PC02 PC03

1.9 1.5 3.5

0.4 0.4 0.4

3.7 3.7 3.2

Petr Lehner et al. / Procedia Structural Integrity 63 (2024) 43–50

3. Numerical analysis 3.1. Geometry and boundary conditions

This paper describes the basic design procedure, numerical analysis, and evaluation of several detail variants. For this purpose, a wooden arch bridge joint was selected from a potential real experimental model. This mentioned arch bridge will be implemented and tested experimentally in the future. Therefore, it is advisable to analyse its joints numerically and determine their stiffness. Fig. 1 shows a simplified numerical model prepared in Ansys Workbech/Mechanical (ANSYS, 2020) software with its boundary conditions. The geometry of the model is based on a main wooden element of 10 x 10 mm cross-section, which is longitudinal, and a second element forming a diagonal upward. These two elements are connected by a 3D printed joint into which they are slid. The diagonal is also secured with two bolts. This model has clearly defined boundary conditions to infer the thrust in the diagonal direction. The contacts between the materials are set to a friction value of 0.4 and the model also contains 2 joints simulating a bolt (see Fig.2). Contacts between materials allow only the transfer of compressive forces. The force in the diagonal direction has a value of 1 KN.

Fig. 1. Part of the FEM model of joint and boundary conditions.

Petr Lehner et al. / Procedia Structural Integrity 63 (2024) 43–50

Fig. 2. Detail view at the diagonal and joint connections.

3.2.Mesh 3D printed structures have problems with the delamination of individual layers, and this effect should be further investigated in future numerical models. This paper shows the first steps in this direction and therefore introduces finite elements with an average size of 0.4 mm into the model. Fig. 3 presents the mesh of finite elements in the longitudinal section plane at the centre of gravity of the model. It is worth noting in this section that there is a great deal of room for analysis of how to properly model 3D printed elements, especially with respect to the direction and orientation of the print layers.

Fig. 3. Graphical demonstration of finite element mesh in models.

Petr Lehner et al. / Procedia Structural Integrity 63 (2024) 43–50

3.3. Results Three FEM models were prepared with the same geometry and the same boundary conditions but with different 3D printed element materials. The results of the numerical analysis are presented in Figure 4 and Figure 5. Figure 5 shows the deformations in the section plane in the middle of the structure so that the separation of the wood and polycarbonate parts can be evaluated. In all cases, this was done. As expected, the tensile part of the wood diagonal transmits the deformations only through the bolts and moves away uniformly. This induces large tensile deformations on the top of the 3D printed joint, and at that moment the first differences between the models can be observed due to the different values of the elastic modulus. The biggest difference is in model PC03, where the joint has higher stiffness, thus producing a larger deformation in the horizontal element. Models PC01 and PC02 deform more and therefore the horizontal wood element deforms less. Figure 6 shows the von-Mises stresses on the 3D printed part only (wooden members are ignored in the plot) for all three models. Large differences can be seen in the stress distributions as well as in the maximum values. The colour scale and legend for these results are set so that values exceeding 80 MPa are in red. The extreme peak of stress for model PC01 is 807 MPa, for model PC02 is 670 MPa, and for model PC03 is 1248 MPa. For all models, extreme values are concentrated around the bolt holes, which is expected. In a real structure, there will be an indentation or a dangerous failure. Furthermore, for the PC03 model, extreme values are observed in the area between the horizontal and oblique parts of the joint. Again, this is due to the higher stiffness of the material, which comes at the expense of toughness.

Petr Lehner et al. / Procedia Structural Integrity 63 (2024) 43–50

Fig. 4. Deformation in the longitudinal section plane in the middle of the model. Model PC01 on top, PC02 on the middle, and PC03 on the bottom.

Petr Lehner et al. / Procedia Structural Integrity 63 (2024) 43–50

Fig. 5. Von-Misses stress on the 3D printed part. Model PC01 on top, PC02 on the middle, and PC03 on the bottom.

4. Conclusions This paper presents a basic view of the numerical modelling of a 3D printed joint applicable to a simple building structure. The aim was to highlight some fundamental requirements and present a process that will be applicable to other selected structures and parts. From the initial steps of the numerical analysis, it was possible to draw some conclusions that need to be considered in future research. Primarily, what needs to be modelled and why is crucial. While this may be as vague information, in 3D printing there is a big difference in every change in geometry or boundary conditions. Another very necessary requirement is the correct understanding and use of the material information provided by the manufacturer. In the paper, it is presented that the difference in parameters compared to the datasheet is 20%, but it is not clearly defined that this is an error. On the contrary, the special behaviour of 3D printed materials, which depends on the printing process itself, has to be taken into account. Another very necessary requirement is to correctly understand and use the material information provided by the manufacturer. The article presents that the difference of parameters from the datasheet is 20%, but it is not clearly defined that this is an error. In contrast, the special behaviour of 3D printed materials needs to be taken into account, which depends on the printing process itself. Future research must focus on comparing numerical models and experimental tests, as well as case studies involving aspects of 3D printing such as delamination, heterogeneity, and brittleness. Acknowledgements This research and this paper were funded by the Ministry of Education, Youth and Sports of the Czech Republic in Student Grant Competition through VSB – Technical University of Ostrava – grant number: SGS SP2024/093. ANSYS, 2020. ANSYS Meshing User’s Guide [WWW Document]. ANSYS User Guide. URL https://customercenter.ansys.com/ (accessed 10.29.20). Arrêteau, M., Fabien, A., El Haddaji, B., Chateigner, D., Sonebi, M., Sebaibi, N., 2023. Review of Advances in 3D Printing Technology of Cementitious Materials: Key Printing Parameters and Properties Characterization. Buildings. https://doi.org/10.3390/buildings13071828 Bathe, K.-J., 2008. Finite Element Method, in: Wiley Encyclopedia of Computer Science and Engineering. John Wiley & Sons, Inc., Hoboken, NJ, USA. https://doi.org/10.1002/9780470050118.ecse159 Cuevas, K., Chougan, M., Martin, F., Ghaffar, S.H., Stephan, D., Sikora, P., 2021. 3D printable lightweight References

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cementitious composites with incorporated waste glass aggregates and expanded microspheres – Rheological, thermal and mechanical properties. Journal of Building Engineering 44, 102718. https://doi.org/10.1016/j.jobe.2021.102718 Dedek, J., Jura č ka, D., Bujdoš, D., Lehner, P., 2024. Mechanical Properties of Wooden Elements with 3D Printed Reinforcement from Polymers and Carbon. Materials 17. https://doi.org/10.3390/ma17061244 Hu, B., 2021. Original Prusa i3: The Self-Replicating 3D Printer. Operations Management Education Review 15. https://doi.org/10.4135/9781529610796 Kozior, T., Bochnia, J., Bochenek, A., Malara, D., Nawotka, M., Jansa, J., Hajnys, J., Wojtowicz, A., Mesicek, J., 2024. Estimating the Uncertainty of Measurements for Various Methods and 3D Printed Parts. Applied Sciences 14, 3506. https://doi.org/10.3390/app14083506 Nguyen, H.S., Ma, Q.P., Hajnys, J., Mesicek, J., Pagac, M., 2023. RESEARCH TREND IN THE FIELD OF ADDITIVE MANUFACTURING WITH BIBLIOMETRICS STUDY. MM Science Journal 2023-June. https://doi.org/10.17973/MMSJ.2023_06_2023032 Nicolau, A., Pop, M.A., Co ș ereanu, C., 2022. 3D Printing Application in Wood Furniture Components Assembling. Materials 15. https://doi.org/10.3390/ma15082907 Su, A., Al’Aref, S.J., 2018. History of 3D Printing. 3D Printing Applications in Cardiovascular Medicine 1–10. https://doi.org/10.1016/B978-0-12-803917-5.00001-8

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Procedia Structural Integrity 63 (2024) 35–42

Keywords: natural frequency; mode shape; stiffness matrix; mass matrix; bisection method 1. Introduction Knowledge of natural frequencies and mode shapes is necessary for structures that are dynamically loaded. Dynamic effects are caused by inertial forces that arise during the accelerated motion of masses. It can be caused by the movement of the structure itself, the movement of objects placed on the structure, or the movement of the structure surroundings (air, water, soil). A number of papers are focused on solving the natural frequencies and mode shapes of structures. Some present analytical analysis, others numerical analysis, and some present experimental work. 22nd International Conference on Modelling in Mechanics 2024 Numerical Solution of Natural Frequencies and Mode Shapes Lenka Koubova a, * a Department of Structural Mechanics, Faculty of Civil Engineering, VSB-Technical University of Ostrava, Ludvika Podeste 1875/17, 708 00 Ostrava-Poruba, Czech Republic Abstract Every construction has a set of their natural frequencies (resonant frequencies) and mode shapes that depend on its material, structure, and boundary conditions. A mode shape is a deflection pattern. It is related to a particular natural frequency and represents the relative displacement of all parts of a construction for that particular mode. This paper deals with numerical solutions of natural frequencies and mode shapes. The method of stiffness constants and bisection method is used. The procedure can be used for any planar bar construction. First, the mode shapes of the simple beam are solved, where the solution is compared with the results obtained using known relationships. The article further describes the solution of the parabolic arc. © 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of 22nd International Conference on Modelling in Mechanics 2024 organizers

* Corresponding author. Tel.: +420 596 991 919. E-mail address: lenka.koubova@vsb.cz

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