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Effect of surface roughness on interface shear strength parameters of sandy soils

  • Hala K. Kadhim EMAIL logo and Mohamad Alyounis
Published/Copyright: June 27, 2024
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Abstract

Understanding the interface shear strength is crucial for the design of geotechnical structures. This study investigates the effect of surface roughness on the interface friction angle, peak interface friction coefficient, and interface shear strength through direct interface shear tests. The experiments were performed on 10 samples of concrete and steel with the level of roughness varying and soil. The objective is to provide soil parameters for a site that is located around 6 km away to the south of Al-Amarah city, Southeast of Iraq where earthquakes hit frequently. The research is intended to investigate the effect of earthquakes on objects that are built in that particular region, by putting emphasis on the interaction between the soil structure and the roughness of the contact surface between the structural parts and the soil. In order to evaluate the roughness nature of structural materials, a test program was conducted using the SRT-6210 Digital Surface Roughness Tester. The average roughness parameter (R a) had the strongest association with shear parameters, and so it is the indicator to explain the shear behavior of sand‒concrete and sand‒steel interfaces. The direct shear box test was employed to find out the soil’s shear strength parameters as well as the interface shear strength parameters. The test shows a profound change in the shear strength characteristics of sand‒concrete and sand‒steel indispensable interfaces. As the roughness index increased. It depicted an upward slope of apparent shear strength and friction coefficient taken at the interface. The shear strength had increased by 25.13% when the roughness of the concrete was below 20 μ m and by 36.26% when the roughness of the steel was below 30 μ m . Moreover, sand‒steel samples interface friction angle increased by approximately 31.5% with increasing surface roughness and sand‒concrete samples by 21.54%. The results also revealed that the peak interface friction coefficient ( μ p ) increased with the increase in R a.

1 Introduction

With the growing emphasis on soil‒structure interaction, comprehending the mechanical attributes of pile-soil interfaces has emerged as a fundamental facet of geotechnical investigation. The stress characteristics exhibited at the interface between the pile and soil have piqued the curiosity of scholars worldwide, capturing their attention to a significant degree. Extensive examinations have been dedicated to acquiring and analyzing shear strength indicators in various loading conditions, aiming to establish correlations between shear strength, normal stress, friction coefficient, and soil strength. Analyzing the influence of the frictional coefficient of the interface and the surface roughness on the shear behavior of the contact interfaces is also of great importance [1,2,3,4].

Laboratory tests, theoretical studies, and field tests are conventionally used for shear properties evaluation at pile-soil interfaces [5,6,7,8,9,10]. Direct shear tests are currently the most widely used indoor testing method due to their versatility, affordability, and ease of use. The experiments are set to different types of soil and external stress conditions so that the researchers obtain those specific parameters that can define the shear behavior and elucidate the influencing factors and mechanisms involved in the pile-soil interaction process. A good grasp of soil-structure interaction behavior is of great importance to geotechnical analysis, design, and supervision structures. Many researchers have examined the variables that have an impact on the shear features of granular interfaces [11,12,13]. Many studies provide evidence of the effect of engineering properties of granular material and the normal stress on interface shear behavior [14,15,16,17,18,19]. Therefore, a higher coefficient of friction is noticed at the interface, as the roughness and normal stress are increased [20].

The research conducted on the behavior of sands with different materials has shown interesting features. Uesugi and Kishida studied the frictional resistance of dry sand and mild steel; they developed the idea of a normalized roughness height. The coefficient of friction at the yield point and the normalized roughness were shown to be significantly correlated [21,22]. Similarly, to Dove and Frost, who carried out shear tests at an interface between sand and smooth polyethylene geomembranes, they showed the impact of particle shape, roughness, normal stresses, and hardness on the strength envelope [23]. The effect of surface roughness on interface friction angle has been extensively studied. Han et al. examined the effects of interface roughness, particle geometry, and sand gradation on the interface friction angle using various steel surfaces with varying degrees of rusting. They observed an upward trend in the interface friction angle as surface roughness increased [24,25,26]. Alyounis investigated the interaction between saturated interfaces in undrained conditions, specifically between steel samples and sand with varying degrees of roughness. The study revealed that sand deformation during shear accounted for a significant portion of overall displacement, and higher surface roughness of the upper steel sample resulted in higher peak strength [27]. Mohammed and Mahmood [28] indicate that a variety of techniques, including statistical variation and correlation models, must be used to assess the behavior and shear strength parameters of the soil.

Al-Shyoukhi et al. [29] employed the technique of finite element analyses to explore the impact of factors, such as additional skirts, internal friction angle of the soil, and relative density, on the bearing capacity of inclined skirted foundations in sandy soils. The results uncovered a substantial enhancement in the bearing capacity of the inclined skirted foundation with an increase in relative density. Similarly, the bearing capacity was impacted by an increase in the internal friction angle. Interestingly, extra skirts did not impact the load ability. In the case of seismic forces, some reinforced concrete (RC) buildings and structures may need repairing or reinforcement in order to increase their load-bearing capacity and thus their ability to withstand such forces. Moreover, the variation in service conditions can necessitate solutions to reinforce structures and avoid deformation or cracks. In such cases, the best alternative would rather be the reinforcement of the structure than the limitation of the use or regular inspection.

Balamuralikrishnan et al. [30] investigated, aiming to determine the flexural, shear, and combined behavior of RC beams strengthened and bonded externally with spent catalyst-based ferrocement laminates. The control beams that were not strengthened were used as a comparison. The research showed that the spent catalyst ferrocement-reinforced beams outperformed the control beams in all indicators.

Elsheikh et al. [31] delved into strengthening reinforced self-compacting concrete (SCC) box beams using carbon fiber-reinforced polymer (CFRP) or epoxy injection method. The purpose was to bridge the splitting caused by shear and see if recycled coarse aggregates (RCA) could replace natural coarse aggregates to produce SCC beams. The result showed that the beams exhibited higher flexibility after the reconstruction. The increased ultimate load of the system was due to the combined effects of epoxy injection and CFRP. Additionally, using CFRP and epoxy injection increased the ultimate strength of RCA beams.

Such studies have offered important knowledge on the behavior of soil-structure interfaces in terms of surface roughness. Nevertheless, further studies are needed to determine the impact harsh topography has on interface shear strength in sandy soils. This research aims to fill this knowledge gap by doing direct interface shear tests on steel and concrete samples with varying surface roughness in sandy soil conditions. Through the analysis of the results, critical parameters for the characterization of the shear strength of sand‒steel and sand‒concrete interfaces can be obtained, which provides useful insights for improving the performance and design efficiency of soil-structural systems.

Knowing the effect of surface roughness on interface shear strength and its consequences could offer more safety, stability, and sustainability to geotechnic structures. Furthermore, the studied area is characterized as seismically active. Therefore, the interaction of the soil and structure under seismic loading is of considerable importance for designing earthquake-resistant structures. This investigation intends to illustrate how surface roughness influences the interface shear strength of sandy soils, thus contributing basic soil parameters to analyzing structures in the seismically active region. Such results can be crucial in assessing structures’ seismic vulnerability and thus strengthen their seismic resistance.

In this study, the roughness parameter of the structural materials was measured. The SRT-6210 was employed to determine the surface roughness of the steel and concrete samples. The obtained roughness data were correlated with shear parameters, with the (R a) parameter showing the highest correlations. The direct shear box test was employed to determine the shear strength parameters of the soil, while the interface shear box test evaluated the parameters of the interface shear strength.

2 Materials and methods

Figure 1 shows the research methodology.

Figure 1 
               The study flowchart.
Figure 1

The study flowchart.

2.1 Surface roughness parameters

The surface profile is represented by surface topography, which is measured in terms of surface roughness. The behavior of interface shear in geologic materials is significantly impacted by it. However, roughness may promote adhesion. Ward [32] reviewed 23 different international standards for roughness measurements, everyone created to accommodate a specific use case. The following parameters are commonly utilized to define interface roughness in the context of interface behavior:

2.1.1 Average roughness (R a)

The average roughness (R a) is defined as the average of the asperity heights on the roughness profile (absolute value) [33].

2.1.2 Root mean square roughness (R q)

It is the standard deviation of the height of asperities located above and below the datum [33].

2.1.3 Maximum peak-to-valley roughness (R t or R max):

This characteristic is denoted by the height measured vertically along the profile’s assessment length. Between the profile’s highest peak and lowest valley [33].

2.1.4 Ten-point height (R z)

It is the height difference along the assessment length of the profile between the average of the five highest peaks and the five lowest valleys. It also facilitates estimating the magnitude of height variations within the profile and shows variations in the surface topography [33,34].

2.2 Interface testing devices

Shear experiments were conducted between sandy soils and samples of concrete and steel with varying roughness levels to examine the interface behavior between sandy soils and components of a structure, typically composed of steel or concrete. Ten steel and concrete samples were utilized in this research. Some of the steel samples were exposed to moisture and air, causing corrosion and producing excessive roughness. These samples have the same size as the shear box (6 cm × 6 cm). Molds were formed of glass and cut to the same dimensions as the shear box device used to acquire the regular shapes and edges for the concrete samples. Especially after the steel and wood molds failed to produce the concrete samples’ regular shapes. In terms of the surface roughness of the concrete samples, jam paper with varying roughness was placed on the samples before they hardened. This approach allows for samples with various roughness.

The equipment used to conduct the test is the direct shear device; load and deformation dial gauges and balance; Tamper (for compacting the soil in the direct shear box); spoon; and samples of steel and concrete.

A Contact Profilometer Digital Surface Roughness Tester SRT-6210 was used to determine the roughness features of the concrete and steel samples, which are illustrated in (Figure 2). The roughness parameters (R a, R z, R q, and R t) for the steel and concrete samples used in this study are summarized in Table 1.

Figure 2 
                  Digital surface roughness Tester SRT-6210.
Figure 2

Digital surface roughness Tester SRT-6210.

Table 1

Roughness parameters for concrete and steel samples that were measured in (µm)

Sample R a R z R q R t
Steel samples
1 1.173 14.65 1.3 12.5
2 3.811 15 3.2 20
3 7.675 76 7 80
4 12.96 97 11 95
5 27.51 109 25.3 113
Concrete samples
1 3.151 48 5.2 51
2 6.871 58 7.95 53.64
3 11.05 69.4 13.2 79
4 15.19 80.5 18.78 85
5 19.01 95 20.3 93

Figures 3 and 4 display the steel and concrete samples, respectively. Steps for utilizing the roughness testing devices are as follows:

  • Fully charge the device.

  • Adjust the device’s horizontality to ensure that the sensor makes contact with the sample.

  • Calibration of the instrument involves calibrating it with a piece of glass with a standard roughness ( R a = 0.82 μ m ) as shown in (Figure 5).

  • Adjusting the device’s sensor movement at a 2.5 mm distance.

  • Place the steel or concrete samples.

  • Adjust the device’s horizontality after each model.

  • Activate the device by selecting Start.

  • The sensor moves forward and backward, and a roughness reading appears on the device screen.

  • Adjust the device’s horizontality and zero the reading before measuring the roughness of each sample.

Figure 3 
                  Steel samples roughness: (a) two-dimensional steel samples, (b) three-dimensional steel samples.
Figure 3

Steel samples roughness: (a) two-dimensional steel samples, (b) three-dimensional steel samples.

Figure 4 
                  Concrete samples roughness: (a) two-dimensional concrete samples, (b) three-dimensional Concrete samples.
Figure 4

Concrete samples roughness: (a) two-dimensional concrete samples, (b) three-dimensional Concrete samples.

Figure 5 
                  Precision reference standard.
Figure 5

Precision reference standard.

2.3 Soil physical characteristics

Laboratory tests or correlations among various physical and mechanical properties of soil are the ways used to determine the properties of soil in any given location [35]. The soil samples are categorized as silty sand soil in accordance with the Unified Soil Classification system. It presents dry and bulk unit weights of 15.8 and 16.4 kN/m3, respectively [36].

2.3.1 Parameters of soil shear strength

Shear experiments were conducted to determine the shear strength of the sandy soil. The direct shear box test was carried out in the Geotechnical Engineering Laboratory at the University of Thi-Qar. Figure 6 shows the direct shear device.

Figure 6 
                     Shear box test.
Figure 6

Shear box test.

The shear box had a square cross-sections, measuring 60 mm by 60 mm by 30 mm (length × width × height). The equipment used to conduct the test is the direct shear device; load and deformation dial gauges; tamper and balance. The steps for conducting the test are as follows:

  • Removing the loading head and shear box assembly.

  • To keep the shear box halves together, insert two vertical pins.

  • Weigh some of soil (depends on the volume of shear box and density of the soil). Add soil with its natural moisture content to the shear box. To compact the soil layers, a tamper might be employed.

  • In the direct shear box test, install the shear box assembly.

  • adjust device horizontal

  • To apply the normal loads to the specimen, hang the dead weights (5.45, 10.9, and 21.8) kPa on the vertical load hanger.

  • Remove the two vertical pins

  • To measure the displacements during the test, attach the horizontal and vertical dial gauges to the shear box.

These steps are shown in (Figure 7). The findings are displayed in Figure 8 and Table 2. The angle of internal friction can be calculated using the direct shear box test and is (37°).

Figure 7 
                     Preparation of the soil sample. (a) preparing the shear box, (b) weighing some of soil, (c) placing the soil on shear box, (d) placement of the vertical Load shed section, (e) adjusting device horizontal, and (f) shedding vertical loads.
Figure 7

Preparation of the soil sample. (a) preparing the shear box, (b) weighing some of soil, (c) placing the soil on shear box, (d) placement of the vertical Load shed section, (e) adjusting device horizontal, and (f) shedding vertical loads.

Figure 8 
                     Shear stress vs horizontal displacement in a direct shear box test for sandy soil.
Figure 8

Shear stress vs horizontal displacement in a direct shear box test for sandy soil.

Table 2

Soil direct shear test for sample

Shear stress (kPa) Normal stress (kPa)
42.9 5.45
83.1 10.9
166.2 21.8

2.3.2 Interfaces’ shear strength parameters

Ten shear box tests were conducted, with five samples examining the interface between sand and steel and five examining the interface between sand and concrete. A steel (or concrete) sample was placed at the bottom half of the shear box so that the top half could freely move over the bottom part. The top half of the box was subsequently filled with soil, as illustrated in Figure 9.

Figure 9 
                     The soil sample’s preparation (Interface Test).
Figure 9

The soil sample’s preparation (Interface Test).

3 Results and discussion

3.1 Interface friction angle

The variation of the interface friction angle (δ) with the roughness of the concrete and steel samples is shown in Figures 10 and 11 respectively. Table 3 illustrates the correlation factors (r 2) for various roughness parameters (R a, R z, R q, and R t) for sand‒steel and sand‒concrete interfaces. The best correlation, provided by (R a), whose fitting correlation coefficient in the following figures ranges from 0.8795 to 0.9876, will be employed in this study.

Figure 10 
                  Variation of roughness parameters with interface friction angle 
                        
                           
                           
                              (
                              δ
                              )
                           
                           \left(\delta )
                        
                      for sandy soil‒concrete interface: (a) R
                     a, (b) R
                     z, (c) R
                     q, and (d) R
                     t.
Figure 10

Variation of roughness parameters with interface friction angle ( δ ) for sandy soil‒concrete interface: (a) R a, (b) R z, (c) R q, and (d) R t.

Figure 11 
                  Variation of roughness parameters with interface friction angle 
                        
                           
                           
                              (
                              δ
                              )
                           
                           \left(\delta )
                        
                      for steel‒sand interface: (a) R
                     a, (b) R
                     z, (c) R
                     q, and (d) R
                     t.
Figure 11

Variation of roughness parameters with interface friction angle ( δ ) for steel‒sand interface: (a) R a, (b) R z, (c) R q, and (d) R t.

Table 3

Correlation factor (r 2) between surface roughness parameters and ( δ )

Roughness Steel samples Concrete samples
δ δ
R a 0.9242 0.9876
R z 0.8795 0.9671
R q 0.9042 0.9759
R t 0.9062 0.9215

As the roughness increased, the interface friction angle showed an increase in trend, as can be seen in the data shown in Figures 10 and 11. In particular, the interface between concrete and sand increased by 21.54%, but the interface between steel and sand increased by 31.5%. This is consistent with the findings of Han et al. [26].

In addition, it is clear that the interface friction angle has smaller values than those found in the soil when comparing the mechanical and physical characteristics of the soil.

3.2 Interface shear strength

The test findings indicate that the shear strength variation curves for the steel or concrete‒soil interface can be constructed with different levels of roughness.

Figures 12 and 13, respectively, provide illustrations of these curves. The shear strength clearly increased in response to an increase in roughness when normal stress conditions were maintained constant.

Figure 12 
                  Relationship for steel sample roughness and shear strength of interface.
Figure 12

Relationship for steel sample roughness and shear strength of interface.

Figure 13 
                  Relation between the roughness of concrete samples and the shear strength of the interface.
Figure 13

Relation between the roughness of concrete samples and the shear strength of the interface.

The interface shear strength increases from 10.4 to 13.89 kPa. This corresponded with a relative rise of 25.13% for concrete samples, when the normal stress is equal to 21.8 kPa. Similar to this, there was a 36.26% relative rise in the interface shear strength for the steel samples, which went from 9.48 to 14.87 kPa. According to these results, the shear strength is highly influenced by the roughness of the sand‒steel (or concrete) contact.

Under equal roughness conditions, Figures 14 and 15, respectively, show the relationship between shear strength and normal stress for the concrete and steel samples. It is evident that under equivalent roughness circumstances, a linear regression describes the relation between shear strength and normal stress.

Figure 14 
                  Relation between shear strength of (sand‒concrete) interface and normal stress.
Figure 14

Relation between shear strength of (sand‒concrete) interface and normal stress.

Figure 15 
                  Relation between shear strength of (sand‒steel) interface and normal stress.
Figure 15

Relation between shear strength of (sand‒steel) interface and normal stress.

3.3 Peak interface friction coefficient

The average roughness parameter, R a, can express the impact of the surface roughness of structural materials (steel and concrete) on the peak interface friction coefficient, μ p = tan ( δ p ) , where δ p is the peak interface friction angle of the granular material [19]. The general trend of the test results shown in Figure 16 indicates that, with increasing R a value, μp values increases. When the roughness of concrete samples R a < 20 μ m and steel samples R a < 30 μ m , the peak interface friction coefficient is ( 0.43 < μ p < 0.7 ) , and the values are close for the two materials. The findings are consistent with the research conducted by Uesugi and Kishida [13,14,19] and Abuel-Naga et al. [37].

Figure 16 
                  Peak interface friction coefficient variation against R
                     a.
Figure 16

Peak interface friction coefficient variation against R a.

4 Discussion

The experimental program conducted in this research aimed to investigate the impact of surface roughness on the interface shear strength parameters of sandy soil in contact with steel and concrete. The surface roughness was evaluated using the SRT-6210 Digital Surface Roughness Tester, which measured four different roughness parameters. The roughness average was the best indicator for sand‒steel and sand‒concrete interfaces to explain the shear behavior while shear parameters showed the best correlation with R a.

Figures 3 and 4 present the surface roughness results of steel and concrete samples. The surface roughness of the steel samples varied from ( R a = 1.173 μ m to R a = 27.51 μ m ) , while the roughness of the concrete samples ranged from ( R a = 3.151 μ m to R a = 19.01 μ m ) . It should be pointed out that when the surface roughness is increased, higher R a values are measured. This reveals that the roughness of the contact surfaces of the structural materials was different and that it might affect the interface shear strength.

Dove and Frost [23] studied shear analyses at interfaces between particles and smooth materials. They investigated the contact area between dense Ottawa sand and smooth polyethylene, considering particle shape, roughness, normal stress, and hardness. Their results indicated that the contact area increased with the normal load, and various factors influenced the form of the strength envelope. This aligns with the current study’s findings regarding the influence of surface roughness on interface behavior.

Moreover, Figures 10 and 11 represent how roughness affects the interface angle of friction. The interface friction angle is an important parameter, which characterizes the shear behavior of the interfaces. The findings demonstrated that an increase in roughness improved the interface friction angle. The interface friction angle of sand‒steel contact increased by 31.5% as the surface roughness increased. Furthermore, the interface friction angle increased by 21.54% with the increase of roughness for the concrete–sand interface.

Han et al. [26] focused on the influence of roughness at the interface, particle geometry, and gradation of sand on the interfacial angle of friction. It was revealed that the interface friction angle increased as the surface roughness was higher for particular types of sand. Such a trend corresponds with the results of the present study.

The results of the direct shear box tests on the sand‒steel and sand‒concrete interfaces have shown extreme dependence on surface roughness. Figures 12 and 13 illustrate the influence of surface roughness on the shear strength parameters of the interfaces. It can be seen that with the increase in the surface’s roughness, the interface’s shear strength increased. Specifically, the shear strength at the concrete samples with roughness less than 20 μ m increased by about 25.13%. Similarly, when the steel samples’ roughness was lower than 30  μ m , the shear strength rose by about 36.26%. These findings suggest that a rougher contact surface between the structural materials and the sandy soil leads to higher interface shear strength.

Besides, the shear strength, the friction angle, and the peak interface friction coefficient ( μ p ) were also examined. Figure 16 shows the effect of surface roughness on the peak interface friction coefficient. The data showed that the peak interface friction coefficient rose as the surface roughness (R a) increased, As such, a larger contact surface between the structural material and sandy soil translates to a higher resistance to sliding and shear deformation at the interface.

The roughness of the contact surface between the structural materials and the sandy soil gives a lesser surface area for particle–particle interaction. It leads to shear strength increment, enhanced frictional resistance, and increased interface friction angle. However, rougher contacting surfaces demonstrate reduced surface area for particle–particle interaction, resulting in higher shear strength and increased frictional resistance in the interface. Uesugi and Kishida [19] tested the frictional resistance between dry sand and steel. They proposed the normal relative roughness notion as a tool to evaluate the relative roughness of the sand‒steel interface. The results of the study revealed a significant link between the coefficient of friction and the normalized roughness, which correlates with the current study’s observations.

The novelty of this study is that it explains the effect of surface roughness on the interface shear strength parameters of sandy soil. The study determines the relationships between surface roughness and particular shear parameters, and valuable insights are provided for the optimization of soil-structural systems. The result points to the necessity of bearing in mind the roughness of the surface while studying the behavior and making predictions about geotechnical systems, especially in zones prone to seismic activity, such as the study area in Iraq.

5 Conclusions

The study was performed through the execution of field tests, which aimed at the evaluation of the roughness effect on the interface shear strength in sandy soils. Consequently, the soil characteristics that were best suited for the site in a moderate seismic activity area were delineated. The objective was to study soil‒structure interactions and contact roughness under seismic activity, which became the focal point of this study.

The SRT-6210 Digital Surface Roughness Tester was used during the experiments covering steel and concrete surfaces during the evaluation of their roughness. It was shown that R a exhibited the highest correlation with all shear parameters that were considered, which means that R a has the strongest tendency among them to describe the shear behavior of sand‒steel and sand‒concrete interfaces.

Preliminary shear tests of soil and the interface tests at the contact point observed a remarkable impact of surface roughness on shear parameters. A jump in interfacial strength in terms of roughness and interface friction angle was noticed with an increase in roughness.

The results revealed that increasing surface roughness led to an improvement in the interface friction angle of sand‒steel by about 31.5% and sand‒concrete samples by approximately 21.54%. In particular, when the steel samples’ roughness was less than 30 μm, the shear strength increased by 36.26%, and when the concrete samples’ roughness was less than 20 μm, it increased by about 25.13%.

The peak interface friction coefficient is entirely dependent on the surface roughness of concrete and steel samples, when the roughness of concrete samples ( R a = 3.151 19.01 ) μ m , the ( μ p = 0.477 0.637 ) , and for roughness of steel samples ( R a = 1.173 27.51 ) μ m , the ( μ p = 0.435 0.68 ) . The results show that the values of the peak interface friction coefficient increased with increasing average roughness parameter (R a).

The characteristics of sand‒concrete friction are similar to those of the friction between sand and steel surface when the roughness values are close.

This demonstrates the necessity and careful assessment of roughness in design and analysis of geotechnical structures. An assessment of the correlation between roughness and interface shear strength of soil-structural systems may lead to better designs that cater to the systems’ performance and safety.

  1. Funding information: Authors state no funding involved.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and consented to its submission to the journal, reviewed all the results, and approved the final version of the manuscript. HKK and MA conceived of the presented idea, carried out the experiment, contributed to the final version of the manuscript, designed, and directed the project; were involved in planning and supervised the work, processed the experimental data, performed the analysis, drafted the manuscript, and designed the figures. The authors discussed the results and commented on the manuscript.

  3. Conflict of interest: The authors state no conflict of interest.

  4. Data availability statement: Most data sets generated and analyzed in this study are comprised in this submitted manuscript. The other data sets are available on reasonable request from the corresponding author with the attached information.

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Received: 2023-12-09
Revised: 2024-03-19
Accepted: 2024-03-25
Published Online: 2024-06-27

© 2024 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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