Applied Research on the Minimum Thickness of Leveling Layer of Non-Adhesive Flat Extruded Board System
1
School of Materials Science and Engineering, Tongji University, Shanghai 201804, China
2
Key Laboratory of Advanced Civil Engineering Materials (Tongji University), Ministry of Education, Shanghai 201804, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2022, 12(9), 4673; https://doi.org/10.3390/app12094673
Submission received: 11 March 2022
/
Revised: 28 April 2022
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Accepted: 5 May 2022
/
Published: 6 May 2022
(This article belongs to the Topic Advances on Structural Engineering)
Abstract
:In order to meet residents’ demands for high sound insulation and thermal insulation performance in buildings, functional materials, such as non-adhesive extruded plastic panels, are added to floor slabs to form the bottom-up “structural layer-functional layer-levelling layer”, common in assembled buildings. The non-adhesive leveling system has gradually become a new floor structure. However, the strength of the functional layer is insufficient. How to determine the minimum thickness of the leveling layer is not fully considered in the current building ground design codes of various countries, which makes the engineering application ahead of the codes and the structural damage problems occur frequently. This must be considered, in order to ensure the safety of the system. Based on the layered elastic half-space theory, the effects of functional layer thickness, leveling layer thickness and leveling layer material on the maximum tensile stress of the system are compared. The results of this research lay a solid foundation for the popularization and application of non-adhesive flat extruded plate systems.
1. Introduction
The global construction industry tends to reduce environmental load and pays attention to energy conservation and emission reduction; at the same time, people’s living demands for housing are increasing with each passing day. Adding thermal insulation and sound insulation functional materials on the floor has become the mainstream, such as non-adhesive extruded boards, etc. However, during the actual laying operation process, construction workers do not always carefully calculate the thickness of the leveling layer under the guidance of the building codes. The constructions are usually empirical and may not be accurate, and the strength of the extruded plate is low. If the thickness of the leveling layer above is insufficient, it is prone to accidents, such as extrusion plate damage [1,2]. Therefore, compared with the ground structure layer laid on the actual rigid bottom layer, the load state of the pea gravel concrete leveling layer must be accurately mastered.
As shown in Figure 1, the distribution of “hard soft hard” in the non-adhesive flat extruded plate system is similar to the layered structure in geophysics [3,4]. Based on a large amount of rigorous research in the past, the analysis and application of the hierarchical structure has been gradually established. Lord Rayleigh [5] studied the free vibration of infinite plates about uniformly isotropic elastic substances by means of mathematical derivations. Mazumdar [6] and Dutta [7] proposed two methods for studying the transverse vibration of thin uniform isotropic elastic plates. Tomar and Gupta [8,9,10,11] studied the free vibration of infinite plates, with linearly varying and parabolic varying thicknesses using the Frobenius method, on the basis of classical plate theory. Subsequently, they studied elastic infinite plates of different thicknesses with non-homogeneous isotropy located on elastic foundations with different combinations of boundary conditions. These provide simple models for researchers in seismology and soil mechanics.
On the basis of these studies, researchers have begun to study hierarchical structures within various domains. In thermodynamics, researchers proposed a method to analyze the deflection of sandwich plates under thermal loads. The nonlinear vibration problem of a homogeneous heated sandwich elliptical plate of homogeneous thickness made of orthotropic materials under thermal load can be derived by means of a constant deflection contour to control the partial differential equation [12,13]. In terms of geotechnical mechanics, the Winkler foundation model was used to discuss the plane problem of Winkler foundation with an empty elastic layer and the plane contact problem of a homogeneous and isotropic elastic layer on Winkler foundation [14,15]. In the acoustics aspect, in order to study the performance of a thick elastic layer or the combination of an elastic layer and thermal insulation layer, researchers considered that the Young’s modulus decreases with the increase in frequency, and adopted the finite element model and TMM model [16]. In order to accurately evaluate the actual acoustic behavior of floating floors, a propriety model to calculate the impact acoustic improvement of floating floors was proposed [17]. In the field of mechanical theory, the transversal shear stiffness of the sandwich panel with corrugations was obtained by finite element method simulation [18,19]. Raphael Höller analyzed and compared the theory of a shear-rigid plate on Winkler foundation, based on Westergaard theory, theory of layered elastic half-space and 3D Finite Element simulations. Finally, it is determined that the theory for the layered elastic half space is more suitable for the discussion of a non-adhesive flat extruded plate system. Then, based on the principle of virtual power, the theory of elastic-supported thin plates with arbitrary boundary conditions was deduced [20,21]. These papers have preliminarily established the calculation model for a layered structure, but they only stay in the stage of theoretical analysis, and there are few practical application cases.
The XPS extruded board is damaged due to the small thickness of the protective layer during the actual use of the ground, which affects the construction safety, as shown in Figure 2. The current building ground design codes in most countries provide a variety of ground bedding cushion construction codes, but do not fully consider how to calculate the minimum thickness of the protective layer on the non-adhesive extruded board [22]. Based on the above theoretical calculation model of layered elastic half space, the thickness of XPS is taken as 40 mm and 60 mm, respectively, and the minimum thickness of the leveling layer of seven groups of different materials is calculated, so as to provide theoretical support for the actual laying of the leveling layer.
Firstly, this paper briefly reviews the theory of a shear-rigid plate on Winkler foundation, based on Westergaard theory, the theory of elastic half space and 3D finite element simulations (3D FE simulations), and compares their applicability [21]. Secondly, the calculation program of the corresponding relationship between the thickness of the leveling layer and the tensile strength of the functional layer material under load is established by using the elastic half-space theory. Then, the minimum thickness of cementitious self-leveling mortar and gypsum base course is calculated, when the thickness of the functional layer is 40 mm and 60 mm, respectively, under the action of 2 kN/m2 floor load. Finally, the numerical solutions of influencing factors, such as elastic modulus and Poisson’s ratio of base material, are obtained by using MATLAB language in the literature [21]. MATLAB integrates many powerful features, such as numerical analysis, matrix calculations, visualization of scientific data, modeling and simulation of nonlinear dynamic systems, etc., providing a comprehensive solution for scientific research, engineering design, and many scientific fields where efficient numerical calculations must be performed.
2. Layered Elastic Half-Space Theory
The layered elastic half space theory was first used to simulate the “layered structure” in geophysics, and later developed for structural engineering. The layered elastic half-space theory simplifies the three-dimensional structural system into four one-dimensional functions of the vertical position in the layered structure. Two of these four functions define the traction vector and displacement vector, related to the horizontal plane in the whole three-dimensional layered half space. As Figure 3 shows, the system in this study also conforms to this “layered structure”; that is, a hard layer (pea gravel concrete leveling layer) is placed on a soft layer (thermal insulation layer), which is placed on a foundation with greater relative stiffness (floor slab).
In the design of an elastic-support plate based on Westergaard theory, the thickness of the structural layer (leveling layer) is determined by the maximum tensile stress of the lower surface edge of the plate (the surface adjacent to the elastic foundation). This theory is based on the assumption that the normal stress perpendicular to the plate plane can be ignored. Therefore, the calculation result is the upper limit of the thickness of the structural layer. The theory for layered elastic half space holds that the failure position appears in the middle of the bottom surface of the plate instead of the edge; according to the 3D FE simulations, the failure load appears at the lower edge or in the middle of the lower bottom, which has little effect on the failure of the system.
For any floor design, the maximum stress calculated by the theory of shear-rigid plate on Winkler foundation is higher than that calculated by the theory of layered elastic half space. The design based on the theory of layered elastic half space is usually 10% more than that based on the theory of shear-rigid plate on Winkler foundation. The 3D FE simulations can provide an accurate algorithm for specific cases, but do not have universality and practical operability. Compared with 3D FE simulation, the theory of elastic half space provides evidence that the change of load position only affects the critical tensile stress at the bottom of the ground leveling layer slightly, which is more convenient to consult the data.
Therefore, considering the applicability of the code, this study intends to use the theory of layered elastic half space to analyze the existing model, and establishes the calculation model based on the theory of elastic half space.
3. Research Scheme
In this research, the common materials and thickness of the functional layer and seven kinds of leveling layer materials in China are selected. This research solves the analytical solution of the system through MATLAB, calculates the tensile stress of the materials under different Poisson’s ratio and elastic modulus, summarizes the influence of Poisson’s ratio and elastic modulus on the maximum tensile stress, and confirms the minimum protective layer thickness meeting the mechanical conditions, according to the tensile strength.
3.1. Material Parameter
In this calculation, 40 mm and 60 mm XPS are used for the extruded board, respectively, and the leveling layer materials are a C20 pea gravel concrete protective layer, gypsum-based self-leveling mortar, cementitious self-leveling mortar, etc.
In this paper, pea gravel concrete, XPS extruded slab and structural layer concrete are mainly considered, and their mechanical parameters are set, as shown in Table 1.
3.2. Load Value
According to the standard value of civil building load specified in the load code for building structures of various countries, the residential load is roughly 2.0 kN/m2. Referring to the Austrian building code OENORM B 3732, which includes the planning and design rules for indoor floor leveling works (no freezing exposure), the load surface diameter is 25 mm [23].
Therefore, on the premise that the tensile stress does not exceed the tensile strength, the width of the XPS layer is 6 m, the edge load P is 2.0 kN/m2, the load diameter is 25 mm, and the thickness is increased from 5 mm to 60 mm.
The horizontal tensile stress of the leveling layer is the first principal stress. When the horizontal tensile stress > the maximum tensile stress of the material, the system failure will occur. Therefore, the influence of the thickness of the first layer is discussed below.
3.3. Calculation Scheme
In this paper, the functional layer adopts 40 mm and 60 mm XPS, and the leveling layer materials are divided into seven categories, including pea gravel concrete, semidry mortar, hemihydrate gypsum self-leveling mortar, sand-free gypsum self-leveling mortar, anhydrous gypsum self-leveling, thick cushion cement self-leveling and UHPC. For each kind of material, different elastic moduli and Poisson’s ratios are taken to solve the analytical solution in MATLAB. There are 123 groups of data in total. For details, see Table A1.
4. Results
4.1. Effect of Thickness of Functional Layer on Maximum Tensile Stress of System
The corresponding relationship between the maximum tensile stress of the pea gravel concrete layer and the thickness of the XPS layer can be obtained through calculation of the subgrade bed coefficient k of Winkler foundation, solution of relative stiffness radius and calculation of maximum stress of edge load.
Figure 4 shows that when the XPS thickness increases, the tensile stress of the pea gravel concrete layer decreases gradually. The pea gravel concrete layer is generally C20 concrete, and its tensile strength is 1.54 MPa. Therefore, the thickness of the XPS layer must be more than 50 mm, and the thickness of the XPS layer has a negative correlation with the maximum tensile stress of the pea gravel concrete layer.
4.2. Effect of Leveling Layer Thickness on Maximum Tensile Stress
According to the layering theory, the first principal stress of the 40 mm and 60 mm pea gravel concrete leveling layer, gypsum-based layer and cementitious self-leveling mortar layer in the middle layer of the 2.0 kN load are calculated, respectively, and the following calculation results are obtained.
Since the maximum tensile stress cannot exceed 1.1 MPa, it can be seen from Table 2 that the thickness of the C20 pea gravel concrete leveling layer of 40 mm and 60 mm in the middle layer must be more than 61 mm.
Table 3 shows that, in order to avoid damage, the maximum tensile stress shall not exceed 1.6 MPa, the thickness of the gypsum base course of 40 mm and 60 mm in the middle layer must be more than 42 mm.
Since the maximum tensile stress cannot exceed 1.2 MPa, it can be seen from Table 4 that if the thickness of the functional layer is 40 mm, the thickness of cementitious self-leveling mortar layer is more than 56 mm, and if the thickness of the functional layer is 60 mm, the thickness of the cementitious self-leveling mortar layer is more than 57 mm.
To sum up, the maximum tensile stress mainly depends on the thickness of the leveling layer, and the thickness of the functional layer has no obvious effect on it.
4.3. Effect of Leveling Layer Material on Maximum Tensile Stress of System
It can be seen from Figure 5 and Table 5 that, for the same material, when the elastic modulus is constant, the greater the Poisson’s ratio, the greater the tensile stress in the leveling layer; when the Poisson’s ratio is constant, an increase in the tensile stress of the leveling layer is roughly equal for a given increase in the elastic modulus.
It can be seen from Table 6, Table 7 and Table 8 that, for the same material, when the Poisson’s ratio is constant, the tensile stress of the leveling layer increases by 0.004 MPa, with each 1.0 GPa increase in the elastic modulus; when the elastic modulus is constant, the tensile stress increases by about 0.008 MPa for every 0.01 increase in Poisson’s ratio.
5. Discussion
In this paper, the theory of layered elastic half space is adopted. Through the MATLAB calculation model, the stress state of the leveling layer in the case of using seven different functional layer materials in the non-adhesive flat extruded plate system is calculated and compared, so as to obtain the corresponding minimum thickness of the leveling layer, and the following conclusions are obtained:
- When the thickness of the functional layer increases, the tensile stress of the leveling layer decreases;
- The maximum tensile stress of the leveling layer mainly depends on the thickness of the leveling layer, and the thickness of the functional layer has no obvious effect on it;
- Both elastic modulus and Poisson’s ratio will cause positive correlation changes in tensile stress. Taking the self-leveling elastic modulus of thick cushion cement as 16 × 103 MPa and Poisson’s ratio of 0.16 as an example, if the elastic modulus increases by 25%, the tensile stress increases by 1.94%; when Poisson’s ratio increases by 25%, the tensile stress increases by 3.54%. It can be concluded that the Poisson’s ratio has a greater influence on tensile stress.
- According to the laws obtained in Section 4.3, it can be inferred that under the same Poisson’s ratio and elastic modulus, the tensile stress of sand-free gypsum self-leveling mortar is the smallest. Therefore, free gypsum self-leveling mortar is the most suitable material for the leveling layer.
Author Contributions
W.J. provided the concept and edited the draft of the manuscript and analyzed the results. W.J. and X.Z. conducted the literature review and wrote the first draft of the manuscript. All authors have read and agreed to the published version of the manuscript.
Funding
The research was financially supported by the National Natural Science Foundation of China, with grant number 52178240, and supported by the Key Laboratory of Advanced Civil Engineering Materials (Tongji University), Ministry of Education, which are gratefully acknowledged.
Institutional Review Board Statement
Not applicable.
Informed Consent Statement
Not applicable.
Data Availability Statement
All data generated or used during the study appear in the submitted article.
Conflicts of Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Appendix A
Table A1.
Summary of maximum tensile stress of common functional layers’ materials.
| No | Types of Common Ground Leveling Materials | Compressive Modulus of Elasticity (GPa) | Poisson’s Ratio | Maximum Tensile Stress (MPa) |
|---|---|---|---|---|
| 1 | Pea gravel concrete | 20 | 0.15/0.20 | 0.884/0.923 |
| 25 | 0.15/0.20 | 0.899/0.939 | ||
| 30 | 0.15/0.20 | 0.910/0.951 | ||
| 2 | Semidry mortar | 16 | 0.20 | 0.906 |
| 3 | Hemihydrate gypsum self-leveling mortar | 15/18/20/22 | 0.20 | 0.901/0.915/0.923/0.930 |
| 4 | Sand free gypsum self-leveling mortar | 13.5 | 0.08/0.10/0.12 | 0.800/0.815/0.830 |
| 14 | 0.08/0.10/0.12 | 0.803/0.818/0.833 | ||
| 15 | 0.08/0.10/0.12 | 0.808/0.823/0.839 | ||
| 5 | Anhydrite self-leveling mortar | 15/18/20 | 0.20 | 0.901/0.915/0.923 |
| 6 | Thick cushion layer cement self-leveling mortar | 15 | 0.13/0.14/0.15/0.16/0.17/ 0.18/0.19/0.20 | 0.847/0.854/0.862/0.869/0.877/ 0.885/0.893/0.901 |
| 16 | 0.13/0.14/0.15/0.16/0.17/ 0.18/0.19/0.20 | 0.847/0.854/0.862/0.869/0.877/ 0.885/0.893/0.901 | ||
| 17 | 0.13/0.14/0.15/0.16/0.17/ 0.18/0.19/0.20 | 0.856/0.864/0.872/0.879/0.887/ 0.895/0.903/0.911 | ||
| 18 | 0.13/0.14/0.15/0.16/0.17/ 0.18/0.19/0.20 | 0.860/0.868/0.876/0.884/0.892/ 0.899/0.907/0.915 | ||
| 19 | 0.13/0.14/0.15/0.16/0.17/ 0.18/0.19/0.20 | 0.864/0.872/0.88/0.888/0.896/ 0.904/0.912/0.920 | ||
| 20 | 0.13/0.14/0.15/0.16/0.17/ 0.18/0.19/0.20 | 0.868/0.876/0.884/0.892/0.899/ 0.907/0.915/0.923 | ||
| 21 | 0.13/0.14/0.15/0.16/0.17/ 0.18/0.19/0.20 | 0.871/0.879/0.887/0.895/0.903/ 0.911/0.919/0.927 | ||
| 7 | UHPC | 44 | 0.20 | 0.972 |
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Figure 1.
Schematic draft of non-adhesive flat extruded board system. 1. decorative layer; 2. steel wire mesh; 3. fine aggregate concrete protective layer; 4. thermal insulation and sound insulation layer (XPS); 5. floor structure layer (including leveling treatment).
Figure 1.
Schematic draft of non-adhesive flat extruded board system. 1. decorative layer; 2. steel wire mesh; 3. fine aggregate concrete protective layer; 4. thermal insulation and sound insulation layer (XPS); 5. floor structure layer (including leveling treatment).
Figure 2.
A case of failure of extruded plate in China. (a) When the strength of the leveling layer does not reach the specified strength, if the deformation of the insulation board is too large and uneven, the leveling layer is easy to crack; (b) due to excessive deformation of the insulation layer over time, the thickness has been reduced by 2–3 cm. This makes the insulation less functional.
Figure 2.
A case of failure of extruded plate in China. (a) When the strength of the leveling layer does not reach the specified strength, if the deformation of the insulation board is too large and uneven, the leveling layer is easy to crack; (b) due to excessive deformation of the insulation layer over time, the thickness has been reduced by 2–3 cm. This makes the insulation less functional.
Figure 3.
Structural model of elastic-supporting plate under vertical load: (a) shear-rigid plate theory on Winkler Foundation; (b) isotropic two-layer elastic half-space theory.
Figure 3.
Structural model of elastic-supporting plate under vertical load: (a) shear-rigid plate theory on Winkler Foundation; (b) isotropic two-layer elastic half-space theory.
Figure 4.
Relationship between XPS layer thickness and maximum tensile stress of pea gravel concrete layer.
Figure 4.
Relationship between XPS layer thickness and maximum tensile stress of pea gravel concrete layer.
Figure 5.
Histogram of tensile stress corresponding to different Poisson’s ratios and compressive elastic moduli of pea gravel concrete.
Figure 5.
Histogram of tensile stress corresponding to different Poisson’s ratios and compressive elastic moduli of pea gravel concrete.
Table 1.
Summary of mechanical parameters of materials.
| Material | Modulus of Elasticity (N/m2) | Poisson’s Ratio (-) | |
|---|---|---|---|
| Structural layer concrete | Pea gravel concrete | 20/25/30 | 0.15/0.20 |
| Semidry mortar | 16 | 0.20 | |
| Hemihydrate gypsum self-leveling mortar | 15/18/20/22 | 0.20 | |
| Sand free gypsum self-leveling mortar | 13.5/14/15 | 0.08/0.10/0.12 | |
| Anhydrite self-leveling mortar | 15/18/20 | 0.20 | |
| Thick cushion layer cement self-leveling mortar | 15–21 | 0.13–0.20 | |
| UHPC | 44 | 0.20 | |
| XPS | 5 × 105 | 0.15 | |
| Pea gravel concrete (Leveling layer) | 28 × 109 | 0.20 | |
Table 2.
Corresponding table of thickness and maximum tensile stress of pea gravel concrete leveling layer.
Table 2.
Corresponding table of thickness and maximum tensile stress of pea gravel concrete leveling layer.
| Thickness of Pea Gravel Concrete Leveling Layer (mm) | 2.0 × 103 N Load + 40 mm Functional Layer | 2.0 × 103 N Load + 60 mm Functional Layer |
|---|---|---|
| Maximum Tensile Stress (MPa) | Maximum Tensile Stress (MPa) | |
| 10 | 22.84 | 23.46 |
| 20 | 7.27 | 7.53 |
| 30 | 3.67 | 3.82 |
| 40 | 2.26 | 2.36 |
| 50 | 1.54 | 1.59 |
| 60 | 1.10 | 1.13 |
| 61 | 1.07 | 1.09 |
| 62 | 1.04 | 1.06 |
| 65 | 0.95 | 0.97 |
| 70 | 0.82 | 0.84 |
Table 3.
Corresponding table of thickness and maximum tensile stress of gypsum-based layer.
| Thickness of Gypsum-Based Layer (mm) | 2.0 × 103 N Load + 40 mm Functional Layer | 2.0 × 103 N Load + 60 mm Functional Layer |
|---|---|---|
| Maximum Tensile Stress (MPa) | Maximum Tensile Stress (MPa) | |
| 10 | 14.85 | 14.09 |
| 20 | 5.23 | 5.50 |
| 30 | 2.73 | 2.84 |
| 40 | 1.69 | 1.74 |
| 42 | 1.55 | 1.60 |
| 45 | 1.37 | 1.41 |
| 50 | 1.14 | 1.17 |
| 60 | 0.82 | 0.84 |
Table 4.
Corresponding table of thickness and maximum tensile stress of cementitious self-leveling mortar layer.
Table 4.
Corresponding table of thickness and maximum tensile stress of cementitious self-leveling mortar layer.
| Thickness of Cementitious Self-Leveling Mortar Layer (mm) | 2.0 kN Load + 40 mm Functional Layer | 2.0 kN Load + 60 mm Functional Layer |
|---|---|---|
| Maximum Tensile Stress (MPa) | Maximum Tensile Stress (MPa) | |
| 10 | 21.03 | 20.97 |
| 20 | 6.81 | 7.09 |
| 30 | 3.44 | 3.57 |
| 40 | 2.11 | 2.20 |
| 50 | 1.44 | 1.50 |
| 56 | 1.18 | 1.18 |
| 58 | 1.10 | 1.15 |
| 60 | 1.04 | 1.08 |
| 65 | 0.90 | 0.93 |
Table 5.
Tensile stress corresponding to different Poisson’s ratios and compressive elastic moduli of hemihydrate gypsum self-leveling mortar, UHPC.
Table 5.
Tensile stress corresponding to different Poisson’s ratios and compressive elastic moduli of hemihydrate gypsum self-leveling mortar, UHPC.
| Types of Common Ground Leveling Materials | Compressive Modulus of Elasticity (GPa) | Poisson’s Ratio | Maximum Tensile Stress (MPa) |
|---|---|---|---|
| Hemihydrate gypsum self-leveling mortar | 15/18/20/22 | 0.20 | 0.901/0.915/0.923/0.930 |
| UHPC | 44 | 0.20 | 0.972 |
Table 6.
Tensile stress corresponding to different Poisson’s ratios and compressive elastic moduli of sand-free gypsum self-leveling mortar layer.
Table 6.
Tensile stress corresponding to different Poisson’s ratios and compressive elastic moduli of sand-free gypsum self-leveling mortar layer.
| Poisson’s Ratio | Compressive Modulus of Elasticity | ||
|---|---|---|---|
| 13.5 GPa | 14 GPa | 15 GPa | |
| 0.08 | 0.800 | 0.803 | 0.808 |
| 0.10 | 0.815 | 0.818 | 0.823 |
| 0.12 | 0.830 | 0.833 | 0.839 |
Table 7.
Tensile stress corresponding to different Poisson’s ratio and compressive elastic modulus of anhydrite self-leveling mortar layer.
Table 7.
Tensile stress corresponding to different Poisson’s ratio and compressive elastic modulus of anhydrite self-leveling mortar layer.
| Compressive Modulus of Elasticity (GPa) | Tensile Stress (MPa) |
|---|---|
| 15 | 0.901 |
| 18 | 0.915 |
| 20 | 0.923 |
Table 8.
Tensile stress corresponding to different Poisson’s ratios and compressive elastic moduli of thick cushion layer cement self-leveling layer.
Table 8.
Tensile stress corresponding to different Poisson’s ratios and compressive elastic moduli of thick cushion layer cement self-leveling layer.
| Poisson’s Ratio | Compressive Modulus of Elasticity | ||||||
|---|---|---|---|---|---|---|---|
| 15 GPa | 16 GPa | 17 GPa | 18 GPa | 19 GPa | 20 GPa | 21 GPa | |
| 0.13 | 0.847 | 0.851 | 0.856 | 0.860 | 0.864 | 0.868 | 0.871 |
| 0.14 | 0.854 | 0.859 | 0.864 | 0.868 | 0.872 | 0.876 | 0.879 |
| 0.15 | 0.862 | 0.867 | 0.872 | 0.876 | 0.880 | 0.884 | 0.887 |
| 0.16 | 0.869 | 0.875 | 0.879 | 0.884 | 0.888 | 0.892 | 0.895 |
| 0.17 | 0.877 | 0.882 | 0.887 | 0.892 | 0.896 | 0.899 | 0.903 |
| 0.18 | 0.885 | 0.890 | 0.895 | 0.899 | 0.904 | 0.907 | 0.911 |
| 0.19 | 0.893 | 0.898 | 0.903 | 0.907 | 0.912 | 0.915 | 0.919 |
| 0.20 | 0.901 | 0.906 | 0.911 | 0.915 | 0.920 | 0.923 | 0.927 |
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Jiang, W.; Zheng, X. Applied Research on the Minimum Thickness of Leveling Layer of Non-Adhesive Flat Extruded Board System. Appl. Sci. 2022, 12, 4673. https://doi.org/10.3390/app12094673
AMA Style
Jiang W, Zheng X. Applied Research on the Minimum Thickness of Leveling Layer of Non-Adhesive Flat Extruded Board System. Applied Sciences. 2022; 12(9):4673. https://doi.org/10.3390/app12094673
Chicago/Turabian StyleJiang, Wei, and Xinyue Zheng. 2022. "Applied Research on the Minimum Thickness of Leveling Layer of Non-Adhesive Flat Extruded Board System" Applied Sciences 12, no. 9: 4673. https://doi.org/10.3390/app12094673
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