Elastic Modulus Prediction Model of Foamed Concrete Based on the Walsh Formula
Abstract
:1. Introduction
2. Micromechanical Analysis of Foamed Concrete Elements
2.1. Walsh Formula
2.2. Spherical Pore Assumption
2.3. Spherical Shell Elastic Modulus of Foamed Concrete
3. Two-Layer Embedded Model Analysis of Foamed Concrete
3.1. Two-Layer Embedded Model
3.2. Prediction Model for the Elastic Modulus of Foamed Concrete
3.3. Calculation Process for the Elastic Modulus of Foamed Concrete
4. Model Validation
4.1. Comparison with Test Results
4.2. Comparison with Existing Research
5. Parameter Sensitivity Analysis
5.1. Porosity of Foamed Concrete
5.2. Poisson’s Ratio of Foamed Concrete Matrix
5.3. Elastic Modulus of Foamed Concrete Matrix
6. Conclusions
- (1)
- According to the internal structure characteristics of foamed concrete, the calculation formula is established for elastic modulus of spherical shell by introducing the Walsh formula and spherical pore hypothesis. Moreover, the elastic modulus prediction model of foamed concrete is constructed based on the two-layer embedded model in inclusion theory.
- (2)
- The uniaxial compression test of foamed concrete is carried out, and the proposed model is compared with the test data and the existing theoretical models. The verification results show that the elastic modulus values calculated using the proposed model are consistent with the experimental data. The values are also in good agreement with the distribution law of the calculation results calculated by using other theoretical models.
- (3)
- The effects of porosity, Poisson’s ratio of matrix, and elastic modulus of matrix on the elastic modulus of foamed concrete are analyzed by the proposed model. The results show that the elastic modulus of foamed concrete decreases with the increase in porosity and matrix Poisson’s ratio, and increases with the increase in matrix elastic modulus.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
Main symbols and notations used in the paper | |
Symbol | Description |
a | inner diameter of spherical shell |
b | outer diameter of spherical shell |
c | outer diameter of equivalent medium |
E | elastic modulus |
E0 | elastic modulus of equivalent medium |
E1 | elastic modulus of the matrix |
E2 | elastic modulus of the spherical shell element |
f | volume percentage of inclusions |
fc | compressive strength of foamed concrete |
n | porosity |
n0 | initial porosity of foamed concrete |
P | radial effective stress at the outer diameter of the equivalent medium |
P0 | radial effective stress at the outer diameter of spherical shell |
P1 | radial effective stress at the inner radius of spherical shell |
ua | radial displacement of the spherical shell |
u0b | displacement of equivalent medium at boundary r = b |
u0c | displacement of equivalent medium at boundary r = c |
u1a | displacement of matrix at boundary r = a |
u1b | displacement of matrix at boundary r = b |
u2a | displacement of spherical shell at boundary r = a |
V | volume of the porous medium |
Vc | pore volume |
W | wet bulk density of foamed concrete |
δ | volume compliance of the overall unit |
δs | volume compliance of the matrix |
ΔVc | change in pore volume |
Δa | change of inner diameter of spherical shell |
Δσ | the action of volume stress |
ρ | density of foamed concrete |
ρs | density of the matrix |
υ | Poisson’s ratio |
υ0 | Poisson’s ratio of foamed concrete |
υ1 | Poisson’s ratio of the matrix |
υ2 | Poisson’s ratio of the spherical shell |
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Test Group Number | Water–Solid Ratio | Bubble Rate | Wet Severity/kN·m−3 | 28-Day Unconfined Compressive Strength/MPa | Elastic Modulus/MPa |
---|---|---|---|---|---|
1 | 1:1.8 | 0.71 | 5.39 | 1.52 | 718 |
2 | 1:1.8 | 0.68 | 5.70 | 1.79 | 826 |
3 | 1:1.8 | 0.68 | 6.03 | 1.67 | 778 |
4 | 1:1.8 | 0.65 | 6.19 | 1.74 | 806 |
5 | 1:1.8 | 0.65 | 6.25 | 1.77 | 818 |
6 | 1:1.8 | 0.65 | 6.32 | 1.90 | 870 |
7 | 1:1.8 | 0.62 | 6.67 | 1.96 | 894 |
8 | 1:1.8 | 0.62 | 7.05 | 2.12 | 958 |
9 | 1:1.8 | 0.59 | 7.07 | 2.54 | 1126 |
10 | 1:1.8 | 0.59 | 7.53 | 2.80 | 1230 |
Matrix Material Parameters | v1 | E1/MPa | μ1/MPa | ρs/kg·m−3 |
---|---|---|---|---|
value | 0.16 | 2450 | 1060 | 1.9 |
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Zhou, Z.; Hu, J.; Li, F.; Zhang, J.; Lei, M. Elastic Modulus Prediction Model of Foamed Concrete Based on the Walsh Formula. Appl. Sci. 2022, 12, 5142. https://doi.org/10.3390/app12105142
Zhou Z, Hu J, Li F, Zhang J, Lei M. Elastic Modulus Prediction Model of Foamed Concrete Based on the Walsh Formula. Applied Sciences. 2022; 12(10):5142. https://doi.org/10.3390/app12105142
Chicago/Turabian StyleZhou, Zhong, Jiangfeng Hu, Fan Li, Junjie Zhang, and Mingfeng Lei. 2022. "Elastic Modulus Prediction Model of Foamed Concrete Based on the Walsh Formula" Applied Sciences 12, no. 10: 5142. https://doi.org/10.3390/app12105142
APA StyleZhou, Z., Hu, J., Li, F., Zhang, J., & Lei, M. (2022). Elastic Modulus Prediction Model of Foamed Concrete Based on the Walsh Formula. Applied Sciences, 12(10), 5142. https://doi.org/10.3390/app12105142