Simulation of the Hygro-Thermo-Mechanical Behavior of Earth Brick Walls in Their Environment
Abstract
:1. Introduction
2. Materials and Methods
2.1. Description of the Simulated Dwelling
- In the so-called “basic” version, all partition walls in the dwelling are lightweight plasterboard walls on a metal frame. The cladding on all walls is considered to be vapor impermeable; also, the hygroscopic properties of the furnishings and textiles in the home are neglected.
- In the “earth” version, the earth brick wall replaces certain partition walls over a surface area of 30.8 m², with the other assumptions remaining identical to the basic version.
2.2. Numerical Model
2.2.1. State-of-the-Art
2.2.2. Description of the Numerical Model Developed
- : specific humidity of the indoor air at time t [kg water/kg dry air]
- : specific humidity of the indoor air at time t+ζ [kg water/kg dry air]
- : time step [s]
- : dry density of indoor air (kg/m3)
- : interior volume of the zone [m3]
- : mass flow rate of the internal water vapor inputs from occupants and processes [kg/s]
- : mass flow rate of water vapor supplied by the CMV. This value is estimated using Equation (17).
- : extracted air volume flow rate [m3/h]
- and : specific humidity of outdoor and indoor air [kg water/kg dry air]
- : mass flow rate of water vapor transferred from the wall to the environment [kg/s]. This value is calculated according to Equation (18).
- : mass flow of water vapor leaving the surface Smod of the model [kg/s]
- : exchange surface area of the model [m²]
- : total exchange surface area of the actual wall (including both faces) [m²]
2.2.3. Simulation of Coupled Behavior
3. Determination of Model Input Parameters
3.1. Characterization of Thermal and Hydric Properties
3.1.1. Sorption Isotherm and Moisture Capacity
- Adsorption: ws = 4.35%, aa = 0.67, φa = 0.68
- Desorption: ws = 4.35%, ad = 0.30, φd = 0.69
3.1.2. Apparent Vapor Permeability
3.1.3. Thermal Conductivity
3.1.4. Calculation of the Water-Induced Eigenstrain Field
3.2. Characterization of Hygro-Mechanical Properties
3.2.1. Compression Test
3.2.2. Tensile Test (Brazilian)
4. Numerical Results
4.1. Annual Study
4.1.1. The Regulating Effects of Partition Walls on Indoor Humidity
4.1.2. Impact of the Choice of Ventilation on Partition Behavior
4.1.3. Mechanical Impacts
- Imposition of horizontal displacements Uy parallel to the plane of the wall at an identical but free value.
- Imposition of vertical displacements Uz at an identical but free value.
4.2. A Detailed Study of a Critical Week
- i.
- This is one-dimensional behavior, which does not take into account the effects of possible confinement due to the weight of the wall and the stress caused by the expansion of the wall elements on the sides (y direction).
- ii.
- There is a wide dispersion in the experimental results. Also, from a design perspective, while it is sensible to take a characteristic or average value, in the aim of modeling actual wall behavior, a probabilistic approach should be used due to the heterogeneity, which leads to great variability in the physical and mechanical characteristics.
- iii.
- Microcracks could form, though they would ultimately close under the effect of confinement and humidity; they should still be taken into account through damageable behavior.
5. Conclusions
- A 50% reduction in annual humidity amplitude occurs with an earth wall compared to a classical plaster wall;
- The stress variation is maximized at the wall surface, which could lead to crack formation;
- Lastly, from a more general perspective, the conclusions drawn from this work may lead to numerous prospects for future studies, namely:
- Improvement of the numerical model by taking free water transfer into account in order to extend the results obtained in the hygroscopic domain to the capillary domain, in addition to modeling the drying phase during the wall construction phase;
- Characterization of the mechanical behavior of earth bricks in the capillary domain in order to control the wall construction phase;
- Choice of a viscoelastic, or even viscoelastoplastic, approach, which proves to be necessary when incorporating changes in the material submitted to high water content.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
Latin symbols | |
C | specific heat capacity (J × kg−1 × K−1) |
L | latent heat of sorption (J × kg−1) |
pv | vapor pressure (Pa) |
pvs | saturation vapor pressure (Pa) |
QT | volumetric thermal source (W × m−3) |
Qw | volumetric water vapor source (kg × s−1 × m−3) |
rh | relative humidity (0 ≤ rh ≤ 1) |
T | temperature (K) |
w | moisture content (kgwater/kgdry material) |
Dw | liquid diffusion coefficient (m2 × s−1) |
Vint | internal volume of the area (m3) |
xint | specific humidity of indoor air (kgwater/kgdry air) |
xext | specific humidity of outdoor air (kgwater/kgdry air) |
Greek symbols | |
δ | vapor permeability (kg × s−1 × m−1 × Pa−1) |
λ | thermal conductivity (W × m−1 × K−1) |
ρ | density (kg × m−3) |
φT | flow density of heat (W × m−2) |
φlw | flow density of liquid water (kg × s−1 × m−2) |
φvw | flow density of water vapor (kg × s−1 × m−2) |
Φw | mass flow of water vapor transferred by the wall to the environment (kg × s−1) |
Φint | mass flow rate of internal water vapor supply (kg × s−1) |
Φvent | mass flow of water vapor supplied by the CMV (kg × s−1) |
Subscripts | |
* | apparent |
0 | anhydrous |
a | adsorption |
d | desorption |
s | saturation |
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Type of Input | Amount of Water Vapor |
---|---|
Occupant | 4 persons, 40 g/h/person (at rest), 60 g/h/person (during activity) |
Kitchen | 1 kg/meal, 0.5 kg/breakfast |
Toilet, showers | 0.5 kg in the morning, 1 kg in the evening |
Washing and drying/laundry | 2 kg/day, distributed between 7 a.m. and 5 p.m. |
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Laou, L.; Ulmet, L.; Yotte, S.; Aubert, J.-E.; Maillard, P. Simulation of the Hygro-Thermo-Mechanical Behavior of Earth Brick Walls in Their Environment. Buildings 2023, 13, 3061. https://doi.org/10.3390/buildings13123061
Laou L, Ulmet L, Yotte S, Aubert J-E, Maillard P. Simulation of the Hygro-Thermo-Mechanical Behavior of Earth Brick Walls in Their Environment. Buildings. 2023; 13(12):3061. https://doi.org/10.3390/buildings13123061
Chicago/Turabian StyleLaou, Lamyaa, Laurent Ulmet, Sylvie Yotte, Jean-Emmanuel Aubert, and Pascal Maillard. 2023. "Simulation of the Hygro-Thermo-Mechanical Behavior of Earth Brick Walls in Their Environment" Buildings 13, no. 12: 3061. https://doi.org/10.3390/buildings13123061
APA StyleLaou, L., Ulmet, L., Yotte, S., Aubert, J.-E., & Maillard, P. (2023). Simulation of the Hygro-Thermo-Mechanical Behavior of Earth Brick Walls in Their Environment. Buildings, 13(12), 3061. https://doi.org/10.3390/buildings13123061