# Comparative Hygrothermal Performance of a Mortar Wall with Micronized Miscanthus Fibers versus a Reference Wall: Experimental and Numerical Analysis

Haoyan Zhang, Franck Komi Gbekou, Karim Benzarti, Rachid Bennacer, Abderrahim Boudenne

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Haoyan Zhang, Franck Komi Gbekou, Karim Benzarti, Rachid Bennacer, Abderrahim Boudenne. Comparative Hygrothermal Performance of a Mortar Wall with Micronized Miscanthus Fibers versus a Reference Wall: Experimental and Numerical Analysis. Journal of Building Engineering, 2025, 108, pp.112899. 10.1016/j.jobe.2025.112899. hal-05077112

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Submitted on 21 May 2025

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# Comparative hygrothermal performance of a mortar wall with micronized miscanthus fibers versus a reference wall: Experimental and numerical analysis

Haoyan Zhang<sup>a, *</sup>, Franck Komi Gbekou<sup>b</sup>, Karim Benzarti<sup>b</sup>, Rachid Bennacer<sup>c</sup>, Abderrahim Boudenne<sup>a, **</sup>

## ARTICLE INFO

**Keywords:**

Miscanthus mortar

Hygrothermal behavior

Numerical simulation

Coupled heat and mass transfer

Wall-scale study

## ABSTRACT

Miscanthus fibres are regarded as a sustainable, eco-friendly material with high hygroscopicity and low thermal conductivity. Although promising at the material scale, further wall-scale evaluations are needed. This study investigates the hygrothermal performance of a biobased mortar wall containing micronized miscanthus fibers, compared to a conventional mortar wall. An experimental bi-climatic device was used to simulate distinct outdoor and indoor environments by exposing each side of both walls to different hygrothermal conditions. Temperature and relative humidity (RH) data were collected using a network of sensors, enabling a thorough analysis of the walls' hygrothermal response at various depths under both dynamic and steady-state regimes. Additionally, a numerical model based on the Künzel approach was employed to predict and compare temperature and humidity behavior within the biobased wall. Results showed good agreement between experimental data and numerical predictions, with a maximum temperature deviation of 4 °C at 5 cm depth. However, RH predictions revealed discrepancies, notably a 5 % deviation at 7.5 cm depth. Statistical validation indicated model accuracy. Furthermore, tests involving cyclic moisture changes under isothermal conditions demonstrated that the miscanthus wall acts as an effective hygric regulator, maintaining stable indoor condition as outdoor relative humidity increases. Higher prediction errors observed at boundary depths (0 and 10 cm) were attributed to external airflow during experiments. Overall, the numerical model reliably predicted temperature variations, and RH estimations were acceptable considering material heterogeneity. These findings confirm the potential of miscanthus fiber-reinforced materials for improving hygrothermal performance in building construction.

## 1. Introduction

The construction industry has a substantial environmental impact, accounting for 43 % of global annual energy consumption [1]. Building envelopes, which contribute over half (51 %) of the total energy consumption in building, are a key contributor in this

<footnote><sup>a</sup> Univ Paris-Est Créteil, CERTES, Créteil, F-94010, France</footnote>

<footnote><sup>b</sup> Univ Gustave Eiffel, Ecole des Ponts, CNRS, Navier, Marne-la-Vallée, F-77447, France</footnote>

<footnote><sup>c</sup> Université Paris-Saclay, ENS Paris-Saclay, CentraleSupélec, CNRS, LMPS - Labo. de Mécanique Paris-Saclay, Gif-sur-Yvette, 91190, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>** Corresponding author.</footnote>

<footnote>E-mail addresses: haoyan.zhang@u-pec.fr (H. Zhang), boudenne@u-pec.fr (A. Boudenne).</footnote>
footprint [2]. As urbanization and construction activities accelerate, pressure on natural resources and ecological concerns is intensifying. Sustainable alternatives are urgently needed to address these environmental challenges.

Bio-based materials, such as date palm, hemp, and straw, offer eco-friendly alternatives to traditional building materials, reducing carbon footprints and energy consumption during production, while also providing improved insulation, durability, and healthier indoor environments [3–6]. The hygrothermal behavior of construction building materials and particular bio-based materials has been widely studied, with hemp being the most commonly used due to its availability and low pesticide requirements. Hemp's rapid growth and carbon dioxide absorption make it an excellent candidate for sustainable construction, contributing to improved hygrothermal performance when incorporated into cement materials. Elfordy et al. [7] reported low values of thermal conductivity between 0.2 and $0.6 \text{ W m}^{-1} \text{ K}^{-1}$ for hemp concrete produced through a projection process. Panesar and Shindman et al. [8] observed a 16% and 36% increase in the thermal resistance of conventional mortars when 10 wt% and 20 wt% cork were added, respectively. Charai et al. [9] noted a 70.8% decrease in thermal conductivity and a 45.7% decrease in thermal resistivity when 30 wt% spent coffee grounds were incorporated into the mortar. Boumhaout et al. [10] observed a 70% decrease in the thermal conductivity of mortars containing date palm fibers. Incorporating natural fibers also improves both thermal insulation and hygric properties of the mortar, contributing to a more comfortable indoor environment in buildings. Charai et al. [11] reported a moisture buffer value of $3.13 \text{ g m}^{-2} \text{ %RH}^{-1}$ when adding 10 wt% alfa fibers to a cement-based mortar. Chennouf et al. [6] reported water vapor permeability values of $3.16 \times 10^{-11}$ for dry cup and $3.59 \times 10^{-11} \text{ kg m}^{-1} \text{ s}^{-1} \text{ Pa}^{-1}$ for wet cup in mortar with date palm fibers.

The hygrothermal properties of bio-based materials at the material scale are generally well-established, as the evolution trend with fiber content remains consistent for most lignocellulosic fibers. These material-scale studies offer essential insights into material behavior and form the basis for larger-scale investigations. However, performing wall-scale hygrothermal characterization, in addition to material-scale studies, is essential for a comprehensive understanding of the thermal and moisture behavior of bio-based materials in real-world conditions. Numerous studies have investigated the hygrothermal behavior of bio-based walls [13–18]. Most researchers have reported that these walls mitigate indoor temperature fluctuations in response to changes in outdoor temperature. Additionally, a strong coupling between heat and mass transfer has been noted, where temperature fluctuations induce changes in relative humidity within the wall, and vice versa. Boumediene et al. [18], in their study of a hemp wall under French and Tunisian summer climates, reported a damping factor of 0.2 between the outer surface and the mid-thickness of the wall. Chennouf et al. [13] observed a thermal amplitude damping of $7.5^{\circ}\text{C}$ from the outdoor surface to the middle of a date palm concrete (DPC) wall. Furthermore, the improved hygric properties of bio-based materials help maintain indoor comfort by effectively limiting vapor diffusion through the wall as outdoor relative humidity conditions change. For instance, Rahim et al. [19] studied a hemp-lime concrete wall exposed to hygric variations ranging from 50% to 85% RH. They found that changes in outdoor RH conditions resulted in a significant increase in RH near the outdoor surface, while only a minimal increase ($<1\%$) in RH was observed in the middle of the wall. Similarly, Collet and Pretot [17] reported a delay in vapor pressure evolution through the thickness of a hemp concrete wall when subjected to an isothermal RH increase from 40% to 80%.

Alongside experimental studies, numerical modelling provides valuable insights into the behaviour of biobased materials under various environmental conditions. Kaoutari et al. [20] conducted numerical simulations of coupled heat and moisture transfer in both single-layer and dual-layer biobased cob building materials. They used the Künzel and Mendes models to predict hygrothermal behavior, with model parameters empirically measured. The numerical results were validated against experimental data, as experiments are crucial for verifying the accuracy of coupled heat and moisture transfer models [21]. Kaoutari et al. [20] found that the Künzel model gave more accurate predictions for single-layer building walls when compared to experimental measurements. Asli et al. [22] conducted both numerical and experimental studies on heat and mass transfer in wall sections made from hemp concrete under real environmental conditions. Their numerical simulations employed the Philipe and De Vries model. The hygrothermal performance of hempcrete was initially determined through laboratory experiments, and the numerical results closely aligned with experimental data. Minor discrepancies in relative humidity, approximately 8.4%, were observed between the simulated and measured data at $7.5$ days, particularly near the indoor environment at a depth of 2 cm. Alioua et al. [12] considered bio-based materials composed of date palm concrete (DPC) and used both the Künzel and Mendes models to simulate wall responses under various hygrothermal scenarios. Both models performed acceptably, through the Künzel model provided results that were closer to the experimental data. When temperature was varied from $23^{\circ}\text{C}$ to $40^{\circ}\text{C}$, these two models show similar behaviors, differing by only a slight margin of less than $0.34^{\circ}\text{C}$. Under relative humidity variations from 33% to 75%, the largest differences were observed at a depth of $7.5$ cm (mid-wall), showing deviations of 7% for the Künzel model and 9% for the Mendes model compared to experimental data.

Among the wide variety of available fibers, miscanthus stands out as a particularly promising option. The miscanthus plant offers great potential for both energy and biomass production, with the added benefit that its cultivation does not compete with food or feed crops [23–25]. Overall, miscanthus fibers are considered to outperform other plant fibers, such as straw or hemp for example, due to their superior firmness and excellent thermal insulation properties. Miscanthus can be cultivated for approximately 15 years, particularly in Europe [26] achieving an annual yield efficiency between 10 and 20 tons. It demonstrates good adaptability to diverse climatic and soil conditions, requiring minimal inputs of water, fertilizers, and pesticides. Furthermore, miscanthus fibers have shown considerable effectiveness as lightweight aggregates in cementitious matrices, facilitating the production of lightweight concrete materials. Due to their low particle density and porous structure of miscanthus significantly enhance water retention. Additionally, the high porosity of miscanthus fibers further contributes to the reduction of thermal conductivity in miscanthus lightweight concrete. Recent studies have investigated the thermal and hygric properties of miscanthus fibers incorporated into concrete. Gbekou et al. [27, 28] reported that adding miscanthus fibers to mortars results in significant enhancements (up to 87%) in thermal resistance. Moreover, increasing fiber content consistently enhances moisture adsorption capacity, moisture buffering effectiveness, water vapor permeability, and capillary absorption performance. However, a knowledge gap remains regarding the hygrothermal behavior of
building materials incorporating miscanthus fibers, particularly at the wall scale.

In this study, the hygrothermal performance of a mortar wall incorporating micronized miscanthus fibers was compared to that of a reference wall made from standard cement mortar. To achieve this, a custom bi-climatic experimental setup was developed, enabling each face of the wall to be exposed to distinct hygrothermal conditions. This setup allowed for comprehensive testing under a wide range of thermal and moisture scenarios. A network of sensors was installed at various depths within the walls to continuously monitor temperature and relative humidity. Numerical simulations of heat and mass transfer were also conducted, initially validated against wall-scale experimental data from the literature. Subsequently, the simulation results for the bio-based wall were compared with our experimental findings. Statistical indicators, including Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and the coefficient of determination (R²), were utilized to assess the accuracy of the numerical model. This research provides valuable insights into the behavior of the miscanthus fiber-reinforced wall, revealing the impact of fiber addition. Moreover, it allows for a comparative assessment with the reference mortar wall, highlighting the significant performance improvements achieved.

## 2. Materials and experimental methods

### 2.1. Materials

This work examined two cement mortar walls. The first wall, referred to as M0, served as the reference and was constructed using a formulation previously documented in the literature [29], originally designed for additive manufacturing. The composition of used cement is providing by the company VICAT (L'Isle-d'Abeau, France) that is based on ordinary Portland cement EXTREMAT® CEM I 52.5 N (denoted OPC), and fast-setting sulfo-aluminous cement (denoted CSA). A standardized sand with a maximum particle size of 2 mm, provided by Société Nouvelle du Littoral in France and superplasticizer (VISCOCRETE TEMPO 11 SP)/water reducer (from SIKA, Baar, Switzerland) were added two the mixture. This reference mix is based on a water-to-cement (W/C) ratio of 0.35. Table 1 provides a detailed composition of the reference mortar M0 [27,28,30,31]. The second wall, referred to as M7.5F, was based on the same cement mortar matrix as the reference, but also included micronized miscanthus fibers. These fibers, provided by Addiplast Group (Saint-Pal-de-Mons, France), came in powder form with particle sizes between 200 and 500 µm (product reference MDDCH0114 MIS-CANTHUS 200-500µm/BFF). Typically, they are predominantly applied in the plastic industry to create bio-based composite components for the automotive sector. The manufacturer's specifications indicate that the conditioned powder contains over 94 % organic matter, with a moisture content ranging between 6 and 8 wt%. The micronation process notably reduces the lignin and hemicellulose contents, resulting in final concentrations of approximately 0.4 % and 6 %, respectively. The cellulose content remains intact, comprising about 94 % of the organic composition. The micronized miscanthus powder was used as supplied, without any additional chemical treatment.

In preliminary material-scale investigations, the addition of miscanthus fibers into the reference mortar M0 was studied to assess its effects on the mechanical and hygrothermal properties of the resulting materials [27,28]. The use of micronized powder has been identified as an effective method for achieving a homogeneous distribution of fibers within the cementitious matrix, which also opens possibilities for developing 3D printable mortar mixes with plant-based fibers. However, this aspect is beyond the scope of the present paper.

Mortar formulation incorporating varying weight concentrations of micronized miscanthus fibers ranging from 0 to 7 wt % were investigated. The results demonstrated a significant improvement in hygrothermal properties with the addition of miscanthus fibers, though this came at the expense of reduced mechanical performance. For example, adding 5.7 wt% of miscanthus fibers to the mortar resulted in an impressive 82 % reduction in thermal conductivity (0.42 W m⁻¹ K⁻¹ compared to 2.3 W m⁻¹ K⁻¹ for the reference mortar M0), while maintaining a compressive strength of approximately 3 MPa, which is acceptable for bio-based insulation materials. This particular formulation, labelled M7.5F, was selected for further investigation at the wall-scale, to compare its hygrothermal response with that of the reference wall M0.

The compositions of both mortars, M0 and M7.5F, are summarized in Table 1. The actual quantities used in the mortar batches, along with the compositions in kg/m³ calculated based on the densities of the component materials, are both provided in the table. Notably, the manufacturing process of the bio-based mortar involved presoaking the dry miscanthus fibers in water for 2 h prior to mixing, which accounts for the significant increase in total water content observed in the M7.5F composition compared to the reference. Further details regarding the manufacturing protocol can be found in Ref. [27].

<table><caption>**Table 1**
Both mortar walls compositions. Actual quantities used in the mortar batches in g.</caption><thead><tr><th>Type of mortar</th><th>OPC (g)</th><th>Sand (g)</th><th>CSA (g)</th><th>SP (g)</th><th>Dry Miscanthus fibers (g)</th><th>Total water (g)</th><th>W/C ratio</th><th>Mass. fraction of fibers (wt. %)</th></tr></thead><tbody><tr><td>M0</td><td>1059</td><td>1350</td><td>79.7</td><td>3</td><td>-</td><td>399</td><td>0.35</td><td>0</td></tr><tr><td>M7.5F</td><td>1059</td><td>1350</td><td>79.7</td><td>3</td><td>217</td><td>1093</td><td>0.96</td><td>5.7</td></tr></tbody></table><table><thead><tr><th colspan="7">Compositions in kg/m³</th></tr><tr><th>Type of mortar</th><th>OPC</th><th>Sand</th><th>CSA</th><th>SP</th><th>Dry fibers</th><th>Total water</th></tr></thead><tbody><tr><td>M0</td><td>833</td><td>1062</td><td>63</td><td>2.3</td><td>-</td><td>314</td></tr><tr><td>M7.5F</td><td>503</td><td>642</td><td>38</td><td>1.4</td><td>103</td><td>519</td></tr></tbody></table>
## 2.2. Material-scale properties of the mortars

As mentioned before, material-scale characterizations have been conducted in previous work, allowing us to assess various properties of the M0 and M7.5F mortars in the hardened state, namely:

- microstructural properties (water-accessible porosity, density), according to NF P18-459 standard [32],

- mechanical strength at 28 days, following NF EN 196-1 standard [33],

- thermal conductivity, thermal diffusivity and volumetric heat capacity were performed using hot-disk setup,

- hygric properties, such as the Moisture Buffer Value (MBV) determined using the Nordtest protocol [34], and sorption isotherms determined by DVS (Dynamic Vapor Sorption method using ProUmid SPS apparatus).

Readers are encouraged to consult references [27,28] for detailed presentation and discussion on the experimental results collected for the reference and the biobased mortars. However, since material-scale properties are used later to interpret wall-scale results and serve as input parameters for numerical modeling, we briefly summarize these properties in this section.

The mechanical testing results and the physical properties of the two mortars are first summarized in Fig. 1. The biobased mortar M7.5F exhibits a much higher porosity and lower density compared to the reference M0. This was attributed to the high intrinsic porosity of miscanthus fibers and to the excess water used for soaking the fibers which evaporates and let place to porosity in the microstructure [27]. In addition, M7.5F exhibits a compressive strength of 2.41 MPa (a reduction of 96.6 % compared to M0) but still retains sufficient resistance for handling and using as insulation or filling material.

The thermophysical properties of the two mortars (thermal conductivity $\lambda$, thermal diffusivity $\alpha$, and thermal capacity $\rho \cdot C_p$) and the moisture buffer values (MBV) are also presented in Fig. 2. M7.5F shows significantly lower thermophysical values compared to M0, which can be attributed to the low thermal conductivity of the miscanthus fibers (0.04 W m$^{-1}$ K$^{-1}$ [35]), and the large increase in porosity of the mortar. The increased porosity promotes thermal transfer though convection within the pores rather than thermal conduction [8]. Similar results are reported in literature for other biobased materials [7–10].

Additionally, the reference mortar M0 has a limited MBV value (0.5 g m$^{-2}$ %RH$^{-1}$) according to the NordTest Classification [34]. In contrast, the biobased mortar shows an MBV close to 2.0 g m$^{-2}$ %RH$^{-1}$, categorizing it as an effective moisture regulator. This improvement in moisture regulation capacity can be attributed to the high intrinsic porosity and specific surface area of the vegetal fibers, as well as the overall porosity of the biobased composite [6,11].

Finally, Fig. 3 presents the experimental sorption isotherm curves for both mortars, obtained with the DVS method at 23 °C. These curves were fitted using the GAB (Guggenheim-Anderson-de Boer) approach, which effectively models the sorption process over a wide range of relative humidity (0–90 %) and is widely adopted in the literature [36]. The fitting adsorption curve calculated with the GAB model shows a good alignment with the experimental measurement values for all humidity range. Based on these data, the reference mortar M0 exhibits a significantly lower moisture adsorption capacity, characterized by relatively slow adsorption kinetics. The incorporation of miscanthus fibers into the cement matrix notably improved its moisture behavior. Compared to the reference mortar M0, the maximum moisture adsorption content of M7.5F increased by approximately 168 %. These data highlight the significant improvement in moisture storage capacity across the entire relative humidity range due to the addition of miscanthus fibers, with this improvement being more pronounced at higher relative humidity levels. For M7.5F, the moisture storage capacity curve shows minimal fluctuation within the 10–50 % relative humidity (RH) range. In contrast, beyond 65 % RH, the moisture storage capacity curve increases significantly. These GAB fittings will be later used as input parameters of the coupled heat and mass transfer model in the numerical part of this study.

<figure><img src="image_2.png" /><figcaption>Fig. 1. Summary of mechanical and density properties of M7.5F and M0 mortars at 25 °C and 50 % RH, based on reference [27].</figcaption></figure>
<figure><img src="image_3.png" /><figcaption>Fig. 2. Summary of thermophysical properties and MBV values for M0 and M7.5F mortars at 25 °C and 50 % RH, based on references [27].</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 3. Experimental sorption isotherms and GAB fitting for M0 and M7.5F mortars.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 4. Picture of experimental device.</figcaption></figure>
## 2.3. Bi-climatic wall test

### 2.3.1. Description of the experimental setup

A custom-designed setup was developed for the wall-scale experiment to simulate a biclimatic environment. This setup allowed the two sides of the wall to be exposed to different hygrothermal conditions, simulating outdoor and indoor environments, respectively.

The bioclimatic setup used a climatic chamber (ICH260 Memmert), with its front door replaced by a custom-built metallic frame, which supports the wall and linked to the chamber. The entire setup was placed in a temperature-controlled laboratory (maintained at 20 °C), with measured taken at ambient hygrometry. The climatic chamber simulated outdoor conditions by subjecting the outer surface of the wall to dynamic temperature cycles, while the inner surface remained exposed to the laboratory environment, replicating indoor conditions at constant temperature and ambient humidity.

To ensure unidirectional thermal exchange through the open area (40 × 45 cm²) between the chamber and the wall, a 6 cm thick layer of insulation material (expanded polystyrene) was positioned between the metallic frame and the chamber, effectively insulating all other boundaries (Fig. 4). This insulation material was then fully covered with a vapor-barrier adhesive plastic film.

### 2.3.2. Wall preparation and sensors insertion

The two mortar formulations M0 and M7.5F were prepared using an automatic mortar mixer, in accordance with EN 196-1 standard [33]. The complete mixing procedure is detailed in Ref. [27].

Immediately after mixing, the mortar was poured into a wooden formwork with internal dimensions of 50 × 50 × 10 cm³. The formwork remained in place for approximately one week before demolding. After demolding, the mortar samples were stocked in the laboratory for several months under control conditions at a constant temperature of 20 °C and ambient hygrometry, allowing the cement matrix's microstructure to stabilize.

Temperature sensors were then installed in each wall by drilling three 25 cm-deep holes into one of the lateral sides, ensuring precise vertical alignment by using a column drilling. The holes were positioned at distances of 2.5, 5, and 7.5 cm from the wall's outer surface, with a vertical spacing of 15 cm between each hole to prevent any interference between the sensors. Three sensors (MSR 145B, TH Industrie) were inserted into the drilled holes, while two additional sensors were mounted on the sides of the wall. This configuration, depicted in Fig. 5, is specifically designed to monitor temperature and relative humidity changes at different depths within the wall.

The sides of the wall were insulated with an expanded polystyrene to ensure that heat transfer occurs in only one-dimensional (1D) through the two exposed surfaces (Fig. 5). Additionally, two sensors were placed in the climatic chamber and the laboratory room to monitor the indoor and outdoor temperature and humidity conditions for reference. Additionally, a thermal camera was also employed to assess the insulation quality of the setup and identify any potential heat loss, ensuring consistent heat transfer across the monitored surface.

### 2.3.3. Boundary conditions and climatic scenarios

The testing procedure began with a stabilization phase, during which the wall was preconditioned at 20 °C and 50 % relative humidity on the outer face, and at 20 °C with ambient humidity in the indoor environment. This phase continued until all sensors consistently recorded stable temperatures, typically taking around one week.

<figure><img src="image_6.png" /><figcaption>Fig. 5. Sensor positions at various depths of the wall.</figcaption></figure>
Following stabilization, various dynamic scenarios involving temperature or moisture variations were systematically applied to the outer face of the walls. These scenarios were programmed into the climatic chamber using the specific control software (Atmo-Control). Throughout the testing process, indoor conditions remained consistent regardless of the outdoor scenario. The indoor environment was maintained at a constant temperature of 20 °C, while the humidity level remained uncontrolled and subject to natural fluctuations.

2.3.3.1. **Scenario 1: dynamic temperature solicitation.** In Scenario 1, the dynamic temperature variation was designed to simulate daily temperature fluctuations during a summer heatwave period. Specifically, the system was subjected to 12 h at 40 °C followed by 12 h at 15 °C, while maintaining a constant relative humidity of 50 %. This corresponds to a square wave excitation, representing the day-night alternation.

2.3.3.2. **Scenario 2: steady-state temperature solicitation.** In the second scenario, the test procedure included a step variation in temperature from 20 °C to 40 °C, followed by a prolonged exposure at 40 °C until a stable steady-state condition was achieved. During the test, relative humidity was kept constant at 50 %.

2.3.3.3. **Scenario 3: dynamic moisture solicitation.** In the third scenario, the wall underwent a stabilization phase at 20 °C and 50 % RH until all sensors recorded a consistent RH level, typically within a range of 50 ± 2 %. Once stabilization was achieved, hygric testing was initiated on the outer surface, with the temperature held constant at 20 °C. The test began with a step change in RH from 50 to 33 %, followed by sustained exposure at 33 % RH for three weeks. Then, another step change increased the RH to 75 %, which was again maintained for a three-week period. Notably, only the M7.5F wall was tested under these conditions because the reference wall M0 failed to stabilize at an initial RH of 50 %, even after several months of drying. This inability was attributed to the poor moisture regulation capacity of the reference mortar, as reflected in its low MBV value.

These three scenarios are summarized in Fig. 6.

### 3. Mathematical modeling

In this section, we first present the values of key hygrothermal properties that were experimentally determined for the two mortars, which serve as input data for the mathematical model. We then outline the coupled heat and moisture transfer equations of the Künzel model and define the boundary conditions. Finally, the model's accuracy is validated by comparing its prediction with experimental data from existing literature.

#### 3.1. Input parameters - hygrothermal properties of the mortars (M0 and M7.5F)

To implement the numerical Kunzel model [37] used in the present paper, several multiphysics properties (such as density, thermal conductivity, heat capacity, sorption isotherm, liquid transport coefficient and water vapor diffusion resistance factor) are required as input parameter in COMSOL Multiphysics software. These properties were experimentally determined as functions of temperature and moisture variations, following international standards (see section 2.2 and references [27,28] for detailed information on the experimental protocols).

Table 2 presents the characteristics obtained for reference and the biobased mortars.

The liquid transport coefficients for suction ($D_{l,ws}$) and redistribution ($D_{l,ww}$) were calculated using the equations provided later in section 3.2.

In the case of M0 mortar, not all necessary parameters are available, particularly the moisture-related coefficients, such as water vapor permeability and resistance to water vapor diffusion. Their determination proved challenging due to the material's poor hygric response. Therefore, coupled heat and mass transfer modeling will not be applicable and only thermal modeling will be performed for the M0 wall in the following.

#### 3.2. Description of the numerical model

This work focuses on modeling the heat and moisture transport process in open porous materials using the main theories of Kunzel [37], with temperature and relative humidity as driving forces. Before introducing the mathematical model, the following assumptions are made:

**Scenario 1:**

<figure><img src="image_7.png" /></figure>

**Scenario 2:**

<figure><img src="image_8.png" /></figure>

**Scenario 3:**

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Representation of the 3 dynamic scenarios applied to the outdoor environment.</figcaption></figure>
<table><caption>**Table 2**

Properties of M0 and M7.5 mortars used as model input parameters, based on references [27,28].</caption><thead><tr><th>Material's characteristics</th><th>Determined values or functions</th><th></th></tr></thead><tbody><tr><td>Dry density ρ<sub>s</sub> (kg/m<sup>3</sup>)</td><td>M0 mortar</td><td>M7.5F mortar</td></tr><tr><td>Specific heat capacity c<sub>p</sub> (J/kg-K)</td><td>2320</td><td>1342</td></tr><tr><td>Thermal conduction λ (W·m<sup>-1</sup>·K<sup>-1</sup>)</td><td>956.22</td><td>894.2</td></tr><tr><td>Water vapor permeability (dry cup) δ (kg/(Pa·m·s))</td><td>2.32</td><td>λ(w) = 0.1069 + 13.522 × w/ρ<sub>s</sub></td></tr><tr><td>Water vapor permeability (wet cup) δ (kg/(Pa·m·s))</td><td>N.A.</td><td>1.811 × 10<sup>-11</sup></td></tr><tr><td>Resistance coefficient to the water-vapor diffusion μ<sup>*</sup> (wet cup) (–)</td><td>N.A.</td><td>5.78 × 10<sup>-11</sup></td></tr><tr><td>Resistance coefficient to the water-vapor diffusion μ (dry cup) (–)</td><td>N.A.</td><td>3.49</td></tr><tr><td>Capillary sorption coefficient A (kg/m<sup>2</sup>·s<sup>0.5</sup>)</td><td>0.023</td><td>11.16</td></tr><tr><td>Moisture content at free saturation w<sub>f</sub> (kg/m<sup>3</sup>)</td><td>103.8</td><td>294.4</td></tr><tr><td>Sorption isotherm – GAB fitting w (kg/m<sup>3</sup>)</td><td><div style="display: inline-block; vertical-align: middle; text-align: center;"><div style="border-bottom: 1px solid black; padding: 0 5px;">u</div><div style="padding: 0 5px;">u<sub>m</sub> =</div></div> <div style="display: inline-block; vertical-align: middle; text-align: center;"><div style="border-bottom: 1px solid black; padding: 0 5px;">m<sup>*</sup>c<sup>*</sup>k<sup>*</sup>RH</div><div style="padding: 0 5px;">(1 – k<sup>*</sup>RH)<sup>*</sup>(1 – k<sup>*</sup>RH + c<sup>*</sup>k<sup>*</sup>RH)</div></div></td><td>m = 27.8, c = 7.72 and k = 0.86</td></tr><tr><td></td><td>m = 6.52, c = –3.41x 10<sup>45</sup> and k = 0.90</td><td>m = 27.8, c = 7.72 and k = 0.86</td></tr></tbody></table>

(1) The material is considered non-deformable, homogeneous, and isotropic.

(2) Local thermodynamic equilibrium is assumed at every point within the material.

(3) Air is considered as a mixture of ideal gases.

Based on these assumptions, the coupled heat and moisture transfer equations of the Künzel model are expressed as follows (please refer to the preliminary Nomenclature for definitions of the various coefficients used):

Heat equation

$$ (\rho_0 c_0 + c_i w) \frac{dT}{dt} = \frac{\partial}{\partial x} \left( \lambda \frac{\partial T}{\partial x} + h_{lv} \left( \delta \frac{\partial \varphi P_{sat}}{\partial x} \right) \right) \quad (1) $$

Mass (Moisture) equation

$$ \frac{\partial w}{\partial \varphi} \frac{\partial \varphi}{\partial t} = \frac{\partial}{\partial x} \left( \delta \frac{\partial (P_{sat}\varphi)}{\partial x} + D_l \frac{\partial \varphi}{\partial x} \right) \quad (2) $$

Where w is the moisture content per unit volume in kg/m³, φ is relative humidity, δ is water vapor permeability of the material; p<sub>sat</sub> is vapor saturation pressure in Pa; ρ<sub>0</sub> is density of the material in kg/m³; C<sub>0</sub> is the specific heat capacity of the dry material in J·kg<sup>-1</sup>·K<sup>-1</sup>; C<sub>l</sub> is the specific heat capacity of the liquid water in J·kg<sup>-1</sup>·K<sup>-1</sup>; λ is the thermal conductivity of material in W·m<sup>-1</sup>·K<sup>-1</sup>; L<sub>hv</sub> is the latent heat of evaporation in J·kg<sup>-1</sup>.

The liquid transfer coefficient under a relative humidity gradient (D<sub>l</sub> (kg·m<sup>-2</sup>s<sup>-1</sup>)) results from various processes depending on different hygroscopic regions:

(a) The liquid conduction coefficient in the hygroscopic region, is defined as:

$$ D_{l,\varphi} = P_{sat} \delta_a \left( \frac{1}{\mu^*(\varphi)} - \frac{1}{\mu} \right) \quad (3) $$

where μ and μ*(φ) are vapor resistance factors obtained from dry and wet cup tests respectively. μ*(φ) can be described as a function of relative humidity depending on the material in question. δ<sub>a</sub> is water vapor permeability of air [38].

(b) The capillary transport coefficient for suction process, expressed as follows [12,37]:

$$ D_{Lws} = D_{ws} \xi_{\varphi} = \left( 3.8 \left( \frac{A_c}{w_l} \right)^2 \cdot 1000^{\frac{w}{w_l} - 1} \right) \xi_{\varphi} \quad (4) $$

Where A<sub>c</sub> is water absorption coefficient in kg/(m<sup>3</sup>s<sup>1/2</sup>) and w<sub>f</sub> is water content at free saturation in kg/m<sup>3</sup>. D<sub>l,ws</sub> is water content dependent and takes place mainly in the capillary region, ξ<sub>φ</sub> = dw/dφ is the isothermal sorption coefficient determined from the experimental data.

(c) Liquid transport coefficient of redistribution is also taken into account; it is estimated according to Refs. [12,37], as one decimal power below the capillary transport coefficient D<sub>l,ws</sub>.

### 3.3. Boundary conditions

Accurately predicting the interfacial transfer between the air and the material (boundary condition) is critical at both the material
and wall scales. The experimental setup imposes constraints at the boundaries, and it necessary to ensure that the theoretical model aligns with the actual test configuration. Therefore, this study focuses exclusively on heat and mass fluxes at the boundaries, excluding external factors such as rain or radiation. The transport contributions of each model are thus represented solely by their respective heat and mass fluxes, as follows:

$$Q_{\Omega} = h_c(T_{\Omega} - T_{amb}) \qquad (5)$$

$$G_{\Omega} = \beta(P_{v,\Omega} - P_{v,amb}) \qquad (6)$$

Where $Q_Ω$ and $G_Ω$ is heat flux and vapor flux, $h_c$ and $\beta$ the convective heat transfer coefficient and convective mass transfer coefficient, $T$ is temperature.

The boundary water vapor transfer coefficient is expressed as:

$$\beta = -7 \times 10^{-9} h_c \qquad (7)$$

The convective heat transfer coefficient $h_c$ was assumed constant. The simulation and test conditions were based on the climatic scenarios. In experimental setup, the external surface of the wall was exposed to a climate chamber designed to simulate outdoor environmental conditions, where forced convection dominates due to internal air circulation mechanisms. Therefore, a convective heat transfer coefficient of 25 W/(m²·K) for the outdoor condition was adopted. This value is consistent with those used in previous studies. For example, Xue et al. [39] used a value of 23 W/(m²·K), and Wu et al. [40] adopted 23.26 W/(m²·K) in their simulations of outdoor conditions. On the inner side, the wall was exposed to an air-conditioned room simulating indoor environmental conditions. While some air movement exists due to the operation of the air condition system. As such, the convection is closer to mixed or forced convection. In the case of pure natural convection, the indoor convective heat transfer coefficient is typically reported to be around 8–9 W/(m²·K), as demonstrated in several studies [39–41]. However, because this work includes an active air-conditioning system, it would not be appropriate to assume a purely natural convention. A comparable approach can be found in the work by Billy Seng et al. [42], in which two chambers were precisely controlled in terms of temperature and relative humidity using electrical resistances, a refrigeration machine, and humidifiers to maintain uniform environmental conditions on both sides of the wall. The convective heat transfer coefficients of 23.5 and 22.85 W/(m²·K) were applied for the cold and hot chambers, respectively. Therefore, the convective heat transfer coefficients of values of 25 W/(m²·K) for the outdoor condition and 22 W/(m²·K) for the indoor condition was selected in the model.

## 3.4. Numerical solution

The heat and moisture governing equations are highly coupled and are therefore expressed as complex nonlinear partial differential equations. In this study, COMSOL Multiphysics 6.1, based on the finite element method, provides a partial differential equation (PDE) interface for solving these problems. The general form of the PDE model in COMSOL is presented as follows:

$$e_a \frac{\partial^2 u}{\partial t^2} + d_a \frac{\partial u}{\partial t} + \nabla \cdot (-c \nabla u - \alpha u + \gamma) + \beta \cdot \nabla u + au = f$$

$$u = [T, RH]^T$$

$$\nabla = \left[ \frac{\partial}{\partial x}, \frac{\partial}{\partial y} \right] \qquad (8)$$

The terms $e_a$, $d_a$, $c$, $\alpha$, $\gamma$ and $f$ are user-defined coefficients, based on the models presented in Section 3.2. The variable $u$ represents the dependent variable, specifically relative humidity and temperature. By using coefficients, the model can be efficiently expressed in matrix form as follows:

$$\begin{bmatrix} \rho_0 c_0 + c_j w & 0 \\ 0 & \xi_{\varphi} \end{bmatrix} \begin{bmatrix} dT \\ d\varphi \end{bmatrix} = \nabla \cdot \left( \begin{bmatrix} \lambda + l_{\nu} \delta_{\nu} \varphi \frac{\partial p_{sat}}{\partial T} & L_{\nu} \delta_{\nu} p_{sat} \\ \delta_{\nu} \varphi \frac{\partial p_{sat}}{\partial T} & \delta_{\nu} p_{sat} + D_{l,\varphi} + \xi_{\varphi} D_{l,ws} + D_{l,ww} \end{bmatrix} \begin{bmatrix} dT \\ d\varphi \end{bmatrix} \right) \qquad (9)$$

This framework offers a comprehensive and adaptable representation of the physical mechanisms controlling heat and moisture transfer in porous materials, allowing precise simulations of the hygrothermal performance of building materials.

## 3.5. Statistical processing

The prediction quality for the two experimental materials was assessed through statistical analysis. To evaluate the model performance, the Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and R-squared (R²) were calculated. The root mean square error (RMSE) is defined as the measure of the differences between values that are predicted by a model and values that are actually observed, and the difference is squared to avoid the cancelation of positive and negative values, while they are summed up. Mean square error (MSE) is also a similar performance measure to RMSE. However, it has a squared unit. R-squared (R²), which is a
measure of how well the prediction/regression line represents the data, is also used. The Mean Absolute Error (MAE), and coefficient of determination (R²), the Root Mean Square Error (RMSE) and the t-statistics (t-value) are calculated as follows [43]:

$$RMSE = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (Y_i - \tilde{Y}_i)^2} \qquad (10)$$

$$MAE = \frac{1}{n} \sum_{i=1}^{n} |Y_i - \tilde{Y}_i| \qquad (11)$$

$$R^2 = 1 - \frac{\sum_{i=1}^{n} |Y_i - \tilde{Y}_i|}{\sum_{i=1}^{n} |Y_i - \bar{Y}|} \qquad (12)$$

where $Y_i$, $\tilde{Y}_i$ are the experimental and numerical data respectively. $\bar{Y}_i = \sum_i Y_i/n$. n is the number of experiments.

### 3.6. Model validation

To validate our implementation of the model in numerical software, we first compared the experimental and numerical data reported by Alioua et al. [12,38] for a wall made of date palm concrete (DPC) with the simulations generated by our model for the same wall. This wall measuring 50 × 40 × 15 cm³ was manufactured in the laboratory, as illustrated in Fig. 7-a, three sensors were inserted at different depths of the wall (3, 7.5, and 12.5 cm) to measure both temperature and humidity fluctuations. The outdoor boundary condition included variations in temperature (condition 1) and relative humidity (condition 2), as illustrated in Fig. 7-b. Indoor conditions were maintained at a relative humidity of 50 % and at a temperature of 23 °C. Before starting the tests, the initial conditions of the wall were also set to 50 % RH and 23 °C for several days until stabilization was achieved.

For this validation, we used the same input parameters (hygrothermal characteristics of the DPC material) and boundary conditions as those employed by Alioua et al. [12,38].

Our numerical implementation of the Künzel model produced similar trends to those reported by Alioua et al. [44] for both temperature (condition 1) and relative humidity (condition 2) variations at depths of 3, 7.5, and 12.5 cm within the DPC wall. Experimental and numerical data at a depth of 7.5 cm are shown in Fig. 8a and 8b for illustration. The results of the Künzel model closely match those reported by Alioua et al. and align with the experimental data for both temperature and humidity variations. We found similar agreement at all depths, which validates the accuracy and reliability of our Künzel model implementation in predicting the hygrothermal behavior of building materials.

## 4. Results and discussion

### 4.1. Experimental results

In this section, we examine the thermal and hygric behavior of two mortar walls: the reference wall (M0) and the bio-based wall (M7.5F) which contain miscanthus fibers. These walls are exposed to the bi-climatic scenarios outlined in Section 2.3.3.

<figure><img src="image_10.png" /><figcaption>Fig. 7. (a) Scheme of the experimental setup and (b) outdoor conditions used by Alioua et al. for their DPC wall [44].</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Fig. 8. Validation of Künzel’s model: Comparison of our numerical predictions with experimental and numerical data from Alioua et al. [44] at a 7.5 cm depth within a DPC wall, under temperature (a) and relative humidity (b) variations.</figcaption></figure>

* Section 4.1.1 focuses on dynamic temperature cycles applied to the outer face of both walls, while the inner faces are kept at constant temperature. This first configuration allows us to evaluate the walls’ thermal response and their repeatability across multiple heating cycles.

* Section 4.1.2 investigates the two walls under steady state heating conditions, highlighting the differences in temperature gradients and thermal behavior resulting from differences in thermal conductivity and porosity.

* Section 4.1.3 analyzes the hygric response of the bio-based wall (M7.5F) to step changes in outdoor relative humidity under isothermal conditions.

The resulting temperature and humidity profiles provide key Heat and Moisture data, which will be crucial for validating the finite element numerical model in the next phase.

### 4.1.1. Scenario 1: temperature step variations at 50 % RH

The indoor surface of both walls was subjected to dynamic temperature cycles, alternating 12h at 40 °C and 12h at 15 °C, while the inner surface was kept at 20 °C under ambient hygrometry. Five cycles were performed to simulate a five-day exposure and evaluate the consistency of the thermal response.

Fig. 9 (a) and Fig. 9 (b) show the temperature variations at different depths within the two walls, highlighting their responses to the cyclic outdoor temperature fluctuations. The results demonstrate that both the reference (M0) and biobased (M7.5F) walls exhibit consistent repeatability across successive cycles under identical boundary conditions, indicating that a single cycle can accurately reflect the behavior of each wall. Although the indoor temperature was set at 20 °C, the measured data indicate slightly lower average indoor temperatures—approximately 19.5 °C for the M0 wall and 18.5 °C for the M7.5F wall. This minor discrepancy can be attributed to typical experimental variations and is considered acceptable. However, it is acknowledged that the slightly lower indoor temperature for M7.5F could have had a minor influence on the thermal response of this wall.

<figure><img src="image_12.png" /><figcaption>Fig. 9. Thermal behavior of the two walls under temperature cycles ranging from 40 °C to 15 °C: (a) M0; (b) M7.5F</figcaption></figure>
Accordingly, Fig. 10 compares the thermal performance of the two walls over a full 24-h heating and cooling cycle. Both walls display a uniform temperature pattern at a specific depth over the 24h cycle. During the heating phase at 40 °C, the outer surface reaches its peak by the conclusion of the heating period, with M0 reaching approximately 35.9 °C and M7.5F reaching 37 °C.

A clear temperature gradient is observed within the depth of both walls, with temperature decreasing from the outdoor to the indoor faces, as shown in Fig. 10 and 11. Near the outdoor face (at positions 0 and 2.5 cm), the recorded temperature is higher for the miscanthus mortar wall compared to the reference wall, with a gap of approximately 1–1.5 °C. This trend reverses from the middle of the wall toward the indoor face. In this region, the temperature in the M7.5F wall falls below that of the M0 wall, and the gap between the two walls progressively widens, reaching approximately 4 °C at the innermost sensor (position 100 mm).

It is noteworthy that the miscanthus wall exhibits distinct behavior in its thermal response. The biobased mortar acts as an effective thermal barrier, especially near the outdoor face and within the first half of the wall, where it accumulates and retains heat. This characteristic significantly hinders heat transfer across the wall. This behavior is primarily due to the lower thermal conductivity of M7.5F compared to M0, resulting in a substantial reduction in heat flux through the wall's thickness. When analyzing the total heat transfer across the wall thickness, a temperature gradient of 15 °C is observed for M7.5F compared to 11 °C for M0, highlighting an approximate difference of 4 °C in the dampening effect. Consequently, M7.5F effectively mitigates the impact of external temperature fluctuations on indoor conditions.

Fig. 11 illustrates the temperature profiles across the two walls at different moments during the heating phase of the temperature cycle. By examining the temperature values at a specific sensor position, we can assess the rate of temperature change during this heating phase. At the outer face (0 cm), the temperature rises rapidly during the first hour and reaches almost its maximum recorded value after 6h. However, as the distance from the heat source increases, the rate of temperature rises diminishes.

During the cooling stage, the temperature gradients exhibit an opposite trend (Fig. 10). At the end of the cooling period, the highest temperature is observed on the inner face (at position 10 cm) with approximately 17.5 °C for M7.5F and 18.4 °C for M0, while the outdoor surface registers the lowest temperature at 15.4 °C for M7.5F and 16.1 °C for M0. It is notable that the M7.5F consistently shows lower temperatures than M0 at all sensor positions, with a maximum gap of approximately 1 °C. This temperature can be explained by the thermal properties of the materials: M7.5F has a significantly lower thermal conductivity than M0, resulting in lower recorded temperatures. At 25 °C, the thermal conductivity of M7.5F is 0.42 W m⁻¹ K⁻¹, compared to 2.32 W m⁻¹ K⁻¹ for M0. This difference in conductivity explains the observed variation in thermal behavior.

Fig. 12 shows the evolution of relative humidity within the two walls during cyclic temperature variations, with a constant RH level in the exterior environment. For both walls, the outdoor RH is maintained constant, while the indoor RH remains relatively stable with minor fluctuations. Significant internal RH variations are observed at different depths within each wall, clearly illustrating the coupled heat and moisture transfer processes. Although the indoor RH remains relatively stable, the stepwise temperature increase in the climatic chamber causes a rise in the wall's internal RH. Notably, the overall RH levels in the conventional mortar wall (M0) are significantly higher than those in the bio-based mortar wall (M7.5F), indicating distinct differences in moisture buffering capacities and hygroscopic behaviours between the two materials.

### 4.1.2. Scenario 2: thermal equilibrium at 50 % RH

Fig. 13 illustrates the temperature evolution across both walls during scenario 2 (steady-state heating solicitation), revealing a trend similar to the heating phase in the cyclic temperature solicitation. Fig. 14 presents the temperature profiles within the wall depth at different times during the heating phase. Notably, the system achieves a steady state after 12h of solicitation, confirming that the maximum temperature in the 24h cycle was reached at the end of the 12h solicitation.

Once again, the miscanthus wall exhibits distinctive behavior. Near the outer face (at positions 0 and 2.5 cm), M7.5F reaches a

<figure><img src="image_13.png" /><figcaption>Fig. 10. Compared thermal responses of the two mortar walls under a 24h cyclic temperature variation between 40 °C and 15 °C.</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>Fig. 11. Temperature profiles across the two walls at different moments of the heating stage: (a) M0 and (b) M7.5F</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 12. Coupled heat and mass transfer in the two walls: RH fluctuations during cyclic temperature solicitation (a) M0 and (b) M7.5F</figcaption></figure>

higher maximum temperature than M0, but this trend reverses towards the middle of the wall. Additionally, the miscanthus wall shows a broader temperature gradient between the outer and inner faces compared to the reference wall, with the inner face being 4 °C cooler. This behavior is primarily due to the low thermal conductivity and high porosity of the miscanthus wall (refer to section 2.2), which together reduce the heat flux traversing the biobased wall.

Fig. 15 compares the evolutions of the vapor pressure within the two walls during the steady-state heating solicitation. The vapor pressure is calculated with the following equation:

$$P_v = \varphi * 610.78e^{\left( \frac{17.08 * \frac{T}{234.18 + T}}{T} \right)} \quad (13)$$

Where, $P_v$ is the vapor pressure (Pa), $\varphi$ the relative humidity level (%) and $T$ the temperature (°C).

At a specific location within the walls, it is evident that the vapor pressure increases and reaches saturation approximately at the same time as the maximum temperature. However, this timing is delayed as the considered position moves deeper into the thickness of the wall.

### 4.1.3. Scenario 3: step change in relative humidity at 20 °C

Fig. 16 displays the response of the bio-based M7.5F wall to hygric solicitation under isothermal condition at 20 °C in the external environment (scenario 3).

Before testing, the wall underwent a 20-day stabilization phase, with both faces maintained at 20 °C. The outer face was exposed to 50 % relative humidity (RH), while the inner face remained at ambient humidity level. After reaching stabilization, the relative humidity on the outer surface was reduced from 50 % to 33 %, and this lower RH level was kept for 20 days. Subsequently, a step increase in RH up to 75 % was applied, and this level was maintained for an additional 20 days. Throughout the test, the temperature across the wall remained stable, with only minor fluctuations recorded between 19.5 °C and 20 °C.
<figure><img src="image_16.png" /><figcaption>Fig. 13. Compared thermal responses of the two mortar walls under steady-state heating solicitation.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>Fig. 14. Temperature profiles across the two walls at different moments of the steady-state heating solicitation.</figcaption></figure>

As previously mentioned, no comparison can be made with the reference wall (M0) since scenario 3 testing was not performed on it. This wall could not achieve initial moisture stabilization around 50 % RH, even after several months of drying, which prevented the test. This result was expected, as M0 mortar is classified as a poor hygric regulator with a low MBV (see section 2.2).

Fig. 16 shows that when the outdoor RH drops to 33 %, the RH within the M7.5F wall experiences only a slight decrease. This evolution stabilizes rapidly, indicating that the indoor environment characterized by a higher RH of approximately 50 % exerts a more substantial influence on the wall's RH. The system reaches a vapor pressure saturation point, suggesting that the dry outdoor condition has minimal impact on indoor comfort.

In contrast, increasing the outdoor RH level to 75 % initiates a vapor transport gradient within the biobased wall. At depths of 2.5 and 5 cm (Fig. 16-a), the increase in RH is delayed compared to the immediate response observed at the outer face. This delay arises because the porosity of the mortar and fibers fills to saturation before moisture migrates through the thickness of the wall. The vegetal fibers improve the moisture storage capacity of the bio-based mortar. At depths of 7.5 and 10 cm within the wall, the recorded RH
<figure><img src="image_18.png" /><figcaption>Fig. 15. Comparative evolution of vapor pressure in both walls under steady-state heating solicitation.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>Fig. 16. Evolution of Relative Humidity in the M7.5F wall under hygric solicitation: (a) measurements at positions 0, 2.5 and 5 cm; (b) at positions 7.5 and 10 cm.</figcaption></figure>

levels remain primarily influenced by indoor hygrometry (Fig. 16-b).

Chennouf et al. [13] reported similar findings for a date palm concrete wall subjected to hygric variations. They noted that the increase in relative humidity within the wall was more pronounced near the outdoor environment, while it remained controlled by the indoor conditions close to the inner face. The authors attributed this phenomenon to the water vapor resistance of the material, suggesting that the absorption capacity of the vegetal fibers may hinder vapor diffusion through the wall. Rahim et al. [19] observed a comparable trend in their study of hemp-lime concrete subjected hygric solicitation between 50 % and 85 % RH. The authors found that sensors positioned near the outdoor environment detected a significant increase in RH, while sensors in the middle of the wall recorded minimal change, less than 1 %. Additionally, they reported a slight temperature increase within the wall as RH rose, which they attributed to the coupling of mass and heat transfer processes. Collet and Pretot [17] examined the hygrothermal behavior of a hemp concrete wall exposed to a controlled increase in RH from 40 % to 80 % at a constant temperature of 23 °C. Their findings revealed an increase in vapor pressure across the wall, with greater and more rapid variation occurring near the source of solicitation (the outdoor side). They also observed a delay in the rise of vapor pressure at greater depths within the wall.

## 4.2. Numerical investigations

This section centers on simulating the thermal and moisture behavior of the M7.5F wall under controlled bi-climatic conditions. The general form Partial Differential Equation (PDE) interface of COMSOL software was used to define and implement the Künzel mathematical model described in Section 3. The mesh generation for the envelope was straightforward due to the simple geometry of the system. The boundary conditions used in the model were based on the actual temperature and relative humidity variations recorded by the sensors in both the indoor and outer environments during the corresponding experiments.
Noteworthy, the thermal behavior of the reference wall M0 under scenario 1 (cyclic temperature variations) was also modelled for the sake of comparison.

### 4.2.1. Scenario 1: temperature step variations at 50 % RH

In this first part, we simulated the thermal behavior of the M7.5F wall under outdoor cyclic temperature fluctuations with a constant relative humidity of 50 % (scenario 1). The initial conditions were set at 20 °C and 50 % RH. Scenario 1 was modelled by applying a step increase in temperature to 40 °C for 12h at the outdoor boundary, followed by a step decrease to 15 °C, maintained for another 12h. This cycle was repeated 4 more times. The simulation ran for 345,600 s (approximately 4 days).

Fig. 17 compares the numerical and experimental values of temperature and relative humidity at various depths within the wall. The outdoor and indoor boundary conditions are presented in Fig. 17-a, while Fig. 17-b displays the simulation results alongside the experimental measurements. In general, numerical predictions are in good agreement with the experimental results, with the differences diminishing as measurements approach the indoor side. For the M7.5F mortar under Scenario 1, the model has shown a strong predictive capability, particularly at depths of 2.5 cm and 7.5 cm, where the statistical indicators confirm excellent agreement. Specifically, at 2.5 cm, the RMSE values are very low at 0.38, and the $R^2$ is as high as 0.99 and a low MAE of 0.15. Similarly, at 7.5 cm, the RMSE values remain relatively low at 0.35, accompanied by an $R^2$ of 0.98 and an MAE of 0.25. Slightly higher deviations are noted at the surface (0 cm depth), with RMSE values of 1.21, an $R^2$ of 0.97 and an MAE of 0.519. Intermediate results at 5 cm depth show an RMSE of 0.62, an $R^2$ of 0.98 and the MAE is 0.554, still indicating strong overall consistency between predicted and experimental measurements values.

Given the consistent response observed across successive cycles, the analysis was streamlined to focus on a single cycle, as shown in Fig. 18. The maximum deviation between the numerical results and measurements reached 0.6 °C at a depth of 5 cm during the temperature rise. Alioua et al. [12] investigated the thermal behavior of a DPM wall under varying temperatures and compared the numerical results provided by the Künzel approach with their experimental data. They obtained the greatest discrepancies at a depth of 3 cm, with differences up to 2 °C during the temperature rise and fall phases. Similarly, Wang et al. [45] improved the heat and moisture transfer model using a temperature gradient coefficient (TGC) and a phase change criterion (PCC). They compared their simulations results for cellulose insulation with the experimental data from Talukdar's experiment [46], focusing on changes in relative humidity and temperature at depths of 60, 120, and 180 mm. During the adsorption phase, the difference between the experimental data and numerical values was less than 2 % for relative humidity and 0.6 °C for temperature. However, during the desorption phase, the maximum differences reached 3.4 % for relative humidity and 1.5 °C for temperature. In conclusion, the maximum temperature deviation of 0.6 °C under the conditions described in this paper demonstrates satisfactory model accuracy.

Following this, we modelled the thermal behavior of the M0 wall under outdoor cyclic temperature variations with a constant relative humidity of 50 % (Scenario 1). Fig. 19 compares the simulated temperatures of the reference wall (M0) and the M7.5F wall in Scenario 1. Both walls exhibit consistent temperature trends at a given depth throughout the cycle. During the 40 °C heating phase, the outer surfaces reach their peak temperatures at the end of the heating phase, with M0 reaching approximately 33.78 °C and M7.5F reaching 37.13 °C. The numerical results mirror the experimental findings. Near the outdoor surface (at 0 and 2.5 cm), the recorded temperature of the Miscanthus mortar wall is higher than that of the reference wall, with a difference of about 3.35 °C. However, this trend reverses from the middle of the wall to the indoor surface. In this region, the temperature of the M7.5F wall is lower than that of the M0 wall, and the temperature gap between the two walls gradually increases. In the numerical results, the temperature gradient between the innermost and outermost surfaces of M0 is approximately 6.64 °C. Experimentally, a temperature gradient difference of 4 °C between M7.5F and M0 is observed at the innermost and outermost surfaces, which is considered acceptable. When analyzing the total heat transfer through the wall thickness, the temperature gradient for M7.5F is 15.26 °C, compared to 6.64 °C for M0, indicating a difference of about 8.63 °C in the damping effect. Therefore, the numerical results confirm that the M7.5F wall effectively reduces the impact of external temperature fluctuations on indoor conditions.

### 4.2.2. Scenario 2: thermal equilibrium at 50 % RH

Scenario 2 represents the steady state test, where the outdoor side of the M7.5F wall was underwent an initial step temperature increase up to 40 °C, which was then kept constant for 2 days, with the relative humidity held 50 %. The outdoor and indoor boundary temperatures are shown in Fig. 20-a, while Fig. 20-b presents the temperature variations at depths of 0, 2.5, 5, 7.5 and 10 cm within the wall. In this scenario, the maximum difference between numerical and experimental results occurred at a depth of 5 cm, with a deviation of 0.6 °C during the temperature increase. Simulations for both scenarios 1 and 2 demonstrated very similar behaviors, with only minimal differences between the numerical and experimental data (approximately 0.6 °C). This result was expected, as both simulations are based on the same heat transfer model. Moreover, the numerical and experimental curves reached a steady state almost simultaneously, in accordance with previous literature [12].

Under Scenario 2, the statistical indicators for the M7.5F material showed elevated RMSE values across all measured depths. Specifically, at the surface (0 cm), an RMSE reached 1.75, with a corresponding MAE of 0.64. At intermediate depths (2.5 cm and 5 cm), RMSE values were 1.06 and 0.99, with a corresponding MAE of 0.64. At greater depths (7.5 cm and 10 cm), these errors decreased slightly, with RMSE values of 0.74 and 0.451, and corresponding MAE values of 0.44 and 0.33. Nevertheless, the $R^2$ remained consistently above 0.92 across all depths specifically, 0.97 (0 cm), 0.98 (2.5 cm), 0.97 (5 cm), 0.95 (7.5 cm), and 0.92 (10 cm)—indicating acceptable overall correlations between numerical predictions and experimental measurements values.

Additionally, the measured temperatures on the outdoor side of the wall were higher than the predicted values, while the opposite trend was observed on the indoor side. This discrepancy may be attributed to several factors. One key factor is the chosen heat transfer mode, as the numerical model was not fully accounted for radiative heat transfer. Without proper consideration of radiative heat loss
<figure><img src="image_20.png" /><figcaption>Fig. 17. (a) Experimental outdoor and indoor boundary conditions used in the model; (b) Comparison between numerical and experimental temperature variations at depths of 0, 2.5, 5, 7.5 and 10 cm within the M7.5F biobased mortar wall for Scenario 1.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>Fig. 18. Numerical and experimental temperature profiles at depths of 0, 2.5, 5, 7.5 and 10 cm within the M7.5F wall during a single temperature cycle.</figcaption></figure>

or gain, the model can overestimate or underestimate surface temperatures, particularly on the outdoor side. The impact of radiative transfer becomes more pronounced when there is a significant temperature difference between the wall and its surroundings, leading to deviations between simulated and experimental results. To improve the accuracy of numerical predictions, further refinement of boundary conditions is needed. This includes incorporating dynamic convective heat transfer modelling and explicitly accounting for radiative exchange, which could enhance the agreement between numerical and experimental measurements.

### 4.2.3. Scenario 3: step change in RH at 23 °C

In scenario 3, the exterior face of the biobased wall was subjected to a step change in relative humidity, increasing from an initial value of 33 % RH to 75 % RH, and then holding this high level for 25 days. Both the outdoor and indoor environments experimental RH profiles (shown in Fig. 21 (a)) were recorded into the model and used as boundary conditions. Additionally, without taking into consideration any hysteresis effects, the GAB fitting of the main adsorption isotherm was used as an input parameter for the calculations (see section 2.2.).

The numerical simulations of RH variations at different depths within the biobased wall are presented in Fig. 21 (b). Comparing experimental and numerical data reveals discrepancies at different depths within the material. The largest difference occurred at a depth of 7.5 cm, near the indoor side, where the numerical predictions differed from the experimental values by 5 %. The closest match between the datasets was observed at a depth of 5 cm (midpoint of the wall), with only a 3 % discrepancy. At a depth of 2.5 cm, an intermediate discrepancy of 4 % was found. These findings align with those of Alioua et al. [12], who subjected a DPC wall to relative humidity variation. Their study also reported the largest discrepancy at the wall's midpoint, with a 7 % difference between Kunzel's
<figure><img src="image_22.png" /><figcaption>Fig. 19. Comparison of numerical temperature profiles at different depths provided by the Künzel model for the reference wall M0 and the M7.5F wall in scenario 1.</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>Fig. 20. (a) The laboratory outdoor and indoor boundary conditions used in the model; (b) Comparison between numerical and experimental temperature variations at depths of 0, 2.5, 5, 7.5 and 10 cm within the M7.5F biobased mortar wall for Scenario 2.</figcaption></figure>

<figure><img src="image_24.png" /><figcaption>Fig. 21. (a) Importing experimental outdoor and interior boundary conditions into the model; (b) Comparison of numerical and experimental RH variations at depths of 0, 2.5, 5, 7.5 and 10 cm within the M7.5F biobased mortar wall for Scenario 3.</figcaption></figure>
model and the experimental data. In the Scenario 3, the M7.5F material demonstrates strong overall fitting performance, characterized by exceptionally low error values. For example, the lowest RMSE and MAE values were observed at a depth of 5 cm (RMSE = 0.01, MAE = 0.01), accompanied by a high R² of 0.95. Similarly good fitting was found at other depths, including at the surface (0 cm) with an R² of 0.96, and at 2.5 cm with an R² of 0.91. However, at a depth of 7.5 cm, an anomalous result emerges, with the R² value sharply dropping to -1.58, accompanied by increased RMSE of 0.05 and MAE of 0.05, and a notable 5% difference between predicted and experimental values. At 10 cm depth, the fitting quality partially recovers, though it remains lower compared to other depths, with an RMSE of 0.03, an MAE of 0.03, and an R² of 0.48.

Overall, during the adsorption phase, our model slightly underestimates the rise in relative humidity within the wall after the step change in outdoor RH. However, given the material's heterogeneity and the inherent uncertainties in its characteristics and measurements (including sensor accuracy), the model's predictions are considered acceptable.

Several other factors could contribute to the differences between the model's predictions and the experimental results. One suspected factor is the limitation of the experimental setup in accurately assessing the wall's initial moisture content, which significantly influences its humidity response [47]. Additionally, while using the primary adsorption curve as input parameter effectively models the wall's moisture storage capacity, it does not account for the hysteresis effect which occurs in biobased materials between adsorption and desorption isotherms of water vapor. Ignoring this lag effect may also contribute to the observed deviations. Addressing these issues by more precisely determining the initial moisture content and incorporating hysteresis into the model could improve the accuracy of predictions and make the model more applicable to real-world scenarios.

## 5. Conclusion

This work investigates the hygrothermal response of a bio-based mortar wall containing micronized miscanthus fibers (M7.5F) compared to a reference mortar wall (M0).

In the first experimental phase, a custom setup was used to study the hygrothermal behavior of walls under bi-climatic conditions, testing various temperature and RH scenarios. The key findings are as follows:

- Under cyclic temperature variations at constant RH, both walls showed a consistent temperature gradient. The miscanthus fiber wall recorded higher temperatures near the outer face but was about 4 °C cooler on the inner face compared to the reference wall. This led to a larger damping amplitude (15 °C vs. 11 °C), attributed to the miscanthus wall's lower thermal conductivity. Despite constant RH, temperature fluctuations on the outer face caused cyclic RH variations within the wall, showing strong heat-moisture coupling.

- During sustained heating, results were very similar to those obtained with scenario 1. All sensors recorded rapid temperature increases, reaching a steady state within 12 h. Heating caused vapor to transfer from the outer face inward. The saturation vapor pressure is swiftly reached within the biobased miscanthus/mortar wall due to the material's porous microstructure and the capacity of the fibers to release moisture.

- Under outdoor moisture fluctuations, the miscanthus wall acted as a barrier. When outdoor RH decreased, internal RH dropped slightly but stabilized, with little impact on the inner face. As outdoor RH increased, RH near the outer face rose, while the indoor side remained primarily influenced by the lab's-controlled RH.

In the second part of the study, a numerical heat and mass transfer model based on the Künzel approach was used to predict temperature and humidity distributions within the biobased M7.5 wall. The model, using experimental boundary conditions, showed good consistency in predicting temperature variations, with a maximum deviation of 0.6 °C at 5 cm depth. However, discrepancies were noted in RH predictions, particularly at 7.5 cm depth, where a 5% difference was observed. These discrepancies are acceptable given material heterogeneity and measurement uncertainties. Statistical analysis using indicators such as Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and the coefficient of determination (R²) validated the numerical model. It is observed that occasional deviations at boundary depths (0 and 10 cm), likely due to experimental uncertainties such as external airflow. The lack of consideration for hysteresis in moisture transfer likely contributes to underestimating water retention during adsorption/desorption, impacting RH predictions. Future work will explore this phenomenon and study the wall's behavior under combined temperature and RH variations. Overall, bio-based materials like miscanthus fibers show promise for environmentally responsible construction.

## CRediT authorship contribution statement

Haoyan Zhang: Writing – review & editing, Writing – original draft, Validation, Software, Methodology, Investigation. Abderrahim Boudenne: Writing – review & editing, Supervision, Methodology, Funding acquisition, Conceptualization. Rachid Bennacer: Writing – review & editing. Karim Benzarti: Writing – review & editing, Supervision, Methodology, Funding acquisition, Conceptualization. Franck Komi Gbekou: Writing – original draft, Methodology, Investigation, Data curation

## Funding

This research received financial support from the Labex MMCD (Multi-Scale Modelling & Experimentation of Materials for Sustainable Construction), through ANR Investments for the Future (program ANR-11-LABX-022-01).
**Declaration of competing 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.

**Acknowledgements**

We also extend our gratitude to the China Scholarship Council (CSC), which provided financial support to H. Zhang under grant number 202308120014.

**Data availability**

Data will be made available on request.

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