## 1 Introduction  
The development of building construction materials using agricultural residues and natural media presents a great interest. Indeed, such materials are useful to limit the energy consumption of the building and to reduce the environmental impact. They present other advantages such as renewability, biodegradability, low density and availability with low cost. Research activities on these materials are increasing these last years. Among them, some works in literature are focused on the thermal characterization of green insulating porous material [1, 2] such as cellulose based aerogel [3, 4], and composite materials using natural fibers such as Hemp shives [5, 6, 7, 8], Flax and straw rape [8], granular cork [9, 10] and palm date fibers [1, 2, 11, 12]. Currently, composite materials have various applications in buildings; in walls, floors and roofs for insulation. Some studies showed that the natural materials embedded in different construction materials (such as plaster, cement, and mortar) allow good thermal insulating performances [13]. The influence of natural fibers content and size on effective thermal conductivity of composite materials has been analyzed [1, 14, 15]. For example, [PERSON] et al. [1] conducted an experimental investigation of the thermal and mechanical properties of composites of mortar mixed with date palm fibers (DPF) by varying the content and the size of the added fibers. They showed that the DPF size does not have significant influence, while having a higher DPF fiber content improves thermal insulation capacity. For DPF loading lower than 15 wt%, the mortar composite represents a good compromise between both thermal and mechanical performance of construction materials. These previous works underlined the importance to study the effect of fiber content on thermal conductivity of composites. Other works present comparison between effective thermal conductivity experimental and analytical model results [5; 9]. The data of analytical models are the fiber volume fraction or porosity and the thermal conductivity of each phase constitutive of composite materials [16; 17]. They are useful to analyze the influence of fiber density, but on the other hand, they required the knowledge of local thermal conductivity. Thus, recently some works in literature are interested in the measurement of thermal conductivity of hemp fiber packed bed [18; 19]. Other works investigated the thermal conductivity of the solid phase of the hemp shives [8; 19]. In this context, this current study investigates new insulating mortar composites containing Juncus maritimus fibers. Juncus maritimus (Var. typicus) is a natural plant growing easily in wet and aquatic places, it counts 200 species of Juncus plant belongs to the family of Juncacae according to [PERSON] et al. [20]. It is worth mentioning that there was no previous work concerning the Juncus maritimus fibers used as reinforcement in a mortar in order to improve its thermal insulating efficiency. We aim to take advantage of these renewable resources to develop new lightweight composites having the same concept and application as the Hemp concrete [2; 13]. The fibers derived from the Juncus maritimus plant are expected to be a good substitute of Hemp fibers considering the availability of this plant throughout the year, while, harvesting the Hemp fibers is periodic. Moreover, there is a low gray energy in the manufacturing of the composite mortar containing Juncus maritimus fibers. In this current work, different samples containing weight fractions of fibers ranging from 0% to 10% are studied. The microstructure of samples is characterized in 2D by SEM and in 3D by micro computed tomography (\(\upmu\)CT). We work on both experimental thermal characterization and theoretical analytical models. Effective conductivity and diffusivity of the sample are measured. An approach is proposed to estimate thermal conductivities of mortar matrix and also the local thermal conductivity of crushed Juncus maritimus (JM) fibers (JM local thermal conductivity).