## 1 Introduction  
Widely used in structural design for their many valuable benefits, such as high strength, low weight, ductility, fast construction, and sustainability, steel members are nonetheless highly vulnerable to fire [1, 2, 3]. When heated, steel undergoes a rapid degradation of strength and elastic modulus, which may lead to a fast and uncontrolled collapse; therefore, it needs to use a fire protection system to decrease the heating rate of the steel members, consequently reducing material property loss and complying with existing standards [4, 5]. In the general context of fire safety, the critical temperature for such members is generally regarded to range from 450 to 550 \({}^{\circ}\)C; in other words, it is the range of temperature at which the structural steel's design resistance equals the design effect of accidental actions [6, 7]. According to EN 1993-1-2 [8], the heating rate of steel members depends, beyond the fire's characteristics, upon the material's surface/volume ratio and its thermal and mechanical behaviour. This is explained by: (i) heat is transferred from molecule to molecule; therefore, heat spread is decreased as the material's contact area reduces and its thickness increases; (ii) thermal conductivity, specific heat, and specific weight directly affect the heat transfer process as the velocity of heating is directly proportional to the first and inversely proportional to the specific heat and weight; and (iii) the material has to resist thermal actions and plastic deformations, as much as possible, to ensure the stability and homogeneity needed to perform its expected insulating function during the fire event. In previous research [9], a large group of mortars was developed and studied, aiming to select the ones with the best thermal behaviour and compare them with the best commercial composition (C). The specimens were subjected to two types of tests: (i) an experimental test to analyse the influence of expanded perlite's and expanded vermiculite's grain size on the thermal performance of laboratory-developed mortars and (ii) an experimental programme of tests carried out on steel square section S355 columns protected by the mortars in the study, under an ISO 834 fire condition and subjected to a preload of 50% of the design value of the load-bearing capacity of the columns at ambient temperature (ULS) [9]. In the end, the best-developed mortar compositions were selected: gypsum as a binder and expanded perlite or vermiculite as aggregates. The main advantage of adding these two minerals is their good insulation properties owing to their highly porous nature. However, due to their porous and lightweight nature, their addition drastically modifies the mortar's mechanical characteristics, reducing its compressive and flexural strengths compared to plain cement/gypsum mortars [10]. Several studies [11; 12; 13; 14; 15; 16] have shown that the addition of nanomaterials, including nano silica, can improve the mechanical properties of cementitious materials. Despite the knowledge of nano silica in cement-based compositions, its addition to gypsum-based mortars is still poorly understood. Therefore, it is important to study the materials mentioned above to understand their importance and effect on the composition of passive fire protection mortars. Some previous studies have followed the statements mentioned above:  
[PERSON] et al. [11] concluded that gypsum-based mortars have better thermal properties than cement. However, it has low strength and poor toughness; moreover, when perlite or vermiculite is added as aggregates, the thermal properties increase, but the mortar's mechanical properties decrease even more. [PERSON] et al. [10] studied the effects of expanded vermiculite in cement-based mortar. Three types of compositions were produced, one of them constituted by cement and sand, and the other two by different amounts of vermiculite added into the cement/sand solution, always with equal water-to-cement ratios.