## 1 Introduction  
The ongoing population growth, which deals with economic, social, and sustainability issues, has resulted in a significant increase in global solid waste generation, which is currently about 17 billion tons and is estimated to become 50 billion tons by 2050 [1]. Therefore, it becomes necessary to seek different solutions and new applications of waste materials, especially in the construction sector. This would reduce the environmental impact of the construction sector, which is responsible for producing 35% of global CO\({}_{2}\) emissions and 45-65% of waste disposed in landfills each year. [2]  
Over the last few decades, attempts have been made to reduce the volume of waste in landfills by converting waste into secondary raw materials [3]. The principal construction materials that could benefit from introducing these secondary raw materials are mortar, concrete, and polyurethane. Currently, the most widely reused waste in mortar and concrete is construction and demolition waste (CDW), which seeks to solve the problem of natural aggregates exploitation and the increasing production of CDW [4]. Glass waste [5], polymer waste [6], and natural fiber waste [7,8] are also involved in improving sustainability and lightness to the final product. To avoid expensive disposal, several hazardous wastes which can be flammable, chemically reactive, or corrosive [9] are currently reused as a substitute for natural aggregates or cement (SCM) [10, 11, 12, 13]. This also results in decreased demand for cement and natural resources and reduced CO\({}_{2}\) emissions [4]. In addition, it was displayed that some waste can promote the compressive strength of cementitious materials under elevated temperatures [14]. In the literature, some work has focused on the use of virgin cork and very few on cork waste in mortar and concrete. As a result of adding a lightweight material into a cementitious matrix, the introduction of cork is known to decrease the mechanical performance of the finished product. However, it has been shown not to affect it excessively, and the final products remain classifiable according to the strength classes of UNI EN 998-2 [15,16]. Density decreases and thermal conductivity depends on the sample curing conditions, thus on the presence of residual water within the cork [15,17]. On the other hand, lignocellulosic fibers, walnut shells, cork, and other organic waste have been considered inside the polyurethane matrix to create thermal insulating construction materials [18, 19, 20, 21]. The main characteristic of polyurethane is thermal insulation [22], and all the additional materials in the mix should not change this characteristic. In this framework, this paper proposes for the first time the valorization of cork waste from the manufacturing of cork bottle caps within both lime-based mortar and polyurethane. Thus, this work aimed to fill the research gap of cork waste recycling, reduce the large volume of waste in landfills or waste-to-energy plants and provide sustainability to the most important construction materials. Cork is a natural material from the bark of the oak Quercus Suber L. and is mainly present in the western Mediterranean Sea area, including Sicily, Sardinia, Maremma of Grosseto, Corsica, Spain, and Portugal. The cork production involves about 20,000 km\({}^{2}\) in the Mediterranean area for an annual extraction of 300,000 [23]. Portugal is the first cork producer with about 52% of world production, followed by Spain (25%) and then all the other countries of the Mediterranean basin including Italy with 6%, concentrated for 4% in Sardinia [23]. Its primary use is in manufacturing wine bottle caps: globally, about 12 billion caps are produced per year [23]. In Italy, particularly in the Emilia Romagna region, and precisely in Reggio Emilia and Parma, cork factories have an ancient tradition. Cork extraction and processing include several phases. The decortication is carried out between May and June when the bark is softer, and the damage to the plant is prevented.