## 1 Introduction and Objectives  
Cavities of significant dimensions may exist in natural rocks, mainly in evaporitic and carbonate rocks but also in volcanic rocks. These cavities can represent a grave risk when a shallow foundation, such as for a building, bridge or other structure, is builtonthem. This fact may substantially determine the calculation results of the foundations. This is a relatively frequent problem worldwide, given the vast areas where these types of rocks appear. In the history of construction, there are many examples of failures of this nature, and the issue is the subject of periodic meetings of experts [1] and of studies evaluating their risk [2]. In Spain, these three types of rock masses are all present, with the surfaces occupied by limestones and dolomites covering 30% of the territory each, while 12% is occupied by evaporitic rocks [3]. The volcanic rocks are mainly located in the Canary Islands, where there are important networks of lava tubes in which safety and stability measures for the vaults must be maximised [4, 5]. In carbonate and volcanic rock masses, the voids are inherited and do not usually evolve in short periods of time, unlike in evaporites, where the cavities can be enlarged by dissolution, compromising the stability of the infrastructures within their useful life. On the other hand, there are many precedents and information in the literature about the stability of anthropic caverns such as tunnels and galleries [6, 7, 8, 9]. However, there are not many studies on the influence of a cavity in the vicinity of a shallow foundation on itultimate bearing capacity. [PERSON] and [PERSON] [10] conducted an analytical calculation on the roof of a karst cavity with a Quaternary cover, which is presented in Mancebo [11] for different cases of flat or semi-spherical roofs with water tables both below and above the roof. There are other stability analyses that consider failures assimilated to landslides. [PERSON] [12] discussed three different processes of karst collapse under the effects of positive and negative pressures, establishing critical mechanical models for each of them. [PERSON] et al. [13] investigated the stability calculation of a known karst cavity, accessible through the stability graph method, which is widely used to analyse polyhedral mining rooms (approach index engineering rock mass classifications). The analytical solutions of [PERSON] et al. [4] are also available, which refer to large cavities in volcanic rocks, in which the size and shape of the lava tube section (rectangular and circular) are correlated with the surface's ultimate bearing capacity by means of simple calculation models (beam under uniformly distributed load for rectangular sections). The analysis of [PERSON] and [PERSON] [14] stands out. This research deals with the cover stability of large cavities near the surface through reduced-scale laboratory tests. From this study, the increase of the failure loads with the cover and the bed/strata thickness can be observed. According to this reference, for a given quality of a typical limestone, the cover stability is ensured when its thickness is 70% of the cave width. In the case of gypsum, because it has a lower strength, a greater cover thickness is required. In the present paper, unlike in the previous reference, the determination of the bearing capacity of a shallow foundation over a rock mass with cavities is analysed by applying sophisticated numerical models to study how its presence influences the ultimate bearing capacity of the footing. Thus, taking one of the most representative cavity geometries in nature as the starting point, the main objective of this study is to obtain the ultimate bearing capacity of the foundation with cavities of different sizes and positions, on rock masses with different strengths and deformation characteristics, by means of the modified Hoek-Brown failure criterion.