###### Abstract
More recently, the finite element limit analysis (FELA) method was used by [PERSON] et al. [17]. Design charts were given for a reduction factor to estimate the ultimate bearing capacity of a strip footing over a rock mass with voids. [PERSON], [PERSON], and [PERSON] [18] applied the same method to assess the undrained bearing capacity above voids in two-layered clays. [PERSON] et al. [19] instead used the discontinuity layout optimization approach to determine the bearing capacity above square voids in cohesive-frictional soils, reporting typical failure patterns. [PERSON] and [PERSON] [20] investigated the bearing capacity above multiple square voids in sandy soils and purely cohesive clays, and they also explored the effect of load inclination. [PERSON] et al. [21] studied the effects of the depth and geometry of the voids, and of the eccentricity of loading on the bearing capacity. Recently, [PERSON] et al. [22] investigated the impact of seismic loading on the bearing capacity of undrained clay with voids. In order to deal with complex problems, which are usually difficult to attack with a purely model-based approach, machine learning (ML) is currently experiencing a burst of popularity in applications, and also in the civil engineering field, see examples [23; 24; 25; 26; 27; 28; 29; 30; 31; 32]. Regarding the foundation engineering field, neural networks have been employed to estimate the settlement and the load carrying capacity of pile foundations [33; 34; 35], and of isolated shallow footings [36; 37; 38; 39; 40]. To the best of the authors' knowledge, no research has been carried out so far to predict the bearing capacity of a shallow strip footing above a void by means of approaches based on ML tools. In the present study, a first attempt is made to set an extensive database dealing with the various factors affecting the said bearing capacity for strip footings above a single unsupported void in either heterogeneous or homogenous soils, under seismic and quasi-static excitations. The considered factors are:  
* Soil cohesion
* Soil internal friction angle
* Heterogeneity
* Distance of the void from the central line of the footing
* Depth of the void
* Shape and size of the void
* Horizontal earthquake acceleration. Results have been obtained as lower and upper bounds on the load bearing capacity of the strip footing via the FELA method. First, a sensitivity analysis has been conducted to quantify the effects of these parameters on the ultimate footing bearing capacity. Next, to predict the seismic bearing capacity, the multiplayer perceptron (MLP), group method of data handling (GMDH), and adaptive-network-based fuzzy inference system and particle swarm optimization (ANFIS-PSO) techniques have been adopted. The proposed procedure, based on the ML tools, can therefore be framed in the following way: for all the problems characterized by the geometry of strip footing and a void similar to the one here considered, and by heterogeneous solids, of which the main properties affecting their resistance are cohesion and friction angle within the investigated ranges, the said ML tools can be assumed already tuned and trained. Practitioners can then use the ML-based models as a kind of black-box, to automatically and quickly obtain an estimation of the seismic bearing capacity of any shallow strip footing, so that the detrimental effects induced by the interaction with the buried, unsupported void can be easily quantified. The remainder of this paper is organized as follows: in Section 2, the attacked problem is defined in detail, and the modeling in Optum G2 is validated with literature results to ensure the accuracy of the solutions in the database. The results of a parametric study, performed to assess how the aforementioned factors affect the solution, are reported in Section 3. The ML tools adopted to learn the link between the input factors and the footing bearing capacity, namely the output, are described in Section 4.