## 1 Introduction
\[q_{a}=\left(32R_{w}\frac{1}{1+4e^{-0.213H}}E^{\prime}\frac{EI}{D_{e}}^{3} \right)^{1/2} \tag{4}\]  
Equation (4) does not depend on the width of the trench nor on the elastic modulus of the lateral fill and, given that exceeding this load on the pipe could imply its failure, it is necessary to verify it by other means. Other researchers, such as [PERSON] et al. [7], propose improvements to the analytical calculations based on the equations of [PERSON] and [PERSON] [3] introducing more variables in a buried pipe installation. Even so, they continue considering the behaviour of the soil in its elastic state and conventional load values. The finite element method (FEM) associated with engineering is mainly due to the research of [PERSON] et al. [8]. They analysed stresses in complex aircraft structures, and their advances soon spread to other areas of engineering (mechanical, civil engineering, etc.). For example, in the geotechnical and pipeline specialties it has been possible for finite element models to adequately simulate the values of experimental tests. Different publications [9; 10; 11; 12; 13; 14] analyse buried pipes under different installation conditions and materials and use the FEM to simulate the values of experimental studies. Below are indicated, according to the research carried out by [PERSON] and [PERSON] and published in the book _Structural Mechanics Buried Pipes_[15], some of the main advantages of using the finite element method compared to using more common calculation procedures:  
* It allows consideration of the nonlinearity and heterogeneity of the soil;
* It allows consideration of the interface between the pipe and the ground, that is, the slip or adhesion between both surfaces;
* It provides greater precision in the analysis of the vertical and horizontal displacements of the pipe;
* It uses mathematical models that allow the materials of the ground and the pipe to be characterized. The present study proposes a parametric model that considers the behaviour under real conditions of a pipe trench located in a facility subjected to surface loads. One of the main contributions of this study is to analyse vehicles with a weight much higher than the weight contemplated in the AWWA M11 standard. Using finite elements, it is also determined which parameters that tend to increase the stresses on the pipe are most influential. The parameters of the finite element model are adjusted through a sensitivity analysis to adequately reproduce [PERSON]'s experimental tests [16]. The deflections and maximum stresses are determined for steel pipes of 36\({}^{\prime\prime}\), 42\({}^{\prime\prime}\) and 48\({}^{\prime\prime}\) with standard weight thickness and ASTM A53 Grade B material. The surface loads produced by the circulation of mining trucks are considered. Table 1 includes the load capacity for the truck models commonly used in mining. The parametric analysis consists of evaluating 108 models that emerged after modifying the following variables (variables identified in previous equations):  
* Pipe outside diameter \(D_{e}\);
* Pipe thickness \(t\), preselected according to hydraulic calculations;
* Pipe bedding angle \(\alpha\), depending on the installation;
* Elasticity modulus of the pipe material, preselected according to the hydraulic calculations \(E_{t}\);
* Elasticity modulus of the trench backfill, determined by a soil survey or recommended values (\(E_{s1}\), \(E_{s2}\), \(\ldots\), \(E_{sn}\));
* The recommended geometric values in the typical trench section as width and height;
* The study was carried out using the mining vehicles shown in Table 1 as a reference.