The accurate description of the flow of water in porous media is of the greatest importance due to its numerous applications in several areas (groundwater, soil mechanics, etc.). The nonlinear Richards equation is often used as the governing equation that describes this phenomenon and a large number of research studies aimed to solve it numerically. However, due to the nonlinearity of the constitutive expressions for permeability, it remains a challenging modeling problem. In this paper, the stationary form of Richards’ equation used in saturated soils is solved by two numerical methods: generalized finite differences, an emerging method that has been successfully applied to the transient case, and a finite element method, for benchmarking. The nonlinearity of the solution in both cases is handled using a Newtonian iteration. The comparative results show that a generalized finite difference iteration yields satisfactory results in a standard test problem with a singularity at the boundary.

Tunnel support design in rock masses requires controlling deformation while maintaining structural safety, constructability, and material efficiency under variable geotechnical conditions. This study presents a Simulation–Optimization–Decision Framework (SODF) for preliminary and comparative tunnel support design. The framework integrates FEM-based numerical modeling in PLAXIS 2D, Particle Swarm Optimization (PSO), and a Multi-Criteria Decision-Making (MCDM) model to evaluate composite support systems composed of shotcrete and steel sets. Deformation at the tunnel crown was used as the primary optimization response, while structural feasibility was verified through axial force–bending moment and axial force–shear force interaction envelopes with a minimum safety factor of $FS\ge 1.5$. Two case studies were analyzed using GSI values of 40, 45, 50, and 55. Case 1 considered $E_{rm}=500,000$ kN/m², with an additional condition of $250,000$ kN/m² at $GSI=40$, whereas Case 2 considered $E_{rm}=545,000$ kN/m², with an additional condition of $300,000$ kN/m² at $GSI=45$. Three PSO configurations were evaluated to compare the search intensity, the diversity of feasible solutions, and the computational effort. The results showed that feasible configurations were mainly concentrated between 10 and 14 cm of shotcrete thickness in Case 1 and between 10 and 12 cm in Case 2, with frequent selection of 254 mm and 305 mm steel sets. The MCDM analysis indicated that the lowest-deformation alternative does not necessarily coincide with the most suitable engineering alternative when material cost, shotcrete applicability, steel-set maneuverability, and local availability are considered.

The common practice of measuring the water content of any soil mass involves a gravimetric methodology by obtaining the dry and wet mass of a soil-water mixture. In terms of execution, this procedure is simple but time-consuming since it requires at least 12 hours to be completed. Therefore, other measuring techniques could be applied, including devices such as sensors to obtain the water contents of soil. There are plenty of sensors in the market whose purpose is to obtain volumetric water content, which is a fundamental parameter of unsaturated soil mechanics. In the present research, three conventional low-cost volumetric water content sensors were evaluated (capacitive-based and resistive-based) in one of the most basic and common geotechnical tests: the Proctor compaction test. This test is appropriate for this assessment given the fact that its objective is to analyze how the dry density of soil varies regarding different water contents when using a specific compaction energy. The soil used in this work corresponds to sandy soil, with fair amount of gravel and fine material (SM). The interface of the sensors was done via an Arduino UNO board, and the data was processed and displayed using Python code. The findings of this research are presented in terms of calibration curves and linear correlation coefficients, and furthermore, a sensor repeatability test was performed in order to evaluate the accuracy of these types of sensors. The results obtained indicate that these low-cost sensors may not be the most recommended devices to use within the context of this specific geotechnical application.

The Tijuana-Ensenada highway crosses the “Salsipuedes Bay”. This zone has been subject to numerous landslides due mainly to geological conditions. The last great landslide occurred on 28 December 2013. The principal causes that triggered the landslide were: the shale weathering, the groundwater, and the seismicity of the zone. In the present study, a deep sensitivity analysis was performed to reproduce the failure mode to understand the failure mechanisms and the factors that triggered the landslide. The results suggest that the seismic activity and water caused the degradation of the shale. To make a close approximation of the real conditions a finite element analysis was carried out using patterns of joints and adopting different shear strengths for the joints. Finally, the failure mechanism was reproduced in a satisfactory form.