## 1 Introduction  
The stability of slopes affected by rainfall is a crucial topic in geotechnical engineering and soil mechanics, with significant implications for infrastructure safety, urban planning, and the mitigation of natural disasters. Slope failures can result from various factors, such as earthquakes and external loads. However, rainfall is the most common cause of failure [1, 2, 3, 4, 5, 6]. As noted in [7], the initial volumetric water content of the soil, its hydraulic characteristics, and the intensity and duration of rainfall are variables that significantly affect pore pressure in slope soils and, consequently, their instability. In regions prone to heavy precipitation, intense and prolonged rainfall can considerably impact slope stability, especially when these slopes are in unsaturated conditions [8]. Infiltration occurs when rainwater or irrigation water penetrates vertically into the soil, with some portion running off the surface, allowing gravitational downward flow to become part of the soil water [9]. This infiltration of rainwater can alter the hydro-mechanical behavior of the soil, generating changes in pore pressure, reducing the material's shear strength, and, therefore, affecting the safety factor, potentially leading to failure in these slopes [10, 11, 12, 13, 14, 15]. Each year, thousands of lives and USD millions are lost due to landslides [16], underscoring the need to study these failure mechanisms in depth and to develop effective prevention, mitigation, and numerical modeling strategies. Although there are numerous studies similar to the present one, most have focused solely on variations in intensity or on fully saturated conditions [17; 18]. However, few works jointly address the effect of key hydro-mechanical variables such as suction, degree of saturation, and their direct impacts on the global safety factor in unsaturated soils. This study aims to fill that gap by integrating these parameters to achieve a more comprehensive slope behavior assessments under intense and prolonged rainfall conditions. Numerous authors have analyzed the impact of rainfall intensity on slope stability [11; 19; 20; 21]. Most have concluded that high-intensity rainfall [22] poses the greatest stability challenges for slopes, as it generates higher pore pressure, reduces soil cohesion, and decreases the internal friction angle compared to low-intensity rainfall [11; 19; 23]. For this study, a rainfall intensity of 30 mm/h was considered, classified as high-intensity [24; 25; 26]. This study differs from others by focusing on the comparative analysis of soils with different gradation characteristics, such as poorly graded sand (SP-SM) and well-graded sand (SW-SM), under rainfall conditions with a constant intensity of 30 mm/h. Unlike other studies that vary rainfall intensity, this study maintains a constant intensity while varying the rainfall duration, soil type, and their hydro-mechanical properties. This approach provides a more precise understanding of how different soil properties influence slope stability under rainfall conditions. Numerical modeling was performed in Plaxis 2D using the Mohr-Coulomb constitutive model. Although both the Mohr-Coulomb and hardening soil models share the same failure criterion and yield similar evaluations of ultimate soil strength [27; 28], the former was selected due to the study's focus. Since the analysis does not aim to capture deformation behavior or strain accumulation, the Mohr-Coulomb model offers a simpler and more efficient solution for this purpose. The unsaturated soil condition considers matric suction and water content in terms of volumetric water content or the degree of saturation as a basis for evaluating slope failures [14; 29; 30] in unsaturated conditions. In this context, suction curves are essential as they describe the relationship between suction and soil water content or degree of saturation. These curves represent the soil's water retention capacity and hydraulic behavior under unsaturated conditions.