DYNA

4.1. Influence of rainy periods

Additional tests were carried out to include the effects of rainy seasons because water infiltration causes an increase in water content. Consequently, the suction decreases and the water level increases reducing the shear strength of the soil. This has a direct influence on the movements of slopes and is considered the main cause of landslides [1,2,17].

Given the importance of the effect of water infiltration in slopes, stability analyses were performed during a period of critical rain. This study was done using the Slope and Seep modules working simultaneously. The rainfall data presented in Fig. 5 were used as input parameters in Seep module in order to estimate the variation of the water table over time. The stability analyses were performed for each increase in the position of the water table.

The SPT tests used to define the stratigraphy of the slope were carried out from October to November 2011, which is characterized as a rainy season in the Southeast Region. However, in analyzing the rain data, there are other periods in which the rainfall can be more intense, as shown in Fig. 5. These data were obtained from the National Institute of Meteorology website (INMET), based on rainfall data provided by the Meteorological Station N° 83075 in Guarulhos, Sao Paulo.

By analyzing the monthly rainfall charts, a long dry period between May and September 2011 was observed, followed by a rainy period lasting from October 2011 through February 2012. In the present work, a dry period was defined as monthly rainfall precipitation lower than 90 mm. In this case, the water level was below the initial water level, which was positioned using SPT information.

This dry period may cause some uncertainty regarding the piezometric level adopted for the drilling, such that it can be erroneously positioned lower than the actual stabilization of the piezometric level of the soil, since a long dry period is capable of lowering the water table.

Figure 5: Average monthly rainfall chart (Weather Station Guarulhos, São Paulo, Brazil).

Source: The authors.

Therefore, the stability analysis was performed using daily and accumulated rainfall data for the months of October 2011 to February 2012, corresponding to 150 days. These data were used as boundary conditions on the external surface of the slope. Moreover, since it is a transient flow analysis, the level of water determined through the SPT tests was taken as an initial condition, as shown in Fig. 3.

Analyses for unsaturated layers were conducted adopting isotropic materials and hydraulic conductivity ratio (ky'/kx') equal 1. The software provides different water content functions for different types of soils. Fig. 6 shows the soil layer curves used to estimate the volumetric water content [18]. Fig. 7 shows the hydraulic conductivity functions for soil layers, estimated through residual water content and hydraulic conductivity coefficient [18].

The results shown in Fig. 8 demonstrate that the position of the water level varies considerably, such that soil layer C appeared practically saturated. The water level variation was estimated through a maximum monthly precipitation of 285 mm. However, it is important to highlight that monthly precipitation higher than 400 mm can occur. Thus, the water level can rise more than the level considered in this analysis. The behavior of pore pressure values can be verified through some reference points in the slope, as seen in Fig. 8. The results showed pore pressure values increasing with time, with an increase of approximately 20 kPa at each point, as seen in Fig. 9. However this value, despite being constant, has the most significant increase for the first ten infiltration days. Aristizabal et al [17] showed that pore pressure values depend on rainfall intensity and soil layer permeability. In the present work, results showed that the smallest values of pore pressure were observed at the surface, as shown in Fig. 9. This behavior indicated that the rainfall intensity is smaller than the permeability of soil layer [17].

Figure 6: Characteristic curves for soil layers.

Source: The authors.

Figure 7: Hydraulic conductivity functions for soil layers.

Source: The authors.

Figure 8: Reference points for analysis of the variation of pore pressure.

Source: The authors.

Figure 9: Influence of water infiltration on pore pressure values.

Source: The authors.

Figure 10: Critical surface (FSmin) taking into consideration the effects of water infiltration.

Source: The authors.

These analyses can be extended to the entire slope, showing the negative effects provided by the action of water infiltration into the soil. These effects act directly on the shear strength of the soil and consequently on the stability of the section studied.

The stability analysis for the critical period of precipitation was performed using the results of the infiltration analyses of the Seep module. The strength parameters used were the same as the initial stability analysis. Fig. 10 shows the critical surface, taking into consideration the effects of water infiltration. The minimum factor of safety obtained was 0.78, representing a 33% decrease compared to the initial stability analysis.

Fig. 11 shows the variation in the factor of safety over time, applying the daily variable rain intensity from INMET data for this time period. In the first ten days, the factor of safety declined approximately 10%, characterizing a state of imminent failure. In the months of November and December the intensity of rainfall did not show great variation and therefore the factor of safety only decreased about 3%. In January and February the intensity of rainfall significantly increased and the factor of safety decreased 9% in each of those months.

Figure 11: Variation of the factor of safety over time.

Source: The authors.

The results show the importance of taking into consideration the effects of rainfall infiltration for stability analysis. As can be seen, the slope, which initially appeared stable, revealed the occurrence of failure after the effects of an intense period of rain.

4.2. Reliability analysis

The following reliability analysis is presented because the factor of safety, widely used in the practice of geotechnical projects, is often determined based only on the designer's experience [7]. However, it is common to extend this experience to other situations without considering the varying degrees of uncertainty involved in each application [6]. A reliability analysis can be performed in a simple manner and using the same data from the conventional analyses. For this reason, it is recommended that the factor of safety and reliability be used together as complementary measures for acceptable design [6,19].

In this study, a reliability analysis was performed based on the uncertainty related to the shear strength parameters of the soil. These parameters were estimated based on the results of SPT. This analysis is considered of great importance because geotechnical engineering is characterized as a science where there are uncertainties related to natural variability, knowledge and forecasting models [10,19-21].

A research conducted by Hidalgo et al. [2] provides reference data for coefficients of variation, based on various published studies. The probability of failure (PF) was determined with the Monte Carlo method and using the coefficients of variation of 7.5% and 40% for the effective angle of friction and cohesion intercept, respectively.

The following analysis presents the variability of shear strength parameters for soil layers A and B, because it was noted that the critical surface develops within these layers, as shown in Fig. 3. Table 3 shows the average, minimum and maximum values for the parameters analyzed.

Table 3: Shear strength parameter data used in reliability analysis.

Source: The authors.

Figure 12: Normal probability distribution function.

Source: The authors.

Fig. 12 shows the normal probability distribution function for the stability analysis of the slope. The results indicated an average factor of safety of 1.16, with minimum and maximum values equal to 0.74 and 1.59, respectively. The standard deviation was 0.11 and the reliability index 1.44, resulting in a probability of failure of 7.7%. These results indicate that the analyzed section presents unsatisfactory stability performance [19].

Fig. 13 shows the normal probability distribution of the factor of safety, where values equal to or lower than 1.0 have a 7.7% probability of occurrence, characterizing the failure of the section analyzed. The reliability analysis shows that despite a factor of safety higher than 1.0, the slope stability has an unsatisfactory performance. Thus, the factor of safety and the probability of failure should be analyzed together.

4.3. Sensitivity analysis

Sensitivity analysis was used to observe the effect of the variability of the shear strength parameters on the stability of the section studied. This analysis can determine whether the stability of the section is more sensitive to the cohesion intercept or the angle of friction [9]. The analysis included soil layers A and B, which are the layers which show development of critical surface. Table 4 shows the range of variation for soil layers A and B.

The results indicated that the cohesion intercept value for soil layer B had a greater influence on the factor of safety than the cohesion intercept value for soil layer A, as shown in Fig. 14. This behavior is coherent since most of the critical surface develops within the surface layer of soil B, including the portions where the application of the surcharge occurs. In

addition, for the analysis performed for soil layer B, the cohesion intercept of soil layer A is held constant and equal to 5 kPa, while in the analysis for soil layer A, the cohesion intercept of soil layer B is kept constant and equal to 10 kPa.

The sensitivity analysis for the effective angle of friction showed that the stability of the section analyzed was also more sensitive for soil layer B, as shown in Fig. 15. These results confirm the results shown in Fig. 14, since the average effective angle of friction of soil layer B is higher than soil layer A. Therefore, the shear strength parameters of soil layer B have more influence on the stability of the section studied.

Additionally, the sensitivity analysis showed that the global stability is more influenced by the cohesion intercept. Results showed that for the cohesion intercept equal to zero, the factor of safety is less than 1, while for the effective angle of friction equal to 15°, the factor of safety is around 1.25, as seen in Fig. 14 and Fig. 15.