Statement 1: Method of slices overestimates the value of factor of safety.

The method of slices is a widely used method for calculating the stability of slopes. It involves dividing the slope into a number of vertical slices and analyzing the equilibrium of each slice. The factor of safety is then calculated by comparing the resisting forces to the driving forces.

In the method of slices, it is assumed that the failure surface is a series of straight lines connecting the center of each slice. This assumption can lead to an overestimation of the factor of safety because it does not take into account the actual shape of the failure surface, which may be curved or irregular. Therefore, statement 1 is correct.

Statement 2: The exact value of factor of safety is obtained in T=0 analysis.

In slope stability analysis, the T=0 analysis refers to the analysis performed at the point of failure, where the factor of safety is equal to 1. However, it is important to note that the T=0 analysis provides an estimate of the factor of safety at failure, but not the exact value.

The exact value of the factor of safety can only be obtained through rigorous analysis using appropriate methods and considering various factors such as soil properties, slope geometry, and external loads. Therefore, statement 2 is incorrect.

Statement 3: Reduction in shearing resistance in embankment is caused by tension crack at the top of it.

When an embankment is subjected to external loads, such as the weight of the embankment itself or additional loads from traffic, the soil experiences compressive stresses. However, if the compressive stresses exceed the shear strength of the soil, it can lead to the formation of tension cracks at the top of the embankment.

These tension cracks result in a reduction in the shearing resistance of the soil, as they create zones of lower effective stress. This reduction in shearing resistance can lead to slope instability and potential failure of the embankment. Therefore, statement 3 is correct.

Statement 4: The plane surface of failure never occurs in saturated soils.

In saturated soils, the pore spaces are completely filled with water, resulting in a higher pore water pressure. This increased pore water pressure can reduce the effective stress and shear strength of the soil.

As a result, when a saturated soil mass is subjected to external loads, the failure surface tends to become curved or irregular due to the development of excess pore water pressure. The presence of excess pore water pressure disrupts the development of a plane surface of failure. Therefore, statement 4 is correct.

In conclusion, the correct statements are:

- Method of slices overestimates the value of factor of safety (Statement 1)
- Reduction in shearing resistance in embankment is caused by tension crack at the top of it (Statement 3)
- The plane surface of failure never occurs in saturated soils (Statement 4)