Evaluation criteria of landslide stability

The theoretical issues related to the definition of the landslide movement for rectilinear and circular cylindrical sliding surfaces are considered. Based on the concepts of the theory of measurement errors, an analysis of the impact of the parameters on the landslide velocity is performed. The formulas obtained allow us to calculate the speeds of landslides during seismic and atmospheric action.


Introduction
The study of landslide processes has always been and will remain an extremely relevant problem in business activities and, particularly, in the field of construction operation. Due to possible landslide movements on the slopes, there is a danger of disrupting the stability of buildings and structures with the result that they lose the ability to fulfill their natural functions. The Ministry of Emergency situations of Russia annually registers the landslides that have already taken place and predicts possible symptoms of landslides throughout our country. It is no accident, therefore, that landslide processes are the subject of comprehensive theoretical research [1][2][3][4][5][6][7][8]. Geotechnical scientists have thoroughly studied such issues as the physical and mechanical properties of soil rocks, pressure distribution in the landslide body from external influences and the stability of slopes. However, there are still many questions to study landslide processes.

Materials and Methods
In [9], it has been suggested to calculate the potential possibility of the momentum of a landslide by the formula: wherein  is the steepness of slope; φ is the angle of internal friction, the tangent of which is equal to the coefficient of internal friction of the soil; c is the specific cohesion; S is the area of a landslide body; m is the mass of a landslide body; g is acceleration of gravity, equal to 9.8 meters per seconds squared. If (1) is less than zero, then the landslide movement is unlikely.
It is clear from (1) that the mobility of landslide depends on the slope steepness  , the angle of internal friction φ, the specific cohesion c, the slope area S and the landslide mass m, which in turn depends on the depth of sliding surface and the soil composition.
For example, consider cases in which the parameters φ and c are variables on the sliding surface, which depend on x (the beginning of break line). Then we need to analyze the formula (1) for different c and φ along the entire length L of the sliding line.
Suppose that φ and c depend on x. For example, consider the case in which these values are constant at certain intervals that are, generally speaking, different. Let φ be a constant on k segments (K partition), with a constant on n segments (N partition). Then the inequality will be viewed as 1 1 (sin cos tg ) 0 Take a sum of K and N partitions as the M partition of the segment L. Then the inequality can be written as 1 1 (sin cos tg ) 0.
The case when for each c j the condition (sin cos tg ) 0, has been met is trivial and does not require a specific analysis. Suppose that this inequality is not fulfilled at some (one or more) of the intervals of i t because of the significant с t value. Then the condition of the landslide movement will be where on the left side of the inequality (4) or, which is the same, where amounts into the square brackets do not include terms with i h numbers. Similarly, consider a landslide with a circular-cylinder sliding surface. Suggest that the landslide body rests on an arc of a circle delimited by lines with angles of inclination 0 Then the inequality can be written as 1 1 (sin cos tg ) 0 (sin cos tg ) 2 sin 0 Thus, according to formulas (8) and (12), it is possible to calculate the likelihood of landslide movement for rectilinear and circular-cylinder surfaces of the landslide "bed", respectively.
From (1), the landslide velocity V can be found from the expression ( sin cos tg ) Analyze the result. The symbol "-" indicates that the landslide stands still. However, the result close to zero means that the landslide is in a stress-strain state and when one of the factors affecting the landslide works the landslide will move.
The parameters , φ, c, S, m are determined empirically and are of stochastic nature, imposing some uncertainty on the accounting result by formula (13). Analyze the impact of the parameters entering formula (13) on the landslide velocity based on the concepts of the theory of measurement errors. Dispersion (13) is equal to: By taking the partial derivatives of this function, we obtain the coefficients for all five arguments: Calculate the sum of the coefficients of equation (16). We obtain: Σ = 0,054. Take this sum for 100% and find the percentage of each coefficient. We get: Consideration of the earthquake action includes two methods: -fictitious slope; -fictitious seismic angle.
The core of the fictitious slope method [10] is that a slope can turn at the angle   at which the resultant of gravitational and horizontally directed earthquake forces is inclined away from the vertical. The action of the earthquake is modeled by the short-term inclination of the slope at an angle, the value of which, depending on the seismic coefficient ε, is given in Table 1 [11].
With the same data and ε = 0,2,   = 12 ○ , we obtain the velocity V = 2 m/sec. The essence of the method of the seismic angle is that the action of the earth-wake is modeled by reducing the angle of internal friction of the soils of the main deformed horizons by seismic magnitude and by changing the value of the normal pressure. The seismic magnitude as a function of the value of earthquake acceleration is given in Table 2.
With the same data and ε = 0,2,  = 12 ○ , we obtain the velocity V = 2 m/sec. The impact of groundwaters on the state of the landslide slope is reflected in various ways, by changing the stress state of the massif and physical and mechanical properties of the soils, as well as by causing the development of filtration deformations and, in particular, shear strength, reducing the value of shearing resistance [12]. At the same time, water, due to the emergence of pore pressure, changes the magnitude of stress having an impact on the soil skeleton.
As is known, the impact of pore pressure on the shear resistance is described by the equation: where u is the pore pressure.
Consider a situation in which the pore pressure is maximum, i.e. u = σ. Then With the same data, we obtain the velocity V = 2 m/sec.