**2. Slope stability analysis**

The stability of a slope can be determined by 2 criteria of considerations, which is the value of the safety factor (FoS) and also the value of the probability of failure (PoF), these two criteria are used to determine the optimal geometry of the pit opening. In order to obtain accurate analysis results, the information data regarding the geotechnical conditions of the model must be repetitive to the actual conditions. In general, the principal of the value of safety factor concept is the ratio between the shear strength along the slip surface required to maintain the slope at a stable condition, and the available shear strength [9]. The above definition can be mathematically described as:

$$\text{FoS} = \frac{\text{S}\_{\text{u}}}{\text{\textdegree}\_{\text{required}}} \tag{1}$$

Based on the Mohr-Coulomb failure criteria, the definition of the value of the

FoS <sup>¼</sup> <sup>c</sup> <sup>þ</sup> <sup>σ</sup>tan<sup>ϕ</sup> τrequired

The probabilistic failure is an approach that consider various input parameters that generates different Factor of Safety (FoS) values [10]. This information is based on the fact that every random input parameter has the same probability to yield a certain value of FoS. Regarding the difficulty and high expense of field and laboratory data collecting, this method is more attractive because of its representativeness. **Figure 2** presents the concept of failure probability and the amount of uncertainty. Slope PoF is determined from the ratio between the area under the curve of the distribution of FoS <1 value to the distribution of FoS ≥1 value. The greater the range of distribution of FoS values, the higher the uncertainty of FoS values with the same PoF values.

By definition there is a linear relationship between the PoF value and the likelihood of failure, while this does not apply to the FoS relationship with the chance of failure [10]. A large FoS does not represent a more stable slope, because the implicit uncertainty is not captured by the FoS value. Slopes with FoS of 3 do not mean that they are 2 times more stable than FoS of 1.5, while slopes with a PoF value of 5% are 2 times more stable than slopes with a PoF value of 10%. Slope stability in general performed in two-dimensional analysis. But in modeling complex geometries, 2D analysis cannot simulate them properly. Therefore, the 3D analysis is considered to be able to describe the conditions in the field better than the 2D analysis. Analysis of slope stability with 3D limit equilibrium

The results of the calculation of slope stability can be expressed in safety factor. In this method, safety factor is not only influenced by the direction sliding, but also by the slip surface that safety factor is sensitive to critical slip surface locations. Therefore, the determination of a critical slip surface is very important. Safety factor can be

Optimal slope geometry is obtained from a step-by-step assessment process [12] state there are 5 stages of the process, which is models, domains, design, analysis

Where c and ϕ are effective cohesion and internal friction angle.

method starts by assuming the geometry of the sliding mass (**Figure 3**).

obtained correctly if the determination of critical slip surface is accurate.

**2.1 Slope design**

**Figure 2.**

**79**

*Concept of probabilistic failure.*

(4)

safety factor can be determined as follows:

*DOI: http://dx.doi.org/10.5772/intechopen.94088*

*Three Dimensional Slope Stability Analysis of Open Pit Mine*

The slope is assumed to be a model of an inclined plane [9]. By determining the resultant overall forces and moments acting in equilibrium state, the slope factor of safety value can be determined by comparing the amount of the resisting force to the driving force, or the resisting moment to overturning moment can see in **Figure 1**.

$$\text{FoS} = \frac{\text{Resisting force}}{\text{Modicated force}} \tag{2}$$

$$\text{FoS} = \frac{\text{Resisting moment}}{\text{Overturning moment}} \tag{3}$$

**Figure 1.** *Equilibrium force and moment in inclined plane [9].*

Based on the Mohr-Coulomb failure criteria, the definition of the value of the safety factor can be determined as follows:

$$\text{FoS} = \frac{\text{c} + \sigma \text{tan}\phi}{\tau\_{\text{required}}} \tag{4}$$

Where c and ϕ are effective cohesion and internal friction angle.

The probabilistic failure is an approach that consider various input parameters that generates different Factor of Safety (FoS) values [10]. This information is based on the fact that every random input parameter has the same probability to yield a certain value of FoS. Regarding the difficulty and high expense of field and laboratory data collecting, this method is more attractive because of its representativeness. **Figure 2** presents the concept of failure probability and the amount of uncertainty. Slope PoF is determined from the ratio between the area under the curve of the distribution of FoS <1 value to the distribution of FoS ≥1 value. The greater the range of distribution of FoS values, the higher the uncertainty of FoS values with the same PoF values.

By definition there is a linear relationship between the PoF value and the likelihood of failure, while this does not apply to the FoS relationship with the chance of failure [10]. A large FoS does not represent a more stable slope, because the implicit uncertainty is not captured by the FoS value. Slopes with FoS of 3 do not mean that they are 2 times more stable than FoS of 1.5, while slopes with a PoF value of 5% are 2 times more stable than slopes with a PoF value of 10%. Slope stability in general performed in two-dimensional analysis. But in modeling complex geometries, 2D analysis cannot simulate them properly. Therefore, the 3D analysis is considered to be able to describe the conditions in the field better than the 2D analysis. Analysis of slope stability with 3D limit equilibrium method starts by assuming the geometry of the sliding mass (**Figure 3**).

The results of the calculation of slope stability can be expressed in safety factor. In this method, safety factor is not only influenced by the direction sliding, but also by the slip surface that safety factor is sensitive to critical slip surface locations. Therefore, the determination of a critical slip surface is very important. Safety factor can be obtained correctly if the determination of critical slip surface is accurate.

#### **2.1 Slope design**

2D analysis, therefore 2D results are considered more conservative [8]. Most existing three-dimensional 3D slope stability analysis methods are based on simple extensions of corresponding two-dimensional 2D methods of analysis and a plane of symmetry or direction of slide is implicitly assumed. 3D asymmetric slope stability

models based on extensions of Bishop's simplified, Janbu's simplified, and

The stability of a slope can be determined by 2 criteria of considerations, which is the value of the safety factor (FoS) and also the value of the probability of failure (PoF), these two criteria are used to determine the optimal geometry of the pit opening. In order to obtain accurate analysis results, the information data regarding the geotechnical conditions of the model must be repetitive to the actual conditions. In general, the principal of the value of safety factor concept is the ratio between the shear strength along the slip surface required to maintain the slope at a stable condition, and the available shear strength [9]. The above definition can be

FoS <sup>¼</sup> Su

τrequired

The slope is assumed to be a model of an inclined plane [9]. By determining the resultant overall forces and moments acting in equilibrium state, the slope factor of safety value can be determined by comparing the amount of the resisting force to the driving force, or the resisting moment to overturning moment can see in

FoS <sup>¼</sup> Resisting force

FoS <sup>¼</sup> Resisting moment

Mobilized force (2)

Overturning moment (3)

(1)

Morgenstern–Price's methods are developed by [8].

**2. Slope stability analysis**

*Slope Engineering*

mathematically described as:

**Figure 1**.

**Figure 1.**

**78**

*Equilibrium force and moment in inclined plane [9].*

Optimal slope geometry is obtained from a step-by-step assessment process [12] state there are 5 stages of the process, which is models, domains, design, analysis

**Figure 2.** *Concept of probabilistic failure.*

**Figure 3.** *Comparison between 3D and 2D single slope analysis [11].*

and implementation. The initial stage of the geotechnical model is determined by 4 parameters, namely the geological model, structural conditions, rock mass and hydrogeological model. At the domains stage, the failure modes are determined by 2 parameters, namely the strength of the material and the condition of the structure. A single slope design arrangement is determined by the regulations or standards used by the company and the capabilities of the equipment used. Determination of the haulage road width and also the overall slope angle is based on mine planning related to the economic aspects of the opening geometry made. Furthermore, the stability analysis of the slope geometry that has been designed refers to the parameters (structure, strength, groundwater, and in-situ stress). After the final design is obtained, a risk assessment is carried out to mitigate the potential for landslides that may occur. In the implementation stage, the functions of dewatering, blasting and monitoring of the progress of the design model and the movement of rock masses (**Figure 4**).
