**2.2 Limit equilibrium method 3D**

These days the needs and pressure to analyze a slope 3 dimensionally is more sounds. This is because 2D analysis assumes that the width of slope is infinitely wide so then it neglects 3D effect [11]. In most of the cases the width to height ratio is not sufficiently long and varies perpendicular to the slide movement. Therefore, 3D analysis is considered important to be done to produce the representative FoS. Moreover, in 3D analysis the volume of failure can also be estimated while 2D analysis cannot. If the volume can be determinate, it can be useful as one of the considerations in giving failure prevention recommendation.

For the 3-dimensional analysis, the mass potential of the slip plane is divided into several columns. Ref. [8] give the equation of the Simplified Janbu method deduced from the Morgenstern-Price method to obtain a safety factor value of

ai is space angle for sliding direction with respect to the projected x – y plane, ax,

With the mohr-coulomb collapse criteria, the safety factor is determined using

<sup>¼</sup> Ci <sup>þ</sup> <sup>N</sup><sup>0</sup>

<sup>i</sup> tan ϕ<sup>0</sup> i

(5)

Si

ay are base inclination along x and y directions measure at the center of each column, Exi, Eyi are inter-column normal forces in x and y directions, respectively, Hxi, Hyi are lateral inter-column shear forces in x and y directions, N'i, Ui are effective normal and base pore watery force, Pvi, Si is vertical external force, and base mobilized shear force, and Xxi, Xyi are vertical inter-column shear force in

> <sup>F</sup> <sup>¼</sup> Sfi Si

3-dimensional analysis (**Figure 5**).

*Three Dimensional Slope Stability Analysis of Open Pit Mine*

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

plane perpendicular to x and y directions.

the following equation:

**81**

**Figure 4.**

*Slope design process [12].*
