**4.1 Generate finite element model for slope stability analysis (step 1** � **10)**

In the first section, the geometric of the slope and the finite element model of FEM are generated. And, to consider the time-dependent deterioration, the SRF is applied to the strength parameter of the soil (step 1 � 3).

#### *4.1.1 Step 1: Generate geometry and mesh of slope*

For the slope stability analysis of the progressive behavior of slope, the geometry and meshes of the finite slope of 10.0 m in height and 1: 1.2 of standard slope were created (**Figure 1**). For this research, the cut-slope modeling is obliged the standard height and incline suggested by the design manuals [19, 38]. The displacements until progressive failure analyzed FEM are compared to the measured data, the criteria come from the inclinometer data.

The boundary condition of left and right side is dx = 0 and same as roller. The boundary condition of the floor is dz. = 0, which is the same as the hinge. The load applied only its own gravity. In the finite element model, the element at the point where the in-place inclinometer is installed should be identified.

#### *4.1.2 Step 2: Soil parameters of Mohr-coulomb model of solpe*

The Mohr-coulomb model was selected for the FEM for which the internal friction angle ∅<sup>0</sup> ð Þ, cohesion (c<sup>0</sup> ), dilatancy angle (ψÞ, Poisson's ratio (υÞ, and unit weight (γ*t*Þ are needed. Among such factors, the relative importance of the dilatancy angle that reflects the change in volume resulting from the yield process is less significant in the analysis of the stability of slope that calculates the safety factor [11]. In this study, the value of dilatancy angle was set 0° to let the change in volume to be constantly applied to the analysis. The values of the physical properties of the soil are as summarized in **Table 1**.

The soil slope behaviors are largely divided into two categories; firstly, ductible behavior in case of small particle soils, at second, brittle behavior in case of coarse particle soils. Mohr-coulomb model is used to analyze those two cases, which is the elastic-perfect plastic model. The case 1 is for the ductile behavior of slope, whose cohesion value is applied as 10 kPa to show the behavior small soil particles. The case 2 is for the brittle behavior of slope, whose cohesion value is 0 kPa to show the brittle slope behavior of coarse soil particles.

*ϕ*0 *<sup>f</sup>* ¼ tan

applied to it as in the case of limit equilibrium analysis.

stages of each strength reduction factor.

internal friction angle, and internal friction angle at the point of failure,

4. Step 4: To conduct the finite element analysis, the calculation of initial

underground stress of slope is important and, the value is calculated under the *k*<sup>0</sup> condition based on the data obtained from subsurface investigation.

5. Step 5: Based on the calculated initial underground stress of the slope, the FOS is calculated through the SAM [37]. In this case, the decrease in the value of safety factor is identified through an iterative analysis to be conducted according to the reduced strength parameter, and the failure surface will be

6. Step 6: The nonlinear static analysis will be conducted to analyze the behaviors of progressive slope failure. The iterative analysis should be continued until the value fails to converge (=until the occurrence of failure) according to the

identified through the iterative analysis conducted according to the strength

8. Step 8: After completing the calculation of cumulative displacement curve of the points of maximum displacement on slope through following the process in Step 7 above, the obtained results should be linked to the plan of the

9. Step 9: The failure model of slope is created by using the velocity curve made from the analytic results and then it will be compared with the cumulative displacement curve made from the measurements collected through the stages

10. Step 10: In this step, plot an inverse-velocity curve for predict the time of

11. Step 11: From this stage, the results of the slope stability analysis are applied to the maintenance method. In step 11, the displacement calculated at the point where the in-place inclinometer is installed is applied to the statistical process control method. And judges whether the management criteria is exceeded by depth of slope. Finally, determine whether the slope failure

12. Step 12: In this step, we calculate the mathematical failure model of the slope. The calculated mathematical failure model is used as a reference for the

13. Step 13: In this step, first order linear equation is calculated by regression analysis of velocity curve of the slope. It is difficult to derive a clear

engineering meaning like the accumulated displacement curve of step 12 and

behavior is occurring and the location of the failure surface.

displacement results measured by the in-place inclination.

7. Step 7: The displacement resulted from the progressive slope failure is

where, c0

*Slope Engineering*

reduction.

measurement of slope.

slope failure.

**164**

of maintenance of the slope.

, *cf* 0 , ϕ<sup>0</sup>

, and *ϕ<sup>f</sup>*

respectively. SRF denote the strength reduction factor.

tan *ϕ*<sup>0</sup> *SRF* �<sup>1</sup>

0 denote the cohesion, cohesion at the point of failure,

(6)

The soil of Case 1 has a cohesive of 10 kPa and an internal friction angle of 30 degrees. The soil of Case 2 has a cohesive of 0 kPa and an internal friction angle of 40 degrees. The slope of Case 1 shows the ductility behavior due to the cohesive of soil, and the slope of Case 2 shows the brittle behavior because the soil has no cohesive and the internal friction angle is large. The analytical results are compared according to the material characteristics of these slopes.

displacements until the slope failure analyzed using the slope stability analysis plot the cumulative displacement curve, velocity curve, and inverse velocity curve and,

*Integrated Analysis Method for Stability Analysis and Maintenance of Cut-Slope in Urban*

In this step, slope stability analysis is performed using the finite element model

**Figure 6** is the distribution of displacement and shear strain by finite element analysis under slope failure condition in the slope of case 1. The legend in **Figure 6(a)** shows the amount of displacement, and in **Figure 6(b)** shows the effective shear strain. When the slope stability analysis is performed by the proposed method, the behavior up to the progressive failure of the slope can be analyzed. The distribution of shear strain can predict the failure surface of the slope. One of the greatest advantages is that the failure surface can be estimated by the finite element analysis in the slope consist of the continuous soil. Step 7 is the same as the general procedure for slope stability analysis using finite element analysis. In this study, only 2D finite element analysis was performed. Three-dimensional analysis is also possible. For finite element analysis using the SRF, see the paper by Wei, et al. [40].

*The results of slope stability analysis in the slope of case 1; (a) factor of safety, (b) SRC vs. displacement curve,*

*(c) SRC vs. velocity curve, (d) SRC vs. inverse velocity curve.*

*4.2.1 Step 4 7: Conduct the slope stability analysis of finite element model and*

generated in the first section. In slope stability analysis using FEM, it is very important to estimate the stress distribution in the slope. In Step 5, the initial stress distribution of slope is estimated at *k*<sup>0</sup> according to the coefficient of earth pressure [37]. Then, the FOS of the slope is calculated by the SAM. As shown in **Figure 3**, the strength parameters according to the SRF is applied, and the FOS of the slope by the SAM is shown in **Figure 4(a)** for case 1 and **Figure 5(a)** for case 2. In Step 6, nonlinear static analysis is performed by gradually reducing the strength parameters of the slope. The nonlinear static analysis is repeated until the analysis is not converged. If the nonlinear static analysis is not converged, the slope has collapsed. As a result of the finite element analysis, the soil failure occurred at SRF 2.075 in

applied to the maintenance methods of the slope.

*DOI: http://dx.doi.org/10.5772/intechopen.94252*

*estimation of behavior until the slope failure*

Case 1 and SRF 1.856 in Case 2.

**Figure 4.**

**167**
