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

In this step, slope stability analysis is performed using the finite element model 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 Case 1 and SRF 1.856 in Case 2.

**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].

#### **Figure 4.**

*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.*

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

*4.1.3 Step 3: Application of strength reduction factor to strength parameter of slope*

In step 3, the time-dependent deterioration of slope was quantified by applying the SRF to the strength parameter of the soil. The strength parameters of the slope shown in **Table 1** were reduced according to the SRF as shown in **Figure 3**. The slope stability analysis is performed with the reduced strength parameters, and iterative analysis is performed until it is not converged. If it does not converge, the slope has collapsed in the finite element analysis. Until now, the modeling is identical to that of the usual strength reduction factor (SRF) method of slope stability

In the second section, and slope stability analysis using finite element model. The FOS is calculated by the stress analysis method (SAM) and the behavior up to the slope failure is analyzed by the nonlinear static analysis with*k*<sup>0</sup> condition. The

**Parameter Case 1 Case 2**

*<sup>m</sup>*<sup>3</sup> 19.0 19.0 E (kPa) 40,000 40,000 υ 0.28 0.28 ∅<sup>0</sup> (°) 30.0 40.0 c<sup>0</sup> (kPa) 10.0 0.0 ψ (°) 0.0 0.0

according to the material characteristics of these slopes.

analysis. [8, 39, 40].

*Slope Engineering*

γ*t*ð Þ *kN=*

**Table 1.**

**Figure 3.**

**166**

**4.2 Slope stability analysis (step 4** � **10)**

*Physical parameters of the soil of slope applied to slope stability analysis.*

*Variation of the strength parameters of slope according to strength reduction factor.*

reached 1.0 when the SRF was 1.5. The calculated displacement at each stage of reduced strength is as illustrated in **Figure 4(b)**–**(d)**. In the cumulative displacement curve plotted in **Figure 4(b)**, the rapid progression of displacement, initiated at the stage of 1.6 of strength reduction factor and then evolved rapidly after the stage of 2.0 of SRF, is illustrated. The failure model of the slope was calculated as in the following 3rd order polynomial equation:y <sup>¼</sup> <sup>2337</sup>*:*6*x*3� <sup>9690</sup>*:*2*x*<sup>2</sup> <sup>þ</sup> <sup>13188</sup>*<sup>x</sup>* <sup>þ</sup> 5864*:*3 . In **Figure 4(d)**, the inverse-velocity curve is estimated as a third order

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

**Figure 5** shows the result of slope stability analysis in the slope of case 2. **Figure 5**(**a)** shows the change of FOS according to SRF. Compared with case 1, the decreasing slope was more moderate. When SRF was 1.0, FOS was 1.27, which was smaller than case 1. When SRF was 1.5, FOS reached 1.0 and was the same as case 1. In the cumulative displacement curve plotted in **Figure 5**(**b)**, compared to that in the case 1 (**Figure 4**(**b)**), the displacement proceeded continuously from the initial stage and the displacement increased rapidly after the stage of 1.6 of the strength reduction factor. The failure model of the slope was calculated as in the following 3rd order polynomial equation:y <sup>¼</sup> <sup>19</sup>*:*391*x*<sup>3</sup> � <sup>73</sup>*:*759*x*<sup>2</sup> <sup>þ</sup> <sup>94</sup>*:*857*<sup>x</sup>* � <sup>25</sup>*:*478 . In **Figure 5**(**d)**, the inverse displacement velocity curve was calculated as a 1st linear equation ofy ¼ �1*:*5461*x* þ 2*:*8683, unlike case 1. The inverse displacement velocity curve is used to predict slope failure time [1, 24]. The inverse displacement velocity

In the last section, the results of the slope stability analysis are applied to the maintenance method. For the maintenance of the slope, the displacement of the slope is measured by tension wire or inclinometer. However, no technique has been proposed to determine management criteria. The typical sensor used for slope maintenance is an in-site inclinometer, which is applied to statistical process control using slope stability analysis results at the same point. The displacement at each depth measured in the inclinometer can be calculated by applying the SPC method to the upper and lower control limits (UCL, LCL). If the displacement exceeds this management criterion, an abnormal behavior has occurred. Next, a mathematical failure model of the slope was predicted using a cumulative displacement curve. The cumulative displacement data of the slope measured over time are compared with the behavior up to the failure estimated by the finite element analysis. This can qualitatively determine whether the slope is causing the failure behavior. And the time of the slope failure was predicted using an inverse velocity curve and, com-

The inverse-velocity curve is a method of predicting the time of failure of the slope. If the measured inverse-velocity curve shows this pattern, it can be predicted the time of slope failure. Finally, the collapse behavior of Selborne in the United Kingdom and Kunini Slope in Japan, as reported by Petley [34], was compared.

In step 11, the displacement calculated at the point where the in-place inclinom-

*4.3.1 Step 11: Determination of abnormal behavior of slope using statistical process*

eter is installed is applied to the statistical process control method. In the finite element analysis, the displacement of the entire slope is estimated. Depending on the SRF, the displacement at the point where the inclinometer is installed can be estimated. The SPC method determines the abnormal behavior at the point where

polynomial of y ¼ �0*:*9401*x*<sup>3</sup> <sup>þ</sup> <sup>5</sup>*:*204*x*<sup>2</sup> � <sup>9</sup>*:*5825*<sup>x</sup>* <sup>þ</sup> <sup>5</sup>*:*873.

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

curves of case 1 and case 2 were compared at step 14.

**4.3 Slope maintenance method (step 11** � **14)**

pared the formulation of Fukuzono [1].

*control method*

**169**

**Figure 5.**

*The results of slope stability analysis in the slope of case 2; (a) factor of safety, (b) SRC vs. displacement curve, (c) SRC vs. velocity curve, (d) SRC vs. inverse velocity curve.*

#### **Figure 6.**

*Distribution of displacement and shear strain by finite element analysis under slope failure condition (case 1).*

## *4.2.2 Step 8 10: Nonlinear static analysis of slope finite element model and summarization of results*

In the third stage, the displacements until the slope failure analyzed using the slope stability analysis plot the cumulative displacement curve, velocity curve, and inverse velocity curve and, applied to the maintenance methods of the slope. In the finite element analysis, the displacements of all nodes are calculated in the finite element model of the slope. Here, only the displacement of the node at the point where the displacement meter such as an inclinometer or a tension wire is installed is used. In particular, the displacement at the crown of the slope is most important. Therefore, in this stage, a graph was created by displacement at the crown of the slope.

**Figure 4** shows the result of slope stability analysis in the slope of case 1. Above all, the FOS was calculated by using the stress analysis method and then, the cumulative displacement curve, the displacement velocity curve, and the displacement inverse-velocity curve was plotted to illustrate the displacement of the upper part of the slope. **Figure 4(a)** Represents the reduction in safety factor resulted from the stress analysis. The FOS was 1.0 when the SRF was 1.0 and the FOS

*Integrated Analysis Method for Stability Analysis and Maintenance of Cut-Slope in Urban DOI: http://dx.doi.org/10.5772/intechopen.94252*

reached 1.0 when the SRF was 1.5. The calculated displacement at each stage of reduced strength is as illustrated in **Figure 4(b)**–**(d)**. In the cumulative displacement curve plotted in **Figure 4(b)**, the rapid progression of displacement, initiated at the stage of 1.6 of strength reduction factor and then evolved rapidly after the stage of 2.0 of SRF, is illustrated. The failure model of the slope was calculated as in the following 3rd order polynomial equation:y <sup>¼</sup> <sup>2337</sup>*:*6*x*3� <sup>9690</sup>*:*2*x*<sup>2</sup> <sup>þ</sup> <sup>13188</sup>*<sup>x</sup>* <sup>þ</sup> 5864*:*3 . In **Figure 4(d)**, the inverse-velocity curve is estimated as a third order polynomial of y ¼ �0*:*9401*x*<sup>3</sup> <sup>þ</sup> <sup>5</sup>*:*204*x*<sup>2</sup> � <sup>9</sup>*:*5825*<sup>x</sup>* <sup>þ</sup> <sup>5</sup>*:*873.

**Figure 5** shows the result of slope stability analysis in the slope of case 2. **Figure 5**(**a)** shows the change of FOS according to SRF. Compared with case 1, the decreasing slope was more moderate. When SRF was 1.0, FOS was 1.27, which was smaller than case 1. When SRF was 1.5, FOS reached 1.0 and was the same as case 1. In the cumulative displacement curve plotted in **Figure 5**(**b)**, compared to that in the case 1 (**Figure 4**(**b)**), the displacement proceeded continuously from the initial stage and the displacement increased rapidly after the stage of 1.6 of the strength reduction factor. The failure model of the slope was calculated as in the following 3rd order polynomial equation:y <sup>¼</sup> <sup>19</sup>*:*391*x*<sup>3</sup> � <sup>73</sup>*:*759*x*<sup>2</sup> <sup>þ</sup> <sup>94</sup>*:*857*<sup>x</sup>* � <sup>25</sup>*:*478 . In **Figure 5**(**d)**, the inverse displacement velocity curve was calculated as a 1st linear equation ofy ¼ �1*:*5461*x* þ 2*:*8683, unlike case 1. The inverse displacement velocity curve is used to predict slope failure time [1, 24]. The inverse displacement velocity curves of case 1 and case 2 were compared at step 14.
