**5. Discussion**

*4.3.3 Step 14: Prediction of the time of slope failure*

Collapse of Kunini Slope' in Japan (**Figure 9(b)**).

prediction formula.

*Slope Engineering*

**Figure 9.**

*movement.*

**Figure 10.**

*experiment.*

**172**

This stage predicts the time of slope failure in slope maintenance. Curve fitting is performed by regression analysis of the inverse-velocity curve by slope stability analysis. According to the existing literature, slopes with ductile behaviors are a third polynomial equation and slopes with brittle behavior are a linear equation. Regression analysis results are also compared with Fukuzono [1]'s slope failure

Fukuzono [1] intended to predict the time of slope failure resulted from progressive behavior with the inverse-velocity curve. The resulted inverse-velocity curves are as illustrated in **Figures 9** and **10**. In the case of the soil strength parameters of the cohesion (10kPa) and internal friction angle (30°) in the Case 1, the displacement inverse-velocity was reduced rapidly to the 3rd order polynomial equation and, the values of A ¼ 4*:*0 and α ¼ 1*:*21 resulted from the equation presented by Fukuzono [1] that showed a convex pattern of the curve (**Figure 9 (a)**). The pattern was similar to the pattern of ductile behavior in the case of 'The

And in the case of the soil strength parameters of the cohesion (0kPa) and internal friction angle (40°) in the Case 2, the displacement inverse-velocity was

*Results of ductile slope (case 1); (a) displacement-inverse velocity curve, (b) failure case of Kunini slope*

*Results of brittle slope (case 2); (a) inverse displacement velocity curve, (b) failure case of Selborne cut-slope*

This study developed an integrated analysis method for stability analysis and maintenance of cut-slopes in urban. To link the slope stability analysis with the maintenance method based on the measured data, the displacement until the slope failure to the finite element model was analyzed and applied to the maintenance method. The integrated analysis method proposed in this study is based on the cutslope and only the strength degradation caused by the time-dependent deterioration is taken into consideration. The proposed method can be used both as soil and rock as a material of cut slope, but the only soil is considered in this study.

The integrated analysis method in this study can complement the disadvantages of the slope stability analysis and integrate it with the maintenance method based on the measured data of slope. The slope stability analysis can be used to quantify the displacement until slope failure as the cumulative displacement curve, velocity curve, and inverse velocity curve. The results of slope stability analysis could be used as management criteria for statistical process control method, mathematical model and the time of slope failure applied to maintenance. Then, the failure behavior of the slope and the generation of the failure surface were confirmed. The displacement of the slope analyzed by the finite element analysis should be the same as the position of the displacement meter installed on the slope.

By the comparison of this model with the failure model based on measured data, the obtained failure model was concluded as a 3rd order polynomial failure model equivalent to that of the site of 'Neureupjae' presented by Han and Chang [41]. **Figure 4(c)** represents the velocity curve. It also shows the rapid progression of displacement velocity at the point of 2.0 of SRF. The corresponding displacement inverse-velocity curve is illustrated in **Figure 4**(**d)**. The inverse-velocity was generated by the following 3rd order equation,y ¼ �0*:*9*x*<sup>3</sup> <sup>þ</sup> <sup>5</sup>*:*2*x*<sup>2</sup> � <sup>9</sup>*:*6*<sup>x</sup>* <sup>þ</sup> <sup>5</sup>*:*9 that rendered the rapid decrease in the inverse-velocity.

The behavior of the slope appeared almost identical with that in the Case 1 and, the 3rd order polynomial equation similar to that of the site of 'Neureupjae' presented by Han and Chang [41] was also derived. The equation appeared in 3rd order polynomial equation: y <sup>¼</sup> <sup>19</sup>*:*4*x*<sup>3</sup> � <sup>73</sup>*:*8*x*<sup>2</sup> <sup>þ</sup> <sup>94</sup>*:*9*<sup>x</sup>* � <sup>25</sup>*:*5. **Figure 5**(**c)** represents the displacement velocity curve of cumulative displacement on which there are two points of inflection at each point of 1.6 and 1.9 of the strength reduction factor. **Figure 5(d)** shows the displacement inverse-velocity curve. Contrary to that in the Case 1, the equation was reduced to the 1st order linear one:y ¼ �1*:*6x þ 2*:*9*:*

The slope stability analysis conducted with conditions defined in the Case 1 rendered following results of the changes in initial soil strength (cohesion) and internal friction varied from 10kPa to 4*:*8kPa and from 30° to 14*:*5°. The mathematical model of slope failure by cumulative displacement curve was reduced to the 3rd order polynomial equation,y <sup>¼</sup> <sup>2337</sup>*:*6*x*<sup>3</sup> � <sup>9690</sup>*:*2*x*<sup>2</sup> <sup>þ</sup> <sup>13188</sup>*<sup>x</sup>* <sup>þ</sup> <sup>5864</sup>*:*3 . The inverse-velocity curve resulted from the analysis of the Case 1 appeared as the 3rd order polynomial equation,y ¼ �0*:*9*x*<sup>3</sup> <sup>þ</sup> <sup>5</sup>*:*2*x*<sup>2</sup> � <sup>9</sup>*:*6*<sup>x</sup>* <sup>þ</sup> <sup>5</sup>*:*9 . The equation presented by Fukuzono yielded values A ¼ 4*:*0 and α ¼ 1*:*21 that determined the convex pattern of the curve similar to the pattern of ductile behavior appeared in the case of 'The Collapse of Kunini Slope' in Japan.

The results obtained from the analysis of the Case 2 showed that the failure resulted from the initial soil cohesion of 0 kPa with the internal friction varied from 40° to 21.5°. The resulted failure model corresponded to this cumulative displacement curve was reduced to the 3rd order polynomial equation, y <sup>¼</sup> <sup>19</sup>*:*4*x*<sup>3</sup> � <sup>73</sup>*:*8*x*<sup>2</sup> þ 94*:*9*x* � 25*:*5 . Contrary to the Case 1, the displacement inverse-velocity curve of the Case 2 showed the pattern of linear equation,y ¼ �1*:*6x þ 2*:*9, and the values of A ¼ 2*:*05 and α ¼ 1*:*79 were obtained therefrom. The pattern of this curve was similar to that in the case of 'The Failure of the Cut Slope of Selborne' in the United Kingdom.
