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

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, compared the formulation of Fukuzono [1].

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.

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

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

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

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

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

**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

*summarization of results*

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

slope.

**168**

**Figure 5.**

*Slope Engineering*

**Figure 6.**

the inclinometer is installed, as described in Section 2.2. This abnormal region appears when a failure surface is formed due to the progressive behavior of the slope. SPC method can be statistically evaluated and have the advantage of setting upper and lower control limits. Finally, determine whether the slope failure behavior is occurring and the location of the failure surface.

*4.3.2 Step 12: Estimate mathematical model of slope failure*

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

installed is used.

**Figure 8.**

**171**

In this Step 12, a mathematical model of slope failure is predicted by the displacement result of the slope stability analysis. As shown in Step 11, the displacement up to the slope failure at the point where the in-place inclinometer is

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

as a management criterion for the measured data of the in-place inclinometer.

*The mathematical failure model using the cumulative displacement curves for each depth (case 1).*

**Figure 8** shows the mathematical failure model using the cumulative displacement curves for each depth. The largest displacement occurs on the ground surface, and the displacement is hardly generated below the failure surface of the slope. The location of the failure surface can be determined in step 4 through the slope stability analysis, as shown in **Figure 6(b)**. As shown in **Figure 8(f)**, little displacement occurred at the 5.0 m depth, because it exists below the failure surface of the slope. The cumulative displacement curve through slope stability analysis can be applied

The in-place inclinometer measures the displacement of the ground at intervals of 1.0 m. From the results of the slope stability analysis, the displacements at each depth were analyzed at intervals of 1.0 m as shown in **Figure 1**. The calculated displacement is applied to the statistical process control method as shown in **Figure 7**. The depth of the horizontal axis shows the depth from the ground surface. The vertical axis shows the displacement of the slope. **Figure 7(a)** shows that when the strength reduction factor is 1.6, **Figure 7(b)** is 1.7, **Figure 7(c)** is 1.8, **Figure 7(d)** is 1.9, **Figure 7(e)** is 2.0 and **Figure 7(f)** is 2.075. **Figure 7(a)** shows the case where the strength reduction factor is 1.6, and the displacement at all depths does not exceed the management criteria of upper control limit. **Figure 7(d)** shows that the strength reduction factor is 1.9 and exceeds the management criteria of upper control limit. From this time, a failure surface of the slope was formed. By applying the SPC method, it is possible to judge the failure behavior of the slope and the generation of the failure surface.

#### **Figure 7.**

*X management chart according to depths (Case 1); (a) SRF = 1.6, (b) SRF = 1.7, (c) SRF = 1.8, (d) SRF = 1.9, (e) SRF = 2.0, SRF = 2.075 (slope failure).*

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

#### *4.3.2 Step 12: Estimate mathematical model of slope failure*

the inclinometer is installed, as described in Section 2.2. This abnormal region appears when a failure surface is formed due to the progressive behavior of the slope. SPC method can be statistically evaluated and have the advantage of setting upper and lower control limits. Finally, determine whether the slope failure

*X management chart according to depths (Case 1); (a) SRF = 1.6, (b) SRF = 1.7, (c) SRF = 1.8,*

*(d) SRF = 1.9, (e) SRF = 2.0, SRF = 2.075 (slope failure).*

The in-place inclinometer measures the displacement of the ground at intervals of 1.0 m. From the results of the slope stability analysis, the displacements at each depth were analyzed at intervals of 1.0 m as shown in **Figure 1**. The calculated displacement is applied to the statistical process control method as shown in **Figure 7**. The depth of the horizontal axis shows the depth from the ground surface. The vertical axis shows the displacement of the slope. **Figure 7(a)** shows that when the strength reduction factor is 1.6, **Figure 7(b)** is 1.7, **Figure 7(c)** is 1.8, **Figure 7(d)** is 1.9, **Figure 7(e)** is 2.0 and **Figure 7(f)** is 2.075. **Figure 7(a)** shows the case where the strength reduction factor is 1.6, and the displacement at all depths does not exceed the management criteria of upper control limit. **Figure 7(d)** shows that the strength reduction factor is 1.9 and exceeds the management criteria of upper control limit. From this time, a failure surface of the slope was formed. By applying the SPC method, it is possible to judge the failure behavior of the slope and the generation of

behavior is occurring and the location of the failure surface.

the failure surface.

*Slope Engineering*

**Figure 7.**

**170**

In this Step 12, a mathematical model of slope failure is predicted by the displacement result of the slope stability analysis. As shown in Step 11, the displacement up to the slope failure at the point where the in-place inclinometer is installed is used.

**Figure 8** shows the mathematical failure model using the cumulative displacement curves for each depth. The largest displacement occurs on the ground surface, and the displacement is hardly generated below the failure surface of the slope. The location of the failure surface can be determined in step 4 through the slope stability analysis, as shown in **Figure 6(b)**. As shown in **Figure 8(f)**, little displacement occurred at the 5.0 m depth, because it exists below the failure surface of the slope.

The cumulative displacement curve through slope stability analysis can be applied as a management criterion for the measured data of the in-place inclinometer.

**Figure 8.** *The mathematical failure model using the cumulative displacement curves for each depth (case 1).*

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

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 prediction formula.

reduced to the 1st order linear equation and rendered values of A ¼ 2*:*05 and α ¼ 1*:*79 showing linear pattern of the curve (**Figure 10**(**a)**). The pattern was similar to that in the case of 'The Failure of the Cut Slope of Selborne' in the United Kingdom

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

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

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

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

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

as a material of cut slope, but the only soil is considered in this study.

as the position of the displacement meter installed on the slope.

rendered the rapid decrease in the inverse-velocity.

the case of 'The Collapse of Kunini Slope' in Japan.

**173**

reported by Petley [34] (**Figure 10(b)**).

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

**5. Discussion**

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

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

**Figure 9.**

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

**Figure 10.** *Results of brittle slope (case 2); (a) inverse displacement velocity curve, (b) failure case of Selborne cut-slope experiment.*

reduced to the 1st order linear equation and rendered values of A ¼ 2*:*05 and α ¼ 1*:*79 showing linear pattern of the curve (**Figure 10**(**a)**). The pattern was similar to that in the case of 'The Failure of the Cut Slope of Selborne' in the United Kingdom reported by Petley [34] (**Figure 10(b)**).
