**2. Theoretical background for stability analysis and maintenance of cut-slope**

#### **2.1 Finite element method (FEM) for slope stability analysis**

The limit equilibrium method (LEM), a deterministic method, compares the shear stress and shear strength applied to assumed the failure surface of slope to present the FOS. However, because the limit equilibrium analysis provides only the minimum of FOS as the analytic result, it cannot present appropriate safety factor applicable to the analysis of progressive slope failure attributable to concurrent continuous displacement induced by a time-dependent deterioration of soil.

The finite element method can provide the measurement system for the maintenance of slope with proper analytic results. It also is an appropriate method to analyze the behavior of progressive slope failure [29]. The progressive slope failure has been examined through the finite element method. Zeinkiewicz, Humpheson and Lewis [8] had presented the strength reduction method that employed the SRF by which the safety factor was calculated as in the case of limit equilibrium analysis. Thereafter, Griffiths [10] had applied the strength reduction method to his analysis of progressive behavior of slope according to diverse soil conditions and geometries and verified the analytical method through comparative analyses with the chart (s) presented by Bishop and Morgenstern [30].

The SAM is a combination of the advantages of simple limit equilibrium method (LEM) and of finite element method (FEM), the advanced method. The stress state in slope is analyzed through finite element analysis, and the FOS of virtual active surfaces of the limit equilibrium analysis are calculated. Thereafter, the minimum of FOS and critical section among active surfaces in the limit equilibrium analysis are calculated. In the finite element analysis, the model of the material constituting

after excavation. These cut-slopes are degraded in strength by time-deterioration

A time-dependent deterioration of soil owing to external environmental change causes progressive slope failure and the traditional analysis of limit equilibrium stability has limitations for an appropriate analysis of the stability [4]. The analysis of progressive slope failure requires finite element analysis that is capable of analyzing the creation and progression of shearing zone [5–7]. The behavior of progressive slope failure can be evaluated through the finite element analysis. Besides, for the analysis of the slope stability, the calculation of safety factor is needed. Zeinkiewicz, et al. [8] have proposed the strength reduction method to calculate the safety factor through finite element analysis and the proposition was followed by many subsequent studies conducted by many researchers [9–11]. Recently, there has been many studies unsaturated slope stability analysis induced by rainfall infiltration [12–16]. In general, rainfall-induced slope failures are caused by increased pore pressure and seepage force during periods of intense rainfall [17, 18]. The factor of safety on the slope is calculated by the equilibrium equation of the force of the failure surface. The pore pressure acting as an active force on the failure surface is increased by seepage of rainfall, and the slope is collapsed when it is larger than

The slope behaviors and exterior environment should be measured continuously to maintain slope. The slope behavior is measured by inclinometer, electro-optical wave distance measuring instrument, groundwater level meter etc., also, the exterior environments, rainfall and temperature are measured by the weather station. The various management criteria of the sensors are developed based on mathematical or statistical methods; the slope reinforcement be done if the management criteria [19]. However, the developments of perfect safety factors and management

In Korea, a lot of researches were done for cut-slope management near roadway [20–22]. The displacements of cut-slope were measured by tension wire, and the data were analyzed by the statistical process control (SPC) method. However, it confirm only the abnormal behaviors of slopes, the factor of safety (FOS) of slope cannot be calculated, therefore, the application of slope reinforcement methods are

Also, many studies had also been carried out to predict the time of the failure of

This study developed an integrated analysis method for stability analysis and

maintenance of cut-slopes in urban. The integrated analysis method for this research treated cut-slope and the failure-inducing factor was considered the shear strength decrease (SRF) by time-dependent deterioration was considered as inducing factor of slope failure. The strength variation of soil slope happens continuously from the variation of weather conditions and infiltration of rainfall. Also, measuring

slope through displacement velocity [1, 23–28]. The researchers have used the inverse-velocity obtained from measurements to predict the time of the slope failure and verified respective applications of the inverse-velocity through actual cases of the slope failure and experiments. However, in cases of slopes, the prediction of the time of the slope failure by using the inverse-velocity curve derived from such measurement is quite difficult because the behavioral aspects of such slope are diverse and the failure surface has to be assumed. So far, the slope stability analysis methods only estimate the FOS of slope and, maintenance methods based on the measured data do not provide clear management criteria. For these reasons, efficient maintenance and prevention of slope failure in urban areas have not been achieved. To solve this problem, the integrated analysis methods of slope stability analysis and maintenance for progressive slope failure due to time-dependent dete-

criteria are very difficult from the analysis of measured data in slope.

determined according to extra slope stability analysis.

rioration should be developed.

**158**

phenomenon, and progressive slope failure is caused.

the resistance force.

*Slope Engineering*

the soil will use the Mohr-coulomb yield criteria identical to the failure criteria used in the limit equilibrium analysis.

The FOS of the slope to be determined by the stress analysis method is as expressed in the following Eq. (1).

$$\text{FOS} = \frac{\int\_{\mathbb{S}} \tau\_f dT}{\int\_{\mathbb{S}} \tau\_m dT} \tag{1}$$

**2.3 Prediction method of the time of slope failure**

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

To predict the time of the slope failure, diverse models employed the correlation between the time and the displacement varying according to the creep behavior of bedrock have been proposed [25, 31]. Since such models were difficult to apply to the prediction of the slope failure as a generalized model, Fukuzono [1] proposed the model of inverse-velocity expressing the changing characteristics of ground displacement as the relationship between time and inverse-velocity. The proposed inverse-velocity model was derived by using the measurements of varying acceleration obtained from the large-scaled actual experiment simulated an artificial landslide. Fukuzono [1] proposed the time of the slope failure as expressed in the following Eq. (4) by taking the trend line of inverse-velocity approaching 0 in

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

*=*

Here, t, *tf* , and V denote the time, time of failure, and displacement velocity; and A and α are the constants introduced for curve fitting. When the value of α is bigger than 2, the shape of curve is convex otherwise the shape of curve would be

To exploit the advantage of the value of inverse-velocity becoming 0 at the time

**Figure 1** is an integrated analysis method for stability analysis and maintenance

The integrated analysis method presented in this study is divided into 14 steps. It is divided into three sections. 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). The integrated analysis method proposed in this study is based on the cut-slope 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

In the second section, slope stability analysis is performed using FEM. The FOS is calculated by the SAM and the behavior up to the slope failure is analyzed by the nonlinear static analysis with*k*<sup>0</sup> condition. The displacements until the slope failure analyzed using the slope stability analysis plot the cumulative displacement curve,

of the slope failure, the relevance between time and inverse-velocity has been widely used [32, 33]. Petley, Bulmer and Murphy [32] have analyzed the patterns of trend lines of the cases the slope failure however, since the patterns were analyzed from the measurements of the displacement after the failure of faces of slopes, it would be very difficult to get actual real-time prediction of the time of failure. Therefore, an analysis on the pattern of inverse-velocity curve at the design stage is needed to predict the time of the slope failure in the stage of performing maintenance works based on measurements. Thus, in this study, the procedure to analyze the progressive slope failure was presented in a way to link the procedure to the

*<sup>α</sup>*�<sup>1</sup> <sup>∙</sup> *tf* � *<sup>t</sup>* <sup>1</sup>

*=*

*<sup>α</sup>*�<sup>1</sup> (4)

accordance with the increasing velocity of displacement into account.

*<sup>V</sup>* <sup>¼</sup> ½ � *<sup>A</sup>*ð Þ *<sup>α</sup>* � <sup>1</sup> <sup>1</sup>

1

maintenance methods based on actual site measurements.

**3. Integrated analysis methods of slope stability analysis**

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

concave with the value of α less than 2.

**and maintenance**

**3.1 Introduction**

of cut-slopes.

**161**

Here, FOS, *τ<sup>m</sup>* and *τ <sup>f</sup>* denote the factor of the safety, induced shear stress, and shear strength according to Mohr-Coulomb failure criteria, respectively.

The FEM can analyze the slope behavior until failure, and if the SRF is applied, it also can quantify the time-dependent deterioration of slope. However, until now the FEM is not used for analyzing and comparing to the measured displacement data of slope.

#### **2.2 Statistical process control method for detecting abnormal behavior of slope**

The representative method used for the domestic maintenance of slope is the statistical process control (SPC) method broadly employed in manufacturing industries to reduce the level of defects of commercial products. The population for the SPC for the maintenance of slope is a set of measurements of the displacement of slope. The values of the mean and standard deviation of the population is used to judge the stability of slope statistically according to respective values plotted on the region beyond or within the control limit determined by the control chart. By using the control chart, the anomaly in the stability of slope can be found easily.

The method above uses the *X* control chart (of mean values) and the R control chart (of standard deviation, the varying range of measurements) simultaneously.

The control limit and centerline of the*X* control chart can be obtained by using the Eq. (2) represented in the following.

$$\text{UCL} = \bar{\bar{x}} + A\_2 \overline{R}$$

$$\text{CL} = \bar{\bar{x}}$$

$$\text{LCL} = \bar{\bar{x}} - A\_2 \overline{R} \tag{2}$$

Where, the constant *A*<sup>2</sup> is a function of sample sizen. *x* is an estimation of μ, the mean of the population; and *R* represents an estimation of σ, the standard deviation of the population.

The control limit and centerline of the R control chart can be obtained by using the Eq. (3) represented in the following.

$$\text{UCL} = D\_4 \overline{R}$$

$$\text{CL} = \overline{R}$$

$$\text{LCL} = D\_3 \overline{R} \tag{3}$$

Where, the constants *D*<sup>3</sup> and *D*<sup>4</sup> are the functions of the sample size n.

KICT [20] applied the measured data of real slope to SPC method. After that, Yoo [22] proposed a statistical decision algorithm for maintenance of the slope based on the measured data. Therefore, it is necessary to calculate the management criteria of statistical process control method by integrating it with the finite element analysis which can simulate the failure of the slope.

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