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

the soil will use the Mohr-coulomb yield criteria identical to the failure criteria used

Ð *<sup>S</sup>τ <sup>f</sup> dT* Ð

Here, FOS, *τ<sup>m</sup>* and *τ <sup>f</sup>* denote the factor of the safety, induced shear stress, and

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

**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 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

> UCL <sup>¼</sup> *<sup>x</sup>* <sup>þ</sup> *<sup>A</sup>*2*<sup>R</sup>* CL <sup>¼</sup> *<sup>x</sup>*

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

The control limit and centerline of the R control chart can be obtained by using

UCL ¼ *D*4*R* CL ¼ *R*

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

LCL <sup>¼</sup> *<sup>x</sup>* � *<sup>A</sup>*2*<sup>R</sup>* (2)

LCL ¼ *D*3*R* (3)

the control chart, the anomaly in the stability of slope can be found easily.

*<sup>S</sup>τmdT* (1)

The FOS of the slope to be determined by the stress analysis method is as

FOS ¼

shear strength according to Mohr-Coulomb failure criteria, respectively.

in the limit equilibrium analysis.

expressed in the following Eq. (1).

the Eq. (2) represented in the following.

the Eq. (3) represented in the following.

analysis which can simulate the failure of the slope.

data of slope.

*Slope Engineering*

of the population.

**160**

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 accordance with the increasing velocity of displacement into account.

$$\frac{1}{V} = [A(\alpha - 1)]^{\mathbb{Y}\_{a-1}} \bullet \left(t\_f - t\right)^{\mathbb{Y}\_{a-1}} \tag{4}$$

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 concave with the value of α less than 2.

To exploit the advantage of the value of inverse-velocity becoming 0 at the time 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 maintenance methods based on actual site measurements.
