Analysis of Slope Failure Behaviour Based on Real-Time Measurement Using the x–MR Method

Sungyong Park 1, Hyuntaek Lim 2, Bibek Tamang 2 , Jihuan Jin 2, Seungjoo Lee 2, Sukhyun Chang 2 and Yongseong Kim 2,* 1 Citizens Safety Division, Yongin City, Gyeonggi-do 17019, Korea; jackie0792@hanmail.net 2 Department of Regional Infrastructure Engineering, Kangwon National University, Chuncheon 24341, Korea; voku93@hanmail.net (H.L.); bibek@kangwon.ac.kr (B.T.); jihuan0123@kangwon.ac.kr (J.J.); bradlee1879@gmail.com (S.L.); lin0124@chol.com (S.C.) * Correspondence: yskim2@kangwon.ac.kr; Tel.: +82-33-250-6463


Introduction
Economic losses and fatalities due to natural hazards, such as slope failure, have increased in number worldwide [1][2][3][4][5]. Recently, slope disasters, such as landslides and slope failures, caused by concentrated torrential rain and typhoons-due to climate change-have occurred in South Korea every year, resulting in massive damage to human life and property [6]. Since two-thirds of the total land in South Korea is mountainous areas, artificial development of the mountainous areas for industrialization and urbanization is inevitable. During this development process, stable slopes are destroyed, which then causes landslides. The scale of this damage also has been increasing simultaneously [7]. The instrumentation of landslide-prone slopes is essential to eventually issue early warning for landslides, to reduce casualties and property damage. To this end, designing a real-time sensing and safety investigation system through real-time monitoring is required. This requires the design and development of instruments and effective maintenance techniques for predicting slope movement and stability by applying various real-time instrumentation techniques [8].
Although many studies are underway to study procedures for reducing damage caused by landslides, it is still almost impossible to predict landslides [9], and there is yet no way to stop a slope from collapsing. Nevertheless, various studies on slope failure occurrence processes, landslide inducing factors, real-time monitoring, and landslide warning systems have contributed to the technical basis of early warning systems [10][11][12][13][14]. Lari et al. [15] proposed a probabilistic approach by expressing

x-MR Control Chart
The x-MR control chart technique, proposed by Shewhart [24], is a statistical management method for analyzing the state and maintaining the stability of the target control object for uniformity in quality. Since the calculation is relatively easy, and its application range is wide, it is used widely for process and quality control [29].
A control chart is a type of statistical quality control technique which is used to inspect and maintain the stability state of a process. It is a statistical method that can maintain the process in a controlled state by use of quality characteristics that indicate the state of the process, provide instant identification of the reasons for quality fluctuation, and take measures to solve the problems. The control chart is a statistical technique, in other words, which is able to set statistical control limit lines, upper, and lower control lines that can make rational decisions at both the top and bottom portions to determine dispersion caused by coincidence or anomaly. It is able to detect instantaneously the cause of an anomaly or coincidence during the process and promptly can detect the dispersion due to coincidence and anomaly by plotting the quality characteristic values (measured values, data) that represent the state of the process. The control chart in Figure 1 consists of the measured value, centerline, control limit line, etc. The control limit line is a criterion for deciding the anomalous state of the measured values. Figure 1 shows a schematic diagram of the statistical control method, in which the data obtained from the control target object is on the Y-axis and time is on the X-axis. The control chart is symmetric about the mean µ and the degree of dispersion σ, where µ is the mean of the normally distributed data and σ is the standard deviation [30]. to determine dispersion caused by coincidence or anomaly. It is able to detect instantaneously the cause of an anomaly or coincidence during the process and promptly can detect the dispersion due to coincidence and anomaly by plotting the quality characteristic values (measured values, data) that represent the state of the process. The control chart in Figure 1 consists of the measured value, centerline, control limit line, etc. The control limit line is a criterion for deciding the anomalous state of the measured values. Figure 1 shows a schematic diagram of the statistical control method, in which the data obtained from the control target object is on the Y-axis and time is on the X-axis. The control chart is symmetric about the mean μ and the degree of dispersion σ, where μ is the mean of the normally distributed data and σ is the standard deviation [30]. Here, the basic concept of the control chart is to evaluate quality control by using the probabilistic method for μ and σ. The control limits, viz. UCL (Upper Control Limit) and LCL (Lower Control Limit), of ±3σ are set with respect to the centerline and, when a point deviates beyond the control limit lines, the data obtained from the process is decided to be an anomaly condition [31].
The control limit line is a baseline that is set for making simple decisions regarding the anomaly condition and the probability distribution of data to be within the range of μ − 3σ x μ + 3σ is approximately 99.73%. The x-MR control chart, used in this study, is a method to analyze the individual control chart (x) that represents individual data of the measured values and the moving range (MR) control chart simultaneously. Seen in Figure 2, the analysis interval (K), upon which the control limit depends, is set. Then, the moving range (MR), indicating the difference between the maximum value (xmax) and the minimum value (xmin) within the interval, is marked on the control chart.   Here, the basic concept of the control chart is to evaluate quality control by using the probabilistic method for µ and σ. The control limits, viz. UCL (Upper Control Limit) and LCL (Lower Control Limit), of ±3σ are set with respect to the centerline and, when a point deviates beyond the control limit lines, the data obtained from the process is decided to be an anomaly condition [31].
The control limit line is a baseline that is set for making simple decisions regarding the anomaly condition and the probability distribution of data to be within the range of µ − 3σ ≤ x ≤ µ + 3σ is approximately 99.73%. The x-MR control chart, used in this study, is a method to analyze the individual control chart (x) that represents individual data of the measured values and the moving range (MR) control chart simultaneously. Seen in Figure 2, the analysis interval (K), upon which the control limit depends, is set. Then, the moving range (MR), indicating the difference between the maximum value (x max ) and the minimum value (x min ) within the interval, is marked on the control chart. to determine dispersion caused by coincidence or anomaly. It is able to detect instantaneously the cause of an anomaly or coincidence during the process and promptly can detect the dispersion due to coincidence and anomaly by plotting the quality characteristic values (measured values, data) that represent the state of the process. The control chart in Figure 1 consists of the measured value, centerline, control limit line, etc. The control limit line is a criterion for deciding the anomalous state of the measured values. Figure 1 shows a schematic diagram of the statistical control method, in which the data obtained from the control target object is on the Y-axis and time is on the X-axis. The control chart is symmetric about the mean μ and the degree of dispersion σ, where μ is the mean of the normally distributed data and σ is the standard deviation [30]. Here, the basic concept of the control chart is to evaluate quality control by using the probabilistic method for μ and σ. The control limits, viz. UCL (Upper Control Limit) and LCL (Lower Control Limit), of ±3σ are set with respect to the centerline and, when a point deviates beyond the control limit lines, the data obtained from the process is decided to be an anomaly condition [31].
The control limit line is a baseline that is set for making simple decisions regarding the anomaly condition and the probability distribution of data to be within the range of μ − 3σ x μ + 3σ is approximately 99.73%. The x-MR control chart, used in this study, is a method to analyze the individual control chart (x) that represents individual data of the measured values and the moving range (MR) control chart simultaneously. Seen in Figure 2, the analysis interval (K), upon which the control limit depends, is set. Then, the moving range (MR), indicating the difference between the maximum value (xmax) and the minimum value (xmin) within the interval, is marked on the control chart.

Real Scale Slope Construction for Slope Failure Simulation
During this study, the displacement data obtained from the cutting process on a real scale model slope were analyzed using an x-MR control chart. The field experiments were performed three times for the reliability of the experimental data. The model slope construction processes of the real scale slope failure simulation are discussed in the following paragraphs.
Soil samples for the model experiment were obtained from natural slopes located in Chuncheon city. Weathered soil is a type of soil formed by weathering of parent rocks due to various causes. It is evenly distributed throughout South Korea and it is considered to be suitable to depict characteristics of the general slope.
The weathered soil, used in this study, was classified as SW according to the Unified Soil Classification System (USCS), therefore, the particle size distribution was well-graded sand, had a dry density (ρ d ) of 17.58 kN/m 3 and fines content of 11.4% (refer to Table 1). The optimum water content (w opt ), obtained through a TP (Test Pit, in-situ density test) and compaction tests, was used during construction so the constructed model slope resembled the ground surface conditions. The model slope reflects the results of the preliminary study through numerical analysis (limit equilibrium analysis). The cross-section of the model slope, as in Figure 3, had a 5.0 m height, and the cutting processes were carried out in three steps. During the model slope construction process, the soil was deposited under free-fall conditions using the bucket of a backhoe to depict deposition and sedimentation of soil due to weathering effects. Lastly, no additional load, such as compaction, was applied to the upper portion of the slope so the prevailing slope conditions could be depicted in which only the self-weight of the soil acts. (refer to Figure 4). Subsequent to completing construction of the model slope, cutting sections (step 1-step 3) were labeled according to the slope cutting plan.

Real Scale Slope Construction for Slope Failure Simulation
During this study, the displacement data obtained from the cutting process on a real scale m slope were analyzed using an x-MR control chart. The field experiments were performed three for the reliability of the experimental data. The model slope construction processes of the real slope failure simulation are discussed in the following paragraphs.
Soil samples for the model experiment were obtained from natural slopes located in Chun city. Weathered soil is a type of soil formed by weathering of parent rocks due to various cause evenly distributed throughout South Korea and it is considered to be suitable to depict characte of the general slope.
The weathered soil, used in this study, was classified as SW according to the Unified Classification System (USCS), therefore, the particle size distribution was well-graded sand, dry density ( ) of 17.58 kN/m 3 and fines content of 11.4% (refer to Table 1). The optimum content (wopt), obtained through a TP (Test Pit, in-situ density test) and compaction tests, was during construction so the constructed model slope resembled the ground surface conditions.  The model slope reflects the results of the preliminary study through numerical analysis equilibrium analysis). The cross-section of the model slope, as in Figure 3, had a 5.0 m heigh the cutting processes were carried out in three steps. During the model slope construction pr the soil was deposited under free-fall conditions using the bucket of a backhoe to depict depo and sedimentation of soil due to weathering effects. Lastly, no additional load, such as compa was applied to the upper portion of the slope so the prevailing slope conditions could be depic which only the self-weight of the soil acts. (refer to Figure 4). Subsequent to completing constru of the model slope, cutting sections (step 1-step 3) were labeled according to the slope cutting .

Slope Failure Simulation by Slope Cutting
During this study, the slope behavior, (slope failure), was simulated artificially by cuttin soil mass from the toe of the model slope in a stepwise manner so the cutting edge was vertic inspect the slope movement, subsurface strain gauges were installed at a position 50 cm apart to Figure 5). The subsurface strain gauge, used in this study, was in the form of a pipe with a dia of 10 mm and consisting of a strain sensor attached at the central part of the pipe, which was ca of sensing the bending deformation occurring in the pipe during the slope movement. The sensors were connected to the data logger, where the measured data were automatically saved interval of one second.  uring this study, the displacement data obtained from the cutting process on a real scale model were analyzed using an x-MR control chart. The field experiments were performed three times reliability of the experimental data. The model slope construction processes of the real scale failure simulation are discussed in the following paragraphs. oil samples for the model experiment were obtained from natural slopes located in Chuncheon eathered soil is a type of soil formed by weathering of parent rocks due to various causes. It is distributed throughout South Korea and it is considered to be suitable to depict characteristics general slope. he weathered soil, used in this study, was classified as SW according to the Unified Soil fication System (USCS), therefore, the particle size distribution was well-graded sand, had a ensity ( ) of 17.58 kN/m 3 and fines content of 11.4% (refer to Table 1). The optimum water t (wopt), obtained through a TP (Test Pit, in-situ density test) and compaction tests, was used g construction so the constructed model slope resembled the ground surface conditions. he model slope reflects the results of the preliminary study through numerical analysis (limit brium analysis). The cross-section of the model slope, as in Figure 3, had a 5.0 m height, and tting processes were carried out in three steps. During the model slope construction process, il was deposited under free-fall conditions using the bucket of a backhoe to depict deposition dimentation of soil due to weathering effects. Lastly, no additional load, such as compaction, pplied to the upper portion of the slope so the prevailing slope conditions could be depicted in only the self-weight of the soil acts. (refer to Figure 4). Subsequent to completing construction model slope, cutting sections (step 1-step 3) were labeled according to the slope cutting plan.  ope Failure Simulation by Slope Cutting uring this study, the slope behavior, (slope failure), was simulated artificially by cutting the ass from the toe of the model slope in a stepwise manner so the cutting edge was vertical. To t the slope movement, subsurface strain gauges were installed at a position 50 cm apart (refer ure 5). The subsurface strain gauge, used in this study, was in the form of a pipe with a diameter Step 2 Step 3 Scale : None Figure 4. Construction of the model slope.

Slope Failure Simulation by Slope Cutting
During this study, the slope behavior, (slope failure), was simulated artificially by cutting the soil mass from the toe of the model slope in a stepwise manner so the cutting edge was vertical. To inspect the slope movement, subsurface strain gauges were installed at a position 50 cm apart (refer to Figure 5). The subsurface strain gauge, used in this study, was in the form of a pipe with a diameter of 10 mm and consisting of a strain sensor attached at the central part of the pipe, which was capable of sensing the bending deformation occurring in the pipe during the slope movement. The strain sensors were connected to the data logger, where the measured data were automatically saved at an interval of one second. Artificial cutting of the model slope surface using a backhoe is shown in Figure 6, and the slope failure that occurred after the cutting is shown in Figure 7.  During the stepwise cutting process, cutting was carried out according to the planned section, maintaining waiting time. A total time of 20 min, cutting and waiting time combined, was applied and the same backhoe was used during slope construction and the cutting process.

Analysis of the Behaviour of Slope Failure
Considering all three cases, we could confirm the failure point by comparing the obtained data and the experimental results. Figure 8 shows the ground displacement characteristics for each case of the slope cutting. Artificial cutting of the model slope surface using a backhoe is shown in Figure 6, and the slope failure that occurred after the cutting is shown in Figure 7. Artificial cutting of the model slope surface using a backhoe is shown in Figure 6, and the slo failure that occurred after the cutting is shown in Figure 7.  During the stepwise cutting process, cutting was carried out according to the planned sectio maintaining waiting time. A total time of 20 min, cutting and waiting time combined, was appli and the same backhoe was used during slope construction and the cutting process.

Analysis of the Behaviour of Slope Failure
Considering all three cases, we could confirm the failure point by comparing the obtained da and the experimental results. Figure 8 shows the ground displacement characteristics for each ca of the slope cutting. Artificial cutting of the model slope surface using a backhoe is shown in Figure 6, and the slope re that occurred after the cutting is shown in Figure 7.  During the stepwise cutting process, cutting was carried out according to the planned section, taining waiting time. A total time of 20 min, cutting and waiting time combined, was applied the same backhoe was used during slope construction and the cutting process.

nalysis of the Behaviour of Slope Failure
Considering all three cases, we could confirm the failure point by comparing the obtained data During the stepwise cutting process, cutting was carried out according to the planned section, maintaining waiting time. A total time of 20 min, cutting and waiting time combined, was applied and the same backhoe was used during slope construction and the cutting process.

Analysis of the Behaviour of Slope Failure
Considering all three cases, we could confirm the failure point by comparing the obtained data and the experimental results. Figure 8 shows the ground displacement characteristics for each case of the slope cutting (Supplementary Materials). In case 1, the onset of a small ground displacement until 13 min, a uniform increase in displacement until 38 min, and a rapid displacement rate until 43 min after the start of the experiment were observed. Thereafter, the rate of increase of displacement was reduced somewhat, and the slope failure finally occurred at about 49.5 min after the start of the experiment.
Case 2 showed irregular movement continuously from the start of the experiment and sudden failure occurred at about 35.0 min. The displacement rate was accelerated rapidly up to about 43.0 min, and since then, there was no progress in ground movement. Finally, the slope failure occurred at about 59.8 min of elapsed time.
Seen in case 3, the ground motion was not observed from the outset of the experiment, but slight motion was monitored at about 14.0 min, and the constant increase rate of displacement was monitored until about 48 min. The displacement rate accelerated rapidly up to about 52.0 min. Thereafter, gradual displacement continued, and sudden failure occurred at about 54.7 min.
Continuous ground displacement was monitored from the outset of the experiment to the final slope failure, which indicates progressive slope failure in all cases.
The Japanese Steep Slope Measurement Control Criterion, which is frequently used in local practice, suggests that the management standard value of the maintenance phase is more than 1 mm/day (Ministry of Public Safety and Security (2016)). Therefore, the value of the acquired data that was less than 1 mm was considered to be abnormal and, also, an insignificant signal caused, due to electrical noise, was not used for the analysis.
As a result, it can be verified that cases 1 and 2, showing a progressive failure tendency that included displacement of 1 mm or more, could detect the slope failure beforehand, whereas it can be concluded that prediction of slope failure was not possible in case 3.

x-MR Control Chart Analysis
During this study, the displacement data obtained from case 1 and case 2, in which prediction of slope failure was possible, were used to perform an x-MR control chart.
Regarding case 1, the data used in the x-MR control chart were displacement data of 7.7 min total time from 41.8 to 49.5 min, until the final collapse occurred (refer to Figure 9). Similarly, the measured data for a total time of 18.3 min, from 41.5-59.8 min, until the final collapse occurred was selected in case 2 (refer to Figure 10). In case 1, the onset of a small ground displacement until 13 min, a uniform increase in displacement until 38 min, and a rapid displacement rate until 43 min after the start of the experiment were observed. Thereafter, the rate of increase of displacement was reduced somewhat, and the slope failure finally occurred at about 49.5 min after the start of the experiment.
Case 2 showed irregular movement continuously from the start of the experiment and sudden failure occurred at about 35.0 min. The displacement rate was accelerated rapidly up to about 43.0 min, and since then, there was no progress in ground movement. Finally, the slope failure occurred at about 59.8 min of elapsed time.
Seen in case 3, the ground motion was not observed from the outset of the experiment, but slight motion was monitored at about 14.0 min, and the constant increase rate of displacement was monitored until about 48 min. The displacement rate accelerated rapidly up to about 52.0 min. Thereafter, gradual displacement continued, and sudden failure occurred at about 54.7 min.
Continuous ground displacement was monitored from the outset of the experiment to the final slope failure, which indicates progressive slope failure in all cases.
The Japanese Steep Slope Measurement Control Criterion, which is frequently used in local practice, suggests that the management standard value of the maintenance phase is more than 1 mm/day (Ministry of Public Safety and Security (2016)). Therefore, the value of the acquired data that was less than 1 mm was considered to be abnormal and, also, an insignificant signal caused, due to electrical noise, was not used for the analysis.
As a result, it can be verified that cases 1 and 2, showing a progressive failure tendency that included displacement of 1 mm or more, could detect the slope failure beforehand, whereas it can be concluded that prediction of slope failure was not possible in case 3.

x-MR Control Chart Analysis
During this study, the displacement data obtained from case 1 and case 2, in which prediction of slope failure was possible, were used to perform an x-MR control chart.
Regarding case 1, the data used in the x-MR control chart were displacement data of 7.7 min total time from 41.8 to 49.5 min, until the final collapse occurred (refer to Figure 9). Similarly, the measured data for a total time of 18.3 min, from 41.5-59.8 min, until the final collapse occurred was selected in case 2 (refer to Figure 10).  Voight [32] suggested a method of estimating the slope failure time using the slope displacement and displacement velocity data transformed into inverse form over time. Park et al. [33] obtained the ground displacement data through field model tests and analyzed slope movement characteristics by using inverse displacement over time. Fukuzono et. al. [34] observed the inverse rate of movement of the extensometer and proposed a method for predicting the time point of slope failure by using the variation of displacement over time. Tamate et. al. [35] used the method of Fukuzono et. al. [34] for predicting the slope failure by the use of shear strain rate. Thus, the reciprocal of displacement, (inverse displacement), has been used for the prediction of slope failure in this study. Figures 11-12 and Figures 13-14 show the x-MR control charts of time-varying inverse displacement and varying k-values using 10-points and 30-points moving average, for data from the start of the experiment to slope failure, for case 1 and case 2, respectively.  Voight [32] suggested a method of estimating the slope failure time using the slope displacement and displacement velocity data transformed into inverse form over time. Park et al. [33] obtained the ground displacement data through field model tests and analyzed slope movement characteristics by using inverse displacement over time. Fukuzono et. al. [34] observed the inverse rate of movement of the extensometer and proposed a method for predicting the time point of slope failure by using the variation of displacement over time. Tamate et. al. [35] used the method of Fukuzono et. al. [34] for predicting the slope failure by the use of shear strain rate. Thus, the reciprocal of displacement, (inverse displacement), has been used for the prediction of slope failure in this study. Figures 11-12 and Figures 13-14 show the x-MR control charts of time-varying inverse displacement and varying k-values using 10-points and 30-points moving average, for data from the start of the experiment to slope failure, for case 1 and case 2, respectively. Voight [32] suggested a method of estimating the slope failure time using the slope displacement and displacement velocity data transformed into inverse form over time. Park et al. [33] obtained the ground displacement data through field model tests and analyzed slope movement characteristics by using inverse displacement over time. Fukuzono et. al. [34] observed the inverse rate of movement of the extensometer and proposed a method for predicting the time point of slope failure by using the variation of displacement over time. Tamate et. al. [35] used the method of Fukuzono et. al. [34] for predicting the slope failure by the use of shear strain rate. Thus, the reciprocal of displacement, (inverse displacement), has been used for the prediction of slope failure in this study. Figures 11-14 show the x-MR control charts of time-varying inverse displacement and varying k-values using 10-points and 30-points moving average, for data from the start of the experiment to slope failure, for case 1 and case 2, respectively.  Considering all cases (excluding moving average = 30, K = 10 of case 1, refer to Figure 12 d), the moving average is confirmed to exceed the μ + 3σ control limit from t0, time point from which Considering all cases (excluding moving average = 30, K = 10 of case 1, refer to Figure 12d), the moving average is confirmed to exceed the µ + 3σ control limit from t 0 , time point from which significant displacement data were obtained, to t 1 , time point of the final failure. It is considered that the degree of risk of slope failure can be evaluated sufficiently depending on whether meaningful data is obtained or not.
When the anomalous state is analyzed for the interval excluding the moving average, it is confirmed that the risk can be evaluated after 0.10-0.67 min for K = 3, 0.05-0.67 min for K = 5, and 0.07-1.47 min for K = 10. Although the timing of risk assessment is not significantly different depending on the analysis interval, it is deemed reasonable to apply K = 3 considering the urgency of failure at the steep slope.
Since the analysis results of this study are obtained from two field experiments, it is expected to be able to be used in the evacuation management standard based on additional field experiments and slope failure case data, if a reliable moving average and analysis interval (K) can be selected.

Proposal for Slope Instrumentation Standards
Presently, there are lots of difficulties in applying a single ultimate standard for various field conditions in South Korea, thus the standard published in 1996 by the Commission of Slope Stability in Japan is being practiced still [36]. Although relevant standards and instrumentation management standards presented and proposed by various research and development projects in the field of slope failure suggest an analysis of displacement rate and maximum (cumulative) displacement, it is infeasible to apply these values in the actual field. Therefore, in this study, a slope instrumentation standard is suggested through the analysis of the results using a statistical control chart technique.
Generally, a slope management standard is a method of recognizing the slope behavior by the amount of displacement and issuing early warning of slope failure by analyzing the actual movement. During this study, we tried to set a standard for evacuation management in steep slope failure by studying the criteria for prediction of steep slope failure and analyzing the displacement data measured for steep slope failure cases.
The slope instrumentation standard is classified into a total of three categories. The displacement section of less than 1mm, which has an insignificant value, is the normal phase, the displacement section of more than 1mm is the anomalous phase, and then the slope failure phase (refer to Table 2). The normal phase is deemed to be safe through the control chart analysis, the anomalous phase is deemed to be unsafe, and the time of progression from the anomalous phase to the slope failure phase is found to be about 7.7-18.3 min. Since the failure phase is a crucial situation, evacuation of local residents near the slope should be completed before the failure phase is reached. Since the evacuation of local residents should proceed within 7.7-18.3 min after the risk detection, it is necessary to establish a strategy to induce evacuation of local residents through temporal and spatial considerations, as well as determine the propagation method of this information. The slope instrumentation standard, proposed in this study, is based on the analysis of limited experimental data, however. Although the limitation is distinct, the reliability of the evacuation management standard can be improved through continuous experiments, and numerical analysis, which easily can consider various slope conditions.

Conclusions
During this study, real scale slope failure simulation experiments were performed to analyze the movement characteristics during slope failure and the results were analyzed through the x-MR control charts based on inverse displacement and K values. The conclusions of this study are as follows: (1) As a result of the real scale slope failure model test, the final slope failure was confirmed in all the cases. However, the slope failure was predictable in cases 1 and 2 beforehand, in which the progressive failure that included displacement exceeding 1 mm was observed. However, in case 3, the pre-prediction was not possible prior to the slope failure. (2) Based on evaluation of the slope failure for various moving ranges (K) through an x-MR control chart on significant displacement data, it is concluded that applying K = 3 is effective. (3) The x-MR control approach of inverse displacement can be applied to make quick and objective decisions about slope failure behavior and for predicting slope failure. (4) It is considered that the analysis method of slope failure proposed through this study can increase the efficiency of the disaster management policy implementation for local government officials by providing more reliable risk assessment results, along with the steep slope failure prediction, early warning system, landslide information system, etc.
Henceforth, it is necessary to establish clear techniques for prediction and analysis of slope failure through continuous research. Those results can be used as the basic data for a slope measurement management standard, which can contribute to mitigation of life and property damage caused by the slope failure hazards.