Failure Prediction of Open-pit Mine Landslide Containing Complex Geological Structure using Inverse Velocity Method: A Case Study in West Open-Pit mine, Pingzhuang, China


 In the field of open-pit geological risk management, landslide failure time prediction is one of the important topics. Based on the analysis of displacement monitoring data, the inverse velocity method (IVM) has become an effective method to solve this issue. In order to improve the reliability of landslide prediction, four filters were used to test the velocity time series, and the effect of landslide failure time prediction was compared and analyzed. The IVM is used to predict the failure time of open-pit coal mine landslide. The results show that the sliding process of landslide can be divided into three stages based on the IVM: the initial attenuation stage (regressive stage), the second attenuation stage (progressive stage), the linear reduction stage (autoregressive stage). The accuracy of the IVM is closely related to the measured noise of the monitoring equipment and the natural noise of the environment, which will affect the identification of different deformation stages. Compared with the raw data and the exponential smoothing filter (ESF) models, the fitting effect of short-term smoothing filter (SSF) and long-term smoothing filter (LSF) in the linear autoregressive stage is better. A slope displacement pixel difference method based on fitting accuracy and field monitoring signals is proposed to determine the point onset-of-acceleration (OOA) that is very important role for landslide prediction. A stratified prediction method combining SSF and LSF is proposed. The prediction method is divided into two levels, and the application of this method is given.

method based on fitting accuracy and field monitoring signals is proposed to determine the point onset-23 of-acceleration (OOA) that is very important role for landslide prediction. A stratified prediction method 24 combining SSF and LSF is proposed. The prediction method is divided into two levels, and the 25 application of this method is given. The feedback dynamic result of the characteristic signal of an event in the past period is used to predict 134 the characteristic information of the event in the future period of time, and the method with predictive 135 ability input indexed by time is abstracted, which can be understood as a time series model. Saito 136 proposed an improved method for landslide time prediction based on the traditional creep theory, by 137 which the creep process was divided into three stages: average deformation, constant deformation and 138 accelerated deformation (Fig. 5). To make the displacement time series data more stable, Fukuzono (1985)  By comparing and analyzing the experimental results, Fukuzono (1985) determined that the value range 146 of the dimensionless parameter was between 1.5 and 2.2. The correlation between displacement rate and 147 landslide time can be expressed as follows: 148 where, v is the displacement change rate sequence, m/s; tf is the predicted landslide time; t is the time 150 course of landslide evolution. 151 In addition, some scholars pointed out that both α and A can change with the change of time stampling, 152 and the different values range of α is directly related to the morphological change of the curve (as shown 153 Fig. 6). When α>2, the curve shows a protruding shape. When α(1,2), the curve is concave; When 154 α=2, the curve is linear. When α=2, the landslide time can be calculated by the following formula: 155 The above relation is expressed as a more universal relation that can better describe the failure rate of the 157 slope, as follows: 158 Where, and are displacement acceleration and acceleration respectively. 160 By substituting Equation (2) and (3) into Equation 4, we can get: 161 If the prediction of landslide time is taken into account, the expression mode of inverse multiplication 163 element of velocity data at slope sliding is regarded as infinite in Eq. (5), and the linear model can be 164 used as a reference for landslide time prediction when the intercept of X-axis is infinitely close. 165 The above time series prediction time model of landslide is obtained under ideal conditions, but in fact 166 the model is limited by the interference caused by measurement error and equipment noise. In particular, 167 the open-pit mine slope is usually affected by cyclical factors such as rainfall, groundwater, freeze-thaw 168 of snow and ice, and artificial mining, etc. In this work, a mathematical model is built to eliminate 169 engineering noise interference for landslide prediction, and noise is divided into the following two  To avoid the dependence of single-point monitoring time series data and extract the periodicity of time 173 as the feature, three smoothing filter algorithms are proposed to denoise the original velocity data. The 174 The selection rules of the smoothing factor are as follows: The smoothing factor determines the 182 smoothing level and the response speed to the difference between the predicted value and the actual result. 183 The situation of the time series model of velocity multiplicative inverse element should be as stable and 184 regular as possible, and the influence of the forward actual value on the fast smooth response degree and 185 the slow smooth response degree of the predicted value should be avoided to the greatest extent, hence, 186 the selection of smoothing factor β=0.5 is more appropriate. 187 This work draws on the noise reduction principle of monitoring equipment of the slope, respectively, to 188 build the short-term noise reduction model (n=3 day) and long-term noise model (n=7 day). While  In addition, the landslide occurrence time can be further classified by using the landslide time prediction 194 model based on gradient rate of change and the IVM model, which is mainly used to test the accuracy of 195  Ground-based Synthetic Aperture Radar is used to monitor the deformation characteristics of the 212 landslide, and its monitoring technology principle is shown in Fig. 8. Several distometric bases were put 213 in place along the perimetral and recorded cumulative displacements since Janurary 1, 2013. Both 214 measuring points were distributed near the tangential crack outcropping along the top, and the monitoring 215 period was 1 January 2013 to April 17, 2013. Because the landslide is sudden type landslide, the 216 characteristics of its velocity curve are quite different from the general three-stage evolution law of 217 landslides. The initial period of constant velocity deformation is more lasting, and the curve morphology 218 changes slowly. In other words, the landslide will remain relatively stable for a long time before the 219 landslide, and there is no obvious macroscopic deformation sign. Instability failure can only occur when 220 the landslide enters the critical kinetic failure stage. This makes Saito M's empirical prediction model 221 limited, hence, it is necessary to seek for a more appropriate landslide time prediction model. The method 222 adopted in this model is to select speed data for testing. Normally, in the process of slope acceleration, 223 velocity, acceleration and displacement are three signals that represent the change of slope. According to 224 previous research results, in the process of the dynamic evolution of landslide, especially near the slide 225 acceleration as there will be a lag time than speed ( Fig. 9), so the acceleration behavior may not be 226 directly cause the deformation of slope failure factors. At the same time, displacement cannot describe 227 the change process of slope on time scale, therefore, velocity data testing model is more suitable for this 228 model. raw data and SSF model, the velocity data processed by SSF has good connectivity between the initial 274 attenuation stage and the second attenuation stage, and the amplitude uniformity is relatively consistent. 275 Since 2013/04/02, the slope has entered a significant linear change stage, that is, the slope has entered an 276 acceleration stage. It can be seen from the curve characteristics that the SSF model, based on the raw 277 data model, makes the ladder shape of the curve have an obvious tendency to eliminate, and the prediction 278 effect is about 0.4 days in advance (∆T=0.4 Day) (Fig. 11b). The prediction effect of SSF model is to 279 make advance prediction before the actual time of landslide. 280 (c) LSF model 281 The transformation results of LSF model is shown in Fig. 11c. In phase of 2013/01/01-2013/02/26, the 282 oscillation amplitude of the measured point data is relatively large, which is also the initial attenuation 283 phase of the LSF model. The displacement in the LSF model attenuates significantly and enters a 284 relatively stable attenuating phase, which are 6 and 11 days later than the Raw data model and the LSF 285 model, respectively. The fluctuation boundary between the regressive stage and the progressive stage is 286 also obvious. Under the LSF model, the curve shows that the slope has entered an obvious linear 287 expression stage since 2013/04/05, which indicates that the slope has entered an acceleration stage. In 288 terms of curve shape, LSF model presents a better fitting state based on raw Data model and SSF model 289 respectively, but the landslide prediction time lags about 2.1 days (i.e. ∆T=-2.1 Day) (Fig. 10c). phase with a large displacement attenuation, which is 6 and 11 days later than that in the Raw data and 294 SSF models, respectively, which is the same as in the LSF model. Under this ESF model, the curve shows 295 that the slope has entered a significant linear change stage since 2013/04/05, that is, the slope has entered 296 an acceleration stage. In terms of curve shape, compared with Raw data model, SSF Model and LSF 297 model, the ESF Model has the lowest fitting accuracy, with a linear fitting correlation coefficient of only 298 0.86, but the predicted landslide time is consistent with the reality (i.e., ∆T=Ta ) (Fig. 11d). 299  shape from 2020/4/01 to 2020/4/11 (Fig. 13a). This is because of noise (disturbance of mining, The data after the inverse velocity transformation using SSF model is shown in Fig. 13b. Fig. 13b shows The velocity raw data transformed by LSF model is shown in Fig. 13c. The period of 2013/01/01-343 2013/02/26 is the regressive stage. Compared with raw data and SSF models, the inverse velocity curve 344 is smoother after using LSF model. In LSF model, the curve shows that the slope has entered a more 345 significant linear regression stage since 2013/04/06, that is, the slope has entered an acceleration stage. 346 Compared with the stepped curves of acceleration stage in Figs. 13a, b, c shows some degree of 347 weakening and good smoothness. The landslide prediction time result obtained by using the LSF model 348 is about 0.2 days before the actual landslide occurrence time (∆T=0.2 Day) (Fig. 13c), which is more in 349 line with the actual situation and has good prediction effect, and can be used as the decision reference 350 for landslide prevention. 351

(d) ESF model 352
The inverse velocity curve of velocity raw data using ESF model is shown in Fig. 13d is characterized by a sudden, the displacement change in the early stage of the landslide is not obvious, 380 but when the landslide is about to happen, the displacement shows a sudden increase. To clearly analyze 381 the difference between the two measurement points, the velocity curve during the accelerated start-up 382 period was enlarged (Fig. 15). The corresponding variation range of measuring points 548-2200 and 461-383 indicates that the slope has entered an acceleration stage. From the curve shape (Fig. 16b)  When the displacement change is small, the prediction effect of the model on the boundary point between 425 the initial regression stage and the second decay stage is not perfect, and there is a hysteresis effect. The 426 raw data and SSF models were not ideal for the landslide acceleration phase when the four models were 427 used for smooth transition. The applicability of the four models can be summarized as follows: when the 428 velocity changes greatly, LSF model is recommended for landslide time prediction, while for short-term 429 irregular data, while ESF model is recommended for landslide time prediction after data preprocessing. 430 The accuracy and rationality of the calculated results are compared between the predicted and actual 431 slope life expectancy. The predicted slope life expectancy curves of the four models and the actual slope 432 life expectancy curves are shown in Figs. 17a-c shows that in the raw data model, the two curves show 433 a parallel convergence trend since 2013/04/13, and the predicted slope life expectancy curve is about 0.8 434 days earlier than the landslide (∆T=0.8Day), which is almost consistent with the fitting result (Fig. 17a). 435 However, this prediction result is seldom used in training fitting data, and its verification results are 436 difficult to be used as a reference for prediction. In SSF model, since 2013/04/10, the curves of the 437 prediction model and the actual model converge approximately in parallel, which adds to the 438 phenomenon of time lag in landslide prediction (Fig. 17b). In the LSF model, the curve has a special 439 shape. Since 2013/04/06, the predicted life expectancy point of the slope is above the actual expected 440 curve of the slope, and is defined as the danger range. In the period of 2013/04/07-2013/04/08, the line 441 between the two expectation points in this stage is approximately parallel to the convergence of the actual 442 slope life expectancy curve, but it is also above the actual slope expectation curve and is still defined as 443 within the danger range. Based on the above analysis, the LSF model has the defect of delayed prediction, while the SFF model 458 is not sensitive enough to the noise change of velocity data. To avoid the shortcomings of the two models 459 and give full play to their respective advantages in landslide time prediction, the expression mode of 460 parallel intersection of the models was used to discuss. Specific methods and steps are as follows. 461 Combined with the monitoring data of LSF and SSF models, an example of measuring point 515-3300 462 was taken for analysis. The displacement variation and data form of the measuring point show great noise. 463 The intersection between a short -and long -term smooth movement is usually one of the most basic 464 signals that indicate a trend change in the source velocity data. The speed curve processed by SSF model 465 (gray curve) and LSF model (red curve) is shown in Fig. 18. The two curves show a cross shape. Based 466 on the performance of long-term and short-term smooth prediction, the following assumptions are is regarded as the end point of the first acceleration. April 1, 2013 is the second intersection, which is the 485 same as trend point (Fig. 18a).

Second order prediction 498
To improve the reliability of the method in predicting landslide instability, the SSF and LSF models were 499 used to transform the data suitable for the inverse velocity model in the first stage to obtain the best 500 fitting curve. Since the prediction performance of the SSF and LSF models is different, they will get 501 different landslide prediction time, and the difference between them is expressed as ∆. The time scale 502 predicted by the two models is assumed, namely,  Schematic diagram of conventional inverse velocity method (modi ed after Chen and Jiang 2020). OOA is the onset of acceleration and TU is the trend update point.   Schematic diagram of the relationship between displacement (S), velocity (v) and acceleration (a).

Figure 10
Velocity dataset and daily precipitation (grey) recorded at the Pingzhuang 4.17 landslide.

Figure 11
The representation method of landslide time prediction under inverse meta-model of velocity data multiplication   The time window expression of slope failure feedback from monitoring points 515-3300, 548-2200 and 461-3250