A new early warning Criterion for assessing landslide risk

A large number of engineering case studies have shown that the traditional early warning criteria, which evolved on the basis of displacement as a single piece of information, have many limitations in practical engineering. The displacement speed ratio (DSR) cannot determine the development trend of landslides due to the influence of periodic external environmental factors. Moreover, when landslides occur, the early warning system will have a false alarm due to the stepwise giant rise of landslides. To solve this problem, this paper proposes a new landslide warning criterion, the trend speed ratio (TSR), and also fuses TSR and DSR into a dual speed ratio method (DSRM) for judging landslide risk changes. We assess these methods by applying DSRM and DSR to 10 landslide cases, respectively. The results show that when TSR is greater than 2.0, the probability of landslide damage is high and when TSR tends to decrease, the landslide tends to be stable. For landslides that rise sharply in steps but are not damaged, DSR has a high false alarm rate, while DSRM can effectively reduce the false alarm rate. In terms of warning applicability, DSR can be applied in only half of the ten landslide cases studied, while DSRM is significantly more applicable. In addition, compared with the traditional method, the new method can determine the direction of landslide development and assess the risk of step-up landslides, providing new technical support for engineers engaged in landslide warning and control.


Introduction
Landslides are one of the most dangerous hazards in the world, which greatly impact human activities, once they occur (Klose et al. 2016;Du et al. 2017;Fu et al. 2020; Bar et al. 2020). Although, landslide development can be slowed down by on-site management, it is often 1 3 difficult to carry out timely survey and management work. (Du et al. 2020a). Particularly, when the landslide enters the creeping deformation stage; thus, pre-landslide warning and forecasting work is the most economical and reasonable means of disaster prevention (Intrieri et al. 2013;Kong et al. 2020;Wanare et al. 2022;Du et al. 2020b).
Landslide displacement information provided by the geotechnical body of the slope in the process of spatial and temporal evolution reflects the state of the slope movement (Booth et al. 2013;Kwan et al. 2015). This has become one of the most important ways of landslide early warning research (Guzzetti et al. 2020). In recent years, with the continuous improvement of monitoring equipment, some studies have proposed the establishment of landslide displacement speed thresholds to predict landslide hazards (Gigli et al. 2014;Lombardi et al. 2017;Segalini et al. 2018). However, due to the different geological conditions of each landslide, it is difficult to determine the hazard level of landslides by only a fixed landslide speed threshold. The classical creep theory of landslides suggests that the landslide deformation process goes through three stages: initial deformation, uniform deformation and accelerated deformation (Saito 1969). Thus, many researchers have proposed setting dimensionless warning criterion values to determine the spatial state of landslides on the basis of the classical creep theory and combined it with the cumulative displacement versus the time diagram of landslides. (LIU et al. 2019;Xu et al. 2011). Among the representative methods is the displacement speed ratio (DSR), which indicates that when the landslide is in the accelerated deformation phase, there is some relationship between the speed at any moment and the ratio of speed in the uniform deformation phase (Wang et al. 2014). The DSR is beyond a certain threshold value when the landslide is damaged. This method is simple but has achieved good results in engineering. However, this method has some limitations. For example, the landslide warning standard only determines the state of the landslide through the landslide displacement data, which does not reflect the future evolution trend of the landslide (wang et al. 2017). The evolution mechanism of the landslide is very complicated and because the introduction of monitoring equipment is arbitrary, it is difficult to determine the displacement speed standard of the landslide in the uniform speed stage (Xie et al. 2020). In addition, when a landslide undergoes stepwise growth, the DSR will increase dramatically, even exceeding the critical slip threshold, which makes it difficult to identify the landslide risk condition (Jeng et al. 2022). These limitations are the epitome of most current landslide warning criteria methods. At the same time, most of the existing early warning methods are assuming the state of landslide acceleration (Intrieri et al. 2019). This is a problem when judging the future evolutionary risk change of landslide when it decelerates. In order to better improve the applicability of monitoring and warning in practical engineering, this problem needs to be address.
Time series theory suggests that the displacement of landslides can be divided into trend displacement and periodic displacement, where the trend displacement represents the future evolutionary trend of landslides (Wang et al. 2021). Based on time series theory, this study attempts to analyse the spatial condition of landslides from the perspective of trend displacement speed ratio (TSR), and proposes a new method for the quantitative evaluation of landslide risk. The improved method can effectively identify the risk changes of landslides and provide reference for better response to landslide warning in engineering.

Method
According to the three-stage theory of landslide creep, the landslide deformation process can be divided into three stages. The first stage is the initial deformation stage. The deformation of the slope body starts from nothing, the slope body starts to produce cracks, and the accumulated displacement deformation curve shows a relatively steep slope. However, with the continuation of time, the deformation gradually tends to a normal state, the slope of the curve slows down and shows the characteristics of deceleration deformation. The second stage is the equal-speed deformation stage. At this stage, on the basis of the initial deformation of the landslide, the slope geotechnical body basically continues to deform at a similar speed under the action of gravity (Scoppettuolo et al. 2020). Due to the influence of external factors, occasionally, the deformation curve may fluctuate, but the overall trend of the cumulative displacement deformation curve at this stage is a sloping curve, and the macroscopic deformation speed remains basically the same. The third stage is the accelerated deformation stage. When the slope body deformation develops to a certain stage, the deformation speed will show a growing trend. The slope of the deformation curve at this stage will keep growing, and the curve will be almost steep when the slope body is destabilized.
The single-speed ratio method is based on the three-stage theory of landslide creep. This is founded on the principle of dividing the displacement speed at any point by the speed of the isokinetic deformation stage to normalize the magnitude, to obtained a dimensionless displacement speed ratio (DSR) for evaluating the deformation state of the landslide, Eq. 1. (Wang et al. 2014) Where V t is proportional to the slope of each point on the displacement-deformation curve. V t is proportional to the slope of the curve in the isokinetic deformation phase. When V t is in the isokinetic deformation phase, t ≈ 1.0, and when V t is in the accelerated deformation phase, t > 1.0. Due to the small displacement, the initial deformation phase is not considered. When a landslide occurs, t >8.0.
The landslide displacement speed in the uniform deformation phase is determined by the average value of the landslide displacement speed in the isokinetic deformation phase of the landslide cumulative displacement versus time (S-T graph), Eq. 2. (Wang et al. 2014) where V i is the deformation speed of a monitoring point at each time period in the main slip direction during the equal speed deformation phase; m is the number of monitoring times.
The DSR criterion can determine the deformation state of a landslide to predict the occurrence time, but it cannot determine the future evolution trend of the landslide, which causes the model to produce false alarms. At the same time, it is difficult to determine the isokinetic deformation speed threshold due to the arbitrary introduction of monitoring equipment (Xie et al. 2020). To address the limitations of a single DSR criterion, it is necessary to introduce a new speed ratio to discern the evolutionary trend of landslides. The new criterion is the trend speed ratio (TSR), which is defined as the trend displacement speed obtained by excluding the periodic displacement speed (the effect of external periodic triggering factors, such as rainfall, reservoir water level rise and fall). The change of the trend displacement represents the future evolution direction of the landslide. When the landslide tends to slide, its displacement speed will increase sharply, and the trend speed ratio of the adjacent monitoring time will become larger and larger, until it collapses, Eq. 3.
where is the trend speed ratio (TSR), v is the displacement speed of the landslide, f is the displacement speed of the periodic term of the landslide, v' is the displacement speed of the trend term of the landslide, and t is the monitoring date. The influence of periodic external triggers on landslides can be expressed by Eq. 4.
where, h t is the equivalent reservoir level on day t, r t is the equivalent rainfall on day t, m t is the magnitude on day t, is the influence coefficient. The trade-offs of the variables in the equation can be considered according to the actual situation of the landslide.
The influence of periodic triggers on landslides usually haves a time lag, so the lag days of triggers can be determined first by gray correlation analysis (Wang and Xiang 2015).
The lagged effect of reservoir water on landslides is not a linear process , and to simplify this process an influence coefficient can be introduced, Eqs. 5 and 6.
where, i is the number of reservoir water lag days, and β is the influence coefficient (0 < β < 1).
As for the influence of rainfall on landslide, according to the "one rainfall process theory", the longer the rainfall time, the smaller the effective rainfall will be, which is a directional attenuation process. The attenuation coefficient can be determined by Eq. 7. (Xiaohu et al. 2018): where: T is the attenuation coefficient and T is the time difference between the previous rainfall and the monitoring t moments.
Then the equivalent rainfall is calculated by Eq. 8.
where: r t is the effective rainfall of the current period, r(l) is the total rainfall of the l-th day, Tl is the attenuation coefficient of the total rainfall of the l-th day on the impact of the current period.
After obtaining the effective rainfall in the current period, the time lag time d corresponding to the rainfall can be obtained by the above gray correlation analysis. The equivalent rainfall in the current period after considering the time lag effect R t can be calculated by Eq. 9.
In order to avoid the calculation error caused by the difference of magnitude of each variable, the method of initial zeroing the data was adopted. The relevant monitoring data volume after processing were brought into the model, and the accumulated deformation data and macroscopic performance of the landslide were considered comprehensively. Eight days were used as a stage for training, and the corresponding periodic factor influence coefficient were obtained according to the Auto Regressive Distributed Lag (ARDL) formula (Khan et al. 2019). The periodic displacement speed f, and the corresponding trend speed ratio were calculated by using Eq. (3). The methodology used is shown in Fig. 1.
For the trend speed ratio ω, when its value fluctuates above and below 1.0, the landslide is in the uniform deformation stage; if its value is greater than 1.0 and is rising, the landslide enters the acceleration stage; if its value is decreasing, the landslide may stabilize.
We call this method that combines TSR and DSR as dual speed ratio method (DSRM). This proposed method assesses the risk of a landslide from the perspective of the creep trend and the state of the landslide at any point in time.
(9) r t = r t−d Fig. 1 Flow of trend speed ratio calculation 1 3

Case study
The landslide site is located on the north side of Wangjia mountain on the right bank of the Riverside Branch Reservoir in the upper reaches of the Jinsha River. The landslide site is 92.4 km away from the dam site, and has an estimated volume of 6.11 million m 3 . After the reservoir is filled with water, the landslide will become unstable, which can produce surges that will affect the lives and property of surrounding residents, and may affect the safety of shipping traffic. Figure 2 shows the distribution of landslide locations and partial deformation details. Figure 3a shows the plot of the cumulative landslide displacement versus reservoir water level. There is a clear relationship between the increased landslide deformation and the rising reservoir water level during the reservoir storage period. The rising reservoir water level lags behind the increased landslide deformation. The relationship between the two speed ratios and the landslide deformation speed is shown in Fig. 3b. In the figure, the displacement speed ratio reaches a maximum value of 2.61 on October 6, 2021, and remains at 2.03 until October 8, 2021, which indicates that the landslide is, according to the method, in the accelerate phase. While the trend speed ratio has decreased from a maximum value of 1.64 on October 5, 2021, to 0.91 on October 8, 2021. The displacement speed ratio can be used to distinguish the accelerated deformation phase of the landslide from the destruction phase, but it cannot determine the evolution trend of the landslide. The real-time relationship between trend speed ratio and landslide displacement speed is shown in Fig. 3c, which shows that the landslide deformation speed reached two maximum extreme points on September 15, 2021 and October 6, 2021. The displacement speed ratio also reached extreme values on these two days, while the trend speed ratio reached a  Fig. 2 The distribution of landslide location and partial deformation details: a The landslide 3D topographic map; b The middle part of the landslide collapsed; c Ground subsidence and ground cracks maximum value the day before and then started to decrease. These values indicate that the trend speed ratio can be more sensitive to the future evolution of landslides by considering the influence of external triggering factors. The experimental data analysis show that the displacement speed ratio can determine the acceleration phase of the landslide and thus predict the time of landslide damage and the trend speed ratio can determine the future evolution direction of the landslide. The DSRM which combines the two methods can help engineers to better evaluate the landslide risk.
In order to investigate whether the trend speed ratio has application value in early warning destruction time, the author collected data of three destroyed landslides. Since, it is difficult to obtain the original data of landslide monitoring, the author took equal spacing values according to the graphs in related literature. The deformation curve obtained by this method is consistent with the shape of the original curve, which ensures the accuracy of the analysis results. In Fig. 4a is the Jigmei landslide in China (Wang et al. 2014); (b) is a landslide in Chile (Wang et al. 2014); and (c) is a landslide in Japan (SIMA 1986). The graphs show that the trend speed ratios of all three landslides are between 2.0 and 3.0 at the time of damage; thus, the trend speed ratios can be used to predict the time of landslide occurrence.
Based on the above case studies, the classification of warning levels derived from DSRM is shown in Table 1. Level I-II warning in the table indicates that the landslide is in a state of accelerated deformation, and it is recommended that the site should be monitored more closely at the necessary locations. This two-level warning is adopted for internal discussion. Level III warning indicates that the possibility of landslide is very high, and close precautions must be taken to evacuate the occupants and reinforce the slope as needed, and this level of warning is released to the public. When the warning level is Level IV, expert consultation needs to be launched to determine the final Fig. 3 Landslide risk assessment analysis in the study area : a Relationship between water level rise in the reservoir area and cumulative landslide displacement; b The trend of each indicator in this slope deformation of the largest few days; c Real-time relationship between trend speed ratio and landslide displacement speed warning scope and warning level with regard to the regional geological environment, rainfall, reservoir water level, existing displacement monitoring and past disaster.
With the existing criteria it is difficult to judge the risk of stepped landslides. The DSR may change drastically when the landslide undergoes stepped deformation (Jeng et al. 2022). This makes it difficult for engineers to quantitatively identify site conditions. The Baijiabao landslide is a typical step-deformation landslide. Firstly, DSR is applied to the landslide. According to methods in the literature (Wang et al. 2014), DSR can be divided into 4 early warning levels. DSR < 2.0 is level I (green), and 2.0 < DSR ≤ 6.0 is level II (yellow), 6.0 < DSR ≤ 8.0 is level III (orange), and DSR > 8.0 is level IV (red). Figure 5 shows the DSR real-time warning. In reality, the landslide has undergone deformation but it is not unstable; however, there are eight red warnings, which are false alarm points, Fig. 5. The eight false alarm points occurring in the 38 time points studied, has a false alarm rate of 21.05%. We applied TSR to the same landslide. Figure 6 shows the real-time situation of DSRM's judgment on this landslide. It can be seen from the figure that the highest warning level of DSRM is level III (orange), which when compared with the traditional method, the false alarm rate is significantly reduced.

Discussion
At present, the single deformation criterion represented by the displacement speed ratio still dominates in the evaluation of slope engineering stability (Wang et al. 2017). However, as this criterion only considers a single landslide displacement speed value, it makes the landslide criterion damage value and the landslide displacement speed limit value appear simultaneously, which leads to a time lag in early warning. Simultaneously, when the landslide gradually stabilises, the conventional model still judges the landslide to be in the acceleration phase, which leads to false alarms (Chae et al. 2017). In Fig. 3c, the TSR reaches its extreme value one day earlier than the DSR, which implies that the landslide is gradually stabilizing. This can enhance the timeliness of field warnings in engineering and reduce the false alarm rate of risk assessment. This unique advantage is due to the fusion of multiple monitoring information with historical data, the ability to focus on the development of the phenomenon over the preceding and following periods, and to indicate short-term changes in the phenomenon, which is of particular importance for stepped landslides. For landslide time prediction, the inverse velocity method is widely used in engineering because of its simple calculation and high prediction accuracy, but such methods still give early warnings when the landslide is decelerating and stabilizing (Du and Song 2022;Zhou et al. 2020;Osasan and Stacey 2014). As TSR is sensitive to changes in landslide development trends, it can provide a discriminatory condition for the use of the inverse velocity method under the right conditions, alleviating unnecessary stress of on-site personnel. Nowadays, we are faced with increasingly complex landslide geology.
Step deformation landslides due to heavy rainfall and other factors have become a major concern for staff, and traditional methods have difficulty in solving such complex engineering problems (Salee et al. 2022). In Fig. 5, the DSR shows a sudden steep increase at the inflection point, with eight false alarm points occurring in the 38 time points studied. In contrast, DSRM, a warning method with multiple indicators, proves its superiority in Fig. 6. In the face of increasingly complex engineering conditions, the traditional single-indicator discrimination method is not as effective when compared to the multi-indicator-based early warning judgment method (Du and Xie. 2022). Further comparing the difference in applicability between the traditional single indicator method and DSRM for early warning, as shown in Table 2, DSR was only applicable to half of the 10 engineering studies, while DSRM was significantly more adaptable for early warning. Clearly, when compared with the traditional method, the multi-indicator-based DRSM has greatly improved the warning accuracy. For engineering sites, DSRM, which integrates DSR and TSR, provides a new  (Suwa et al. 2010) No √ √ Town of Peace River (Kim et al. 2010) No √ √ technical support for landslide risk management and can effectively predict the future evolution of landslides, which has certain practical application value. As the scope of human engineering activities expands further, the challenges of an increasingly complex engineering geological environment will require the development of more effective landslide risk analysis methods (Ju et al. 2020). Therefore, this study proposes a new indicator and improves on the shortcomings of traditional risk analysis methods, thus showing that landslide risk analysis based on multi-source data indicators is more reliable than single indicator warnings. Consequently, we suggest that more research efforts should be mobilized to conduct research on landslide risk assessment technologies that integrate multi-information big data analysis, so as to achieve the prevention and control goals of intelligent early warning systems.

Conclusion
In this study we proposed, a new landslide warning criterion TSR, and a dual speed ratio method (DSRM) incorporating DSR to assess the degree of landslide deformation. The main conclusions are as follows: 1. Taking the landslide on the reservoir bank of the upper Jinsha River reservoir in China the landslide displacement velocity reached 267.53 mm/d on September 15 and 578.39 mm/d on October 6, 2021. DSR also reached the extreme value at the same time, while TSR reached the extreme value one day earlier than DSR, 1.131 and 1.643, respectively. Thereafter, TSR showed a decreasing trend until the landslide gradually stabilized. These results indicate the advantage of TSR in identifying the change of landslide evolution direction. 2. Taking three failed landslides as examples, the Jigmei landslide in China, a landslide in Chile and a landslide in Japan, the trend speed ratios were calculated these were 2.743, 2.268 and 2.269, respectively. These were in the range of 2.0-3.0, indicating that the trend speed ratios are feasible for predicting landslide failure. 3. In response to the difficulty of identifying the stepwise deformation surge of landslides by traditional methods, the trend speed ratio was calculated for the Baijiabao landslide in China. The results indicate that the trend speed ratios of the two points with the largest stepwise deformation surge of landslide displacement were 1.84 and 1.21, both of which were lower than 2.0. This implies that the magnitude of the trend speed ratio may have some relationship with the risk posed by the stepwise deformation surge of landslides. 4. Taking the Baijiabao landslide as an example, eight false positive points appeared in the DSR when the landslide was violently deformed, and the false positive rate reached 21.05% in the time period studied. On the other hand, the use of the newly proposed DSRM for early warning significantly reduced the false alarm rate. 5. The traditional displacement-speed ratio discriminant method and DSRM were applied to 10 engineering examples. It was found that the proposed method considers the stability trend of landslides and is more applicable than the traditional method, which provides new technical support for a better response to landslide warning in engineering.