Numerical simulation has emerged as a powerful technique for landslide failure mechanism analysis and accurate stability assessment. However, due to the bias of simplified numerical models and the uncertainty of geomechanical parameters, simulation results often differ greatly from the actual situation. Therefore, in order to ensure the accuracy and rationality of numerical simulation results, and to improve landslide hazard warning capability, techniques and methods such as displacement back-analysis, machine learning, and numerical simulation are combined to create a novel landslide warning method based on DBA-LSTM (displacement back-analysis based on long short-term memory networks), and a numerical simulation algorithm is proposed, i.e., the DBA-LSTM algorithm is used to invert the equivalent physical and mechanical parameters of the numerical model, and the modified numerical model is used for stability analysis and failure simulation. Taking the Shangtan landslide as an example, the deformation mechanism of the landslide was analyzed based on the field monitoring data, and subsequently, the superiority of the DBA-LSTM algorithm was verified by comparing it with DBA-BPNN (displacement back-analysis based on back-propagation neural network); finally, the stability of the landslide was analyzed and evaluated a posteriori using the warning threshold calculated by the proposed method. The analytical results show that the displacement back-analysis based on the machine learning (DBA-ML) algorithm can achieve more than 95% accuracy, and the deep learning algorithm exemplified by LSTM had higher accuracy compared to the classical BPNN algorithm, meaning that it can be used to further improve the existing intelligent inversion theory and method. The proposed method calculates the landslide's factor of safety (FOS) before the accelerated deformation to be 1.38 and predicts that the landslide is in a metastable state after accelerated deformation rather than in failure. Compared to traditional empirical warning models, our method can avoid false warnings and can provide a new reference for research on landslide hazard warnings.
Keywords: deep learning; LSTM; displacement back-analysis; numerical simulation; warning thresholds
With the expansion of human activities and the intensification of global climate change, landslide geological hazards are occurring with increasing frequency, causing serious economic losses and casualties. China is one of the regions with the highest number of landslide incidents, and to date, thousands of landslide hazards still occur annually, causing hundreds of deaths and billions of USD (United States dollar) of economic losses, and the hazard prevention and mitigation situation remains severe [[
Deformation monitoring is an essential means for the active prevention and control of landslide hazards, and with the rapid development of computer technology and geomatics science and technology, novel monitoring technologies such as GNSS, InSAR, and UAV vision have made positive contributions to landslide hazard monitoring and early warning systems [[
Due to the complexity of landslide occurrence in terms of the geological conditions, genesis mechanism, and external influencing factors, problems related to accurate landslide warnings cannot be solved fundamentally by purely relying on deformation monitoring [[
However, determining physical and mechanical parameters of rock and soil mass is crucial for establishing numerical models. The displacement back-analysis method [[
In this study, we constructed a DBA-LSTM model, and we used it to develop a method to calculate the landslide warning threshold based on DBA-LSTM and the numerical simulation algorithm. Taking the Shangtan landslide in Zhaoping County, Guangxi Province, China as an example, the deformation mechanism of this landslide was analyzed based on GNSS and rainfall data, and then the failure warning threshold of the landslide was investigated using the proposed method. Before the numerical simulation work, the DBA-LSTM algorithm was used to correct the shear strength parameters of the numerical model, and the displacement warning thresholds of this landslide under metastable state and unstable state were then obtained through a series of simulations; finally, the effectiveness of the warning thresholds in this paper was verified by comparing the empirical warning models.
The Shangtan landslide is located in the K195 + 100~K196 + 060 section of Guiwu Expressway, Zhaoping County, Guangxi Province, China, and occurred after the rainy season in 2007. The volume of the landslide is 151.2 × 104 m
According to field investigations and drilling, the stratigraphic units of the landslide area are divided into the alluvial layer and colluvium layer according to the genesis type [[
Based on the above information and topographic data, a 3D mesh model was established, as shown in Figure 2. Defining the numerical model: the landslide mainly consists of clay soil (Sub clay), gravel soil (Gravel soil), and a siltstone layer (Rock), and the regions are defined as continuously distributed materials, and the constitutive model adopts the Mohr–Coulomb model, with the slope surface set as a free boundary and the bottom and surrounding of the model set as fixed boundary constraints. The initial ground stress field was generated using the elastic–plastic solution in stages.
The landslide is still in the process of continuous development, and, due to the large scale of this landslide as well as the thickness of the surface sediment, loose structure, and the large porosity, there is still a possibility of failure under the influence of rainfall and other factors. In November 2018, a small rupture occurred at the retaining wall and an anti-slip pile in a part of the landslide, which was determined through site investigation shown in Figure 3. Considering the existence of civil buildings and traffic arteries around the landslide, a GNSS landslide monitoring system was constructed to ensure the safety of surrounding residents and the normal operation of the highway, and has been operating since April 2019 [[
Considering that rainfall is the main factor that affects landslide deformation, as well as realizing the real-time monitoring of the landslide and road status, the main monitoring content of this landslide incorporates ground displacement, rainfall, and the field environment, and the GNSS monitoring location and video monitoring stations are shown in Figure 4. GD01–GD08 are ground displacement monitoring stations, GD01–GD07 are located on the landslide surface and are hereinafter referred to as monitoring stations. GD08 is located on the roadside opposite to the landslide and acts as a reference station for the relative stability. The rainfall monitoring station GFZ01 and the monitoring station GD08 are located at the same location. In view of the large span of the landslide, three cameras, VS01–VS03, are arranged along the road to achieve comprehensive video coverage of the landslide and the road. The monitoring content and methods are listed in Table 1.
Displacement back-analysis is a method that can be implemented to find the best valuation of inverted parameters by establishing an objective function model based on the least squares optimization criterion according to the functional relationship among the observed displacement and the forward calculated displacement. The general expression of the objective function model is as follows [[
(
where, if the basic displacement back-analysis data contain
The LSTM network can avoid the problem of gradient disappearance by changing the internal structure of the cell, adding input gates, forget gates, and output gates into its memory cell, which controls whether to forget historical information or to update the state of the cell via the gating unit [[
(
where
(
where
The DBA-LSTM model was constructed as follows:
Step 1: Prepare the training samples. Let there be
(
where
Step 2: Eliminate the different magnitudes between the different parameters, and the initial information matrix
Step 3: Determine the parameters of the LSTM network model, where the input feature dimension L, the number of network layers K, and the number of neurons S, are considered to be the key parameters. In the DBA-LSTM model, the dimension of the input features is the number of displacement data in a set of training samples, i.e.,
Step 4: Network training: The training algorithm of the LSTM network is the BP algorithm, which can be regarded as the training process that alternates between forward propagation and backward propagation, and mainly uses the error principle of backward propagation to feedback the errors generated during the network training process to the LSTM network by continuously adjusting the connection weight of each neuron in the network until the error is reduced to the specified range, at which time the system stops learning.
Step 5: Network testing. After establishing the DBA-LSTM inversion model, the performance of the model is generally evaluated by calculating the goodness of fit
(
where
Numerical simulations can not only analyze the current landslide stability but can also simulate the landslide failure scenario and calculate the landslide failure warning threshold. To ensure the accuracy of the numerical simulation results, the proposed method suggests that the physical and mechanical parameters of a numerical model should be corrected by the DBA-LSTM algorithm according to the relative displacement of rock and soil mass caused by dynamic construction or other reasons before implementing the numerical simulation. The algorithm flow is shown in Figure 6, and the detailed steps are as follows:
Step 1: Establish a landslide grid model based on the topographic data, collect and organize the deformation monitoring data information, including the pre-processing of the original data and the node information of its grid located according to the coordinates of monitoring points, and define the numerical model based on the geological data.
Step 2: When there are geotechnical parameters with uncertainty in the numerical model, construct machine learning training samples using the orthogonal test method, and after training, to obtain a reliable DBA-LSTM model, correct these uncertain parameters using the measured data and take them as the current equivalent mechanical parameters of the landslide.
Step 3: Based on the modified numerical model, the current landslide factor of safety is calculated using the tension–shear damage strength reduction method [[
(
where
Step 4: Determine the potential failure conditions of the landslide, such as the dynamic excavation, groundwater level changes, etc. Taking the changes in the groundwater level as an example, the seepage module is invoked in the numerical simulation software to simulate and calculate the displacement calculation results under the limit equilibrium state of the landslide by continuously adjusting the water level conditions, and the corresponding warning criteria (e.g., water level and relative displacement thresholds) can be obtained.
To verify the validity of the proposed method, experiments were designed in the following three parts. In the first part, the deformation mechanism was analyzed based on the GNSS and rainfall data from the monitoring system. In the second part, an orthogonal test scheme was used to generate the training samples, and the validity of the DBA-LSTM algorithm was verified by comparing it to DBA-BPNN. In the third part, based on the measured data, the DBA-LSTM was used to invert the shear strength parameters of this landslide, the equivalent mechanical parameters were substituted into the numerical model, and the corresponding displacement warning thresholds were then calculated by simulating the failure conditions.
From April 2019 to the end of 2019, the system recorded the development of Shangtan landslide deformation process. Figure 7 shows the landslide's cumulative deformation time series curves and monthly rainfall–time curves (as space is limited, the analysis is conducted for the Y-directional displacement, which has the largest deformation). Significant displacements from the GD03 and GD04 monitoring stations were observed, and the deformation of the Shangtan landslide can be roughly divided into three stages. Slow deformation stage: The accumulated landslide deformation increased slowly in April and May, and the accumulated deformation of the seven GNSS monitoring stations was about 10–20 mm. Evenly accelerated deformation stage: The results from most of the GNSS monitoring stations showed that the landslide deformation displayed an increasing trend in June, and the deformation rate remained stable, with a maximum average rate of 19.2 mm/d and a minimum average rate of 4.8 mm/d. Variable acceleration deformation stage: The GNSS monitoring results show that the landslide entered a stage of accelerated deformation in early July, and the accumulated deformation increased sharply, with the maximum deformation rate of the GD03 and GD04 monitoring stations reaching 119.6 mm/d (15.3 mm/h) and 148.4 mm/d (17.9 mm/h); the accumulated deformation was more than 1 m by the end of September. It is worth stating that the accumulated displacement of GD08 did not exceed 10 mm, indicating that the road foundation is mostly stable and it is an effective relative stability reference station.
By counting the rainfall data, the cumulative rainfall in 2019 was 2806.6 mm, and the cumulative rainfall from July to October was 2400.0 mm, accounting for 86%, with the concentrated rainfall showing obvious time–domain distribution characteristics. According to the relationship between the accumulated landslide deformation and rainfall in Figure 7, it can also be seen that there is an obvious positive correlation between landslide deformation and the concentrated rainfall, and the influence of the concentrated rainfall on the rate of landslide deformation is significant, indicating that rainfall is the main factor inducing the accelerated deformation of the Shangtan landslide.
However, when the displacement data were analyzed using the empirical warning model [[
According to the algorithm flow shown in Figure 6, we located the nodes in the grid model based on the coordinates of monitoring stations, with GD01–GD07 corresponding to id = 534, 598, 4334, 2810, 2742, 5336 and 6258, respectively. Then, to determine the inversion parameters, it was already known from previous analyses that rainfall is the main factor influencing landslide deformation, resulting in precipitation seepage through the surface into the landslide, which increases the water content of the sub-clay layer mud and reduces the slip resistance, leading to accelerated landslide creep deformation. Therefore, we took the shear strength parameter of the sub-clay layer as the inversion target parameter. Meanwhile, the infiltration of rainfall would increase the groundwater pressure, and these elevated pressures would, in turn, trigger slope motion, necessitating a fluid–structure interaction analysis for this landslide. The next step was the generation of the training samples and the training of the network model.
The orthogonal test is an effective way to construct DBA-ML samples. It starts with the determination of the test factors and their levels as well as the selection of a reasonable orthogonal table for the table header design based on the factors and levels. Considering that the number of target parameters is six and the interaction between the internal friction angle and cohesion is not considered, we planned to choose an orthogonal table with eight factors and eight levels. According to the field investigation report and some bibliographic data [[
According to the orthogonal table
The 49 sets of sample data in Table 3 were used as the training sets, the displacement data were treated as the input layer, and the target parameters to be inverted were treated as the output layer for training. According to the literature [[
Comparing the results of DBA-BPNN and DBA-LSTM, it can be found that both algorithms are in good agreement with the predicted and theoretical values, which indicates that the DBA-ML algorithm can effectively invert the equivalent physical and mechanical parameters of the landslide. However, from Figure 8, it is clear that the fitting effect of DBA-LSTM is significantly better than DBA-BPNN, and by counting the MAPE (average absolute percentage error) of the two algorithms, the accuracy of the DBA-LSTM algorithm (0.62%) is improved by 62.0% compared to the DBA-BPNN algorithm (1.63%).
Among DBA-ML algorithms, the BPNN model was the earliest-applied and is the most frequently employed network model, and the experimental results in this paper show that the accuracy of DBA-LSTM is substantially improved compared to that of DBA-BPNN, but it does not deny the feasibility of DBA-BPNN. In order to further verify the accuracy of the two algorithms in this test, the inversion results of the two algorithms were entered into the numerical model to carry out forward calculation of the landslide displacement, and the actual input displacement data were compared to the actual input displacement data to calculate the differences in the absolute error. The results are shown in Figure 9, where the vertical coordinates correspond to seven groups of test samples.
From the calculation results, it can be seen that for the DBA-BPNN algorithm, the maximum errors of the calculated displacements for this scheme in the Y-direction and Z-direction are 4 mm and 2 mm, respectively, but from Figure 9a,c, it can be seen that DBA-BPNN only demonstrates large deviations at GD03 and GD04. Considering that the relative displacement of these two stations is much larger than others, by calculating the relative errors, it was found that the relative error is less than 5% for all of the stations in the seven groups of samples. Therefore, the DBA-BPNN algorithm is feasible for landslide inversion. The computational accuracy of the DBA-LSTM algorithm in both the Y- and Z-directions is less than 1 mm, which indicates that the landslide parameters in the inversion of the DBA-LSTM algorithm are more accurate.
In short, machine learning for displacement back-analysis can effectively invert the equivalent physical and mechanical parameters with higher accuracy, but the deep learning algorithm has better prediction performance in terms of landslide inversion.
The period from April to June 2019 was used as the input parameter for the DBA-LSTM model, the shear strength parameters in the numerical model were modified, and the RMSEs in the Y- and Z-directions were calculated to be 3.9 mm and 1.8 mm, with a maximum deviation of 6.1 mm at the point, indicating that the numerical simulation results are basically consistent with the field monitoring results and that the analytical model can be further used for stability analysis. Figure 10 shows the displacement in the Y-direction calculated based on the inversion results, where the data in the figure represent the calculated displacement values of each monitoring station. The displacement nephograms in the X- and Z-directions are not shown, due to space limitations.
Based on the modified model, the stability of the current state of the landslide was analyzed according to the strength reduction method, and the FOS was calculated to be 1.38. According to the Technical Code for Building Slope Engineering (GB50330-2013) published by the Chinese Ministry of Housing and Urban–Rural Development, it can be determined that Shangtan landslide was in a stable state at the end of June.
A follow-up was carried out to determine the warning criterion for different landslide stages according to the evolutionary conditions. Simulating the deformation of this landslide, apart from considering the changes in the stress field under the action of gravity, the changes in the pore pressure field generated by groundwater changes and seepage should also be considered. First, two combinations of shear strength parameters with safety factors of 1.05 and 1.10 were obtained according to the discount factor, and the ultimate groundwater level was set to simulate two cases: the metastable state and unstable state, and the calculation results are shown in Figure 11. The upper part of the figure shows the displacement calculation results when the simulated safety factor was 1.05 (i.e., sub-stable state), and the bottom part of the figure shows the displacement calculation results of the unstable state.
According to the calculation results of the two evolutionary states, two sets of displacement warning criteria can be set (Table 5). When the relative displacement monitoring results reach the first set of thresholds, it means that the landslide is in a metastable state and should take corresponding management measures, and when the displacement reaches the second set of thresholds, it means that the landslide is about to become unstable and emergency warning measures should be taken.
The tangent angles obtained from GD03 and GD04 in July exceeded 85° several times, implying that the empirical warning model predicted that the landslide would show signs of damage in July. However, according to the GNSS displacement monitoring results from July to September (Table 6), in which the same GD03 and GD04 monitoring stations were used as the target of analysis, and assuming that landslide deformation usually develops until mid-September, the measured results of the model are still some distance away from the second set of unstable warning criteria, indicating that the method in this paper indicates that the landslide will not be destabilized and will be in a metastable state. Thus, the method of this paper obtained results that were different from the warning results of the empirical model.
According to the accumulated deformation in 2019 (Figure 7) and the information in Table 6, it can be seen that the accelerated deformation trend of the Shangtan landslide stabilized in mid-September. Meanwhile, according to the site inspection results after the accelerated landslide deformation (Figure 12), we found that some new cracks appeared at the site but that no phenomena such as slippage or collapse were observed, which verifies the feasibility of the warning results of the proposed method and allows incorrect warnings to be avoided.
Landslide deformation and damage occur under the joint action of various influencing factors such as geological conditions, rainfall, and groundwater. This study takes the Shangtan landslide as the research object and determines the interaction mechanism between the geological structure, mechanical mechanism, and landslide deformation by constructing a modifiable numerical model, and the damage mechanism of this landslide was analyzed by numerical simulation. Moreover, a novel approach using deep learning algorithms for displacement back-analysis was proposed for the first time.
Based on the GNSS and rainfall data, we found the Shangtan landslide showed slow deformation, uniformly accelerated deformation, and variable accelerated deformation, with the largest cumulative displacement change in being observed in the north–south direction and the maximum deformation rate reaching 148.4 mm/d. Furthermore, the concentrated rainfall in the rainy season led to the softening of the sub-clay layer and a reduction in the slip resistance strength, which was the main reason for the variable accelerated deformation of the landslide. Particularly, to determine the shear strength parameters of the sub-clay layer, two DBA-ML models were constructed, and both algorithms showed satisfactory performance in terms of prediction accuracy, demonstrating relative errors of less than 5%. The DBA-LSTM algorithm improved the computational accuracy by 62.0% compared to DBA-BPNN, implying that the deep learning algorithm has better landslide displacement back-analysis performance. However, the prediction ability of both algorithms was dependent on the accuracy of the model parameter settings. Therefore, the application of the Auto-ML technique for displacement back-analysis to enable the model to learn the appropriate parameters automatically is also one of the important works in the subsequent research. Furthermore, to accurately assess the degree of landslide stability, a novel landslide warning method based on DBA-LSTM and the numerical analysis algorithms was proposed. Two sets of displacement warning criteria corresponding to two levels of the metastable state and unstable state were determined by numerical simulations. The validation results show that the criteria in this paper are more reasonable than those of the empirical warning model and have a certain reference value for landslide hazard warnings.
Graph: Figure 1 Location of the Shangtan landslide.
Graph: Figure 2 The 3D mesh model of the Shangtan landslide.
Graph: Figure 3 Gutter extrusion deformation (left); retaining wall cracking (right).
Graph: Figure 4 Location of landslide monitoring stations.
Graph: Figure 5 (a) LSTM network model structure; (b) LTSM cell structure.
Graph: Figure 6 Threshold calculation process.
Graph: Figure 7 Monitoring data.
Graph: Figure 8 Fitting relationship and goodness of fit R2.
Graph: Figure 9 Residual plots.
Graph: Figure 10 Simulated displacement nephogram based on the inversion results.
Graph: Figure 11 Displacement simulation results for a given evolutionary condition.
Graph: Figure 12 Field inspection photos. (a) Around the station of GD01. (b) Station of GD03. (c) Station of GD03. (d) Around the station of GD04.
Table 1 Monitoring content and methods.
No. Content Methods Instruments 1 Ground displacement GNSS Huace H3 GNSS Receiver 2 Rainfall Rain gauge GFZ01 digital rain gauge 3 Environment Video Hikvision surveillance camera
Table 2 Physical and mechanical parameters and target parameters of the landslide.
Group Sub clay1–3 2200 20–40 13–22 10–14.5 10–16 400 50 Gravel soil 2200 60 36 16 18 1000 50 Bedrock 2900 1300 800 400,000 48 - -
Table 3 Training samples.
Num. Output Layer Input Layer Y Z 1 10 10 10 10 10 10 −95.4 −57.8 2 10 11 10.75 11 10.75 11 −84.2 −51.8 3 10 12 11.5 12 11.5 12 −76.9 −47.9 4 10 13 12.25 13 12.25 13 −72.5 −45.8 5 10 14 13 14 13 14 −69.6 −44.5 6 10 15 13.75 15 13.75 15 −67.3 −43.4 7 10 16 14.5 16 14.5 16 −65.4 −42.4 8 10.75 10 10.75 12 12.25 14 −94.7 −57.4 9 10.75 11 11.5 13 13 15 −85.2 −52.3 10 10.75 12 12.25 14 13.75 16 −69.7 −42.7 45 14.5 12 10.75 10 14.5 15 −74.9 −49.4 46 14.5 13 11.5 11 10 16 −71.3 −47.6 47 14.5 14 12.25 12 10.75 10 −68.7 −46.3 48 14.5 15 13 13 11.5 11 −58.5 −39.3 49 14.5 16 13.75 14 12.25 12 −57.1 −38.3
Table 4 Test samples.
Output Layer Input Layer Y Z 1 10 10 10 10 10 10 −95.4 −57.8 2 10.75 13 13 15 14.5 10 −66.5 −41.5 3 11.5 12 13 16 10.75 13 −72.6 −44.7 4 11.5 16 10.75 13 13.75 10 −63.3 −42.4 5 12.25 15 10.75 14 10 13 −67.6 −45.0 6 13 16 12.25 10 13 11 −68.5 −47.4 7 14.5 13 11.5 11 10 16 −71.3 −47.6
Table 5 Two sets of displacement warning thresholds (unit/mm).
State GD01 GD02 GD03 GD04 GD05 GD06 GD07 metastable −477.3 −232.2 −1166.1 −1347.8 −661.7 −370.8 −334.9 unstable −848.5 −343.1 −2622.3 −3132.4 −1482.4 −881.5 −635.2
Table 6 July–September GNSS displacement monitoring sequence (unit/mm).
Time GD01 GD02 GD03 GD04 GD05 GD06 GD07 7/15 −75.2 −32.5 −531.0 −838.3 −34.1 −25.0 −23.0 7/31 −75.0 −31.9 −844.3 −1188.3 −34.2 −23.4 −22.6 8/15 −74.4 −27.8 −839.7 −1187.7 −36.4 −21.6 −21.2 8/31 −88.9 −39.0 −1128.7 −1430.6 −43.1 −28.3 −30.0 9/15 −112.0 −49.6 −1434.4 −1689.8 −46.6 −29.9 −37.7 9/30 −109.5 −44.7 −1430.9 −1684.7 −44.5 −30.6 −29.8
Conceptualization, W.D.; methodology, Y.D. and W.D.; writing—original draft preparation, Y.D.; writing—review and editing, W.D. and W.Y.; resources, D.B.; visualization, Y.D.; funding acquisition, W.D. All authors have read and agreed to the published version of the manuscript.
Not applicable.
Not applicable.
The data presented in this study are available on request from the corresponding author.
The authors declare no conflict of interest.
The following abbreviations are used in this manuscript:
DBA Displacement Back-Analysis DBA-LSTM Displacement Back-Analysis based on Long Short-Term Memory networks DBA-BPNN Displacement Back-Analysis based on Back-Propagation Neural Network DBA-ML Displacement Back-Analysis based on the Machine Learning FOS Factor Of Safety GNSS Global Navigation Satellite System INSAR Interferometric Synthetic Aperture Radar GB-InSAR Ground-Based Interferometric Synthetic Aperture Radar AEWG Active Waveguides UAV Unmanned Aerial Vehicle FLAC3D Fast Lagrangian Analysis of Continua 3D GD Ground Displacement station VS Video Surveillance station
The authors would like to thank the editor and the reviewers for their contributions.
By Yue Dai; Wujiao Dai; Wenkun Yu and Dongxin Bai
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