
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

39266643
72154
10.1038/s41598-024-72154-z
Article
Research on failure mechanism of landslide with retaining-wall-like locked segment and instability prediction by inverse velocity method
Chen Jia-Xing jia-xingchen@foxmail.com

1
Liu Han-Dong 23
Guo Zhi-Fei 4
Liu Jing-Jing 23
Feng Ling-Yun 23
Liu Shuai 23
1 https://ror.org/008m8sh03 grid.412544.2 0000 0004 1757 3374 College of Architecture & Civil Engineering, Shangqiu Normal University, Shangqiu, 476000 China
2 https://ror.org/03acrzv41 grid.412224.3 0000 0004 1759 6955 College of Geosciences and Engineering, North China University of Water Resources and Electric Power, Zhengzhou, 450045 China
3 Henan Key Laboratory of Geomechanics and Structure Engineering, Zhengzhou, 450045 China
4 Power China Guiyang Engineering Corporation Limited, Guiyang, 550081 China
12 9 2024
12 9 2024
2024
14 2135929 4 2024
4 9 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
The locked segment is critical for determining the stability of locked segment-type landslides. Research indicates that the volume expansion point marks the transition from the secondary creep stage to the tertiary creep stage in a landslide’s evolution, and also separates the stable crack growth stage from the unstable crack growth stage in the locked segment. Identifying the volume expansion point is essential for early warning and predicting locked segment-type landslides. A series of instruments (resistance strain gauges, acoustic emission system, piezoelectric acceleration sensors, etc.) were used to conduct physical model tests of the landslide with retaining-wall-like locked segment under external load on the landslide’s trailing edge. The evolution process of this landslide was analyzed through changes in slope shape and stress response characteristics. The experimental results reveal the failure mechanism of the landslide with retaining-wall-like locked segment: the upper part of the landslide thrusts and slides, the middle part squeezes and uplifts, the retaining-wall-like locked segment produces a locking effect, and compression-shear fracture of the retaining-wall-like locked segment leads to landslide failure. Based on the deformation and acoustic emission characteristics of the locked segment, a method for identifying the volume expansion point was established. This point was used as the onset of acceleration point in the inverse velocity method to predict the failure time of the locked segment-type landslides, incorporating the three-stage creep model and Fukumoto’s theory.

Keywords

Landslide with retaining-wall-like locked segment
Physical model test
Failure mechanism
Instability prediction
Inverse velocity method
Subject terms

Environmental sciences
Natural hazards
Henan Provincial Science and Technology Research Project, China242102320035 Chen Jia-Xing National Key R&D Program of China2019YFC1509704 Liu Han-Dong issue-copyright-statement© Springer Nature Limited 2024
==== Body
pmcIntroduction

Many scientists have confirmed the existence of locked segments in many large-scale landslides1–8. Large-scale landslides are generally accompanied by the sudden brittle failure of a locked segment on the sliding surface3,9. Landslides can be divided into two types depending on whether there are locked segments that control stability: locked segment type and non-locked segment type10. The key to resolving landslide early warning and prediction is to investigate the evolution of the locked segment's deformation process. Therefore, it is critical to carry out physical model tests to study how landslides with a retaining-wall-like locked segment fail and deform. This research helps in early identification, warning, and prevention of landslide disasters11–15.

Locked segment-type landslides can be divided into five types based on the occurrence characteristics of locked segments: “cross-layer shear,” “bedding direct shear,” “homogeneous rock bridge,” “retaining wall,” and “supporting arch”14. The evolution mechanism and deformation characteristics of locked segment-type landslides vary16–20. Rock bridges play an anti-shear role in slopes with rock bridge-locked segments, and the stability of slopes is mainly controlled by the rock bridges21. There have been many studies on the mechanical properties of rock masses with rock bridge-locked segments22–24, giving rise to rock bridge failure theory25–27. Liu et al.8 proposed that the locked segment-type landslides in western Henan Province, China, mainly include "bedding direct shear type," "cross-layer shear type," and "retaining wall type" based on the area's geological evolution, environmental conditions, and engineering geological characteristics. They chose the Dongmiaojia landslide as a typical example of a landslide with retaining-wall-like locked segment. Zhong et al.28 used the limit equilibrium analysis method to theoretically study the stability of retaining-wall-like locked segments during shear failure mode. Liu et al.29 carried out physical model tests of landslides with retaining-wall-like locked segments under rainfall conditions. They revealed the catastrophic process and macroscopic deformation instability characteristics of these landslides when subjected to rainfall.

The slope’s creep process is divided into three stages (Fig. 1a): (1) primary creep, (2) secondary creep, and (3) tertiary creep. The tertiary creep stage is a key criterion of slope instability14. Researchers have studied the brittle failure behavior of locked segments and established a connection between the creep process of locked segment-type landslides and the deformation and failure of the locked segment (Fig. 1)14,30–33. The deformation and failure process of the locked segment can be divided into five stages (Fig. 1b): (I) crack closure (OA), (II) elastic deformation (AB), (III) stable crack growth (BC), (IV) unstable crack growth (CD), and (V) post-peak failure (DE). The volume expansion point (point C in Fig. 1b) of the locked segment marks the transition from the secondary creep stage to the tertiary creep stage in the slope's evolution. It also indicates the shift from stable crack growth to unstable crack growth in the locked segment31,32,34. Xue et al.10 used the Weibull distribution and renormalization group theory to establish a relationship between shear displacement along the sliding surface and key points like the volume expansion point, peak strength point, and residual strength point, with displacement being the main parameter. They developed a physical prediction model for slopes with locked segments. Once the locked segment is damaged to the volume expansion point, internal cracks rapidly and spontaneously develop, eventually leading to macroscopic fracture35,36, after which sliding and instability occur on the locked segment-type slope. Thus, damage reaching the volume expansion point in the locked segment can serve as the precursor information for the locked segment fracture and the failure of the locked segment-type landslide. There is, however, no systematic or effective method for determining the volume expansion point of locked segments.Fig. 1 (a) Typical creep curve and (b) the deformation and failure process of a rock specimen or locked segment subjected to compressive or shear loading. The symbols (1), (2) and (3) in (a) indicate the primary, secondary and tertiary creep stages, respectively14.

Many researchers believe that the study of landslide failure prediction began in the 1960s, with the Japanese scholar Saito. After decades of development, there are now dozens of landslide failure prediction models, such as the Verhulst model37, grey theory model38–40, catastrophe theory model41, Markov chain theory model42, and inverse velocity prediction model43. The inverse velocity (INV) method considers that the logarithm of the surface displacement velocity is proportional to the logarithm of the surface displacement acceleration during the tertiary creep stage of a landslide43.1 Ω¨=AΩ˙α

where A and α are parameters to be calibrated according to the displacement–time curve; Ω is the displacement; Ω˙ and Ω¨ represent velocity and acceleration, respectively.

Fukuzono (1985) concluded that the inverse velocity of a slope exhibits concave, convex, and linear relationships with time, based on the analysis of slope displacement monitoring data obtained in laboratory experiments. When α ˃ 1, the inverse velocity can be expressed as follows:2 1/v=Aα-11/(α-1)tf-t1/(α-1)

where v is velocity; t is time; and tf is landslide time. When α = 2, the inverse velocity model is linear. The predicted landslide failure time can be obtained by fitting Eq. (2) based on the measured data.

Research shows that when the parameter α equals 2, the linear relationship between inverse velocity and time is a straightforward and effective method for predicting landslides. Many landslide failure predictions have confirmed that linear fitting can achieve better prediction results44–46. Due to its simple characteristics, the INV method is the most widely employed for landslide failure prediction. To improve the accuracy of results, the INV method requires the inverse velocity and time curve after the onset of acceleration (OOA) point, but the accurate determination of the OOA point remains to be studied further. Carlà introduced a method for identifying the OOA point in the INV method. This point is determined by finding where the short-term simple moving average (v-SMA) of velocity intersects with the long-term simple moving average (v-LMA) of velocity47–49. Some researchers suggested that when predicting slope failure using the inverse velocity method, the starting point (SP) for data analysis should be reset after identifying the OOA point. However, they did not specify a method for doing this47,50.

The volume expansion of rock is caused by the increase in inelastic volumetric strain after the elastic stage. At the microscopic level, the volume expansion of rock is caused by the accelerated initiation and tensile expansion of micro-cracks caused by differential stress. Acoustic emission (AE) technology shows that the occurrence of cracks in rock is accompanied by a sharp increase in AE events and energy51,52. Locked segment-type landslides are accompanied by the sudden brittle failure of the locked segment. Studies have shown that the AE events and energy increase significantly before the brittle failure of a rock mass. The volume expansion point marks the transition from the secondary creep stage to the tertiary creep stage in slope evolution. Therefore, AE technology can be used to identify the volume expansion point of the locked segment and the OOA point in the INV method53,54.

Based on the above analysis, current research has conducted some theoretical and physical model tests on locked segment-type landslides, yielding useful scientific results. However, there are only a few studies on the failure mechanisms and instability prediction of landslides with retaining-wall-like locked segments. This paper investigates two key issues: the failure mechanisms and instability prediction of landslides with retaining-wall-like locked segments using the INV method. A series of physical model tests on landslide evolution are carried out using a self-developed testing device designed specifically for these experiments. This study analyzed the deformation evolution process of landslides with retaining-wall-like locked segments under external load on the landslide’s trailing edge and summarized the deformation and AE characteristics of these locked segments. Methods for identifying the volume expansion point, OOA point, and SP point using AE are proposed. The study further reveals the failure mechanism of landslides with retaining-wall-like locked segments, which is crucial for effective slope monitoring and landslide early warning.

Materials and methods

Experimental apparatus

This study used a self-developed physical model test device (Fig. 2) to carry out a series of experiments on landslides with retaining-wall-like locked segment under external load. The physical model test device includes a loading system and a model box. The loading system is connected to a DHS 3816 acquisition instrument via a pressure sensor for load measurements. The size of the model box is 1.15 m × 0.5 m × 0.8 m (length × width × height).Fig. 2 Experimental equipment.

Experimental materials

The test model mainly includes a sliding mass, a sliding belt, and a retaining-wall-like locked segment. The sliding mass is made of silt, and the sliding belt is composed of silty clay. The mechanical parameters of the sliding mass and sliding belt were obtained by indoor direct shear tests (Table 1).Table 1 Model landslide parameters.

Name	Dry density ρd (g/cm3)	Moisture content w (%)	Cohesion c (kPa)	Internal friction angle (°)	
Sliding mass	1.67	16	8.1	31.6	
Sliding belt	1.77	18	9.9	13.5	

The size of the retaining-wall-like locked segment in the model test was 49 cm × 19 cm × 1 cm (length × height × thickness). The angle between the retaining-wall-like locked segment and the sliding belt was 90° (Fig. 2). The retaining-wall-like locked segment was created through complete mixing of gypsum, fine sand, and water. The ratio of water: gypsum: sand was 1:0.8:1. Cylindrical samples, with a sample size of φ50 mm × 100 mm were created. The uniaxial compressive strength was 1.1 MPa as determined by a YAW6206 electro-hydraulic servo pressure testing machine (Fig. 3). The bedrock of the model was fashioned from a combination of gypsum, brick, and mortar, thereby causing it to have a sufficiently high strength and preventing it from deforming.Fig. 3 Uniaxial compressive strength curve.

Experimental measurements

The model tests used micro earth pressure sensors to measure the change in the model’s earth pressure. The earth pressure sensor was of the DMTY type; it was 22 mm in diameter and 6.5 mm thick, with a measuring range of 0–20 kPa and a precision of ≤ 0.5% full scale (FS). During the tests, DHS 3816 recorded the changes in earth pressure inside the slope with an acquisition frequency of 1 Hz. In these model tests, three earth pressure sensors were placed along the central axis of the landslide: one on the trailing edge, one on the retaining-wall-like locked segment, and one on the front edge of the landslide (Fig. 4, drawn by Rhinoceros 6 software, Robert McNeel & Associates, CO, USA).Fig. 4 Layout of sensors.

Resistance strain gauges, acoustic emission systems, and piezoelectric acceleration sensors were used in the model tests to study the displacement and deformation characteristics of the locked segment. Three resistance strain gauges were arranged at the interface between the retaining-wall-like locked segment and the bedrock. The resistance strain gauge was of the BF120-20AA-X30 type, with a sensitivity coefficient of 2.0% and a resistance value of 120.0 Ω. Two piezoelectric acceleration sensors and two acoustic emission sensors were arranged at different positions of the retaining-wall-like locked segment. The piezoelectric acceleration sensor was of the YD-34D type, with a sensitivity of 0.01 V/ms−2, a range of 500 ms−2, and a resolution of 0.002 ms−2. The acoustic emission equipment used was a PCI-II device with R6 acoustic emission probes, and the test surface was made of ceramic material. The preamplifier adopted a 40 dB gain adjustable amplifier, the sampling frequency was 2 MHZ, and the threshold voltage was 100 MV. The model tests employed a data acquisition instrument to dynamically collect data from the strain gauges and acceleration sensors at an acquisition frequency of 100 Hz (Fig. 4). The sensors were calibrated before installation to ensure their sensitivity and accuracy.

The FARO X330 3D laser scanner was used to record the change in the slope’s shape during the evolution and instability of the landslide. The scanning accuracy is ± 1 mm. During the test, the slope surface was scanned once under each load, and the slope shape at different stages was recorded using three-dimensional point cloud data. Then, three-dimensional digital terrain models of the slope shape at different stages were constructed using Surfer (Golden Software, Golden, CO, USA). The deformation characteristics of the slope’s surface during the evolutionary instability process of the landslide with the retaining-wall-like locked segment were studied using the three-dimensional terrain models at different stages. To capture the formation and evolution of landslide cracks, a high-definition camera was used to take regular photographs of the slope surface (Fig. 5).Fig. 5 Landslide model and layout of instruments.

Results and analysis

Stress response and slope deformation characteristics

The model tests were conducted using a self-developed physical model test loading device designed specifically for locked segment-type landslides (Fig. 2). The average loading rate was 200 N/s.

According to the earth pressure and loading process curves (Fig. 6), the landslide was gradually pushed and squeezed from back to front due to the external load, causing the earth pressure to increase as the load increased. During the first loading, the landslide was mainly compacted and consolidated from the retaining-wall-like locked segment towards the trailing edge. The slope shape (Fig. 7) and displacement cloud map (Fig. 8) show that the area from the retaining-wall-like locked segment to the trailing edge was extruded and uplifted due to the external load, with the maximum displacement reaching approximately 1.5 cm.Fig. 6 Curves of earth pressure and load with time.

Fig. 7 Evolution of the landslide with retaining-wall-like locked segment.

Fig. 8 Cumulative vertical displacement cloud maps of the landslide with retaining-wall-like locked segment.

As the load was continuously applied, the earth pressure sensor EPS-1 recorded a decrease at 441 s during the second loading process (Fig. 6). The decrease in earth pressure at EPS-1 indicated that failure occurred in the upper part of the landslide and shear cracks appeared in the trailing edge (Fig. 7).

According to the slope shape (Fig. 7) and displacement cloud map (Fig. 8), the landslide was gradually pushed and squeezed from back to front due to the external load, and the sliding mass from the retaining wall-like locked segment to the trailing edge was extruded and uplifted. With increasing load, the upper part of the landslide was destroyed during the second loading. After the shear failure of the upper part, the irresistible load was gradually transferred to the retaining-wall-like locked segment. The retaining-wall-like locked segment undertook most of the external load, and its vertical displacement was the largest (about 1.5–3 cm).

During the third loading, the landslide was pushed forward under the external load, and the load on the retaining wall-like locked segment gradually increased. The earth pressure at EPS-2 on the retaining wall-like locked segment decreased at 722 s, indicating that compression-shear fracture failure occurred at the retaining-wall-like locked segment under external load. Subsequently, the earth pressure at EPS-3 decreased, and the sliding mass sheared out from the leading edge, forming shear cracks (Fig. 7). This led to the overall failure of the landslide.

According to the vertical displacement cloud map (Fig. 8), after the shear failure of the upper part, the irresistible load was gradually transferred to the retaining-wall-like locked segment. The retaining-wall-like locked segment undertook most of the external load, and the sliding mass at the retaining-wall-like locked segment was extruded and uplifted under the external load. With continuous loading, the retaining-wall-like locked segment reached its shear strength in the third loading process, and the retaining-wall-like locked segment suffered compression-shear fracture failure. The energy stored in the retaining-wall-like locked segment was released after fracturing, resulting in landslide instability and sliding. The landslide displacement increased, and the maximum displacement was about 2–4 cm. At the same time, the sliding mass sheared out from the leading edge, forming shear cracks.

Deformation characteristics of the retaining-wall-like locked segment

The creep process of a landslide is divided into three stages: primary creep, secondary creep, and tertiary creep14. Studies have categorized the deformation and failure process of the locked segment into the crack closure stage, elastic deformation stage, stable crack growth stage, unstable crack growth stage, and post-peak failure stage. These studies have established the relationship between the creep process of locked segment-type landslides and the different stages of deformation and failure in the locked segment (Fig. 1)14,30–32. Building on existing research, this paper summarizes the deformation, acoustic emission, and acceleration characteristics at each stage of the locked segment. It further divides the unstable crack growth stage into two sub-stages: the fracture cluster stage and the energy accumulation stage.

Primary creep stage (oa)

In the early stage of the model test, the landslide was pushed and squeezed under the external load. The retaining-wall-like locked segment was in the compaction stage and the internal cracks were closed. According to the curves of displacement, acceleration, and AE ringing count rate over time (Fig. 9), the locked segment displacement was small at this stage. In the primary creep stage, the locked segment produced a small number of micro-cracks under external load. At this point, there was no discernible change in the locked segment's acceleration, and the acceleration fluctuated slightly when cracks appeared within the locked segment.Fig. 9 Curves of displacement, acceleration, and AE ringing count rate of the retaining-wall-like locked segment with time.

Secondary creep stage (ac)

According to the deformation rate, this stage can be further divided into the elastic deformation stage (ab) and the stable crack growth stage (bc).

Elastic deformation stage (ab)

After the primary creep stage, the landslide was pushed forward from the trailing edge under the external load. The locked segment displacement curve (Figs. 9, 10) shows that the displacement of the locked segment increased steadily under external load, but the growth rate was slow. In the elastic deformation stage, with the continuous application of external load, a small amount of AE events occurred, and the acceleration changed little.Fig. 10 Curves of displacement, AE ringing count, and energy rate of the retaining-wall-like locked segment.

Stable crack growth stage (bc)

After the failure of the upper part of the landslide, the irresistible load was gradually transferred to the retaining-wall-like locked segment. The locked segment undertook most of the external loads, and the displacement growth rate of the locked segment increased (Fig. 10). The near-linear turning point of the displacement curve is the dividing point b from the elastic deformation stage to the stable crack growth stage. The cracks in the locked segment developed during the stable crack growth stage as a result of the external load, and the cumulative ringing count curve rose.

After the secondary creep stage, the landslide entered the tertiary creep stage. The volume expansion point marks the transition from the secondary creep stage to the tertiary creep stage and also serves as the boundary between the stable and unstable crack growth stages of the locked segment31,32,34. Identifying the volume expansion point is a key focus in these model tests. Based on the displacement time curve, Carlà et al.48 proposed that the OOA point in the INV method can be found where the short-term simple moving average (v-SMA) of velocity intersects with the long-term simple moving average (v-LMA) of velocity. This OOA point is usually regarded as the beginning of the tertiary creep stage. Microscopic mechanisms reveal that the volume expansion of rock results from the rapid formation and tensile growth of micro-cracks due to differential stress. AE technology indicates that the occurrence of cracks in rock is accompanied by an increase in AE events and energy51. Therefore, AE technology can be used to identify the volume expansion point. This paper introduces using the ratio of AE accumulative ringing count to accumulative energy (ΣN/ΣE) and the b value to more precisely identify the volume expansion point.

In the damage evolution process of the retaining-wall-like locked segment, ΣN/ΣE is inversely proportional to the cumulative energy. The increase in ΣN/ΣE indicates a large number of low-energy AE events associated with crack propagation in the retaining-wall-like locked segment. The decrease in ΣN/ΣE indicates that a small number of high-energy AE events occurred in the locked segment, with the possibility of fracture failure becoming greater. The b value reflects the inhomogeneity of the rock. ΣN/ΣE shows that during the deformation and failure of the locked segment, a large number of low-energy AE events occurred in the early stage, and ΣN/ΣE did not decrease significantly. At 716.2 s, the ratio of cumulative acoustic emission ringing count to cumulative energy (ΣN/ΣE) decreased, and the b value also decreased, reaching its lowest point at the time of the locked segment's fracture (Fig. 11). Using the method proposed by Carlà et al.48 to identify OOA points (Fig. 12), the v-SMA curve crosses above the v-LMA curve at 716.0 s. Based on the displacement time curve and this analysis, the volume expansion point (point c) of the locked segment in the model test is at 716.2 s.Fig. 11 Volume expansion point identification method.

Fig. 12 Velocity short term moving average (SMA) and velocity long term moving average (LMA).

Tertiary creep stage (ce)

After the volume expansion point (point c) was reached, the damage to the locked segment progressed to the unstable crack growth stage, while the landslide progressed to the tertiary creep stage. The unstable crack growth stage can be further subdivided into the fracture cluster stage (cd) and the energy accumulation stage (de) based on ringing counting rate and energy rate curves (Fig. 10). In the fracture cluster stage (cd), micro-cracks in the locked segment developed densely, releasing a significant amount of energy (point c). This was accompanied by a sharp increase in the cumulative ringing count curve. In the energy accumulation stage (de), the energy released by the internal cracks in the retaining-wall-like locked segment was low, indicating a "quiet period" with minimal energy release. After the energy accumulation stage, the retaining-wall-like locked segment reached its shear strength under external load, and brittle fracture occurred (point e). The energy stored in the locked segment was released, and the energy rate reached its peak (Fig. 10). At the same time, when the retaining-wall-like locked segment fractured, the acceleration at the retaining-wall-like locked segment reached its peak (Fig. 13). After brittle fracture of the locked segment, the deformation rate dropped sharply (Fig. 11).Fig. 13 Curves of displacement, acceleration, and AE cumulative ringing count of the locked segment (tertiary creep stage).

Landslide failure prediction using the inverse velocity method

Based on the previous analysis, a decrease in the AE b value and ΣN/ΣE can be used as criteria for identifying the volume expansion point. For locked segment-type landslides, the volume expansion point is the beginning of the tertiary creep stage, which can be used as the OOA point for predicting failure time using the inverse velocity method.

After determining the volume expansion point and the OOA point, the displacement data following the OOA point were used to predict the failure time using the inverse velocity (INV) method. This was done by applying the velocity, v-SMA, and v-LMA methods individually (Fig. 14).Fig. 14 Linear fitting by the inverse velocity method.

The predicted failure time obtained by linear fitting using the INV method (Table 2) shows that it is close to the actual failure time. The failure time obtained by the three methods, however, has a certain amount of lag.Table 2 Comparison between predicted failure time and actual failure time.

Inverse velocity method	Predicted failure time (s)	Actual failure time (s)	
Velocity	721.73		
v-SMA	721.90	721.60	
v-LMA	721.85		

Landslide failure mechanism

This study analyzed the deformation and stress response characteristics of a landslide with a retaining-wall-like locked segment under external load on the landslide’s trailing edge through physical model tests. The evolution process of the landslide with the retaining-wall-like locked segment can be summarized as follows. Under the action of external load, the trailing edge of the landslide with the retaining-wall-like locked segment gets compacted and compressed, and then gradually pushes forward and gets squeezed. Shear failure and shear cracks appear at the upper part of the landslide. After the failure of the upper part, the sliding mass is gradually pushed and squeezed to the locked segment due to the external loads. Then, the sliding mass transfers the irresistible load to the retaining-wall-like locked segment. The locking effect causes the sliding mass at the trailing edge of the retaining-wall-like locked segment to be squeezed and raised. As the load continues to increase, the sliding mass at the trailing edge of the locked segment pushes and squeezes the retaining-wall-like locked segment, which results in compression-shear fracture failure. Failure of the locked segment leads to the overall failure of the landslide.

The failure mechanism of the landslide with the retaining-wall-like locked segment under external load is as follows: the upper part of the landslide thrusts and slides, the middle part extrudes and uplifts, the retaining-wall-like locked segment produces a locking effect, and compression-shear fracture of the locked segment leads to landslide occurrence.

Discussion

This paper discusses the evolution process of a landslide with retaining-wall-like locked segment under external load and summarizes the deformation and AE characteristics of the locked segment. A method for identifying the volume expansion point and the OOA point in locked segment-type landslides is established. Additionally, the inverse velocity (INV) method is used to predict the landslide failure time. Based on the above research, the failure mechanism of a landslide with retaining-wall-like locked segment under external load is revealed.

The locked segment plays an important role in controlling the stability of locked segment-type landslides. For locked segment-type landslides, the volume expansion point is the beginning of the tertiary creep stage31,32,34, which can be used as the OOA point to predict the time of failure using the INV method. After the OOA point is determined, the failure time can be predicted using the INV method (Table 2). The results show that the failure time prediction of the INV method, using displacement data after the OOA point, is close to the actual failure time, but there is still a certain degree of lag. To address this issue, Bozzano et al.47 proposed that the inverse velocity method should re-select the data starting point (SP) after the OOA point when predicting the landslide time. To address this, a gradual approximation method was used to predict the failure time, starting from the OOA point. The first step involves predicting the failure time using displacement data from after the OOA point at 716.2 s, resulting in a predicted failure time of 721.73 s. The second step uses data from after 716.3 s, leading to a predicted failure time of 721.74 s. The failure time prediction curve is derived by stepwise approximation (Fig. 15). According to this predicted failure time curve (Fig. 15) and the acoustic emission ringing count and energy rate curves (Fig. 10), the predicted failure time aligns with the actual failure time during the energy accumulation stage.Fig. 15 SP point identification.

The energy accumulation stage (719.6 s) was taken as the SP of the INV method. With the update of the monitoring displacement data, the predicted failure time continuously approached the actual failure time (Table 3). The predicted failure time after 721.0 s was consistent with the actual failure time.Table 3 Predicted failure time.

Time (s)	Predicted failure time (s)	Time (s)	Predicted failure time (s)	
719.60	–	720.60	721.746	
719.70	–	720.70	721.710	
719.80	–	720.80	721.671	
719.90	–	720.90	721.610	
720.00	721.799	721.00	721.601	
720.10	722.790	721.10	721.599	
720.20	723.222	721.20	721.596	
720.30	721.986	721.30	721.595	
720.40	721.930	721.40	721.592	
720.50	721.863	721.50	721.593	

Conclusions

This study analyzed the evolution process and failure mechanism of the landslide with retaining-wall-like locked segment under external load based on physical model tests. This study investigates the identification method for the volume expansion point of retaining-wall-like locked segments and uses the inverse velocity method to predict failure time, based on the deformation and acoustic emission characteristics of the locked segment. It also discusses methods for selecting the SP in the inverse velocity method. The main conclusions are summarized as follows.The failure mechanism of the landslide with retaining-wall-like locked segment under external load is revealed based on experimental results: the upper part of the landslide thrusts and slides, the middle part extrudes and uplifts, the retaining-wall-like locked segment produces a locking effect, and compression-shear fracture of the locked segment leads to landslide failure.

Based on the deformation and acoustic emission characteristics of the retaining-wall-like locked segment, this study explains the deformation and instability stages of the retaining-wall-like locked segment. The secondary creep stage in the deformation evolution process of the locked segment is divided into the elastic deformation stage and the stable crack growth stage. The tertiary creep stage is divided into the fracture cluster stage and the energy accumulation stage.

Using acoustic emission data from the deformation and failure of the locked segment, this study establishes methods for identifying the volume expansion point and the OOA point in the inverse velocity method. A decrease in the acoustic emission b value and ΣN/ΣE, along with acoustic emission events with higher energy levels, can be employed as criteria to identify the volume expansion point. For locked segment-type landslides, the volume expansion point marks the transition from the secondary creep stage to the tertiary creep stage. This point can be used as the OOA point in the inverse velocity method. Accurately identifying the volume expansion point is crucial for providing effective early warnings and preventing locked segment-type landslides.

Failure time predictions using the inverse velocity method based on the volume expansion point (OOA point) have a certain degree of lag. To address this, predictions were made based on the deformation and acoustic emission characteristics of the locked segment. The energy accumulation stage was used as the SP point in the inverse velocity method. These predictions were consistent with the actual failure time.

Supplementary Information

Supplementary Information.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-024-72154-z.

Acknowledgements

This study was supported by the Henan Provincial Science and Technology Research Project, China (No. 242102320035) and the National Key R&D Program of China (No. 2019YFC1509704). The authors particularly appreciate the valuable comments made by the editors and reviewers to make a substantial improvement to this manuscript.

Author contributions

J.X.C. wrote the main manuscript text, Z.F.G. and J.J.L. analyzed the data, L.Y.F. and S.L. drew the figures and charts, and H.D.L. revised the manuscript.

Data availability

All data generated or analysed during this study are included in this article and its Supplementary information files.

Competing interests

All authors contributed to the study's conception and design. No conflict of interest exists in this manuscript, and the manuscript is approved by all authors for publication. I would like to declare on behalf of my co-authors that the work described was original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part. All authors read and approved the manuscript. The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
==== Refs
References

1. Zhou Y Simulation analysis of 3D stability of a landslide with a locking segment: A case study of the Tizicao landslide in Maoxian County, southwest China Nat. Hazards Earth Syst. Sci. 2024 24 891 906 10.5194/nhess-24-891-2024
Zhou, Y. et al. Simulation analysis of 3D stability of a landslide with a locking segment: A case study of the Tizicao landslide in Maoxian County, southwest China. Nat. Hazards Earth Syst. Sci. 24, 891–906 (2024).10.5194/nhess-24-891-2024
2. Chen H Qin S Xue L Xu C Why the Xintan landslide was not triggered by the heaviest historical rainfall: Mechanism and review Eng. Geol. 2021 294 106379 10.1016/j.enggeo.2021.106379
Chen, H., Qin, S., Xue, L. & Xu, C. Why the Xintan landslide was not triggered by the heaviest historical rainfall: Mechanism and review. Eng. Geol. 294, 106379 (2021).10.1016/j.enggeo.2021.106379
3. Huang RQ Mechanisms of large-scale landslides in China Bulletin of Engineering Geology and the Environment 2012 71 161 170 10.1007/s10064-011-0403-6
Huang, R. Q. Mechanisms of large-scale landslides in China. Bulletin of Engineering Geology and the Environment 71, 161–170 (2012).10.1007/s10064-011-0403-6
4. Li SY Formation and failure mechanism of the landslide: A case study for Huaipa, Western Henan, China Environ. Earth Sci. 2021 80 478 10.1007/s12665-021-09781-6
Li, S. Y. et al. Formation and failure mechanism of the landslide: A case study for Huaipa, Western Henan, China. Environ. Earth Sci. 80, 478 (2021).10.1007/s12665-021-09781-6
5. Yin YP Sun P Zhang M Li B Mechanism on apparent dip sliding of oblique inclined bedding rockslide at Jiweishan, Chongqing, China Landslides 2011 8 49 65 10.1007/s10346-010-0237-5
Yin, Y. P., Sun, P., Zhang, M. & Li, B. Mechanism on apparent dip sliding of oblique inclined bedding rockslide at Jiweishan, Chongqing, China. Landslides 8, 49–65 (2011).10.1007/s10346-010-0237-5
6. Pan XH Types, formation conditions and pre-decision method for large landslides with potential locked patches J. Eng. Geol. 2014 22 1159 1167
Pan, X. H. et al. Types, formation conditions and pre-decision method for large landslides with potential locked patches. J. Eng. Geol. 22, 1159–1167 (2014).
7. Tang HM An evolution model of large consequent bedding rockslides, with particular reference to the Jiweishan rockslide in Southwest China Eng. Geol. 2015 186 17 27 10.1016/j.enggeo.2014.08.021
Tang, H. M. et al. An evolution model of large consequent bedding rockslides, with particular reference to the Jiweishan rockslide in Southwest China. Eng. Geol. 186, 17–27 (2015).10.1016/j.enggeo.2014.08.021
8. Liu HD Zhang YB Lu LP Types of the locked section landslide in the western Henan Province J. North China Univ. Water Resour. Electr. Power (Natural Science Edition) 2018 39 1 7
Liu, H. D., Zhang, Y. B. & Lu, L. P. Types of the locked section landslide in the western Henan Province. J. North China Univ. Water Resour. Electr. Power (Natural Science Edition) 39, 1–7 (2018).
9. Tang Y Lin H Wang YX Zhao YL Rock slope stability analysis considering the effect of locked section Bull. Eng. Geol. Environ. 2021 80 7241 7251 10.1007/s10064-021-02366-4
Tang, Y., Lin, H., Wang, Y. X. & Zhao, Y. L. Rock slope stability analysis considering the effect of locked section. Bull. Eng. Geol. Environ. 80, 7241–7251 (2021).10.1007/s10064-021-02366-4
10. Xue L Mechanism and physical prediction model of instability of the locked-segment type slopes J. Eng. Geol. 2018 26 179 192
Xue, L. et al. Mechanism and physical prediction model of instability of the locked-segment type slopes. J. Eng. Geol. 26, 179–192 (2018).
11. Zheng Y Chen CX Liu TT Zhang W Song YF Slope failure mechanisms in dipping interbedded sandstone and mudstone revealed by model testing and distinct-element analysis Bull. Eng. Geol. Environ. 2018 77 49 68 10.1007/s10064-017-1007-6
Zheng, Y., Chen, C. X., Liu, T. T., Zhang, W. & Song, Y. F. Slope failure mechanisms in dipping interbedded sandstone and mudstone revealed by model testing and distinct-element analysis. Bull. Eng. Geol. Environ. 77, 49–68 (2018).10.1007/s10064-017-1007-6
12. Smith A Dixon N Fowmes GJ Early detection of first-time slope failures using acoustic emission measurements: Large-scale physical modelling Geotechnique 2017 67 138 152 10.1680/jgeot.15.P.200
Smith, A., Dixon, N. & Fowmes, G. J. Early detection of first-time slope failures using acoustic emission measurements: Large-scale physical modelling. Geotechnique 67, 138–152 (2017).10.1680/jgeot.15.P.200
13. Eberhardt E Twenty-ninth Canadian geotechnical colloquium: The role of advanced numerical methods and geotechnical field measurements in understanding complex deep-seated rock slope failure mechanisms CaGeJ 2008 45 484 510
Eberhardt, E. Twenty-ninth Canadian geotechnical colloquium: The role of advanced numerical methods and geotechnical field measurements in understanding complex deep-seated rock slope failure mechanisms. CaGeJ 45, 484–510 (2008).
14. Chen HR Qin SQ Xue L Yang BC Zhang K A physical model predicting instability of rock slopes with locked segments along a potential slip surface Eng. Geol. 2018 242 34 43 10.1016/j.enggeo.2018.05.012
Chen, H. R., Qin, S. Q., Xue, L., Yang, B. C. & Zhang, K. A physical model predicting instability of rock slopes with locked segments along a potential slip surface. Eng. Geol. 242, 34–43 (2018).10.1016/j.enggeo.2018.05.012
15. Liu H-D Liu J-J Chen J-X Guo Z-F Qiu L Experimental study on tilting deformation and a new method for landslide prediction with retaining-wall locked segment Sci. Rep. 2023 13 5149 10.1038/s41598-023-32477-9 36991041
Liu, H.-D., Liu, J.-J., Chen, J.-X., Guo, Z.-F. & Qiu, L. Experimental study on tilting deformation and a new method for landslide prediction with retaining-wall locked segment. Sci. Rep. 13, 5149 (2023).36991041 10.1038/s41598-023-32477-9
16. Huang RQ Chen GQ Tang P Precursor information of locking segment landslides based on transient characteristics Chin. J. Rock Mech. Eng. 2017 36 521 533
Huang, R. Q., Chen, G. Q. & Tang, P. Precursor information of locking segment landslides based on transient characteristics. Chin. J. Rock Mech. Eng. 36, 521–533 (2017).
17. Chen GQ Zhang Y Huang RQ Guo F Zhang GF Failure mechanism of rock bridge based on acoustic emission technique J. Sens. 2015 2015 964730 10.1155/2015/964730
Chen, G. Q., Zhang, Y., Huang, R. Q., Guo, F. & Zhang, G. F. Failure mechanism of rock bridge based on acoustic emission technique. J. Sens. 2015, 964730 (2015).10.1155/2015/964730
18. Liu H Zhao Y Dong J Wang Z Experimental study of the dynamic response and failure mode of anti-dip rock slopes Bull. Eng. Geol. Environ. 2021 80 6583 6596 10.1007/s10064-021-02313-3
Liu, H., Zhao, Y., Dong, J. & Wang, Z. Experimental study of the dynamic response and failure mode of anti-dip rock slopes. Bull. Eng. Geol. Environ. 80, 6583–6596 (2021).10.1007/s10064-021-02313-3
19. Liu H-D Experimental study on the evolution mechanism of landslide with retaining wall locked segment Geofluids 2022 2022 7923448
Liu, H.-D. et al. Experimental study on the evolution mechanism of landslide with retaining wall locked segment. Geofluids 2022, 7923448 (2022).
20. Bao M Experimental study on the sliding instability mechanism of slopes with weak layers under creeping action Measurement 2023 212 112690 10.1016/j.measurement.2023.112690
Bao, M. et al. Experimental study on the sliding instability mechanism of slopes with weak layers under creeping action. Measurement 212, 112690 (2023).10.1016/j.measurement.2023.112690
21. Tang P Chen G-Q Huang R-Q Zhu J Brittle failure of rockslides linked to the rock bridge length effect Landslides 2020 17 793 803 10.1007/s10346-019-01323-3
Tang, P., Chen, G.-Q., Huang, R.-Q. & Zhu, J. Brittle failure of rockslides linked to the rock bridge length effect. Landslides 17, 793–803 (2020).10.1007/s10346-019-01323-3
22. Prudencio M Jan MVS Strength and failure modes of rock mass models with non-persistent joints Int. J. Rock Mech. Min. Sci. 2007 44 890 902 10.1016/j.ijrmms.2007.01.005
Prudencio, M. & Jan, M. V. S. Strength and failure modes of rock mass models with non-persistent joints. Int. J. Rock Mech. Min. Sci. 44, 890–902 (2007).10.1016/j.ijrmms.2007.01.005
23. Li H Experimental and numerical study on the mechanical behaviors and crack propagation of sandstone containing two parallel fissures ThAFM 2023 126 103965
Li, H. et al. Experimental and numerical study on the mechanical behaviors and crack propagation of sandstone containing two parallel fissures. ThAFM 126, 103965 (2023).
24. Chen GQ Critical tension crack depth in rockslides that conform to the three-section mechanism Landslides 2021 18 79 88 10.1007/s10346-020-01471-x
Chen, G. Q. et al. Critical tension crack depth in rockslides that conform to the three-section mechanism. Landslides 18, 79–88 (2021).10.1007/s10346-020-01471-x
25. Kemeny J Time-dependent drift degradation due to the progressive failure of rock bridges along discontinuities Int. J. Rock Mech. Min. Sci. 2005 42 35 46 10.1016/j.ijrmms.2004.07.001
Kemeny, J. Time-dependent drift degradation due to the progressive failure of rock bridges along discontinuities. Int. J. Rock Mech. Min. Sci. 42, 35–46 (2005).10.1016/j.ijrmms.2004.07.001
26. Dong JY Wang C Huang ZQ Yang JH Xue L Dynamic response characteristics and instability criteria of a slope with a middle locked segment Soil Dyn. Earthq. Eng. 2021 150 106899 10.1016/j.soildyn.2021.106899
Dong, J. Y., Wang, C., Huang, Z. Q., Yang, J. H. & Xue, L. Dynamic response characteristics and instability criteria of a slope with a middle locked segment. Soil Dyn. Earthq. Eng. 150, 106899 (2021).10.1016/j.soildyn.2021.106899
27. Hu K Zhao X-Y Zhang G-Z Dynamic behaviors of rockslides subjected to brittle failure of locked segments J. Mt. Sci. 2023 20 532 541 10.1007/s11629-022-7470-y
Hu, K., Zhao, X.-Y. & Zhang, G.-Z. Dynamic behaviors of rockslides subjected to brittle failure of locked segments. J. Mt. Sci. 20, 532–541 (2023).10.1007/s11629-022-7470-y
28. Zhong Z Huang D Huang RQ Anti-sliding stability of locked patch of rock slopes with landslide mode of retaining wall collapse Chin. J. Geotech. Eng. 2016 39 1734 1740
Zhong, Z., Huang, D. & Huang, R. Q. Anti-sliding stability of locked patch of rock slopes with landslide mode of retaining wall collapse. Chin. J. Geotech. Eng. 39, 1734–1740 (2016).
29. Liu HD Li DD Wang ZF Geng Z Li LD Physical modeling on failure mechanism of locked-segment landslides triggered by heavy precipitation Landslides 2020 17 459 469 10.1007/s10346-019-01288-3
Liu, H. D., Li, D. D., Wang, Z. F., Geng, Z. & Li, L. D. Physical modeling on failure mechanism of locked-segment landslides triggered by heavy precipitation. Landslides 17, 459–469 (2020).10.1007/s10346-019-01288-3
30. Qin SQ Wang YY Ma P Exponential laws of critical displacement evolution for landslides and avalanches Chin. J. Rock Mech. Eng. 2010 29 873 880
Qin, S. Q., Wang, Y. Y. & Ma, P. Exponential laws of critical displacement evolution for landslides and avalanches. Chin. J. Rock Mech. Eng. 29, 873–880 (2010).
31. Xue L Qin SQ Pan XH Chen HR Yang BC A possible explanation of the stair-step brittle deformation evolutionary pattern of a rockslide Geomat. Nat. Hazards Risk 2017 8 1456 1476 10.1080/19475705.2017.1345793
Xue, L., Qin, S. Q., Pan, X. H., Chen, H. R. & Yang, B. C. A possible explanation of the stair-step brittle deformation evolutionary pattern of a rockslide. Geomat. Nat. Hazards Risk 8, 1456–1476 (2017).10.1080/19475705.2017.1345793
32. Xue L New quantitative displacement criteria for slope deformation process: From the onset of the accelerating creep to brittle rupture and final failure Eng. Geol. 2014 182 79 87 10.1016/j.enggeo.2014.08.007
Xue, L. et al. New quantitative displacement criteria for slope deformation process: From the onset of the accelerating creep to brittle rupture and final failure. Eng. Geol. 182, 79–87 (2014).10.1016/j.enggeo.2014.08.007
33. Yang B Qin S Xue L Chen H The reasonable range limit of the Shape parameter in the Weibull distribution for describing the brittle failure behavior of rocks Rock Mech. Rock Eng. 2021 54 3359 3367 10.1007/s00603-021-02414-1
Yang, B., Qin, S., Xue, L. & Chen, H. The reasonable range limit of the Shape parameter in the Weibull distribution for describing the brittle failure behavior of rocks. Rock Mech. Rock Eng. 54, 3359–3367 (2021).10.1007/s00603-021-02414-1
34. Pan X-H Sun H-Y Wu Z-J Lü Q Study of the failure mechanism and progressive failure process of intact rock patches of rock slope with weak surfaces Rock Mech. Rock Eng. 2017 50 951 966 10.1007/s00603-016-1143-5
Pan, X.-H., Sun, H.-Y., Wu, Z.-J. & Lü, Q. Study of the failure mechanism and progressive failure process of intact rock patches of rock slope with weak surfaces. Rock Mech. Rock Eng. 50, 951–966 (2017).10.1007/s00603-016-1143-5
35. Zhao XG Cai M A mobilized dilation angle model for rocks Int. J. Rock Mech. Min. Sci. 2010 47 368 384 10.1016/j.ijrmms.2009.12.007
Zhao, X. G. & Cai, M. A mobilized dilation angle model for rocks. Int. J. Rock Mech. Min. Sci. 47, 368–384 (2010).10.1016/j.ijrmms.2009.12.007
36. Alejano L Alonso E Considerations of the dilatancy angle in rocks and rock masses Int. J. Rock Mech. Min. Sci. 2005 42 481 507 10.1016/j.ijrmms.2005.01.003
Alejano, L. & Alonso, E. Considerations of the dilatancy angle in rocks and rock masses. Int. J. Rock Mech. Min. Sci. 42, 481–507 (2005).10.1016/j.ijrmms.2005.01.003
37. Li X Kong J Wang Z Landslide displacement prediction based on combining method with optimal weight Nat. Hazards 2012 61 635 646 10.1007/s11069-011-0051-y
Li, X., Kong, J. & Wang, Z. Landslide displacement prediction based on combining method with optimal weight. Nat. Hazards 61, 635–646 (2012).10.1007/s11069-011-0051-y
38. Li SH Wu LZ Chen JJ Huang RQ Multiple data-driven approach for predicting landslide deformation Landslides 2020 17 709 718 10.1007/s10346-019-01320-6
Li, S. H., Wu, L. Z., Chen, J. J. & Huang, R. Q. Multiple data-driven approach for predicting landslide deformation. Landslides 17, 709–718 (2020).10.1007/s10346-019-01320-6
39. Zhang W Xiao R Shi B Zhu H-H Sun Y-J Forecasting slope deformation field using correlated grey model updated with time correction factor and background value optimization Eng. Geol. 2019 260 105215 10.1016/j.enggeo.2019.105215
Zhang, W., Xiao, R., Shi, B., Zhu, H.-H. & Sun, Y.-J. Forecasting slope deformation field using correlated grey model updated with time correction factor and background value optimization. Eng. Geol. 260, 105215 (2019).10.1016/j.enggeo.2019.105215
40. Xu J Ni Y Prediction of grey-catastrophe destabilization time of a granite residual soil slope under rainfall Bull. Eng. Geol. Environ. 2019 78 5687 5693 10.1007/s10064-019-01510-5
Xu, J. & Ni, Y. Prediction of grey-catastrophe destabilization time of a granite residual soil slope under rainfall. Bull. Eng. Geol. Environ. 78, 5687–5693 (2019).10.1007/s10064-019-01510-5
41. Tao Y Cao J Hu J Dai Z A cusp catastrophe model of mid–long-term landslide evolution over low latitude highlands of China Geomo 2013 187 80 85 10.1016/j.geomorph.2012.12.036
Tao, Y., Cao, J., Hu, J. & Dai, Z. A cusp catastrophe model of mid–long-term landslide evolution over low latitude highlands of China. Geomo 187, 80–85 (2013).10.1016/j.geomorph.2012.12.036
42. Das I Stein A Kerle N Dadhwal VK Landslide susceptibility mapping along road corridors in the Indian Himalayas using Bayesian logistic regression models Geomo 2012 179 116 125 10.1016/j.geomorph.2012.08.004
Das, I., Stein, A., Kerle, N. & Dadhwal, V. K. Landslide susceptibility mapping along road corridors in the Indian Himalayas using Bayesian logistic regression models. Geomo 179, 116–125 (2012).10.1016/j.geomorph.2012.08.004
43. Fukuzono T A method to predict the time of slope failure caused by rainfall using the inverse number of velocity of surface displacement J. Jpn. Landslide Soc. 1985 22 8 13
Fukuzono, T. A method to predict the time of slope failure caused by rainfall using the inverse number of velocity of surface displacement. J. Jpn. Landslide Soc. 22, 8–13 (1985).
44. Segalini A Valletta A Carri A Landslide time-of-failure forecast and alert threshold assessment: A generalized criterion Eng. Geol. 2018 245 72 80 10.1016/j.enggeo.2018.08.003
Segalini, A., Valletta, A. & Carri, A. Landslide time-of-failure forecast and alert threshold assessment: A generalized criterion. Eng. Geol. 245, 72–80 (2018).10.1016/j.enggeo.2018.08.003
45. Rose ND Hungr O Forecasting potential rock slope failure in open pit mines using the inverse-velocity method Int. J. Rock Mech. Min. Sci. 2007 44 308 320 10.1016/j.ijrmms.2006.07.014
Rose, N. D. & Hungr, O. Forecasting potential rock slope failure in open pit mines using the inverse-velocity method. Int. J. Rock Mech. Min. Sci. 44, 308–320 (2007).10.1016/j.ijrmms.2006.07.014
46. Zhou X-P Liu L-J Xu C A modified inverse-velocity method for predicting the failure time of landslides Eng. Geol. 2020 268 105521 10.1016/j.enggeo.2020.105521
Zhou, X.-P., Liu, L.-J. & Xu, C. A modified inverse-velocity method for predicting the failure time of landslides. Eng. Geol. 268, 105521 (2020).10.1016/j.enggeo.2020.105521
47. Bozzano F Mazzanti P Moretto S Discussion to: ‘Guidelines on the use of inverse velocity method as a tool for setting alarm thresholds and forecasting landslides and structure collapses’ by T. Carlà, E. Intrieri, F. Di Traglia, T. Nolesini G. Gigli and N. Casagli Landslides 2018 15 1437 1441 10.1007/s10346-018-0976-2
Bozzano, F., Mazzanti, P. & Moretto, S. Discussion to: ‘Guidelines on the use of inverse velocity method as a tool for setting alarm thresholds and forecasting landslides and structure collapses’ by T. Carlà, E. Intrieri, F. Di Traglia, T. Nolesini G. Gigli and N. Casagli. Landslides 15, 1437–1441 (2018).10.1007/s10346-018-0976-2
48. Carlà T Guidelines on the use of inverse velocity method as a tool for setting alarm thresholds and forecasting landslides and structure collapses Landslides 2017 14 517 534 10.1007/s10346-016-0731-5
Carlà, T. et al. Guidelines on the use of inverse velocity method as a tool for setting alarm thresholds and forecasting landslides and structure collapses. Landslides 14, 517–534 (2017).10.1007/s10346-016-0731-5
49. Carlà T Reply to discussion on “Guidelines on the use of inverse velocity method as a tool for setting alarm thresholds and forecasting landslides and structure collapses” by F. Bozzano, P. Mazzanti, and S. Moretto Landslides 2018 15 1443 1444 10.1007/s10346-018-0991-3
Carlà, T. et al. Reply to discussion on “Guidelines on the use of inverse velocity method as a tool for setting alarm thresholds and forecasting landslides and structure collapses” by F. Bozzano, P. Mazzanti, and S. Moretto. Landslides 15, 1443–1444 (2018).10.1007/s10346-018-0991-3
50. Dick GJ Eberhardt E Cabrejo-Lievano AG Stead D Rose ND Development of an early-warning time-of-failure analysis methodology for open-pit mine slopes utilizing ground-based slope stability radar monitoring data CaGeJ 2015 52 515 529
Dick, G. J., Eberhardt, E., Cabrejo-Lievano, A. G., Stead, D. & Rose, N. D. Development of an early-warning time-of-failure analysis methodology for open-pit mine slopes utilizing ground-based slope stability radar monitoring data. CaGeJ 52, 515–529 (2015).
51. Moradian OZ Einstein H Ballivy G Detection of cracking levels in brittle rocks by parametric analysis of the acoustic emission signals Rock Mech. Rock Eng. 2016 49 785 800 10.1007/s00603-015-0775-1
Moradian, O. Z., Einstein, H. & Ballivy, G. Detection of cracking levels in brittle rocks by parametric analysis of the acoustic emission signals. Rock Mech. Rock Eng. 49, 785–800 (2016).10.1007/s00603-015-0775-1
52. Li S Yang D Huang Z Gu Q Zhao K Acoustic emission characteristics and failure mode analysis of rock failure under complex stress state ThAFM 2022 122 103666
Li, S., Yang, D., Huang, Z., Gu, Q. & Zhao, K. Acoustic emission characteristics and failure mode analysis of rock failure under complex stress state. ThAFM 122, 103666 (2022).
53. Meng Q Zhang M Han L Pu H Li H Effects of size and strain rate on the mechanical behaviors of rock specimens under uniaxial compression Arab. J. Geosci. 2016 9 527 10.1007/s12517-016-2559-7
Meng, Q., Zhang, M., Han, L., Pu, H. & Li, H. Effects of size and strain rate on the mechanical behaviors of rock specimens under uniaxial compression. Arab. J. Geosci. 9, 527 (2016).10.1007/s12517-016-2559-7
54. Chen J Ye Y Pu Y Xu W Mengli D Experimental study on uniaxial compression failure modes and acoustic emission characteristics of fissured sandstone under water saturation ThAFM 2022 119 103359
Chen, J., Ye, Y., Pu, Y., Xu, W. & Mengli, D. Experimental study on uniaxial compression failure modes and acoustic emission characteristics of fissured sandstone under water saturation. ThAFM 119, 103359 (2022).
