sustainability-logo

Journal Browser

Journal Browser

Slope Stability Analysis and Landslide Disaster Prevention

A special issue of Sustainability (ISSN 2071-1050). This special issue belongs to the section "Sustainable Engineering and Science".

Deadline for manuscript submissions: closed (1 May 2024) | Viewed by 37899

Special Issue Editors


E-Mail Website
Guest Editor
Department of Civil Engineering, Beijing Forestry University, Beijing 100083, China
Interests: slope stability; landslide disaster prevention; ecological geotechnical engineering; constitutive modeling; numerical simulation

E-Mail Website
Guest Editor
School of Soil and Water Conservation, Beijing Forestry University, Beijing 100083, China
Interests: slope stability; root reinforcement; plant root testing; fieldwork; analytical modeling; numerical simulation
School of Soil and Water Conservation, Beijing Forestry University, Beijing 100083, China
Interests: landslide; debris flow; fieldwork; analytical modeling; numerical simulation
School of Soil and Water Conservation, Beijing Forestry University, Beijing 100083, China
Interests: soil microstructure; soil dynamic behavior; root reinforcement; ecological geotechnical engineering

Special Issue Information

Dear Colleagues,

Geologic disasters cause enormous losses of human lives and properties and serious ecological environment imbalances. Geologic disaster prevention and mitigation are essential, especially considering the effects of global climate change. New methods, technology, and materials are crucial to assessing slope stability and geologic disaster prevention. The improved numerical method enables simulations of complex geological site conditions and provides a deeper understanding of slope failure on the micro-level. Advanced experimental equipment and methods allow better prediction and evaluation of slope failure mechanisms.

Given these developments, this Special Issue invites original submissions, including recent advances in any aspect of slope stability and geologic disasters prevention from theoretical, numerical, or experimental perspectives.

Topics may include but are not limited to:

  • Landslides;
  • Debris flows;
  • Mountain hazards;
  • Slope stability evaluation;
  • Engineering geology and geological engineering;
  • Geomechanics numerical simulation;
  • Strong seismic motion and geological hazard;
  • Disaster prevention strategy and management;
  • Geological disaster monitoring, warning, and risk assessment;
  • Hydropower engineering geological disaster prevention;
  • Climate change and disaster prevention technology;
  • Integrated disaster risk governance—assessment and management;
  • Ecological geotechnical engineering;
  • Soil freezing and thawing;
  • Water loss and soil erosion.

Dr. Jiankun Huang
Prof. Dr. Yunqi Wang
Dr. Liqun Lyu
Dr. Jun Li
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Sustainability is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mountain hazards
  • slope stability
  • numerical method
  • landslide disaster prevention
  • disaster monitoring
  • disaster warning
  • risk assessment
  • ecological geotechnical engineering
  • soil erosion

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue polices can be found here.

Published Papers (21 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

23 pages, 12248 KiB  
Article
Effect of the Connectivity of Weak Rock Zones on the Mining-Induced Deformation of Rock Slopes in an Open-Pit Mine
by Cheng Zhang, Amagu amagu Clement, Jun-ichi Kodama, Atsushi Sainoki, Yoshiaki Fujii, Daisuke Fukuda and Shuren Wang
Sustainability 2024, 16(14), 5974; https://doi.org/10.3390/su16145974 - 12 Jul 2024
Cited by 2 | Viewed by 1781
Abstract
Geological structures significantly influence mining-induced deformations in open-pit mines, with their variations and interactions adding complexity to the excavation process and introducing uncertainties in deformation outcomes. This study utilized numerical simulations to analyze the impact of weak rock zones in a specific open-pit [...] Read more.
Geological structures significantly influence mining-induced deformations in open-pit mines, with their variations and interactions adding complexity to the excavation process and introducing uncertainties in deformation outcomes. This study utilized numerical simulations to analyze the impact of weak rock zones in a specific open-pit limestone quarry in Japan on mining-induced deformation. The simulation results were both qualitatively and quantitatively validated against field measurements, enhancing the reliability of the findings. Subsequently, four conceptual models were developed based on the characteristics of the quarry to investigate the mechanisms by which weak rock zones affect rock slope deformations. Our analyses demonstrated that slip deformation occurred exclusively when two weak rock zones were connected. This deformation was associated not only with shear failure in the upper weak rock zone but also with the contraction and bending of the lower weak rock zone. Furthermore, the simulation results were consistent with field data and supported by the conceptual models, confirming that the proposed sliding mechanisms can effectively explain the observed deformation behaviors. The insights gained from these models provide valuable references for managing similar geological challenges in other open-pit mines. Full article
(This article belongs to the Special Issue Slope Stability Analysis and Landslide Disaster Prevention)
Show Figures

Figure 1

18 pages, 23726 KiB  
Article
Solidification Mechanism of Bayer Red Mud under the Action of Calcium Hydroxide
by Zhiwei Song, Guoju Ke, Pengju Qin, Suli Han, Xiuhua Guo and Zhiqiang Zhang
Sustainability 2024, 16(11), 4770; https://doi.org/10.3390/su16114770 - 4 Jun 2024
Viewed by 884
Abstract
Because of the strong alkalinity of red mud, it is difficult to recycle, and the long-term accumulation of red mud causes environmental pollution. The study shows that the solidification characteristics of bayer red mud (RM) under the action of Ca(OH)2 (CH) are [...] Read more.
Because of the strong alkalinity of red mud, it is difficult to recycle, and the long-term accumulation of red mud causes environmental pollution. The study shows that the solidification characteristics of bayer red mud (RM) under the action of Ca(OH)2 (CH) are obvious. The mechanical properties of Bayer RM paste with different amounts of CH at different ages were tested. The strength of RMCH gradually increases with the increase in CH content and age, reaching a turning point in strength at 26.4% content of CH, with the highest strength at 28 days, reaching 2.73 MPa. The solidification products were characterized by XRD, FTIR, TG-DTG, and SEM-EDS. The results show that under the action of CH, the main solidification products of RM are C-(A)-S-H, hemicarboaluminate, and monocarboaluminate. In the solidification process, hydroxysodalite and faujasite-Na react with CH to generate C-S-H, Al(OH)4, and Na+, then react to generate hemicarboaluminate, monocarboaluminate and C-(A)-S-H, among which hemicarboaluminate is transformed into monocarboaluminate in the presence of calcite, and further monocarboaluminate decomposes to generate calcite. It provides a basis for the study of the interaction mechanism between a single substance and RM and provides a research basis for the sustainable utilization of red mud. Full article
(This article belongs to the Special Issue Slope Stability Analysis and Landslide Disaster Prevention)
Show Figures

Figure 1

16 pages, 4538 KiB  
Article
Influence of Calculation Parameters on the Slope Stability of the Historical Rasos Cemetery in Vilnius (Lithuania)
by Ryszard Chmielewski, Aleksandra Bąk, Paweł Muzolf and Kamil Sobczyk
Sustainability 2024, 16(7), 2891; https://doi.org/10.3390/su16072891 - 30 Mar 2024
Cited by 2 | Viewed by 1034
Abstract
Many objects of cultural and religious importance are located on naturally or artificially shaped hills. In such cases, the stability of the slopes determines both the safety of users and the facilities themselves and thus the preservation of cultural heritage. The analysis of [...] Read more.
Many objects of cultural and religious importance are located on naturally or artificially shaped hills. In such cases, the stability of the slopes determines both the safety of users and the facilities themselves and thus the preservation of cultural heritage. The analysis of the slope stability requires the assessment of the soil shear strength, defined as the ratio of resistance forces to driving forces. An important issue in the slope stability analysis is the proper determination of soil mechanical parameters, including their changes due to soil moisture. This paper presents an assessment of the slope stability of the Rasos Cemetery in Vilnius (Lithuania), where, due to a partial slope sliding, some of the tombstones were destroyed by being covered with soil. An analysis of the slope stability (factor of safety) was performed for two cross-sections using six calculation schemes. In each of them, calculations were carried out for three groups of soil parameters and for four design approaches (characteristic values, DA2, DA3a, and DA3b in accordance with the geotechnical standard applicable in the European Union—Eurocode 7: Geotechnical design). For the calculation approach (DA3a) for different groups of soil parameters, the values of the slope stability factors of safety were practically below 1.0. If the value of the factor of safety is less than 1.0, the slope is unstable. In the range of values 1.0–1.3, there is a serious risk of slope instability, and only when the factor of safety value reaches above 1.3 is the slope classified as stable. The comparison of the slope stability factors obtained with different design approaches (in relation to the DA3a) shows that the most unfavorable stability factor is approximately 43% lower than the result obtained from the characteristic values, approximately 21% lower than the result obtained using the DA2 design approach, and approximately 24% lower than the result obtained using the DA3b design approach. The analytical and numerical method (GEO5) analysis showed that, regardless of the adopted calculation approach, the required slope stability factor was not obtained. The article shows that selecting the correct geological cross-section to determine the critical slope slip surface and adopting the relevant design approach is crucial for slope sustainability. Based on the analysis, a proprietary solution for the construction work was proposed, which will ensure both the full stability of the slope and the safety of all graves and consequently landslide disaster prevention. Full article
(This article belongs to the Special Issue Slope Stability Analysis and Landslide Disaster Prevention)
Show Figures

Figure 1

21 pages, 8941 KiB  
Article
Slope Stability Analysis Based on the Explicit Smoothed Particle Finite Element Method
by Xichun Jia, Xuebing Jiang, Jun Huang, Shunchao Yu and Bingjun Liu
Sustainability 2024, 16(2), 702; https://doi.org/10.3390/su16020702 - 13 Jan 2024
Cited by 3 | Viewed by 1520
Abstract
A landslide is a common natural disaster that causes environmental damage, casualties and economic losses, which seriously affects the sustainable development of society. In geomechanics, it is one of the largest deformation problems. Herein, the GPU-accelerated explicit smoothed particle finite element method (eSPFEM) [...] Read more.
A landslide is a common natural disaster that causes environmental damage, casualties and economic losses, which seriously affects the sustainable development of society. In geomechanics, it is one of the largest deformation problems. Herein, the GPU-accelerated explicit smoothed particle finite element method (eSPFEM) for large deformation analysis in geomechanics was developed on the CUDA platform based on high-performance computing using a self-designed eSPFEM program code. The eSPFEM combines the strain smoothing nodal integration techniques found in the particle finite element method (PFEM) framework, which allows for the use of low-order triangular elements without volume locking and avoids frequent information transfer and mapping errors between Gaussian points and particles in PFEM. A numerical simulation of slope instability using the eSPFEM and based on a strength reduction technique was conducted using various examples, including a cohesive homogeneous slope, a non-cohesive homogeneous slope, a non-homogeneous slope and a slope with a thin soft band. The calculation results show that the eSPFEM can be applied to slope stability analysis under different working conditions, simulating the entire process of slope instability initiation, sliding and reaccumulation, and obtaining reliable FOS values. A numerical simulation was conducted to analyse a landslide that occurred in the Zhangjiazhuang tunnel on the Lanzhou–Xinjiang high-speed railway line on 18 January 2016. A natural unsaturated soil slope, a soil slope with a high moisture content and a soil slope with a high moisture content subjected to an earthquake were analysed. The findings of this study are in good agreement with the actual slope failure conditions. The primary triggers identified for the landslide were heavy rainfall and earthquakes. The verification results indicate that the eSPFEM can effectively simulate an actual landslide case, showcasing high accuracy and applicability in simulating the large deformation behaviour of landslides. Full article
(This article belongs to the Special Issue Slope Stability Analysis and Landslide Disaster Prevention)
Show Figures

Figure 1

18 pages, 18435 KiB  
Article
The Momentum Transfer Mechanism of a Landslide Intruding a Body of Water
by Zhenzhu Meng, Jianyong Hu, Jinxin Zhang, Lijuan Zhang and Zhenxia Yuan
Sustainability 2023, 15(18), 13940; https://doi.org/10.3390/su151813940 - 20 Sep 2023
Cited by 1 | Viewed by 1023
Abstract
Landslide-generated waves occur as a result of the intrusion of landslides such as mud flows and debris flows into bodies of water such as lakes and reservoirs. The objective of this study was to determine how the momentum is transferred from the sliding [...] Read more.
Landslide-generated waves occur as a result of the intrusion of landslides such as mud flows and debris flows into bodies of water such as lakes and reservoirs. The objective of this study was to determine how the momentum is transferred from the sliding mass to the body of water on the basis of theoretical analysis and physical model experiments. Considering the viscoplastic idealization of natural landslides, the theoretical model was established based on the momentum and mass conservation of a two-phase flow in a control volume. To close the theoretical equations, slide thickness and velocity passing through the left boundary of the control volume were estimated by lubrication theory, and the interaction forces between the slide phase and water phase, including hydrostatic force and drag force, were given by semiempirical equations fitted with experimental data obtained using the particle image velocimetry (PIV) technique. The near-field velocity fields of both the sliding mass and the body of water, as well as the air–water–slide interfaces, were determined from the experiments. The theoretical model was validated by comparing the theoretical and experimental data of the slide thickness and slide velocity, as well as the momentum variations of the two phases in the control volume. Full article
(This article belongs to the Special Issue Slope Stability Analysis and Landslide Disaster Prevention)
Show Figures

Figure 1

24 pages, 8001 KiB  
Article
One-Dimensional Compressibility and Creep Characteristics of Unsaturated Compacted Loess Based on Incremental Loading and Constant Rate of Strain Methods
by Pengju Qin, Qingchen Yan, Yu Lu, Chungang Yang, Zhiwei Song and Chunbao Li
Sustainability 2023, 15(18), 13854; https://doi.org/10.3390/su151813854 - 18 Sep 2023
Cited by 3 | Viewed by 1347
Abstract
In engineering practice, unsaturated compacted loess is often utilized as a filling material in the loess regions. The loess inevitably undergoes one-dimensional compressibility and creep deformation due to the long-term effects of the upper soil layers and buildings. When the deformation is large [...] Read more.
In engineering practice, unsaturated compacted loess is often utilized as a filling material in the loess regions. The loess inevitably undergoes one-dimensional compressibility and creep deformation due to the long-term effects of the upper soil layers and buildings. When the deformation is large enough, it tends to damage buildings and threaten engineering safety. In this regard, the one-dimensional compressibility and creep properties of unsaturated compacted loess based on incremental loading (IL) and constant rate of strain (CRS) methods have been studied. First, soil materials with an initial moisture content of 15% were prepared and then compacted into soil samples with an 80 mm diameter and a 10 mm height. Second, the compressibility and creep properties of the compacted loess samples obtained via the IL and CRS compression tests were compared and analyzed. In this study, several parameters, including the primary compression index Cc and secondary compression index Cα, were derived. Meanwhile, the moisture content of the samples was measured via electrical resistivity methods. Finally, the microstructural characteristics were derived via nuclear magnetic resonance (NMR) and scanning electron microscopy (SEM) tests. The results showed that Cc and Cα increased with the increase in moisture content and vertical stress; Cα/Cc ranged from 0.026 to 0.042. Compared with the compression parameters and deformation of the samples, those obtained via the CRS tests are a little larger than those obtained via the IL tests for a given loading and initial moisture content. The electrical resistivity depends on pore water-connected channels, which were deeply affected by the initial moisture content, vertical stress and loading duration (or strain rate). Moreover, as vertical stress increased, the pore size and pore area gradually decreased, the coarse particles were broken, and the fine particles increased. The contacts between particles changed from point-to-point contacts and edge-to-edge contacts to face-to-face contacts. Meanwhile, as vertical stress and loading rate increased, the loess particles were apt to vary from irregular elongated particles to equiaxial circular particles. This investigation can provide a theoretical base and experimental support for improving ground stability and preventing landslide disasters in loess regions. Full article
(This article belongs to the Special Issue Slope Stability Analysis and Landslide Disaster Prevention)
Show Figures

Figure 1

20 pages, 6477 KiB  
Article
Response of the Anchoring Performance at Betula platyphylla’s Root–Soil Interface to Cyclic Loading
by Shihan Yang, Xiaodong Ji, Donghui Zhao and Shusen Liu
Sustainability 2023, 15(17), 12791; https://doi.org/10.3390/su151712791 - 24 Aug 2023
Viewed by 1067
Abstract
In dealing with issues such as soil erosion and slope instability, plant roots enhance the shear strength of the soil mass through their anchoring effect. However, in nature, cyclic loads such as flash floods and blizzards indirectly impose fatigue effects on plant root [...] Read more.
In dealing with issues such as soil erosion and slope instability, plant roots enhance the shear strength of the soil mass through their anchoring effect. However, in nature, cyclic loads such as flash floods and blizzards indirectly impose fatigue effects on plant root systems. To explore the impact of cyclic loads on the anchoring capacity of plant roots, this paper selects the roots of Betula platyphylla as the research object and uses a monotonic load and cyclic load as two loading modes. Under different loading amplitudes (25%, 50%, and 75%), root diameters and burial depths (50 mm, 100 mm, and 150 mm), and soil moisture contents (11.85%, 13.85%, and 15.85%), the effects of each factor on the anchoring capacity of the roots under cyclic loading are analyzed. The results showed that the root–soil interface exhibited two failure modes under different cyclic load amplitudes, and the cyclic load significantly reduced the maximum friction of the root–soil interface. As the cyclic load amplitude increased (from 25% to 75%), the hysteretic curve envelope area increased, and the growth rate of cumulative residual slip changed from decreasing to decreasing and then increasing. A good correlation was found between cumulative residual slip and the number of loading cycles, and the three characteristic slips were correlated with loading amplitude but not significantly with diameter. The increase in soil moisture content, root embedment depth, and diameter led to an increase in the ratio of the two maximum friction forces. It was shown that a certain degree of plasticity exists at the root–soil interface to resist environmental stresses in nature. At high fatigue stress levels, the root–soil interface is more nonlinear, and as the load amplitude increases, more energy is dissipated, and bond damage between the root–soil interface becomes more pronounced. The root–soil interface gradually degraded under long-term cyclic loading, whereas the increase in root depth and soil water content could resist the negative effect of cyclic loading on anchorage capacity, and the resistance effect became more and more obvious with the increase in diameter. Full article
(This article belongs to the Special Issue Slope Stability Analysis and Landslide Disaster Prevention)
Show Figures

Figure 1

16 pages, 6550 KiB  
Article
Reliability Analysis of Seismic Slope Incorporating Interactions among Multiple Sliding Blocks Using Imbalance Thrust Force Method in Primary Sliding Direction
by Chunli Li, Guangming Yu, Liang Li, Hongbiao Yu, Yanxiang Fan, Jun Lei and Zhen Xu
Sustainability 2023, 15(16), 12350; https://doi.org/10.3390/su151612350 - 14 Aug 2023
Cited by 2 | Viewed by 887
Abstract
This paper proposes a methodology for reliability analysis of seismic slope stability that incorporates interactions among multiple sliding blocks. The primary sliding direction is first determined using the vector sum method and then the imbalance thrust force along the primary sliding direction is [...] Read more.
This paper proposes a methodology for reliability analysis of seismic slope stability that incorporates interactions among multiple sliding blocks. The primary sliding direction is first determined using the vector sum method and then the imbalance thrust force along the primary sliding direction is calculated using the slice-wise strategy and, finally, the double integration strategy is adopted to calculate the accumulated sliding displacement within the earthquake duration. The interactions among multiple sliding blocks are incorporated by checking the potential of occurrence for each of the multiple sliding modes. The proposed method is applied to a soil slope with two sliding surfaces. The comparative studies demonstrate that the mean and standard deviation of the sliding displacement considering the interaction of multiple sliding blocks are approximately three times larger than that of a single sliding mode, and the COV (mean value divided by standard deviation) of the two are slightly different. For the single sliding mode, the mean and standard deviation of the sliding displacement calculated using the proposed method are about 1/2 of the traditional Newmark sliding block model, and the failure probability obtained by the proposed method is lower than that from the traditional Newmark sliding block model owing to the difference in the sliding direction. The Peak Ground Acceleration (PGA) exhibits a significant effect on the statistics of 10,000 sliding displacements. The interactions among multiple sliding blocks and the PGA are required to be properly considered in seismic slope reliability analysis. Full article
(This article belongs to the Special Issue Slope Stability Analysis and Landslide Disaster Prevention)
Show Figures

Figure 1

21 pages, 9647 KiB  
Article
Impact of Rock Fragment Shapes and Soil Cohesion on Runoff Generation and Sediment Yield of Steep Cut Slopes under Heavy Rainfall Conditions
by Jing Luo, Peng Yang, Xiangjun Pei, Junhao Li, Shihan Shan, Yuying Duan and Yingping Huang
Sustainability 2023, 15(14), 10841; https://doi.org/10.3390/su151410841 - 11 Jul 2023
Cited by 2 | Viewed by 1478
Abstract
The erodibility and erosion resistance of Quaternary sediments play a pivotal role in both the hydrologic and erosion processes of soil cut slopes. To investigate the runoff and sediment yield of soil cut slopes along the Pai-Mo road, we performed indoor simulated rainfall [...] Read more.
The erodibility and erosion resistance of Quaternary sediments play a pivotal role in both the hydrologic and erosion processes of soil cut slopes. To investigate the runoff and sediment yield of soil cut slopes along the Pai-Mo road, we performed indoor simulated rainfall experiments under a 50° steep slope and high rainfall intensity (120 mm/h), based on the area’s climatic characteristics and Quaternary sediment properties. The experiments included various rock fragment contents (30%, 40%, and 50%), different levels of rock fragment roundness (i.e., rounded gravel, angular gravel), and varying soil cohesion. The results indicated that the average infiltration rate of the uncemented rounded gravel soil slope (URGSS) was higher than that of the uncemented angular gravel soil slope (UAGSS), resulting in less runoff and a delayed initial runoff time. The runoff shear stress, runoff power, drag coefficient, and Reynolds number of the URGSS were smaller than those of the UAGSS. In contrast, the Froude number and flow velocity of the URGSS were larger, resulting in a stronger runoff erosion capacity. The sediment yield of the URGSS was approximately two times that of the UAGSS, and the cumulative sediment yield was about 20% higher. The cemented angular gravel soil slope (CAGSS) had a larger runoff rate, runoff shear stress, runoff power, and flow velocity than those of the UAGSS, leading to less sediment yield. Overall, a more rounded shape and a larger radius of curvature of the spherical particles resulted in stronger erosion, due to local turbulence. Therefore, the rill density and cumulative sediment yield of the steep alluvial cut slope were greater than that of the steep colluvial cut slope under heavy rainfall. Moreover, due to its strong cohesion, only raindrop splash erosion and inter-rill erosion occurred on the steep moraine cut slopes under heavy rainfall. Full article
(This article belongs to the Special Issue Slope Stability Analysis and Landslide Disaster Prevention)
Show Figures

Figure 1

36 pages, 2546 KiB  
Article
Surrogate Model Development for Slope Stability Analysis Using Machine Learning
by Xianfeng Li, Mayuko Nishio, Kentaro Sugawara, Shoji Iwanaga and Pang-jo Chun
Sustainability 2023, 15(14), 10793; https://doi.org/10.3390/su151410793 - 10 Jul 2023
Cited by 2 | Viewed by 1856
Abstract
In many countries, slope failure is a complex natural issue that can result in serious natural hazards, such as landslide dams. It is associated with the challenge of slope stability evaluation, which involves the classification problem of slopes and the regression problem of [...] Read more.
In many countries, slope failure is a complex natural issue that can result in serious natural hazards, such as landslide dams. It is associated with the challenge of slope stability evaluation, which involves the classification problem of slopes and the regression problem of predicting the factor of safety (FOS) value. This study explored the implementation of machine learning to analyze slope stability using a comprehensive database of 880 homogenous slopes (266 unstable and 614 stable) based on a simulation model developed as a surrogate model. A classification model was developed to categorize slopes into three classes, including S (stable, FOS > 1.2), M (marginally stable, 1.0 ≤ FOS ≤ 1.2), and U (unstable, FOS < 1.0), and a regression model was used to predict the target FOS value. The results confirmed the efficiency of the developed classification model via testing, achieving an accuracy of 0.9222, with 96.2% accuracy for the U class, 55% for the M class, and 95.2% for the S class. When U and M are in the same class (i.e., the U + M class), the test accuracy is 0.9315, with 93.3% accuracy for the S class and 92.9% accuracy for the U + M class. The low accuracy level for class M led to minor inaccuracies, which can be attributed to a data imbalance. Additionally, the regression model was found to have a high correlation coefficient R-square value of 0.9989 and a low test mean squared error value of 5.03 × 10−4, which indicates a strong relationship between the FOS values and the selected slope parameters. The significant difference in the elapsed time between the traditional method and the developed surrogate model for slope stability analysis highlights the potential benefits of machine learning. Full article
(This article belongs to the Special Issue Slope Stability Analysis and Landslide Disaster Prevention)
Show Figures

Figure 1

17 pages, 18136 KiB  
Article
The Characteristics and Seepage Stability Analysis of Toppling-Sliding Failure under Rainfall
by Jing Luo, Xiangjun Pei, Ronghao Jiang, Tiantao Li, Hao Sun, Bo Jin and Qian Li
Sustainability 2023, 15(10), 7736; https://doi.org/10.3390/su15107736 - 9 May 2023
Cited by 1 | Viewed by 1936
Abstract
Toppling-sliding failure is a typical mode of deep-seated toppling failure. In this mode, massive collapsed rock masses form the main sliding body, which is sensitive to rainfall events and prone to instability under rainfall due to its unique slope structure. In the present [...] Read more.
Toppling-sliding failure is a typical mode of deep-seated toppling failure. In this mode, massive collapsed rock masses form the main sliding body, which is sensitive to rainfall events and prone to instability under rainfall due to its unique slope structure. In the present study, based on the detailed investigation on the geology and deformation characteristics, we studied the deformation and failure mechanism of a large-scale deep-seated toppling in Nandongzi Village, Pingquan City, Hebei Province. We constructed an engineering geology model to describe the toppling-sliding failure under rainfall. In addition, based on the saturated–unsaturated seepage theory and using the SLOPE/W and SEEP/W modules in the GeoStudio software, we explored the seepage law and factors controlling the seepage failure of toppling-sliding under rainfall. From surface to interior, the slope can be divided into topplingalling zone, strong toppling zone, slight toppling zone, and non-deformation zone. The geological structure consisting of an upper strong slab and an underlying weak rock layer, controls the early deformation, and the deformation and failure mode is compressing-bending-toppling. Due to the influence of excavation and rainfall, the sliding movements occur along planar rupture planes in the toppling-falling zone in the later stage, during which the failure mode switches to creeping-cracking. At present, the stability of the slope is highly sensitive to rainfall. When the rainfall intensity exceeds 220 mm/day (50 years return period storm), the factor of safety will fall below 1.05 and subsequently the sliding failure may be triggered. Because of the difference in permeability characteristics between the toppling-falling zone and the strong toppling zone, high pore-water pressure is developed at their boundary, leading to a drastic decrease in the factor of safety. Specifically, the more considerable difference in permeability, the lower the safety factor. Overall, this study is significant in scientific guiding for evaluating and preventing such slope failures. Full article
(This article belongs to the Special Issue Slope Stability Analysis and Landslide Disaster Prevention)
Show Figures

Figure 1

16 pages, 4227 KiB  
Article
Mechanical Analysis of Palm-Fiber-Reinforced Sand through Triaxial Tests
by Yuxiao Tang, Shaowei Wei, Xueyan Liu, Wen Liu and Teng Liu
Sustainability 2023, 15(6), 5461; https://doi.org/10.3390/su15065461 - 20 Mar 2023
Cited by 2 | Viewed by 1192
Abstract
Triaxial tests were employed to investigate palm-fiber-reinforced sand under consolidated drained conditions in this study. Sixteen series of triaxial tests were carried out to investigate the properties of palm-fiber-reinforced sand. One series of pure sand was also employed for comparison. The deviator stress, [...] Read more.
Triaxial tests were employed to investigate palm-fiber-reinforced sand under consolidated drained conditions in this study. Sixteen series of triaxial tests were carried out to investigate the properties of palm-fiber-reinforced sand. One series of pure sand was also employed for comparison. The deviator stress, stress path, shear strength, volume change, void ratio, and enhanced coefficient of fiber-reinforced sand were studied with different fiber lengths varying from 8 mm to 20 mm and fiber contents varying in mass from 0.3% to 0.9%. The test results indicate that palm fibers were beneficial for enhancing the shear strength of the sand. Compared to the peak shear strength increase of about 10% to 20%, the critical shear strength increased much more, by a little over 100%. Therefore, the fibers played a key role in enhancing the critical shear strength of the sand but not the peak shear strength of the sand. The addition of fiber to sand resulted in prolongation of the axial strain required to reach the critical void ratio and improved the sand’s ability to resist larger deformations, enhancing its toughness. Furthermore, the critical shear strength of the sand was positively correlated with both fiber content and fiber length, and the axial strain required to reach the critical shear strength increased with increasing fiber content and length. This study provides valuable experimental data and serves as a reference for temporary reinforcement in geotechnical engineering. Full article
(This article belongs to the Special Issue Slope Stability Analysis and Landslide Disaster Prevention)
Show Figures

Figure 1

20 pages, 6119 KiB  
Article
Landslide Susceptibility Mapping Using DIvisive ANAlysis (DIANA) and RObust Clustering Using linKs (ROCK) Algorithms, and Comparison of Their Performance
by Deborah Simon Mwakapesa, Yimin Mao, Xiaoji Lan and Yaser Ahangari Nanehkaran
Sustainability 2023, 15(5), 4218; https://doi.org/10.3390/su15054218 - 26 Feb 2023
Cited by 5 | Viewed by 1941
Abstract
Landslide susceptibility mapping (LSM) studies provide essential information that helps various authorities in managing landslide-susceptible areas. This study aimed at applying and comparing the performance of DIvisive ANAlysis (DIANA) and RObust Clustering using linKs (ROCK) algorithms for LSM in the Baota District, China. [...] Read more.
Landslide susceptibility mapping (LSM) studies provide essential information that helps various authorities in managing landslide-susceptible areas. This study aimed at applying and comparing the performance of DIvisive ANAlysis (DIANA) and RObust Clustering using linKs (ROCK) algorithms for LSM in the Baota District, China. These methods can be applied when the data has no labels and when there is insufficient inventory data. First, based on historical records, survey reports, and previous studies, 293 landslides were mapped in the study area and 7 landslide-influencing attributes were selected for modeling. Second, the methods were clustered in the study area mapping units into 469 and 476 subsets, respectively; for mapping landslide susceptibility, the subsets were classified into 5 susceptibility levels through the K-means method using landslide densities and attribute values. Then, their performances were assessed and compared using statistical metrics and the receiver operating curve (ROC). The outcomes indicated that similarity measures influenced the accuracy and the predictive power of these clustering models. In particular, when using a link-based similarity measure, the ROCK performed better with overall performance accuracy of 0.8933 and an area under the curve (AUC) of 0.875. The maps constructed from the models can be useful in landslide assessment, prevention, and mitigation strategies in the study area, especially for areas classified with higher susceptibility levels. Moreover, this comparison provides a new perspective in the selection of a considerable model for LSM in the Baota District. Full article
(This article belongs to the Special Issue Slope Stability Analysis and Landslide Disaster Prevention)
Show Figures

Figure 1

21 pages, 7464 KiB  
Article
Slope Stability Analysis for a Large Hydropower Station in China
by Dongbin Yin, Huifen Liu, Jingwen Yan and Jianqiang Wang
Sustainability 2023, 15(4), 3561; https://doi.org/10.3390/su15043561 - 15 Feb 2023
Viewed by 2169
Abstract
Hydropower plants (including the switching station) built in the middle and southern section of the north–south zone of China are always situated in complex geological settings of transition zones from strong to weak earthquakes with active faults. It is of great importance to [...] Read more.
Hydropower plants (including the switching station) built in the middle and southern section of the north–south zone of China are always situated in complex geological settings of transition zones from strong to weak earthquakes with active faults. It is of great importance to carry out careful evaluation of the slope stability considering various loading scenarios to ensure safe operation of the power stations. By using the rigid body limit equilibrium method and the finite element method, the effects of long-term load and seismic load on slope stability for a large hydropower station were studied. The results show that the slope safety factors of the station meet the stability requirements when the slope is under long-term load and under the action of the Wenchuan and Lushan earthquake loads. The stability of the slope is guaranteed. However, the risk analysis of the slope stability under the action of the design earthquake load shows that the slope safety factor is less than the accidental working condition safety factor of 1.05. Under the action of a strong earthquake, the crumbling block gravel soil layer in the shallow natural slope slides and destabilizes, which is obviously beyond its protection capacity, and therefore, effective seismic defense measures should be developed to ensure the safety of the personnel and equipment operating in the power station and switching station. Full article
(This article belongs to the Special Issue Slope Stability Analysis and Landslide Disaster Prevention)
Show Figures

Figure 1

15 pages, 4330 KiB  
Article
Hydrogeotechnical Predictive Approach for Rockfall Mountain Hazard Using Elastic Modulus and Peak Shear Stress at Soil–Rock Interface in Dry and Wet Phases at KKH Pakistan
by Ehtesham Mehmood, Imtiaz Rashid, Farooq Ahmed, Khalid Farooq, Akbar Tufail and Ahmed M. Ebid
Sustainability 2022, 14(24), 16740; https://doi.org/10.3390/su142416740 - 14 Dec 2022
Cited by 5 | Viewed by 1958
Abstract
Predicting the susceptibility of rockfall mountain hazards for block-in-matrix soils is challenging for critical steep cuts. This research illustrates a hydrogeotechnical approach for the prediction of rockfall triggering by performing laboratory tests on low-cohesive-matrix soil collected from steep slopes with 85° to 88° [...] Read more.
Predicting the susceptibility of rockfall mountain hazards for block-in-matrix soils is challenging for critical steep cuts. This research illustrates a hydrogeotechnical approach for the prediction of rockfall triggering by performing laboratory tests on low-cohesive-matrix soil collected from steep slopes with 85° to 88° angles at the Tatta Pani site, Karakorum Highway (KKH), and then real-scale moisture-induced rockfall was conducted on site for the validation of laboratory data. Laboratory data of forty quick direct shear tests on samples collected from the field depicted a 3-fold drop in peak shear stress (PS) at the soil–soil interface and a 9.3-fold drop at the soil–rock interface by varying the moisture content from 1% (taken as dry phase) to a critical laboratory moisture content (MC)LC of 21% (taken as wet phase). Similarly, a drop in the elastic modulus (ES) was observed to be 5.7-fold at the soil–soil interface and 10-fold at the soil–rock interface for a variation of moisture content from 1 % to 21% for the matrix with a permeability (k) range of 3 × 10−4 to 5.6 × 10−4 m/s, which depicts the criticality of moisture content for the rockfall phenomenon. The critical moisture content evaluated in laboratory is validated by an innovative field-inundation method for thirty-two moisture-induced real-scale forced rockfall cases, which showed the rock-block triggering at field dry density (γd)f and the critical field moisture content (MC)FC of the matrix ranging from 1.78 g/cm3 to 1.92 g/cm3, and 1.3% to 25.4%, respectively. Hydrogeotechnical relations, i.e., MC versus PS and ES, at the soil–rock interface are developed for the prediction of rockfall triggering. The proposed correlations may be helpful in the prediction of rockfall hazards by using expected rainfall in the field for disaster warning and landslide disaster prevention at ecological geotechnical engineering projects. The results revealed that the critical (MC)FC and (MC)LC are within 20%, depicting a good confidence level of the outcomes of this research. Full article
(This article belongs to the Special Issue Slope Stability Analysis and Landslide Disaster Prevention)
Show Figures

Figure 1

14 pages, 4996 KiB  
Article
Study on the Microstructure Evolution and Strength Damage Mechanism of Dolomite under Dissolution Condition
by Wenlian Liu, Pengen Liu, Hanhua Xu, Bocheng Gong and Feng Ji
Sustainability 2022, 14(18), 11447; https://doi.org/10.3390/su141811447 - 13 Sep 2022
Cited by 2 | Viewed by 1457
Abstract
Dolomite is a common type of natural soluble rock. The strength of rock decreases under the action of corrosion, which has a significant impact on the self-stability and long-term safety of the tunnel surrounding the rock. To reveal the microscopic structure evolution and [...] Read more.
Dolomite is a common type of natural soluble rock. The strength of rock decreases under the action of corrosion, which has a significant impact on the self-stability and long-term safety of the tunnel surrounding the rock. To reveal the microscopic structure evolution and strength-damage law of carbonate rock caused by chemical corrosion, a series of tests such as rock chemical corrosion test, rock uniaxial compression test and electron microscope scanning test are conducted at different pH values on the dolomite of the Doushantuo Formation. The rock dissolution at different pH values exhibits four typical stages: the initial dissolution stage, secondary dissolution acceleration stage, stable dissolution rate stage and dissolution attenuation stage. During the dissolution process, the initial dissolution rate is 25.91 times that of the stable stage, and the maximum strength attenuation is 76.2% after 21 days of dissolution. For macroscopic failure, the rock is developed from 1 to 2 external fractures to multiple internal and external fractures and penetrated, and the specimen transforms from brittle to flexible. For microstructure, the sample exhibits corrosion characteristics along the joint surface, intensified corrosion at the edge, etc. The porosity increase rate is 0.6%/d; however, the length–width ratio of the pores is maintained at 1.7–1.85, indicating that the development rate of pores in different directions is similar. The results of this study have enriched the study of the dolomite dissolution mechanism and, in addition, have important reference value for the stability evaluation of tunnel surrounding rock in karst environments. Full article
(This article belongs to the Special Issue Slope Stability Analysis and Landslide Disaster Prevention)
Show Figures

Figure 1

18 pages, 6590 KiB  
Article
Stability Analysis of a High-Steep Dump Slope under Different Rainfall Conditions
by Shaoling Li, Chi Qiu, Jiankun Huang, Xiaoping Guo, Yucun Hu, Al-Shami Qahtan Mugahed and Jin Tan
Sustainability 2022, 14(18), 11148; https://doi.org/10.3390/su141811148 - 6 Sep 2022
Cited by 14 | Viewed by 2315
Abstract
The existing slope stability research, which is based on the fluid–solid coupling theory, is mainly focused on the slopes of central and eastern China. The impact of rainfall on the stability of the dump slope has often been ignored. It is worthwhile to [...] Read more.
The existing slope stability research, which is based on the fluid–solid coupling theory, is mainly focused on the slopes of central and eastern China. The impact of rainfall on the stability of the dump slope has often been ignored. It is worthwhile to reveal the mechanism of the fluid–solid coupling mechanics of dump slopes in the arid desertification area of northwest China under the maximum precipitation. The method of combining the seepage mechanics theory with the geomechanics theory was adopted. Darcy’s law and the mass conservation law were introduced to derive and establish the fluid–solid coupling analysis method. Taking the Xinxing Coal Mine in Wuhai City, China, as an example, the finite element software ABAQUS was used to construct the fluid–solid coupling model for slope stability analysis with unsaturated soil. The equivalent rainfall intensity of 68 mm/h for 1 h and 18 mm/h for 24 h was designed in the simulation, respectively. Four different types of initial water content (i.e., 1.72%, 7.34%, 14.69%, and 22.03%) of the dump slopes were defined as the initial conditions. The high-steep slope was compared to the standard slope. Therefore, a set of sixteen rainfall schemes was proposed. The variation regularity of slope stability was thoroughly discussed in regards to four areas: vertical deformation, pore water pressure distribution, equivalent plastic strain, and safety factor. As was expected, the research showed that the slope height and angle have a significant effect on the slope stability. When high-intensity rainfall occurs for a short duration, the slope tends to be more stable as the initial water content increases on the slope. When low-intensity rainfall occurs over a long period, the slope stability reduces if the initial water content is too high or too low in the slope. Full article
(This article belongs to the Special Issue Slope Stability Analysis and Landslide Disaster Prevention)
Show Figures

Figure 1

18 pages, 5007 KiB  
Article
Analysis of Ecological Environmental Quality Change in the Yellow River Basin Using the Remote-Sensing-Based Ecological Index
by Zekang Yang, Jia Tian, Wenrui Su, Jingjing Wu, Jie Liu, Wenjuan Liu and Ruiyan Guo
Sustainability 2022, 14(17), 10726; https://doi.org/10.3390/su141710726 - 29 Aug 2022
Cited by 17 | Viewed by 2881
Abstract
Establishing a method for characterizing spatiotemporal changes in the quality of the ecological environment in a timely and accurate manner is of great significance for the protection and sustainable development of the ecological environment in the Yellow River Basin (YRB). In this study, [...] Read more.
Establishing a method for characterizing spatiotemporal changes in the quality of the ecological environment in a timely and accurate manner is of great significance for the protection and sustainable development of the ecological environment in the Yellow River Basin (YRB). In this study, the Google Earth Engine (GEE) platform was used as a basis for constructing the remote-sensing-based ecological index (RSEI), and the RSEI was used to evaluate the quality of the ecological environment in the YRB. The results indicated that the mean of the RSEI values showed two stages of rapid improvement and slow improvement during 1990–2020. From 1990 to 2000, the average growth trend was 0.005/a with a growth rate of 21.15%, with the main contributions of bad to poor (101,800 km2), poor to medium (56,900 km2), and medium to good (70,800 km2) ecological environmental quality levels. From 2000 to 2020, the average growth trend was 0.002/a with a growth rate of 2.13%, with main contributions of poor to bad (65,100 km2) and good to medium (35,200 km2) ecological environmental quality levels. From 1990 to 2020, there was a 76.38% improvement in the ecological environmental quality of the entire YRB, in which significant improvement accounted for 26.14%. The reductions in the ecological environmental quality accounted for 23.62%, of which significant reductions accounted for just 1.46%. The improvement in the ecological environmental quality of the YRB showed a trend of increasing sustainability, which is expected to continue. The distribution of the ecological environmental quality in the YRB showed obvious regional aggregation, whereby cold spots were concentrated in the northern and central regions of the YRB, which are the sandy and hilly ravine areas of the Loess Plateau. However, the areas corresponding to hot spot clusters decreased with time, and their significance also decreased. Thus, our study demonstrates that the GEE platform can be used to determine the spatiotemporal changes in the ecological environmental quality of the YRB in a timely and accurate manner. Full article
(This article belongs to the Special Issue Slope Stability Analysis and Landslide Disaster Prevention)
Show Figures

Figure 1

15 pages, 6553 KiB  
Article
An Experimental Study on the Dynamic Evolution Characteristics of Soil Arching and the Rational Spacing of Anti-Slide Piles
by Wei Zhong, Shuai Zhang and Na He
Sustainability 2022, 14(14), 8566; https://doi.org/10.3390/su14148566 - 13 Jul 2022
Cited by 2 | Viewed by 1487
Abstract
In order to analyse the dynamic evolution characteristics of soil arching during sliding processes, we conducted a series of model push-pile and direct shear tests. The tests’ results were used to design a relative displacement monitoring system and to introduce two dimensionless parameters [...] Read more.
In order to analyse the dynamic evolution characteristics of soil arching during sliding processes, we conducted a series of model push-pile and direct shear tests. The tests’ results were used to design a relative displacement monitoring system and to introduce two dimensionless parameters (the push–compaction ratio (e) and the different degrees of push–compaction (t)) to investigate the degree of uneven soil deformation during the sliding processes. This innovative method was used to analyse the rational spacing between adjacent anti-slide piles. The results revealed that there was a push-to-compaction effect in sliding soil during the sliding process. Firstly, in terms of space, the gradual transfer characteristics of the landslide thrust and push-to-compaction effect, rather than a uniform deformation over the entire area, were revealed. In terms of time, the results demonstrated a law for the variation in push-to-compaction ratios: The expansion of e occurred earlier in the rear sliding body than in the front e, while the growth rate of front e was faster than that of e in the rear sliding body. The dynamic evolution process was divided into three stages: an elastic formation stage, a plastic development stage, and a failure stage. Secondly, during the sliding process, the shear strength parameters of the sliding soil did not have constant values but underwent a dynamic process of strengthening, and cohesion responded more efficiently than friction. Finally, the degree of mobilisation of the anti-sliding effect of the sliding soil can be used as a new means of quantitative analysis for rational spacing. The results indicated that the rational spacing between adjacent piles should be five times the width of the pile. Full article
(This article belongs to the Special Issue Slope Stability Analysis and Landslide Disaster Prevention)
Show Figures

Figure 1

13 pages, 3059 KiB  
Article
Study on Influence Factors of Compressive Strength of Low Density Backfill Foamed Concrete Used in Natural Gas Pipeline Tunnel
by Chunbao Li, Xiaotian Li, Di Guan, Shen Li, Wenpu Lv, Ziqin Cong, Valentina Y. Soloveva, Hojiboev Dalerjon, Pengju Qin and Xiaohui Liu
Sustainability 2022, 14(14), 8333; https://doi.org/10.3390/su14148333 - 7 Jul 2022
Cited by 6 | Viewed by 1911
Abstract
Foamed concrete is mostly used for backfilling of long-distance tunnels and compressive strength is an important technical index to control the quality of foamed concrete. The influence factors on compressive strength of low-density foamed concrete were obtained by the single factor test method [...] Read more.
Foamed concrete is mostly used for backfilling of long-distance tunnels and compressive strength is an important technical index to control the quality of foamed concrete. The influence factors on compressive strength of low-density foamed concrete were obtained by the single factor test method based on the targeted dry density and compressive strength. The results show that the HT composed of pollution-free animal protein oil and vegetable oil is an efficient foaming agent and can produce stable foams. The cementation ability of cement can be fully expressed when a water to cement ratio of 0.45~0.5 is employed, making foamed concrete have a compressive strength higher than 2 MPa. The foam content is inversely proportional to the compressive strength and dry density of foamed concrete, and the volume ratio of slurry to foam should be 2:1~3:1. The content of fly ash is also inversely proportional to the compressive strength but positively proportional to the dry density. When the content of admixture is 40~55%, the compressive strength of foamed concrete with low density is not less than 2 MPa. The mixing proportion can be changed in the reasonable range to meet the requirements of different projects. Full article
(This article belongs to the Special Issue Slope Stability Analysis and Landslide Disaster Prevention)
Show Figures

Figure 1

19 pages, 30680 KiB  
Article
Effects of Soil Properties and Tree Species on Root–Soil Anchorage Characteristics
by Shusen Liu, Xiaodong Ji and Xiao Zhang
Sustainability 2022, 14(13), 7770; https://doi.org/10.3390/su14137770 - 25 Jun 2022
Cited by 4 | Viewed by 2108
Abstract
Root anchoring provides nonnegligible assistance to prevent soil erosion and stabilize slopes. The anchoring ability of plants suffers a tremendous impact from the soil conditions and the root characteristics. To reveal the root reinforcement effect, a group of pullout tests was conducted on [...] Read more.
Root anchoring provides nonnegligible assistance to prevent soil erosion and stabilize slopes. The anchoring ability of plants suffers a tremendous impact from the soil conditions and the root characteristics. To reveal the root reinforcement effect, a group of pullout tests was conducted on five different tree root systems (Pinus tabulaeformis, Betula platyphylla, Larix gmelinii, Quercus mongolica, and Ulmus pumila) with different soil moisture contents and soil dry weights. The results indicate that the root property (species, diameter, and tensile strength) and soil condition (water content 9.72%, 12.72%, 15.72%, 18.72%, and dry weight 1.32 g/cm3, 1.42 g/cm3, 1.52 g/cm3) had a significant effect on the anchoring effect of the soil. The anchoring effect is more obvious for the roots with a larger diameter and higher tensile strength. With the increase in the soil water content and the dry weight, the root system is more prone to failure but the root anchoring effect of soil with an optimum soil water content performs the best. Among the five different tree species, Pinus tabulaeformis roots were the least effective in anchoring the soil and Betula platyphylla roots performed the best. Full article
(This article belongs to the Special Issue Slope Stability Analysis and Landslide Disaster Prevention)
Show Figures

Figure 1

Back to TopTop