Discussion on “Analytical technique for stability analyses of the rock slope subjected to slide head toppling failure mechanisms considering groundwater and stabilization effects” by Bowa and Gong (2021)

The contributions of the current analytical models on the prediction of the stability of the slope subjected to slide head toppling failure mechanisms, have always focused on the idealized geometry comprising regular blocks dipping into the slope face. Besides, the influence of groundwater and stabilizations from the lowermost block of the slope have been overlooked in the available literature. In this article, the analytical solutions that incorporates the kinematic mechanisms of the jointed rock slope under the influence of groundwater and stabilizing the lowermost block subjected to slide head toppling are derived based on the limit equilibrium. Furthermore, a real slide head toppling failure case history was studied to illustrate the effectiveness of the presented analytical solutions. The investigation results indicate that the presence of groundwater in the jointed rock slope, lowers the distributions of the normal and shear forces thereby inducing slide head toppling. Reinforcing the lowermost block of the slope, enhances the distributions of the normal and shear forces thus improving the stability of the jointed rock slope. The study results depict that the presented analytical solutions can provide an accurate and efficient stability analyses of the jointed rock slope subjected to slide head toppling failure mechanisms considering the presence of groundwater and stabilization effects.

In this research, Two and three-dimensional slope stability analyses of final slope for Miduk copper mine is investigated by using distinct element code. These analyses were repeated in three positions (dry- drained- wet) and were done for four walls of the mine; including eastern wall, northern wall, western wall and southern wall. The stability of Miduk copper mine walls were accomplished by distinct element code (UDEC&3DEC). Both 2D and 3D slope stability analyses were performed to establish the representative shear strength parameters to use in the analyses and to examine the differences in the results. The extended Mohr–Coulomb failure criterion was used for analyses. The rock mass was assumed to be permeable and also by the obtained data from surveying, laboratory tests and field observations. The results are as follows: - Water and pore pressure in the faults and main joints were the most important destabilizer factors in these analyses. - The factor of safety after the drainage improved (27–34) % and (20–28) % based on the 3D and 2D slope stability analyses, respectively. - The difference in factors of safety between the 2D and 3D slope stability analyses for the deeper groundwater table (water level in the elevation 2540 on the walls) is less than 7 %. The factors of safety obtained from 2D slope stability analyses are not necessarily more conservative than 3D slope stability analyses. Analyses of the slope after lowering of groundwater table by horizontal drains showed that the factor of safety of the slope has improved tremendously. The differences in factors of safety for 2D and 3D slope stability analyses are greater for low groundwater table as compared with those for high groundwater table. The results illustrated how 3D slope stability analyses have become less daunting to perform and can be incorporated into routine slope designs.

Landslides are among one of the most devastating natural disasters affecting millions of people, causing tens of thousands of deaths and resulting in millions to billions of dollars of damage annually. Examination of historical data suggests an increase in the number of slope failures along with an increase in the two major triggers—an increase in the number of significant earthquakes and wetter than average annual precipitations. These trends highlight the continued need to improve landslide science and understanding. This paper presents a summary of the recent advances in knowledge pertinent to the methods of slope stability and deformation analyses starting with the state of practice as detailed by Prof. J. Michael Duncan in 1996. Specifically, the paper focuses on the improvements to the computational and graphical capabilities with the widespread use and availabilities of computers, the ability to perform macro level stability analysis for regions, the advent of probabilistic slope stability analyses, developments in slope stability analyses of unsaturated slopes, and new methods to perform deformation analyses. Several case studies highlighting these advances are also included.KeywordsSlope stabilityMacro level stability analysesProbabilistic slope stabilityUnsaturated slopesDeformation analysesBack-analyses

Stability analyses of geotechnical structures in rock are traditionally performed using deterministic methods. In Europe, Eurocode7, introduced in the beginning of the 21st century, adopts limit state design and semi-probabilistic methods, using partial factors for the design of geotechnical structures. Meanwhile, reliability-based design, using probabilistic methods, is becoming more common in practical cases. The paper considers an intentionally simple case study—the analysis of a slope in a rock mass with one discontinuity, considered in a discrete way, forming a rock block to be stabilised by anchors—to compare the results obtained with the different methods. The objective is to calculate the force applied by the anchors so that the ultimate limit states of sliding of the rock block is verified. Deterministic-based design optimization considering both the traditional global safety factor approach and the partial factor approach following the Eurocode 7 are first applied. A reliability-based design optimization procedure—which takes geometrical and mechanical properties of the discontinuities as random variables—is then used, and the results are compared to the former ones. A discussion is presented concerning the consistency of the obtained results.

ABSTRACThe influence of woody vegetation on the reliability of a sandy levee was investigated using field data in seepage and slope stability analyses. Field data were collected from selected sites within a 10‐km segment of a channel levee on the Sacramento River near Elkhorn, California. Root architecture and distribution were determined using the profile‐wall method in which root cross sections were exposed in the vertical wall of an excavated trench. Transects running both parallel and perpendicular to the crest of the levee were excavated at six sites. Each site was dominated by different plant species: five sites were adjacent to trees or woody shrubs, while one supported only herbaceous growth. Lateral plant roots were primarily restricted to, and modified, the near‐surface soil horizons to a depth of approximately 1 meter. Root area ratios (RARs) did not exceed 2.02 percent and generally decreased exponentially with depth. At depths greater than 20 cm, mean RARs for sites dominated by wood species were not significantly different from the mean RAB for the herbaceous site. No open voids clearly attributable to plant roots were observed. Roots reinforced the levee soil and increased shear resistance in a measurable manner. Infinite slope and circular arc stability analyses were performed on the landward and riverward slopes under different hydraulic loading conditions. Infinite slope analyses indicated increasing root area ratio from 0.01 percent to 1 percent increased the factor of safety from less than one to more than seven. Circular arc analyses indicated that even the lower measured root concentrations sufficed to increase safety factors for arcs with maximum depths of about 1 m from less than one to about 1.2. Our findings suggest that allowing woody shrubs and small trees on levees would provide environmental benefits and would enhance structural integrity without the hazards associated with large trees such as wind‐throwing.

ABSTRACTIn the traditional analytical models for evaluating block toppling failure mechanisms of the slope, a single weak plane angle is assumed, running from upper rock columns and daylighting on the slope face. However, for some physical rock slopes, the weak plane bounding the potential toppling blocks may be dipping at two diverse angles within the rock masses and may not daylight on the predictable point on the face of the slope due to varying characteristics of the weak plane. The mathematical technique for estimating the counter-tilted angle of the weak plane has been proposed and incorporated into the modified analytical technique for evaluating slope stability subjected to block toppling failure. The physical slope with pre-existing weak plane dipping at two diverse angles within the rock slope subjected to block toppling was analysed using the modified analytical technique and results were validated using the discrete element method. The obtained simulated failure mode zones are consistent with those obtained by the modified analytical technique. The influence of the relative counter-tilted angles of the weak plane on slopes stability was studied and the results show that, progressive increase in the counter-tilted angles of the weak plane lead to gradual increase in slope instability.

In rock slopes where sedimentary rock masses dip into the face of the slope, failure may occur by block toppling. In traditional analytical models, the failure surface is assumed to be single plane running from the upper columns to the toe of the slope which may be inconsistent with the physical situation where the weak plane has undergone counter-tilting within the rock slope due to variation of lithology and weak plane characteristics. To better reflect the physical situations, the failure surfaces ought to be determined instead of basing it on assumptions and incorporated in the existing analytical methods for stability analyses. Therefore, an analytical technique for determining counter-tilted failure surface angle has been proposed and traditional analytical model for evaluating the stability of rock slopes subjected to block toppling failure mechanisms has been modified by incorporating the counter-tilted weak plane angle. The physical slope with counter-tilted failure surface was comprehensively analysed using the modified analytical model, and results were validated using the numerical simulations models. The simulated failure mode zones are consistent with the failure mode zones obtained by the modified analytical method. The influence of relative angles of counter-tilted failure surface on the slopes’ stability has been studied, and the results show that progressive increase in the counter-tilted failure surface angles leads to gradual increase in slope instability. The proposed analytical method could provide precise applications to evaluate the slope instability in rock slopes with counter-tilted failure surface.

<p>In the aftermath of Hurricanes Katrina and Rita in 2005, significant damages to the Hurricane Protection System (HPS) were observed in the New Orleans, Louisiana and Mississippi Gulf Coast areas. Pile supported T-walls are one of the most important components of the HPS in the New Orleans area and its vicinity. Due to the unsatisfactory performance of some of the HPS measures, during the above hurricanes, the New Orleans District of the U.S. Army Corps of Engineers and others have undertaken an extensive investigation and re-evaluation of the design criteria of the T-walls from the perspective of its stability against future hurricane loadings. These resulting guidelines are being incorporated in the Hurricane and Storm damage Risk Reduction Guidelines (HSDRRG, 2007). The stability analysis and modeling of T-walls are significantly different from the stability analysis of other structures. They must be analyzed for unbalanced loads arising from the stability analysis which are assumed to be carried by the supporting piles beneath the wall and the analysis should not consider any water load acting directly on the structure, as these loads are presumed to be carried by the supporting piles. Historically, the U.S Army Corps of Engineers had generally relied upon the simplified Method of Planes (MOP) slope stability analysis of T-wall, which satisfies only force equilibrium. However, their recent evaluation revealed that MOP is not very suitable for the stability modeling and analysis of T-walls. Thus, there is a need for a comprehensive slope stability modeling and analysis procedure based on total limit equilibrium (such as Spencer's method of analysis) that can be incorporated in the new design guidelines. MOP can then be retained as a design check for the results obtained using Spencer's analysis.</p><p>In this paper, a comparative evaluation of the slope stability analyses of T-walls are presented using the above two distinct approaches of slope stability analysis. In addition, the effect of optimization of the failure surfaces on the stability analysis results is investigated in detail. Numerical example of a typical T-wall stability analysis using the two different procedures is presented to demonstrate the above procedures. The findings have indicated that the MOP analysis appeared to be conservative compared to the total limit equilibrium method.</p>

Stability analyses of slopes have been a challenge for engineers, requiring development of complex numerical models to assess the risk levels and potential hazards. The numerical models involve combination of analysis methods and integrated optimization approaches, which generally induce intense engineering calculations with upscale time complexity. To obtain good and quick solutions, a robust optimization algorithm is necessary, leading to an efficient and reliable stability analysis framework. Within this context, various optimization techniques involving deterministic and metaheuristic approaches were proposed in the past decades. The proposed methods often suffer from convergence issues have time deficiencies, which highlights a necessity of development of an effective optimization algorithm. In this study, a modified version of Differential Evolution (DE) algorithm named Elitist Differential Evolution (EDE) is proposed to solve slope stability analysis problems. To develop a complete analysis framework, EDE is integrated with a non-circular failure surface generation method and limit equilibrium based stability analysis techniques. Its performance is compared with other optimization algorithms such as conventional DE, Particle Swarm Optimization and Grey Wolf Optimizer using benchmark problems reported in the literature. The experiments demonstrate that EDE greatly improves the results of other alternatives, validating the applicability of the algorithm to slope stability analysis. Furthermore, statistical performance of EDE has become prominent in the experiments, which further emphasizes its robustness.

Exploiting excavation-induced displacement for slope heterogeneity characterization and stability analysis

The research area was located in the west pit of the open pit coal mine of PT. Tawabu Mineral Resource (TMR) which is located in Bengalon District, East Kutai Regency, East Kalimantan Province, Indonesia. The research was driven by several landslides that occurred in the research area, but the engineering geological conditions and stability of the remaining slopes have not been evaluated. The objectives of this study were to better understand the engineering geological conditions and stability of the research area. The engineering geological conditions (i.e., geomorphology, rock and soil, geological structure, and groundwater conditions) were evaluated by photogrametric analyses, field observations, and analyses of borehole logs and laboratory test results. The slope stability analyses were firstly carried out by conducting back stability analyses of failed slope on the northern lowwall slope segment. The shear strength parameters obtained from the back analyses were then used for forward stability analyses of the remaining 10 lowwall and highwall slopes. The slope stability analyses involved deterministic and probabilistic analyses, under static and dynamic using the limit equilibrium method (LEM). The results showed that the research area and the surrounding consisted of two geomorphological units, namely the alluvial plain and structural hills. Rocks in the study area consisted of claystone, sandstone, and coal with a general layer strike direction of N59°E – N63°E with a dip of 19°-26°. These rocks were grouped into two lithological units, namely the alternating of claystone and sandstone unit and alternating of sandstone and claystone unit. The geological structures were identified on the highwall, from west to east namely major sinistral shear fault with a relative direction of NNE-SSW, two minor sinistral shear faults with a relative direction of NE-SW, and a major dextral shear fault with a relative direction of NW-SE. These geological structures were interpreted as being formed by the folding process. The groundwater level was estimated at a level of -45 m to 20 m. The slope stability analyses showed that only the East HW-4 slope, which was located on the east highwall, was unstable. It is recommended to optimize the slope by either lowering the groundwater elevation by 4 m from the actual level or by reducing the angle the overall slope to 31°.

Probabilistic stability analyses of slopes using the ANN-based response surface

This paper covers two key aspects concerning slope analysis and design. In the first part, different analytical methods are reviewed and a method of limit equilibrium slope analysis that allows the interslice force inclinations to vary is presented. The new approach (referred to as the Arup Method), applicable on both circular and non-circular slips, is a further refinement on the popular Bishop and Janbu methods and is designed to overcome the numerical difficulties stemming from interlock. The proposed approach achieves overall horizontal, vertical and moment equilibrium of the slope, while also keeping every slice in horizontal and vertical equilibrium. Illustrative examples are presented to compare results from this method against recognized methods of analysis, including Morgenstern-Price, which employs a user-defined interslice force function. In the second part of the paper, development of a digitalised workflow for slope analyses and design is discussed and the authors demonstrate how customised coding enables optimisation of slope design involving soil nailing.

The study of unsaturated slope stability is one of issues in geotechnical engineering. Firstly, the different treatments of matric suction in the Sarma method are analyzed based on the Bishop’s unsaturated strength theory and Fredlund’s unsaturated strength theory respectively. Then, application of the developed method on the stability analyses of an unsaturated soil slope is also discussed. Through the comparison on the computational results, it still can be concluded that the computational error is slights, which analyzed by means of the developed Sarma method based on the Bishop’s unsaturated strength theory and Fredlund’s unsaturated strength theory.

The study of slope stability is one of the traditional and eternal issues in Geotechnical Engineering. There are a lot of previous achievements on stability of unsaturated soil slope are reviewed in this paper. Firstly, the influence of matric suction impacted on the strength of unsaturated soil is summarized. Secondly, the different treatments of matric suction in some commonly used slice methods such as the Sweden slice method, the simplified Bishop's slice method and the Janbu's slice method are analyzed based on the Bishop's unsaturated strength theory and Fredlund's unsaturated strength theory respectively. Finally, the advantages and disadvantages of these methods in application on the stability analyses of unsaturated soil slope are also discussed. Though these developed and modified slice methods may consider the matric suction in sliding zone, it still can be concluded that these slice methods have to neglect the other matric suction outside of the slip surface, which lead to underestimating the influence of the matric suction in the stability analyses of unsaturated soil slope in fact.