Circular Failure Surface Research Articles

Observations on the role of internal sand moisture dynamics in wave-driven dune face erosion

Understanding and predicting dune erosion is crucial for coastal hazards mitigation, ecosystem preservation, as well as the protection of human settlements and infrastructure along sandy coastlines. However, our knowledge regarding the influence and potential importance of internal sand moisture content on wave-driven dune face erosion processes remains limited. This paper presents the findings from an extensive series of controlled wave flume experiments of eroding, unvegetated dunes, combining a range of wave conditions and water levels. A further variable that is studied directly for the first time is the internal moisture content of the dune. The initial moisture content and its evolving dynamics within the eroding dune face are quantified, revealing this to be a determining factor of the observed erosion rates, the final horizontal erosion distance, and the dune face failure type. Importantly, infiltration into the dune with each wave was not a driving mechanism of observed failures, but rather the rapid increase and then decrease of the phreatic surface within the dune, resulting in excess pore pressures and destabilization of the sediment matrix. Based on these observations two distinct mechanisms of shear failure and resulting dune face slumping are identified for unsaturated dunes corresponding to ‘minimum’ and ‘field capacity’ internal moisture content: Type 1 is associated with a circular failure surface in the absence of notching at the base of the dune, while for Type 2, notching is present and the failure surface is vertical. Under fully saturated conditions, the phreatic surface is observed to decouple from the wave runup, with excess water continuously exiting the dune face near the base. This results in rapid shear failure with no notching (Type 3). Significantly, dunes with saturated initial pore moisture content above the capillary fringe are observed to have up to 35 % greater erosion potential, consistently receding further landward than the two unsaturated counterparts as well as undergoing slumping in the absence of wave impact. A new conceptual framework is presented, comprising of a three-phase erosion sequence that directly links dune face failure mechanisms to wave runup and prevailing groundwater conditions.

A novel stability equation for the estimation of the factor of safety for homogeneous dry finite slopes

AbstractThis paper introduces a novel closed‐form equation (surrogate model) for approximating the Morgenstern–Price estimate of the factor of safety of homogeneous dry finite slopes with circular failure surfaces. Unlike typically used methods, the proposed equation does not require the definition of a critical failure surface, splitting the soil mass into slices, or the iterative reduction of soil resistance to the limit state. It can be easily programmed into calculators or computers and accurately determines the minimum factor of safety based on the shear strength parameters and slope geometry—meaning that it is ideally suited for integration into reliability calculations. The equation is determined parametrically for various soil parameters and slope geometry using the Morgenstern–Price method and compares favorably with conventional techniques, such as slope stability charts, limit equilibrium, and strength reduction methods (SRM). From a practical perspective, the proposed equation greatly simplifies the analysis of the slope stability as the creation of a numerical model is not required and is suited to use in the feasibility stage of a project, for example, for large linear infrastructure projects with differing slope geometries or in situations where a quick assessment is desired.

Stability analysis of mine overburden dump and improvement by soil nailing

The conventional method for carrying out stability analysis of dump involving Limit Equilibrium Method (LEM), when compared with the strength reduction method (SRM) using Finite Element Method (FEM) approach, resulted in overprediction of the factor of safety (FoS). In the present study, slope stability analysis of external overburden dump in Sonepur Bazari opencast mine has been carried out. Morgenstern Price method using constant inter-slice force function conducts the analysis of LEM using Geo-studio Slope/w, and the FEM analysis is carried out using the PLAXIS 2D 2016. The study is carried out to assess the effect of the dump’s friction angle, slope angle, height, and bench configuration. Further, the analysis considering the soil nailing is also conducted by optimizing the number of nails, the distance between nails, length of the nails, nail inclination angle. The stability analysis found that the dump is in a critical state (FoS = 0.92) with a circular failure surface. The optimum slope angle is found to be 30˚. It is observed that LEM cannot detect the increased localized stress concentration at the bench edge. Reinforcement of the dump using the soil nailing technique has affected the dump stability substantially, with an increase of 11% in the FoS; however, the effect of nail orientation on dump stability was less pronounced. Further bench provision to the dump slope increases the FoS by 27%, 21% and 19%, considering the total height of 60 m, 80 m and 100 m, respectively.

Investigation on the ultimate uplift capacity for asteroid exploration in drilling anchoring process: Numerical modelling and DEM simulation

Due to the microgravity environment on the asteroid surface, the asteroid probe can not stay on the asteroid surface for a long time for in situ exploration. Therefore, an anchoring device is required to provide enough ultimate uplift capacity to hold the asteroid probe on the asteroid’s surface. In this work, based on the circular arc failure surface hypothesis, a numerical model is proposed to predict the ultimate uplift capacity of the anchor rod of the anchoring devices during the anchoring process. The discrete element method (DEM) simulation is adopted to calculate the ultimate uplift capacity and analyze the geomaterial behavior. To accurately simulate material properties, the parameters of three typical geomaterials are calibrated by the calibration tests. The anchoring experiment verifies the DEM simulation results, and the error between the anchoring experiment results and DEM simulation results is less than 14%. The distribution of loaded particle forces in the geomaterials under various anchoring angles(30°–60°) and the anchoring depths(20 mm–40 mm) in the simulation are compared and analyzed. Compared with the DEM simulation results, the ultimate uplift capacity’s numerical model prediction results have an error of 5%. This work provides a new approach to predict the ultimate uplift capacity of the anchor rod of the anchoring devices during the asteroid exploration process.

Computational tools for the analysis of circular failure of rock slopes

Among other types of failure in slopes created by excavation or filling, circular (also referred to as rotational) type of failure plays an important role in the design and stability analysis of high rock slopes, such as those encountered in deep open pit mines. When a rock slope of significant height involves predominantly one type of jointed rock mass, the scale of the problem is frequently such that the rock mass (intact rock and rock discontinuities) can be regarded as a homogeneous isotropic material. In such case, if the rock slope is unstable and collapse occurs, circular (or rotational) failure as in failed slopes in soils is also observed for the rock slope. One main goal in practical design of deep open pit mines is to determine safe inclination angles for the pit faces to be excavated to avoid failure. Computational tools for quick assessment of the stability conditions, in particular determination of factor of safety and location of the critical circular failure surface, are useful during the preliminary stages of open pit design. Among others, such tools allow the engineer to gain insight in the role that the different variables controlling the problem have in defining the stability conditions for the rock slope. This paper provides first an overview of typical numerical techniques used to assess the stability of high rock slopes. For the case of slopes in rock masses that are assumed to obey the Mohr-Coulomb or the Hoek-Brown failure criteria, the paper discusses how application of transformation rules leads the criteria to be re-casted in dimensionless form, so when these are applied to the solution of slope problems, the results (factor of safety and coordinates that define the location of the critical circular failure surface) can be summarized in dimensionless compact forms. The paper presents then computational tools in the form of dimensionless charts and computer spreadsheets for stability analysis. These are developed from numerical limit equilibrium models that use the mentioned transformation rules. Among others, the computational tools allow the concept of mechanical similarity of rock slopes to be naturally introduced. Finally, the paper presents various rock slope examples that illustrate the use of the computational tools. In these examples, results from limit equilibrium models are also compared with results obtained with full numerical analysis, in particular with finite difference models implementing the shear strength reduction technique.

A New Approach for Evaluating the Soil Slope Reinforcement Tensile Forces Using Limit Equilibrium Methods

Limit equilibrium methods have been extensively used in the design of reinforced soil structures using various types of failure surfaces. A significant problem in limit equilibrium analysis of reinforced soil is the need to know the force at each reinforcement layer in the limit state. Limit equilibrium analysis with log spiral failure mechanism has been employed to locate the critical failure surfaces emerging at or above the toe and to study the behavior of geosynthetic-reinforced soil slopes. This paper describes a numerical procedure, using limit equilibrium methods, to evaluate the distribution of the soil slope reinforcement tensile forces. Both, log spiral and circular slip surfaces are considered. The effect on the required tensile forces of the target safety factor value, the ratio of the mobilized soil shear strength, and the reinforcement layer spacing are examined. Results show that the distribution of reinforcement tensile forces is dependant on reinforcement layer spacing; however, the total reinforcement force is not. The total reinforcement force required to ensure equilibrium is strongly dependant on the target safety factor value and the ratio of the mobilized soil shear strength. Modified Bishop Method with circular failure surface and Shiwakoti–Leshchinsky log spiral failure surface led to comparable results.

Slope stability analysis using Bishop and Finite Element Methods

Analysis of slope stability in this study aims to determine the safety factor (SF) of the landslide for the existing and the reinforcement condition. The study case was in STA 84+910 of national road Meulaboh-Geumpang, West Aceh Regency in Aceh Province. The condition of the Meulaboh-Geumpang road often causes landslides due to the topography of the area and is also triggered by rainfall. The analysis of safety factor for the existing condition was calculated by using the Bishop method that assumes a circular failure surface and the calculation was also validated by the finite element method using 2D Plaxis version 8.6 software. However, computation requires iterative procedures because of the nonlinear relationship for the safety factors. The result obtained from calculations using the Bishop method for the existing condition is 1.08, while by using Plaxis software, the result is 1.10, which means the slopes are in unstable conditions and need to be reinforced to prevent landslides. Alternative reinforcement was conducted by using sheet pile and calculations performed using 2D Plaxis version 8.6 software. Variations in the placement of sheet piles are at the upper and middle of the slope. The results obtained from the calculation of the safety factor after reinforcement are 1.57 (with a 12m sheet pile depth at the upper slope) and 1.48 (with a 10m sheet pile depth in the middle of the slope).

Slope Stability Analysis of the Gbeni Earth Dam (GB3) in Rutile - Sierra Leone

Earth slopes stability analysis is important in the design and construction of earth dams under different loading conditions. Several factors such as difference in water level or rapid drawdown in the reservoir, right after construction, and steady - state seepage may result in instability of Earth Dams for all possible combinations. In this study, three scenarios were evaluated for the Gbeni Earth Dam (GB3) at Sierra Rutile Mining Company in Sierra Leone. It is a zoned earth-filled embankment dam with respective upstream and downstream slopes of 1:3 and 1:2, having a horizontal sand blanket downstream. The upstream slope was subjected to both rapid drawdown in the reservoir of the earth dam and end of construction condition when there is no water present in the reservoir, whilst the downstream slope was assessed for steady seepage and end of construction conditions. The shape of the critical slip surface of both slopes was evaluated using a circular failure surface. The objective of this study was to assess the stability of these slopes under the above conditions using traditional analysis according to the theory of limit states and safety factor in GEO 5 software and its subprograms. The level of water on the upstream and downstream banks, the geotechnical properties of soil materials and boundary conditions of the dam were used as contribution variables and safety factors as the desired output. The study found out that the factor of safety against sliding of the upstream slope marginally drops within the short period after the start of rapid drawdown of water in the reservoir of the dam. Also, the downstream slope was found to be more stable under steady seepage. This accounts for the uncertainties involved in the strength of material, pore pressures in impervious clay core material, and long-term loading condition.

Prediction of the sliding type and critical factor of safety in homogeneous finite slopes

In this paper, the effect of soil material parameters including soil specific weight (γ), cohesion (C), angle of internal friction (emptyset), and geometric parameter of slope including angle with the horizontal (β) for a constant slope height (H) on factor of safety (Fs) was investigated. Fs was considered in two scenarios: (1) slope with dry condition, and (2) with steady-state saturated condition that comprises water level drawdown circumstances. In addition, the type of slip circle was also investigated. For this purpose, the SLOPE/W software as a subgroup of Geo-Studio software was implemented. Results showed that decreasing of water table level and omitting the hydrostatic pressure on the slope consequently would result in safety factor decrement. Comparison of the plane and circular failure surfaces showed that plane failure method produced good results for near-vertical slopes only. Determination of slip type showed that for state (30° < β < 45°), the three types of failure circles (toe, slope or midpoint circle) may occur. For state (45° < β < 60°), two modes of failure may occur: midpoint circle and toe circle. For state (β > 60°), the mode of failure circle is only toe circle. Linear and nonlinear regression equations were obtained for estimation of slope safety factor.

What is the role of tensile cracks in cohesive slopes?

The traditional limit equilibrium method (LEM) is often used to search for the failure surface with a minimum safety factor of slope. In this method, the failure surface is considered as a shear surface, irrespective of its form. However, tensile cracks are frequently found at the outcrops of landslides. In this study, three sets of tests on small-scale landslides with different inclination angles were conducted. The test results demonstrated that tensile cracks could arise in the slope sliding process and the failure surface is composed of both a shear and a tensile fracture surface. Based on the test results, we used the improved LEM, and replaced the traditional shear failure surface by a tensile-shear coupling one, thus new tensile failure modes for slope stability analysis can be established. The safety factors of slope in different failure modes were compared, which show that when considering soil tensile failure and tensile strength less than a certain value (e.g. 15 kPa, 44 kPa and 55 kPa for linear, circular and logarithmic spiral failure surfaces, respectively), the safety factors of slope with three different failure surfaces are less than the one that did not consider the tensile failure. The most critical failure surfaces of the slope may be composed of shear and tensile damages because the tensile strength of the soil cannot be generally greater than its cohesion.

Continuous Slip Surface Method for Stability Analysis of Heterogeneous Vertical Trenches

Evaluating the reliability of trenches against sliding failure is complicated by the fact that most alluvial deposits are heterogeneous and spatially variable. This means that instead of perfectly circular or linear failure surfaces, trench failure tends to be more complex, following the weakest path or zones through the material, thereby, a new method named Continuous Slip-Surface (CSS) is adopted for calculating the critical excavation depth. CSS runs an algorithm to seek for continuous slip surface. The Finite Difference Method (FDM) coupled with random field theory and CSS method is well suited to slope stability calculations since it allows the failure surface to seek out the weakest path through the soil. For an unsupported vertical cut, it was shown that the critical excavation depth acquired from CSSM is indeed an upper bound solution. It was further shown both numerically and analytically through an idealized variation model that increasing the un-drained shear strength density fades the effect of shear strength variability. Correlation structure of the input variable was also shown to influence the results, although the behaviour was found different in low and high scales of fluctuation.

Failure Mechanism and Factor of Safety for Spatially Variable Undrained Soil Slope

This paper aims to investigate the differences in factor of safety (FS) and failure mechanism (FM) for spatially variable undrained soil slope between using finite element method (FEM) , finite difference method (FDM), and limit equilibrium method (LEM). The undrained shear strength of cohesive soil slope is modeled by a one‐dimensional random field in the vertical direction. The FS and FM for a specific realization of random field are determined by SRT embedded in FEM‐ and FDM‐based software (e.g., Phase2 6.0 and FLAC) and LEM, respectively. The comparative study has demonstrated that the bishop method (with circular failure surface) exhibits performance as fairly good as that of SRT both in FS and FM for the undrained slope cases where no preferable controlling surfaces such as hydraulic tension crack and inclined weak seams dominate the failure mechanism. It is, however, worthwhile to point out that unconservative FM is provided by the Bishop method from the aspect of failure consequence (i.e., the failure consequence indicated by the FM from the Bishop method is smaller than that from SRT). The rigorous LEM (e.g., M‐P and Spencer method with noncircular failure surface) is not recommended in the stability analysis of spatially variable soil slopes before the local minima and failure to converge issues are fully addressed. The SRT in combination with FEM and/or FDM provides a rigorous and powerful tool and is highly preferable for slope reliability of spatially variable undrained slope.

Stability Analysis and Confidence Level Evaluation of Backfill Mining under High and Steep Rock Slopes

To extract the 6.3 million tons of high-quality phosphate resources, a stability analysis and confidence level evaluation of backfill mining under high and steep rock slopes (HSRS) were conducted using the Slide software and a Monte Carlo simulation. The geological model of HSRS was constructed based on a geotechnical investigation. A series of laboratory tests were conducted to obtain the engineering parameters of the rock mass, and the mechanism of action of the backfill mining method was analyzed. After the stability analysis, the average safety factors of HSRS for normal operation are 1.575 (backfill method) and 1.509 (open-stope method), and for seismic conditions, they are 1.470 (backfill method) and 1.380 (open-stope method). According to the confidence level evaluation, the average failure probability of HSRS by using the backfill mining method is 0.0143. The results showed that using the backfill mining method under HSRS had better seismic stability and lower potential levels of destruction than using the traditional open-stope mining method. In addition, the backfill mining method can prevent the development of a circular failure surface, reduce the destructive effect of mining to a minimum, and maintain the lower failure probability of HSRS.

A cone surface in three-dimensional analyses of slopes with tension cut-off

A three-dimensional limit analysis of slopes is presented in this paper, based on a right circular cone failure surface. The associated translational mechanism appears to yield better assessment of the safety in isotropic rock than the traditional wedge-type mechanism. The strength of a bonded geomaterial was described using a linear strength envelope truncated in the tensile regime. The tensile strength cut-off so introduced constitutes a non-linear portion of the strength envelope, and it allows constructing failure mechanisms that include rupture modes, in addition to the shear deformation mode. Consequently, the mechanisms in materials with tension cut-off are more critical than those in materials with a traditional linear strength envelope. It is also demonstrated that the failure mechanism based on the right circular cone failure surface in vertical slopes yields results as good as or better than the more complex rotational mechanisms, although the difference is not very significant.

Locating Critical Circular and Unconstrained Failure Surface in Slope Stability Analysis with Tailored Genetic Algorithm

Abstract This article presents an efficient search method for representative circular and unconstrained slip surfaces with the use of the tailored genetic algorithm. Searches for unconstrained slip planes with rigid equilibrium methods are yet uncommon in engineering practice, and little publications regarding truly free slip planes exist. The proposed method presents an effective procedure being the result of the right combination of initial population type, selection, crossover and mutation method. The procedure needs little computational effort to find the optimum, unconstrained slip plane. The methodology described in this paper is implemented using Mathematica. The implementation, along with further explanations, is fully presented so the results can be reproduced. Sample slope stability calculations are performed for four cases, along with a detailed result interpretation. Two cases are compared with analyses described in earlier publications. The remaining two are practical cases of slope stability analyses of dikes in Netherlands. These four cases show the benefits of analyzing slope stability with a rigid equilibrium method combined with a genetic algorithm. The paper concludes by describing possibilities and limitations of using the genetic algorithm in the context of the slope stability problem.

Seismic stability of slope using modified pseudo-dynamic method

The paper presents evaluation of factor of safety of slope assuming circular failure surface under seismic loading condition. The centre of most critical circle is located using Fellenius method. Adopting limit equilibrium method, under the influence of weight of potential sliding mass and seismic inertia forces, factor of safety is evaluated applying new pseudo-dynamic method based on visco-elastic behaviour of soil which satisfies zero-stress boundary condition and considers soil amplification inherent to soil properties. Results are presented and compared with available results from literature. Detailed parametric studies are also carried out to observe the variation of safety factor at different soil strength and seismic forces and these can serve as very good criteria for design of slopes.

Seismic Stability of Slope Considering Rayleigh Wave

ABSTRACTIn the present paper factor of safety of slope under seismic loading condition is evaluated assuming circular failure surface. Using Fellenius method the center of most critical circle is located. Adopting limit equilibrium method, under the influence of weight of potential sliding mass and seismic inertia forces, factor of safety is evaluated considering Rayleigh wave along with primary wave and shear wave. Results are presented and compared with the available results from literature. Detailed parametric studies are also carried out to observe the variation of safety factor at different soil strength and seismic forces.

Optimal design of Reinforced Concrete Cantilever Retaining Walls considering the requirement of slope stability

A Reinforced Concrete Cantilever Retaining Wall (RCCRW) is one commonly used soil retaining structure in engineering practice. Various optimization techniques to obtain the optimal design of cantilever walls have been proposed, where the three basic geotechnical constraints of overturning, sliding and bearing failures have generally been taken into consideration. However, none of these approaches have considered the geotechnical requirement of slope stability. In this paper, a novel formulation for the optimal design of RCCRWs that considers the more complete requirements of geotechnical stability of overturning, sliding, bearing and slope failures, is described. The objective function of the minimum cost of materials, geotechnical constraints of wall failures (overturning, sliding and bearing) and the structural requirements for steel reinforcements in the wall sections all followed the conventional approaches used in previous works. Using the Ordinary Method of Slices (OMS) with a circular arc failure surface (CAFS), the factor of safety against slope failure (FSOMS) for a RCCRW was implicitly derived. Constraints for ensuring that the minimum FSOMS was higher than the required factor were enforced in the formulation. Design variables were the dimensions of the wall sections, corresponding steel reinforcements and the x-y coordinate of center of the CAFS, where the latter are the additional unknowns in this novel formulation. Computational performance of the proposed optimization method is demonstrated and verified through its application to the optimal design of two examples of RCCRWs.

Temperature and Suction Effects on Slope Stability under Undrained Condition

In this paper, the variation of safety factor of unsaturated soil slope with temperature and matric suction was simulated. The simulation was performed using modified ordinary method of slices for unsaturated soil slope including temperature and suction effects. The expression for factor of safety of unsaturated soil slope at elevated temperature under undrained condition was derived. The ranges of temperature and suction in simulation were 25 to 60 degree Celsius and 0 to 100 kPa, respectively. The simulation was performed using soil parameters presented in literature. The simulation results shows the variation in factor of safety of soils slope with matric suction and temperature. The factor of safety of soil slope with circular failure surface increased with increasing matric suction for all values of temperature but decreased with increasing temperature for all values of matric suction.

Stability analysis of rock-fill tailing dam: an Indian case study

This paper presents the comprehensive stability analysis of the rock-fill tailing dam constructed at Rampura Agucha zinc mine in Rajasthan, India. The results of the feasibility study carried out prior to the expansion of the dam height from existing 27 to 51 m have been presented. The final cross-section of the tailing dam was arrived based on the extensive stability analysis considering both the upstream and downstream methods of embankment rising. The factor of safety values was calculated from Bishop’s simplified method, Janbu’s method and Spencer’s method by considering the circular failure surfaces. Further, the dynamic stability analyses were also carried out using the pseudostatic approach. The results from the limit equilibrium approaches were validated with the shear strength reduction technique using finite difference-based Fast Lagrangian Analysis of Continua in 2D analysis. The factor of safety values calculated from the different approaches was found to be in good agreement with each other. In addition, the safety and stability of the tailing dam was found unaffected by the ongoing mining activities as the observed peak particle velocity at the site was less than 15 mm/s. Analysis of the last 25 year’s rainfall data suggested that the designed freeboard of 2 m above settled tailings can accommodate a single rainfall spell of approximately 2000 mm without endangering its structural stability.