Factor of safety of strain-softening slopes

Stability analysis of strain-softening slopes is carried out using the shear strength reduction method and Mohr-Coulomb model with degrading cohesion and friction angle.The e ffect of strain-softening behavior on the slope factor of safety is investigated by performing a series of analyses for various slope geometries and strength properties.Stability charts and equations are developed to estimate the factor of safety of strain-softe ning slopes from the results of traditional stability analysis based on perfectly-plastic behavior.Two example applications including an open pit mine in weak rock and clay shale slope with daylighting bedding planes are presented.The results of limit equilibrium analysis and shear strength reduction method with perfectly-plastic models were in close agreement.Using perfectly-plastic models with peak strength properties led to overly optimistic results while adopting residual strength properties gave excessively conservative outcomes.The shear strength reduction method with a strain-softening model gave realistic factors of safety while accounting for the process of strength degradation.

A Calculation Method of Double Strength Reduction for Layered Slope Based on the Reduction of Water Content Intensity

The calculation of the factor of safety(FOS)is an important means of slope evaluation.This paper proposed an improved double strength reductionmethod(DRM)to analyze the safety of layered slopes.The physical properties of different soil layers of the slopes are different,so the single coefficient strength reduction method(SRM)is not enough to reflect the actual critical state of the slopes.Considering that the water content of the soil in the natural state is the main factor for the strength of the soil,the attenuation law of shear strength of clayey soil changing with water content is fitted.This paper also establishes the functional relationship between different reduction coefficients.Then,a USDFLD subroutine is programmed using the secondary development function of finite element software.Controlling the relationship between field variables and calculation time realizes double strength reduction applicable to the layered slope.Finally,by comparing the calculation results of different examples,it is proved that the stress and displacement distribution of the critical slope state obtained by the improved method is more realistic,and the calculated safety factor is more reliable.The newly proposedmethod considers the difference of intensity attenuation between different soil layers under natural conditions and avoids the disadvantage of the strength reduction method with uniform parameters,which provides a new idea and method for stability analysis of layered and complex slopes.

Probabilistic Analysis of Slope Using Finite Element Approach and Limit Equilibrium Approach around Amalpata Landslide of West Central, Nepal

The stability study of the ongoing and recurring Amalpata landslide in Baglung in Nepal’s Gandaki Province is presented in this research. The impacted slope is around 200 meters high, with two terraces that have different slope inclinations. The lower bench, located above the basement, consistently fails and sets others up for failure. The fluctuating water level of the slope, which travels down the slope masses, exacerbates the slide problem. The majority of these rocks are Amalpata landslide area experiences several structural disruptions. The area’s stability must be evaluated in order to prevent and control more harm from occurring to the nearby agricultural land and people living along the slope. The slopes’ failures increase the damages of house existing in nearby area and the erosion of the slope. Two modeling techniques the finite element approach and the limit equilibrium method were used to simulate the slope. The findings show that, in every case, the terrace above the basement is where the majority of the stress is concentrated, with a safety factor of near unity. Using probabilistic slope stability analysis, the failure probability was predicted to be between 98.90% and 100%.

Upper bound solutions of stability factor of shallow tunnels in saturated soil based on strength reduction technique

Based on the upper bound theorem of limit analysis,the factor of safety for shallow tunnel in saturated soil is calculated in conjunction with the strength reduction technique.To analyze the influence of the pore pressure on the factor of safety for shallow tunnel,the power of pore pressure is regarded as a power of external force in the energy calculation.Using the rigid multiple-block failure mechanism,the objective function for the factor of safety is constructed and the optimal solutions are derived by employing the sequential quadratic programming.According to the results of optimization calculation,the factor of safety of shallow tunnel for different pore pressure coefficients and variational groundwater tables are obtained.The parameter analysis shows that the pore pressure coefficient and the location of the groundwater table have significant influence on the factor of safety for shallow tunnel.

The Hidden Earthquake Induced Liquefaction Risks in the Rohingya Refugee Camp Hills & Surrounding Areas of Ukhiya, Cox’s Bazar, Bangladesh—A Geotechnical Engineering Approach

Liquefaction is one of the major catastrophic geohazards which usually occurs in saturated or partially saturated sandy or silty soils during a seismic event. Evaluating the potential liquefaction risks of a seismically prone area can significantly reduce the loss of lives and damage to civil infrastructures. This research is mainly focused on the earthquake-induced liquefaction risk assessment based on Liquefaction Potential Index (LPI) values at different earthquake magnitudes (M = 5.0, 7.0 and 8.0) with a peak ground acceleration (amax) of 0.28 g in the Rohingya Refugee camp and surrounding areas of Ukhiya, Cox’s Bazar, Bangladesh. Standard Penetration Test (SPT) results have been evaluated for potential liquefaction assessment. The soils are mainly composed of very loose to loose sands with some silts and clays. Geotechnical properties of these very loose sandy soils are very much consistent with the criteria of liquefiable soil. It is established from the grain size analysis results;the soil of the study area is mainly sand dominated (SP) with some silty clay (SC) which consists of 93.68% to 99.48% sand, 0.06% to 4.71% gravel and 0% to 6.26% silt and clay. Some Clayey Sand (SC) is also present. The silty clay can be characterized as medium (CI) to high plasticity (CH) inorganic clay soil. LPI values have been calculated to identify risk zones and to prepare risk maps of the investigated area. Based on these obtained LPI values, four (4) susceptible liquefaction risk zones are identified as low, medium, high and very high. The established “Risk Maps” can be used for future geological engineering works as well as for sustainable planning, design and construction purposes relating to adaptation and mitigation of seismic hazards in the investigated area.

Upper bound analysis of slope stability with nonlinear failure criterion based on strength reduction technique

Based on the upper bound limit analysis theorem and the shear strength reduction technique, the equation for expressing critical limit-equilibrium state was employed to define the safety factor of a given slope and its corresponding critical failure mechanism by means of the kinematical approach of limit analysis theory. The nonlinear shear strength parameters were treated as variable parameters and a kinematically admissible failure mechanism was considered for calculation schemes. The iterative optimization method was adopted to obtain the safety factors. Case study and comparative analysis show that solutions presented here agree with available predictions when nonlinear criterion reduces to linear criterion, and the validity of present method could be illuminated. From the numerical results, it can also be seen that nonlinear parameter rn, slope foot gradient ,β, height of slope H, slope top gradient a and soil bulk density γ have significant effects on the safety factor of the slope.

Numerical analysis and geophysical monitoring for stability assessment of the Northwest tailings dam at Westwood Mine

The Westwood Mine aims to reuse the tailings storage facility #1(TSF #1) for solid waste storage, but,downstream of the Northwest dike is considered critical in terms of stability. This paper uses numerical modeling along with geophysical monitoring for assessing the Northwest dike stability during the restoration phase. The impact of waste rock deposition in the upstream TSF #1 is considered. The geophysical monitoring is based on electrical resistivity methods and was used to investigate the internal structure of the dike embankment in different deposition stages. The numerical simulations were performed with SLOPE/W code. The results show a factor of safety well above the minimum recommended value of 1.5. Geophysical monitoring revealed a vertical variation in the electrical resistivity across the dike, which indicates a multilayer structure of the embankment. Without any current in situ data, the geophysical monitoring helped estimating the nature of the materials used and the internal structure of the embankment. These interpretations were validated by geological observation of geotechnical log of the embankment. Based on this study, it is recommended that the water polishing pond be partly filled before waste rock is deposited in TSF #1. In addition, to ensure the stability of the dike, the piezometric head monitoring prior to and during waste rock deposition is recommended.

Principles of rockbolting design

This article introduces the principles of underground rockbolting design.The items discussed include underground loading conditions,natural pressure zone around an underground opening,design methodologies,selection of rockbolt types,determination of bolt length and spacing,factor of safety,and compatibility between support elements.Different types of rockbolting used in engineering practise are also presented.The traditional principle of selecting strong rockbolts is valid only in conditions of low in situ stresses in the rock mass.Energy-absorbing rockbolts are preferred in the case of high in situ stresses.A natural pressure arch is formed in the rock at a certain distance behind the tunnel wall.Rockbolts should be long enough to reach the natural pressure arch when the failure zone is small.The bolt length should be at least 1 m beyond the failure zone.In the case of a vast failure zone,tightly spaced short rockbolts are installed to establish an artificial pressure arch within the failure zone and long cables are anchored on the natural pressure arch.In this case,the rockbolts are usually less than 3 m long in mine drifts,but can be up to 7 m in large-scale rock caverns.Bolt spacing is more important than bolt length in the case of establishing an artificial pressure arch.In addition to the factor of safety,the maximum allowable displacement in the tunnel and the ultimate displacement capacity of rockbolts must be also taken into account in the design.Finally,rockbolts should be compatible with other support elements in the same support system in terms of displacement and energy absorption capacities.

A New Approach to the Determination of the Critical Slip Surfaces of Slopes

A new method for the determination of the critical slip surfaces of slopes is proposed in this paper. In this paper, the original critical slip field method is extended in terms of the total residual moment, values of residual work as well as the unbalanced thrust force at the exit point for a given non-circular slip surface. The most critical slip surface with the maximum representative value for a prescribed factor of safety will be optimized and located using the harmony search algorithm. The prescribed factor of safety is modified with certain tiny interval in order to find the critical slip surface where the maximum representative value is zero. The aforementioned approach to the location of the critical slip surface is greatly different from the traditional limit equilibrium procedure. Three typical soil slopes are evaluated by use of the proposed method, and the comparisons with the classical approaches have illustrated the applicability of the proposed method.

Study on embedded length of piles for slope reinforced with one row of piles

The embedded length of anti-slide piles for slope is analyzed by three-dimensional elastoplastic shear strength reduction method. The effect of embedded pile length on the factor of safety and pile behavior is analyzed. Furthermore, the effects of pile spacing, pile head conditions, pile bending stiffness and soil properties on length and behavior of pile are also analyzed. The results show that the pile spacing and the pile head conditions have significant influences on the critical embedded length of pile. It is found that the critical embedded length of pile, beyond which the factor of safety does not increase, increases with the decrease in pile spacing. The smaller the pile spacing is, the larger the integrity of the reinforced slope will be. A theoretical analysis of the slip surface is also conducted, and the slip surface determined by the pressure on piles, considering the influences of both soil and piles for slope, is in agreement with the ones in previous studies.

Limit equilibrium stability analysis of slopes under external loads

Two calculation modes for the effect of external load on slope stability, i.e., mode I in which the external load is thought to act on slope surface, and mode II in which the external load is thought to act on slip surface along the force action line, were considered. Meanwhile, four basic distribution patterns of external load were used, of which complex external loads could be composed. In analysis process, several limit equilibrium methods, such as Swedish method, simplified Bishop method, simplified Janbu method, Spencer method, Morgenstern-Price(M-P) method, Sarma method, and unbalanced thrust method, were also adopted to contrast their differences in slope stability under the external load. According to parametric analysis, some conclusions can be obtained as follows:(1) The external load, with the large magnitude, small inclination angle, and acting position close to the slope toe,has more positive effect on slope stability;(2) The results calculated using modes I and II of external load are similar, indicating that the calculation mode of external load has little influence on slope stability;(3) If different patterns of external loads are equivalent to each other, their slope stability under these external loads are the same, and if not, the external load leads to the better slope stability,as action position of the resultant force for external load is closer to the lower sliding point of slip surface.

Seismic analysis of nailed vertical excavation using pseudo-dynamic approach

An attempt has been made to study the behavior of nailed vertical excavations in medium dense to dense cohesionless soil under seismic conditions using a pseudo-dynamic approach. The effect of several parameters such as angle of internal friction of soil （φ）, horizontal （kh） and vertical （kv） earthquake acceleration coefficients, amplification factor （fa）, length of nails （L）, angle of nail inclination （a） and vertical spacing of nails （S） on the stability of nailed vertical excavations has been explored. The limit equilibrium method along with a planar failure surface is used to derive the formulation involved with the pseudo-dynamic approach, considering axial pullout of the installed nails. A comparison of the pseudo-static and pseudo-dynamic approaches has been established in order to explore the effectiveness of the pseudo-dynamic approach over pseudo-static analysis, since most of the seismic stability studies on nailed vertical excavations are based on the latter. The results are expressed in terms of the global factor of safety （FOS）. Seismic stability, i.e., the FOS of nailed vertical excavations is found to decrease with increase in the horizontal and vertical earthquake forces. The present values of FOS are compared with those available in the literature.

3D Identification and Stability Analysis of Key Surface Blocks of Rock Slope

Complicated geological structures make it difficult to analyze the stability of rock slopes, such as faults, weak intercalated layers or joint fissures. Based on 3D geological modeling and surface block identifying methods, an integrated methodology framework was proposed and realized to analyze the stability of surface blocks in rock slopes. The surface blocks cut by geological structures, fissures or free faces could be identified subjected to the four principles of closure, completeness, uniqueness and validity. The factor of safety(FOS)of single key block was calculated by the limit equilibrium method. If there were two or more connected blocks, they were defined as a block-group. The FOS of a block-group was computed by the Sarma method. The proposed approach was applied to an actual rock slope of a hydropower project, and some possible instable blocks were demonstrated and analyzed visually. The obtained results on the key blocks or block-groups provide essential information for determining potential instable region of rock slopes and designing effective support scheme in advance.

Slope stability analysis of Balia Nala landslide, Kumaun Lesser Himalaya, Nainital, Uttarakhand, India

Balia Nala is the outlet of the Nainital lake, flowing towards southeast direction. Presence of Nainital habitation at its right bank has high socio-economic importance. This study presents the stability analysis of a ravine/valley along Balia Nala. Variegated slates(lower Krol and upper Blaini formations) are the main rock types, wherever the outcrop does exist and rest of the area is covered by slope wash and river borne materials. Three sets of joints are presented in the area, but 4 sets of joints also exist at some locations. Nainital lake fault intersected by Manora fault from southwest direction passes through eastern side of the study area, and some small faults, which are sub-branches of Nainital lake fault, are observed(with 10 m offset) and promote the landslide in the area. This study shows that different kinds of discontinuities(joints, faults and shear zones) and rapid down cutting by the stream due to neotectonic activity affect the stability of the slope. The fragile lithology and deep V-shaped valley further accelerate the mass movement in the study area. In addition, rock mass rating(RMR), factor of safety(FOS) and graphical analysis of the joints indicate the study area as landslide-prone zone. This study will be helpful in not only reducing the risk on life of people, but also in assisting the ongoing civil work in the study area.

Stability analysis of complex terrain slope based on multi-source point cloud fusion

Numerical modelling is a common routine for slope stability analysis in the complex terrain,and the accuracy of topographic survey has a great impact on the results.In this study,a combination of unmanned aerial vehicle(UAV)photogrammetry and 3D laser scanning technique was first proposed to establish a high-precision digital elevation model(DEM),which could be accurate to 0.2 m,fulfilling the engineering requirements.Then,a series of 3D/2D finite element models(FEM)were constituted on the basis of DEM to investigate the slope stability in the complex terrain.The results indicate that the deformation of complex terrain slope is chiefly triggered by compression-shear failure and the failure zones are mostly distributed on the middle-upper part and the scarp.Furthermore,the complex terrain slope is divided into concave,convex,concave-convex and convex-concave slope according to the topographical curvature,and the factor of safety(FOS)is as follows:the maximum value 1.8504 for the concave-convex slope,the minimum value 1.1129 for the convexconcave slope,and the median for either concave or convex slope.The inflection points and curvature of the slope jointly determine the shape of nonlinear slope,dominating the morphological effect on the slope stability,so the rational use of section morphological effect will be conducive to the overall stability of the slope.For four representative slopes,the plastic deformation first emerges into the middle,then progressively develops to the upper,and finally forms the connected failure zones.

Influence of rainfall infiltration on the stability of unsaturated coal gangue accumulated slope

The slope instability is associated with increasing rate of rainfall infiltration which cause shear strength reduction and suction loss and the slope tend to failure. The influences of rainfall infiltration on the stability of clayey and sandy slopes have been analyzed but the effect of rainfall infiltration on the stability of unsaturated coal gangue accumulated slope was needed to study. Therefore, a coal gangue accumulated slope prone to failure in Fuxin area of Northeast China was considered to evaluate its failure mechanism under different rainfall events. The effects after five different rainfall events on slope stability were physically analyzed, numerically investigated and the results from both uncoupled(hydraulic) and coupled(hydromechanical) responses were compared using finite element analysis. It was observed that the decisive soaking and leaching under different rainfall conditions caused maximum deformation at the crest of slope due to maximum value of permeability coefficient of coal gangue. The critical duration of moderate intensity(147 mm/day) of rainfall for the instability of coal gangue accumulated slope is declared as five days. The results from finite element analysis in this paper further clarifies that increase in duration of rainfall infiltration process cause hysteretic change in positive pore-water pressure causing decrease in factor of safety and increase in deformation. It is concluded that the stability of unsaturated coal gangue accumulated slope is greatly influence by the coupled effect of stress and porewater pressure in comparison of uncoupled(hydraulic) analysis as the obtained factor of safety values after five days of rainfall infiltration were 0.9 and 1.1 respectively.

Finite element analysis of slope stability by expanding the mobilized principal stress Mohr's circles-Development, encoding and validation

In recent years,finite element analysis is increasingly being proposed in slope stability problems as a competitive method to traditional limit equilibrium methods(LEMs)which are known for their inherent deficiencies.However,the application of finite element method(FEM)to slope stability as a strength reduction method(SRM)or as finite element limit analysis(FELA)is not always a success for the drawbacks that characterize both methods.To increase the performance of finite element analysis in this problem,a new approach is proposed in this paper.It consists in gradually expanding the mobilized stress Mohr’s circles until the soil failure occurs according to a prescribed non-convergence criterion.The present approach called stress deviator increasing method(SDIM)is considered rigorous for three main reasons.Firstly,it preserves the definition of the factor of safety(FOS)as the ratio of soil shear strength to the mobilized shear stress.Secondly,it maintains the progressive development of shear stress resulting from the increase in the principal stress deviator on the same plane,on which the shear strength takes place.Thirdly,by introducing the concept of equivalent stress loading,the resulting trial stresses are checked against the violation of the actual yield criterion formed with the real strength parameters rather than those reduced by a trial factor.The new numerical procedure was encoded in a Fortran computer code called S^(4)DINA and verified by several examples.Comparisons with other numerical methods such as the SRM,gravity increasing method(GIM)or even FELA by assessing both the FOS and contours of equivalent plastic strains showed promising results.

Stability of submarine slopes in the northern South China Sea: a numerical approach

Submarine landslides occur frequently on most continental margins. They are effective mechanisms of sediment transfer but also a geological hazard to seafloor installations. In this paper, submarine slope stability is evaluated using a 2D limit equilibrium method. Considerations of slope, sediment, and triggering force on the factor of safety （FOS） were calculated in drained and undrained （4=0） cases. Results show that submarine slopes are stable when the slope is 〈16° under static conditions and without a weak interlayer. With a weak interlayer, slopes are stable at 〈18° in the drained case and at 〈9° in the undrained case. Earthquake loading can drastically reduce the shear strength of sediment with increased pore water pressure. The slope became unstable at 〉13° with earthquake peak ground acceleration （PGA） of 0.5 g; whereas with a weak layer, a PGA of 0.2 g could trigger instability at slopes 〉 10°, and 〉3 ° for PGA of 0.5 g. The northern slope of the South China Sea is geomorphologically stable under static conditions. However, because of the possibility of high PGA at the eastern margin of the South China Sea, submarine slides are likely on the Taiwan Bank slope and eastern part of the Dongsha slope. Therefore, submarine slides recognized in seismic profiles on the Taiwan Bank slope would be triggered by an earthquake, the most important factor for triggering submarine slides on the northern slope of the South China Sea. Considering the distribution of PGA, we consider the northern slope of the South China Sea to be stable, excluding the Taiwan Bank slope, which is tectonically active.

Hill slope instability of Nainital City,Kumaun Lesser Himalaya,Uttarakhand,India

Nainital City of Kumaun Lesser Himalaya is prone to mass wasting processes during monsoon season,which mischievously triggers the hill slope instability in this region. Slate, dolomitic limestone, silty sandstone and rhythmite of the Krol Formation are the main rock types. The present study focuses on the investigation of slope stability in the region in terms of potential seismicity and landslide. Geological and geotechnical mapping indicates that the major portion of the area is characterized by slope wash materials and buildings. The combination of 3-4 joint sets with one random joint is the main structure at outcrops.The major geological structures of this area are Nainital lake fault passing from the center of the lake, Main Boundary Thrust at SW, and Khuriya Fault passing from the SE direction of Nainital City. This work finds that different types of discontinuities(e.g. joints and faults), overburden due to unplanned civil structures,and neotectonic activity in the vicinity of this ara affect the stability of the city. The slate forms the base of the city, dipping slightly towards the lake side along the NW direction, thus accelerating the instability of this area. Rock mass rating(RMR), slope mass rating, factor of safety(FOS) and graphical analysis of the discontinuity for slope kinematics indicate that the study area is a landslide-prone zone. This study can facilitate reducing the risk of human life, and contribute to the ongoing construction works in the area.

Analytical solution for slope instability assessment considering impact of confined aquifer

An analytical approach was presented for estimating the factor of safety(FS) for slope failure, with consideration of the impact of a confined aquifer. An upward-moving wetting front from the confined water was assumed and the pore water pressure distribution was then estimated and used to obtain the analytical expression of FS. Then, the validation of the theoretical analysis was applied based on an actual case in Hong Kong. It is shown that the presence of a confined aquifer leads to a lower FS value, and the impact rate of hydrostatic pressure on FS increases as the confined water pressure increases, approaching to a maximum value determined by the ratio of water density to saturated soil density. It is also presented that the contribution of hydrostatic pressure and hydrodynamic pressure to the slope stability vary with the confined aquifer pressure.