The stability safety factor calibration based on the reliability index

When the bridge structure stability safety factor of the first type is 4, the research that whether the structure reliability index will reach target reliability index under the more-likely-to-happen collapse situation of the second type is necessary. The stability calculations of the first and the second type are made respectively for single layer and single span rigid frame bridge. Based on the critical load obtained from the stability calculation of the first type, the stability safety factor of the first type is taken as 4, and the first order reliability method is used to program and calculate the reliability index. Then, the load effect under the stability reliability index cal- culation of the first type and the critical load of the second type are employed to calculate the reliability index of the second type. The evaluation of structure stability safety factor is discussed according to reliability index. Based on the discussion above, parameter analysis of the stable critical loads of two types is made, and the in- fluence of critical load change on reliability index is researched. The result shows that stability analysis should identify collapse state; when the stability safety factor of the first type is 4, but the structure has the collapse of the second type, the reliability index cannot be ensured to reach the target reliability index under certain condi- tions.

Three-dimensional stability of landslides based on local safety factor

Unlike the limit equilibrium method(LEM), with which only the global safety factor of the landslide can be calculated, a local safety factor(LSF) method is proposed to evaluate the stability of different sections of a landslide in this paper. Based on three-dimensional(3D) numerical simulation results, the local safety factor is defined as the ratio of the shear strength of the soil at an element on the slip zone to the shear stress parallel to the sliding direction at that element. The global safety factor of the landslide is defined as the weighted average of all local safety factors based on the area of the slip surface. Some example analyses show that the results computed by the LSF method agree well with those calculated by the General Limit Equilibrium(GLE) method in two-dimensional(2D) models and the distribution of the LSF in the 3D slip zone is consistent with that indicated by the observed deformation pattern of an actual landslide in China.

Limit equilibrium method(LEM) of slope stability and calculation of comprehensive factor of safety with double strength-reduction technique

When the slope is in critical limit equilibrium(LE) state, the strength parameters have different contribution to each other on maintaining slope stability. That is to say that the strength parameters are not simultaneously reduced. Hence, the LE stress method is established to analyze the slope stability by employing the double strengthreduction(DSR) technique in this work. For calculation model of slope stability under the DSR technique, the general nonlinear Mohr–Coulomb(M–C) criterion is used to describe the shear failure of slope. Meanwhile, the average and polar diameter methods via the DSR technique are both adopted to calculate the comprehensive factor of safety(FOS) of slope. To extend the application of the polar diameter method, the original method is improved in the proposed method. After comparison and analysis on some slope examples, the proposed method's feasibility is verified. Thereafter, the stability charts of slope suitable for engineering application are drawn. Moreover, the studies show that:(1) the average method yields similar results as that of the polardiameter method;(2) compared with the traditional uniform strength-reduction(USR) technique, the slope stability obtained using the DSR techniquetends to be more unsafe; and(3) for a slope in the critical LE state, the strength parameter φ, i.e., internal friction angle, has greater contribution on the slope stability than the strength parameters c, i.e., cohesion.

Stability evaluation method of large cross-section tunnel considering modification of thickness-span ratio in mechanized operation

Purpose-This study aims to research the large cross-section tunnel stability evaluation method corrected after considering the thickness-span ratio.Design/methodology/approach-First,taking the Liuyuan Tunnel of Huanggang-Huangmei High-Speed Railway as an example and taking deflection of the third principal stress of the surrounding rock at a vault after tunnel excavation as the criterion,the critical buried depth of the large section tunnel was determined.Then,the strength reduction method was employed to calculate the tunnel safety factor under different rock classes and thickness-span ratios,and mathematical statistics was conducted to identify the relationships of the tunnel safety factor with the thickness-span ratio and the basic quality(BQ)index of the rock for different rock classes.Finally,the influences of thickness-span ratio,groundwater,initial stress of rock and structural attitude factors were considered to obtain the corrected BQ,based on which the stability of a large cross-section tunnel with a depth of more than 100 m during mechanized operation was analyzed.This evaluation method was then applied to Liuyuan Tunnel and Cimushan No.2 Tunnel of Chongqing Urban Expressway for verification.Findings-This study shows that under different rock classes,the tunnel safety factor is a strict power function of the thickness-span ratio,while a linear function of the BQ to some extent.It is more suitable to use the corrected BQ as a quantitative index to evaluate tunnel stability according to the actual conditions of the site.Originality/value-The existing industry standards do not consider the influence of buried depth and span in the evaluation of tunnel stability.The stability evaluation method of large section tunnel considering the correction of overburden span ratio proposed in this paper achieves higher accuracy for the stability evaluation of surrounding rock in a full or large-section mechanized excavation of double line high-speed railway tunnels.

Slope Stability Analysis: Case of the West Wall of the EMZ Pit at the Essakane Gold Mine in Burkina Faso (West Africa)

Knowledge of the state of stability of mining pits is both a basic condition, an essential axis and a safety benchmark for mining operations. This stability is largely based on the knowledge of the rock mass sheltering the mining works and this requires a perfect characterization of all of its structural formations through mapping (manual or digital). The families of discontinuities, namely family 1 (bedding), family 2 (Joint 2) and family 3 (Joint 1) obtained through structural mapping in the Essakane open pit mine, made it possible to analyze the failure modes at the origin of rock instabilities. The respective dips of these different directional families are: 77˚ - 85˚/N 058˚ - 068˚, 66˚ - 74˚/N 133˚ - 143˚, 25˚ - 35˚/N115˚ - 130˚. An average safety factor of 4.3 was estimated for the area with a quality of the rock mass (RMR) estimated at 47. The results obtained reflect on the one hand the risks of instability associated with the quality of the rock mass studied and on the other hand highlights the state of stability of the study area.

Study of Slope Stability Using the Bishop Slice Method: An Approach Combining Analytical and Numerical Analyses

The importance of slope stability in civil engineering cannot be underestimated, as failure of these structures can result in significant damage to downstream infrastructure and property. In this study, we used the Bishop slice method, combining both an analytical approach and a numerical approach using the SLOPE/W module of the Geostudio 2018 R2 software. The results obtained from these two methods showed that increasing soil cohesion helps to improve slope stability. The safety coefficients obtained by the analytical method vary between 0.621 and 1.422, while those obtained by the numerical method vary between 0.622 and 1.447, for cohesion values ranging from 4 kPa to 20 kPa. The results obtained by these two methods show a linear relationship between the safety coefficients and soil cohesion. The equation of the analytical method is y = 0.0496x + 0.4407, while that of the numerical method is y = 0.0512x + 0.4357. The results of the analytical approach indicate that a safety coefficient of 1.5 is reached when the cohesion reaches a value of 22 kPa, while the numerical approach shows a safety coefficient of 1.5 reached at a cohesion of 21 kPa. The difference between these two cohesion values can be explained by the number of slices used, which is smaller in the analytical method. However, the equation derived from the analytical method can be used as a general guide to assess the evolution of the safety coefficient of an overloaded slope in long-term behaviour with an increase in cohesion. However, it is important to stress the importance of verification using specialised software based on the finite element method.

Safety Level and Reliability Index for Bank Slope Stability

Based on statistics and analysis of the safety factor of unstable bank slopes, the relation between safety level and reliability index of stability is studied and discussed, and then the elementary calibrating calculation is carried out to the levels of safety and reliability for bank slope stability in the range of safety factors stipulated in existing China Technical Specifications for Port Engineering - Foundation Part (1987) and to those reached by some stable bank slopes already built. The results show that the reliability index beta in the effective stress method is able to reach a high value of 2.4 similar to 4.1 (mid-value 3.25), while the value of beta in other three kinds of total stress method can just reach a lower value of 0.5 similar to 2.8 (mid-value 1.65), which are in conformity with the engineering experience in China, and thus acceptable. Some suggestions are also given in this paper to the adoption of the value of beta(0)-objective reliability index for bank slope stability.

Investigating the Effect of Weather and Seasonal Factors on Root Stability Using Dynamic Measurements

The dynamic tree stability assessment technique allows trees to be measured efficiently, under realistic weather conditions. In this study, the stability of four trees, including two conifers and two broad-leaved species was assessed in the Botanical Gardens of the University of Sopron, Hungary. The examined trees included Horse chestnut, Japanese zelkova, Douglas fir and Giant sequoia. Each tree was measured in various weather and seasonal conditions. Results show that the seasons affected the stability of broadleaved trees significantly, due to considerable changes in the crown surface area, while this difference was much lower in softwoods. Rainy weather loosens the topsoil, which adversely affects the stability of trees with relatively shallow roots. Lower layers take longer to saturate, and therefore trees with very deep roots are usually unaffected by the looser topsoil, while the increased weight of the top layer compacts the lower layers and improves stability, as evidenced by results measured on Sequoia. Snow accumulation on the branches increases the inertia of the tree, which imposes higher torque on the root collar, decreasing stability. In the meantime, the increased resistance offered by frozen ground stabilizes the tree, which more-or-less counterbalances this effect. A more extensive database of tree stability under different conditions is being built to allow for more comprehensive analysis of various factors, like wind direction, tree health and morphology, shading, etc.

Probabilistic stability analyses of undrained slopes by 3D random fields and finite element methods

A long slope consisting of spatially random soils is a common geographical feature. This paper examined the necessity of three-dimensional(3 D) analysis when dealing with slope with full randomness in soil properties. Although 3 D random finite element analysis can well reflect the spatial variability of soil properties, it is often time-consuming for probabilistic stability analysis. For this reason, we also examined the least advantageous(or most pessimistic) cross-section of the studied slope. The concept of"most pessimistic" refers to the minimal cross-sectional average of undrained shear strength. The selection of the most pessimistic section is achievable by simulating the undrained shear strength as a 3 D random field. Random finite element analysis results suggest that two-dimensional(2 D) plane strain analysis based the most pessimistic cross-section generally provides a more conservative result than the corresponding full 3 D analysis. The level of conservativeness is around 15% on average. This result may have engineering implications for slope design where computationally tractable 2 D analyses based on the procedure proposed in this study could ensure conservative results.

Early warning system for shallow landslides using rainfall threshold and slope stability analysis

A combined cluster and regression analysis were performed for the first time to identify rainfall threshold that triggers landslide events in Amboori, Kerala, India. Amboori is a tropical area that is highly vulnerable to landslides. The 2, 3, and 5-day antecedent rainfall data versus daily rainfall was clustered to identify a cluster of critical events that could potentially trigger landslides. Further, the cluster of critical events was utilized for regression analysis to develop the threshold equations. The 5-day antecedent(xvariable) vs. daily rainfall(y-variable) provided the best fit to the data with a threshold equation of y = 80.7-0.1981 x. The intercept of the equation indicates that if the 5-day antecedent rainfall is zero, the minimum daily rainfall needed to trigger the landslide in the Amboori region would be 80.7 mm. The negative coefficient of the antecedent rainfall indicates that when the cumulative antecedent rainfall increases, the amount of daily rainfall required to trigger monsoon landslide decreases. The coefficient value indicates that the contribution of the 5-day antecedent rainfall is～20% to the landslide trigger threshold. The slope stability analysis carried out for the area, using Probabilistic Infinite Slope Analysis Model(PISA-m), was utilized to identify the areas vulnerable to landslide in the region. The locations in the area where past landslides have occurred demonstrate lower Factors of Safety(FS) in the slope stability analysis. Thus, rainfall threshold analysis together with the FS values from slope stability can be suitable for developing a simple, cost-effective, and comprehensive early-warning system for shallow landslides in Amboori and similar regions.

Limit equilibrium analysis for stability of soil nailed slope and optimum design of soil nailing parameters

Reinforcement of slopes using soil nailing can effectively improve slope stability, and it has been widely used in upgrading cut slopes. Based on the assumptions of stresses on the slip surface, a new method for analyzing the stability of a slope reinforced with soil nails was established in the limit equilibrium theory framework, by considering that slope sliding occurs owing to shear failure of the slip surface, which subjects to Mohr–Coulomb(M–C) strength criterion. Meanwhile, in order to easily analyze the stability of a soil nailed slope in actual engineering and facilitate optimum design of parameters for soil nailing, factor of safety(FOS) contour curve charts were drawn on the basis of the established linear proportional relationship between the spacing of soil nails and slope height, and the length of soil nails and slope height. Then, by analyzing and verifying the results obtained from classic examples, some conclusions can be got as follows: 1) The results obtained from the current method are close to those obtained from the traditional limit equilibrium methods, and the current method can provide a strict solution for the slope FOS as it satisfies all the static equilibrium conditions of a sliding body, thus confirming the feasibility of the current method; 2) The slope FOS contour curve charts can be used not only to reliably analyze the stability of a soil nailed slope, but also to design optimally the parameters of soil nailing for the slope with a certain safety requirement.

Opposition-Based Firefly Algorithm for Earth Slope Stability Evaluation

This paper introduces a new approach of firefly algorithm based on opposition-based learning （OBFA） to enhance the global search ability of the original algorithm. The new algorithm employs opposition based learning concept to generate initial population and also updating agents’ positions. The proposed OBFA is applied for minimization of the factor of safety and search for critical failure surface in slope stability analysis. The numerical experiments demonstrate the effectiveness and robustness of the new algorithm.

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.

Couple analysis on strength reduction theory and rheological mechanism for slope stability

Considering the rheological properties of rock and soil body,and exploiting the merit of strength reduction technique,a theory of couple analysis is brought forward on the basis of strength reduction theory and rheological properties.Then,the concept and the calculation procedure of the safety factor are established at different time.Making use of finite element software ANSYS,the most dangerous sliding surface of the slope can be obtained through the strength reduction technique.According to the dynamic safety factor based on rheological mechanism,a good forecasting could be presented to prevent and cure the landslide.The result shows that the couple analysis reveals the process of the slope failure with the time and the important influence on the long-term stability due to the rheological parameters.

Stability Analysis of Bohai Oil-Drilling Ship No. 6 Under Static and Cyclic Loads

This paper presents a procedure to calculate the safety factor against sliding of a marine gravity structure subjected to a combination of static and cyclic loads. This procedure claculates the stress at the sliding surface by the finite element method (FEM) and takes the dynamic properties of clay into account. With this procedure, the stability of a Bohai oil-drilling ship is analyzed. The calculated safety factor is much smaller than 1, indicating that this oil-drilling ship would fail just as what had happened to it.

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.

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.

A Coal Mine Dump Stability Analysis—A Case Study

The present paper mainly deals with a case study of failed dump slope in western coalfield limited, Nagpur, India. A huge mass of debris flow had happened during the routine the activity of mining. The failed dump had a height of 75 m with 43? slope angle which had slipped forward by 18m. Representative loose dump material samples were collected from the site and tested to determine the physico-mechanical properties of dump material. The dump material consisted of loose fragments and lumps of friable sandstone, shale, clay and carbonaceous shale. To evaluate the condition of failure, a well known, shear strength reduction tech-nique has been applied to achieve the desired factor of safety using two dimensional finite element code. Fi-nally, a economical, sustainable and stable dump angle and height has been suggested for smooth and safe disposal of the dump.

Evaluation of the stability of vegetated slopes according to layout and temporal changes

Vegetation in slopes can effectively improve slope stability.However,it is difficult to estimate the effects of vegetation on slope stability because of variations in plant species and environmental conditions.Moreover,influences of plant growth on slope stability change with time,resulting in changes in the safety factor.This study was conducted to evaluate the stability of vegetated slopes with time and investigate the effects of different layouts of plant species on slope stability.Here,we used a plant growth model and slope stability analysis to build an evaluation model.To accomplish this,one species of tree,shrub and grass was chosen to set six layout patterns.A slope with no vegetation served as a control.The safety factors of the seven slopes were then calculated using the developed evaluation model and differences in the safety factors of slopes were compared and discussed.The slope vegetated with Platycladus orientalis reached the most stable state at the age of 60 years.Shrub slope(Vitex negundo)had the maximum safety factor after 20 years.Overall,the safety factor of vegetated slopes increased from 12.1%to 49.6% compared to the slope with no vegetation.When wind force was considered,the safety factor value of the slope changed from 3.5%to 43.5%.Vegetation mixtures of trees and grasses resulted in the best slope stability.Planting grasses on slopes can improve slope stability of trees to a greater degree than that of slopes with shrubs in the early stage of growth.

Slope Stability Evaluations by Limit Equilibrium and Finite Element Methods Applied to a Railway in the Moroccan Rif

Since 1930, the analysis of slope stability is done according to the limit equilibrium approach. Several methods were developed of which certain remain applicable because of their simplicity. However, major disadvantages of these methods are (1) they do not take into account the soil behavior and (2) the complex cases cannot be studied with precision. The use of the finite elements in calculations of stability has to overcome the weakness of the traditional methods. An analysis of stability was applied to a slope, of complex geometry, composed of alternating sandstone and marls using finite elements and limit equilibrium methods. The calculation of the safety factors did not note any significant difference between the two approaches. Various calculations carried out illustrate perfectly benefits that can be gained from modeling the behavior by the finite elements method. In the finite elements analysis, the shape of deformations localization in the slope is nearly circular and confirms the shape of the failure line which constitutes the basic assumption of the analytical methods. The integration of the constitutive laws of soils and the use of field’s results tests in finite elements models predict the failure mode, to better approach the real behavior of slope soil formations and to optimize its reinforcement.