Simplified Bishop Method Research Articles

Slope stability analysis in Lusi River, Kedungrejo using limit equlibrium method

The slope is a ground has a certain angle to the horizontal plane. The stability of slope depends on the magnitude of the retaining force and the driving force present in the slip. Characteristics of soil mass are determined by laboratory test of core drilling method is conducted to determine the subsurface condition at the area of study. Assessment of slope stability is using limit equilibrium method with comparing Bishop, Janbu, and Spencer method using Slide 6.0 Program. In this study area is composed of clay with the firm to stff structure. The result of the analysis slope stability using manual method using Bishop simplified method obtained the factor of safety is 1,680 and 1,14 and based on Slide 6.0 program, the Janbu simplified method is resulting the smallest factor of safety 1,130. Therefore it can be classified as unstable condition according to the terzaghi and peck (1976) factor of safety criteria. It means that reinforcement is required to improving the slope stability. Then, the result of analysis provide information that simulation model using micropiles reinforcement is the most effetive to improving the factor of safety value. The increasing of safety factor became 1.630 on treated slope using micropiles with the space between piles is 1 m.

Effectiveness of Geogrid for Protecting Polder in Sundarban Coastal Region

Numbers of large scale polders are constructed to protect low-lying coastal area of Sundarban in Bangladesh during 1960s. At present, there are number of polders occupying an area of about 1.2 million hectares, which are vulnerable to breach and cause immense misery to millions of people every year. The purpose of this study is to assess the safety factors (FoS) of those Polder embankments during diurnal tidal cycle in coastal area and provide solution to improve the stability of embankment through installation of geogrid layers. To investigate vulnerability of the embankment failure, soil samples are collected from several borehole locations in Satkhira, a coastal site of Sundarban area. Field test—SPT and several Laboratory tests—direct shear test and Sieve analysis test have been carried out to determine shear strength, angle of internal frictions and grain size distribution. Slope stability analysis are performed using Geo5 software under several conditions—high water table (HWT), low water table (LWT) and rapid drawdown (RD) with side slope are 1:1, 1:1.5 and 1:2 and embankment height are 5m, 7.5m and 10m. The safety factor has been found lowest at rapid drawdown condition because of rapid recession of external water level. The lower FoS have been found 0.68, 0.89 and 0.92 which can be improved to 1.23, 1.34 and 1.24 respectively by installing several geogrid layers. Simplified Bishop Method have been used in Geo5 to perform the stability analysis under various conditions. In our investigation, HDPE biaxial geogrid have been taken to strengthen of polder embankments, which are timesaving, cost effective and efficient, side by side suitable for Sundarban area. The findings and solutions proposed by the study will help geotechnical engineers to reduce the vulnerability of Polder embankment under similar coastal conditions.

Study on the theory of three-dimensional limit analysis of soil and practical calculation

Based on the stress analysis of a point in space, the stress analysis of a point on a surface is performed, and then the relationship among the normal stress, the shear stress, and the stress component of a point on a surface and the first order partial derivative of the surface equation is deduced. Equilibrium equations of soil columns between the sliding surface and the top surface of the slope are established, which include differential equilibrium equation of force, equilibrium equation of force, and equilibrium equation of moment. These equilibrium equations and Coulomb yield condition can form the fundamental equations of three-dimensional slope stability analysis. Applying the supposition similar to that applied in the simplified Bishop method, a kind of three-dimensional slope analysis method can be obtained. An example is presented to show that the computation method is reasonable and applicable.

Seepage and Slope Stability Analysis of Myittha Multipurpose Dam Project, Gangaw Township, Magway Region, Myanmar

Myittha Multipurpose Dam Project is constructed on Myittha River to be implemented for hydropower production of installed power 40 MW and average annual energy 170 million kWh for regional development and irrigation network of 12,000 acres. Myittha dam has two portions of embankment: main dam (rockfill zone type) and long saddle dam (homogeneous type). The purpose of this paper is the evaluation of seepage and slope stability conditions of Myittha embankments (Myanmar) based on three different cases of operations: end of construction before filling the reservoir, steady state seepage and rapid drawdown of the reservoir. Seepage and slope stability analysis were done in two ways: analytical and computer approaches. Analytically, seepage analysis was done by using Laplace equation based on Darcy's law and slope stability analysis was done by using Ordinary Method of Slices and Bishop Simplified Method. This analytical approach was used to access based on the earthen dam details and geotechnical design parameters of embankment materials. On this research, SLOPE/W and SEEP/W soft-wares were used as computer approach. The analysis results presented in this research confirm the safety of Myittha dam against combined seepage and slope stability under all cases of operation.

The study on length and diameter ratio of nail as preliminary design for slope stabilization

Soil nailing technology has been widely applied in practice for reinforced slope. The number of studies for the effective design of nail-reinforced slopes has also increased. However, most of the previous study was focused on a safety factor of the slope; the ratio of length and diameter itself has likely never been studied before. The aim of this study is to relate the length and diameter ratio of the nail with the safety factor of the 20 m height of sand slope in the various angle of friction and steepness of the slope. Simplified Bishop method was utilized to analyze the safety factor of the slope. This study is using data simulation to calculate the safety factor of the slope with soil nailing reinforcement. The results indicate that safety factor of slope stability increases with the increase of length and diameter ratio of the nail. At any angle of friction and steepness of the slope, certain effective length and diameter ratio was obtain. These results may be considered as a preliminary design for slope stabilization.

The analysis of Stability reliability of Qian Tang River seawall

Qiantang River seawall due to high water soaking pond by foreshore scour, encountered during the low tide prone slope overall instability. Considering the seawall beach scour in front of random change, using the simplified Bishop method, combined with the variability of soil mechanics parameters, calculation and analysis of Qiantang River Xiasha seawall segments of the overall stability.

Geo-risk analysis of slopes bounding a deep gully erosion site in Uyo, Akwa-Ibom State, Southeastern Nigeria

The stability of slopes around a deep gully erosion site is the subject of this article. The site geology is the Coastal Plain Sands. To carry out stability analysis, the slopes were first characterized by deployment of cone and standard penetration tests (CPT and SPT) equipment. The slopes are highly stratified, and consist of numerous layers up to the depth of investigation which is about 37.0 m. The slope is made up of five layers of materials up to the gully valley floor. The soils of the five layers in succession from the top are clayey sand (SC), clayey/silty sand (SC–SM), gravelly clay (GC), poorly graded gravel with well graded sand mixture (GP–SW), and well graded sand (SW). Two locations on the eastern side of the of the gully site which poses serious risk to lives and properties were chosen for the analysis. The first position with the highest slope of 16.0 m gave a critical factor of safety less than 1.5 based on simplified Bishop method of analysis indicating unstable slope, while the second location results in a factor of safety greater than 1.5 suggesting a more stable slope, although there is a potential of sheet erosion on the slope at this location.

3D stability analysis method of concave slope based on the Bishop method

In order to study the stability control mechanism of a concave slope with circular landslide, and remove the influence of differences in shape on slope stability, the limit analysis method of a simplified Bishop method was employed. The sliding body was divided into strips in a three-dimensional model, and the lateral earth pressure was put into mechanical analysis and the three-dimensional stability analysis methods applicable for circular sliding in concave slope were deduced. Based on geometric structure and the geological parameters of a concave slope, the influence rule of curvature radius and the top and bottom arch height on the concave slope stability were analyzed. The results show that the stability coefficient decreases after growth, first in the transition stage of slope shape from flat to concave, and it has been confirmed that there is a best size to make the slope stability factor reach a maximum. By contrast with average slope, the stability of a concave slope features a smaller range of ascension with slope height increase, which indicates that the enhancing effect of a concave slope is apparent only with lower slope heights.

Stability assessment of homogeneous slopes loaded with mobile tracked cranes—An artificial neural network approach

The assessment of stability of homogeneous slopes found as part of embankments, approach ramps, in bridge construction or flood protection levees could be a complex task. Either during construction or at a point in the operating life of the earth structure it can be subjected to loads from the equipment operating on it. Mobile tracked cranes used in heavy lifting or dredging operations can apply loads due to their substantial self-weight combined with the load carried by them. It is important to be able to determine the minimum factor of safety for such slopes. However due to the combination of soil parameters, slope geometry and the variable nature of loading imposed, a substantial number (measured perhaps in hundreds of combinations) slope stability analyses would be required to find the minimum factor of safety. One approach to reduce the number of analyses needed is to develop an Artificial Neural Network, train it using a representative dataset of stability analyses, and rely on its predicting capabilities to determine the minimum factor of safety for the slope for any combination of model parameters. Artificial Neural Networks can simulate the central nervous system of a human brain, by training them using the input data and target data one can build a neural network and use them for the factor of safety prediction. Since this thesis considers the case of homogeneous constructed slopes, thus the slope stability analysis was performed using Bishop Simplified Method, and the load distribution due to mobile tracked cranes was represented by an equivalent triangular distribution acting on the slope surface. The slope stability analysis was performed using Slide (from rocscience Inc.) to obtain the training dataset and MATLAB was used to develop and train the artificial neural network. A detailed investigation to assess and improve the network accuracy was carried out, and it was established that by increasing the neuron numbers and hidden layers, the ultimate average error in predicting the factor of safety for an independent test data set was 0.677%. This error, considering the inherent uncertainty of soil properties, instils confidence in using the Artificial Neural Network for predicting the factor of safety of homogeneous slopes loaded by mobile cranes.

PERFORMANCE OF ANALYSIS METHODS OF SLOPE STABILITY FOR DIFFERENT GEOTECHNICAL CLASSES SOIL ON EARTH DAMS

The aim of this study was to evaluate the performance of less accurate analysis methods of slope stability, in order to reduce the number of operations used by the most accurate methods available in the literature. The study evaluated four methods for calculating slope stability. Fellenius (FELLENIUS, 1936), Bishop (BISHOP, 1955), Simplified Bishop (BISHOP & MORGENSTERN, 1960) and Simplified Janbu (JANBU, 1973) were compared with the Spencer method (SPENCER, 1967), which is considered an accurate method for calculating the factor of safety (FS). The procedure was performed in scenarios with different soil groups according to the Unified Soil Classification System (USCS) (ASTM 2011), heights and slope inclinations, and under conditions of reservoir subject to fast and slow emptying. Thus, comparative analyses were made using the correlation index “r”, the accuracy index “d” (WILLMOTT et al, 1985) and the performance index “c” (CAMARGO & SENTELHAS, 1997). The methods that had optimal performance for the analyzed conditions were the Simplified Bishop, the Simplified Janbu and the Bishop methods; the Simplified Bishop method obtained a correlation coefficient of 99%. Thus, they can be used as alternative methods to replace the Spencer method in the analysis of slope stability on earth dams.

Limit equilibrium method for slope stability based on assumed stress on slip surface

In the limit equilibrium framework, two- and three-dimensional slope stabilities can be solved according to the overall force and moment equilibrium conditions of a sliding body. In this work, based on Mohr-Coulomb (M-C) strength criterion and the initial normal stress without considering the inter-slice (or inter-column) forces, the normal and shear stresses on the slip surface are assumed using some dimensionless variables, and these variables have the same numbers with the force and moment equilibrium equations of a sliding body to establish easily the linear equation groups for solving them. After these variables are determined, the normal stresses, shear stresses, and slope safety factor are also obtained using the stresses assumptions and M-C strength criterion. In the case of a three-dimensional slope stability analysis, three calculation methods, namely, a non-strict method, quasi-strict method, and strict method, can be obtained by satisfying different force and moment equilibrium conditions. Results of the comparison in the classic two- and three-dimensional slope examples show that the slope safety factors calculated using the current method and the other limit equilibrium methods are approximately equal to each other, indicating the feasibility of the current method; further, the following conclusions are obtained: 1) The current method better amends the initial normal and shear stresses acting on the slip surface, and has the identical results with using simplified Bishop method, Spencer method, and Morgenstern-Price (M-P) method; however, the stress curve of the current method is smoother than that obtained using the three abovementioned methods. 2) The current method is suitable for analyzing the two- and three-dimensional slope stability. 3) In the three-dimensional asymmetric sliding body, the non-strict method yields safer solutions, and the results of the quasi-strict method are relatively reasonable and close to those of the strict method, indicating that the quasi-strict method can be used to obtain a reliable slope safety factor.

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.

Reliability analysis of slopes in strain-softening soils considering critical slip surfaces

Abstract The paper concerns to the reliability analysis of slopes in strain-softening cohesive soils, using the first order reliability method (FORM). The performance function is based on the Bishop simplified method adapted to take strain-softening into account in terms of the residual factor R F over a potential slip surface, estimated based on a progressive failure model available in the literature. The reliability analysis is carried out on the surface of minimum factor of safety determined using the sequential quadratic programming (SQP). The random shear strength parameters are assumed to follow normal distribution while the residual factor has been considered both as a deterministic parameter and a beta-distributed random variable. The results obtained for an illustrative example shows substantial reduction (21 %) in the value of reliability index when R F is considered as a random variable with an assumed COV of 0.3. Results of FORM-based sensitivity analyses also reveal that R F has the most dominating influence on reliability and thus justifies its inclusion as one of the random variables. A parametric study, varying the assumed correlation coefficient between the random shear strength parameters from 0 to 1, shows that there is a maximum reduction of 16 % in reliability index.

Rainfall thresholds for landslide early warning system in Nakhon Si Thammarat

Transient seepage in unsaturated soil slope is one of the significant triggering factors in rainfall-induced landslides. Rainfall infiltration leads to the decrease in stabilizing effect because of increased positive pore-water pressures. SEEP/W and SLOPE/W used in this study have been widely employed to describe frameworks for understanding transient seepage in soil slope, and to perform slope stability analyses, respectively. The study area is in Sichon District in Nakhon Si Thammarat Province, southern Thailand. A landslide there was investigated by modeling the process of rainfall infiltration under positive and negative pore-water pressures and their effects on slope stability. GIS (Geographic Information System) and geotechnical laboratory results were used as input parameters. The van Genuchten’s soil water characteristic curve and unsaturated permeability function were used to estimate surface infiltration rates. An average rainfall was derived from 30-year monthly rainfall data between 1981 and 2011 in this area reported by the Thailand Royal Irrigation Department. For transient condition, finite element analysis in SEEP/W was employed to model fluctuations in pore-water pressure during a rainfall, using the computed water infiltration rates as surface boundary conditions. SLOPE/W employing Bishop simplified method was then carried out to compute their factors of safety, and antecedent precipitation indices (API) calculated. Heterogeneous slope at the site became unstable at an average critical API (APIcr) of 380 mm, agreeing well with the actual value of 388 mm.

Interpretasi Letak Bidang Longsor dan Faktor Aman Lereng dengan Bahasa Pemrograman MATLAB

Slope stability analyses can be performed using computer program, such as Matrix Laboratory (MATLAB). In the current work, a computer program for slope stability analysis named JOZLOPE based on MATLAB and using Bishop simplified analysis method was used to determine the location of a slip surface and its safety factor. The validation is carried out by analyzing three simple slope models and comparing their results by JOZLOPE and some comparator slope stability analysis programs. It is found that the variations between JOZLOPE’s results and those of the comparators are less than 1% for bottom circle-slope geometry intersection, less than 7% for top circle-slope geometry intersection and less than 4% for Safety Factor. These findings demonstrates that the a MATLAB program is successfully compiled and it produced measured values that agree with those of their respective comparator.

Numerical Analysis on Stability of Caisson-Type Breakwaters under Tsunami-Induced Seepage

In this study, distinct element method (DEM) analysis and slip analysis based on the simplified Bishop method have been carried out in order to investigate stability of a caisson-type breakwater under tsunami-induced seepage and establish the design method of the caisson foundation. The effect of seepage on the bearing capacity of the caisson foundation was introduced as the reduction of the effective weight of the rubble mound in the both analyses. As a result of the distinct element (DE) analysis, it has been revealed that the shear strain of the rubble mound increases due to the tsunami-induced seepage. Moreover, from the slope stability analysis, it has been indicated that the safety factor decreases by 7–10 % due to the seepage force, which is approximately corresponding to the increase rates of shear deformation in DE analysis.

Effect of Extreme Rainfall on Cut Slope Stability: Case Study in Yen Bai City, Viet Nam

This paper addresses the effects of extreme rainfall on the stability of cut slopes in Yen Bai city, Northern Viet Nam. In this area, natural slopes are excavated to create places for infrastructures and buildings. Cut slopes are usually made without proper site investigations; the design is mostly based on experience. In recent years, many slope failures have occurred along these cuts especially in rainy seasons, resulting in properties damaged and loss of lives. To explain the reason that slope failure often happens during rainy seasons, this research analyzed the influence of extreme rainfalls, initial ground conditions, and soil permeability on the changes of pore water pressure within the typical slope, thereafter determining the impact of these changes on the slope stability factor of safety. The extreme rainfalls were selected based on all of the rainfalls triggering landslide events that have occurred over the period from 1960 to 2009. The factor of safety (FS) was calculated using Bishop's simplified method. The results show that when the maximum infiltration capacity of the slope top soil is less than the rainfall intensity, slope failures may occur 14 hours after the rain starts. And when this happens, the rainfall duration is the deciding factor that affects the slope FS values. In short, cut slopes in Yen Bai may be stable in normal conditions after the excavation, but under the influence of tropical rain storms, their stability is always questionable.

Calculating Stability Factor Using Linear Sliding Method is Not Suitable for all Sandy Soil Slopes

To analyze the reasonable cohesion range of slope stability factor calculated using linear sliding method, different internal friction angles (20°,30°,40°) and cohesion (≤10kPa) of 36 slopes were calculated using linear sliding method, simplified Bishop method and strength reduction finite element method. The results show that, simplified Bishop method and the strength reduction finite element method are close to the stability factors; linear sliding method when cohesion is not considered is conservative, linear sliding method when cohesion is considered is partial to risk; calculating stability factor using linear sliding method is not suitable for all sandy soil slopes, only when the cohesion values not more than 1.5 kPa, the calculation results of linear sliding method are in accordance with engineering practice.

Investigation of the evolutionary process of a reinforced model slope using a fiber-optic monitoring network

The stability condition of a reinforced slope is influenced by many factors, such as surface loading, adjacent excavation, groundwater seepage, rainfall infiltration, and earthquake. In order to investigate the evolution of stability condition of a soil slope reinforced with soil nails, a physical model test at 1g condition was conducted in the laboratory. In the model test, an innovative quasi-distributed fiber-optic sensing network based on the fiber Bragg grating (FBG) technology was developed to monitor the strain distributions of the soil nails, the slope subsurface displacements, and the internal strains of the soil mass, together with laser displacement transducers for surface displacement measurement. The sensor installation and temperature compensation methods of the monitoring system were presented in detail. During testing, the surcharge loading was applied on the slope crest in stages using hydraulic jacks and the slope behavior was carefully monitored. The simplified Bishop's method was performed beforehand to obtain the factors of safety and the critical slip surfaces of the model slope. It is found that the measured strains of the model soil nails had a close relationship with loading magnitudes. The bending stiffness of the model soil nails contributed to the stability of the model slope when considerably large deformation occurred. The variation of slope movements and the distribution pattern of internal strains in the active and passive zones were further discussed, which indicates the progressive evolutionary process of the reinforced slope. It is verified that the fiber-optic monitoring data can identify the evolutionary stages of a reinforced slope effectively.

Simplified Bishop Method Homogeneous Soil Slope Stability Analysis Based on the C# Language

A computer program was compiled based on the C# language of Microsoft Visual Studio 2008 and the principle of simplified Bishop method. The program will calculate the minimum factor of safety, and automatically draw the two-dimensional (2-D) critical slip surface after user input the basic parameters. Through testing a lot of examples, the program has good stability, high precision, fast speed and good visibility.