Search

The article addresses stability analysis of complicated slopes having weak soil layer sandwiched between two strong layers. The search for critical failure surface and associated optimum/minimum factor of safety (FOS) among all potential failure surfaces can be posed as an optimization problem. Two different variants of particle swarm optimization (PSO) models, namely inertia weight-based PSO (IW-PSO) and contemporary standard PSO (CS-PSO), are used to obtain optimum global solution. Detailed comparison between the global optimum solutions obtained from two PSO variants and the effect of swarm size is studied. The performance of IW-PSO and CS-PSO are studied by observing the convergence behavior of the respective algorithms with respect to iteration count. The influence of velocity clamping on the optimized solution is investigated and its use is found beneficial as it prevents the solution from overflying the region with global best solution. The studies related to swarm diversity demonstrating the exploitation and exploration behaviors of the algorithms are also presented.

In this study, seepage through the body of an earthen embankment for construction of railway lines in Mokama in Bihar is estimated using finite element method. Seepage of water through the body of earthen embankment adversely affects its stability. In order to check the reliability of the constructed railway embankment stretching for a long distance, Random Finite Element Method (RFEM) originally developed by Fenton and Griffiths (Fenton and Griffiths, 1996) is used. The influence of variability in spatially distributed hydraulic conductivity/permeability field of the embankment is investigated by carrying out seepage analysis. Local Averaging Subdivision (LAS) technique is used to build the random field of hydraulic conductivity of soil domain under consideration. Afterwards, Monte Carlo simulation is performed for 1000 such random fields. The mean of total flow rate $$\left( {m_{Q} } \right)$$ , mean of logarithmic of total flow rate $$\left( {m_{\ln Q} } \right)$$ and variance of logarithmic of total flow rate $$\left( {s_{\ln Q}^{2} } \right)$$ from seepage analyses for 1000 realizations of random field are reported. The results show that as the correlation length decreases, the output parameters $$m_{Q}$$ , $$m_{\ln Q}$$ and $$s_{\ln Q}^{2}$$ follow a decreasing trend and vice versa. These variations are studied for the embankment with and without drain. The effect of drain on the mean hydraulic conductivity and hydraulic gradient standard deviation of the embankment are investigated in which the embankment with drains is found safer than embankment without drain.

The solution of slope stability problems requires determination of critical failure surface and associated optimum/minimum factor of safety (FOS) value. Investigation of critical failure surface in any soil slope can be posed as a constrained global optimization problem. In this article, a simplified technique of generation of segmented non-circular failure surface is proposed. Unified particle swarm optimization (UPSO) method is utilized to search for the critical failure surface and associated minimum FOS of the slope. Limit equilibrium technique-based Morgenstern–Price method is used to evaluate the FOS value of the potential failure mass which satisfy both force as well as moment equilibrium. To demonstrate the performance of UPSO and its competence in yielding critical failure surface along with minimum FOS value, three benchmark problems with differing complexities are chosen from existing literatures. The results obtained are compared and are found to be in accord with the published literatures. The performance of UPSO as a solution algorithm for slope problems are established through convergence studies of various related parameters.

Two dimensional generalized Hoek et al. (2002) criteria is very popular for determining the strength of rock materials worldwide. While using this criterion, it is usually required to determine the minor principal stress first. Since, GHB criteria is a nonlinear function of minor principal stress, its solution is not very straightforward and simple. Few analytical and numerical solution to find out the value of minor principal stress already exist. Some solutions are unable to give acceptable value of minor principal stress for whole range of geological strength index (GSI) values of rocks. In the present paper, a solution strategy based on Newton–Raphson method to determine the value of minor principal stress from GHB criteria in two dimensions is presented. The obtained solution of minor principal stress for few problems are compared with the solutions from existing literature. The proposed solution strategy can determine the value of minor principal stress for whole range of GSI (0–100) very accurately with very less computational effort. Finally, the variation of various rock strength parameters such as angle of internal friction, cohesion and shear stress are investigated for different values of GSI and disturbance factor (D).

In this study, reliability analysis of slope failure of Durgawati earthen embankment has been performed using two different methods specifically multivariate adaptive regression splines (MARS) and relevance vector machine (RVM). Reliability index $$(\beta )$$ is calculated using both MARS and RVM under steady-state and transient-state seepage conditions. The analyses are performed for two different sections CH 21.0 and CH 22.0 at RD 640.09 m and RD 670.57 m, respectively. The Durgawati dam is situated in Kaimur district of Bihar, India. The FOS values of Durgawati earthen dam is calculated for using modified Bishop’s method for different seepage conditions, i.e., steady state and transient state. The seepage and slope failure analysis of Durgawati earthen dam is performed using SEEP-W and SLOPE-W modules of Geo-Studio 2007 software. The FOS values are calculated for these conditions for different realizations of the material parameters $$(c,\varphi ,\gamma )$$. After that, MARS and RVM have been applied to estimate the reliability index $$(\beta )$$ for the estimated FOS values for different realizations over the body of the dam. The computed reliability index $$(\beta )$$ under different situations indicates that the performance of the dam is satisfactory.

In the present work, the results of rock slope analyses incorporating nonlinear Hoek–Brown yield criterion with equivalent Mohr–Coulomb strength parameters to simulate rock mass behaviour are presented. The factor of safety (FOS) of rock slopes are calculated using Morgenstern–Price and Spencer’s method. A simplified method of generating non-circular segmented failure surface is proposed. The search of minimum FOS and associated critical non-circular failure mass for rock slopes is performed by Particle swarm optimization (PSO) technique. A MATLAB code is developed incorporating nonlinear Hoek–Brown criteria with equivalent Mohr–Coulomb strength parameters and coupled with PSO to analyze stability of rock slopes. The efficiency and accuracy of the developed MATLAB code is established by comparing the obtained results with those from existing literatures. Furthermore, the analyses of slopes are performed with varying height and slope angle for an intact rock slope with varying material parameters such as Hoek–Brown constant $$m_{i}$$ and uniaxial compressive strength $$\sigma_{ci}$$ for rock material. It is found that the FOS value follows a decreasing pattern if height and the slope angles are increased.

Stability charts present a graphical approach for the estimation of factor of safety (FOS) of a finite slope with uniform soil properties which are routinely used by geotechnical engineers. They provide a way for quick and efficient determination of stability of slopes sidestepping the need for carrying out actual analysis. In the present work, authors have developed stability charts of rock mass to determine global minimum FOS for rock slope stability problems. The rock mass is modelled by incorporating generalized Hoek–Brown strength criterion proposed by Hoek et al. (Hoek–Brown criterion—2002 edition, 2002). Limit equilibrium technique based Morgenstern and Price (Geotechnique 15:79–93, 1965) method is used to determine the value of factor of safety of the rock slope against failure. An evolutionary optimization method i.e. Particle swarm optimization (PSO) is used to search for the minimum FOS values and the associated critical failure surface out of all possible slip surfaces. A MATLAB code has been developed for this purpose. The charts have been developed for the entire range of Geological Strength Index (GSI) values ranging from 0 to 100 for intact rock mass characterized by the disturbance factor D = 0 for both static and seismic loading conditions. The seismic slope analysis is performed by an equivalent static method using a horizontal seismic coefficient (kh) with values ranging from 0.10 to 0.30. Stability charts contain stability numbers which are inversely proportional to FOS value of the slope. In the present work, stability numbers are plotted for different inclination angles ( $$\beta$$ ) equal to 15°, 30°,45°, 60° and 75+°, respectively, for both static and seismic conditions considering the variations of other material parameters such as $$m_{i}$$ and $${\text{GSI}}$$ . Stability numbers are observed to increase with an increase in angle of inclination ( $$\beta$$ ) of the slope and correspondingly FOS values follow a decreasing trend. However, stability numbers follow a decreasing pattern with increasing values of material parameters $$m_{i}$$ and $${\text{GSI}}$$ designating improved rock quality with corresponding increase in FOS values of the rock slope.

In the present paper, multivariate adaptive regression splines (MARS) method is used to carry out reliability analysis of Durgawati earthen dam. The steady and transient state seepage is considered while calculating reliability index \(\left( \beta \right)\). The earthen dam is an important water retaining structure and serves the catchment area of Durgawati River in Bihar, India. The factor of safety (FOS) of the earthen dam against slope failure under steady and transient state is performed using GeoStudio-07 software. In order to account for the variability of material parameters over the body of the dam, a data set of material parameters [i.e., cohesion (\(c\)), angle of internal friction \(\left( \varphi \right)\) and soil unit weight (\(\gamma\))] are prepared, and MARS is used to calculate reliability index \(\left( \beta \right)\) for different realizations over the dam geometry. The reliability index \(\left( \beta \right)\) thus estimated shows that the dam is stable and safe from slope failure point of view under different seepage loadings.

This article presents results of slope analyses employing a simple technique of generating segmented non-circular failure surfaces. The formulation of slope analysis is performed as an optimization problem with four constrained control variables characterizing the failure surface. In this study, different variants of particle swarm optimization (PSO) methods such as inertia weight equipped and contemporary standard PSO (CS-PSO) are utilized to obtain optimum control variables and associated critical failure surface. The factor of safety of the slope or the objective function of the constrained optimization problem is determined by Morgenstern–Price method. To explore the competence of proposed method with different PSO models, three benchmark problems are analysed for different maximum number of function evaluations such as 1000, 2500 and 5000. A series of sensitivity analyses are performed for various parameters such as swarm size with maximum iteration count of 100. The swarm diversity behaviour is also studied in relation with converged or promising global optimum solution. It is found that contemporary standard PSO (CS-PSO) with or without velocity clamping maintains better swarm diversity and preserves the balance between swarm “exploration” and “exploitation” efficiently. Velocity clamping and positional clamping are recommended as they prevent the solution/control variable from overflying the swarm best position.

Detection of critical failure surface and associated minimum factor of safety (F) constitutes a constrained global optimization problem during the task of slope analysis. Morgenstern–Price method is an established limit equilibrium-based technique satisfying both moment and force equilibrium of all slices in the failure mass has been used to evaluate F against slope failure. The main objective of current study is to investigate the applicability and efficiency of grey wolf optimization (GWO) in solving slope stability problem. GWO is a nature inspired metaheuristic optimization method which mimics the social interaction between a pack of grey wolves in their endeavour to search, hunt and prey. The effectiveness of the recently developed GWO is examined by analyzing four different slope problems. Each soil slope model has been analysed for wolf pack size (NP) range 10–50 and maximum iteration count $$ (k_{\hbox{max} } ) $$ range 50–250. In effect, the number of evaluated functions (NFE) is found to lie in the range of 500–12,500. The results demonstrate that the GWO technique can detect the critical failure surface with very good accuracy. Furthermore, the statistical analysis is presented in terms of best $$ F_{\text{b}} $$ , worst $$ F_{\text{w}} $$ , mean $$ \overline{F} $$ , standard deviation (SD) and % error (%E) of the optimum solutions i.e. factor of safety (F) from 10 independent runs. The effect of GWO parameters such as NP and $$ k_{\hbox{max} } $$ to obtain optimum solution are also presented. The $$ F_{\text{b}} , \, F_{\text{w}} , \, \overline{F} \;{\text{and}}\;{\text{SD}} $$ for 1st slope model are (1.7295, 1.7296, 1.7295, 0.000038) and they have been obtained for maximum NFE equal to 12,500. Similarly, for 2nd and 3rd slope model, the respective values are (1.4032, 1.4038, 1.4034, 0.000209) and (1.2530, 1.2546, 1.2537, 0.000741). The discrepancy or percentage error (%E) in best $$ F_{\text{b}} $$ from optimum (F) for NFE up to 500 are found to be equal to (0.0615, 0.2531, 0.8419) for studied slope models respectively. The evaluation of safety factor F for the fourth slope model has been studied for four different combinations of earthquake loadings and pore water pressures. The values of SD for all four cases are reported for maximum NFE equal to 12,500. It is found that uncertainty in reported F reduces if higher numbers of objective function evaluations are performed. This proves the excellent performance of GWO in evaluating minimum F of the slope.

Searching for critical failure surface (CFS) with minimum factor of safety (FOS) of any slope require application of optimization. A particle swarm optimization (PSO) based MATLAB code is developed to search for CFS and associated minimum FOS of slopes by minimizing the objective function. The FOS against slope failure is determined by Bishop’s method based on limit equilibrium technique, which also serves as the objective function. With this goal, another computer code is developed in MATLAB to solve non-linear nature of equation of FOS. The effectiveness of developed code is investigated through study of different parameters such as swarm size, iteration count and slice numbers etc. The applicability of PSO is evaluated for homogeneous and layered slopes considering the effect of seepage and seismic loading.

Analysis of dam slopes is of much importance because its failure may prompt loss of lives and properties. In this paper, both seepage and slope stability analyses of the earthen embankment dam of Durgawati reservoir project in the region of Kaimur–Bihar is presented. The analyses are performed using geotechnical software GEOSTUDIO 2007 (SEEP/W in Seepage analyses, Software permitted for limited period of use by GeoSlope Office, Canada, 2007; SLOPE/W in Stability Analysis, Users guide version 5, GeoSlope Office, Canada, 2002). Two sections of the Durgawati reservoir project have been considered for detailed stability analysis namely one from RD 640.09 m CH 21.00 and another from RD 670.57 m CH 22.00. Both upstream and downstream slopes, located at the dam site have been investigated for long-term stability for full reservoir condition (i.e. steady-state seepage) and drawdown condition (i.e. transient-state). It has been observed that the Factor of safety against slope failure at the upstream face is substantially greater than that of the downstream slope because of resisting effect of the reservoir water on the upstream slope. The stability of the upstream slope of the dam decreased considerably during drawdown condition. The structure lies in the earthquake prone area Zone III as per IS 1893-2002. Therefore, a pseudo-static analysis has been performed using different horizontal earthquake coefficient in combination with both steady-state as well as transient-state seepage condition.